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Introduction to

Clastic Sedimentology
(Notes for a University level, second year, half-credit course in clastic sedimentology)


R.J. Cheel
Department of Earth Sciences
Brock University
St. Catharines, Ontario, Canada L2S 3A1

© 2005 R.J. Cheel


The author thanks the following publishers for granting permission to reproduce figures for which they
hold copyright:

Prentice Hall Inc., Englewood Cliffs, New Jersey, figures 2-2, 2-19, 2-14, 2-21,4-17, 4-20, 5-15, 5-17, 5-5;
SEPM (Society for Sedimentary Geology), Tulsa, Oklahoma, figures 2-15, 2-16, 2-17, 5-6, 5-12, 5-13, 5-14,
6-7, 6-8, 6-9, 6-10, 6-12, 6-17, 6-18; Academic Press, New York, figure 2-31A; Springer-Verlag, New York,
figures 2-6, 2-39, 3-1, and table 3-5; The University of Chicago Press, figure 2-20; Chapman and Hall, U.K.,
figures 2-4 and 5-24. All permissions were granted free of charge.

Mike Lozon (Department of Earth Sciences, Brock University) is thanked for preparing several of the figures.

Table of Contents

Chapter 1. Introduction 5

Why study clastic sedimentology? 5

About this book 6
Comprehensive sedimentology textbooks 7

Chapter 2. Grain Texture 8

Introduction 8
Grain Size 8
Volume 8
Linear dimensions 9
Direct measurement 9
Sieving 10
Settling velocity 10
Stoke's Law of Settling 11
Grade scales 14
Displaying grain size data 16
Describing grain size distributions 18
Median 18
Mean 19
Sorting coefficient 19
Skewness 20
Kurtosis 20
Paleoenvironmental implications 20
Why measure grain size? 22
Grain Shape 22
Roundness 22
Wadell 22
Dobkins and Folk 22
Power's visual comparison chart 22
Sphericity 23
Wadell 23
Sneed and Folk 24
Riley 24
Clast form 24
Significance of grain shape 25
Source rock 25
Transport 25
Porosity and Permeability 28
Porosity 28
Controls on porosity 28
Packing density 28
Grain size 29
Sorting 30
Post-burial processes 30
Compaction 30
Cementation 30
Clay formation 30
Solution 31
Permeability (Darcy's Law) 31
Controls on permeability 34

Porosity and packing 34

Grain size and sorting 34
Post-burial processes 35
Directional variation in permeability 36
Grain Orientation 36
Introduction 36
Measuring grain orientation 36
Types of grain fabric 37
Isotropic fabric 37
Anisotropic fabric 37
a(t)b(i) 38
a(p)a(i) 38
Complex anisotropic fabric 38
The problem with measuring grain orientation on thin sections 39
Displaying directional data 39
Statistical treatment of directional data 42
Interpretation of grain orientation 44

Chapter 3. Classification of terrigenous clastic rocks 47

A fundamental classification of sediments 47

Terrigenous clastic sediments 49
Classification of sandstone 49
Basis of the classification 49
Genetic implications 52
Level of classification 54
Classification of rudite 54
Classification of lutite 54

Chapter 4. Unidirectional fluid flow and sediment transport 55

Introduction 55
Unidirectional fluid flows 55
Flow between two plates 55
Fluid gravity flows 56
Classification of fluid gravity flows 58
Shear stress and velocity in turbulent flows 59
Structure of turbulent flows 61
Organized structure of turbulent flows 63
Sediment Transport 66
Modes of transport 66
Quantitative interpretation of grain size curves 67
Threshold of movement 67
Threshold of grain suspension 71

Chapter 5. Bedforms and stratification under unidirectional flows 74

Introduction 74
Bedforms under unidirectional flows 74
Terminology 74
The sequence of bedforms 75
Bedform stability fields 85
Cross-stratification formed by bedforms under unidirectional flows 88
Terminology 88

Origin of cross-stratification 90
Cross-stratifcation produced by asymmetrical bedforms 95
Ripple cross-lamination 96
Cross-stratification formed by dunes 97
Upper plane bed horizontal lamination 99
In-phase wave stratification 101

Chapter 6. Flow, bedforms and stratification under oscillatory

and combined flows 102

Introduction 102
Characteristics of gravity waves 102
Bedforms and stratification under purely oscillatory currents 105
Initiation of motion 105
Bedforms under waves 106
Stratification formed by oscillatory currents 109
Bedforms and stratification under combined flows 113
The enigma of hummocky cross-stratification 114
HCS - description and associations 116
Characteristics of HCS 116
Grain size 116
Morphology and geometry 116
HCS associations 118
Discrete HCS sandstone 118
Amalgamated HCS sandstone 119
The HCS debate 119
Experimental evidence 121
Evidence based on grain fabric 121
The origin of HCS? 122
Conclusion 124

Appendix 1. 125

Appendix 2. 127

References 129


Clastic sedimentology is the branch of geology that studies sediment and sedimentary rocks that are made
up of particles that are the solid products of weathering at or near the Earth’s surface. Thus, clastic sedimentology
is concerned with gravel, sand and mud and the rocks that form by the induration (formation into rocks) of these
particulate materials (rudites, sandstones and shales; see Chapter 3). The goal of this book is to introduce the
terminology and fundamental concepts that are necessary for the description and interpretation of sediment and
sedimentary rocks.


There are at least two good reasons for studying clastic sedimentology. The first is because humans, and
most other species on the planet, interact with the Earth largely at its surface. Sedimentary rocks make up only 7.9%
of the total crust of the Earth which is dominated by igneous and metamorphic rocks (Fig. 1-1). However, the surface
of the Earth is dominated by sedimentary rocks and almost 50% of that surface is made up of clastic sedimentary
rocks (predominantly shale and sandstone). Humans are not uniformly distributed over the Earth’s surface and
if we were to further consider the proportion of the human population that lives immediately on clastic sediments
we would find that almost all of us interact with the Earth’s surface through a cover of clastic sediments and/or
sedimentary rocks. We interact with this sedimentary surface in a variety of ways. We grow food within it and raise
livestock on it so that it is crucial to global food requirements. We build our homes on it and take water and other
resources from it. At the same time we hide our garbage in it and we modify its physical and chemical properties
in such a way as to render it unsuitable for many of our needs. Thus, given our uses and abuses of the Earth's surface
it is particularly important that we understand the various properties of sediments and have systematic methods
of describing these properties.

A second reason for studying clastic, and all other, sedimentary rocks is because they preserve the record
of changing environmental conditions at or near the Earth’s surface over almost the whole of geologic time. All
sediment and sedimentary rocks were deposited at the Earth’s surface, either in the oceans or on the continents.
As such, these deposits were influenced by processes that were acting on the Earth’s surface, in their environments
of deposition. A large part of clastic sedimentology is devoted to the development of criteria for the recognition
of the action of various processes on sediments in their environment of deposition. By developing tools for the
recognition of the signature of these processes in a sediment we can unravel the history of environmental change
that is preserved in the stratigraphic sequence of rocks that has been laid down over geologic time.

Relative abundance of rocks in Relative abundance of rocks

the earth's crust at the earth's surface

Metamorphic Igneous & Shale


27.4% Metamorphic 35%


Limestone Sandstone
16.5% 14.5%

Figure 1-1. Relative abundance of rock types in the Earth's crust and at the Earth's surface.

About these notes

These notes were first compiled in 1992 from the author's lecture notes that were prepared over six years
of teaching Clastic Sedimentology at the Junior Undergraduate level, first at Brandon University and later at Brock
University, and are meant to provide an inexpensive "text" to support this half-credit second year course.
Sedimentologists will notice that these notes contain material similar to that in some of the "classic" sedimentology
textbooks but also includes much of my own bias and understanding. I was fortunate enough to have been (and
will likely always be) a student of Gerry Middleton at McMaster University and a significant proportion of Chapters
2, 3 and 4 are derived from an understanding (or perhaps misunderstanding in some cases) of the great experiences
that I have had with one of the father's of modern sedimentology. At McMaster I was also provided the opportunity
to learn much from Roger Walker, another Canadian sedimentologist of significant stature. Despite these
opportunities, any shortcomings within these notes reflect my own limitations and are certainly despite the input
of these two great educators.

These notes do not aim to cover all of the important aspects of clastic sedimentology but only those that the author
has decided to stress in this one semester, introductory course. A list of more comprehensive texts is given at the
end of this introductory chapter. Some of the examples and figures in these notes were modified from these texts
and they will provide a more detailed treatment of several topics that are covered in this course. These notes are
expected to evolve with time as new sections are added and old ones dropped, although sections that are removed
from the course will remain in the notes, provided that the cost to students remains reasonable. In an earlier addtion
of these notes I added several colour plate. Unfortunately these plates resulted in a doubling of the cost of the
notes. For that reason I have not included the plates here.

In 2005 I began to put Power Point lecture presentations that I created for the course onto the World Wide
WEB. I subsequently added the full course notes to the Web in the hope that they would provide a resource for
students at other Universities. These notes, and the Power Point presentations are available free of charge to anyone
who wants to download them; they are available at In some cases the notes may
be downloaded and provided to students by a third party. My condition for such downloading and reproduction
is that under no circumstances will a profit be added to the cost of the notes to students, other than a charge of
up to 20% of reproduction costs for distribution by a University book store or similar service that prints the notes
for sale to students. There will be no charge that incurs a profit to any other person or group, including myself.
The reason for these notes is to provide an inexpensive but useful resource for students. If your school would like
to reproduce these notes for sale to students I ask that I be approached for permission to do so. Please direct such
requests to me at with the subject line "SedNotes Request" and include the per unit reproduction
costs and the proposed sale price. I will respond to such requests promptly.

The notes begin with a section on the most fundamental properties of clastic sediments, those properties
that collectively make up the "texture" of a sediment. The next section reviews the criteria for classifying sediment
and sedimentary rocks, criteria that are commonly based on the texture of the rocks. The remainder of the notes
focus on the behaviour of sediments in response to processes in subaqueous settings, the most common settings
in which sediments are deposited. This begins with an examination of some of the important characteristics of
unidirectional fluid motion (like the currents in a river) and the manner in which sediment is moved by such fluid
motion. This is followed by a section that examines the bulk response of a sediment to unidirectional fluid motion
(i.e., bedforms) and the criteria for interpreting hydraulic condition on the basis of the internal structure of sediments
and sedimentary rocks (i.e., internal stratification and cross-stratification). The final chapter briefly considers all
of these aspects of fluid motion and sediment response but for currents that reverse in direction over relatively short
periods (seconds to tens of seconds) and are generated by water surface waves that are common in many marine
and lacustrine environments.

Comprehensive sedimentology textbooks

ALLEN, J.R.L., 1985, Principles of physical sedimentology. George Allen and Unwin, Boston, 272 p.
ALLEN, J.R.L., 1985, Experiments in physical sedimentology . George Allen and Unwin, Boston, 63 p.
ALLEN, J.R.L., 1982, Sedimentary structures: their character and physical basis (Two volumes) Elsevier, New York,
593 p. (v. 1) and 663 p. (v. 2).
ALLEN, J.R.L., 1970, Physical processes of sedimentation. An introduction. George Allen and Unwin, London,
248 p.
BLATT, H., MIDDLETON, G.V., AND MURRAY, R., 1980, Origin of sedimentary rocks. (Second Edition) Prentice-Hall,
New Jersey, 782 p.

Boggs Jr., Sam, 2001, Principles of Sedimentology and Stratigraphy (3rd Edition). Prentice Hall, New Jersey, 770
DAVIS, R.A., 1983, Depositional systems: a genetic approach to sedimentary geology. Prentice-Hall, Toronto, 669
HARMS, J.C., SOUTHARD, J.B., AND WALKER, R.G., 1982, Structures and sequences in clastic rocks. Society of
Economic Mineralogists and Paleotologists, Short Course Number 9, 249 p.
HSÜ, K.J, 1989, Physical Principles of Sedimentology: a readable textbook for beginners and experts. Springer-
Verlag, New York, 233 p.
LEEDER, M.R., 1982, Sedimentology: process and product. George Allen and Unwin, London, 344 p.
MIDDLETON, G.V. AND SOUTHARD, J.B., 1984, Mechanics of sediment movement. (Second Edition) Society of
Economic Mineralogists and Paleontologists, Short Course Number 3, 394 p.
PETTIJOHN, F.J., 1975, Sedimentary rocks. (3rd Edition). Harper and Row, New York, 628 p.
PETTIJOHN, F.J., Potter, P.E., and Siever, R., 1973, Sand and sandstone. Springer-Verlag, New York, 618 p.
POTTER, P.E., MAYNARD, J.B., AND PRYOR, W.A., 1980, Sedimentology of shale. Springer-Verlag, New York, 306 p.
REINECK, H. -E. AND SINGH, I.B., 1980, Depositional sedimentary environments, with reference to terrigenous
clastics. (Second Edition). Springer-Verlag, New York, 549 p.
SELLEY, R.C., 1982, An introduction to sedimentology. Academic Press, New York, 417 p.



All clastic sediment is made up of discrete particles termed grains or clasts. Thus, any description of a clastic
sediment must describe the particles, including their individual and bulk properties. Such properties collectively
define the texture of a sediment or sedimentary rock and include individual properties such as grain size and shape
and bulk properties such as grain size distribution, fabric (orientation and packing of particles), porosity and
permeability. These properties are important for any complete description of a sediment. In addition, because these
properties are governed by processes that act at the time of deposition and, in some cases, after burial, they might
provide insight into the history of a sediment. Furthermore, many of these properties will govern how a sediment
will behave when used in a particular way, for example, as a final resting place for garbage. This chapter focuses
on the concepts and terminology used to describe sediment texture and shows how texture may be used in making
basic interpretations about the history of a sediment.


One might expect that the description of the size of particles that make up a clastic sediment would be the
simplest property to describe. However, most sediment is composed of particles with a variety of irregular shapes
and may extend over a range of sizes. Therefore, the characterization of the size of particles within a sediment may
not be so straight forward.

Consider an irregularly-shaped pebble that is large enough to cover the palm of your hand. How might you
tell someone else precisely how big this pebble is without actually showing it to them? You might decide that the
pebble is “moderately large” and describe it as such but this is a rather ambiguous expression that could be easily
misunderstood by the other person. In this case we need some way of measuring the size of the pebble and then
we need some consistent terminology to describe the size; a terminology that everyone else will use so that they
will know what is meant by an expression such as “moderately large”.

Grain Volume

There are several methods that will provide a quantitative measurement to describe the size of a particle. The
easiest method would be to physically measure some linear dimension of a particle. This is simple enough if the
particle is a perfect sphere, it will have only one linear dimension: its diameter. However, natural particles are
commonly not very spherical and one linear dimension may not adequately describe their size. A measure of size
that can be determined while neglecting the shape is the volume (V) of a particle. A simple way to determine the
volume of a particle is to determine its mass (m) and calculate volume from the relationship:

m = Vρ Eq. 2-1

where r is the density of the particle. The mass can be determined by weighing the particle. We might assume a
reasonable density of the particle, say that of quartz (2650 kgm-3), and solve for V. However, the actual density of
the material comprising the particle may vary significantly from the assumed value.

The volume of the particle may also be determined directly by measuring the volume of fluid displaced by
the particle when it is immersed in the fluid within a graduated cylinder or beaker. This method does not require
an assumption of the density of the particle but may derive error if the particle is made up of a porous material and
all of the pores do not become saturated with the fluid. We can often neglect this source of error.

In the case of particles that are perfect spheres of non-porous solid we can calculate the volume of the particle
with diameter d from:
πd 3
V= Eq. 2-2



Figure 2-1. Definition of principle axes of a sedimentary particle.

Linear Dimensions

Direct Measurement

As noted above, the easiest way the determine and express the size of a particle is by describing its linear
dimensions. Because a sedimentary grain is rarely a perfect sphere we normally treat each grain as if it was a triaxial
ellipsoid (Fig. 2-1) and its linear dimensions are described in terms of the lengths of the three principle axes: the long
axis (a-axis or dL), the intermediate axis (b-axis or dI), and the short axis (c-axis or dS)

To measure these lengths on a particle follow the steps below and refer to figure 2-2.

1. Determine the plane of maximum projection of the particle. This is an imaginary plane passing through the particle
such that the intersection of the particle and the plane produces the largest possible surface area (i.e., the maximum
projection area).

2. Establish the maximum tangent rectangle for the maximum projection area. This is a rectangle that, when placed
around the maximum projection area, results in the maximum possible tangential contact with the outline of the

3. Measure the length of the a- and b-axes such that the a-axis length is the length of the long side of the maximum
tangent rectangle and the b-axis length is the length of the short side of the maximum tangent rectangle.
Note that the plane of maximum projection is the a-b plane of the particle.

4. Measure the c-axis length as the longest distance through the particle, perpendicular to the a-b plane.

The above procedure is used so that different workers can produce comparable results; it provides a standard
for all workers. For large particles, reportedly as small as 0.25 mm, all three axes may be measured. For larger particles,
in excess of a few millimetres, callipers may be used to measure the axes. For smaller grains the axes may be measured
under a binocular microscope. When a grain is too small to allow it to be rotated to see the short axis the long and
the intermediate axis may be measured. A common practice is to measure only dL and different particles may be
compared only in terms of their maximum axes lengths. However, this practice may lead to considerable error,
especially if the shapes of particles varies considerably.

In many studies of particle size, especially coarse particles, grain size is expressed in terms of the nominal
diameter (dn): the diameter of a sphere having the same volume as the particle. If the three principle axes lengths
are known this expression of grain size is easily calculated by:

d n = d L d I dS Eq. 2-3

Nominal diameter is just one of a large number of expressions of linear dimension that have been used to describe

dL dI

u m ea
x im n ar dS
Ma ctio
r oje
Maximum Tangent Rectangle/a-b plane

Figure 2-2. Sketch showing the method for determining the lengths of the principle axes of a particle. After Blatt,
Middleton and Murray, 1980.

the size of a particle.


Sieving is a method that is widely used to directly measure the sizes of a large number of grains (samples
range from 40 to 75 grams) and is normally limited to particles in the range from as fine as 0.0625 mm up to as large
as 64 mm. The detailed procedure that should be followed when sieving a sediment sample is outlined in Appendix
1. Again, a specific procedure has been derived so that results of different workers will be reliably comparable. The
equipment that is used world-wide for sieving includes a shaker and a series of nested, square holed screens (the
screen with the largest holes on top, down the smallest holes on the bottom). The sediment sample is passed through
the screens, by shaking, and the weight of sediment that accumulates on each screen is weighed. Thus, the
information obtained is not the absolute size of each grain but the frequency of grains (by weight), in a sample, that
fall between the range of sizes represented by the square holes in the screen above and in the screen on which the
grains are resting. The actual dimension of the grains that might be considered is "the largest square hole through
which the grains will pass". This dimension is approximately the intermediate axis length. The procedure and the
meaning of grain size data will become more clear later in this chapter.

Settling Velocity

Another very useful measure of grain size is the settling velocity of a particle. A particle's settling velocity
(or fall velocity) is normally defined as the terminal velocity that a particle will reach while falling through a still fluid,
normally water. A particle's settling velocity (ω) is related directly to its size (d) and also to its density (ρs) but is
also influenced by fluid properties such the fluid density (ρ) and the viscosity (µ); for all fluids these properties
vary with temperature.

To measure the settling velocity of a particle we may simply, but accurately, record the time that it takes to
fall a known distance through a column of still fluid contained within a transparent tube (termed a settling tube).
This is relatively simple if we are timing the settling rate of only one or a few grains but becomes difficult if we must
deal with a sample from a population of grains of non-uniform size (and therefore varying settling velocity). In this
case we must time the settling rate of large numbers of grains. A variety of types of settling tube have been devised
and these are described in several publications (see Blatt et al. 1980).

When using settling tubes a number of factors that will influence the results must be considered. First, when

Figure 2-3. Forces acting on a spheri-

cal particle falling through a still
FB FB: Bouyant Force fluid.

FG: Gravity Force

FD FD: Drag Force



a particle first begins to fall through the fluid it will accelerate from rest (i.e., zero velocity) to some constant (terminal)
velocity. Thus, the settling velocity may be under-estimated if the distance over which the particle passes during
the phase of acceleration is large in comparison to the total distance over which settling is timed. This can be
overcome by using a tube that is long enough so that the distance over which acceleration takes place is relatively
small. This may be a problem for relatively large particles but for less than 1 mm diameter particles of quartz-density
the distance required to achieve terminal velocity is less than a centimetre. When dealing with samples of more
that one particle care must be taken that the grains settle independently and do not interact during passage through
the fluid. Sample sizes will depend on the type of settling tube used and should generally be less than 10 grams.
Samples that are too large may cause settling en masse so that the velocity determined will not be the velocity of
individual grains. Also, large quantities of grains in the tube may interact directly (e.g., collide), altering the settling
rate, or indirectly by causing the fluid itself to move (i.e., cause turbulence) so that the velocity of the grains is not
that in still fluid. A further requirement of apparati for measuring settling velocity is that the tube diameter must
be at least five time the average diameter of the particles that will pass through it. When a particle passes through
a fluid it must "push" the fluid out of its path. At the tube wall the fluid is more difficult to push than it is well away
from the wall region due to fluid viscosity. Thus, a small ratio of tube to particle diameter may result in the passage
of grains too close to the tube walls where they will be travel slower than they would through fluid that is not
significantly influenced by wall effect.

Stokes’ Law of Settling

The relationship between grain size (e.g., diameter) and settling velocity is an interesting one that reflects
a variety of principles that will be of interest later in these notes. The relationship is relatively complex due to a number
of factors. Theoretical relationships have been developed and compared to experimental data collected by actually
measuring settling velocity in settling tubes. One such theoretical relationship between grain size and settling
velocity is Stokes' Law of settling.

The derivation of Stokes' Law is simple but instructive. It is based on a simple balance of forces that act
on a grain as it is falling at terminal velocity through a still fluid and the knowledge that the velocity will be affected
by grain size (d), grain density (ρs), fluid viscosity (µ), fluid density (ρ), and the acceleration due to gravity (g).
Consider the forces acting on the spherical particle falling through a still fluid as shown in figure 2-3. As the particle
begins its passage through the fluid three forces are involved: the gravity force (FG), which is the weight of the
particle acting to move it downward through the fluid; a buoyant force (FB), acting to move the particle upward
through the fluid; and a drag force (FD) that retards the movement of the particle through the fluid. The gravity
and buoyant forces may easily be quantified. The gravity force is just the weight of the particle and is equal to the
volume of the particle times its density times the acceleration due to gravity:

FG = ρ s gd 3 Eq. 2-4
FG acts in the downward direction, causing the particle to settle. The buoyant force acts in the opposite direction
and is simply the weight of the fluid that is displaced by the particle (i.e., the weight of fluid with a volume equal
to that of the particle):
FB = ρgd 3 Eq. 2-5

Because FG and FB act in opposition the net force that acts on the particle ( FG' ) is given by:
π π π
FG' = FG − FB = ρs g d 3 − ρg d 3 = (ρs − ρ)g d 3 Eq. 2-6
6 6 6

Clearly, when the density of the particle exceeds the density of the fluid it will settle through the fluid because
FG > FB . Note that the expression on the right hand side of Eq. 2-6 is termed the submerged weight of a particle.
The drag force exerted on the settling particle is more difficult to determine. This force arises from the resistance
of the fluid to deformation due to the fluid property termed dynamic viscosity and is normally given the symbol m,
and is expressed as Nsm-2. Fluids that offer a large resistance to deformation have a high viscosity (e.g. molasses)
whereas fluids with low viscosity deform readily. Experiments have shown that the drag on a particle varies with
the velocity at which the particle passes through the fluid. Specifically, experiments have shown that at relatively
low settling velocities the drag force can be calculated from:
FD = 3πdµU Eq. 2-7
Stokes derived his law of settling from the two forces acting on a settling particle: the submerged weight and the
drag force. When a particle is settling at its terminal velocity no net force must be acting on it (i.e., the velocity is
constant, neither accelerating or decelerating, therefore experiencing no net force). Therefore, when a particle
reaches terminal velocity FD and FG' must be equal in magnitude but act in opposite directions (FD acts upwards
and the submerged weight acts downwards). Thus, when a particle reaches terminal settling velocity:
FD = FG − FB Eq. 2-8
Setting this equality and substituting with equations 2-6 and 2-7:
3πdµU = ( ρ s − ρ ) gd 3 Eq. 2-9
Because the particle is falling at its terminal velocity the velocity term in FD is the settling velocity so that U=w.
Therefore, we can solve Eq. 2-9 for ω:
π 1 ( ρ − ρ ) gd 2
ω= ( ρ s − ρ ) gd 3 × = s Eq. 2-10
6 3πdµ 18µ
Thus, Stokes' Law of Settling is simply:

( ρ s − ρ ) gd 2
ω= Eq. 2-11
Table 1 shows an example calculation of the settling velocity of a particle using Stokes' Law. Note that when
making such a calculation you must state all of the conditions (e.g., sediment and fluid density, fluid temperature
and viscosity), in many cases these conditions must be assumed. The statement of conditions is particularly
important because there are severe limitations to the use of Stokes' Law of Settling. These limitations are outlined
in the following paragraphs.

Stokes’ Law is reliable only for grain sizes finer than approximately 0.1 mm. Figure 2-4 shows that Stokes'
Law predicts the settling velocity of quartz-density particles quite reliably up to a grain size of approximately 0.1
mm, beyond which the theoretical relationship increasingly overestimates the observed settling velocity. This
overestimation is due to the fact that Stokes' Law only includes viscous drag on the particle. When larger grains

Table 2-1. Example of Stokes' Law of Settling

Consider a spherical quartz particle with a diameter of 0.1 mm, in still, distilled water.

ρs= 2650 kg/m3

ρ= 998.2 kg/m3, density of water at 20°C

µ = 1.005x10-3 N.s/m2, water at 20°C

g = 9.806 m/s2

(note that in the calculation, for consistent units, the diameter of the particle is expressed as 0.0001 m)

By Stokes’ Law the Settling, the terminal fall velocity of this particle is 8.954 x 10-3 m/s (~ 9 mm/s).

settle they travel at relatively high velocities through the fluid and eddies develop in their wake. These eddies impart
an additional form of resistance that acts to further reduce their terminal settling velocity. Because Stokes' Law
neglects this additional force of resistance it predicts a larger settling velocity than that determined by actual
experiments (Fig. 2-4). Figure 2-5 shows an additional shortcoming of Stokes' Law when applied to sedimentary
particles that settled in a fluid for which the temperature is not known. Because of the effect of temperature on fluid
density and, especially, fluid viscosity, the settling velocity of a particle will vary over almost an order of magnitude
through the range of temperatures that might naturally occur at the earth's surface. Thus, application of Stokes'
Law to predict the settling velocity of a particle in some unknown depositional environment (and unknown
temperature) may lead to considerable error.

A further problem that arises when applying Stokes’ Law to natural sedimentary particles is that it only
applies to spherical particles. Grain shape can have a dramatic effect on settling velocity. In a simple case, shape
can effect the orientation of the grain as it settles thus affecting the surface drag that acts on the particle as it passes
through the fluid. A more dramatic example is that of a platy particle (e.g., a flake of mica) which tends to drift back
and forth as it settles rather than falling vertically though the fluid.

Finally, Stokes’ Law applies to particles falling through a still fluid. That is, the fluid is at rest except where


Figure 2-4. Somewhat schematic illustration showing the


' La

ur settling velocities of spherical, quartz-density particles in

lc still water at 20°C, as predicted by Stokes' Law of Settling,
Fall velocity (mm s-1 )

100 en compared to experimentally-determined settling velocities


im of similar particles. After Leeder (1982).



0.01 0.1 1.0 10
Quartz sphere diameter (mm)

Stokes' settling velocity:

0.1 mm quartz grain in still water
Stokes' Settling Velocity (mm s )

Figure 2-5. Effect of fluid temperature on set-

tling velocity. Curve shows settling velocity
calculated using Stokes' Law of Settling applied
to a 0.1 mm diameter quartz sphere setting through
still water.

0 20 40 60 80 100
Temperature (˚C)

it is accelerated, due to viscosity, by the passage of the particle itself. Therefore, it is unreasonable to apply Stokes’
Law to the settling velocity of particles in a moving, particularly turbulent, fluid (e.g., particles in a river) where fluid
forces will act to move the particle up, down and sideways.

Before leaving Stokes' Law of Settling we can return to the discussion of the expression of grain size as some
linear dimension of a particle. Sedimentologists have traditionally preferred to express grain size as some linear
dimension and Stokes' Law can also be used to determine such a dimension for comparison of different sedimentary
particles. This linear dimension of a particle is termed Stokes' Diameter (ds; also termed settling diameter) of a particle
and is defined as the diameter of a sphere with the same settling velocity as the particle. We can determine the
Stokes' Diameter of a particle by measuring its settling velocity in still water and by solving for particle diameter
in Eq. 2-11. Thus, if the settling velocity of a particle is known, Stokes' Diameter may be calculated from:

ds = Eq. 2-12
(ρ s − ρ) g

Grade Scales

In the introduction to this chapter we posed the question of how do we verbally describe the size of a particle
in such a manner that would be understood by others. A grade scale provides such a standard for verbally
expressing and quantitatively describing grain size. Any good grade scale should:

(i) Define ranges or classes of grain size (grade is the size of particles between two points on a scale. e.g., “very
fine sand”, is a grade between maximum and minimum size limits),


(ii) Proportion the grade limits so that they reflect the significance of the differences between grades. For example,
the change in size from 1 mm to 2 mm diameter sand is an increase of 100%, however, the change in size from 10 mm
to 11 mm is on the order of 10%. Therefore, a grade scale in which grade limits vary by 1 mm would not be useful.

The most widely-used grade scale is the Udden-Wentworth Grade Scale (Fig. 2-6). Note that most of the grade

Size Size Measurement techniques

(mm) (φ)
256 -8

Direct Measurement
64 -6
4 -2
2 -1
Very Coarse Sand

Binocular Microscope

Settling Tube
1 0
Coarse Sand
0.5 +1

Medium Sand
0.25 +2
Fine Sand
0.125 +3
Very Fine Sand
0.0625 +4


0.0039 +8

Figure 2-6. The Udden-Wentworth Grade Scale defining the range of sediment sizes per size class and the verbal
expression used to describe each size class. Also shown are the techniques that may be used to measure grain size and
the grain size limits over which they should be used. After Pettijohn, Potter and Siever, 1973.

boundaries increase by a factor of 2, reflecting significant changes in grain size. Also, the scale defines limits for
the verbal expression of grain size. "Very fine sand" is sand which ranges in size from 0.0625 mm to 0.125 mm

Krumbein (1934) introduced a logarithmic transformation of the scale which converts the boundaries
between grades to whole numbers. This scale is known as the Phi Scale, it’s values being denoted by the Greek
letter phi (φ), where:
φ = -log2 d(mm) Eq. 2-13
where d(mm) is just the grain size expressed in millimetres. For example:

-log2 1(mm) = 0 φ
-log2 1/4(mm) = 2 φ
-log2 4(mm) = -2 φ

φ was later redefined:

φ = -log2 d/do 2-14

where d is the size in millimetres and do is a standard size of 1 mm; division by 1 mm does not alter the value of φ
but makes it dimensionless.

With a hand calculator the conversion from φ to mm and from mm to φ is as follows:

φ → mm d(mm) = 2-φ

mm → φ φ = -( log10 d)/log10 2

Note that it is traditional among sedimentologists to plot grain size on a phi scale with decreasing grain size to the
right as shown in figure 2-7.

Figure 2-7. Conventional phi scale showing grain size
increasing to the left and decreasing to the right.

increasing grain size decreasing grain size

Grain Size (φ)

Displaying Grain Size Data

Most data describing the grain size distribution of a bulk sample of sediment are in the form given in Table
2-2 which shows the frequency distribution (in terms of weight) of sediment per size class (here grain size classes
are at 0.5 φ intervals). In the case of data derived from sieving a sediment sample each value in column 2 is the weight,
in grams, of sediment accumulated on the sieve with openings indicated by the grain size class (column 1). To
facilitate comparison of samples of different weight the frequency distribution is more commonly calculated as a
weight expressed as a percentage of the total weight of the sample (column 3). Column 4 is the cumulative weight
(%) derived by incrementally summing the values in column 3. Several ways in which such data may be plotted
to graphically display the grain size distribution of a sample are shown in figure 2-8.

Histograms, such as figure 2-8A, are valuable because they readily show the relative proportions of each
size class and the modal class of the distribution (the size class with the largest frequency). Also shown in figure
2-8A is the frequency curve for the data, a smoothed version of the histogram formed by joining the midpoints of
each size class on the histogram. Note that there are two vertical scales in this example, one shows the absolute
weight per size class and the other shows the weight expressed as a percentage of the total sample weight per size
class. In this case the data are normally distributed and the frequency curve forms a bell-shape which is symmetrical
about its highest point. Figures 2-8B and C are cumulative frequency curves for the data in Table 2-2, column 4.

Table 2-2. Example of grain size data produced by sieving (note these data are plotted in Figure 2-8).

1. Grain Size 2. Weight 3. Weight 4. Cumulative Weight

Class (φ) (grams) (%) (%)

-0.5 0.40 1.3 1.3

0 1.42 4.6 5.9
.5 2.76 8.9 14.8
1 4.92 15.9 30.7
1.5 5.96 19.3 50
2 5.96 19.3 69.3
2.5 4.92 15.9 85.2
3 2.76 8.9 94.1
3.5 1.42 4.6 98.7
4 0.40 1.3 100.0
Total 30.92 100

A. Histogram and frequency curve B. Cumulative frequency curve C. Cumulative frequency curve
on an arithmetic scale on a probability scale
20 100 99.99
6 Frequency
Individual Weight (grams) curve 90

Cumulative Weight (%)

5 80 99

Cumulative Weight (%)

Individual Weight (%)
70 90
4 80
3 10 50 50
40 20
2 30 10
20 1
0 0 0 0.01
-1 0 1 2 3 4 -1 0 1 2 3 4 -1 0 1 2 3 4
Grain size (φ) Grain size (φ) Grain size (φ)

Figure 2-8. Various ways in which grain size data (Table 2-2) may be graphically displayed.

One of the major benefits of plotting grain size data as cumulative frequency curves is that the data form a unique
curve for each possible grain size distribution. Such curves may be plotted on graphs with arithmetic axes (Fig.
2-8B) or more commonly on graphs with a vertical “probability” scale which expands the low and high ends of the
scale and compresses the middle of the scale (Fig. 2-8C). One advantage of plotting such data on a probability scale
(Fig. 2-8C) is that normally-distributed data plot as a straight line. Moreover, if the sediment sample is made up of
several normally-distributed subpopulations its’ cumulative frequency curve, plotted on a probability scale, will
form straight-line segments, each corresponding to a subpopulation of the total sediment (Fig. 2-9B). Another
benefit of constructing cumulative frequency curves is that percentiles can be taken directly off the graph (Fig.
2-9A). The nth percentile (denoted φn in this context) is the grain size, in units of φ, which is finer that n % of the
total sample. In figure 2-9A φ20 is shown to be 0.86 φfor the hypothetical sample. Several descriptive measures
of grain size distributions have been based on percentiles taken directly from cumulative frequency curves (see
Table 2-3).

Describing Grain Size Distributions

A. Definition of Percentile B. Grain size population of three normally

distributed subpopulations
99.99 99.99

99 99
Cumulative Weight (%)

Cumulative Weight (%)

90 90
80 80
50 50
20 20
10 10

φ20 = 0.86 φ 1

0.01 0.01
Grain size (φ) Grain size (φ)

Figure 2-9. A. Illustration showing how a percentile may be determined from a cumulative frequency curve. B. Schematic
illustration showing the cumulative frequency curve of a sediment population composed of three subpopulations. Note that
both graphs are plotted on probability scales.

Table 2-3. Descriptive measures of sediment size distribution.

Measure Graphic Method Moment Method

(Folk and Ward, 1957) (after Boggs, 1987)
Median (Md) φ 50 —

Mean (M)
φ16 + φ 50 + φ 84 ∑ fm
3 100

Standard Deviation (s)

φ 84 − φ16
φ 95 − φ 5 ∑ f (m − M ) 2

4 6. 6 100

Skewness (Sk)
φ 84 + φ16 − 2φ 50 φ 95 + φ 5 − 2φ 50
+ ∑ f (m − M ) 3

2( φ 84 − φ16 ) 2( φ 95 − φ 5 ) 100σ 3

Kurtosis (K)
φ 95 − φ 5 ∑ f (m − M ) 4

2. 44 ( φ 75 − φ 25 ) 100σ 4

where: φn is the nth percentile of the size distribution taken from the cumulative frequency curve;
φ is the weight of sediment per size class as a percentage of the total sample weight;
m is the midpoint of the size class.

There are several different properties of grain size distributions that may be described both qualitatively and
quantitatively. The most common of these are outlined below. Table 2-3 summarizes some widely-used formulae
for computing the descriptive measures of grain size distributions. Note that the graphic method uses percentiles
taken directly from cumulative frequency curves (see Fig. 2-10)

Median (Md)

This is the mid-point of the distribution (i.e., the grain size for which 50% of the sample is finer and 50% is coarser).

Mean (M)

The mean is the arithmetic average size of the distribution (Fig. 2-11). For perfectly symmetrical normal

Example calculation of grain size statistics by the graphical method


99.9 Folk and Ward Formula for Graphic Mean:

Figure 2-10. Example of calculating the mean of a
99 φ + φ + φ 84
Mz =
16 50 size distribution by the graphical method.
95 3
Cumulative Frequency (%)

from the cumulative frequency curve:
60 φ16 = -0.59 φ
30 φ 50 = 0.35 φ
10 φ 84 = 1.27 φ

0.2 −0.59 + 0.35 + 1.27
0.1 Mz = = .34 φ
φ16 φ 50 φ 84 3
-3 -2 -1 0 1 2 3 4
Grain Size ( φ )

Individual weight (%)

Figure 2-11. Relationship between sorting coefficient
(standard deviation) and mean of a normal distribution.
After Friedman and Sanders (1978).

1σ M 1σ
coarse fine
Grain size (φ)

distributions the mean is equal to the median. Note that the true mean cannot be determined from data collected
by sieving but can be approximated by the formulae shown in Table 2-3.

Sorting or Dispersion Coefficient (σ

This is the standard deviation of the distribution and reflects the variation in grain sizes that make up a
sediment. Its’ calculated value relates to the mean of the distribution as illustrated in figure 2-11. This figure shows
that 68% of the distribution (i.e., 68% of a sediment sample, by weight) has a grain size that is within ±1σ of the mean.
For example, if the mean of the distribution is 1.45 φ and the sorting coefficient is 0.30 φ, then 68% of the sample
lies in the size range from 1.15 φ to 1.75 φ. Therefore, the larger the sorting coefficient the greater the range of grain
sizes that make up the sediment. A sediment that consists of only a small range of grain sizes (i.e., σ is small) is said
to be well sorted whereas a sediment made up of a wide range of grain sizes (i.e., σ is large) is said to be poorly sorted.
Figure 2-12 very schematically illustrates the appearance of various degrees of sorting. Descriptive grades of sorting
0 < σ < 0.35φ very well sorted
0.35 < σ < 0.5φ well sorted
0.5 < σ < 0.71φ moderately well sorted
0.71 < σ < 1.00φ moderately sorted
1.00 < σ < 2.00φ poorly sorted
2.00 < σ < 4.00φ very poorly sorted
σ > 4.00φ extremely poorly sorted

Very well sorted Well sorted

Figure 2-12. Schematic illustration of vari-

ous degrees of sorting. After Anstey and
Chase, 1974.
Moderately sorted Poorly sorted

Individual weight (%)

Mo = M = Md Sk = 0

coarse fine
Grain size (φ)
Individual weight (%)

Individual weight (%)

Mo Sk > 0 Mo Sk < 0
Md Md
Excess fine Excess coarse
particles particles

coarse fine coarse fine

Grain size (φ) Grain size (φ)

Figure 2-13. Schematic illustration of the various types of skewness. Note that dashed lines indicate the symmetrical
distribution for comparison with fine and coarse skewed frequency curves. M is mean, Md is median and Mo is mode.After
Friedman and Sanders (1978).

Skewness (Sk)

Skewness is a measure of the symmetry of the grain size distribution about the mean; it has a maximum
possible value of +1 and a minimum possible value of -1. A of skewness that is close to zero indicates that the
distribution is very symmetrical and the mean is equal, or nearly so, to the median and both fall within the modal
class. A positive value of skewness indicates that the distribution has a larger proportion of fine grains than if the
distribution were symmetrical. Conversely, if the value of skewness is negative the distribution is enriched in coarse
grains. Figure 2-13 schematically shows the various “types” of skewness.

Descriptive terms for skewness are: Sk >+0.3 strongly fine skewed

+0.1 < Sk < +0.3 fine skewed
-0.1 < Sk < +0.1 near symmetrical
-0.3 < Sk < -0.1 coarse skewed
Sk < -0.3 strongly coarse skewed

Kurtosis (K)

Kurtosis is a measure of the degree of “peakedness” of the distribution. Oddly enough, while it is one of
the common descriptive parameters for grain size distributions it is widely thought to be essentially of no value (see
just about any textbook). None-the-less, it has become somewhat of a tradition. Figure 2-14 schematically shows
differences between the three types of kurtosis that a distribution might display: leptokurtic (sharp-peaked; K >
1), mesokurtic (normal; K = 1), and platykurtic (flat-peaked; K < 1).

Paleoenvironmental Implications of Grain Size

For many years it was thought (and hoped) that the characteristics of grain size distributions were governed
largely by processes within the depositional environment. Therefore, properties like mean size, sorting, skewness,
etc., would cumulatively reflect these processes and provide a basis for interpreting ancient depositional
environments. This was a powerful reason for sedimentologists to study grain size distributions and many did just

Individual weight (%)

Figure 2-14. Examples of different types of kurtosis. After
Blatt, Middleton and Murray (1980).



coarse fine
Grain size (φ)

that throughout much of the 20th century. There was limited success. Results of one successful study are shown
in figure 2-15 and suggest that beach and river sediment can be distinguished on the basis of a simple plot of
skewness versus standard deviation (sorting coefficient). This figure shows relatively good separation of beach
sands (generally coarse skewed and better sorted) and river sands (fine-skewed and somewhat less well sorted).
The difference arises because rivers are capable of transporting a relatively wide range of grains sizes, particularly
a large proportion of fine sediment that is transported in suspension when the rivers are in flood. The river deposits,
therefore, tend to be relatively poorly sorted and enriched in fine grained sand (i.e., fine skewed). In contrast,
beaches experience the ongoing swash and backwash of waves running up and down the beach slope. These very
shallow flows tend to segregate the sediment very efficiently, particularly in washing fine-grained material out to
the sea or lake. Thus, beach deposits are rather well-sorted and somewhat enriched in the coarser grain size (i.e.,
coarse skewed)

The success of this approach to paleoenvironmental interpretation has been very limited. The main problem
is that factors other than processes in the depositional environment have a profound affect on grain size
distributions. For example, the size distribution of the constituents of the source rock (i.e., the rock that weathers
to produce the sediment) may be reflected in the size distribution of the deposited sediment. If a river is transporting
sand that has weathered out of a pre-existing rock formed of sand that was laid down millions of years ago on a
beach, the river sediment will continue to display a size distribution which is inherited form the beach deposits.



+1.50 Figure 2-15. Plot of skewness versus sorting

coefficient based on samples of river and beach
sands. After Friedman, 1967.






-2.50 River sand

Beach sand (ocean)
-3.00 Beach sand (lake)
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40



Thus, if we plotted that river's sediment on figure 2-15 we would mistakenly interpret the deposit as that of a beach.

Why measure grain size?

There are many reasons to quantitatively describe grain size distributions. Some of these are:

1. Grain size is important to determining the strength of currents that transported the sediment. Therefore, we need
a precise measurement of size to quantitatively interpret paleohydraulic conditions.
2. Sorting reflects the ability of the transport mechanism to segregate grains by size.
3. Skewness reflects the ability of the transport mechanism to selectively remove coarse or fine grain sizes.
4. It appears that grain size distributions like that shown in figure 2-9B have very specific interpretations in terms
of how the sediment moved while it was in transport. (More on points 1 through 4 later in Chapter 4.)
5. We need basic descriptors of sediment size to allow us to communicate with others.
6. Grain size and various properties of its distribution are important in determining a sediment's porosity and


Grain shape is another fundamental property of particles and one that may provide important information
about the history of a sediment. Like grain size, shape may be expressed in several different ways, including:
Roundness, a measure of the sharpness of the corners of a grain; Sphericity, a measure of the degree of similarity
between a grain and a perfect sphere; Form, an expression of the overall appearance of a particle. Methods of
quantitatively describing these three expressions of grain shape are outlined below.


The roundness of a particle refers to the degree of rounding (or angularity) of the edges of a particle. Of
the three shape properties it is the most difficult to quantify.

Wadell’s Roundness (Rw)

Wadell (1932) introduced this method of determining particle roundness; it is the most accurate method but
it involves the greatest effort and time. Rw is defined as the ratio of the average radii of curvature of the corners
of a grain (Σr/N; N is the number of corners) to the radius of the largest inscribed circle within the particle (R;
Fig. 2-16). The maximum possible value of Rw is 1 when the particle has no measurable corners (i.e., R = r). Thus,

RW =
∑r Eq. 2-15

Dobkins and Folk Roundness (RF)

Dobkins and Folk (1970) introduced a less tedious (and less accurate) method of calculating roundness
(symbolized as RF here) that is defined as the ratio of the radius of curvature of the particle's sharpest corner (r)
to the radius of the largest inscribed circle (R). Thus,
RF = Eq. 2-16
once again, RF approaches a value of 1 for perfectly rounded grains (i.e., no sharp corners).

Powers’ visual comparison chart

The easiest way to determine the roundness of a particle is by visual comparison with standard forms. Powers


R Figure 2-16 Wadell Roundness (see Eq. 2-15; after Boggs, 1967).

Grain outline

(1953) provided what has become the most widely used chart of grain roundness (Fig. 2-17) and is a basis for terms
describing roundness. Note that each box in figure 2-17 shows a particular roundness class and the appropriate
term to describe each class. Also shown are values of Rw and ρ (a logarithmic transformation of Rw to whole numbers)
that quantitatively define the limits of each roundness class.


Various measures of the degree to which a particle resembles a sphere (i.e., its sphericity) have been devised.
Sphericity not only describes one aspect of the shape of a particle but it may also be useful to understanding other
properties of the particle such as its settling velocity. Remember, Stoke’s Law of Settling applies accurately only
to spherical particles (less that 0.1 mm in diameter) and its error increases as the shape of the particle deviates from
that of a true sphere. Therefore, a measure of particle sphericity provides a means of quantitatively determining
how well Stokes’ Law will predict a particles’ settling velocity. Note that sphericity is normally given the symbol
“ψ”, the lower case Greek letter psi.

Wadell’s Sphericity (ψ

Wadell (1932) defined sphericity as the ratio of the diameter of a sphere with volume equal to that of the
particle to the diameter of the sphere which will circumscribe the particle. Wadell’s measure of sphericity may
take the form:
ψ=3 Eq. 2-17
where VS is the volume of the sphere with volume equal to that of the particle and VC is the volume of the
circumscribing sphere. In this form VS may be determined by measuring the volume of water displaced by the particle

Rw .17 .25 .35 .49 .70 1

ρ 1 2 3 4 5 6
Very angular Angular Sub-angular Sub-rounded Rounded Well-rounded

Figure 2-17. Powers’ (1953) visual comparison chart for grain roundness with appropriate terms for describing shape classes
defined by Rw and ρ.

and VC may be calculated from the formula for the volume of a sphere taking the maximum axis length of the particle
(dL) to be the diameter of the circumscribing sphere:
VC = d L3 Eq. 2-18
VC may also be calculated for a particle with shaped approximately like a triaxial ellipsoid (Fig. 2-1) by:
VS = d L d I dS Eq. 2-19
Substituting these expressions for Eqs. 2-18 and 2-19 into Eq. 2-17 yields:
dI ds
ψ=3 Eq. 2-20
d L2
As ψ approaches 1 the shape of the particle approaches that of a perfect sphere. Eq. 2-20 can be used to calculate
sphericity on the basis of measurements of the principle axes of a particle.

Sneed and Folk Sphericity (yP)

Sneed and Folk (1958) argued that the volume of a particle is not as important as its maximum projection area
in determining its settling velocity because drag forces act on the particle’s surface. Therefore, any measure of
particle sphericity must be reflect the maximum projection area of a particle. They defined maximum projection
sphericity (ψP) as the ratio of the maximum projection area of a sphere with volume equal to that of the particle
to the maximum projection area of the particle. ψP may be calculated from the formula:

ψP = 3 Eq. 2-21
This is the most widely-used expression of sphericity.

Note that an expression that is very similar to ψP and based on similar reasoning, termed the Corey Shape
Factor (S.F.), is widely by used engineers to describe the overall shape of a sediment particle:
S . F .= Eq. 2-22

Riley Sphericity (ψR)

The main problem in calculating ψ and ψP is that both require the measurement of dS. This is not difficult
for gravel-size particles but it becomes very impractical for sand-size sediment. Riley suggested a method of
calculating sphericity that relies on measurements that can be taken from the two-dimensional view of a sand grain
as seen through a microscope (Fig. 2-18). He defined an expression of sphericity as:
ψR = Eq. 2-23
where dc is the diameter of a circle that circumscribes the grain and di is the diameter of a circle that inscribes the
grain (Fig. 2-18). Again, as ψR approaches unity as sphericity increases.

Clast Form

There are two commonly used methods of describing the overall form of a particle, both based on various
ratios of dL, dI, and dS. Figure 2-19 shows the so-called Zingg diagram (after Zingg, 1935) that defines four form
fields and provides terms for clast form according to which field the axes ratios of a clast plot. The clast forms defined
by the Zingg Diagram are largely independent of sphericity, except for “equant” clasts which tend to have values
of sphericity near 1.

Figure 2-18. Illustration showing the measurements required to calculate

sphericity by the method proposed by Riley.


Figure 2-20 shows a second commonly-used scheme for classifying grain form that was proposed by Sneed
and Folk (1958). This method classifies form into 10 possible classes and the appropriate terms for each form class
is shown in figure 2-20 along with blocks that are drawn in the approximate proportions for each form field. Note
also that maximum projection sphericity may also be taken directly from this diagram and that different form classes
may have the same sphericity (i.e., form and sphericity are independent).

Significance of grain shape

Like grain size, the shape of a particle will provide some basis for making fundamental interpretations about
the “history” of a sediment, particularly something of the source rock of the grains and of their transport history.

Source Rock

The lithology of the source rock exerts a strong control on the form of particles, especially gravel-size clasts.
Bedded source rocks (e.g., horizontally bedded limestones) tend to produce platy clasts, due to the parallel planes
of weakness that the bedding produces. Massive source rocks (e.g., granites that have equal strength in all
directions) tend to produce more equant clasts. The hardness of the source rock will also control the overall shape

Zingg form index


0.9 Figure 2-19. Zingg diagram showing the classifica-

tion of grain form. After Zingg (1935) and Blatt,
0.8 Middleton and Murray, 1980.





0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Sneed & Folk form index


COMPACT Figure 2-20. Sneed and Folk (1958) classification of

0.7 grain form.
ds EL CO

ψp =

0.5 0.8

ds dL

0 0.33 0.67 1
dL d I
dL ds

of a particle, particularly after prolonged periods of transport (see below).


While in transport a grain will change in shape due to two major processes that may act in the transporting
medium. Interaction between grains during transport results in a change in shape and a reduction in grain size. As
grains move along their sharp edges are lost due to chipping and grinding, increasing their roundness and sphericity
and producing debris as finer sediment. Even when large clasts are partially buried in sediment beneath a current
their exposed surfaces are sand-blasted by particles in transport, thereby increasing their overall roundness.
However, grains may be crushed during transport, producing smaller, more angular and less spherical grains.
Overall, the most common outcome of transport is an increase in roundness and sphericity.

Figure 2-21 shows a plot of data derived by Humbert (1968) from experiments in which angular pebble-size
clasts of chert (a very hard rock type) and limestone (relatively soft) were transported over several hundreds of
kilometres in a circular flume. Note that the roundness of the limestone increased more rapidly with transport that
the chert because the softer limestone clasts are more prone to breakage (which increases rounding) than the harder
chert clasts. Also, the rate of increase in rounding with increased transport distance is initially very large but
becomes smaller as the grains became rounder. This reflects the fact that an angular clast, with very sharp corners,
easily becomes rounder as the fragile corners are broken off. However, a consequence of this increased rounding
is that the remaining corners are more massive and difficult to break off. Therefore, as the degree of rounding
increases the rate of rounding decreases. The change in the sphericity of limestone clasts shown by the top curve
in figure 2-21 is at a comparatively low rate throughout the entire distance of transport. This is because the changes
that are required to increase sphericity involve removal of a considerable amount of material from the clasts in
contrast to the removal of relatively small sharp corners that results in initially dramatic increases in clast roundness.

Changes in roundness and sphericity with transport of gravel-size clasts occur at much greater rates than
for sand-size grains (e.g., Kuenen, 1964). Because little quantitative research on changes in grain shape with
transport has been conducted on fine-grained sediment we can infer something of such changes from studies of
the weight loss of sand with transport (increased rounding and sphericity both require weight loss). It has been
estimated that under water flows (e.g., rivers) the rate of weight loss of quartz grains finer than 2 mm is less than
0.1% per 1000 km of transport. The rate increases only by a factor of two for feldspar grains. In all cases the rate
of weight loss decreases sharply with decreasing grain size and becomes negligible for sizes finer than 0.05 mm.
Such low rates of weight loss in very fine sediment is largely attributed to the fact that the particles spend much
of their time in transport in suspension well above the bed where interaction between particles is less frequent. In

0.9 Limestone sphericity
Roundness or Sphericity 0.8
0.7 undness
Limestone ro
0.5 Chert roundn
0 50 100 150 200
Distance of transport in a circular flume (Km)

Figure 2-21. Change in rounding (Rw) and sphericity (yP) with transport distance in a circular flume. Based on experiments
by Humbert (1968). After Blatt, Middleton and Murray, 1980.

air the rate of weight loss increases by a factor of 100 to 1000 times the rate in water. In water the abrasion between
particles that is required for such weight loss is inhibited by two factors: (1) the small submerged weight of the grains
gives them only little momentum during collisions, momentum that is required to cause damage; and (2) the viscosity
of the water between colliding grains tends to dampen the collisions (further decreasing the transfer of momentum).
In air, which has a considerably lower density and viscosity than water, the transfer of momentum between colliding
grains is much more effective and the resulting damage to the particles is more extensive. This (partly) explains the
common observation that wind-blown (eolian) sands are typically much rounder and have higher values of
sphericity than sands from other environments. In ancient sediment that is clearly not of eolian origin good rounding
and high sphericity are commonly interpreted to indicate that the sediment has been multi-cycled (i.e., the product
of several cycles of weathering and erosion of pre-existing sedimentary rocks).

Transport may have another effect on the shape by selectively sorting clasts by shape. For example, imagine
a cube and a sphere resting on the bed of a river. The sphere need only roll almost effortlessly along the bed in
response to the fluid drag of the flowing water. In contrast, the cube must pivot over 45°, against its own weight,
to roll a distance equal to its own length (if friction between the clast and the bed is large enough to inhibit it from
sliding). Thus, the sphere will more readily move under the river’s current and after a short time it will be separated
from the cube by a considerable distance. This processes is termed selective sorting by shape whereby easily
transported round, spherical clasts are removed from a sediment much more readily than their angular counterparts,
even if both clast types have essentially the same weight. This mechanism has been suggested by studies of some
modern river gravels where there is an increase in roundness and sphericity in the downstream direction that cannot
be explained solely by abrasion (e.g., Gustavson, 1974).

There has been limited success in distinguishing ancient depositional environments on the basis of clast
form. One such study showed that the deposits of gravel beaches and rivers (remember grain size) can be
distinguished on the basis of clast form. When data from these environments are plotted as in figure 2-20 the beach
gravels tend to fall towards the bottom of the graph, in and about the very platy and very bladed fields, and the
river gravels tend to fall near the top of the graph, in and about the compact field. The distinction may be attributed
to two causes. First, due to selective sorting of bladed clasts on the beach slope where rounded, compact clasts
would be easily rolled off the beach by the backwash (water running back off the beach after a wave has rushed
up its slope- the uprush is termed swash). This process would tend to enrich the beach with bladed clasts over
time. Second, the swash and backwash act to move larger, less mobile particles up and down the beach slope without

moving them entirely. This back and forth motion would result in abrasion along the basal plane of the clast and
as it is periodically flipped over it would become increasingly flat (i.e., bladed or platy). These two mechanisms are
absent in rivers where currents can more efficiently roll the more compact particles along their beds.
In conclusion, grain shape is an important sediment property that, like grain size, provides hints as to the
processes that acted to transport particles in ancient depositional environments. It is also an important variable
in determining the conditions that will cause a sediment to be transported by a specific mechanisms (see chapter
4). However, as with grain size, caution must be used in inferring ancient depositional conditions on the basis of
grain shape because it is also controlled by factors other than those acting in the depositional environment.


Porosity, the proportion of void or pore space in a sediment, and permeability, which is related to how well
the voids are connected, are important properties of any sediment or sedimentary rock. This is particularly true
because of the possible fluids that might be contained within sedimentary deposits; e.g., water, oil and/or gas,
contaminants that humans have added to the earth surface. This section defines and discusses porosity and
permeability and shows how they are related.


Any sediment contains a certain proportion of void space; that is, the proportion of the sediment that is not
occupied by particulate solids (i.e., grains). Porosity (P) is defined as the ratio of void volume (VP) to total rock or
sediment volume (VT), expressed as a percentage of the total sediment volume. Therefore,
P= × 100 Eq. 2-24
The pore volume is generally difficult to measure whereas the total volume of grains in a sediment (VG) is relatively
easy to determine (by weighing a specimen or by placing it in water and measuring the total displacement). Because
total volume is the sum of pore and grain volumes VP can easily be calculated: Vp = VT-VG. Substituting for VP in
Eq. 2-24, porosity is most commonly defined as:
P= × 100 Eq. 2-25
Porosity in natural sediment varies from 0 to approximately 70% due to a number of factors.

What Controls Porosity?

Packing Density

There are a variety of ways that grains may be arranged in a sediment and the spacing of the particles, referred
to as the packing density, exerts a strong control on porosity. This may be very simply illustrated by the manner
in which perfect spheres of equal size may be packed (Fig. 2-22). This figure shows the two-dimensional view of
spheres resting with cubic and rhombohedral packing. In the case of cubic packing the grains are stacked directly
on top of and beside each other and the pore space is relatively large (48% porosity). In contrast, with rhombohedral
packing each grain rests in the space between the subjacent grains so that the grains fill more of the space and the
porosity is lower (26%). These two styles of packing produce the theoretical maximum (cubic) and minimum
(rhombohedral) porosities of any sediment composed of perfectly spherical particles of equal size. In nature,
particles may be arranged in styles intermediate to these two end-members and their porosities will also be of an
intermediate value (i.e., between 26 and 48%). The rate of deposition of a sediment exerts considerable control over
grain packing. Rapidly deposited sands tend to have a more open framework (like cubic packing) whereas slow
rates of deposition often lead to tighter packing and therefore lower porosity.

Natural sediment is rarely composed of spheres so that porosity varies over a wider range than predicted
above. Porosity varies particularly with grain shape due to the differences in packing density that may be achieved
by non-spherical grains. Figure 2-23 shows how much greater porosity may vary when the particles are non-

Cubic packing Rhombohedral packing

48% porosity 26% porosity

Increasing packing density, decreasing porosity

Figure 2-22. End-member styles of packing of spheres of equal diameter and their associated porosities.

spherical. In nature, angular grains tend to support a looser packing arrangement (with larger porosity) than rounded

Grain Size

By itself, grain size has no direct effect on the porosity of sediment. For example, for a sediment composed
of equant spheres with cubic packing it can be shown that Eq. 2-25 reduces to
P = (1 − ) × 100 Eq. 2-26
and is, therefore, constant (P = 48%) and clearly independent of grain size.

Indirectly grain size may have some influence on porosity. For example, packing of a sediment tends to
increase with the settling velocity of the particles. When relatively larger particles, with high settling velocities,
impact on a substrate they tend to jostle the previously-deposited grains into tighter packing (with lower porosity).

Several studies have shown various relationships between grain size and porosity that could be explained
in terms of other factors. In unconsolidated sands porosity tends to increase as grain size decreases. This is because
the finer sand tends to be more angular than coarse sand and, therefore, will support a more open packing. In
sandstones the opposite trend has been recognized: porosity tends to increase with increasing grain size. This
outcome is due to the greater tendency of fine sand to lose volume when compacted upon burial (see below)
compared to the lower compaction of coarse sand. Thus, the conflicting apparent relationships between grain size
and porosity are due to factors other than grain size.

A. Porosity of sediment of tabular particles B. Bivalve shells

<50% Porosity 0% Porosity P>90%

Figure 2-23. Influence of particle shape on packing and porosity.


Decreasing sorting

fine sand

Porosity (%)
coarse sand
0 1 2 3 4
Standard deviation (φ)

Figure 2-24. Schematic illustration showing the relationship between sorting and porosity in clay-free sands. Based on data
from Nagtegaal (1978) and Beard and Weyl (1973).


The relationship between sorting and porosity is fairly straight-forward: as sorting becomes poorer (i.e.,
the standard deviation of the grain size distribution increases) porosity decreases. This is illustrated in figure 2-
24 for the case of clay-free sand. The reason for this relationship is obvious: the poorer the sorting the wider range
of grain sizes within the sediment and the greater likelihood of finer grains filling the void spaces between larger
grains. What is perhaps less obvious is the reason for the differences in the curves for fine and coarse sand (Fig.
2-24). Note that the minimum porosity for fine sand is greater than the minimum porosity for coarse sand. This is
because a poorly sorted coarse sand has an abundance of fine material to clog the large pore spaces between the
coarse grains. However, a poorly sorted fine sand which is free of clay (as in the case of the curves shown above)
the poor sorting is by virtue of the presence of coarser sands that will not clog the pores of the finer sand. A similar
difference in minimum sorting would not be expected if clay were available to clog the pores of the fine sand. Indeed,
the presence of clays tends to significantly reduce the porosity of sediment.

Post-burial Processes

Several different processes act in conjunction to alter porosity after a sediment has been buried due to
subsequent sedimentation on the overlying depositional surface. Figure 2-25 shows the typical reduction of
porosity of sands with burial (although the forms of such curves vary) that can be explained by the processes
summarized below. Note that some post-burial processes cause an increase in porosity; such porosity is refered
to as secondary porosity. The expression Primary granular porosity is often used to distinguish porosity due to
the character of the sediment prior to burial from porosity due to changes after burial.

Compaction ⎯ With burial the weight of overlying sediment may force the sediment into a tighter packing, thereby
reducing its porosity. Quartz sand shows little response to compaction; experiments have reduced the porosity
of quartz sand by only a few percent due to rearrangement and breakage under stress. The reduction in porosity
with compaction increases with increasing proportions of ductile (deformable) particles, especially clays minerals.
When first deposited, some muds (composed largely of clays) have a very high porosity (in excess of 70%) but
compaction with burial under a thousand metres of sediment reduces that porosity to 5 to 10%.

Cementation ⎯ The precipitation of cements within a sediment may begin almost immediately following deposition
or make take place after millions of years and relatively deep burial. The most common cements are calcite and quartz
that precipitates out of solution from saturated waters between grains and gradually fills in the previously open
void space, potentially reducing porosity to 0%.

Clay formation ⎯ Chemical alteration of some minerals, particularly feldspars which are a common constituent of

Depth of burial (km)
Figure 2-25. Illustration showing the reduction in
3 porosity of tertiary sands in Louisiana. After Blatt,
Middleton and Murray (1980).

12 16 20 24 28 32 36 40 44
Porosity (%)

clastic sediment, results in the formation of very fine-grained clay minerals that tend to accumulate within the pore
spaces between primary sediment grains. The formation of clays, therefore, may increase the total volume of the
rock at the expense of the pore volume, thereby reducing porosity.

Solution ⎯ Waters within and passing through sediment and sedimentary rocks may not precipitate cements. If
the waters are undersaturated with respect to the minerals with which they are in contact, these waters may dissolve
the sediment grains, leaving a cavity or vug where there had once been solid rock (note that the vugs can range
from microscopic in size to the size of caverns). Such solution increases the total void space at the expense of the
total rock volume; i.e., it increases the porosity. The additional void space produced by solution is termed secondary
porosity. Carbonate rocks (which are relatively soluble) are particularly prone to the development of secondary
porosity by solution.

Pressure solution is a process that can cause a reduction in porosity following burial when mineral grains
begin to dissolve at the grain contacts (Fig.2-26). Minerals under stress solution tend to dissolve more readily than
unstressed minerals. Within a sediment the weight of overlying material is transferred between particles at the points
where they are in contact. At the contacts the pressures can be immense and solution may occur as long as there
is fluid within the adjacent pore spaces. The tangential contacts between grains become increasingly flat as material
is removed into solution. The boundary between grains that have undergone pressure solution is said to be sutured.
As the grains lose material at their contacts the pore space becomes markedly shorter and its volume is reduced.
Concurrent with pressure solution insoluble material may accumulate in the pore space along with cements.
Combined, the reduction of pore length and the deposition of material in the remaining space can cause a dramatic
reduction in pore space. Once again, carbonate rocks are most prone to pressure solution and it has been
documented to occur at burial depths of only a few tens of metres. Modern carbonate sediment has porosities
ranging from 40 to 80% but carbonate rocks rarely have porosities larger than 15%. Much of this reduction can
be attributed to pressure solution. Siliciclastic sedimentary rocks can also undergo pressure solution but this is
much less effective in reducing porosity than in carbonates.

Fracturing ⎯ Fracturing of any rock, sedimentary or otherwise, will lead to an increase in porosity. Such additional
porosity contributes to the secondary porosity of a rock. Fracture porosity may be especially important in rocks
in which primary granular porosity is not well preserved.

Permeability (Darcy's Law)

Permeability (k) is related to the ability of a fluid (liquid or gas) to flow through any porous substance (e.g.,
a sediment). It was first defined by the French hydrologist Henri Darcy in 1851. Figure 2-27 very schematically
illustrates how permeability is defined. Darcy’s Law (Eq. 2-27) is an empirical formula that predicts the rate of flow
of fluid through a sediment. It can be used to experimentally determine permeability by measuring the rate of

Porosity reduction by pressure solution

Decreasing porosity

Figure 2-26. Schematic illustration showing the reduction in porosity due to pressure.

discharge of fluid of known viscosity through a specimen under a known pressure gradient and solving for k in
Eq. 6-3. Note that k is just an empirical constant, that depends on conditions within the rock , but one which has
an important physical interpretation (termed permeability).
A ∆p
Darcy's Law: Q=k Eq. 2-27

The terms are defined in figure 2-27.

For the sake of simplicity we will re-arrange the formula as follows:

Q 1 ∆p
=k× × Eq. 2-28
A µ L
Q/A is equal to the average (apparent) velocity (V, in cm s-1) at which the fluid is being discharged from the sediment.
Assuming that there is no compression of the fluid this is also the average velocity at which the fluid will pass through
the sediment. Eq. 2-28 may be re-written:
V =k× × Eq. 2-29
µ L
Beginning with the right-hand-side of this formula, ∆/L is the pressure gradient along the distance of flow and

Darcy's Law

p ∆p
Q is the fluid discharge (cm3 s-1);
k is permeability (darcies, cm2);
A is cross-sectional area (cm2);
µ ∆p is the pressure difference (bars, g cm-2);
k L is distance over which the flow passes (cm);
µ is the fluid viscosity (centipoises, g cm-1 s-1 x 10-1).

Figure 2-27. Schematic illustration defining Darcy’s equation. See text for discussion.

Region of low velocity

and high resistance

Figure 2-28. The relationship between the cross-sec-

tional area of a pathway and the relative proportion of that
cross-sectional area where fluid velocity is small due to
viscous resistance along the wall of the pathway.

represents the force that is acting to push the fluid through the sediment. As the pressure gradient increases so
will the average velocity. The term 1/µ is a measure of how easily the fluid can flow through the sediment (i.e., as
viscosity, a measure of fluid resistance to deformation, increases, 1/µ decreases). Therefore, as viscosity increases
the velocity must decrease. So the velocity of a fluid passing through a sediment depends on the force applied
to that fluid and on how much the fluid will resist flow through the sediment. But we have not yet considered how
the sediment itself will influence the velocity of the fluid passing though it; that is the role of the permeability term
in the Darcy’s Law. Permeability is a measure of how the pathway(s) through the sediment will affect the resistance
of the flow of fluid; that is, it is related to the average diameter and total length of the pathways. Certainly if the
“holes” or “pathways” through the sediment are small it will be more difficult to push the fluid through than if the
holes are large. This is because the greatest viscous resistance to flow occurs along the walls of the pathway; the
smaller the diameter of the pathway the greater the viscous resistance. This is illustrated in figure 2-28 which shows
that for a pathway with a small cross-sectional area the region close to the wall of the pathway, where flow velocity
is low due to viscous resistance, will be a relatively large proportion of the total cross-sectional area of the pathway.
Conversely, when the cross-sectional area is large the region of low velocity will be relatively small compared to
the total cross-sectional area of the pathway. Because k has units of cm2 (this is required to make the equation
dimensionally correct) it is useful to think of permeability as some measure of the cross-sectional area of the
pathways through which the fluid flows. Therefore, all other things being equal, a large pathway with large cross-
sectional area (i.e., k is large) will allow fluid to move at a higher average velocity, in response to a given pressure,
than will a smaller pathway (k is small) with fluid under the same pressure. Of course, the pathways through a
sediment are very variable in size so that permeability should be thought of as some average cross-sectional area
for the entire network of pathways through a sediment. This is a simplistic but useful view of permeability. The
total viscous resistance will also vary with the total distance that the fluid must pass along the pathways; thus,
permeability also varies inversely with the tortuosity of the pathways. In this context tortuosity is a measure of
the degree of deviation of a pathway from a straight line; the more irregular the pathway the greater the tortuosity
(Fig. 2-29). Thus, the larger the tortuosity of the pathways through a rock the lower the permeability. Again, this
is related to the degree of resistance to flow that is due to the total character of the pathway.

The units of permeability are termed darcies (d) and have dimensions of cm2. However, the permeability
of many rocks is much less than 1 darcy so that it is commonly expressed in terms of millidarcies (md; 1/1000 of a
darcy). As originally defined, 1 darcy is the permeability which allows a fluid of one centipoise viscosity to flow

Tortruosity = L2/L1
Figure 2-29. Definition of tortuosity. See text for


Permeability, k (Darcies)
5 4 3 2 -1 -2 -3 -4 -5
10 10 10 10 10 1 10 10 10 10 10

clean sands, Very fine sands, silts, Unweathered

Clean mixtures of sand, silt clays
gravel mixtures of clean
sands and gravels and clay, glacial till,
stratified clays, etc.

Figure 2-30. Values of permeability of unconsolidated sediments. After Pettijohn, Potter and Siever, 1973.

at one centimetre per second, given a pressure gradient of one atmosphere per centimetre. Figure 2-30 shows the
range of permeability of unconsolidated sediment.

Controls on Permeability

It should be obvious from the above discussion that any property of a sediment that controls the size of
the pore spaces and/or the tortuosity of the pathways will control the permeability. These are much the same as
the controls on porosity, with a few notable exceptions.

Porosity & Packing

Figure 2-31A schematically shows the general relationship between porosity and permeability. Permeability
tends to increase with increasing intergranular porosity. The reason for this should be made clear by re-examining
figure 2-22: the tighter the packing (and the lower the intergranular porosity) the smaller the “pathways” through
which a fluid will move and the lower the permeability of the sediment. Therefore a sediment of a given size with
cubic packing will have a higher permeability than a sediment of the same size with rhombohedral packing. However,
many rocks (especially shales and some carbonates, particularly those with secondary porosity formed by solution)
may have high porosity but low permeability. This occurs when the pore spaces are not well interconnected and
the “average” pathway size is very small. Conversely, the presence of fractures in rocks may significantly increase
the permeability while increasing the porosity only slightly. A fracture of 0.25 mm width. in a rock will allow the
passage of fluid at a rate equal to that passing through 13.5 metres of unfractured rock with a uniform permeability
of 100 md. The relatively large permeability along fractures is due to a combination of their size, compared to the
pore spaces of many rocks, and also because they are especially well-connected. Thus a rock with very low porosity
may have very high permeability if it is extensively fractured.

Grain Size and Sorting

Unlike porosity, permeability varies with the grain size of the sediment. This arises from the fact that, in
addition to packing, the size of the pores between grains is determined by grain size. To illustrate the relationship
between grain size and pore area consider a sediment of uniform spheres with cubic packing (see Fig. 2-22). It can
be shown that the average pore area (PA) is related to sphere diameter (d) by:

PA = 0.74 d2 Eq. 2-30

Figure 2-32 illustrates the graph of the solution to Eq. 2-30 and shows how pore area increases with increasing grain
size. Because the pore spaces form the pathways for fluid flow, the permeability of the sediment varies in a similar
manner: as grain size increases so does the size of the connected pores (although the total pore volume remains
unchanged) so that, all other factors being constant, and permeability also increases. This tendency also is shown


m ll ll

e e

w yw







40 ity 100 0
ros coa
rs e
po sand

Permeability (md)
Shale, chalk and

Depth of burial (km)

30 vuggy rocks nu 10 me 1
Porosity (%)

a d iu
gr m
er san
int d
y 1 fin
20 ar es 2
Prim Fractures an
10 0.1 fi n
es 3

0 0.01 4
0.1 1.0 10 100 1000 0 1 2 3 0.1 1 10 100 1000
Permeability (md) Standard deviation (φ) Permeability (md)


Figure 2-31. A. Schematic illustration showing the relationship between porosity and permeability (after Selley, 1982).
B. Illustration showing the effect of grain size and sorting on the permeability of clay-free, unconsolidated sands (based on
data from Nagtegaal, 1978 and Beard and Weyl, 1973). C. A graph showing the reduction of permeability with burial based
on data from the Ventura Oil Field, California (based on data from Hsü, 1977).

for natural sands in figure 2-31B.

The sorting of a sediment will have an obvious effect on its permeability. Well-sorted sands will have open
pore spaces and, therefore, high permeability. As sorting becomes poorer the finer fraction will tend to clog pores
(i.e., reduce their average area) and pathways so as to retard the flow of fluid, thereby reducing permeability. Figure
2-31B shows that sorting may cause permeability to vary over several orders of magnitude in sediment of the same
mean size.

Post-burial Processes

Like porosity, processes acting after burial of a sediment can have a considerable influence on permeability.
Figure 2-31C shows an example of the typical decrease in permeability that occurs with increasing burial depth.


Grain size (mm)

Figure 2-32. Relationship between grain

diameter and average pore area for
10 spheres with cubic packing. Curve
graphically illustrates solutions to Eq. 2-


.001 .01 .1 1 10 100 1000

Pore area (mm2)


Compaction, cementation, pressure solution, and formation of clay minerals all act to reduce the permeability of a
rock by reducing the size of pore spaces and by increasing the tortuosity of the pathways. As noted above, however,
fracturing can increase permeability immensely. Also, solution along pathways may enhance permeability.

Directional Variation of Permeability

An important attribute of the permeability of many rocks is that it may vary with direction. Such anisotropic
(not equal in all directions) permeability is particularly notable in bedded sediment where permeability is generally
greatest along planes parallel (or at a slight angle) to bedding. The presence of bedding usually reflects some
variation in grain size through a package of sedimentary rock. Layers of fine sediment bounding coarser layers will
impede permeability in the direction perpendicular to bedding and fluid will flow most easily through the coarser
layers, parallel to the plane of bedding. Permeability may also be larger in a given direction along the plane parallel
to bedding. When elongated grains are abundant in a deposit they commonly have a preferred orientation and fluids
moving through the sediment will receive least resistance along the direction parallel to the grain axes. Fractures
in rocks commonly develop with a preferred strike direction and permeability will be greatly enhanced in the direction
parallel to strike.



In sedimentology the term fabric refers to all aspects of the spatial arrangement of particles in a sediment
and includes both packing (which was dealt with in the previous section) and grain orientation. However, in practice,
the term has come to refer principally to the orientation of grains (this practice may have been inherited from
metamorphic geology). Grain orientation is one of the fundamental sediment properties and should be included
in any complete description of an in situ sediment or sedimentary rock. It may influence other properties such as
permeability; therefore, grain orientation may be an important consideration in predicting the direction of movement
of contaminant through a sediment.

Grain orientation is a potentially powerful tool for the interpretation of processes that acted on a sediment
at the time of deposition. As we have seen, other sediment properties have been of limited value in interpreting
sedimentary processes. Both grain size distribution and grain shape may reflect something of the processes in the
depositional environment but both may also preserve characteristics inherited from the source material that
produced the sediment. In contrast, grain orientation is determined at the time that the sediment was deposited;
it inherits no attribute from its source material. Once a particle has attained a preferred orientation at the time of
deposition it remains constant unless: (1) it is modified by compaction, a trivial concern in sand-size sediment; (2)
it is modified by post-depositional disturbance: soft-sediment deformation or bioturbation (both relatively easily
recognized); (3) it is modified by tectonic deformation (shearing and folding by tectonic processes). This section
of these notes describes the nature of grain orientation, how directional data are graphically displayed and treated
statistically, and how such data may be used to infer processes that acted in ancient depositional environments.

Measuring grain orientation

The orientation of a grain is determined by measuring the directional attributes of the long (a-axis) and
intermediate (b-axis) axes of particles. In gravel-size sediment we may use a compass to directly measure the trend
of a clasts a-axis and the strike and dip of its a-b plane (Fig.2-33), with respect to the plane of the surface on which
the particle lies. The angle of dip of the a-b plane is termed the imbrication angle and the direction of dip is termed
the imbrication direction of the clast and such a dipping clast is said to be imbricate. From studies of modern
sediment it is well known that particles tend to be imbricate into the flow (i.e., the imbrication direction points in
the up-current direction).

In sand-size sediment the orientations of the apparent axes are measured in thin sections but such
measurements are generally limited to grains with apparent length to width ratios of 3:2 (this ensures that the true

of bed
imbrication strike a-b plane

Figure 2-33. Illustration showing the directional attributes of gravel size sediment that are commonly measured in outcrop.
Note that the a-b plane is the plane passing through the clast such that the surface defined by the intersection of the clast
and the plane has the maximum possible area (i.e., the a-b plane is the maximum projection plane) and that the c-axis of
the particle is orthogonal to the a-b plane. In practice, for such a clast we measure the trend of the a-axis, the strike of the
a-b plane and its dip direction, which is at 90° to the strike, and angle; termed the imbrication direction and angle,

longest axis is measured; when grains have lower ratios it is difficult to distinguish the length from the width). Note
that for the measured directions of axes to be of any value the orientation of the specimen in its original position
in outcrop must be marked directly on the specimen; aspects of the original orientation include: direction to top,
direction to north, the plane of bedding seen in outcrop and the horizontal plane. It is particularly important to note
the orientation of the plane of bedding because grains will have been aligned on their depositional surface, the same
surface that controls the geometry of bedding . The trends of the apparent a-axes are measured on thin sections
cut in the plane parallel to bedding in a specimen of sediment or rock. The imbrication direction is determined from
thin sections cut in the vertical plane (normal to bedding). The determination of imbrication direction must be made
on the basis of two thin sections: one in the vertical plane that is parallel to the mean long axis trend, as measured
on the bedding plane, the other in the vertical plane trending normal to the mean long axis trend. The reasons for
this will become apparent in the following section.

Types of grain fabric

The grain fabric of a sediment, determined by either method described above, may be classified into two broad
groups: isotropic fabric and anisotropic fabric. The latter may be further classified according to the specific
directional attributes of the particles.

Isotropic fabric

A sediment that displays no preferred alignment of grains is said to have an isotropic fabric (i.e., grain
orientation varies uniformly and displays no preferred alignment of particles; syn. disorganized fabric; Fig. 2-34).
Such a fabric will appear the same in every plane through a specimen. Any sediment that consists of particles with
a high sphericity will appear isotropic for the simple reason that it is not possible to measure axes orientations (Fig.
2-34A). In sediment of non-spherical particles (Fig. 2-34B) such fabrics may be primary (i.e., developed at the time
of deposition) or result from reworking of the sediment by burrowing organisms.

Anisotropic fabric

Any sediment that displays a preferred alignment of particles in any direction and in any plane is said to
have an anisotropic fabric (i.e., not equal in all directions). Figure 2-35 shows the two common forms of anisotropic
fabric that develop in sand and gravel.

Isotropic fabrics

bedding bedding

Figure 2-34. A. Isotropic fabric in a sediment made up of spherical particles. B. Isotropic fabric due to random alignment
of grains.

a-axis transverse, b-axis imbricate [a(t) b(i)]

The particle shown in figure 2-33 has this orientation. Figure 2-35A also shows this fabric as it would be
seen in three orthogonal planes through a sediment or sedimentary rock. From studies of modern sediment, where
current directions are known, we recognize this style of fabric as being characterized by a-axes (seen on the plane
of the depositional surface; shown as the bedding plane in Fig. 2-35A and B) that are aligned transverse to the current
direction. Imbrication of the a-b plane is up-current (i.e., into the flow) and the direction of imbrication is along the
trend of the b-axis. Hence, the shorthand notation: a(t) b(i) - a-axis transverse to flow and b-axis imbricate. Note
that the grains appear horizontal in the vertical plane parallel to a-axes on bedding.

a-axis parallel, a-axis imbricate [a(p) a(i)]

This fabric is shown in figure 2-35B. In this case the a-axis of each grain is aligned parallel to the current
and the a-b plane is imbricate into the flow; the imbrication direction is along the trend of the a-axis. The short-
hand notation for this fabric is a(p) a(i): a-axis parallel to flow and a-axis imbricate. The mean trend of grains seen
in the vertical plane aligned normal to a-axes is essentially parallel to bedding or nearly horizontal.

Complex anisotropic fabric

Some sediment displays an equal or unequal mixture of a(t) b(i) and a(p) a(i) fabrics. Such sediment has a
complex fabric that may be difficult to distinguish from an isotropic fabric.

Anisotropic fabrics

a(t)b(i) a(p)a(i)
bedding bedding

Figure 2-35. Schematic illustration showing examples of anisotropic fabric. A. Grain a-axes are aligned transverse to flow
and b-axes dip into the flow. B. Grain a-axes are aligned parallel to and dip into the flow. See text for further explanation.

A Figure 2-36. Illustration showing the relationship between

apparent axes lengths and orientation due to the position of the
plane of section. A. A three-dimensional sketch of a particle
as viewed at an angle to its a-b plane. B. Shaded area shows
Plane of sectio the form and area of the grain at its intersection with a plane
B n
(termed the plane of section) that is parallel to the a-b plane,
but well above the a-b plane. Note the reduction of axes
lengths in the image seen on the plane of section. C. Shaded
C Plane of sectio
n area shows a larger form and area than in B as the plane of the
section moves nearer to the a-b plane of the grain. Note that
true axes lengths will be seen only if the plane of the section
is in the a-b plane of the particle. D. Shaded area shows the
form of a grain in section oblique to the a-b plane of the particle.
Plan Note that apparent axes (on the shaded area) are not parallel
e of
sect to the true axes of the grain. Similar distortion arises when
grains have variable orientation with respect to a fixed plane
of section.

The problem with measuring grain orientation on sections

Take a close look at figure 2-35 (A and B) and consider how the angular relationship between the grain and
the plane of view will influence the apparent axes lengths and orientations. In figure 2-35A, on the plane of bedding,
we see the a-axes lengths but the b-axes lengths are shortened by an amount that depends on the angle of imbrication
(the steeper the angle the shorter the apparent b-axis; if the grains were vertical we would see the c-axes on that
plane). In the plane that is vertical to bedding and transverse to the trend of a-axes we see the form of the grain
that is defined by the b-c plane. In the vertical plane that trends parallel to the long axes on the bedding-parallel
plane we see the form of grains that is defined by the a-c plane (actually the apparent c-axis will exceed the true c-
axis length as the angle of imbrication increases; if the grains were vertical we would see the b-axis on this plane).
This illustrates the problem that the two dimensional view of a three dimensional object depends on the angular
relationship between the directional attributes of the object and the orientation of the plane of view.

In thin sections cut from rocks this problem is compounded by the fact that we have little control over where
the plane of view will intersect the grains. The control on apparent axes lengths by the plane of intersection of the
surface with the grain is shown in figure 2-36B and C. Figure 2-36D shows how the angular relationship between
a grain and the plane of section will affect not only its apparent axes lengths but also their orientations. Specifically,
if the plane of view is not in and parallel to the a-b plane of the particle we will see a distorted form of the grain. Thus,
we have a considerable error in measuring grain orientation in rocks consisting of sand-size sediment. This is
minimized if care is taken to prepare the first section in the plane of bedding (a known surface with a predictable
relationship to the orientation of the grains). Also, because the angle at which the grains dip below the bedding
surface is relatively small (averaging up to approximately 25°) the distortion of form and orientation is relatively small.
Finally, when collecting such data we must ensure that a large enough number of grains are measured to balance
out such error (i.e., normally in excess of 100 grains must be measured but this number will vary depending on the
amount of true variation in grain orientations). It should be clear from this that when such data are described it is
very important to make it clear that data are based on measurements made on apparent axes, not true axes; all such
data collected from thin sections have this limitation. In all remaining figures that deal with grain orientation in this
chapter only data on apparent axes are reported.

Displaying directional data

Grain orientation is just one of a large number of types of directional data that may be gathered by a
sedimentologist (well see others through the course of these notes). When such data have been compiled they
must be displayed to recognize, at least visually, any significant directional trends that may be interpreted. For

15 N 15 N

(Number of observations per class)

10 0 5 10 15 10 62

Number of observations 0 5 10 15
Number of observations

5 5

0 0
0˚ 90˚ 180˚ 270˚ 360˚ 0˚ 90˚ 180˚ 270˚ 360˚
Direction Direction

Figure 2-37. Examples of directional data plotted as conventional histograms and as rose diagrams (inset).

example, if we have a set of measurements of the imbrication direction of a number of particles we will need to
determine whether the data are consistent and what is the mean imbrication direction. The imbrication direction
will indicate the upstream direction with respect to the current that deposited the sediment. If such deposits contain
fine gold particles we might want to know where the sediment came from so that we might find its source; the
imbrication direction will point towards that source. Statistical treatment of directional data will be considered in
the next section.

Sedimentologists display directional data on a form of circular histogram that is commonly referred to as a
rose diagram. Consider the directional data plotted in the form of an ordinary histogram in figure 2-37A. The number
of measurements (i.e., the frequency) in 30° classes is shown over the range 0 to 360° (a full circle; north is generally
taken to be towards 0°). You can see from this histogram that the modal direction is in the range 120-149° (the
southeast) and the data varies almost symmetrically about that mode. Inset in figure 2-37A is a rose diagram for
the same data and it shows the same trend. However, it is obviously easier to visualize the directional significance
of the data plotted on the rose diagram. Figure 2-37B shows another set of data plotted on a regular histogram and
a rose diagram. In this case we can recognize two prominent modes, one from 0 to 29° and another from 330 to 359°.
It is not readily apparent how these two modes are related until we look at the form of the rose diagram (inset in Fig.
2-37B). The rose diagram more clearly shows the overall trend of the directional data (in this case pointing towards
the north-northwest). The visual impact of a rose diagram is important when we compare different data sets and
particularly when we plot such diagrams on maps.

Figure 2-38 illustrates how rose diagrams are constructed using the example of data describing imbrication
direction. The class intervals define the angle of curvature of pie-shaped segments that have a length equal to the
number (this may be expressed as a percentage) of observations per class (i.e., the frequency per class). In figure
2-38 the class interval is 30° and the scale of frequency is shown radiating from the centre of the circle. The centre
of a rose diagram is commonly reserved to note the total number of observations used to construct it.

Two forms of rose diagram are shown in figure 2-38 based on the data given in the table. In rose A the distance
(L) from the centre of the circle to each value representing the number of observations per class (N) is equal to the

A frequency Data recording imbrication direction

0˚ 0˚
330˚ 30˚ Raw data: 96, 121, 135, 146, 152, 30˚
5 330˚ 5
(degrees) 160, 165, 172, 178, 185, 4
186, 201, 209, 212, 219 2
300˚ 3 60˚ 300˚ 60˚
2 Class Interval Frequency 1
270˚ 15 90˚ 90-119˚ 1 270˚ 15 90˚
120-149˚ 3
150-179˚ 5
240˚ 120˚ 240˚ 120˚
180-209˚ 4
210-239˚ 2
210˚ 150˚ 210˚ 150˚
180˚ Total: 15 180˚

Equal length Equal area

Figure 2-38. Illustration showing the construction of a rose diagram. See text for explanation.

value itself; that is L = N in whatever units you like; the distance between each value on the frequency scale is equal.
Thus, a segment of the rose corresponding to a class containing 5 observations is five times longer (extending
outward from the origin) than a segment corresponding to a class containing only 1 observation. Rose B shows
another frequency scale that many argue is more appropriate. In the case of Rose B the distance from the centre
of the circle to any value is given by L = N0.5. Therefore, the spacing of the frequency increments decreases outward
form the centre of the circle. The reason for this is that in this type of diagram the frequency of observations per
class is not shown in terms of the length of the segments but is shown by the relative area of each segment. For
example, when such a scale is used the area of a segment of the rose representing 5 observations is equal to five
times the area of a segment representing 1 observation. Because rose diagrams are used for their visual impact,
some sedimentologists argue that this is a more representative scale than the linear scale. Note the difference in
the form of the two roses in figure 2-38. The equal area scale reduces the visual impact of the difference between
intervals (compare the relative sizes of the segments corresponding to the 180-209° and 210-239° intervals). All rose
diagrams in these notes will be presented with a linear frequency scale.

The form of the rose diagram indicates the directional trends of the data in a visually useful manner. Like
any such data, the distribution may have one or more modes and is termed unimodal if one mode is present, bimodal
if two modes are present (bipolar if the modes are at 180° to each other) or polymodal if more than two modes are
present (Fig. 2-39). Also, the data may vary symmetrically or asymmetrically about the mode(s). The interpretation
of the form of a rose will depend on what directional attributes of a sediment have been measured to collect the data.
In the case of grain imbrication, the rose points towards the average direction of dip of the a-b planes of the particles
and this direction is at 180° to the current that formed the imbrication. Therefore, the rose shown in figure 2-38 shows
a mean imbrication direction to the south-southeast, produced by a current flowing towards the north-northwest.
Many other directional attributes point in the direction of the current under which they formed and the roses that
they produce will point directly in the flow direction.

Many types of directional data are like that shown in figure 2-38 based on grain imbrication; i.e., the
imbrication direction is a specific direction determined by the dip of the a-b plane of a particle. However, many
features for which directional data may be collected do not point to a specific direction. Consider the long axis
orientation of a particle; it does not point in a given direction but rather lies on a directional trend. For example,
an a-axis oriented towards 10° has the same orientation as an a-axis oriented towards 190°. Thus, the a-axis of the
grain is said to trend along 10-190°. Such directional data are said to be bidirectional; pointing in either of two
directions which are at 180° to each other. Figure 2-40 shows how such data are commonly dealt with in the
construction of rose diagrams. Note that rose diagrams based on bidirectional data are symmetrical with only one
side of the rose representing actual measurements and the other side is just its mirror image to give the impression
of the bidirectional nature of the data. Figure 2-41 shows the forms of rose diagrams produced by measuring grain

Unimodal Bimodal Polymodal


22 28 29 44


Figure 2-39. Classification of form of rose diagram. After Pettijohn, Potter and Siever, 1973. See text for explanation.

axes orientation in sediment with the anisotropic fabrics described in the previous section. A word of caution: be
careful to note what is represented by any rose diagram. For example, truly directional data, based on structures
produced by tidal currents that flow in directions that vary by 180° over time, may produce essentially symmetrical
roses like those shown in figures 2-40 and 2-41.

Statistical treatment of directional data

Normally, directional data are collected in sets of N observations from some particular deposit or associated
structure. Like grain size data, a set of directional data will be distributed about some mean direction and will have
a range of variation about the mean direction. Unlike grain size data, directional data cannot be treated by regular
statistics because each value in a set is a vector quantity and each vector has two components: each observation
in a set of directional data will have a direction (θ) and a magnitude (normally each vector has unit magnitude, i.e,
its magnitude equals 1; such a vector is termed a unit vector). The descriptive statistics are similar to those applied
to scalar quantities (like grain size) but their computation is fundamentally different. Without going into the details
of vector algebra this section provides an outline of the various statistics and their implications.

For any distribution of directional data the mean is the resultant vector (sometimes called the vector mean)
formed by summing all of the unit vectors that comprise the data set (e.g., Fig. 2-42). Once again, the resultant vector
includes a direction ( θ ) and a magnitude (R):
θ = tan −1 Eq. 2-31

Figure 2-40. Illustration showing the significance of a rose diagram based

on bidirectional data. In this case, the rose diagrams represent the long axis
orientation of grains seen on a bedding plane; one particle is shown but the
+ 68 N
roses represent a population of grains with a mean a-axis orientation
parallel to that shown on the example particle. Because the a-axis of a
particle (like that shown in the illustration) has a trend but no absolute
direction, either of the top roses may equally well describe its orientation.
However, visually these two roses give two diametrically opposing impres-
sions of the a-axes they represent because they impart a sense of direction
to the data; the left-hand rose suggests that the axes point to the west and
= 68 the right-hand rose suggests that the axes point to the east. To counter this
perceived sense of direction it is common practice to construct rose
axis of symmetry diagrams that are symmetrical, as shown in the lower part of the figure.
Note that the lower rose has doubled in size without increasing the number
of measurements on which it is based.

(i) (ii)

68 A 68
A a(p)a(i)



C B S 68 N
S 68 N

C bedding
C bedding

W 68 E
W 68 E

Figure 2-41. Rose diagrams representing two forms of anisotropic fabric (see Fig. 2-35 but note that the blocks shown here
are rotated at 180° to the blocks in Fig. 2-35).

Note that θ must be corrected as follows: if w > 0 and v > 0 then θ = Eq. 2-31;
if w > 0 and v < 0 or w < 0 and v < 0 then θ = Eq. 2-31 + 180˚;
if w < 0 and v > 0 then θ = Eq. 2-31 + 360˚

R = v2 + w Eq. 2-32

N or NC
w= ∑ n sin θ
i =1
i i Eq. 2-33

N or NC
v= ∑ n cos θ
i =1
i i Eq. 2-34

and N is the number of observations in the data set. Note that directional data may be treated as either individual
measurements (i.e., as raw data) or grouped data (i.e., data are expressed as frequency per class interval). In the
case of ungrouped data ni is equal to 1 (unit magnitude of each vector) and θi represents each of the measured
directions (from i = 1 to N) of the N vectors in the data set. When data are grouped the quantities above are: ni is
the number of observations in each class interval (from i = 1 to NC) and θi is the mid-points of each class interval
(from i = 1 to NC) and NC is the number of class intervals (i.e., NC = 360°/CI, where CI is the class interval in degrees).

The magnitude of the resultant vector can also be expressed as a percentage (L) of the total number of

θ1 = 346˚
+ 3
r1 = 1
Figure 2-42. Example of the derivation of a resultant vector
θ2 = 24˚ 2 = (syn. vector mean; large arrow) by the summation of unit vectors
r2 = 1 +
(small numbered arrows). Each unit vector has the direction
θ = 25.5˚ shown and a magnitude (ri) of 1. Use Equations 2-31 to 2-35 to
demonstrate the calculation of the direction and magnitude of
θ3 = 67˚ 1 R = 2.52
the resultant vector. Note that the arithmetic mean would be
r3 = 1 L = 84% 146° and clearly not representative of the three vectors.

observations (or more specifically, as a percentage of the total length of the unit vectors that comprise the data
L= × 100 Eq. 2-35

The magnitude of the resultant vector, particularly when it is expressed as a L reflects the amount of
dispersion of the data (i.e., the degree of variation of directions in the data set). Another, more important, measure
of the dispersion of the distribution of directional data is p (defined as the probability that the data are from a
population that is uniformly distributed) where:
p = e −1( L N × 0.0001)
Eq. 2-36

p ranges in value from 0 to 1 where p = 0 indicates that there is no chance that the data are uniformly distributed
(i.e., the data are from a population that has a preferred orientation) and p = 1 indicates that the data are from a
population that is definitely uniformly distributed (i.e., the population has no preferred orientation).

Table 2-4 provides an example of the treatment of directional data, both as ungrouped and grouped data.
With a little experience it is possible to acquire some intuition about these statistical properties on the basis of the
form of the rose diagram representing a data set.

Interpretation of grain orientation

In the previous section one interpretive use of imbrication direction has already been established; it points
in the direction 180° to the direction of the current that acted on the particles. Most workers who have included
grain fabric in studies of ancient rocks have used their results to reconstruct paleoflow directions. However, there
are several other ways in which fabric may be interpreted. To begin with, the anisotropic fabrics can be interpreted
in terms of how the particles moved under a flowing current. The a(t)b(i) fabric is produced by currents that roll
the particles along the bottom. This is the typical fabric of gravel size sediment; because of their large mass it is
difficult to move them in any other way but to roll them along the bottom. In contrast, the a(p)a(i) fabric tends to
be the most common fabric in sands and is thought to develop under relatively high rates of deposition and sediment
transport and high sediment concentration. Thus, for a given grain size a(p)a(i) fabrics in gravel will be produced
under much more energetic currents than those that produce a(t)b(i) fabric. The classic experimental studies of
gravel orientation by Johansson (1965, 1976) are required reading for anyone concerned with gravel fabrics.
Isotropic fabrics may result from rapid deposition of thick slurries which restrict the independent movement of a
particle, hindering the establishment of a preferred orientation.

Figure 2-43 shows an example of a complex anisotropic fabric based on data collected from a sandstone that
was deposited in a shallow-marine environment. Two major modes, at 90° to each other, are clearly seen on the rose
diagram. This fabric was produced by oscillating currents induced by storm waves in a shallow sea and the
bimodality is interpreted in terms of a mixture of transport modes at the time of deposition. The NW-SE mode
represents grains with long axes aligned normal to the wave-induced current; these grains were rolled along the
bed. The SW-NE mode represents grains that were aligned with their a-axes trending parallel to the current and
represent sand that was rapidly deposited from suspension. In this particular case, the bimodality of the fabric
reflects processes that act under currents produced by waves and may provide a basis for inferring wave-induced
currents in other ancient deposits.

In most sands the imbrication angles of grains range from 5 to 20°, although higher angles have been recorded
in sands that are very rapidly deposited by sediment gravity flows. Some research has suggested that imbrication
angle may also reflect the power of the current that act to align particles. Experiments by Gupta et al. (1987) showed
a distinct steepening of imbrication angles with increasingly strong flows. However, recent experiments have shed
some doubt on the relationship between imbrication angle and flow strength (Arnott and Hand, 1989).

Results of one recent study have suggested that grain imbrication may be particularly useful in interpreting
the nature of transporting currents. Specifically, the results suggested that variation in imbrication angle through

Table 2-4. Example of the statistical treatment of ungrouped and grouped directional data.

Raw data: 184 187 191 196 198 201 204 205
(degrees) 205 207 208 210 212 214 216 222

Grouped data:
Class Interval Midpoint Frequency

180-189° 184.5° 2
190-199° 194.5° 3
200-209° 204.5° 6
210-219° 214.5° 4
220-229° 224.5° 2

Total: 17

Treatment of ungrouped data:

w = ∑ ni sin θ i = −7. 04 v = ∑ ni cos θ i = −15.13
i =1 i =1

−7. 04
θ = tan −1 = 24 . 95; w < 0 and v < 0 then θ = Eq. 2 − 31 + 180 o ∴ θ = 24 . 95 + 180 = 204 . 95o

16. 69
R = ( −15.13 ) 2 + ( −7. 04 ) 2 = 16. 69; L= × 100 = 98.17%

p = e −1( 98 . 17 × 17 × 0 . 0001)
= 7. 67 × 10 −8

Treatment of grouped data:

w = ∑ ni sin θ i = 2 sin 184. 5o + 3 sin 194 . 5o + 6 sin 204 . 5o + 4 sin 214 . 5o + 2 sin 224. 5o = −7. 06
i =1

v = ∑ ni cos θ i = 2 cos 184. 5o + 3 cos 194. 5o + 6 cos 204. 5o + 4 cos 214. 5o + 2 cos 224 . 5o = −15. 08
i =1

−7. 06
θ = tan −1 = 25. 09; w < 0 and v < 0 then θ = Eq. 2 − 31 + 180o ∴ θ = 25. 09 + 180 = 205. 09 o
−15. 08

16. 65
R = ( −15. 08 ) 2 + ( −7. 06 ) 2 = 16. 65; L= × 100 = 97.95%

p = e −1( 97 . 95 × 17 × 0 . 0001)
= 8. 25 × 10 −8

Note the slight discrepancy between calculations based on grouped and ungrouped data due to the use
of the class mid-points in the case of grouped data.

Apparent a-axes orientations from

a shallow marine sandstone
N Figure 2-43. An example of a complex anisotropic fabric. Rose diagram
shows the trend of apparent long axes seen in the plane parallel to bedding
from the Upper Cretaceous Chungo Member (Wapiabi Formation) in the
Rocky Mountain Foothills. Note the prominent bimodality of the rose. See

text for explanation. After Cheel and Leckie (1992).


10 observations

a sediment may record changes in current strength and direction over time. Figure 2-44 shows data collected by
determining the mean imbrication angle in thin (0.1 to 0.2 mm) vertically contiguous layers through a sediment. In
the plots in figure 2-44 each point represents the mean imbrication angle (and direction ) in one such layer. The
rose diagrams in figure 2-44 are based on all data in the subjacent plot. Figure 2-44 A shows data from the deposits
of a river in which currents flowed consistently in the same direction over the course of deposition of the sediment
(such currents are said to be “unidirectional”). Within these river deposits the mean imbrication angle is at
approximately 13°, dipping into the current. There is little systematic variation in imbrication angle through the
deposit, reflecting the constant nature of the flow strength over the period of deposition. For comparison, figure
2-44B shows data from the deposits of a shallow marine setting that was influenced by waves, specifically powerful
storm-generated waves. The currents produced by such waves would flow back and forth over 180° over periods
on the order of 10 seconds, and are termed oscillatory or “bidirectional” currents. In contrast to the river-formed
fabric, the mean imbrication angle is parallel to bedding, reflecting the alternating direction of the current (i.e., the
number of grains that are imbricate in one direction are essentially cancelled out by the equal number of grains that
are imbricate in the opposing direction). The plot showing variation in imbrication through the shallow marine
sandstone is also strikingly different: there is wide variation in imbrication angle and it appears to vary symmetrically
about a mean of 0°. Not only is this variation symmetrical, but it is also has a cyclicity that can be proven statistically.
The cyclic variation in imbrication angle through the deposit records variation in the magnitude of flow strength
under waves: flow strength decreases, from a maximum in one direction, to zero and then increases to a maximum
in the opposing direction. Thus, detailed studies of the variation in imbrication angle in sediment may provide a
powerful tool in distinguishing the products of unidirectional and oscillatory currents.

A. Fabric produced by unidirectional B. Fabric produced by oscillatory

current in an ancient river current under waves in an
ancient shallow sea
B θ B
186 341
Figure 2-44. Comparison of the fabric of sandstones
deposited in fluvial (A) and shallow-marine (B)
FLOW FLOW settings. See text for discussion. After Cheel

4 (1991).


0 0
-90 0 90 -90 0 90


In nature there is a wide variety of sedimentary rocks and each type differs from all other types in terms of physical
properties, composition and/or mode of origin. The classification of sedimentary rocks is a necessary exercise
that provides consistent nomenclature to facilitate communication between sedimentologists (i.e., the classification
sets limits to the attributes of any given class) and most classification schemes are based on characteristics that
have some genetic significance. This chapter briefly describes the classification of sedimentary rocks on various
scales and then focuses on a particular class: terrigenous clastic sedimentary rocks.


Figure 3-1 shows the the relationship between sedimentary rock classificaiton and the origin of the sediment
that makes up the rocks. All sedimentary rocks are composed of the products of “weathering”, the process that
causes the physical and/or chemical breakdown of a pre-existing rock (termed a source rock). These “products”
include detrital grains (chemically stable grains) and material in solution. Detrital grains are normally dominated
by quartz, with lesser amounts of feldspars, rock fragments, micaceous and clay minerals, insoluble oxides, and a
small proportion (normally less than 1%) of what are termed “heavy minerals” because they have a higher density
than the quartz and feldspars. The heavy minerals may be relatively non-reactive to chemical weathering but form
only a small proportion of a source rock (e.g., tourmaline and zircon) or they may be less stable minerals that comprise
a relatively large proportion of the source rock (e.g., the amphiboles and pyroxenes). Rock fragments (syn. lithic
fragments) may include as wide a range of particles as there are source rocks but only fragments composed of
relatively resistant (physically and/or chemically) minerals withstand transport over great distances. Detrital grains
also include some micaceous and clay minerals and insoluble oxides that are formed by chemical reactions on the
surfaces of some minerals during chemical weathering. The micaceous minerals produced by weathering are
relatively unstable. However, clay minerals, dominated by kaolinite, illite and montmorillonite, and insoluble oxides,
including hematite, bauxite, laterite, and gibbsite, are generally very stable. The exact composition of detrital grains
produced by weathering will depend on the relative importance of chemical and physical weathering and the
composition of the source rock.

Sediment formed from the products of weathering are normally deposited following a period of transport to some
site of deposition. The various types of sedimentary rocks may be most fundamentally classified according to the
type of weathering product from which they form: as chemical sediment, composed of material that was transported
in solution and deposited by precipitation from solution, or clastic sediment, that include all of the particulate
products of weathering (i.e., the detrital grains produced by weathering) that are transported to their site of
deposition by a variety of physical processes: by running water (rivers, currents in lakes, seas and oceans), glaciers,
wind, volcanic eruptions (non-igneous rocks produced by explosions and breakage during lava flow), and gravity
(e.g., landslides).

The chemical sediment may be further subdivided according to the specific mode of formation. Sediment that
precipitates directly from solution is termed orthochemical sediment (e.g., halite, gypsum, some limestone and
dolomite) whereas those that are precipitated by organisms, to form their own shell material, are termed biogenic
sediments. Biogenic sediment is dominated by calcium carbonate (i.e., they form many limestones or have been
diagenetically altered to dolomite) but also include siliceous sediment (e.g., biogenic chert) composed of the
exoskeletons of siliceous-shelled organisms (e.g., diatoms).

Clastic sediment may also be divided into subclasses on the basis of their composition and mode of origin. The
most common is the terrigenous clastic sediment, including all sediment composed of detrital grains (derived from
any source rock) that were transported to their site of deposition. Clastic sediment that is derived from the products
of volcanic eruptions is termed pyroclastic sediment. A third, special type, of clastic sediment that spans between
clastic and biogenic sediment is the bioclastic sediment that is composed of reworked biogenic sediment (i.e., shell
material that is reworked by currents). Each of these subclasses of clastic sediment can be subdivided according

ical and Chemical weathe

ys ring

Source Rock
solutions solid particles
detrital grains
Rivers insoluble oxides
Oceanic currents
Volcanic explosions

Precipitation Cessation of movement

Chemical Sediment Clastic sediment


as s





Orthochemical Biogenic Terrigenous Pyroclastic

sediment sediment clastic sediment

Figure 3-1. Illustration showing the relationship between sedimentary rock classification and the origin of the sediment
making up the rocks.

to a variety of characteristics and the remainder of this chapter will focus on the classification of terrigenous clastic
sediment. However, note that many of the criteria for subdividing terrigenous clastic sediment may also be used
to further subdivide pyroclastic and bioclastic sediment.


Most widely-used classifications of terrigenous clastic sediment or sedimentary rocks are based on the
descriptive properties of a rock (e.g., grain size, grain shape, grain composition). The classifications summarized
here are largely descriptive but they are based on properties that may have important genetic implications (see

A descriptive classification of any rock may be made at various levels and precision. The classification of
terrigenous clastic sediment and rocks given in Table 3-1 represents the simplest subdivision and is based solely
on grain size (note that the boundaries between sediment/rock types are from the Udden-Wentworth grade scale).
This classification should be considered a “first-order” classification and each class may be further subdivided on
the basis of a variety of characteristics.

Table 3-1. Classification of terrigenous clastic sediment/rocks based on grain size.

Grain size1 Sediment name Rock name Adjectives


>2 Gravel Rudite cobble, pebble, well-sorted, etc.

0.0625 - 2 Sand Sandstone or arenite coarse, medium, fine, well-sorted, etc.

<0.0625 Mud Mudstone or lutite silt or clay

For the purposes of this general classification we will assign the rock or sediment name shown if more than
50% of the particles are in the size range shown. More detailed classification schemes will limit terms on
the basis of different proportions of sediment within a give size range (see text).


Basis of Classification

Sandstones may be further classified on the basis of the composition of the grains and the proportion of the
rock that is fine-grained matrix (dominated clay size sediment), as determined by examination of specimens in thin
section. The major components of most sandstones are: quartz (including chert and polycrystalline quartz),
feldspars, rock fragments and matrix; most other minerals are not sufficiently stable to survive significant transport
and comprise only a small proportion of grains in comparison to the major components, and are neglected in most
classifications. Note that sediment with the composition described is commonly termed siliciclastic sediment.
Several schemes for classifying sandstones have been proposed, based on the relative proportions of the major
components listed above. Figures 3-2 and 3-3 show a classification proposed by Dott (1964), defining the
compositional limits of each subclass of sandstone. Note that in this classification Dott defines matrix as all particles
finer than 0.03 mm; within the range of clay-size particles. This classification limits the term arenite to rocks with
less than 15% matrix while a rock with between 15% and 75% matrix is termed a “graywacke” (also spelled
“greywacke” or, in German, “grauwacke”; commonly abbreviated as “wacke”). All sedimentary rocks with more
than 75% matrix are termed mudstones in this scheme. The arenites and graywackes are further subdivided on the
basis of the relative proportions of their major constituents (excluding matrix) by plotting their relative proportions
on a ternary diagram. Figure 3-2 is rather schematic so take a close look at figure 3-3 to see the limits assigned to
each subclass of arenite and graywacke. According to figure 3-3A a quartz arenite contains no less than 90% quartz
grains and a subarkose contains between 5 and 25% feldspars, less than 25% rock fragments (but the proportion



Quart Quart
z aren z
ite 75%

Subark 5

ose 5
Sublith w
25 e

25 )
Felds 3 mm
pa 0.0
Grayw thic (<
acke Lithic
Grayw atrix
acke n tm

50 rce


Arenit Lithic
10 spa

0% rs

Roc 100%
k fr

Figure 3-2. Classification of sandstones. After Dott, 1964, as modified by Potter, Pettijohn and Siever, 1972.

Table 3-2. Example of the treatment of data collected by determining the proportions of quartz (Q), feldspars (F),
rock fragments (Rf) and matrix, as seen in thin section. A. Total composition, including matrix, indicates that the
rock is defined as a graywacke. B. Proportions of quartz, feldspars, and rock fragments "normalized" to 100% so
that the data may be plotted on a ternary diagram (see Fig. 3-2B).

A. Total rock B. Quartz, feldspars and rock fragments

Component Proportion Component Proportion 1

% %

Quartz 26 Quartz 45
Feldspar 20 Feldspar 34
Rock fragments 12 Rock fragments 21
Matrix 42 (∴ a graywacke)
Total: 100
Total: 100
Total Q, F, and Rf: 58 The proportions above plot in the field classifying this rock
as a feldspathic graywacke (see Fig. 2B).

Calculated as the proportion of each component in the
total rock divided by the total proportion of quartz,
feldspars and rock fragments (in this example this total is

A. Classification of arenites QUARTZ

1 60% QUARTZ
10% ROCK FRAGMENTS } Arkosic
2 40% QUARTZ










40 2

















B. Classification of graywackes QUARTZ
see table 2.

3 45% QUARTZ
} Feldspathic


























Figure 3-3. Details of the classification of arenites and graywackes as depicted in figure 3-2. Note that the corners of the
triangles represent 100% of the constituent indicated and solid and dashed lines (at 5% intervals) within the ternary
diagrams delineate lines of equal proportion of each component, decreasing to 0% for a given component on the side of the
triangle opposite each corner labelled for that component.

of feldspars always exceeds the proportion of rock fragments) and between 50 and 95% quartz. Figure 3-3A also
shows the compositions of two rocks and points, based on the relative proportions of their constituents, plotted
on the ternary diagram. Note that the proportions plotted on a ternary diagram must be recalculated from the original
data describing the total composition of the rock so that quartz, feldspars and rock fragments total 100% (i.e., the
proportions of quartz, feldspars and rock fragments must be “normalized” to 100%; see table 3-2). This procedure
must be applied to all such data that includes any proportion of matrix (i.e., arenites and graywackes).

Note that clastic sediment may contain detrital grains made up of chemical sedimentary rocks (i.e., they have
been eroded from a source rock that was a chemical sediment and subsequently transported to the site of deposition
of the clastic rock in which they occur). Particles derived from chemical sediment are generally relatively unstable
(with obvious exceptions like chert) and do not survive transport to a distant site of deposition and are not
considered here. However, the classification of terrigenous clastic rocks may be more specific than that shown here.
For example, the lithic arenites may be further classified on the basis of the relative proportion of the types of rock
fragments (e.g., proportions of sedimentary, metamorphic or igneous rock fragments). The rock names given in
figure 3-2 may also be modified to refer to the type of cement; e.g., a calcareous quartz arenite would have a calcium
carbonate cement. Howe in these notes we will limit the level of classification to that shown in figure 3-2.

Genetic implications

Rock names based on the relative proportions of their constituents not only provide us with a basis for
systematic classification but also tell us something about the history of the rock.

Textural maturity refers to the maturity of a rock in terms of its grains size distribution and shape. As a population
of sediment undergoes more and more transport, and/or cycles of erosion-transportation-deposition, it tends to
become better sorted (sands are said to become “cleaner’ as they lose their silt and clay fractions) and its’ particles
become rounder and more spherical in shape (see the section on Grain Shape and consider the generalizations made
here in light of all of the constraints on grain shape). A sedimentary rock is said to be mature if it well-sorted and
consists of rounded clasts. Thus, a quartz arenite, with less than 15% matrix, is texturally more mature than a lithic
graywacke (in terms of sorting and also in terms of grain shape; graywackes commonly have more angular grains
than arenites). Clearly, the name applied to a terrigenous sedimentary rock reflects is textural maturity and, therefore,
has implications related to the distance from the source that the sediment was transported prior to deposition and/
or the nature of the source-rock that produced the sediment.

Compositional maturity refers to the relative proportions of stable and unstable grains comprising a sediment
(quartz is the most stable component whereas feldspars and rock fragments are less stable). Like textural maturity
the degree of compositional maturity of a rock increases with transport and number of cycles of erosion-
transportation-deposition (i.e., as a sediment matures it loses its less stable components and becomes better sorted).
The unstable grains are destroyed by a variety of processes during weathering and transport: these processes
include physical processes (e.g., removal of unstable minerals by breakage) and chemical processes (e.g., solution
or transformation of unstable minerals to produce clay minerals). For example, the average proportion of feldspars
in igneous and metamorphic rocks is approximately 60% whereas the average proportion of feldspars in sandstones
is 12%. The difference is due to the relative ease with which feldspars may be destroyed by abrasion and/or chemical
weathering, in comparison to quartz that dominates most sandstones, and the fact that source rocks commonly
include older sandstones that have already been through the geologic cycle (maybe several times). Rock fragments
are also generally less stable than quartz grains and so that their proportions are smaller in mature sandstones than
in immature sandstones. As such, a quartz arenite is the most compositionally mature clastic sedimentary rock. The
ultimate formation of a quartz arenite commonly requires several passes through the geologic cycle. Clearly, textural
and compositional maturity go hand in hand, both depending on many of the same factors.

The composition, and therefore the rock name derived from the above classification, will also reflect something
of the nature of the source rock and the tectonic setting of the source area (referred to as the provenance of a
sediment). Taking a very simplistic view, we can think of the feldspars in a sediment as reflecting the contribution
from a granitic source and the rock fragments as reflecting a volcanic or low-rank metamorphic source (these typically
fine-grained rocks tend to produce abundant rock fragments rather than individual mineral grains). Thus, we can


Latitude (degrees north of equator)




0 10 20 30 40 50 60 70 80
% Feldspar

Figure 3-4. Proportion of feldspars in sands plotted against the latitude at which the sands were collected. Data are from
eastern and southern North America as summarized in Pettijohn, Potter and Siever (1973).

make some broad inferences regarding the nature of the source area of a sediment comprising a sedimentary rock,
given its formal name and an understanding of the basis for the name: e.g., an arkose represents a sedimentary rock
with sediment derived from a source area with abundant granitic rocks, a shield area for example. Of course,
knowledge of the specific type of feldspar or the specific composition of the rock fragments will tell much more about
the source rock and the tectonic setting of the source area.

To summarize the above discussion, the class of terrigenous clastic rock, by virtue of its basis on texture and
composition, reflects something of: (1) the intensity of weathering that the material experienced (related to the climate
ad relief of the sources area); (2) the extent of transport that the material has undergone; and (3) the nature of the
source rock (original mineralogy and/or rock type: e.g., igneous, sedimentary or metamorphic) and the tectonic
setting of the source area. To illustrate, consider the data plotted in figure 3-4 which shows a general decrease in
the feldspar content of sands in the southward direction, through eastern and southern North America (these sands
would form arenites, specifically arkosic and quartz arenites, if they were cemented). This southward decrease
reflects several factors. First, in the north the source rocks are dominated by rocks of the Canadian Shield that include
a variety of feldspathic igneous and metamorphic rocks. Such source rocks provide a local supply of feldspars so
that the sands are relatively rich in that mineral. In contrast, to the south there are fewer igneous and metamorphic
source rocks and sediment is derived, to a greater extent, from weathering of pre-existing sedimentary rocks that
have gone through a least one cycle of weathering and lost a proportion of their feldspars. The second factor is
the difference in the style of weathering in the north and south. In the south, a warmer, moist climate facilitates
chemical weathering that readily alters feldspars, producing soluble products and clay minerals. In the north,
physical weathering is more important (especially during the Pleistocene glaciation of the region that originally
produced much of the sand-size sediment in modern rivers of glaciated areas). Thus, the chances of feldspars
surviving weathering are greater in the north. Finally, for the data set described, from north to south, the average
transport distance from the original source tends to increase. The sands in the north are closer to their richest source
of feldspars than the sands in the south that include particles that originated on or near the Canadian Shield but
which have lost much of their feldspar content due to abrasion and further chemical weathering over the great
distance of transport. These are broad generalizations and the extensive scatter of points in figure 3-4 reflects the
complex interaction of these and other factors.

As noted earlier, other minerals only rarely make up more than a few percent of terrigenous clastic sediment but
these may be of great interpretive importance. For example, a sandstone may consist of a relatively large portion
of detrital carbonate, such as limestone or dolomite particles, derived from a carbonate source rock. However, these
grains will be destroyed within a short distance of transport from their site of origin. Thus, the presence of detrital

carbonate grains in a sediment reflects close proximity to exposed carbonate rocks at the time that the sediment was

Level of classification

How specifically a rock is classified depends on the purpose of the study for which the classification is made.
In many cases classification based only on grain size will be adequate (especially if the origin of the sediment particles
is not of interest). However, there are many different types of study that require a more detailed classification. In
studies that aim to delineate the geological history of a region the identification of the various classes shown in
figure 3-2 will help with the interpretation of aspects of the nature of the source rock and source area and the extent
of transport from the site of weathering. In another situation a sedimentologist may be required to provide
information to engineers who are planning to excavate or drill through sedimentary rocks. In this case the
classification based on composition will be necessary to determine the cost of the work in terms of time required
and the type of excavating or drilling apparatus that must be used. Both time and equipment influence the cost of
such a project so that a sedimentologist must conduct the necessary petrographic analyses to describe the rock
and give it a name (that reflects its’ composition). For example, an arkosic graywacke will contain a smaller proportion
of quartz than a quartz arenite. Because the quartz grains, that make up more than 95% of a quartz arenite, are harder
than the matrix and feldspars that make up a relatively large proportion of a feldspathic graywacke, the cost of
excavating or drilling an arkosic graywacke may be less than for the quartz arenite.

Note on genetic classification of sedimentary rocks

It is worth commenting here that some rock and sediment names that are commonly used are based on the mode
of origin of the rock (i.e., based on a genetic classification). The broad classification into clastic and chemical
sediment described at the beginning of this chapter is such a genetic classification. The classification of sandstones
is descriptive but those rocks may also be classified according to their origin at very specific levels. For example,
the term “turbidite” is applied to any rock that was deposited from a turbidity current (a type of sediment gravity
flow). A turbidite may be composed of carbonate or siliciclastic sediment that may range in grain size from gravel
to mud, but will contain a certain arrangement of internal structures and will occur in a particular stratigraphic context.
Hence, the term turbidite is largely independent of the fundamental properties of the rock and is defined in terms
of the mode of origin of the rock. The term “tillite” is another rock name based on mode of origin: a rock deposited
as glacial till. A tillite is typically composed of poorly sorted clasts, ranging from mud to boulders. Therefore, the
classification of a rock as a tillite requires a knowledge of the overall depositional environment that can only come
from a regional study of the tillite and associated rocks. In contrast, descriptive classifications of rocks may be made
equally well in the field, in the original stratigraphic context, or in hand specimens where the stratigraphic context
may not be known. In any study of a suite of sedimentary rocks it is usually advisable to classify rocks according
to their descriptive properties, at least in the beginning, possibly later classifying them on a genetic basis when
the depositional setting is better understood.


Rudites have not been subjected to as much detailed subdivision as the sandstones. However, rudites may
be further classified on the basis of shape, packing and the composition of the lithic fragments that dominate this
class of terrigenous clastic sediment. Table 3-3 reviews the classification of rudites by summarizing the common
terminology, including a brief description of the distinctive characteristics and possible genetic significance of each
type of rudite. This classification is largely descriptive but in some cases the basis includes an understanding of
the genesis of the clasts (e.g., the intraformational and extraformational rudites). While this discussion of the
classification of rudites is limited to the broad generalizations contained in Table 3-3, it is important to realize that
the concepts of textural and compositional (lithological ) maturity apply to rudites in a manner similar to sandstones.


A detailed treatment of the classification of lutite, that is dominated by the fine-grained clay minerals produced
by weathering, is beyond the scope and purpose of these notes. The definitions given in Table 3-4 should be learned

Table 3-3. Definition of terms used to classify rudites.

Term Distinguishing Characteristics Genetic Significance

Conglomerate A rudite composed predominantly of Rounded clasts may indicate considerable dis-
rounded clasts. tance of transport from source. The signifi-
cance will vary with the lithology of the clast
(i.e., limestone clasts will become round a short
distance from their source whereas quartzite
will require much greater transport).

Breccia A rudite composed predominantly of Generally indicates that the clasts have not
angular clasts. traveled far from their source or were trans-
ported by a non-fluid medium (e.g., gravity or
glacial ice).

Diamictite A rudite composed of poorly sorted, mud Commonly refers to sediment deposited from
to gravel-size sediment, commonly with glaciers or sediment gravity flows, particularly
angular clasts. debris flows.

Note: in the following the rock names are given for rudites consisting of rounded clasts (conglomerates) but the term
conglomerate may be replaced with the term "breccia" if the clasts comprising the rock are angular.

Orthoconglomerate A conglomerate in which all clasts are in Clast-supported framework is typical of grav-
(clast-supported conglomerate) contact with other clasts (i.e., the clasts els deposited from water flows in which gravel-
support each other). Such conglomer- size sediment predominates. Open framework
ates may have no matrix between clasts suggests an efficient sorting mechanism that
(open framework) or spaces between caused selective removal of finer grained sedi-
clasts may be filled by a matrix of finer ment. Closed framework suggests that the
sediment (closed framework). See figure transporting agent was less able to selectively
3-5. remove the finer fractions or was varying in
competence, depositing the framework-filling
sediment well after the gravel-size sediment
had been deposited.

Paraconglomerate A conglomerate in which most clasts are Typical of the deposits of debris flows or water
(matrix-supported not in contact; i.e., the matrix supports flows in which gravel size clasts were not
conglomerate) the clasts. See figure 3-5. abundant in comparison to the finer grain

Polymictic conglomerate A conglomerate in which clasts include Conglomerates that include clasts from a wide-
several different rock types. variety of source rocks, possibly derived over
a wide geographical area or a smaller but
geologically complex area.

Oligomictic conglomerate A conglomerate in which the clasts are Suggests that the source area was nearby or
made up of only one rock type. source rock extended over wide geographic

Intraformational A conglomerate in which clasts are de-

conglomerate rived locally from within the deposi- Deposition in an environment where muds
tional basin (e.g., clasts composed of accumulated. Muds were in very close proxim-
local muds torn up by currents; such clasts ity to the site of deposition as the clasts would
are commonly termed "rip-up clasts" or not withstand considerable transport.
"mud clasts").

Extraformational A conglomerate in which clasts are ex- Clasts derived from a distant source.
conglomerate otic (i.e., derived from outside the depo-
sitional basin).

Orthoconglomerates Paraconglomerate

Clast-supported Clast-supported Matrix-supported
(open framework) (closed framework)

Figure 3-5. Schematic illustrations of orthoconglomerates and paraconglomerate. Refer to Table 3-3.

in order to begin to understand nomenclature that has developed around this class of terrigenous clastic sediment
and sedimentary rocks. Table 3-5 outlines several descriptive properties of lutite and offers a descriptive
terminology. Table 3-5A summarizes a detailed classification of lutites that is promoted by Potter, Maynard and
Pryor (1980), based on the composition and bedding characteristics of lutite. Note that the term indurated (Table
3-5A) refers to any rock that is hardened by pressure and/or cementation; an indurated sediment is a rock and a
non-indurated sediment is an unconsolidated sediment. Table 3-5B summarizes the terms used to describe the
layering (stratification) of lutite and the manner in which a lutite “parts” or breaks along planes that are parallel to
primary bedding. Lutites, in particular, are characterized by their parting which is well-developed due to the parallel
alignment of platy minerals along the bedding planes (rendering the bedding planes particularly weak and termed
“parting planes”). In Table 3-5B “thickness” refers to the thickness of slabs of lutite that break along parting planes.
For those with additional interest the book by Potter, Maynard and Pryor (1980) is an invaluable text on the topic
of lutites.

Table 3-4. Definition of terms used to desribe mudrocks.

Term Definition

Shale The general term applied to this class of rocks (> 50% of particles are finer than
0.0625 mm).
Lutite A synonym for "shale".
Mud All sediment finer than 0.0625 mm. More specifically used for sediment in which
33-65% of particles are within the clay size range (<0.0039 mm).
Silt A sediment in which >68% of particles fall within the silt size range (0.0625 - 0.0039
All sediment finer than 0.0039 mm.
Refers to the tendency of lutite to break evenly along parting planes. The greater
the fissility the finer the rock splits; such a rock is said to be "fissile".
A blocky shale, i.e., has only poor fissility and does not split finely (see table 5).
Argillaceous sediment
A sediment containing largely clay-size particles (i.e., >50%).
A dense, compact rock (poor fissility) composed of mud-size sediment (low grade
metamorphic rock, cleavage not developed)
Normally a fine-grained sandstone but sometimes applied to rocks of predominantly
silt-size sediment.
A rock composed largely of silt size particles (68-100% silt-size)

Table 3-5. A. Classification of lutite. B. Terminology for stratification and parting in lutites. From Potter, Mayard
and Pryor (1980).

Table 3-5A
clay-size 0 - 32 33 - 65 66 - 100

adjective Gritty Loamy Fat or slick

> 10 mm


< 10 mm




> 10 mm



< 10 mm



Degree of metamorphism





Table 3-5B
Thickness Stratification Parting Composition
30 cm

Increasing sand, silt, and carbonate content

3 cm Slabby
Increasing clay and organic content

10 mm

Thick Flaggy
5 mm

Medium Platy
1 mm

Thin Fissile
0.5 mm
thin Papery



In this chapter we will examine the important characteristics of unidirectional fluid flows and sediment
transport under such flows. An understanding of the nature of fluid flow is crucial in sedimentology because
the particles that comprise most sediments and sedimentary rocks were deposited following transport in a fluid
medium (either water or air). The treatment of this subject, below, concentrates on the properties and charac-
teristics of fluid flow that are particularly relevant to the interpretation of sediments. Note that the principles
outlined below are also important to environmental geology because particulate contaminants and solutions
are commonly transported by a fluid media, including surface waters.

In order to understand fluid flows a basic knowledge of Newtonian Mechanics and calculus are neces-
sary and the treatment below assumes both. However, because students of GEOL 2P31 have a “mixed”
background the derivation of the following relationships will not be stressed on tests and assignments.
Instead, you will be expected to understand and be able to apply some of the more important relationships. A
summary of symbols and important relationships are given in Appendix 2. Whenever problems must be solved
in tests and exams a copy of Appendix 2 will be provided.


Unidirectional flows are characterized by a constant mean flow direction, in contrast to oscillatory flows
that periodically reverse in direction. This section begins by examining the causes of fluid flow in terms of the
forces that act on a fluid. Next, the classification of fluid flow is discussed followed by a detailed description
of the “structure” of a particular type of flow termed a “turbulent flow”. Note that the best detailed account of
unidirectional fluid flows is given by Middleton and Southard (1984).

Flow between two parallel plates

To understand how fluid flow takes place imagine the flow of fluid trapped between two parallel plates
(Fig. 4-1): a top plate that is moving at some velocity, U, and a bottom plate that is stationary (i.e., its’ velocity
is zero). When the top plate just begins to move (in response to some force F; see t1 in Fig. 4-1) the layer of
fluid in immediate contact with it will be accelerated to exactly the same velocity as the plate itself (i.e., there is
no slip between the plate and the fluid; the fluid will have the same velocity as a solid surface with which it is
in contact). The fluid is accelerated as the force that is acting on the plate is transferred to the fluid along the
contact between the fluid and the plate. At some time (t6 in Fig. 4-1) the plate will achieve some terminal
velocity (U) when the force that is driving it is balanced by a force of equal magnitude acting in the opposite
direction. This second force is imparted on the fluid by the stationary plate. Note that both forces acting on
the fluid are shear forces (i.e., they are tangential to the surface of contact with the fluid). Once the top plate
reaches its terminal velocity the entire column of fluid between the two plates will have reached some terminal
velocity that decreases linearly from a maximum equal to the velocity of the top plate to zero where the fluid is
in contact (with no slip) with the lower, stationary plate.

Why does the entire package of fluid go into motion rather than the just the top layer of fluid that is in
contact with the moving plate and why does the plate and fluid reach some terminal velocity rather than
accelerating infinitely? Because of the viscosity of the fluid (dynamic viscosity is given the symbol µ; SI
units of dynamic viscosity are Ns/m2 or kg/ms). Viscosity is the property of a fluid that acts to resist
deformation and it arises because of the attraction between fluid molecules; it can be thought of as a “force”
that resists deformation (although it is not a real force) and is sometimes referred to as “fluid friction”. When a
force is applied to a fluid molecule the molecule will accelerate and its’ momentum (its’ mass times its’ velocity)
will be increased. Because of viscosity, that molecule will cause adjoining molecules to accelerate as well, thus
it must exert a force on those molecules in order to change their momentum. This force between molecules in a

Force U
Moving plate


Shear stress (τ)
t4 y
within the fluid.
Stationary plate

Figure 4-1. Schematic illustration of fluid flow between two parallel, sliding plates. See text for details.

fluid can be thought of as a shear force acting along an almost infinite number planes lying parallel to the
plates in figure 4-1. Thus, because of the viscosity of the fluid, the shear forces exerted by the plates are
transferred through the fluid and when they balance each other exactly the top plate reaches its terminal
velocity. Also, when terminal velocity is reached the shear forces acting across any plane within the fluid
must be balanced (i.e., of equal magnitude but opposite direction above and below each plane) and equal to
the shear force imparted by the plate. The shear force within a fluid is typically referred to as the shear stress
in the fluid (and given the symbol τ and has units of force per unit area: N/m2 or kg/ms2). The shear stress
along any such plane through the fluid is given by:
τ=µ Eq. 4-1
where du/dy is the velocity gradient or the rate of change in velocity in the direction normal to the two plates
(note that du is not grain size times velocity). This is equal to the slope of the line defining the velocity
between plates (Fig. 4-1). In figure 4-1 this line is straight, its’ slope is constant and so is the velocity gradient.
Therefore, it should be obvious from equation 4-1 that the shear stress acting though the fluid is the same
along every plane between the two plates. Note that Eq. 4-1 applies only to so-called Newtonian Fluids, fluids
that deform at constant rate regardless of the applied stress (i.e., µ is constant).

From Eq. 4-1 we can develop a general relationship to predict the velocity at any point between the two
plates. As noted above, the shear stress within the fluid is equal to the shear force (F) applied to the plate in
motion: i.e., τ = F/A, where A is the area over which the force is acting. Substituting into Eq. 4-1 and
rearranging the terms:
τ du
= Eq. 4-2
µ dy
We can solve for u (velocity at height y from the stationary plate) by integration with respect to y:

dy = z
dy + c = y + c
µ z Eq. 4-3
where c is the constant of integration (the velocity at y = 0). Because we know that there is no slip at the
boundary then u = 0 at y = 0, therefore c = 0. Thus, the velocity (u) at any distance (y) above the stationary
plate is given by:
u= y Eq. 4-4
Clearly, the velocity between the two plate increases linearly from 0 against the lower plate (y = 0) to a
maximum at the upper plate and the magnitude of velocity varies directly with the magnitude of the applied
force and inversely with the viscosity of the fluid.

Fluid gravity flows

Flows of water, like that in a river, move down a slope and are driven by gravity: gravity acting on the

τy = F
G = ρg(D

water su


y τy

B τy = ρg(D
-y) sinθ
u = ρg sinθ
µ (yD - y 2
2 )


Figure 4-2. Schematic illustration of steady, uniform laminar flow down an incline due to the force of gravity. A. A
block of fluid with unit width and length to illustrate the shear stress acting on a plane passing through the fluid. See text
for details. B. The distribution of shear stress and velocity through a steady, uniform laminar flow.

fluid causes it to flow down-slope. This situation is illustrated in figure 4-2 for a steady, uniform flow1 down a
surface dipping at some angle θ. For the sake of simplicity, this example is for the case of open channel flow
where every fluid molecule is moving downslope along a straight path that is parallel to the lower, rigid surface
(termed the boundary). Note that this is the special case where shear stress is transferred through the fluid by
viscous forces only (i.e., this is a laminar flow, see below).

In the example of flow between two plates the force that caused the fluid to flow was the force applied
to the top plate and this force was transferred though the fluid due to its viscosity; only the fluid molecules in
contact with the plate directly experienced the driving force. In contrast, when gravity drives a fluid every
molecule “feels” this driving force. The shear stress acting along any plane parallel to the boundary, is equal
to the downslope component of the weight of fluid above the plane. Consider the shear stress acting on a
planar surface at some distance y above the bed and overlain by a volume of fluid of unit width and length
and height equal to D-y (see Fig. 4-2A). The volume of fluid above that surface is (D-y)×1×1 and its weight is
ρg(D-y)×1×1 (where D= flow depth, ρ = fluid density, and g is the acceleration due to gravity; note that
because we are dealing with unit width and length we will express the volume only in terms of D-y). The
downslope component of the weight of fluid (FG) in this volume is given by FG = ρg(D-y) sin θ: it acts in the
downslope direction along the plane that is tangential to the flow boundary. Thus, the shear stress acting on
the bottom of this volume of fluid is also:
τ = ρg ( D − y ) sin 0 Eq. 4-5

This distribution of shear stress through such a flow is shown in figure 4-2B. Note that within fluid gravity
flows the shear stress is not uniform, as in the fluid between two plates, but increases linearly from a minimum
of zero at the free surface (where y = D) to a maximum at the boundary (Fig. 4-2B).

Note that the term “steady” means that the flow depth and velocity are not changing with time and the term “uniform”
means that the flow depth and velocity are not changing along the flow direction.

Figure 4-3. Schematic illustration of Reynolds’ experiments on

R < 1000 the nature of fluid flow. See text for a detailed discussion.

1000 < R < 2000

R > 2000

Note that the shear stress acting on the boundary represents the case where y = 0 (such that D-y = D)
and is termed the boundary shear stress (given the symbol τo). From Eq. 4-5:
τ = ρgD sin 0 Eq. 4-6.
This is a particularly important component of fluid shear because it acts on the bottom of a flow where much
sediment is transported (i.e., it is the force per unit area acting on the boundary and is the force that causes
sediment in contact with the bottom to move).

Given the relationship shown in Eq. 4-1 we see that the velocity gradient cannot be uniform within a
fluid gravity flow but must vary from a maximum at the boundary to a minimum at the water surface. Combin-
ing Eq. 4-1 and Eq. 4-3 we derive:
du ρg sin 0( D − y )
= Eq. 4-7
dy µ
By integrating Eq. 4-7 with respect to y we can solve for u (the velocity at height y above the bed):
u= z dudy dy = ρg sin
z ( D − y )dy + c =
ρg sin 0
( yD −
)+c Eq. 4-8

Given that u = 0 at y = 0 (i.e., no slip along the boundary) we find that the constant of integration (c) is equal to
zero, such that:
ρg sin 0 y
u= ( yD − ) Eq. 4-9
µ 2
Thus, the velocity of such a flow varies as a parabolic function from 0 at the bed (y = 0) to a maximum at the
surface (y = D). This velocity distribution is shown schematically in comparison to the distribution of shear
stress in figure 4-2B.

Classification of fluid gravity flows

In his classic experiments Osborne Reynolds (circa 1883) described that fluid motion could be charac-
terized as laminar (i.e., fluid motion follows a linear path that parallels the flow boundaries) or turbulent (i.e.,
fluid motion follows a chaotic path that appears to be random and varies in magnitude in 3 dimensions: it
includes downstream, upward and lateral components of motion). Reynolds’ experimental set-up is schematically
illustrated in figure 4-3. A tank filled with fluid was drained through a transparent tube such that the velocity
of fluid flowing through the tube was dictated by the height of fluid in the tank and the tube diameter. Dye

was injected into the fluid at the entrance of the tube and the behaviour of the flow was visualized by watching
the behaviour of the dye streak in the tube. For a given fluid and constant tube diameter Reynolds found that
at low velocities the streak of dye followed a linear path through the length of the tube. At high velocities the
fluid paths were very irregular and the dye was quickly distributed uniformly through the tube (i.e., no dye
streak persisted through the tube). At intermediate velocities a dye streak persisted but its’ path was rather
irregular and not parallel to the walls of the tube. By conducting the experiments using a variety of fluids (of
different viscosity) and different tube diameters Reynolds found that he could predict whether a flow would be
laminar or turbulent (the intermediate flow type is termed “transitional”) by the relationship:
R= Eq. 4-10
where U is the mean flow velocity and D can be flow depth in channels that are much wider than they are deep
or D can be tube or pipe diameter. Viscosity is commonly expressed as kinematic viscosity (ν, where ν = µ/ρ; SI
units are m2/s) and Eq. 4-7 is commonly written:
R= Eq. 4-11

R is termed the flow Reynolds Number and it is dimensionless (i.e., it has no dimensions). In open channels
flow is laminar when R < 500 and turbulent when R > 2000 and transitional when 500 < R < 2000 (these limits are
somewhat different for flow through tubes or pipes; see Fig. 4-3).

The flow Reynolds’ Number can be thought of as the ratio between inertial forces (flow inducing
forces) to viscous forces (flow resisting forces). When viscous forces are large, relative to the inertial forces
the structure of the flow will be dominated by viscosity (i.e., momentum is transferred by way of viscous
attraction between fluid molecules) and the flow is laminar. Flow is turbulent when viscous forces are small
compared to inertial forces (i.e., deep fast flows) and momentum is transferred by turbulence (see below).

Fluid flows with a free surface (i.e., excluding flows in pipes) can also be classified by the another
dimensionless number termed the Froude Number (F), where:
F= Eq. 4-12
F can be thought of as ratio of inertial forces acting on the fluid to gravity forces that act on the water surface.
When F < 1 a flow is said to be subcritical or tranquil and when F > 1 a flow is said to be supercritical or
shooting (a flow for which F = 1 is said to be critical). In practical terms F is significant in two related ways.
First, the term gD is equal to the celerity of waves on a water surface (i.e., the speed at which such waves
propagate over the water surface). As such, if F < 1 then U < gD and water surface waves will propagate
upstream because their celerity is faster than the flow velocity. If F > 1 then U > gD and water surface waves
will be swept downstream. A more important implication of F to our later consideration of bedforms under
unidirectional flows is shown in figure 4-4. When F < 1 the water surface may be out-of-phase with a mobile
sediment bed whereas when F > 1 the water surface is in-phase with the mobile sediment bed.

Shear stress and velocity distribution in turbulent flows

Most fluid flows that are geologically important are turbulent and their characteristics vary consider-
ably from the laminar flows that were described earlier in this section. Among other things, because fluid
motion is so irregular (and three-dimensional) turbulent flows are very difficult to treat mathematically. Thus,
this section will consider turbulent flows in a much more qualitative manner.

Figure 4-5 compares the velocity profiles of laminar and turbulent flows. For now, disregard the
difference in turbulent flows over rough and smooth boundaries and focus on comparing the forms of the

F<1 F>1
Water surface water su r f a c e

Figure 4-4. Schematic illustration showing the significance of the Froude Number in terms of the phase relationship
between the free water surface and a mobile sediment bed.

curves for laminar and turbulent flows. Note that the lower portions of the curves for turbulent flows are like a
compressed version of the curve for laminar flow (i.e., there is an initially rapid increase in velocity away from
the boundary). However, the remainder of each curve for turbulent flows shows a much lower rate of increase
in velocity than does the curve for a laminar flow (i.e., in turbulent flows du/dy in the upper portion of the flow
is much more uniform than is the case for laminar flows). These two features reflect the fundamental differ-
ences in the manner in which shear stress is distributed though the flows.

In laminar flows the momentum of the fluid was determined by the viscous shear stress acting on that
fluid within the flow. However, as figure 4-6 illustrates, in turbulent flows fluid momentum is also changed as
packages of fluid move up and down throughout the flow (the characteristics of these moving packages will be
described below). Low-speed fluid from near the boundary moves up into the region of high speed fluid, at
some distance from the boundary, and the high speed fluid loses momentum. Conversely, high speed fluid
from the region away from the boundary may move downward and increase the momentum of the fluid near the
boundary. This physical movement of fluid through the flow accounts for the more uniform distribution of
velocity, well above the boundary region. This transfer of momentum differs fundamentally from viscous
shear stress but it has the same outcome and is often termed turbulent shear stress or reynolds stress.
Viscous shear stress is also important within a turbulent flow, in fact it predominates in the region closest to
the boundary where the velocity gradient is large. Thus, the total shear stress along any plane passing
through a turbulent flow depends on the viscous and turbulent components of shear stress and takes a form
similar to Eq. 4-1:
τ = (η + µ) Eq. 4-13
which can also be written:

Water Surface


Laminar Flow Turbulent Flow Turbulent Flow

(smooth boundary) (rough boundary)

Figure 4-5. Schematic illustration comparing the distribution of velocity through turbulent and laminar flows. See text
for a detailed discussion.

shear stress

du du dominated
τ =η +µ D Figure 4-6. Schematic illustration of
dy dy the nature of shear stress in a turbulent

flow. See text for details.
shear stress Viscosity

du du
τ=η +µ Eq. 4-14
dy dy
where η (the Greek letter eta) is termed the “coefficient of eddy viscosity”, a measure of the effectiveness with
which momentum is transferred through the flow by eddies (packages of fluid). Figure 4-6 illustrates the above
discussion and shows that the upper portions of a turbulent flow are dominated by turbulent shear stress
while the region nearest the boundary is dominated by viscous shear stress. In fact, the boundary itself is so
much dominated by viscous shear that the boundary shear stress for turbulent flows may be determined by
the same relationship used for laminar flows. (i.e., Eq. 4-6). However, the velocity distribution within a
turbulent flow is considerably different from that in a laminar flow (compare curves in Fig. 4-5) and can only be
described in terms of experimentally-determined relationships: one for turbulent flow over smooth boundaries
and another for rough boundaries (i.e., covered with sediment and/or bedforms composed of sediment). The
formula for predicting flow velocity (u) at some distance (y) from a rough boundary (the most common type of
boundary of concern in sedimentology) is given by:
u 2. 3 y
= 8. 5 + log Eq. 4-15
U* κ yo
where κ is termed “von Karman’s constant” and is equal to 0.4 for most fluids, yo is a measure of the height of
the roughness elements on the boundary (either the grains and/or the bedforms) and U* is termed the shear
velocity of the flow and it is related to the boundary shear stress by:

U* = Eq. 4-16
Shear velocity has the dimensions of velocity and is a convenient way in which to express boundary shear
stress. By Eq. 4-15 the velocity is zero at some point just beneath the surface of the rough boundary, in
contrast to turbulent flow over smooth boundaries where velocity is zero at the boundary surface (see Fig. 4-
5). Note that the mean velocity of a turbulent flow over a rough boundary occurs at y = 0.4D. Thus Eq. 4-15
can be used to calculate mean velocity by substituting this value.

Structure of turbulent flows

Turbulent flows can be subdivided into three zones on the basis of the way in which momentum is
transferred (Fig. 4-7); these subdivisions are also characterized by difference in the behaviour of the flow. The
viscous sublayer is the zone that extends upwards from the boundary and is dominated by viscous shear
(much like a laminar flow). The thickness of the viscous sublayer (δ) is given by:

Figure 4-7. Subdivisions of turbulent flows based on the major mecha-

outer nisms of momentum transfer. The outer layer is dominated by turbulent
D layer shear stress while the viscous sublayer is dominated by viscous shear.

transition layer
viscous sublayer

12 ν
δ= Eq. 4-17
and may range from a fraction of a millimetre to several millimetres in thickness. Many older texts refer to the
viscous sublayer as the “laminar sublayer” of a turbulent flow but flow in this zone is not strictly laminar
because it experiences fluctuations in velocity (in both speed and direction) due to interaction with turbulence
from higher levels in the flow. The buffer layer is the zone which has characteristics that are intermediate
between those of the viscous sublayer and the outer layer; it is a region of transition from turbulent shear to
viscous shear. The outer layer is the zone where turbulence is dominant, i.e., momentum is transferred
predominantly through turbulent shear stress. This zone extends from the free surface to the buffer layer and
is characterized by eddies (packages of rotating fluid to be discussed in detail in a later section).

As noted in the previous section, the velocity profile of a turbulent flow depends on the nature of the
boundary (whether it is smooth or rough) and turbulent boundaries may be classified on the basis of the
relationship between the thickness of the viscous sublayer and the size of the grains on the boundary. A
boundary is said to be dynamically smooth when the viscous sublayer is thicker than the height of grains on
the bed (i.e, the grains are entirely within the viscous sublayer) and dynamically rough when the grains are
higher than the viscous sublayer (i.e., they protrude out of the viscous sublayer). This is an important
concept because whether a turbulent boundary is dynamically smooth or rough will influence, among other
things, the forces that act to move particles on the bed (see below).

Turbulent boundaries may be classified by a form of Reynolds number termed a boundary Reynolds
Number (R*, also termed a grain Reynolds number), where:
R* = Eq. 4-18
where d is the average grain size of the bed material. We can easily determine R* for the condition (between
dynamically smooth and rough boundaries) where a boundary is covered by spherical grains of uniform size
that extend exactly to the top of the viscous sublayer (i.e., δ = d). Substituting Eq. 4-17 for d in Eq. 4-18:
U*δ U* 12 ν
R* = = × = 12
ν ν U*
Thus, when the height of the grains on the bed is exactly equal to the thickness of the viscous sublayer, R* =
12. In actual fact, partly because natural sediments are not composed of uniform spheres, it has been found
that boundaries behave as dynamically smooth when R* < 5 and as dynamically rough when R* > 70. Turbu-
lent boundaries are said to be transitionally rough when 5 < R* < 70. Figure 4-8 schematically defines turbulent
boundaries in the manner outlined above. Note that on beds of grains much larger than the thickness of the
viscous sublayer the sublayer develops over the surface of the large particles.

δ >d δ ≈d δ <d
δ δ δ
R* < 5 5 < R* < 70 R* > 70
Smooth Transitional Rough
Figure 4-8. Classification of turbulent boundaries on the basis of the relationship between the thickness of the viscous
sublayer and the size of grains on the boundary.

Organized Structure of Turbulent Flows

As described above, turbulent flows are characterized by a chaotic pattern of fluid flow and water
particles are accelerated and decelerated in all directions due to the transfer of fluid momentum through the
outer zone of the flow. However, organized structures within turbulent flows can be recognized on a variety of
scales. Figure 4-9 shows a hypothetical curve depicting the variation in velocity (in the downstream direction)
over time in a turbulent flow (i.e, if velocity at some depth were measured instantaneously and repeatedly over
time). Note that the pattern of variation in velocity can be thought of as consisting of two components: a
slowly varying component and a relatively rapidly varying component. These two components represent
different patterns of organized fluid motion that act on different scales along with essentially random fluid
motions. The organized patterns of motion are known to result from “structures” within a turbulent flow that
behave in a quasi-regular manner.

The outer layer of a turbulent flow is dominated by secondary flows and eddies of various type that
interact in a complex manner. Secondary flows in the outer layer can be considered as rotating packages of
fluid that spiral along an axis that is parallel to the mean flow direction; secondary flows impart a cross-channel
and vertical component of fluid motion onto the mean, downstream flow. In straight channels two such spiral
flows typically develop, side-by-side and counter-rotating. In sinuous or meandering channels the form of
such secondary flows varies as shown in figure 4-10; one spiral at the bends of the meander (with surface flow
towards the outside of the bend) and two spirals at the points of inflection between bends. In fact, channels
meander because of the variation in the distribution in boundary shear stress and sediment transport that is
caused by secondary flows. Boundary shear stress is greatest on the outside of the bend (enhancing erosion)

Figure 4-9. Schematic illustration of the variation in downstream velocity at a point in a turbulent flow, measured over
time. Solid line shows the rapidly varying component of turbulence; dashed line shows the slowly varying component of
turbulence. See text for discussion.

A A'


B B'

C C'

Figure 4-10. Secondary, spiral flows superimposed on the mean, downstream flow in a meandering channel. Arrows
indicate the direction of the component of fluid motion due to secondary flows that are superimposed on the mean flow.
See text for discussion.

and smallest on the inside of the bend, enhancing deposition. Deposition is further enhanced on the inside of
the bed due to the component of flow velocity that acts from the outside towards the inside of the bend,
transporting sediment in that direction.

Eddies or vortices in a flow are packages of fluid that rotate about an axis that extends perpendicular to
the direction of mean flow and these eddies travel in the mean direction at a speed equal to 0.8U∞, where U∞ is
the free-surface velocity of the flow (i.e., the downstream velocity that the water surface is moving). They may
be of smaller scale than secondary flows and may be superimposed on secondary flows. Eddies may extend
through the entire thickness of the outer zone and may have smaller eddies superimposed on them. As eddies
move in the mean flow direction they result in temporal and spatial variation in boundary shear stress due to
the changes in the rate of shear that they induce in the viscous sublayer. Figure 4-11 shows a particular type
of eddy that does not move along the flow direction but develops in the lee of a negative step on the
boundary (such a step might be produced by a bedform; see below). Over such a step the flow is said to
“separate”, become detached from the boundary, and becomes attached to the boundary at some point down
stream. Upstream of the attachment point, below the step, the flow is directed in the upstream direction and
forms a “roller vortex”, or “roller eddy”, that extends across the flow in the lee of the step. Downstream of the
attachment point the flow “attaches” to the boundary and behaves essentially identical to flow before the step
on the boundary. The development of such roller eddies in the lee of a step is important to the formation of
many of the bedforms that will be described and discussed in the following chapters.

0 0 0 0


Figure 4-11. Development of a roller vortex in (v) the lee of a negative step on a boundary. Curves show the velocity
distribution in the flow near the boundary below. The letter “s” indicates the point where the flow separates from the
boundary and the letter “a” indicates the position of the attachment point. See text for a discussion of details.

A component of the flow structure of the viscous sublayer includes a series of mean-flow-parallel,
alternating (across the flow direction) rows of high-speed and low-speed fluid termed streaks (Fig. 4-12A). In
the absence of sediment in transport by a current the spacing of streaks (λ) is given by:
λ U*
≈ 100 Eq. 4-19
This spacing increases when sediment is in transport over the bed (Weedman and Slingerland, 1985). Some of
the small-scale fluctuations in velocity in a turbulent flow are due to a process termed the bursting process, or
bursting cycle, that begins in the viscous sublayer due to some instability of streaks. Ideally, the bursting

A. Streaks View looking down onto alternating high-speed

and low-speed streaks in the viscous sublayer


B. The bursting process

A burst Figure 4-12. Organized structure of the
viscous sublayer. A. The distribution of
4 alternating high- and low-speed streaks along
3 the boundary (lengths of arrows are pro-
portional to fluid speed). B. The bursting
viscous 1 3 1&2 process or cycle. Left hand side
sublayer schematically shows the behaviour of fluid
in and near the viscous sublayer (numbered
sequentially over time). The right hand side
y shows the effect of the movement of fluid
A sweep
on the near-boundary velocity profile (num-
2 bers correspond to events shown on the
2 left hand side). See text for a detailed dis-
1 3
sublayer 1 4
3 4

Modes of particle movement

A. contact B. saltation

C. suspensive saltation D. intermittent suspension


Figure 4-13. Modes of transport of the components of bed material load. See text for detailed discussion.

cycle includes two events (Fig. 4-12B): bursts, which involve the ejection of low speed fluid away from the
viscous sublayer, out into the outer layer, and sweeps, which involve the injection of high speed fluid from the
outer layer, into the viscous sublayer. Note that bursts and sweeps have a significant effect on the local
velocity profile and, therefore, local instantaneous boundary shear stress: high boundary shear stress under
sweeps, low boundary shear stress under bursting. Most sweeps involve packages of fluid that had previ-
ously been ejected away from the boundary by bursting and many burst are initiated by disturbance of the
viscous sublayer by incoming sweeps. However, while bursts and sweeps occur with similar periodicity and
frequency, not every burst will result in a sweep and not every sweep will induce a burst. None-the-less, the
bursting process is a particularly important process in generating turbulence and bursts may provide an
effective mechanism of suspending sediment (see below). Finally, note that bursting does not require a well-
developed viscous sublayer. Even on boundaries dominated by sediment that is much larger than the viscous
sublayer the bursting process is known to occur although its origin is not well understood.


Unidirectional flows have the potential to transport sediment (depending on the “flow strength” and
the size of sediment that is available for transport). Thus, on the basis of preserved sediments or sedimentary
rocks we might be able to make some fundamental interpretations about the paleohydraulics of ancient
depositional environments on the basis of an understanding of the relationship between sediment transport
and flow conditions.

Modes of sediment transport

The sediment that is transported by unidirectional currents can be classified into two broad types: wash
load and bed material load. Wash load is the part of the total sediment “load” that is transported continuously
in suspension by the current; that is, fine-grained sediment (silt and clay) that is held in the main body of the
current and rarely settles to the bed (it makes up generally <1% of the material on the bed). In rivers this
component of the total sediment load is in transport regardless of the rivers’ rate of discharge. In contrast, bed
material load is the part of the total sediment load that is in transport only during periods of high discharge
(e.g., when a river experiences an annual flood due to runoff of snow meltwater). This material may include
sand to boulder size sediment that will only move under the strongest flows. During periods of “normal”
discharge this component of the total sediment load is stored in the bed (hence it is called “bed material load”).
Because most sand-size sediment that forms sedimentary rocks was laid down during periods of maximum
discharge (e.g., flooding events) it is useful to focus on the hydraulic significance of the bed material load.

Bed material load includes three components: contact load, saltation load and intermittent suspension


95 Figure 4-14. Interpretation of a segmented cumulative grain size

90 frequency curve in terms of sediment transport sub-populations.

Cumulative Frequency (%)




10 inte
5 d
2 t a ct n
1 n t i o
co alta
-3 -2 -1 0 1 2 3 4
Grain Size (φ )

load (Fig. 4-13). Contact load or traction load is the part of the total sediment in transport that moves only in
contact with the bed (Fig. 4-13A). This normally includes the largest particles in transport that move by rolling
or sliding over the bed. Saltation load includes all sediment that moves only by a series of short “hops” that
follow an approximate ballistic trajectory (i.e., there is a brief upward motion of the grain, due to lift forces
exerted by the fluid, followed by a period over which the grain returns to the bed while being carried down-
stream by the fluid; Fig. 4-13B). In water, a saltating particle will ascend only 2 to 4 grain diameters above the
bed but will travel 30 to 50 grain diameters downstream during its return to the bed. Intermittent suspension
load includes all grains that undergo transport while held up by the vertical component of turbulence (i.e., the
component of the turbulent velocity of the flow associated with upward movements of fluid and sediment).
Figure 4-13D shows the path of a particle in intermittent suspension load. Note that suspension of this part of
the bed material load occurs only “intermittently”, i.e., under the most powerful flows associated with high
discharge events. Figure 4-13C shows a form of transport that is intermediate between saltation and intermit-
tent suspension when the ballistic path of the particle is interrupted by fluid motions (possibly bursting); we
describe such transport as suspensive saltation.

The grains that make up the transport modes described above differ in terms of size (and density, and
to a lesser extent shape) because of the different mechanisms that cause them to be transported. Thus, when
they comprise the bed material, as they do most of the time, they may be distinguished on the basis of their
grain size characteristics. In the chapter on grain size distributions it was mentioned that segmented cumula-
tive frequency curves, plotted on a probability scale, commonly consist of subpopulations corresponding to
specific transport modes. Figure 4-14 shows the interpretation of these transport modes in terms discussed
above. Most such curves consist of at least three segments corresponding to: contact and saltation loads (the
coarsest sub-population), the intermittent suspension load (the middle sub-population) and the wash load (the
finest sub-population). Two grain sizes, “X” and “Y”, are noted on figure 4-14. “X” corresponds to the largest
grain size that was transported by the flow as contact load and “Y” is the largest grain size that was sus-
pended by the flow. Each of these sizes is particularly amenable to quantitative interpretation.

Quantitative interpretation of grain size curves

Threshold of grain movement

The coarsest grain size in the contact load (“X” in Fig. 4-14) is the largest size that could be transported
by the flow, if we assume that there are no limitations on the grain sizes available for transport; any size
coarser would not be moved by the flow and would be present in the bed material. Thus, we can quantitatively

Hjulstrom's diagram
con erosion
2.0 sol
Velocity (m/s)

1.0 mu
unconsolidated mud
0.10 deposition

clay and silt sand gravel








Grain size (mm)

Figure 4-15. Hjulstrom’s diagram showing the critical velocity required to move sediment of a given grain size. Note that
the relationship shown is limited to a flow depth of 1 m and that the data for silt and clay size sediment are few in number.
After Sundborg (1956).

interpret this grain size by asking the general question “What is the critical flow condition that will cause a
given particle to move?”. This question can only be answered by experimentation where flow conditions
(velocity, depth, boundary shear stress, etc.) are recorded for the instant a particle just begins to move under a

Figure 4-15 shows results from classic experiments by Hjulstrom (1939) that provide a possible answer
to the above question. The experiments on which this figure is based were conducted in a flume, at a flow
depth of 1 metre, over a wide range of grain sizes. The experimentally-determined curve tells us the velocity
required to cause the initiation of movement of a particle of a given size. For example, the maximum grain size
that could be transported by the current that deposited the sediment represented by the cumulative frequency
curve in figure 4-14 was approximately -1.5 φ or approximately 2.8 mm. From figure 4-15 we see that a velocity
of approximately 0.20 m/s is required to move such a particle. Therefore, we infer the current that transported
and deposited this sediment was flowing at 0.20 m/s, such that 2.8 mm particles were the coarsest grains that
would move. Thus, we have made a quantitative interpretation of the nature of the current that deposited the
sand with the distribution shown in figure 4-14.

Unfortunately, the simple approach possible with Hjulstrom’s diagram is severely limited. Intuition
should tell us that the condition for initial motion must depend on the boundary shear stress rather than
velocity (boundary shear stress is the force that does the work to move sediment). Certainly boundary shear
stress is related to velocity (see Eq. 4-15) but it depends on flow depth (Eq. 4-6). In addition, sediment
properties will influence the condition of initial movement, certainly a particle of a given size with a relatively
high density, will offer more resistance to movement than a grain of the same size but lower density.

Figure 4-16 shows the forces that act on a grain resting on the boundary beneath a fluid flow. The main
force that resists movement is the weight (W) of the grain on the boundary. The fluid forces that contribute to
the movement of the grain are the shear force exerted by the fluid on the grain (the boundary shear stress, τo)
and a lift force (L). This lift force is due to variation in pressure around the particle; the pressure exerted on the
particle is inversely related to the velocity of the flow in contact with the particle. Flow is fastest across the
top of the particle (imagine a grain resting in the viscous sublayer of a turbulent flow where the velocity

το L

rc i d
fo flu
Figure 4-16. Schematic illustration of the forces acting

L on a particle beneath a flowing fluid. “W” is the weight
of the particle and “L” is the lift force acting on the
W το particle.

gradient is strong), therefore pressure is least over the top, and their is a net pressure force directed upwards.
Together, the lift and shear forces act at some angle, upwards from the horizontal, in the direction of flow.
When these forces exceed some threshold such that they overcome the weight of the particle, it will move
along the boundary in the flow direction. Note that the larger the magnitude of the lift force, the smaller the
boundary shear stress required to move the grain.

Shields’ (1936) approach to the question of the critical condition for the initiation of sediment move-
ment considered the forces acting on a particle as outlined above. Based on experiments over a wide range of
grain sizes and grain densities he constructed the curve shown in figure 4-17. In figure 4-17 the condition for
the initiation of motion is defined in terms of the boundary Reynolds number and the ratio of the boundary
shear stress to the weight of grains per unit area of the bed. This ratio is expressed as:

Shields' Diagram

Shields' β

0.2 d 0.1(ρs - 1)gd

ν ρ
2 3 4 5 6 8 10 20 30 40 60 80 100 200 300 500 700 1000
(ρs - ρ)gd





0.1 .2 .3 .4 .5 .6 .8 1.0 2 3 4 5 6 8 10 20 30 40 60 80 100 200 300 500 700 1000

Boundary Reynolds number

Figure 4-17. Shields’ diagram for determining the critical boundary shear stress required to move a grain on a bed of
uniform spheres of equal size. See Table 4-1 for an example of the use of Shields’ diagram. After Blatt, Middleton and
Murray, 1980.

Table 4-1. Determination of the critical boundary shear stress required for the initiation of motion of a particle
using Shields’ diagram.

In this example we will solve for the critical boundary shear stress for the initiation of motion of the
largest particle in the contact load of the bed material with the grain size distribution shown in Fig. 4-14
(i.e., d=1.5φ)

Values needed to calculate to:

d = -1.5φ = 2.8 mm = 0.0028 m (see Fig. 14).

ν = 1.1 x 10-6 m2/s (water at 20ºC)
ρs = 2650 kg/m3 (density of quartz)
ρ = 998.2 kg/m3 (density of water at 20ºC)
g = 9.806 m/s2

d ρs
Step 1. Calculate the value of 0. 1( − 1) gd , which, in this case equals 172.
ν ρ
Step 2. Find the value calculated in step 1 on the scale in the middle of Shields’ diagram and follow the
diagonal line down to the curve. Read the value of β off the vertical scale on the left.

In this case β = 0.047.

β =
Step 3. We can solve (ρ − ρ)gd for τo by rearranging to form: τo = β(ρs - ρ)gd

In this case τo = 2.13 N/m2. This is the critical boundary shear stress required to move a 2.8 mm diameter
quartz grain on a bed of uniform spheres under a flow of water at 20ºC.

d dm
τc > τcs: d <1; d < dm

τcs (Shield's) τc = τcs: d =1; d = dm


τc < τcs: d >1; d > dm

1 d

Figure 4-18. A schematic illustration showing the error in estimating critical boundary shear stress using Shields’ diagram
due to variation in the size of grain relative to the average size of the bed material. Note that τc is the actual critical
boundary shear stress for the initiation of motion of a grain and tcs is the critical boundary shear stress predicted from
Shields’ diagram; d is the grain size for which τc and τcs apply and dm is the mean size of the bed material over which the
grain will move.

(ρ − ρ)gd Eq. 4-20
where ρs is the density of the grains, ρ is the fluid density, g is the acceleration due to gravity and d is grains
size. This ratio is referred to as Shields’ Beta (β β). The curve illustrated in figure 4-17 the shows the
experimentally determined relationship between β and boundary Reynolds Number, on beds of spherical grains
of uniform size. For a grain of given size and density β varies with the boundary shear stress required to move
that grain. Thus, the form of the curve reflects how the boundary shear stress required to move a grain varies
with boundary Reynolds Number due to changes in the magnitude of the lift force acting on a grain. For
example, β decreases with increasing R* to a minimum value of 0.032 at R* = 12 (the theoretical limit for smooth
turbulent boundaries) and then increases to a constant value of 0.06 at R* > 600 (i.e., over beds covered with
very coarse particles). The decrease in β at low boundary Reynolds numbers is due to a corresponding
decrease in the boundary shear stress required to move a particle because the lift force acting on the grain
increases as the velocity gradient increases in the thinning viscous sub-layer (compare Eqs. 4-17 and 4-18).
The value of β subsequently increases with increasing R* because the boundary shear stress required to move
the grain increases as the viscous sublayer is disrupted the lift forces acting on the grain are reduced (because
the strong velocity gradient in the viscous sublayer is reduced). A final, constant value of β is reached when
R* exceeds approximately 600 and the lift force acting on the grains no longer varies with increasing R* and the
critical boundary shear stress required to move a grain varies only with grain size.

Shield’s diagram may be used to determine the boundary shear stress required to move a particle by the
procedure outlined in Table 4-1, applied to the example of the maximum grain size in the bed material repre-
sented by the cumulative frequency curve shown in figure 4-14. From the results of the calculations in table 4-
1 we may assume that the current that transported the sand represented by figure 4-14 exerted a boundary
shear stress of approximately 2.13 N/m2. If the boundary shear stress were greater, larger sizes (>2.8 mm)
would be preserved in the deposit (i.e., we assume that there were no limitations on the grain sizes available for
transport). If the boundary shear stress were below this value, the current could not have moved the 2.8 mm
sand and it would not be present in the bed material. However, this approach is limited because it does not
consider all the variables that will determine the critical condition for movement. For example, the Shields’
curve does not include the effect of shape and packing (see section on grain shape). More angular particles
will be more difficult to move than the spheres used in the experiments to determine the curve shown in figure
4-17. More important, however, the experimental curve is based on beds of uniform grain size. Thus, errors in
estimating the critical boundary shear stress for motion over a bed will depend on the size of the particle for
which to is being determined, relative to the average size of the bed material. Specifically Shields’ curve will
underestimate the critical boundary shear stress to move a grain if the grain if much smaller than the average
size of the grains that make up the bed on which it rests. This is because a small grain will tend to become
trapped in the space between larger particles on the bed, making it more difficult to move. Conversely, Shields’
curve will overestimate the critical boundary shear stress to move a grain that is much larger than the average
size of the particles that make up the bed on which it rests (Fig. 4-18). This is because a large grain will roll
more easily over a bed of much finer particles than over particles of the same size. This is a major limitation on
the use of Shields’ diagram (see discussion by Komar, 1987).

Threshold of grain suspension

The particles in transport as suspension load are supported (i.e., kept off of the bed) by the vertical
component of turbulence. Middleton (1976) argued on theoretical grounds that the critical flow condition at
which a particle became suspended was when the average component of turbulence that acts in the upward
direction (we’ll give this the symbol “v”) is exactly equal to the settling velocity (ω) of the particle. Clearly,
when the v < ω the particle will eventually settle to the bottom. Thus, Middleton’s criterion for suspension is:
a grain will be suspended by a flow when upward velocity of the vertical component of turbulence exceeds its’
settling velocity. Unfortunately, the mean upward component of turbulence is difficult to measure. However,
experiments have shown that the shear velocity of a flow is essentially equal to the upward component of
turbulence so that Middleton’s criterion for suspension may be stated in a more practical manner as in figure 4-

Middleton's criterion for suspension:
Figure 4-19. Schematic illustration defining
Middleton’s (1976) criterion for suspension of a
Suspension when V ω particle. See text for a detailed discussion.

where V is the upward component of velocity

due to turbulence and ω is the settling velocity
ω of the particle.

19. Therefore, the largest grain that will be suspended by a flow (i.e., the coarsest grain size in the intermittent
suspension population of a bed material) is one with a settling velocity equal to the shear velocity of the flow.
So we have another means of interpreting grain size curves such as figure 4-14 in terms of the hydraulics of the
currents that transported (and deposited) a sediment. Table 4-2 shows the relationship between the maximum
shear velocity of a number of rivers and the settling velocity of the coarsest grain size in the intermittent
suspension load of the bed material of these rivers. The theoretical relationship is respectably close. In the
case of the grain size curve shown in figure 4-14 the largest grain size in the intermittent suspension load is
1.3φ (0.41 mm) and the shear velocity of the flow can be estimated by calculating the settling velocity of this
grain size. We could use Stokes’ Law to calculate ω, by making all of the necessary assumptions, but we
cannot overcome the error due to the fact that the grain size exceeds 0.1 mm. As an alternative, there are
several experimentally-derived relationships to determine the settling velocity of particles beyond Stokes’
range, one of these is shown in figure 4-20 (for quartz-density particles in water at 20ºC). Figure 4-20 indicates
that a quartz-density, spherical grain with a mean diameter of 0.41 mm has a settling velocity of 0.044 m/s. This
suggests that the flow that transported the bed material had a shear velocity of 0.044 m/s. We can compare
this result with that based on Shields’ diagram by determining the shear velocity produced by to = 2.13 N/m2
(see Eq. 4-16) and we find U* = 0.046 m/s, very close to that predicted by Middleton’s criterion.

Figure 4-20 also shows the critical shear velocity for the initiation of movement of grains on a bed (from
Shields’ diagram). Note that below the curve for the initiation of motion grains will not move. Between the two
curves grains will move as part of the contact load and above the curve U* = ω grains will be in suspension.
An important point that is illustrated by this figure is that very fine sand (less than 0.15 mm) tends to go into
suspension essentially as soon as it begins to move. This has very important implications to a variety of
sedimentary processes.

Table 4-2. Comparison of measured peak shear velocities of flows in rivers to the settling velocity of the
coarsest particles in the intermittent suspension population of bed samples taken from each river. Data from
Middleton, 1976.

River U* ω
(cm/s) (cm/s)

Middle Loup 7-9 7-9

Middle Loup ≈20 ≈20
Niobrara 7 - 10 7-9
Elkhorn 7-9 2.5 - 5.0
Mississippi (at Omaha) 6.5 - 6.8 2.5 - 5.0
Mississippi (at St. Louis) 9 - 11 3 - 12
Rio Grande 8 - 12 ≈10


grain suspension

U or ω (m/s)

Figure 4-20. Curves showing the

critical value of U* for the initiation of

motion (based on Shields’ diagram)

0.05 and suspension as a function of grain

' size. Note that the curves apply to

e lds
S hi quartz-density grains in water at 20ºC.
After Blatt, Middleton and Murray,
no movement 1980.
0.01 0.1 1.0 10.0
Grain diameter (mm)

Chapter 5. Bedforms and stratification under unidirectional flows


When the flow of water (or air) over a bed of non-cohesive sediment is strong enough to move the particles
of the bed material the bed becomes molded into some topographic form with vertical relief ranging from fractions
of millimetres to up to several metres. The three-dimensional geometry of the bed topography is governed by the
interaction of the fluid and the sediment. Experimental studies in flumes and in modern rivers and in intertidal areas
have found that their are a few common forms of bed geometry that develop under unidirectional current and that
the overall geometry depends on the flow conditions and the sediment properties. The overall geometry of such
a bed is referred to as a bed configuration and it is made up of many individual topographic elements termed bed
forms (or bedforms).

Over the past century much work has been directed at the description of the characteristics and behaviour
of bedforms under unidirectional flows. This extensive research has been conducted by both sedimentologists
and civil engineers for two very different reasons. Civil engineering is concerned with the effects of fluid flow on
mobile sediment beds because this broad field includes the practical problems associated with moving water from
one place to another (e.g., for hydroelectric generation, irrigation, or city water supplies). Open canals are often
excavated in unconsolidated sediment and the flow of water through the canals may cause sediment to be
transported and ultimately results in the formation of bedforms. The most fundamental problem with the
development of bedforms in canals is that they alter the character of the flow and affect fundamental flow properties
such as discharge. For example, in chapter 4 Eq. 4-15 shows that the velocity of a turbulent flow varies with the
inverse logarithm of the size of the roughness elements on the boundary (yo; i.e., the greater the boundary roughness
the slower the velocity). Most bedforms comprise major roughness elements that are many times larger than the
roughness due to the grains on the bed. Hence, the presence of bedforms will retard fluid flow and their presence
and forms must be predictable in order to design canals on unconsolidated sediments. Sedimentologists have
benefited greatly from the work of engineers in their study of bedforms. However, sedimentologists derive their
interest from the fact that bedforms are commonly preserved on ancient bedding planes in sedimentary rocks.
Bedforms are primary sedimentary structures; structures that form at the time of deposition of the sediment in
which they occur and they reflect some characteristic(s) of the depositional environment. In addition, bedforms
produce a variety of forms of cross-stratification (also primary sedimentary structures) that are very common in the
geologic record. Because bedforms and their behaviour are governed by fluid processes, they, and their
stratification, provide an unequalled basis for making paleohydraulic interpretations of ancient depositional
environments. The work conducted by engineers, that attempted to predict the types of bedforms that develop
on the basis of the sediment and flow characteristics, has been particularly useful in contributing to our ability to
make paleohydraulic interpretations of bedforms and their associated stratification. The aspects of paleohydraulics
that can be inferred from the forms of cross-stratification include the relative flow strength, the direction of the
current, the type of current (e.g., upper or lower flow regime).

This chapter will focus on the types of bedforms that develop under unidirectional flows and emphasize
aspects of their character and behaviour that are particularly useful in the interpretation of sediments and
sedimentary rocks. In addition, the final sections of this chapter will describe the forms of stratification that the
various bedforms produce.



As we will see below, there are a variety of bedforms that are most precisely classified on the basis of their
geometry and relationship to the water surface. However, the broadest classification of unidirectional flow bedforms
is based on the flow regime under which the bedforms develop. This concept is widely used by sedimentologists
and was introduced by Simons and Richardson (1961; a pair of civil engineers) who distinguished lower flow regime
and upper flow regime, partly on the basis of the bedforms that are produced under unidirectional flows. Table
5-1 summarizes the main criteria for distinguishing these two flow regimes. Note particularly that the relationship

Table 5-1. Definition of the flow regime concept of Simons and Richardson (1961).

Flow Regime Bedforms Characteristics

Lower flow regime Lower plane bed, • F < 0.84-1.0*;

Ripples, Dunes • low rate of sediment transport,
dominated by contact load;
• bedforms out-of-phase with the
water surface.

Upper flow regime Upper plane bed, • F > 0.84 - 1.0*;

In-phase waves, • high rates of sediment transport,
Chutes and pools high suspended load;
• bedforms in-phase with the water

*Note that Simons and Richardson (1961) set F < 1.0 for lower flow regime and F > 1.0 for upper flow
regime. However, subsequent work indicated that in-phase waves began to develop over the range 0.84
< F < 1.0. Because in-phase waves were particularly characteristic of the upper flow regime the limiting
value of F has been adjusted accordingly here.

between the bedform and the water surface figures prominently in this scheme. The lower flow regime is dominated
by bedforms that are out-of-phase with the water surface and the upper flow regime is dominated by bedforms that
are in-phase with the water surface.

Figure 5-1 defines the general terms that will be used to describe bedforms in the following section. Terms
for asymmetric bedforms (including ripples and dunes; these are out-of-phase with the water surface) are well-
established and widely used. The descriptive terms for symmetrical bedforms (the in-phase waves) produced under
unidirectional flows are of only limited scope. The in-phase waves have been relatively little studied and a more
complete descriptive terminology will certainly follow the current peak in interest in this class of bedform.

The sequence of bedforms

By “sequence” of bedforms we refer to the hypothetical, sequential development of different bedforms on

a mobile sediment bed with increasing flow strength (e.g., increasing velocity with constant flow depth). The
concept of bedform sequence is useful in describing bedforms because it provides a basis for a qualitative
appreciation for the relative flow strengths that are required to form them. As we will see later, not all of the bedforms
describe in this sequence will develop on a bed of any one size of sediment; some bedforms are limited to coarse
bed material while others are limited to fine bed material. Thus, we can consider the following to be a “hypothetical”
sequence but one that provides valuable insight into the interpretation of bedforms and their stratification. Figure
5-2 (A and B) schematically illustrate the variety of bedforms, in sequence, with increasing flow strength. Note that
the two sequences in figures 5-2 A and B form a continuum, more-or-less.

We can think of the sequence of bedforms in terms of the changes in bed geometry under a flow that is slowly
and incrementally increasing in velocity, at constant depth, over a mobile sediment bed. Each specific bedform
represents the equilibrium bed state for a constant flow velocity and depth. On beds of relatively coarse sand, just
as the flow strength exceeds the threshold required for sediment movement, the first bed configuration will be a
flat, planar surface. Such a bed is termed a lower plane bed to distinguish it from another type of plane bed that
develops under higher flow strengths. The lower plane bed will only form on beds of sediment coarser than 0.7
mm and is characterized by its planar surface and relatively low rates of sediment transport (limited to contact load).
The limitation of lower plane beds to relatively coarse sand indicates that this bed configuration will only form under
dynamically rough turbulent boundaries (i.e., relatively large boundary Reynolds numbers). Sand that is deposited
on a lower plane bed is characterized by relatively low angles of particle imbrication (both up- and downstream-
dipping; see Fig. 5-3).

Anatomy of an asymmetrical bedform

symbol for water surface

Water surface out-of-phase with bed surface



ss L
Sto sli ee
Height (H) pf or
stoss slope angle
lee slope angle

Length (L)
Spacing (S)

Anatomy of a symmetrical bedform

ce in-phase with
er surfa
Wat bed
su rfac


Height (H)

Length (L)
Spacing (S)

Figure 5-1. Definition of terms used to describe asymmetrical and symmetrical bedforms that develop under unidirectional

On beds of sediment finer than 0.7 mm, just as the current exceeds the flow strength required for sediment
movement, the bed will be molded into a series of small, asymmetrical bedforms termed ripples (some texts call these
bedforms “small ripples”). Figure 5-4 shows the form of a ripple and the flow pattern that it induces near the boundary.
Ripples behave like negative steps on a boundary and result in flow separation at the brink of the ripple and
attachment just downstream of the trough where fluctuations in boundary shear stress are particularly large and
erosion is intense. Ripples migrate downstream, in the direction that the current is flowing, as sediment is eroded
from the trough and lower stoss slope and moves up the stoss slope to become temporarily deposited at the crest.
As the deposit grows on the crest it eventually becomes unstable and avalanches down the lee slope where it is
deposited. The avalanche deposit is subsequently buried by continued avalanching and the entire ripple form
migrates downstream. In this way the pattern of flow separation, which is governed by the ripple geometry, also
moves downstream, as does the site of erosion at the point of flow attachment. Over time, as the region of scour
migrates downstream the sediment deposited previously on the lee slope is eroded from the bed and begins its cycle
of transport all over again. Hence, migration results from the pattern of spatial variation of erosion and deposition
along the length of the ripple.








Figure 5-2A. The sequence of bedforms that develop under lower flow regime conditions (after Simons and Richardson, 1961).
Note that washed-out dunes (Fig. 2B) are also lower flow regime bedforms.

Ripples range in length from approximately 0.05 m to about 0.6 m and in height from 0.005 m to just less than
0.05 m. The size of a ripple is independent of flow depth but there is a crude correlation between ripple length and
grains size; length (L) increases with grain size (d) such that L≅1000d. The lee slope angle of ripples is close to angle
of repose for the sediment, in the range of 25 to 30°. In plan form ripples are highly variable and a terminology has
developed to describe these forms (see Fig. 5-5). The first ripples that form when sediment is moved over a bed
are straight-crested (2-dimensional) but these do not appear to be a stable bedform because they rather quickly
evolve into 3-dimensional forms (with irregular crests). Some experimental evidence suggests that the forms shown



Washed-out dunes STRATIFICATION

Upper Plane Bed


0.84 < F < 1.0

Inphase waves increasing in amplitude and wave-length




Direction of bedwave/water surface wave migration.

Water surface

Figure 5-2B. The sequence of bedforms that develop under upper flow regime conditions (after Cheel 1990a). Note that washed-
out dunes are actually lower flow regime bedforms.

Grain Imbrication Angles

Upper plane bed

Lower plane bed
0 90 180


Figure 5-3. Comparison of vector mean imbrication angles, from the plane normal to the depositional surface and parallel to
flow, of lower plane bed and upper plane bed deposits. After Gupta et al. (1987).

in sequence in figure 5-5 develop with increasing flow strength. Note that ripples form on beds of sediment finer
than 0.7 mm, suggesting that they are typical of dynamically smooth turbulent boundaries. In fact, ripple
development seems to require the presence of a well-developed viscous sub-layer. Irregularities on an otherwise
planar bed over which sediment is transported may protrude through the viscous sub-layer and cause flow
separation, much like that over fully developed ripples (see Fig. 5-4). Once established, the flow character associated
with separation and attachment will cause erosion just downstream of the irregularity and deposition even further
downstream. Thus, an irregularity on the bed that is high enough to protrude through the viscous sublayer will
set up a pattern of erosion and deposition that will propagate laterally and downstream, causing ripples to form.

Dunes are the next bedform to develop with increasing flow strength beyond the upper limit of ripples. They
are similar in form to ripples (i.e., asymmetric bedwaves) but are larger than ripples with lengths ranging from greater
than 0.75 m to in excess of 100 m and heights ranging from greater than 0.075 m to in excess of 5 m. Dunes tend
to be most common on sand beds with a mean size in excess of 0.15 mm. Over the past decade several books and
articles have considered dunes to be just large ripples (and they have been termed “large ripples” or “megaripples”
in the literature). However, dunes appear to be distinctly different bedforms and there is not a clear continuum in
size from ripples to dunes. For example, when we plot bedform length against height of ripples and dunes we see
that they are related in the same linear fashion but there is a distinct break between the fields defined by ripples
and dunes (Fig. 5-6). This break indicates that asymmetric bedforms with lengths and height over the range of the

Flow over a ripple

Figure 5-4. Flow separation over the
FLOW DIRECTION negative step on a boundary due to a
de vala
po nc

sit hi
ion ng

ion ion
eros eros

Discriptive term 2-dimensional 3-dimensional

for crest-line
Straight Sinuous Caternary Linguoid Lunate

Plan-view shapes
of ripples


Increasing flow duration and/or (?) strength

Figure 5-5. Terms used to describe plan forms of asymmetrical bedforms (ripples and dunes). After Allen, 1968 and Blatt,
Middleton and Murray, 1980.

break are largely absent in nature. Thus, dunes appear to be distinctly different bedforms than ripples. In fact, under
certain hydraulic conditions dunes may have ripples superimposed on their stoss sides (Fig. 5-7). In the lee of dunes
large rotating eddies develop (due to the negative step on the bed) and when the upstream velocity of the current
generated by the eddy is large it will actually cause the formation of upstream-migrating ripples on the lee slope of
the dune (termed “regressive” ripples; Fig. 5-7). Unlike ripples, dune size seems to be not related to the grains size
of the bed material but is related to the flow depth (i.e., mean dune length and mean height increase with mean flow
depth). This relationship between dune size and flow depth suggests that the bedforms result from some interaction
between large eddies in the flow and the sediment bed. Furthermore, dunes appear to interact with the water surface
by producing a “boil” or bulge on the water surface just downstream of the trough due to the ejection of eddies
from the trough outwards towards the water surface (it has been suggested that these boils are a form of bursting
associated with dunes).

Dunes have been among the most studied bedforms and this has led to considerable confusion of the
terminology applied to dunes and to their descriptive characteristics. Finally, in 1989 a symposium was held to arrive
at a consensus on many fundamental concerns, beginning with the name to give to these large bedforms (they agreed
to call them dunes). Table 5-2 summarizes the main conclusions of this symposium and outlines the descriptive
characteristics of dunes that are thought to be important (and these are listed in their order of importance). This

H = 0.0677 L
r = 0.98
n = 1491 Figure 5-6. Schematic illustration of the field (shaded
areas) of ripples and dunes as defined in terms of the lengths
1 (L) and heights (H) of these bedforms. Solid line is based
Height (m)

s on a linear regression applied to measurements of 1491

Du bedforms. After Ashley, 1990.


0.01 0.1 1 10 100 1000

Spacing (m)

A compound dune



e rip

Figure 5-7. Schematic illustration of a dune with ripples migrating up its stoss side (a compound dune). Note that “regressive”
ripples (i.e., upstream-migrating ripples) are also shown in the trough and basal lee slope of the dune.

table provides a basis for a consistent terminology regarding dune size and indicates that their are two fundamentally
different types of dunes that can be distinguished in terms of their shape: 2-dimensional dunes and 3-dimensional

2-dimensional and 3-dimensional dunes are so different that many workers have suggested that they are
fundamentally different bedforms. However, we now believe that they are part of a continuum of dune forms over
the range of flow conditions over which they are stable (the two types of dunes do not form separate fields in plots
such as figure 5-6). None-the-less, these two types of dunes differ in many ways and produce distinctive styles
of cross-stratification (Fig. 5-2A shows some of the subtle differences between these two types of dunes). 2-
dimensional dunes develop under somewhat lower flow strengths than 3-dimensional dunes and they tend to be
relatively long and low and straight-crested. The length of the crest is relatively long, in terms of the distance from
the summit to the brink. The lee slopes of 2-dimensional dunes are approximately at angle of repose (25-30°) and
scour in the troughs is not well-developed. The lee face forms a rather straight, planar surface. Sediment transport
may be dominated by contact load and avalanching down the lee slope. Under higher flow velocities 2-dimensional
dunes are replaced by 3-dimensional dunes which range from sinuous to lunate in plan form, are shorter and higher,
overall, than 2-dimensional dunes and have shorter crests. They have lee slopes that are less than angle of repose
and their basal lee faces form curved surfaces extending down into deeply scoured troughs. Sediment transport
over 3-dimensional dunes includes contact, saltation and intermittent suspension loads.

With increasing flow strength the 3-dimensional dunes become much longer and lower and their lee slopes
undergo a reduction in angle. Such dunes are commonly termed “washed-out” dunes because the strong current
seems to wash out the dune form. The heights of such dunes become progressively smaller and their lengths become
longer as the flow strength increases and they may form very subtle bedforms as long as several metres with heights
on the order of a few millimetres (and may not be considered as dunes as described above). They appear to form
a very gradual transition with the next bed form with increasing flow strength: the upper plane bed. Note that washed
out dunes are shown in figure 5-2B. The reasons for relating this type of dune to plane beds and in-phase waves
will become apparent in the section on stratification.

The development of upper plane bed marks the onset of upper flow regime conditions in the scheme of Simons
and Richardson (1961). However, this is the one upper flow regime bedform that doesn’t really fit into this scheme.
While all other upper flow regime bedforms require a free-water surface, upper plane bed does not (unlike in-phase
waves, upper plane bed will form in conduits that are completely full, i.e., have no free water surface). In addition,
upper plane beds can develop at Froude numbers significantly less than 0.84 (i.e., as low as F = 0.4 under deep flows

Table 5-2. Classification and descriptive characteristics of dunes.

Classification scheme for large-scale, flow transverse bedforms (excluding in-phase waves)
recommended by the SEPM Bedforms and Bedding Structures Research Symposium (Austin,
Texas, 1987). After Ashley, et al. 1990.

General class: Subaqueous dune. The modifier “subaqueous” should only be used when a
clear distinction between eolian and subaqueous dunes in necessary.

First order descriptors (necessary)


Spacing 0.6-5m 5-10m 10-100m >100m

Height1 0.075-0.4m 0.4-0.75m 0.75-5m >5m

Term small medium large very large

1Based on the relationship: H = 0.0677L0.8098 where H is height, L is spacing


2-dimensional. Straight-crested, little or no scour in trough.

3-dimensional. Sinuous to short-crested, deep scour in trough.

Note: no quantitative expression of shape has been agreed upon.

Second order descriptors (important)


Simple. No bedforms superimposed.

Compound. Smaller bedforms superimposed (note size and relative orientation).

Sediment characteristics:



Third order descriptors (useful)

Bedform profile: note stoss and lee slope length and angles.

Full-beddedness: fraction of bed covered by bedforms.

Flow structure: time velocity characteristics (e.g., steady flows, tidal flows, etc.)

Relative strengths of operating flows: (e.g., tidal asymmetry)

Dune behaviour-migration history: vertical and horizontal accretion of bed with migration.

A A = vector mean a-axis orientation

L = orientation of current lineation
AL Figure 5-8. Long axes orientations of sand
grains deposited on an upper plane bed. A.
Long axes orientations, measured on a bedding

plane, in comparison to the trend of flow-
parallel current lineation. B. Apparent long
axes, measured in the plane parallel to flow and
perpendicular to bedding. After Allen (1968).
0 10 20 %
B B = bedding I = vector mean imbrication angle


over very fine sand). Upper plane bed seems to have been placed among the upper flow regime bedforms as a matter
of convenience to distinguish this bedform from the lower plane bed. Upper plane bed is most common on beds
of fine sand and under deep flows and is absent on beds of coarse sand and/or under shallow flows.

Upper plane bed (short for “upper flow regime plane bed”; synonyms include “upper stage plane bed”) is
widely defined as a flat, planar bed configuration with no significant relief beyond a few grain diameters. The one,
widely acknowledged form of regular relief consists of flow-parallel ridges, a few grain diameters high, that are termed
current lineation that are thought to form due to streaks on the boundary (Weedman and Slingerland, 1985). Current
lineations are commonly visible on bedding planes within upper plane bed deposits (and also on the planar stoss
slopes of some dunes). In addition to streaks, the bursting process is thought by some to be particularly important
to forming horizontal lamination under upper plane bed conditions (more on this below). Several workers have
recently suggested that a variety of very low relief bedforms are actually present on upper plane beds (see Bridge
and Best, 1988, 1990; Paola et al, 1989; Cheel 1990a,b; Best and Bridge, 1992). The question of the existence of a
true plane bed, as defined above, remains and is beyond the scope of these notes.

Sediment transport over upper plane beds is intense as contact, saltation and suspension load and near the
bed the concentration of sediment is transport is particularly high. So high, in fact, that a “bedload layer” is
commonly prominent that appears as a sheet of moving sediment that been termed a “rheologic layer” by some,
a “traction carpet” by others. Grain imbrication is generally well-developed and relatively steep (up to 25° from
bedding, dipping consistently into the current; see Figs. 5-3 and 5-8B) and grain a-axes are aligned parallel to the
flow (Fig. 5-8A). Note that a-axes alignment on bedding surfaces is bimodal, as seen in plan view with respect to
the alignment of current lineation and flow direction; i.e., one mode on either side of the trend of the lineation. This
well-developed, flow-parallel alignment of grains is responsible for a structure that is seen in consolidated
sandstone termed parting step lineation: a structure that occurs on bedding plane exposures of upper plane bed
deposits that reflects the tendency for sedimentary rocks that were deposited under upper plane bed conditions
to break along vertical planes that are parallel to the direction of flow that deposited the sediment. Note that both
current and parting step lineation are useful in determining the “sense” of paleoflow direction. However, because
they are lineation they are bidirectional and, therefore, cannot be used alone to determine the absolute paleoflow
direction. One common method of determining the absolute paleoflow direction from such lineation is to cut thin
sections in the plane perpendicular to bedding and parallel to the lineation. The upstream imbrication direction,
seen on that plane, can then be used to infer the absolute flow direction. An easier method of determining absolute

Directional significance of heavy mineral shadlows

mineral concentra
decreasing heavy


current lineation

Figure 5-9. Heavy mineral shadows on a current-lineated bedding surfaces on an upper plane bed. Note that the absolute flow
direction can be determined as being parallel to the lineation, in the direction of decreasing heavy mineral concentration through
the shadow. After Cheel (1984).
paleoflow direction is possible if heavy minerals are abundant on bedding plane exposures of upper plane bed
deposits. On upper plane beds heavy minerals commonly form patches on the active bed that display a downstream-
decreasing gradient in the concentration of heavy minerals. Such heavy mineral patches are termed heavy mineral
shadows and may be used, in conjunction with parting and/or current lineation, to determine the absolute paleoflow
direction from upper plane bed deposits (Fig. 5-9).

With increasing flow strength beyond the true plane bed very low, asymmetrical bedwaves develop. These
bedforms reflect the gradual on-set of the formation of in-phase waves that takes place over a range of Froude
numbers from 0.84 to 1.0. Note that on beds of sand coarser than approximately 0.3 mm the transition from dunes
to inphase waves may not include a true upper plane bed. Instead, washed-out dunes may pass directly, but
gradually, into in-phase waves, with increasing flow strength, and their may be a stage where dune-like forms and
in-phase waves co-exist (and this has been reported by Southard and Boguchwal, 1990).

In-phase waves are a class of bedform that are all characterized by their symmetrical form and in-phase
relationship with the water surface (although not all in-phase waves are always symmetrical and/or in-phase with
the water surface all of the time); hence, in-phase waves are generally described in terms of the water surface wave
and the corresponding bedwave and in the description that follows when the bed and water surface wave are
behaving in the same fashion these two elements will not be separated. Unlike the other bedforms described above,
in-phase waves derive their form and behaviour from the interaction of the water surface and the mobile sediment
bed under supercritical (shooting) flows. Cheel (1990a) reviewed literature that indicated that with increasing flow
strength, over the range of conditions for in-phase waves, a sequence of different forms of in-phase wave developed
(see Fig. 5-2B). Starting with upper plane bed, the first form of in-phase wave is a very low (millimetres high; see
Fig. 5-10), downstream-migrating form that increases in height and length with increasing flow velocity. Note that
all in-phase waves scale with flow velocity by the relationship U =
(Kennedy, 1963). As flow strength

continues to increase the symmetrical bedwaves cease to move downstream and remain stationary on the bed. This
type of in-phase wave is termed a “standing” or “stationary” wave. Finally, with a further increase in flow strength
the in-phase waves are characterized by upstream migrating forms that Gilbert (1914) first termed “antidunes” (for
their upstream migration in contrast to the downstream migration of dunes). Note that all of the forms of in-phase
wave may not form on beds of a given sand size or flow depth. Further experimental work is required to establish
the fields of hydraulic stability of this class of bedform.

Upper plane bed

Post aggradation bed surface

Height above flume floor (m)
15 16 17
8 10 12 14 16
Low in-phase waves
Post aggradation bed surface
.14 .136
.12 .132
15 16 17
8 10 12 14 16
Distance from entrance (m) Distance from entrance (m)
Vertical exaggeration X40 Vertical exaggeration X50

Figure 5-10. Profiles of the sand bed on a flume of upper plane bed and very low in-phase waves. Note the vertical scale. Note
that “entrance” refers to the entrance to the flume channel. From Cheel (1990a).

The term antidune is one of the most abused terms used for any bedforms; in many texts it has come to apply
to all forms of in-phase waves, a practice that has limited the understanding of these bedforms for almost 30 years.
Bed behaviour associated with the antidunes of Gilbert (1914) is very complex; the actual bed state at any one time
may be plane bed, downstream-migrating in-phase waves, stationary waves or true antidunes (i.e., upstream
migrating). The change in state of the bed associated with antidunes is cyclic, and figure 5-11 shows the sequence
of stages of water surface and bed behaviour through a complete cycle of events associated with true antidunes.
Note that under flow conditions that produce antidunes all of the stages shown in figure 5-11 may not occur during
any particular cycle. For example, the bed and water surface may develop to the stage where stationary in-phase
waves form and then the waves may subside back to a plane bed. In addition, all waves on the water surface may
not break simultaneously, as shown. In most cases one wave will break and it will disrupt the flow to cause other
waves to break subsequently. All of the forms of in-phase waves shown in figure 2B are 2-dimensional (i.e., straight-
crested). At flow strengths greater than those required to form 2-dimensional antidunes there are a variety of 3-
dimensional in-phase waves (short-crested) of which we know virtually nothing.

Bedform stability fields

In the above description of bedforms we developed some vague idea that certain factors will control which
bedforms will develop, depending on flow strength and/or grain size. In fact, many related factors will govern which
bedforms will develop on a mobile sediment bed. These factors include those related to the fluid: flow velocity (U),
flow depth (D), flow temperature (which controls fluid viscosity and density), and those related to the sediment:
grain size (d), grain density (ρs), sediment sorting, and particle shape. The effects of particle shape and size sorting
on bedforms are not well known and will not be considered here. However, largely because of experimental flume
research, carried out by John Southard and his students at the Massachusetts Institute of Technology, we now
have a good picture of the fields of hydraulic stability of bedforms on sand beds representing a wide range of grain
sizes. Figures 5-12 and 5-13 are “bedform stability” diagrams and show the range of conditions over which the
bedforms are stable on diagrams plotting flow velocity versus grain size (each diagram for a given range of flow
depths) and flow depth versus flow velocity (each diagram for a given range of grain sizes). Note that the variables
on each diagram are scaled to represent conditions where the flow temperature is 10°C. Thus, they are limited to
flows of that temperature but they are fairly representative of most natural flows.

All of these figures show that with increasing flow velocity the exact sequence of bedforms that will develop
will vary with flow depth and the grain size of the bed material. For example, figure 5-12 shows that with increasing







Figure 5-11. A highly schematic illustration showing a complete cycle of the stages of bed and water surface behaviour associated
with true antidunes. Note that dashed lines indicate the previous position of bed and/or water surface waves in each stage. The
development of cross-stratification is also shown (solid lines within the bed). After Udri (1991). Stage 1: under conditions
favouring antidune development the bed may remain essentially flat for part of the time. Horizontal lamination may form during
this initial stage. Stages 2 & 3: stationary in-phase waves develop as sinusoidal water surface waves grow in place and form
a sinusoidal bed wave, of lower amplitude. In this stage the bed is molded by erosion under high velocity flow under water surface
wave troughs and deposition under the relatively lower flow velocities under the water surface wave crests. In-phase wave
drape laminae may develop during this period of in situ growth of the bedforms. Stage 4: after the water surface wave reaches
some critical height and steepness it begins to slowly migrate in the upstream direction. Stage 5: the bedwave slowly responds
by similarly migrating upstream; the bed and water surface are slightly out-of-phase during this stage. Low-angle backset bedding
develops during this stage. Stage 6: as the water surface wave continues to migrate upstream and become steeper the bedwave
develops what appears to be an asymmetrical bedform on its upstream side; growth of this bedwave is particularly rapid as
the water surface wave begins to break by collapsing in the upstream direction. Breaking of the water surface wave results in
upstream sediment transport and large quantities of sediment are taken into suspension. Relatively steep (>15°) backset bedding
may develop over this stage. Stage 7: following collapse of the water surface wave the water surface becomes flatter and the
bedwaves are planed off by the very rapid flow. This bed-planing stage involves erosion from the wave crests and deposition
in the troughs in the form of a fast-moving, asymmetrical bedform that migrates downstream. Relatively high angle down-stream-
dipping cross-strata may develop as this bedform migrates across the trough of pre-existing in-phase wave. Stage 8: the water
and bed surfaces are planar and the cycle may begin again with deposition of horizontally laminated sand, truncating the
underlying cross-stratification produced by the in-phase waves.

4.0 4.0
In-phase waves Transition
In-phase waves F = 0.84

10˚C-equivalent mean flow velocity (m/s)

ua 3-D
2.0 F=1 2.0 ad
Transition Gr
F = 0.84
Upper plane bed
Upper plane bed l 3-D
dua Abrup Dunes
1.0 Gra 1.0 t
0.8 Dunes 0.8
Ab l
rup dua l
Ab l 0.6 Gra dua
0.6 rup dua l t
t Gra dua 2-D be d G
2-D d G ra lan
b er p
0.4 la 0.4 Low
er p Ripples
Ripples Low
No movement
No movement
0.2 0.2
D = 0.30 m D = 1.0 m
0.1 0.1
.06 0.1 0.2 0.4 0.6 1.0 2.0 .06 0.1 0.2 0.4 0.6 1.0 2.0

10˚C-equivalent sediment size (mm) 10˚C-equivalent sediment size (mm)

Figure 5-12. Velocity/grain size diagrams showing the fields of bedforms stability for two ranges of flow depth (all variables
are scaled to 10°C water temperature). See text for discussion. After Southard and Boguchwal (1990).

10˚C-equivalent mean flow depth (m)

0.6 Upper
0.4 bed

movement Figure 5-13. Depth/velocity diagrams showing the fields
Ripples of bedforms stability for three ranges of grain size (all
variables are scaled to 10°C water temperature). See text

0.1 for discussion. After Southard and Boguchwal (1990).



1. 4



d = 0.10 - 0.14 mm

0.1 0.2 0.4 0.6 0.8 1.0 2.0


1.0 1.0

0.8 0.8
10˚C-equivalent mean flow depth (m)

10˚C-equivalent mean flow depth (m)

to upper plane bed




0.6 0.6

2-D 3-D

0.4 No 0.4 Dunes

itio Up

movement 2-D 3-D

tra gradua


0.2 0.2 movement


lane bed


0.1 0.1

.08 .08
.06 .06
Lower p

= .84

In-phase In-phase
F =0
1. 4


.04 .04

waves waves


d = 0.40 - 0.60 mm d = 1.30 - 1.80 mm


.02 .02
0.1 0.2 0.4 0.6 0.8 1.0 2.0 0.1 0.2 0.4 0.6 0.8 1.0 2.0
10˚C-equivalent mean flow velocity (m/s) 10˚C-equivalent mean flow velocity (m/s)

velocity, flow over a bed of 0.1 mm sand will produce the sequence ripples → upper plane bed → in-phase waves,
whereas the same flow over a bed of 1 mm sand will produce the sequence lower plane bed → dunes (2-D followed
by 3-D) → in-phases waves (with upper plane bed following dunes under deep enough flows). Lower plane bed
and dunes are limited to relatively coarse grain sizes whereas ripples and upper plane beds dominate fine grain sizes
(particularly for the narrow range of flow depths represented by the figures: 1 to 3 m). Note that the maximum velocity
at which dunes and plane beds are stable increases with flow depth and is governed by the flow Froude number.
Also, note that the transitions form ripples to dunes and from ripples to plane bed are abrupt whereas all other
transitions form one bedform to another are gradual. The effect of flow depth on the sequence of bedforms that
develop with increasing flow velocity is apparent in figure 5-13. For example, the depth/velocity diagram for 0.4
mm to 0.60 mm sand shows that at flow depths less than 0.1 m the sequence of bedforms that develops with increasing
flow velocity is ripples → dunes (2-D followed by 3-D) → in-phase waves. However, at depths above 0.1 m upper
plane bed becomes stable and the sequence of bedforms becomes: ripples → dunes (2-D followed by 3-D) → upper
plane bed. → in-phase waves. Figure 5-13 also shows that the range of flow velocities over which ripples are stable
decreases with grain size, presumably because the viscous sublayer is destroyed under increasingly lower
velocities as the boundary roughness increases. Dunes and upper plane bed are both stable over wider ranges
of velocities as flow depth increases (again, because their upper limit is governed by the flow Froude number). In
contrast, lower plane bed exists over an increasingly narrower range of velocities as depth increases. Note that
the in-phase waves are not subdivided in diagrams like these because most experimental studies to date do not
extend through the upper flow regime.

Figure 5-14 shows how the height and lengths of dunes varies as a function of flow depth and velocity and
grain size, within the dune stability field. The effect of flow depth on dune size (that was mentioned earlier) is clearly
evident in the depth/velocity diagrams: as flow depth increases dunes become both longer and higher. The velocity/
grain size diagrams show that dune length increases with flow velocity but also with decreasing grain size: the
longest dunes develop on beds of the finest sand. In contrast, dune height is only loosely determined by grain
size (fine sand has a greater likelihood of developing higher dunes). For all sand sizes, with increasing flow velocity,
dune height first increases and then decreases towards the upper velocity limit of dune stability. This reflects the
washing out of dunes described above.

Figures like those shown here are necessary for the interpretation of paleoflow conditions based on the
bedforms that are preserved in ancient sediments. However, they continue to allow only qualitative interpretations
regarding the relative flow strength. A major limitation of data like that shown in figures 5-12 to 5-14 is that they
are based on relatively shallow flows depths, no more than a couple of metres deep whereas natural flows may range
up to several tens of metres, beyond the range represented by the experimental data. As our understanding of the
controls on bedform stability improve so will our ability to interpret these structures.


Cross-stratification is a type of primary structure that occurs in a wide variety of forms and develops in
sediments and sedimentary rocks due to temporal and spatial variation in deposition and erosion on a bed, normally
in association with the migration of bedforms. In this section we will see how the form of cross-stratification may
be used to infer type bedform that produced it and of the bedform behaviour (which may also be used to infer
something of the conditions in the depositional environment). However, first the terminology that has been
developed for describing cross-stratification must be introduced.


Once again, consistent terminology is required so that sedimentologists can communicate with each other.
Agreement on definitions of terms is not always easy (for example a symposium had to be held to come to a consensus
on the name “dune” for large, asymmetrical, flow transverse bedforms). However, there is a fairly consistent and
simple set of terms to describe layered sediments; the general terms will be defined here and more specific terms
will be introduced in the following section.

Figure 5-15 shows a hypothetical sequence of layered sediments or sedimentary rocks in order to illustrate

Dune spacing (length)



0.4 m
10˚C-equivalent mean flow depth (m) 1.5 Upper plane bed
& in-phase waves

2 1.0
0.2 Ripples m m
4 m
1 0.8
5 0.6
0.1 1m
Upper plane bed
.08 Dunes
& in-phase waves Ripples
.06 Lower
d10 = 0.30 - 0.40 mm D = 0.25 - 0.40 m plane bed

0.4 0.6 0.8 1.0 1.5 0.2 0.4 0.6 1.0

10˚C-equivalent mean flow velocity (m/s) 10˚C-equivalent sediment size (mm)

Dune height

0.4 10˚C-equivalent mean flow velocity (m/s)

10˚C-equivalent mean flow depth (m)

cm 1.5 Upper plane bed

12 & in-phase waves 6 cm

6 cm
0.2 Ripples 1.0
12 c
3 cm m
0.8 Dunes
6c m
0.6 3c
Upper plane bed
.08 Dunes Ripples
& in-phase waves
.06 Lower
d10 = 0.30 - 0.40 mm
D = 0.25 - 0.40 m plane bed

0.4 0.6 0.8 1.0 1.5 0.2 0.4 0.6 1.0


Figure 5-14. Bedform stability diagrams showing variation in dune spacing and dune height as a function of grain size, flow
depth and flow velocity (all scaled to 10°C water temperature). See text for discussion. After Southard and Boguchwal (1990).

some of the fundamental aspects of sedimentary layering. The term stratum (plural: strata) is a general term applied
to any layered rock unit that is clearly distinguishable from units above and below due to some discontinuity in
rock type (i.e., composition or texture). Any stratum may be simple (i.e., not internally divisible) or complex
(composed of a number of distinguishable internal units). A bed is any stratum that is greater than 1 cm thick and
a lamination (or lamina, plural is laminae) is any stratum that is less than 1 cm thick. The term layer is reserved for
a part of a bed which is bounded by some minor, but distinct, discontinuity in texture or composition. The contact
between beds is very distinct (e.g., the contact between beds in Fig. 5-15 is reflected by the abrupt vertical change
from shale to sandstone). The contact between layers is generally much more subtle and may represent an erosional
surface between packages of similar lithology. Such erosional surfaces between layers are termed amalgamation
surfaces. A division is a layer, or part of a layer, that is characterized by a particular association of primary
sedimentary structure. A band is a laterally continuous (on outcrop scale) portion of a layer that is distinguishable
on the basis of colour, composition, texture or cementation. A lens is a laterally discontinuous (on outcrop scale)



Division of cross-stratification

layer Division of horizontal lamination

Lens of pebbles
bed Amalgamation surface

Cementation band

Band of concretions

Band of pebbles

Figure 5-15. Terms used to describe various types of layering in sediments. Note that the lithology that is black is shale and
the white lithology is sandstone. After Blatt, Middleton and Murray (1980).

portion of a layer that is distinguishable on the basis of colour, composition, texture or cementation.

All stratification that is inclined due to primary processes (i.e., not tectonic deformation or tilting) is referred
to as cross-stratification. Cross-stratification typically includes packages of parallel beds or laminae that are
bounded by planar surfaces (bedding planes that are termed bounding surfaces). The upper bounding surface is
normally an erosional surface and truncates underlying internal strata. (Note that this allows us to determine the
original direction to top in tectonically deformed sediments.) The strata between bounding surfaces are often termed
internal strata or internal stratification. Internal strata are distinguishable as beds or laminae on the basis of often
subtle changes in grain size and/or mineralogical composition. A group of similar internal cross-strata, between
bounding surfaces, is referred to as a cross-strata set; a group of similar sets of cross-strata is referred to as a coset.
Any description of cross stratification must include the form of the internal cross-strata (see Fig. 5-16), the thickness
of the sets, the direction of dip of internal strata, the form and geometry of the bounding surfaces and the thickness
of cosets. Figure 5-17 outlines some of the common forms of cross-stratification and provides terms for describing
these structures. Note that the term cross-stratification is a general one; more specific terms are cross-laminae
(internal strata are less than 1 cm in thickness) and cross-bedding (internal strata are greater than 1 cm).

Origin of cross-stratification

The occurrence of bedding plane exposure of bedforms is relatively rare in outcrop. We typically can see
only the two-dimensional view (in vertical section) of the internal structure produced by bedforms as they move
over a bed surface. Because bedforms essentially migrate through each other (see above and further discussion

Major types of internal cross-strata

(in cross-section, parallel to dip-direction)

Angular internal cross-strata:

angular contact with top and
bottom bounding surfaces.

Tangential internal cross-strata:

bases of cross-strata are in tangential
contact with bottom bounding surface,
angular contact with top bounding surface.

Sigmoidal internal cross-strata:

tops and bases of internal cross-strata
are in tangential contact with bounding

Figure 5-16. Forms of internal cross-strata. Note, parallel horizontal lines are bounding surfaces.

below) we are usually limited to only partial preservation of that internal structure. The internal structure of the
bedform that we normally see is some expression of the lee face and trough of the bedform, and only rarely (for
anything but ripples) the stoss slope. The expression of these aspects of bedforms form may be visible as layers
due to subtle variation in grain size and/or mineralogy (seen as variation in colour) on the surfaces preserved within
the deposits. These layers comprise packages of inclined strata (internal strata paralleling depositional surfaces)
within the deposits that may be cut by erosional surfaces (bounding surfaces).

The following discussion is directly relevant to the formation of cross-stratification by asymmetric bedforms
but also illustrates principles that are important to the formation and preservation of forms of stratification produced
by other bedforms. Figure 5-18 shows the hypothetical lateral migration of an inclined surface (like the lee slope
of a bedform) due to periodic deposition of sediment on the surface (from times t1 to t9 forming layers L1 to L8). Each

Planar tabular cross-stratification Planar wedge-shaped cross-stratification

Set Set

Set Coset
Set Coset

Trough cross-stratification


Figure 5-17. Terminology for cross-stratification. Note that planar tabular cross-stratification is characterized by planar,
parallel bounding surfaces, wedge-shaped cross-stratification is characterized by planar but not parallel bounding surfaces, and
trough cross-stratification is characterized by trough- or scoop-shaped bounding surfaces (also called festoon cross-
stratification). After Blatt, Middleton, and Murray, 1980.

Formation of internal cross-strata by bedform migration

Figure 5-18. Illustration showing the for-
Position of brink over time
mation of internal stratification with bedform
t1 t2 t3 t4 t5 t6 t7 t8 t9 migration by episodic deposition on the lee
slope. Insets show internal form of cross-
strata formed by avalanching (A; inversely
A graded), periodic fallout from suspension
B (B; normally graded) and deposition of heavy
C mineral-enriched sediment (C). See text for
A B C further discussion.
1 2 3 4 5 6 7 8

layer, termed a foreset layer or foreset, represents a particular depositional event on the inclined surface. Each
individual layer may be visible due to some mineralogical and/or textural differences between layers that might arise
from a number of possible sorting mechanisms that act while they are deposited. For example, a particular foreset
layer may preserve variations in grain size that developed as the sediment avalanched down the inclined surface;
avalanche deposits tend to be inversely graded (i.e., become coarser within cross-strata, in the direction of migration,
normal to the lee face; Fig. 5-18A). Avalanching induces shearing within the sliding sediment and the grains exert
a “dispersive pressure” (a force per unit area acting in the direction pointing away from the solid surface that arises
due to grain collisions) which forces coarse grains upwards relative to fine grains. The largest grains also tend to
roll further down the lee slope so that internal strata tend to become finer-grained up slope and sets of such cross-
strata are normally graded (i.e., become finer upward) vertically through a cross-strata set. Internal strata formed
by avalanching tend to have angular contacts with underlying bounding surfaces (see Fig. 5-16). In contrast to
avalanching, sediment that falls periodically and in pulses from suspension tends to be normally graded (i.e.,
becomes finer, within cross-strata in the direction of migration, normal to the lee face; Fig. 5-18B) because the largest
particles tend to reach the depositional surface first, followed by increasingly finer grains (i.e., the grains are sorted
according to their settling velocities; internal strata produced by this mechanism tend to be tangential or sigmoidal
in form, see Fig. 5-16). Alternatively, the layers that are deposited on the lee surface of the bedform may reflect
variation in mineralogy; any particular layer may be formed when a heavy mineral accumulation is swept over the
brink of the bedform to deposit as a heavy mineral rich foreset (Fig. 5-18C). In addition, particularly in the case of
ripples, micaceous minerals commonly lie more-or-less parallel to the plane of the lee slope and highlight the internal
stratification. Note that because internal strata lie on the plane of the lee face of the bedform they dip in the direction
of bedform migration and this direction is, on average, also the direction of current flow. Therefore, the dip direction
of internal stratification produced by ripples and dunes is a valuable paleocurrent indicator and one that is very
easy to measure in the field, in contrast to grain orientation. The majority of paleocurrent data are based on the
geometry of cross-stratification.

The above example of deposition on an inclined surface is instructional to visualize how internal stratification
develops but it neglects the fact that as bedforms migrate so do the regions of deposition and erosion that they
generate by their interaction with the flow. Deposition is largely limited to the lee face of the bedform (as outlined
above) and erosion occurs from the trough and continues along the stoss side of the bedform. As the bedform
migrates by deposition on the lee face it forces the trough, and its region of scour, further downstream, up the stoss
slope of the next-downstream bedform. Thus, as one ripple migrates it consumes the next-downstream ripple, and
so on. Figure 5-19A illustrates the condition where there is no net deposition on a bed during ripple migration; as
the bedform migrates the volume of sediment deposited on the lee face will equal the volume of sediment removed
from its stoss side. Only if there is net deposition on the bed (i.e., more sediment is added to the bedform than is
removed with erosion) will all or any part of a bedform survive destruction associated with ripple migration. Figure
5-19B shows the example where there is sufficient deposition on the bed (i.e., the bed undergoes aggradation while
the bedform migrates) for preservation of the form of the bedform with downstream migration. In this case, the

sediment sediment
eroded deposited
A. Migration with no net deposition

t1 t2

B. Migration with net deposition.


Height of bed aggradation

due to net deposition.

Figure 5-19. Schematic illustration of the pattern of erosion and deposition with ripple migration. A, with no net deposition
or erosion on the bed the volume of sediment eroded from the stoss side of the ripple must equal the volume deposited on the
lee slope. Thus, with migration by one ripple wavelength, from time t1 to t2 all of the sediment contained within ripples at t1
will have been eroded and deposited within the ripples at t2. B, with net deposition on the bed no erosion takes place and the
entire ripple form is preserved.

volume of sediment added to the bed over the time for migration by one ripple wavelength (for example, sediment
deposited by fall-out from suspension) is more than the volume of each bedform so that the complete form of the
bedform is preserved. Note that if the volume of sediment added to the bed were less than the volume of the bedform
only partial preservation of the bedform is possible.

The extent to which a bedform is preserved depends on the relationship between the rate at which the bed
is aggrading and the rate at which the bedform is migrating. Figure 5-20 shows how various proportions of bedforms
(and their associated internal stratification) will be preserved as a function of these two variables. Figure 5-20A
shows that the path of a migrating bedform on a bed that is aggrading may be defined as a vector that is the sum
of the net migration and net bed aggradation over some fixed period of time. If the bed is aggrading the vector
describing this path is inclined upward, in the direction of bedform migration, and the bedform is said to “climb”
along this path. The angle of climb (β) is determined by the ratio of the aggradation rate to the migration rate. Note
that if we consider the migration path with a point of origin in the bedform trough then it delineates a line of erosion
as the bedform migrates (or plane of erosion if we consider three dimensions); everything above the migration path
is eroded due to scour in the trough and everything below the line of migration is preserved and buried by
subsequent deposition. This plane of erosion results in the bounding surfaces that define cross-strata sets and
the internal strata are formed directly by deposition on the lee slope of the bedform and preserved between the
bounding surfaces. Thus, in figure 5-20B, where there is no bed aggradation, the migration path is simply the path
of ripple migration and the line of erosion is horizontal. As in figure 5-19A, all downstream bedforms are planed
off by erosion in the trough of the migrating upstream bedform. In this case the only internal stratification that would
be preserved would be within any ripple forms that survived after migration (and presumably the current) had
stopped. In figure 5-20C bedform migration is accompanied by a moderate rate of bed aggradation compared to
the ripple migration rate and the internal deposits of bedforms are partially preserved. However, the path of the
migrating ripple trough climbs at an angle that is smaller than the angle of the stoss slope (α) of the bedform. As
the ripple migrates the plane of erosion passes beneath the stoss slope of the next downstream bedform and the
top portion of the internal strata of the downstream ripple are eroded. Whenever α > β only part of the internal strata
will be preserved; as a approaches equality with β more and more of the internal stratification will be preserved. Figure
5-20D shows the situation where the aggradation rate is high, relative to the migration rate, such that the angle of
climb is larger than the stoss slope angle of the bedform (i.e., α < β) and all of the internal deposits of the bedforms

A. Definitions
path of migrating trough
(a plane of erosion)
α (stoss angle) β (angle of climb)
bed aggradation

ripple migration

B. No preservation of ripples with migration and no net deposition.

α >> β, β = 0
ripple migration

t1 t2

C. Partial preservation of ripples with migration and relatively little net deposition.

α > β, β = 0

bed aggradation
ripple migration



D. Complete preservation of ripples with migration and considerable deposition.

bed aggradation

ripple migration



Figure 5-20. Illustration of the effect of the relative aggradation rate and bedform migration rate on the preservation of the internal
deposits of asymmetric bedforms. Note that dashed lines indicate the portions of ripples at t1 that are eroded with migration
to positions shown for t2. See text for discussion.

are preserved as they migrate downstream.

From the above discussion it should be clear that cross-stratification, like that shown in figures 5-16 and
5-17, forms in response to bedform migration and the particular style of cross-stratification that is preserved will
depend on: (1) the type of bedform (this controls, among other things the thickness of the cross-strata sets and
the thickness of internal strata); (2) the relative rates of bedform migration and bed aggradation; (3) the nature of
sedimentation on the bedding surfaces. Figure 5-21 illustrates how the various forms of cross-stratification shown
in figure 5-16 might develop. Angular internal strata (Fig. 5-21A) form when deposition on the lee face of the bedform
is dominated by avalanching (resulting in the angular basal contact of internal strata with the lower bounding

A. Angular lee slope dominated by avalanching with partial

preservation of lee slope deposits forming angular Figure 5-21. Styles of internal stratification shown in
internal cross-strata. terms of their mode of formation and style of preserva-
tion (see text for discussion).

B. Concave lee slope with avalanching plus fallout from

suspension with partial preservation of lee slope
deposits forming tangential internal cross-strata.

C. Concave lee slope with avalanching plus fallout from

suspension with complete preservation of lee slope
deposits preserving sigmoidal internal cross-strata.

surface) and the top portions of internal strata are removed by erosion because the angle of climb of the bedform
is less than its stoss slope angle (resulting in an angular contact with the upper bounding surface). Tangential
internal strata (Fig. 5-21B) form when deposition on the lee face of the bedform includes an important component
of sediment that is falling out of suspension (much of it having gone into suspension after passing over the brink
of the bedform). The base of the lee face is gently curved and tangential with the lower bounding surface formed
by erosion in the downstream trough. The tops of the internal strata have an angular contact with the upper
bounding surface where they are erosionally truncated. Sigmoidal internal strata (Fig. 5-21C) form when bedforms
with a concave lee slope climb at relatively high angles such that the erosional bounding surface passes close to
the bedform crest. This form of cross-stratification is especially well-developed by bedforms with long crests and
relatively short lee faces (e.g., washed out dunes).

Cross-stratification produced by asymmetrical bedforms

There are two major differences in the forms of cross-stratification produced by ripples and dunes. Because
of the small size of ripples the internal stratification is typically thin (i.e., they are cross-laminae, < 1 cm in thickness)
whereas dunes commonly produce thicker internal strata (commonly cross-bedding, > 1 cm in thickness). Also
because of the small size of ripples they tend to form a variety of forms of climbing ripple cross-stratification. Because
of the relatively small volume of sediment in a ripple the aggradation rates required to cause these bedforms to climb
at relatively steep angles are not difficult to achieve in nature. However, large dunes contain such large volumes
of sediment that it is only rare that aggradation rates are large enough to cause the bedforms to climb at angles greater
than their stoss slopes. Ripples and dunes bear the common characteristic that their plan form dictates the overall
form of cross-stratification. Straight-crested (2-dimensional bedforms) tend to form planar tabular and planar-
wedge-shaped cross-stratification (the planes of erosion associated with trough migration are relatively flat). In
contrast, 3-dimensional forms produce trough cross-stratification because the planes of erosion are highly irregular,

Styles of ripple cross-stratification β

b α

migration α = angle of stoss slope

Subcricritically climbing ripple cross-stratication

β = angle of climb

α >> β


Supercricritically climbing ripple cross-stratication


α << β

Figure 5-22. Forms of ripple cross-stratification that develop as a function of the angle of climb of the bedforms. See text
for discussion of details.

like the troughs and crests of the bedforms, and internal strata are best preserved where the bedforms migrate into
a particularly deeply scoured trough.

Ripple cross-lamination

Internal laminae produced by ripples can have a variety of forms: from angular to sigmoidal and planar to
trough-shaped in cross-section. The thickness of sets of ripple cross-lamination is limited by the upper limit to ripple
height, approximately 0.05 m. Most ripple cross-lamination is classified according to the angle of climb of the
bedforms and the resulting forms of internal laminae. Figure 5-22 shows a variety of ripple cross-lamination types.
Figure 5-22A is a form of horizontal lamination that is produced when the angle of climb of the ripple is negligible
(i.e., much less that the stoss slope of the bedform). Any deposits that are preserved between bounding surfaces
as the ripples migrate over the bed surface are too thin to allow the recognition of internal laminae. With increasing
angle of climb beyond some critical angle, that will depend on the sorting and mineralogy of the sediment, the
deposits between bounding surfaces become thick enough to preserve visible internal lamination (Fig. 5-22B).
Because the angle of climb is smaller than the stoss slope angle of the bedform (i.e., α > β) the foreset laminae are

increasing fallout from suspension

decreasing ripple migration rate

Figure 5-23. A relatively common vertical sequence of climbing ripple cross-stratification that is produced by waning, sediment
laden flows. Note that the angle of climb increases continuously upwards as the current wanes, resulting in a temporally increasing
rate of fallout from suspension and a decreasing rate of ripple migration.

truncated on top and all of the stoss slope deposits have been eroded. Such ripple cross-stratification is often termed
subcritically climbing ripple cross-stratification; subcritical means that α > β. This form of cross-stratification
develops under moderately low rates of bed aggradation due to fallout from suspension onto the bed. With
increasing angle of climb such that α < β the entire ripple form is preserved with ripple migration, including deposits
of the stoss slope (Fig. 5-22D; such internal strata are often termed formsets). Such stratification is termed
supercritically climbing ripple cross-stratification. (Note that when α = β the stratification is referred to as
critically climbing ripple cross-stratification and the entire foresets are preserved.) With increasing angle of climb
the thickness of the stoss-slope deposits increases and when the angle of climb reaches 90° the stoss and lee slope
deposits are equal in thickness. The forms of ripple cross-stratification that develop with particularly high angles
of climb indicate very rapid deposition from suspension while ripples were actively (but relatively slowly, migrating
on the bed. Note that the forms of ripple cross-lamination shown in figure 5-22 occur in nature as a continuous range
of forms from 0 ≤ β ≥ 90. Figure 5-23 is a sketch of a common vertical sequence of the forms of ripple cross-
stratification and shows the interpretation of this sequence that develops under waning flows, in terms of the rate
of ripple migration and the rate of bed aggradation due to fallout from suspension..

The forms of climbing ripple cross-stratification shown in figure 5-22 are often termed ripple-drift cross-
lamination. In addition to the terminology described above many workers use the classification scheme of Jopling
and Walker (1968). In that scheme subcritically climbing ripple cross-stratification (such as that shown in Fig. 5-
22B) is termed Type A ripple-drift cross-lamination; critically to slightly supercritically climbing ripple cross-
stratification is termed Type B ripple-drift cross-lamination (e.g., Fig. 5-22C); and highly supercritically climbing
ripple cross-stratification is termed sinusoidal ripple-drift cross-lamination (Fig. 5-22D).

Cross-stratification formed by dunes

As noted above, dunes produce forms of cross-stratification that are geometrically similar to cross-
stratification produced by ripples. Figure 5-24 shows two forms of cross-stratification formed by dunes: planar
crossbedding (both tabular and wedge-shaped) and trough cross-bedding. Both of these are distinguished from
ripple cross-stratification by their larger scale and the cross-stratification produced by dunes is commonly termed
“large-scale cross-stratification” in contrast to the “small-scale cross-stratification” produced by ripples. The
geometry of the internal strata will be governed as outline in figure 5-21 and the bounding surfaces depend on the
angle of climb of the bedform (although, as noted above, large dunes only rarely climb at high angles). The thickness
of cross-strata sets formed by migrating dunes are generally larger than that produced by ripples (because dunes
are higher) but set thickness is also governed by the angle of climb of the bedform. As noted above, the thickness

2-dimensional dunes 3-dimensional dunes

(planar tabular or wedge-shaped (trough cross-stratification)


Figure 5-24. Forms of large-scale cross-stratification produced by dunes. See text for details. After Allen, 1970.

of internal strata is also greater than those produced by ripples; their is a general tendency for the thickness of
internal strata to increase with the height of the lee face of the bedform.

Large scale planar cross-stratification is produced by 2-dimensional dunes that are dominated by deposition
by avalanching on their lee slopes (i.e., internal strata may be inversely graded). Internal strata typically dip at angles
of approximately 30° and typically range in thickness from a few decimetres up to several metres. In outcrop caution
must be made in interpreting such cross-strata because the form will vary due to the relationship between the
orientation of internal stratification and the orientation of the exposure. For example, in figure 5-24, planar cross-
stratification looks like a horizontal stratification when viewed on a vertical section aligned normal to the flow
direction (the direction of bedform migration; note that the internal strata seen in this view need not parallel the lower
bounding surface exactly, as shown). Thus, to avoid mistakenly interpreting such cross-stratification you must
try to view it on at least two vertical planes. Note that in plan view, through a planar cross-strata set, the straight,
parallel strikes of the planar internal strata are visible, aligned normal to the direction of bedform migration. The
internal strata, in plan view, may be traced laterally for up to tens of metres. To determine the paleoflow direction
based on planar cross-stratification, we need to find the strike of internal strata and the dip direction: the paleoflow
direction will be perpendicular to the strike, into the direction of dip.

Large scale trough cross-stratification is produced by 3-dimensional dunes where deposition on the lee face
includes both contact and suspended loads. Dip angles of internal strata vary from 20 to 30°, generally lower than
the planar forms, and sets range from a few decimetres to several metres in thickness. The form of such trough cross-
stratification varies significantly depending of the view of the exposure. In vertical sections, parallel to the flow
direction, sets may appear very similar to planar cross-stratification. However, in the vertical plane, normal to the
flow direction, the diagnostic trough-shape is apparent. In plan view the form the stratification appears as inter-
cutting, elongate troughs (defined by the bounding surfaces) and internal strata are curved, into the direction of
bedform migration, where they terminate against their lower bounding surfaces; thus, their concave surfaces face
the direction of migration. Such troughs, in plan view and in vertical section may extend for up to several tens of

Quartz & B. Low in-phase waves

Garnet F.U. ?
C.U. ?

A. Upper plane bed

7.0 F.U.

F.U. ?


6.0 C.U. ? 6.0
? F.U. ?
C.U. ?

5.0 5.0
4.0 4.0
C.U. ?
3.0 3.0

C.U. F.U.
2.0 2.0 C.U. ?
? F.U.
1.0 1.0

C.U. F.U.
0.0 0.0
0.05 0.10 0.15 0.20 0.25 0.05 0.10 0.15 0.20 0.25 0.30 0.35

(mm) (mm)

Figure 5-25. Internal grading and the distribution of heavy minerals in horizontally-laminated sediments: (A) deposited on
plane beds, and (B), deposited on low, downstream-migrating in-phase waves. All points in each plot indicate the mean grain
size in thin, contiguous layers up through the horizontally-laminated deposits. CU indicates coarsening-upwards lamina and
FU indicates fining-upwards lamina. Question marks indicate that the textural interpretation is rather uncertain. See text for
detailed discussion. After Cheel, 1990a.

Upper plane bed horizontal lamination

Deposition under upper plane bed conditions produces a variety of forms of horizontal lamination (sometimes
termed “parallel lamination”, although parallel laminae need not be horizontal). While one might think that horizontal
lamination would be the simplest form of stratification to interpret (i.e., deposition on a planar, horizontal surface),
this has actually been one of the most controversial styles of lamination. For example, a recent (not soon-to-be-
published) manuscript listed no less than 20 hypotheses for the origin of horizontal lamination formed under upper
plane bed conditions. Each such hypothesis suggests various sorting mechanisms that segregate sediment on
upper plane beds into “packages” of distinct grains size (and/or sorting) or mineralogy that comprise laminae. It
is likely that there are several mechanisms that cause the sorting of the sediment that leads to the formation of
lamination on upper plane beds (or nearly plane beds with low bedwaves). The major mechanisms can be listed
as: (1) local and small-scale sorting by the bursting process (both bursts and sweeps) on a true plane bed; (2)
selective sorting by size, shape and density on a true plane bed; (3) migration of low bedforms over which sediment
size, shape and density varies regularly. Each of these will be discussed below.

Bridge (1978) was the first to suggest that horizontal lamination (that is, thin, < 1 mm, horizontal lamination)
formed in response to the bursting cycle. He postulated that temporally decreasing boundary shear stress
associated with bursting would lead to deposition of increasingly finer sediment over the period of bursting and
this sediment would be preserved as a fining-upwards lamination. However, Cheel and Middleton (1986) showed
that horizontally-laminated sand and sandstone deposited under upper plane bed conditions were not composed
of predominantly fining-upward lamination but consisted of a mixture of fining- and coarsening-upwards laminae
of limited lateral extent (several millimetres across the flow direction). Such laminae are shown in figure 5-25A from

∆ X

Figure 5-26. Schematic illustration showing the formation of fining-upward laminae with heavy minerals concentrated in the
laminae tops due to migration of low in-phase waves with heavy minerals concentrated on their crests. Upper diagram shows
the migration path of in-phase waves (lines with open arrows) during bed aggradation of ∆Y and bed wave migration of ∆X
from time T1 to T2. Lower diagram is the enlarged view of boxed area showing the nature of grading and the distribution of heavy
minerals on the in-phase wave and within laminae produced with migration. θ is the angle of climb: θ = tan-1 (∆Y /∆X). Vertical
exaggeration approximately X25. From Cheel, 1990a.

upper plane bed deposits of a flume (the same textural and mineralogical characteristics were found in ancient
sandstones and modern inter-tidal deposits). In addition to these “textural” laminae, they identified “mineralogical
laminae” that were much more extensive than the textural laminae and were made up of very thin sheets of heavy
minerals (termed “heavy mineral sheets”) that seemed to be predominantly associated with coarsening-upwards
textural laminae. They attributed the textural laminae to the bursting cycle and the heavy mineral sheets to the
migration of heavy mineral accumulations over the active plane bed (e.g., heavy mineral shadows). In their model
fining-upward laminae formed by bursting. They suggested that the ejection of fluid away from the boundary carried
sand upwards and as the burst decayed this sand fell back to the bed, the largest, heaviest grains first, followed
by the smaller, lighter grains (i.e., see Stokes’ Law of settling); thus the material deposited on the bed following
bursting would form an upward-fining layer. In their model coarsening-upwards laminae formed as an in-coming
sweep locally increased the shear stress acting on the granular boundary and the sediment that was taken into
transport would re-deposit just downstream as the sweep decayed. Shearing within the material in transport would
cause the grains to experience dispersive pressure which pushes coarse grain upwards relative to the finer grains
in the moving sediment layer on the bed. Deposition of this coarsening-upwards layer of moving sediment would
form the coarsening-upwards lamination. Heavy mineral sheets represent a lag of fine-grained heavy minerals left
behind as a heavy mineral accumulation passed over the bed. The fine, high-density grains would easily become
deposited, particularly in the spaces between immobile quartz grains on the bed. The association of heavy mineral
sheets with coarsening-upwards laminae suggests that the heavy mineral accumulations were responsive to the
high bed shear stress due to sweeps but essentially armoured the bed to the effects of bursting. The formation
of heavy mineral sheets, described above, is an example of lamination formation by selective sorting by size and
density. Extensive horizontal lamination are probably commonly formed by this mechanisms (and low bedforms;
see below) whereas the laminae formed by the bursting cycle comprise laterally less extensive lamination in upper
plane bed deposits.

The formation of heavy mineral sheets may also represent an example of the formation of horizontal
lamination by the migration of low bedforms or bedwaves. A heavy mineral accumulation may be thought of as

a mineralogical bedform that migrates over the bed. In fact, the formation of a variety of textural laminae that are
of much greater extent that the textural laminae formed by bursting must involve the migration of bedforms over
an otherwise plane bed. This raises the question, again, of whether a bed with even the lowest bedwaves is really
a plane bed (e.g., see Fig. 5-10). For now, we will extend the definition of upper plane bed to include “true” plane
beds and “nominally” plane beds over which low bedforms may migrate. This is probably a reasonable extension
of the definition of plane bed, for the purposes of our discussion of horizontal lamination because low bedwaves
are definitely responsible for some forms of this structure.

It has long been known that very low bedforms such as washed-out dunes will produce a horizontal
lamination if the preserved deposit generally lacks internal stratification (because the lamination is too thin to see
the cross-stratification or because the sediment is too well-sorted to undergo significant segregation by size on
the lee of the bedform). Indeed, as we saw in the section of bedform migration (see Fig. 5-22A) any asymmetric
bedforms with a very low angle of climb might produce a form of horizontal lamination. However, there have been
several suggestions of upper plane bed horizontal lamination formed by migration of low bedwaves on a nominally
plane bed. For example, Allen (1984a) suggested that the passage of eddies over a bed would produce low-relief,
downstream-migrating bedforms that would form extensive horizontal lamination. He described the predicted
characteristics of such bedwaves in detail but such waves, with those characteristics, have not been identified in
experimental or field studies. However, experimental work by Bridge and Best (1988) and Paola et al. (1989) and Cheel
(1990a) have described a variety of low bedwaves that are thought to be responsible for the formation of extensive
horizontal lamination under what are essentially upper flow regime plane bed conditions.

Bridge and Best (1988) described low, asymmetrical bedforms (possibly very washed out dunes) and noted
that they formed extensive laminae in the bed material of their flume. Paola et al. (1989) described very low symmetrical
bedwaves (presumably similar to those shown in Fig. 5-10) that migrated downstream. By recording the bed
behaviour with high speed video photography they observed very low angle, parallel lamination (essentially
horizontal lamination) formed by a combination of small-scale fluctuations of turbulence (bursting), selective
sorting, and bedwave migration. Cheel (1990a) described the internal grading and distribution of heavy minerals
in low, downstream-migrating symmetrical bedwaves on which grain size became finer towards the tops of the
bedwaves and heavy minerals were concentrated in their tops. With migration of such low bedforms predominantly
fining-upwards laminae formed with heavy minerals concentrated in the tops of such laminae (compare with the
distribution of heavy minerals in true plane bed horizontal lamination, Fig. 5-25). Figure 5-26 illustrates the form
and origin of such laminae. Coarsening-upward laminae, and some thin fining-upwards laminae, also associated
with this form of horizontal lamination, were attributed to the action of bursts and sweeps, concurrent with bedform

As for a conclusion to the origin of horizontal lamination, it is likely that all of the major mechanisms (and
some others not discussed here) will lead to the formation of this structure. Some or all of the three major mechanisms
listed above may act together to form horizontal lamination under the same flow conditions and any one deposit
of upper plane bed, horizontally laminated sand or sandstone, probably preserve laminae formed by at least two,
and possibly all three of these mechanisms. The laterally extensive forms of horizontal lamination certainly involve
the migration of coherent sediment structures over an active plane bed (heavy mineral accumulations or full-fledged
bedforms) whereas the more subtle laminae are produced by processes associated with near-boundary turbulence.
The key to distinguishing the products of these various mechanisms likely lies in detailed studies of the textural
characteristics (including grain size, shape and orientation) within individual laminae.

In-phase waves stratification

Descriptions of in-phase wave stratification have been limited and figure 2B shows rather “ideal” forms of internal
stratification associated with the variety of forms of in-phase waves. The section on the formation of cross-
stratification described conditions that are also necessary for preservation of in-phase wave stratification (i.e., net
bed aggradation is require to form thick sequences of in-phase stratification, in conjunction with sorting by size
and/or mineralogy that is required to produce visible stratification). However, relatively little is known about the

specific origin of internal stratification produced by in-phase waves so that the discussion that follows will be largely
limited to its geometry. Note that figure 2B is largely based on descriptions in the literature of such stratification,
some of which is reviewed below.

Power (1961) coined the term “backset bed” for upstream-dipping cross-strata (becoming finer-grained
towards their tops) formed under antidunes (while Power coined this widely-used term the so-called backset beds
that Power described are probably not formed by antidunes at all!). Middleton (1965) characterised in-phase wave
stratification by its association with upper plane bed horizontal lamination, low angle (<10°) cross-laminae dipping
both upstream and downstream, and by the confinement of cross-laminae to symmetrical lenses related to the form
of the in-phase wave. Hand, Wessel & Hayes (1969) described in-phase wave stratification in which cross-laminae
dip at angles of up to 24°. Based on flume experiments, McBride et al. (1975) documented thin (0.2 to 4 mm thick),
laterally extensive, near-horizontal, parallel lamination, characterised by alternating coarse and fine laminae, which
formed by downstream migration of low in-phase waves. Allen (1966) noted that in-phase waves will form lenses
of backset cross-strata only if the water waves break and/or migrate upstream, whereas undulating parallel laminae
draped over the symmetrical bed forms are produced if the water surface wave grows in place during net deposition.
Furthermore, downstream dipping cross-strata form if the in-phase waves migrate downstream (Allen, 1966; also
see Allen, 1984b, Fig. 10-21). Barwis & Hayes (1985; p. 908) suggested that the occurrence of low angle truncation
surfaces in massive or horizontally laminated sands may indicate the presence of in-phase waves. They also
provided an excellent description of the variability of in-phase wave stratification on a washover fan in a barrier
island complex. They noted that down-fan, in the flow direction, in-phase waves decreased in length (reflecting
decreasing flow velocity) and amplitude and passed into plane bed. The form of the in-phase wave cross-strata
within the deposits also varied downfan from: (1) lenses of backset cross-laminae, to (2) lenses of laminae subparallel
to bounding surfaces, and to (3) lenses of foreset laminae. This sequence was interpreted to reflect downfan
variation in the relationship between the water and bed surfaces from: (1) upstream-migrating in-phase waves, to
(2) in-phase waves under stationary water surface waves, to (3) downstream-migrating antidunes. Langford &
Bracken (1987) described variation in in-phase wave stratification in a fluvial setting, as lenses of backset and foreset
cross-laminae of smaller downstream extent than cross-stratification formed under lower flow regime conditions.

Figure 2B shows the ideal forms of stratification produced by the specific behavioural forms of in-phase
waves that have been recognized and shows a gradual continuum of stratification styles through the transition from
washed-out dunes to antidunes. Washed-out dunes (climbing at a low angle) and upper plane bed, forming
horizontal lamination, develops as the upper flow regime threshold is exceeded. Low (on the order of millimetre high)
downstream-migrating in-phase waves develop next and form horizontal lamination of the characteristics described
here (termed in-phase wave horizontal lamination; see Fig. 5-26). As the in-phase waves grow in height and
wavelength they continue to migrate downstream, producing lenses of downstream-dipping cross-laminae (termed
in-phase wave foreset cross-laminae). The absence of visible cross-stratification formed by low in-phase waves
is likely due to the very small thickness of the deposit and to the relatively poor development of sorting and fabric
along the low-angle lee of the bed form. The next bed phase is characterised by standing in-phase waves which
produce laminae which approximately parallel the bed forms (termed in-phase wave drape-laminae). With the onset
of upstream-migrating and/or breaking wave antidunes, lenses of upstream-dipping cross-laminae form (termed
antidune backset cross-laminae). This sequence applies to the 2-dimensional forms of in-phase wave only. The
3-dimensional forms are not well known from flume studies and are not included here. Also not included in figure
2B are associations of the various forms of in-phase wave stratification, due to temporal variation in the form of
in-phase waves. Given the behaviour of the in-phase waves bedforms shown in figure 5-11 it is certain that such
complex associations are very important and may be diagnostic of stratification formed by in-phase waves.




Bedforms and stratification produced by unidirectional flows are well understood after almost a century of
study in flumes and natural settings. However, in the geologic record of marine and lacustrine depositional
environments other classes of fluid flow are important in producing structures that are preserved and form an
interpretive basis for those deposits. Figure 6-1 summarizes a continuum of flow types, from purely unidirectional
flows to purely oscillatory flows, between which are a range of mixed flows and their components are shown in the
lower half of the figure. In this section we will begin by examining the nature of currents, bedforms and stratification
produced by wind-generated waves on a free water surface (i.e., purely oscillatory flow). This will be followed by
a very brief description of the bedforms and stratification that develop when unidirectional and oscillatory currents
are superimposed to produce a general class of flow termed a combined flow. Note that figure 6-1 is a simplification
of possible natural flows. To begin with, the classification shown in figure 6-1 does not consider the angular
relationship between the oscillatory and unidirectional components: the resultant current produced by co-linear
flows (i.e., both act in the same direction) will be much less complex than in the case where the oscillatory component
acts at some angle to the unidirectional component. In addition, in natural flows several different oscillatory and
unidirectional components may act simultaneously to result in a very complex flow pattern. In nature such patterns
exist and experimental work, like that described in the section on bedforms, is limited to the relatively simplistic


Waves generated by wind blowing over a water surface are prevalent in most marine and lacustrine settings.
Such waves are commonly referred to as gravity waves because gravity is the most important force acting to dampen
these waves (i.e., gravity acts to restore the water surface to a flat surface after a wave has been generated by wind).

Combined flows
Flow Class:
Symmetrical Asymmetrical Pulsing Pulsing Steady
oscillatory oscillatory discontinuous continuous continuous
flow flow flow flow flow

Resultant Flow
50 50 50 50 50

0 0 0 0 0
5 10 5 10 5 10 5 10 5 10
Velocity (cm/sec)

-50 -50 -50 -50 -50

Flow components Oscillatory component

50 50 50 50 50

0 0 0 0 0
5 10 5 10 5 10 5 10 5 10

-50 -50 -50 -50 -50

Time (seconds)

Figure 6-1. Flow classes defined in terms of the relative strength of their oscillatory and unidirectional components. Top graphs
illustrate the pattern of variation of velocity over time of the net flow and the lower graphs show the oscillatory and unidirectional
components of each flow separately. After Swift et al., 1983.

Figure 6-2. Wave classification by wave period

and the mechanisms that generate waves on large
water bodies such as oceans. Each shaded bar shows
Mechanism of wave generation Sun/moon the range of wave periods generated by each mecha-
(tides) nism and the solid black bars indicate the wave
period that generates the maximum wave energy in
diurnal semi-diurnal
the oceans due to each generating mechanism. The
(tsunamis) bar at approximately 10 seconds represents wind-
generated waves by average wind conditions on the
oceans; the bar representing a period of just over
storms 100 seconds is associated with long period and wave
length “swell” generated by storms. The bar asso-
ciated with wave periods of approximately 2000
seconds (about half an hour) are waves generated by
wind-generated gravity waves
earthquakes (Tsunamis). The two bars on the far
0.01 0.1 1 10 100 1,000 10,000 100,000 1,000,000 right represent, from left to right, tides with
Wave Period (seconds) semidaily (or semidiurnal; two tidal cycles per day)
and daily (or diurnal; one tidal cycle per day)

Gravity waves are just one particular type of wave that acts in large water bodies such as oceans (Fig. 6-2) and they
account for much of the total energy possessed by the worlds oceans.

The majority of gravity waves on a water surface are generated by wind moving over that surface. While
the exact mechanisms of wave formation are not well understood the response of the water surface to wind is well
known. Waves develop as sinusoidal oscillations of the water surface that propagate (i.e., travel) in the direction
of the wind. The characteristics of wind-generated gravity waves (e.g., their size) depends on a number of factors
that include wind speed, duration of wind and the distance over which the wind acts on the water surface (this
distance is termed fetch). Waves will propagate beyond the region of wave generation and may travel thousands
of kilometres and take days to dissipate. Waves that have left their region of generation are termed swell. Swell
waves are typically very long, relatively low and straight-crested.

Any description of gravity waves must include wave length (L; also referred to as wave spacing), wave
height (H), wave celerity (C; the speed at which the wave moves along the water surface, and wave period (T, where
T = L/C; the time required for one full wave-length to pass a fixed point). All of these wave characteristics are
determined by the intensity, duration and fetch (the distance over which the wind acts on a water surface) of the
wind that generates them. To illustrate figure 6-3 shows the scales of waves produced by various wind speeds acting
over seas with unlimited fetch.

Gravity waves are classified by the relationship between their wave length and the depth of water through
which they are moving (this affects the form of the waves and waves in deep water undergo a number of changes
as they move into shallow water; see below). Deep water waves are waves with lengths that are no more than two
times the depth (h) of water over which they are moving (i.e., h > L/2; note that this depth is commonly called wave
base). Transitional waves have longer wave lengths relative to water depth, between the limits L/20 < h < L/2. Shallow
water waves are waves have lengths that are at least 20 times the water depth (i.e., h < L/20).

The geologically important result of gravity waves on the water surface is the fluid motion that they generate,
motion that may result in sediment transport and the formation of primary sedimentary structures. The nature of
fluid motion associated with waves is very complex and this section will only discuss this topic in a very superficial
manner and in terms that will be particularly important to later discussion of the sedimentary structures generated
by waves. The best general text that describes gravity waves and their products is that by Komar (1976).

To begin the discussion of fluid motion under waves we will consider so-called deep water waves that do
not interact significantly with the bottom (i.e., the sediment substrate at some depth below the water surface is
unaffected by the passage of such waves). Figure 6-4A shows the characteristics of a train of deep water waves.
Fluid motion beneath such waves is complex and is shown in a simple but instructive manner in Fig. 6-4A. If we

Wind speed (km/h)

0 1 2 3 4 5 6 7 8 9 10111213 0 20 40 60 80 100 120 140 160 180 200 0 1 2 3 4 5 6 7 8 9 10111213
Average height (m) Average length (m) Average period (s)

Figure 6-3. Wave conditions as a function of wind speed for a fully developed sea. Data from Thurman, 1988.

follow the path of a single water molecule as a wave passes one complete wave-length the path appears circular:
motion is in the direction of propagation under the crest and in the opposing direction under the trough and at
intermediate angles and directions, through 360°, at other positions beneath the passing wave (Fig. 6-4A). This
circular path is referred to as the wave orbital and its diameter is termed the orbital diameter (do). Under deep water
waves the orbital diameter becomes exponentially smaller with depth until it is of negligible size and the orbital
diameter is related to depth by:

do = He L Eq. 6-1
where y is a negative number indicating the distance below the water surface and L is the wave length. The wave
orbitals persist but become negligible below the depth equal to L/2. The speed of fluid motion about the orbitals
at any time during the passage of a single wave is termed the orbital speed. The orbital speed just as the crest and
trough pass by is termed the maximum orbital speed (Um); Um is equal but acts in opposite directions beneath the
crest and trough, as outlined above. The maximum orbital speed varies with depth by its relationship to the orbital
diameter, given by:
Um = Eq. 6-2

A. Deep water (h > L/2) B. Transitional waves (L/20 < h < L/2)

still water level still water level
+um H H

do do wave crest

-um Time
h y 0.5T T
y h
wave trough

h < L/2

y = L/2

Figure 6-4. Characteristics of deep water and transitional waves. See text for discussion.

At the water surface the orbital diameter is equal to the wave height (i.e., do = H), such that:
Um = Eq. 6-3
As waves propagate into shallow water (at depths less than L/2) they begin to interact with the bottom and
undergo several changes and the relationships given above no longer hold. A particularly important change
involves the refraction of the wave crests to a position that parallels the isobaths of the bottom (isobaths are lines
joining points of equal depth). Because isobaths approximately parallel the shoreline, refraction also aligns the
waves parallel to the shoreline. In addition, waves become steeper due to an increase in H and the formulae given
above no longer accurately describe the behaviour of the current that they generate. Steepening increases until
the deep water wave height becomes 75% of the water depth (i.e., h = 4H/3); at this depth the wave will break.
Concurrent with steepening of the wave the wave orbitals become elliptical, and increasingly flatter with depth until
along the bottom (Fig. 6-4B) the motion of fluid molecules (and any sediment in transport) follows a line that is parallel
to the bottom surface. Under transitional waves the rate of decrease in orbital diameter with depth is much less than
the rate under deep water waves (Fig. 6-4B). Under transitional waves the orbital diameter is given by:

HT g
do = Eq. 6-4
2π h
where g is the acceleration due to gravity. Note that under shallow water waves the orbital diameter does not change
with distance below the water surface but is constant. The maximum orbital speed under transitional waves is given
by the general relationship for shallow water waves :
Um = gh Eq. 6-5
(note that from here on we will assume that Um is the maximum orbital speed acting on the bottom because that is
where the sedimentologically important work is done).


As under unidirectional flows, bedforms begin to develop under oscillatory flows as soon as the flow
conditions exceed some threshold for the initiation of movement of sediment. Also, the forms of bedforms, and
their associated internal stratification, vary with the strength of the current. However, because of the very
fundamental differences between unidirectional and oscillatory flows the properties of the flow that control when
sediment will move and what bedform will be stable must also differ.

Initiation of sediment motion under waves

It is the to and fro fluid motion acting on the bottom that may produce bedforms and stratification if the
strength of the oscillatory current exceeds some threshold condition required for the initiation of particle motion.
Under unidirectional flows we saw that the critical flow condition for motion of a particle depends on the size and
density of the particle, the density of the fluid, and the boundary shear stress (that was related to the flow velocity
and depth). The condition for the initiation of motion of sediment under oscillatory currents may be similarly
determined by the fluid and sediment properties but the flow strength is normally represented by the maximum orbital
speed and the orbital diameter or wave period. Orbital diameter and wave period are important components of flow
strength because they determine the spatial extent over which the maximum orbital speed acts and its duration.
Komar and Miller (1973) determined that the critical condition for the movement of sediment under waves can be
defined in a manner that is superficially similar to Shield’s criterion for motion under unidirectional flows, by the
general relationship:

ρU t

( ρ s − ρ ) gD
Eq. 6-6

where Ut is the threshold maximum orbital speed required to move sediment; ρ is the fluid density, ρs is the density


Figure 6-5. Schematic illustration of classical “wave ripples” or 2-D vortex ripples. Note the cross-sectional form and straight
to gently bifurcating crestlines. The direction of oscillation and inferred shoreline orientation are shown for comparison. Note
that no scale is shown but ripple spacing may range from centimetres to in excess of a metre, increasing with grain size. See
text for discussion.

of the sediment, g is the acceleration due to gravity, and D is the size of the particles. C and n are constants that
are determined by the size of the sediment. For grain sizes finer than 0.5 mm C = 0.21 and n = 0.50. For grain sizes
coarser than 0.5 mm C = 1.45 and n = 0.25. Note in Eq. 6-6 that do varies with wave period (see Eq. 6-2 and 6-4) so
that the threshold maximum orbital speed similarly varies with wave period: the longer the wave period the larger
the threshold maximum orbital speed required to move the sediment.

Bedforms under waves

For many years one particular type of bedform has been considered diagnostic of the influence of waves
on a sediment substrate: symmetrical ripples (commonly called wave ripples and the modern term is 2-D vortex
ripples). Today we know that there are actually a variety of bedforms that develop under waves but before
considering these in detail we will briefly focus on the common wave ripple.

So-called “wave ripples” are distinct from the “current ripples” produced by unidirectional flows by their
symmetrical profile, relatively peaked crest and broad trough, and by their straight to bifurcating crestlines (Fig.
6-5). These are a very common bedform in shallow marine sediments and occur extensively on bedding plane
exposures. The spacing of such ripples (λ) ranges form centimetres to in excess of a metre and they range in height
from millimetres to about a decimetre. The overall size of wave ripples varies directly with grain size and small scale
symmetrical ripples form in fine sand and large scale symmetrical ripples form in gravel. When such ripples form
they are molded on the bed beneath the propagating gravity waves and their crests are aligned parallel to the crests
of the water surface waves (but do not confuse these with in-phase waves of unidirectional flows). An important
implication of the alignment of ripple crests is that, like the wave crests, such ripples will be aligned parallel to regional
shoreline (a characteristic that was nicely demonstrated by Leckie and Krystinik, 1989). Some symmetrical ripples
have two crests, aligned at approximately 90° to each other, and normally one crest is better-developed (the dominant
crest) than the other. For many years such ripples were termed interference ripples and taken to represent the
condition when symmetrical ripples form under two sets of gravity waves that propagate at right angles to each
other. However, recent, as-yet unpublished, experimental studies have shown that interference patterns of ripple
crests can develop under certain conditions when only one wave train is active. Thus, the standard interpretation

? Figure 6-6. Schematic illustration show-

do ing the relationship between symmetrical
λ 0.50 mm sand ripple wave-length and the diameter of
wave orbitals. Data are not shown. The
Ripple spacing (λ; cm)
dark, shaded line (labelled “orbital rip-
0.25 mm sand ples”) is defined by ripples with lengths
equal to 80% of their associated wave


orbitals. Solid lines (labelled with grains

sizes) indicate the limiting ripple wave-

10 0.125 mm sand

length for the grain size indicated. The


shaded area represents the region of



do anorbital ripples. The drawings illustrate



the relationship between symmetrical rip-


ples and their wave orbital for orbital rip-


ples (upper left) and anorbital ripples (lower

right). See text for further discussion.
1 5 10 100 1000
Orbital diameter (do; cm)

of this particular form of symmetrical ripple is now in doubt.

Many basic textbooks that discuss the humble wave ripple point out that the spacing of such ripples is
determined by the diameter of the circular wave orbital that forms them. In general, the ripple spacing is slightly
less than the orbital diameter acting on the sediment substrate (see Eq. 6-8). Considering the above discussion this
idea makes sense for transitional waves under water depths just less than L/2 when a more-or-less circular orbital
is present. However, it is difficult to conceive of shallow-water waves (as described above) producing such ripples.
Figure 6-6 schematically illustrates observations of symmetrical ripple spacing (λ, the orthogonal distance between
crests) from natural and experimental settings where the orbital diameters of the formative waves are known. When
we plot ripple spacing against orbital diameter the data occur in two indistinct groups. Some ripples have spacings
that are directly related to wave orbital diameter by the relationship:
λ = 0. 8 do Eq. 6-7
Such wave ripples are termed orbital ripples. However, many wave ripples do not fall on the line defined by Eq.
6-7 but deviate from that line because their wave-lengths are much shorter than the orbital diameter and such ripples
are termed anorbital ripples. Ripples with wave-lengths that fall between these two classes are termed suborbital
ripples. Note that with increasing grain size the maximum ripple wave-length also increases (i.e., the coarser the
sediment the larger the maximum possible ripple wave-length). This suggests that for any grain size there is an upper
limit to the size of ripples that will form. Below the limit, a single orbital ripple will exist for every orbital diameter
acting on the sediment surface and beyond that limit several individual anorbital ripples will be stable under a
relatively long orbital diameter. The relationship between ripples and wave orbitals is shown schematically in figure

The above discussion points to the fact that there are a variety of bedforms that develop under oscillatory
flows. Over the past decade, experimental studies have helped describe these bedforms in terms of their morphology
and behaviour and the hydraulic conditions that are necessary to form them. Harms et al. (1982), based largely on
experimental work in John Southard’s labs at M.I.T., described bedforms under oscillatory flows in the manner that
the unidirectional bedforms are described. In the remainder of this section we will consider the sequence of bedforms
that develop under oscillatory flows much like we did the unidirectional flow bedforms in the previous chapter of
these notes.

Consider an experiment where we induce oscillatory fluid motion (i.e., back and forth) over a sandy substrate
in a closed tunnel. There is no free-water surface but the speed of the oscillatory current varies gradually in both

;;;;;;;;;;;;;;;;;;;; FLAT BED

(long wave periods)


;;;;;;;;;;;;;;;;;;;;;; ROLLING - GRAIN

Figure 6-7. Schematic illustration of the bedforms that develop under oscillatory currents. From the bottom upwards the
sequence of bedforms reflects the sequence that develops with increasing maximum orbital velocity (except for the reversing
crest ripples). See text for further discussion. After Harms et al. (1982).

speed and direction (over 180°) and the maximum velocity, in either direction, is comparable to the maximum orbital
velocity under waves. The duration of the current in either direction is related to the wave period and the distance
over which the current moves during one oscillation is related to the wave orbital diameter. Like the mental experiment
that we conducted to describe bedforms under unidirectional flows, in this case we will consider the sequence of
bedforms that develops with increasing flow strength (maximum orbital speed) holding all other variables constant.
Note that not all of the following bedforms will develop under a given wave period or bed grain size, as we shall
see when we look at a bedform stability diagram for oscillatory flows.

The sequence of bedforms that develops under oscillatory flows is shown schematically in figure 6-7. Just
as the current begins to move the sediment (i.e., the maximum orbital speed exceeds the threshold for motion) the
first bedforms that develop are termed rolling grain ripples. These bedforms are small with lengths less than 10
cm and heights on the order of a few millimetres to approximately 1 centimetre. Rolling grain ripples are symmetrical
in profile, have low slopes, and are straight-crested. Sediment movement over rolling grain ripples is as traction:
grains roll back and forth under the oscillating current. This bedform is thought to be “metastable”, that is, over
time they slowly grow in size (particularly height) and become vortex ripples. Under somewhat larger maximum
orbital velocities vortex ripples develop quickly and are stable. Vortex ripples include the common form of wave
ripple described above in the opening paragraphs of this section on bedforms. As noted above, they are symmetrical
in cross-section and have slopes that are steeper than rolling grain ripples. Vortex ripple lengths very from
centimetres in fine sand to in excess of a metre in gravel and similarly vary in height from approximately a centimetre
to a decimetre. Sediment transport over vortex ripples is both in traction and suspension. The first vortex ripples
to develop are straight-crested (2-dimensional) as depicted in figure 6-5. However, as the orbital speed increases
vortex ripples become increasingly 3-dimensional in plan view. The 3-D vortex ripples grow larger (with wave-
lengths in excess of 1 m) and form rounded bedforms with hummocks (areas of positive relief) and swales (areas
of negative relief) on the bed (see top block diagram in Fig. 6-11). Such large, 3-D vortex ripples are sometimes referred
to as “hummocky ripples”. Note that these large ripples may someday become thought of as dunes under oscillatory
flows. With a further increase in maximum orbital speed the 3D-vortex ripples become flatter and somewhat shorter



(sand movement)


EE -
0.4 DIM
( in p
( start as rolling - grain ripples )

0.2 AL


1 2 4 6 8 10 20

PERIOD T (sec)

Figure 6-8. Diagram illustrating the fields of stability of wave-formed bedforms on beds of fine sand (0.15 to 0.21 mm). After
Harms et al. (1982).

to form post-vortex ripples. These bedforms can be thought of as transitional forms with flat bed, an essentially
flat, featureless bedform that develops under the highest orbital velocities and experiences intense sediment
transport. The so-called flat bed of oscillatory flows is morphologically similar to upper plane bed of unidirectional
flows (and many authors term the oscillatory bedform plane bed). Another bedform that develops under oscillatory
currents, but only under waves with relatively long periods, is termed reversing-crest ripples. These bedforms
are generally less than 10 cm long and rather low and are somewhat asymmetrical. They derive their name from the
fact that they reverse in direction as the current reverses. This characteristic is possible because under waves with
long periods the duration of flow in one direction is sufficiently long to generate a small, asymmetrical ripples (like
ripples under unidirectional flows). Thus with each oscillation the current reverses and so does the direction of
migration of the asymmetric ripples. These particular bedforms illustrate that bedforms under oscillatory flows are
very similar to those under unidirectional flows but the current acting in one direction, under normally short period
waves, does not persist long enough to generate bedforms like those under unidirectional flows.

Figure 6-8 shows a bedform stability diagram for fine, quartz sand (0.15 to 0.21 mm) in terms of orbital speed
and wave period (we are ignoring the effects of temperature). Note that diagrams for other grain sizes will have
similarly formed fields but at different positions (i.e., for coarse sand the fields shift upwards so that all transitions
occur at higher maximum orbital velocities). Figure 6-8 shows that the sequence of bedforms with increasing
maximum orbital speed are essentially as outlined above and reversing-crest ripples appear to replace other
bedforms at significantly high wave periods. The range of conditions over which post-vortex ripples are stable
extends to lower maximum orbital velocities with increasing period. Figure 6-8 is after Harms et al. (1982) but more
recent experiments by Southard et al. (1990) have documented, in more detail, the development of vortex ripples
with increasing orbital speed.

Stratification formed by oscillatory currents

Like bedforms that develop under unidirectional flows, bedforms under oscillatory currents result in a variety
of forms of cross-stratification that differ in detail due to the geometry and behaviour of the generative bedforms.

Flat bed
Near - horizontal fine laminae

Three - dimensional vortex ripples

( flatter)
λ dm - m, I 15 - 20
Swaley sets of cross laminae with
set contacts sloping less than 10˚,
hummocks rarely preserved

Three - dimensional vortex ripples

( steeper)
λ dm - m, I~10
Hummocky sets of cross laminae
with set contacts sloping as much
as 10 - 15˚

Two - dimensional vortex ripples

λ cm - dm, I= 6 - 10
Small intricately "braided" sets
of cross laminae

Rolling grain ripples

λ cm, I large
Thin laminae, low angle cross
lamination or flat lamination

Figure 6-9. Forms of cross-stratification produced by wave-generated bedforms on slowly aggrading beds. Note that “I” is
the ripple index (ratio of length to height). After Harms et al. (1982).

To make a broad generalization: the features of wave-formed cross-strata that distinguish them from those formed
by unidirectional flows are (1) a wide variation in cross-strata dip directions (although this is not always the case;
see below) and (2) the symmetrical, curved bounding surfaces that are sometimes preserved, reflecting the
symmetrical form of the bedform. In addition, as we saw in the section on grain fabric, particle alignment in the
deposits of wave-generated currents is distinctly different from that under unidirectional flows; under purely
oscillatory flows the vector mean dip of particles may be horizontal.

Figure 6-9 depicts the forms of cross-stratification that develop under waves with increasing maximum orbital
velocity (i.e., under the various bedforms described in the previous section) under conditions of vertical aggradation
of a bed. Note that exact forms of stratification will vary, depending on the aggradation rate and the rate of ripple
migration (if any; see below). This description follows that of Harms et al. (1982) and remains somewhat speculative
although the discussion below includes some observations from recent experiments by Southard et al. (1990) and
Arnott and Southard (1990).

Rolling grain ripples produce thin, sub-parallel laminae that may or may not display internal cross-lamination.
As the bedforms grow to 2-D vortex ripples the internal cross-laminae become prevalent and the form of cross-
stratification is complex. Under purely oscillating currents the internal cross-strata produced by 2-D vortex ripples
form sets of alternately dipping laminae bounded by curved erosional surfaces. Such sets are sometimes said to
be “braided” and form a particular type of cross-stratification that is termed chevron cross-stratification. The exact
form of the cross-stratification produced by 2-D vortex ripples will depend on the behaviour of the bedform, which
in turn depends on the symmetry of the oscillatory current. The thickness of cross-strata sets depends on the size
of the ripples that form them; therefore, set thickness will be strongly influenced by the grain size of the sediment
(larger bedforms and cross-strata sets are possible in sediment of coarse grain size). The form of cross-stratification


aggradation, no migration

migration + aggradation
large angle of climb

migration + aggradation
small angle of climb

migration, no aggradation

Figure 6-10. Schematic illustration showing the idealized forms of cross-stratification produced by 2-D vortex ripples as a
function of their rate of migration and the rate of bed aggradation. After Harms et al. (1982).

shown in figure 6-9 is limited to purely oscillatory flows but in nature it is not unusual for even wave-generated
currents in shallow water to have an asymmetry that induces a somewhat stronger current in one direction. Such
asymmetrical currents may cause 2-D vortex ripples to migrate in the direction of the strongest component of the
oscillatory current. Like current ripples, the form of cross-stratification that is preserved will vary with the rate
aggradation of the bed. Thus, there are a variety of forms of cross-stratification produced by 2-D vortex ripples
that depend on the combined effects of bed aggradation and the rate of ripple migration. Figure 6-10 shows the
continuum of forms of cross-stratification that may be produced by 2-D vortex ripples as a function of bed
aggradation and ripple migration rates. Note that with ripple migration and no bed aggradation the internal cross-
strata dip only in one direction and might appear like cross-strata produced by current ripples under unidirectional
flows. The similarities continue for the migrating ripples as increasing aggradation rates produce climbing forms
of ripple cross-stratification. The preservation of symmetrical ripple forms is probably necessary to allow reliable
distinction of cross-stratification produced by waves from current ripple cross-stratification formed under similar
conditions of bed aggradation. In addition, even the migrating wave-generated bedforms may preserve local sets
of cross-strata that dip in the direction opposing the average direction of ripple migration, the presence of such
sets should suggest wave-generated currents. Only when the ripples do not migrate in a preferred direction will
true chevron cross-stratification develop in which the proportion of cross-strata dipping in one direction or the other
are approximately equal.

Returning to figure 6-9, with increasing maximum orbital velocity, as the bedforms grow and become more
rounded and three-dimensional, the forms of cross-stratification change to mimic the morphology of the bedforms.
As depicted in figure 6-9 there are two forms of stratification produced by 3-D vortex ripples. The first to develop,

cm - dm

B Hummock
S w ale
cm - dm

Third-order surface
Second-order surface

First-order surface
Sole marks

Figure 6-11. Schematic illustrations of hummocky cross-stratification. A. A block diagram showing the form of the
three-dimensional bedform that is thought to produce HCS (3-D vortex ripples). B. The details of the internal structure
of HCS. See text for details. From Cheel and Leckie (1992).

with increasing orbital velocity above that which 2-D vortex ripples are stable, is characterized by sets of both
concave- and convex-up internal strata (termed swaley strata and hummocky strata, respectively) bounded by
similarly shaped bounding surfaces. This form of cross-stratification is termed hummocky cross-stratification
(HCS), consistently one of the most enigmatic primary sedimentary structures over the past two decades (see the
final section of this chapter for a closer look at this form of cross-stratification and the debate that it has generated).
Figure 6-11 shows a large, hummocky, 3-D vortex rippled bed surface and the form of HCS that the bedform is thought
to produce. Internal lamination in HCS dip at angles up to 15° and are isotropic (i.e., dip with equal frequency in
all directions). Based on the descriptions of the bedforms that are believed to generate HCS, the spacing of
hummocks should vary from approximately a decimetre to in excess of a metre. With increasing maximum orbital
velocity figure 6-9 suggests that the next form of stratification is similar to HCS except for two distinctive
characteristics: internal laminae dip at shallower angles (not exceeding 10°) and only swaley (concave) laminae are
preserved. This form of cross-stratification is termed swaley cross-stratification (SCS). The different form of SCS,
compared to HCS, may be attributed to the lower relief of the bedforms and the greater scour of the bed (planing
off hummocks) under the greater maximum orbital velocities. With increasing maximum orbital velocity, through
the field of post-vortex ripple stability, the internal strata and their bounding surfaces must become increasingly
flat and produce a form of horizontal lamination by deposition on a wave-generated flat bed. This form of horizontal
lamination has not been extensively studied and descriptions of such lamination does not provide a basis for
distinguishing it from upper plane bed horizontal lamination of unidirectional flows. Intuition suggests that internal
fabric may provide a diagnostic criterion for the identification the formative processes responsible for this structure.
Note that the internal structure of reversing crest-ripples is not well known. Presumably, with bed aggradation, they
will form laterally and vertically alternating (or at least varying) sets of cross-strata that dip in opposing directions.

current - dominated wave - dominated

Current Combined - Flow Oscillation

Ripples Ripples Ripples

Figure 6-12. Plan view of ripples produced on beds of 0.28 mm sand by current, waves and combined flows. Note that net
flow is from right to left and the boxes are 75 cm across. After Harms (1969).

The asymmetrical ripple form, if preserved, should distinguish this form of such cross-stratification from that
produced by 2-D vortex ripples.


This brief section relies heavily on the results of recent work on the bedforms and stratification that develop
under combined oscillatory and unidirectional flows. The flows considered are the result of the superposition of
wave-generated currents (see above) on simple unidirectional currents to produce temporal variation in flow
strength (e.g., velocity) as shown for combined flows in figure 6-1. Because this section is brief, the description
of both bedforms and their stratification will be combined.

Figure 6-12 shows the differences in plan form of wave ripples (2-D vortex ripples; formed under purely
oscillatory flows), current ripples (produced under purely unidirectional flows) and combined flow ripples. Note
that the major differences are the smaller spacing, straighter crests of wave ripples, and symmetrical profile of wave
ripples, compared to combined flow and current ripples, and the changes are gradual from one ripple type to the
other. Internal stratification may reflect the differences in ripple behaviour: current ripples may have better
developed unimodal dip directions of internal cross-strata. However, as noted above, true wave ripples may also
migrate in one direction to produce similarly unimodal-dipping internal cross-strata.

Figure 6-13 is based on experimental work by Arnott and Southard (1989) who used a combined flow wave
duct to simulate waves with an 8.5 second period acting on a bed of very fine sand. The apparatus was similar to
that used to simulate purely oscillatory flows but included a recirculating pump to induce a unidirectional current
within the duct. The graph shown in figure 6-13 is one of many such graphs that could be constructed for combined
flow, each representing a narrow range of grain size and wave periods. The sequence of bedforms along the vertical
axis is the sequence described for purely oscillatory flows (note that they did not go to high enough maximum orbital
velocities to produce a wave-formed flat bed). Note also, that this figure suggests that there is a gradual transition
from 2-D vortex ripples to 3-D vortex ripples and current ripples. The large 3-D vortex ripples have been termed
hummocky ripples in an attempt to emphasize that these bedforms likely produce the hummocky cross-stratification
that is common in the geologic record of shallow marine sediments. These hummocky ripples appear to be stable

10 cm scale in
ripples Figure 6-13. Very schematic illustration show-
ing the bedforms and their internal stratifica-
Maximum orbital speed (m/s)

tion produced in a duct by combined flows with

Flat bed an oscillatory component with a period of 8.5
seconds acting on a bed of very fine sand. Note
0.6 3-D dunes that structures along the vertical axis are formed
under purely oscillatory flows and structures
Low angle high angle along the horizontal axis are formed under
purely unidirectional flows. After Arnott and
ition 3-D ripples Southard (1989) and Duke, Arnott and Cheel
2-D r al
0.2 ipples (1991).
no movement current ripples
0 .04 .08 .12 .16 .20 .24
Unidirectional current speed (m/s)

only under purely oscillatory flows or under combined flows with only a very weak unidirectional component. When
the velocity of the unidirectional component of a combined flow is only a few percent of the oscillatory velocity
the hummocky bedforms become asymmetric in profile and migrate in the direction of the unidirectional component,
producing low angle inclined cross-strata that are isotropic (dip in one direction in contrast to the anisotropic dip
of hummocky cross-strata). With a further increase in the strength of the unidirectional component the bedforms
become steeper and more asymmetric and produce high angle cross-stratification. Note that these large bedforms,
formed under combined flows are termed dunes in figure 6-13 (they were termed “large ripples” in the original paper
by Arnott and Southard, 1989) and that they form under much lower unidirectional velocities than under purely
unidirectional flows because of the superimposed oscillatory current. Indeed, combined flows appear to produce
large, dune-like bedforms that would not develop under purely unidirectional flows over fine sand. In addition, the
superposition of an oscillatory component reduces the threshold unidirectional flow strength required to produce
upper plane bed (or flat bed).

Figure 6-14 is similar to figure 6-13 but includes a wider range of orbital and unidirectional flow velocities
and figure 6-15 schematically shows the forms of cross-stratification produced by the various bedforms. Figure
6-15 indicates that there is a more-or-less gradual change in the styles of cross-stratification produced by oscillatory
and combined flows but that the overall geometry of the stratification should provide a basis for distinction of the
generating flow types. However, this work is currently in its infancy and will require further experimentation and
observations from the ancient record before we have a good foundation for interpreting the formative processes
that produce these primary structures.


Note: Earlier in this chapter we introduced a form of cross-stratification termed hummocky cross-stratification (HCS) and
attributed its formation to the presence of 3-D vortex ripples on an aggrading bed. This view of HCS is one of several that appear
in the literature and the debate on the origin of this primary sedimentary structure is ongoing. This section aims to focus on
HCS and to show that its interpretation is not so straight-forward.

Hummocky cross-stratification became popular during the late 1970’s and early 1980’s as its widespread
recognition followed description by Harms et al. (1975), although it had been earlier reported under different names
(e.g., truncated wave-ripple laminae, Campbell, 1966; crazy bedding, Howard, 1971; truncated megaripples, Howard,
1972). The presence of HCS has since become a prime criterion for the recognition of ancient shallow-marine storm
deposits; however, its reliability as an unequivocal criterion for this environment is now less certain. Despite the
fact that HCS is widely accepted to be the product of waves, the structure continues to be the focus of ongoing
debate regarding its mode of formation and, by implication, its specific paleohydraulic interpretation. HCS in marine
deposits has been variously attributed to formation by oscillatory flows produced by waves, combined oscillatory
and unidirectional flows, and purely unidirectional flows. This diversity of hypotheses for HCS formation is justified



Oscillatory flow dominant
Large 3-D ripples

Maximum orbital speed (cm/s)

weakly asymmetrical

60 Plane bed (flat bed)

3-D dunes


40 asymmetrical
3-D dunes
weakly asymmetrical
3-D ripples

3-D ripples


small, strongly asymmetrical Unidirectional flow dominant

10 no 3-D ripples
asymmetrical 3-D ripples

0 10 20 30 40 50 60 70 80 90 100
Unidirectional flow velocity (cm/s)

Figure 6-14. Extended bedform stability diagram for combined flows with an 8.5 second period oscillatory component acting
on a bed of fine sand. Compare with figure 6-15 for the forms of cross-stratification produced under the conditions shown.
After Myrow and Southard (1991).

Plane bed

Figure 6-15. Highly schematic

illustration showing the forms of
cross-stratification produced by
symmetrical dunes (HCS)
Weakly asymmetrical combined flows with an 8.5 sec-
dunes (anisotropic HCS?)
Increasing strength of oscillatory component

ond period oscillatory component

strongly asymmetrical dunes
(large-scale trough cross-stratification) Plane bed acting on a be dof fine sand. Com-
symmetrical ripples
pare with figure 6-15. Based on
(small-scale HCS ?)
Myrow and Southard (1991).
weakly asymmetrical ripples
(small-scale anisotropic HCS?)

2-D symmetrical ripples

(wave-ripple cross-lamination)
strongly asymmetrical ripples
(small-scale trough cross-stratification)

Current ripple cross-lamination Plane bed


Increasing strength of unidirectional component


because the basis for its interpretation is not as sound as that for many other sedimentary structures that are readily
visible in modern settings or produced in laboratories. For example, our knowledge of the relationship between
paleohydraulics and stratification formed under unidirectional flows is quite advanced because we can easily
dissect recognizable bedforms developed under known hydraulic conditions in rivers, intertidal areas and flumes,
to precisely document the geometry of their internal structure. In contrast, HCS is found largely in ancient sediments
and sedimentary rocks where paleohydraulic conditions must be inferred from associated deposits and structures.
Thus, HCS has been largely interpreted on the basis of inference rather than direct observation of the relationship
between hydraulic processes and the form of the structure. The argument over the origin of HCS has been further
complicated by the recognition of similar forms of stratification in settings in which wind-generated water surface
waves were an unlikely mechanism in its formation. The growing range of physical settings in which HCS-like
stratification may have formed may justify the suggestion (Allen and Pound, 1985) that HCS has become just a
“bucket term” that embodies similar stratification styles that may be generated by a variety of processes or
combinations of processes.

This section of these notes aims to describe HCS, in detail, and indicate that there is no consensus at this
time as to the exact origin of this form of cross-stratification although recent data points to an origin of HCS under
purely or strongly oscillatory dominant flows.

HCS — description and associations

Because of the paucity of modern and experimental examples of HCS, its paleohydraulic interpretation has
largely been based on its preserved characteristics in the geological record. The following description will review
the basis for the recognition of HCS, including its common stratigraphic and sedimentologic associations, and
stress characteristics that have led to the various ideas on HCS formation.

Characteristics of HCS

Grain Size

The grain size of sediment in which HCS occurs varies from coarse silt to fine sand (Dott and Bourgeois,
1982; Brenchley, 1985; Swift et al., 1987). HCS in coarser sediment is relatively rare but has been reported. Brenchley
and Newall (1982) described HCS in sandstones with mean grain sizes ranging from 0.7 - 1.1 mm (i.e., up to coarse
sand). Walker et al. (1983) noted that gravel may comprise beds displaying HCS. However, in cases where gravel-
size sediment is present in HCS, the gravel normally makes up a small proportion of the total grain size distribution
and is found largely as lag-deposits on surfaces within or at the base of beds displaying HCS. Therefore, the
consensus seems to be that HCS is most common in very fine to fine-grained sand with the frequency of its
occurrence decreasing dramatically with increasing grain size.

Morphology and geometry

Harms et al. (1975, p. 87) provided an early description of HCS (Fig. 6-11A) that has remained fundamental
over the years (cf. Harms et al., 1982). They pointed to four essential characteristics of individual cross-strata sets
as being: (1) low-angle (generally less than 10° but up to 15°), erosional bounding surfaces; (2) internal laminae
that are approximately parallel to the lower bounding surface; (3) individual internal laminae that vary systematically
in thickness laterally and their angle of dip diminishes regularly; (4) dip directions of internal laminae and scoured
surfaces are scattered (i.e., dipping with equal frequency in all directions). They also postulated that the
stratification was due to deposition on a scoured bed surface characterized by low hummocks (bed highs) and
swales (bed lows) with a spacing of one to a few metres and with a total relief of between 10 and 50 cm. Hence,
the form of the internal stratification was one of convex-upward hummocky laminae and concave-upward swaley
laminae, essentially draped over the hummock and swale topography of the basal scoured surface (Fig. 6-11B).

Following Campbell (1966), Dott and Bourgeois (1982) employed a hierarchy of surfaces (Fig. 6-11B) to
provide a careful description of HCS based on their observations. Here we employ their descriptive terms but details
also come from other sources (Bourgeois, 1980; Hunter and Clifton, 1982; Brenchley, 1985).

First-order surfaces are surfaces of lithic change in discrete HCS beds (discussed below) and may bound
HCS cosets or beds containing a sequence of various structures. The basal surface is commonly nearly flat and
erosional, although local relief, up to several tens of centimetres may occur due to the presence of tool marks
(scratches, grooves, prod-marks), gutter casts and/or rare flutes. This surface may be mantled with a lag of coarse
debris of inorganic (intraclasts and/or extraclasts) or biogenic origin (e.g., shell or bone material). In some instances,
the upper surface is deeply-scoured with a hummocky appearance whereas in many other cases this surface is
rippled. Cosets of HCS range from decimetres to several metres in thickness, although the thickest cosets may
actually consist of several amalgamated beds.

Second-order surfaces are erosional surfaces within HCS cosets and are normally responsible for the form
of the stratification. They cut third-order surfaces but are contained by the first-order surfaces and therefore bound
HCS sets (Fig. 6-11B). These surfaces commonly form the distinctly “hummocky” surfaces in HCS that are
characterized by laterally alternating synforms (swales) and antiforms (hummocks), although the antiforms are
generally less common than the synforms. The relief on second-order surfaces ranges from several centimetres
to approximately 50 cm (the same relief reported for hummocks and swales) with rare, extreme dip angles of up to
35°. HCS sets range from several centimetres up to two metres in thickness although the latter extremes are probably
the result of the amalgamation of beds. The erosional character of these surfaces may be obvious where relatively
sharp, angular discordances occur between second and third-order surfaces or may be subtle where third-order
surfaces are nearly tangential with second-order surfaces. The angular relationship commonly varies laterally,
giving second-order surfaces the appearance of changing from discordant to concordant surfaces along an
individual bed. The visibility of second-order surfaces is due largely to their angular relationship with underlying
strata. A change in grain size is typically not evident across second-order surfaces although they may be mantled
by dispersed shale and/or siderite rip-up clasts, pebbles and shell debris. Such surfaces, exhumed in outcrop,
typically display the hummock and swale topography described above. Most commonly, the plan form of
hummocks and swales is circular, although elongate forms have also been reported (e.g., Handford, 1986). Exhumed
second-order surfaces may display forms of parting lineation including parting-step lineation (McBride and Yeakle,
1963) and current lineation (Allen, 1964).

Third-order surfaces bound individual laminae within HCS sets and account for many of the diagnostic
characteristics of this structure although their visibility may depend on such fortuitous factors such as the degree
of weathering of the outcrop and cementation. Third-order surfaces are nearly concordant with underlying second-
order surfaces which normally determine their overall geometry of internal laminae. Angles of dip are typically
highest directly above erosional second-order surfaces but decrease upwards. Third-order surfaces are commonly
mantled by mica, clay or comminuted plant debris (in many post-Silurian examples). Laminae defined by third-order
surfaces tend to pinch and swell laterally and are most commonly thickest within swales, thinning upwards over
hummocks. Individual laminae may or may not display internal grading, depending largely on the sorting of sand-
size particles; well-sorted sand may not have a sufficiently wide range of grain sizes available to develop visible
grading. For example, Bourgeois’ (1980) observations of the Upper Cretaceous Cape Sebastian Sandstone of
southwest Oregon reported centimetre-scale internal laminae in which grading was not detectable. However,
Hunter and Clifton (1982), also working on the Cape Sebastian Sandstone, noted that under certain conditions,
light/dark couplets that comprise the internal laminae bore characteristics that suggested that they were normally
graded. Like second-order surfaces, exhumed third-order surfaces may display various forms of parting lineation.

The scour and drape form of HCS is the most common variety of this structure although other forms have
also been recognized, including vertical accretionary forms and migrating forms (Fig. 6-16). Several workers (e.g.,
Hunter and Clifton, 1982; Bourgeois, 1983; Brenchley, 1985; Allen and Underhill, 1989) described vertical
accretionary HCS in which internal laminae thickened over hummocks rather than swales. As such, the hummocks
appeared to have grown by accretion rather than formed by erosion of second-order surfaces. However, this
“accretionary” HCS was thought to be relatively rare. A variant of this form of HCS displays internal laminae that
parallel the hummock and swale morphology of second order surfaces (e.g., Allen and Underhill, 1989). Another
type of HCS, described by Nöttvedt and Kreisa (1987) and Arnott and Southard (1990), is characterized by low-
angle cross-strata sets (generally >5 cm thick) filling shallow scours (swales) and which have a preferred, unimodal
dip direction; hummocks are generally rare to absent. This latter structure has been termed “low angle trough cross-

Forms of HCS in shallow-marine sandstones

Oscillatory to oscillatory-
dominant combined flow

Scour and
Isotropic HCS


cm - dm



Figure 6-16. Schematic illustration showing the various forms of hummocky cross-stratification. Note that the unidirec-
tional component of the flow forming anisotropic HCS is from right to left. See text for discussion.

stratification” by Nöttvedt and Kreisa (1989) and “anisotropic” HCS by Arnott and Southard (1990) in contrast
to the more common isotropic HCS.

The adherence by later workers to the essentials of the definition of HCS given by Harms et al., 1975) above
has been a matter for some debate. For example, Brenchley (1985) reported slopes on hummocky surfaces up to
35° and spacings as small as the spacing of wave ripples (i.e., centimetres). These deviations from the original
definition have led some to suggest that these smaller forms (commonly termed micro-HCS) are not true HCS as
Harms et al. (1975) had defined it. For example, Duke (1987, p. 345) argued that HCS-like stratification with hummock
spacings below the “1 m lower limit assigned to HCS by Harms et al. (1975)” is not true HCS. However, the first
experimentally-produced analogs of HCS identified by Harms et al. (1982) had spacings on the order of a couple
of decimetres (and Harms et al., 1982, point out the discrepancy with HCS observed in the field). The scale of HCS
may or may not be a limiting factor in defining HCS but may represent a natural variation in scale that reflects the
breadth of conditions over which this structure may form. Sherman and Greenwood (1989; p. 985) emphatically
state that “there is no apparent physical rationale for the 1 m lower limit on hummocky cross-stratification
wavelength” and Campbell (1966) suggested that hummocks may occur with wavelengths of 0.1 to 10 m.
Alternatively, many of the examples of HCS that differ significantly from the form defined above may represent
similar stratification styles that formed by different processes. The breadth of variation in form of HCS that has
grown in the literature may be partly responsible for the similar proliferation of ideas regarding its mode of formation
that is discussed below.

HCS associations

With the onset of widespread recognition of HCS, several studies reported its occurrence in particular
associations with other structures (e.g., Hamblin and Walker, 1979; Dott and Bourgeois, 1982; Brenchley, 1985).
The most common occurrences of HCS in the ancient record can be classified into two such associations: (1) discrete
sandstone beds interbedded with mudstones (commonly termed HCS storm beds), and (2) amalgamated sandstones;
however, specific associations vary widely in nature (cf. Dott and Bourgeois, 1983).

Discrete HCS sandstones

Dott and Bourgeois (1982) were the first to propose an “ideal sequence” or model showing structures that

are preferentially associated in outcrop within sandstone beds containing HCS; an ideal sequence that began a
lineage of such sequences for HCS sandstones. This sequence consisted of sharp-based sandstone interbedded
with bioturbated mudstone; the basal-scour surface includes sole marks and is mantled by a lag of coarse debris
overlain by an interval of hummocky cross-stratification passing upward into flat lamination and ultimately to cross-
laminae associated with symmetrical ripple forms that cap the sandstones. A similar sequence of associations was
proposed by Walker et al. (1983) which differed in detail from that proposed by Dott and Bourgeois (1982; 1983)
by the occurrence of a basal parallel (horizontal to sub-horizontal) laminated interval directly overlying the basal
erosional surface. The evolution of the model continued as more observations were made and data collected. For
example, figure 6-17 (Leckie and Krystinik, 1989) shows a recent version of the early ideal sequences and contains
considerably more information and more variability than the earlier sequences; the new information includes the
occurrence of parting lineation on surfaces within HCS, paleocurrent relationships and a range of ripple types
capping the beds, from purely wave-formed ripples through to purely current ripples. The trend of the parting
lineation is generally orthogonal to wave-ripple crests and sub-parallel to sole marks at the bases of hummocky
beds (e.g., Brenchley, 1985; Leckie and Krystinik, 1989). Rarely, a polymodal trend of parting lineation has been
observed on second or third-order surfaces (D.A. Leckie and L.F. Krystinik, unpublished observations). Capping
wave-ripples are typically straight crested with bifurcating patterns, although irregular forms are not uncommon,
including: polygonal, ladderback and box patterns (all forms of interference ripples). In addition, Leckie and
Krystinik (1989) include directional relationships between structures in the HCS beds with regional shoreline and
paleoslope (Fig. 6-17). Specifically, they showed that directional structures such as sole marks and parting lineation
indicate paleoflows directed offshore, orthogonal to regional shoreline-trend indicators. Similarly, capping ripples
have crests aligned approximately parallel to regional shoreline and the internal cross-laminae, when present,
indicate migration offshore. Such relationships had been suggested earlier on the basis of local studies (e.g.,
Hamblin and Walker, 1979; Brenchley 1985, Rosenthal and Walker, 1987) but data provided by Leckie and Krystinik
(1989) suggested that the directional associations may be the norm for discrete HCS sandstones.

Amalgamated HCS Sandstones.

This association of HCS is characterized by thick (up to several tens of metres) sandstones and differs from
the other association by the lack of mudstones (except as local lenses) and the absence of a preferred sequence
of structures. Amalgamated HCS commonly occur above the discrete HCS beds in regressive shoreline
successions (e.g., Hamblin and Walker, 1979; Leckie and Walker, 1982) and is representative of sedimentation in
the lower shoreface. First-order surfaces may be recognized within amalgamated sandstone beds by the presence
of a lag or where they overlie intensely bioturbated horizons, discontinuous mudstone beds or concentrations of
mica and fine plant debris.

Swaley cross-stratification, as originally defined by Leckie and Walker (1982), is not the amalgamated HCS
as described here, although there is a growing tendency amongst some authors to state this. For example, Dott
and Bourgeois (1983), McCrory and Walker (1986) and Plint and Walker (1987) suggest that the swaley cross-
stratification is typical of amalgamated sandstone beds. Duke (1985, p. 171), however, specifically stated that
swaley cross-stratified sandstones do not show evidence of amalgamation. In a vertical, progradational succession
discrete HCS is overlain by amalgamated HCS which, in turn, is overlain by SCS.

The HCS Debate

When Harms et al. (1975) first introduced HCS they suggested that the structure was the product of the
interaction of waves with a sandy substrate during powerful storms (i.e., the waves that produced HCS were
particularly large and powerful). Emplacment of sand by storms is widely accepted because discrete HCS bed,
encased in shale, must represent extreme sediment transport events that introduced sand into a marine setting that
received only deposition of mud during periods of “normal sedimentation”; storms are known to provide such a
mechanism of sand emplacment. The specific depositional setting of the HCS storm beds is thought to be at depths
above 200 m (the approximate maximum depth of the continental shelf) but blow the depth where normal, fairweather
waves will affect a sediment substrate (i.e., below effective fairweather wave base). This setting is suggested by
the normal mud deposition and by the trace fossils and body fossils associated with HCS storm beds. In support
of a storm origin are estimates of the recurrence intervals of emplacement of the sands forming discrete storm beds.

Figure 6-17. Ideal sequence of structures found in HCS storm beds. See text for discussion. From Leckie and Krystinik (1989).

Table 6-2 shows that independent estimates suggest that HCS storm beds are emplaced only every few thousand
years. Hence the intensity of storms that transported the sand out onto the shelf and formed the sequence of
structures within the deposits were likely of an intensity not yet recorded. However, as more became known about
HCS the role of waves in its formation became less certain. Particularly, the presence of unidirectional paleocurrent
indicators (such as sole marks on the bases of HCS storm beds), along with the recognition of anisotropic HCS,
suggested that unidirectional currents may play a role in forming this structure. The importance of unidirectional
currents in the emplacement of HCS storm beds in settings that normally received mud is obvious: the sand is
transported offshore, from beach and near-shore environments where it dominates during fairweather conditions,
and such transport requires a directed current (i.e., a unidirectional current). Furthermore, such unidirectional
currents are well known to modern oceanographers who have measured their intensity during historically moderate
to large storms.

In light of the recognition of the importance of unidirectional currents in emplacing HCS storm beds several
new mechanisms of HCS formation were proposed, stressing the importance of unidirectional currents. Swift et
al. (1983) reported HCS on modern shelves in 15 to 40 m water depth. Their examples of HCS collected from wave-
modified dunes that formed under combined flows, with a powerful unidirectional component, generated by storms.
Box cores taken from the bedforms displayed wedge-shaped sets of heavy mineral-rich laminae in fine to very fine-
grained sands. Swift et al. (1983) explained the wedge-shaped sets as curved lamina intersections and likened the
structure to HCS. Hence, the HCS was attributed to combined flows, and specifically to wave modification of what
would have otherwise been dunes under unidirectional flows. Elsewhere, Greenwood and Sherman (1986)
suggested that, in a lacustrine setting, a unidirectional flow (in their case, a longshore current) was crucial to the
formation of HCS. They argued that without the combined-flow component, purely oscillatory waves would only
produce flat-bed conditions. Similarly, Allen (1985) argued convincingly on theoretical grounds that oscillatory
currents alone could not form hummocky bedforms of metre-scale wavelength, the development of which required
a unidirectional current.

The above debate progressed on the basis of inference from the ancient record and from observations in

Table 6-2. Estimates of recurrence intervals between events (storms?) that emplaced HCS storm beds.

Age Recurrence Interval Author

Kimmeridgian 3,200 - 4,000 years Hamblin and Walker (1979)

Walker (1985
Devonian 400 - 2,000 years Goldring and Langenstrassen (1979)
Ordovician 10,000 - 15,000 years Brenchley et al. (1979)
Triassic 2,500 - 5,000 years or Aigner, 1982
5,000 - 10,000 years
Ordovician 1,200 - 3,100 years Kreisa, 1981

the modern , shallow-marine environments where no unequivocal HCS could be identified. Over 1990-91 the results
of two different approaches to the study of HCS were reported that added more factual knowledge of HCS that
pointed to a return to the original ideas on HCS formation under waves. The new data included experimental studies
and studies of grain fabric in HCS sandstones.

Experimental Evidence

Southard et al. (1990) conducted experiments in a wave duct that produced three-dimensional bedforms
(large, 3-D vortex ripples) that behaved in such a way under the purely oscillatory currents that they would produce
a form of stratification that very closely resembled HCS observed in the ancient record (Fig. 6-18). This experimental
evidence showed that purely oscillatory flows could form HCS but did not rule out the possibility that combined
flows could also produce this structure. However, the combined-flow experiments of Arnott and Southard (1990)
appeared to eliminate combined flows as having an important role in forming HCS. In their experiments, symmetrical
bedforms could only be produced under purely oscillatory flows or combined flows with a negligible unidirectional
component (Fig. 6-13). As soon as the velocity of the unidirectional component exceeded a few percent of the
maximum orbital velocity the bedforms became asymmetrical and the stratification that they produced would appear
as anisotropic HCS. These experiments suggested that combined flows with strong unidirectional currents could
not form HCS, in contrast to the result of Allen’s theoretical analysis and the suggestions of oceanographers.

Evidence based on grain fabric

A detailed study of grain fabric (Fig. 6-19) was reported by Cheel (1991) based on samples oriented with
respect to sole marks on the base of discrete HCS sandstone beds interbedded with shale. This study showed
that particle a-axes, measured in plan view (Fig. 6-19A) varied widely but displayed modes oriented approximately
normal to sole marks and parallel to the associated ripple crest. This suggests that a-axis alignment of grains in
HCS develops by rolling (a-axes transverse to the oscillatory current) and the wide variation in a-axes orientation
points to deposition under a complex array of surface gravity waves with a mode aligned parallel to the shoreline.
In vertical section through HCS sandstones imbrication of grains varied about a mean of 0°, parallel to visible
lamination (Fig. 6-19B). In some cases, this variation in imbrication was markedly cyclic about the 0° mean. This
pattern of imbrication was interpreted in terms of the action of symmetrically oscillating currents during the

Figure 6-18. HCS simulated from large 3-D vortex ripples. Total length of bed shown in 2.15 m. From Southard et al.




D 0
-90 0 90
ANGLE ( ˚ )

A 294 L



C 1

-90 0 90
ANGLE ( ˚ )


Figure 6-19. Grain fabric in a hummocky cross-stratified sandstone. A. Apparent grain long axes as seen in plan view on surfaces
cut parallel to bedding. B and C. Apparent grain long axes seen in vertical section on surfaces cut perpendicular to bedding
and parallel from inferred flow direction. Note that the relative positions of A and B are shown in the block diagram.

formation of isotropic HCS. In contrast, in the basal parallel-laminated interval of an HCS bed, the mean particle
imbrication was approximately 13° into the flow direction (based on the sole marks) and varied quasi-cyclically about
that mean (Fig. 6-19C). The interpretation of this pattern of variation in fabric suggested that an offshore-directed
unidirectional current was active during deposition of the horizontally-laminated portion of HCS storm beds
(producing the onshore imbrication). However, when the HCS formed this unidirectional component had either
stopped or had become too weak to influence grain fabric. Thus, in the HCS storm beds it appeared that HCS forms
in response to oscillatory flows, the same conclusion that arose from the experimental evidence.

Origin of HCS?

Given the above interpretation of HCS storm beds we must explain the different forms of HCS that have been
observed (Fig. 6-20). The HCS storm beds displaying isotropic HCS form as sediment is delivered onto the shelf
by offshore-directed combined flows generated by storms; combined flows with powerful oscillatory components
due to large gravity waves and offshore (or offshore-oblique) unidirectional components. Such currents are well-
known to modern oceanographers, although their directional relationship to the shoreline is more complex than
described here (see Duke 1990 for a full discussion). While the unidirectional component of the current is active
not only is the sediment transported offshore but erosion of the substrate occurs, forming the basal solemarks
oriented onshore-offshore and any directional solemarks (such as flutes and prod marks) are directed offshore.


cm - dm




Figure 6-20. Schematic illustration of the temporal variation in currents involved in the formation of HCS storm beds. See
text for discussion. After Cheel (1991), Duke, Arnott and Cheel (1991) and Cheel and Leckie (1992).

With the onset of sand deposition conditions are initially on a flat bed (which has a wide stability field under
combined flows; see Fig. 6-14) but this bed state is replaced by large, 3-D vortex ripples as the unidirectional current
wanes and only a powerful oscillatory current continues. Deposition under this oscillatory flow forms isotropic
HCS. As the oscillatory flow wanes small, 2-D vortex ripples are formed, capping the sandstone. Under fairweather
conditions, following the storm, muds are deposited, encasing the storm-deposited sandstone bed.

The above scenario accounts for much HCS associated with HCS storm beds but it does not explain the
variety of forms of HCS shown in figure 6-16. Certainly, the isotropic forms are likely formed by oscillatory currents.
However, the interaction of these currents with a sandy substrate must differ in detail to produce scour and drape
versus vertical accetionary HCS. In the case of the scour and drape form of HCS the fact that internal laminae drape
and diminish the hummocky relief suggests that a hummocky bedform is not stable under conditions that form the
structure but are only stable during periods of intense flow that causes erosion of the hummocky surface. Such
erosion during a storm might occur due to the temporary development of constructive waves on the water surface.
Swift et al. (1983) described the generation of thick clouds of sediment that rose off the bottom during a storm with
the passage of groups of exceptionally high waves formed by constructive interference. The formation of these
clouds must involve the local addition of sediment into suspension by erosion that might form hummocky second-
order surfaces. Between periods of wave construction the “normal storm waves” would act as sediment continued
to deposit, causing the temporal variation in flow strength that results in the formation of internal laminae. In this
scenario the hummocky surface is not due to the generation of a stable bedform but is inherited from the form of
an erosional surface, a surface that might mimic the morphology of the stable bedform under the same conditions
but with net deposition on the bed. Subsequent deposition of sediment onto the hummocky erosional surface acts
to bring the topography into equilibrium with the normal storm-wave conditions (and this equilibrium bed appears
to be more-or-less flat). Hence, the currents that produce the hummocky form are associated with erosion, during
the most intense conditions on the bed.

Vertical accretion forms (Fig. 6-16), characterized by thickest laminae within hummocks, appears to involve
the growth of a depositional hummocky topography. This type of HCS might represent the product of currents,
possibly produced by sustained constructional waves that are less transient than the case of scour and drape.
Under conditions of rapid deposition, such sustained currents, capable of building a stationary hummocky bedform
that is in equilibrium with the prolonged, oscillatory currents generated by the constructional waves, would form
vertical accretionary sets. Hummocky bedforms that would produce such stratification were produced under purely
oscillatory flows and strongly oscillatory combined flows by Arnott and Southard (1990). In this case, a true
bedform is constructed under conditions of net aggradation.

The low angle migratory forms (Fig. 6-16) may represent similar bedforms that form accretionary HCS but
which migrate over the substrate, preferentially preserving internal laminae that dip in the direction of migration
(Nöttvedt and Kreisa, 1982). Arnott and Southard (1990) produced stationary and migrating bedforms experimen-
tally in a wave duct. The stationary forms were stable under oscillatory flows and strongly oscillatory-dominant
combined flows. However, migrating forms developed when the velocity of the unidirectional component exceeded
a few percent of the orbital velocity of the oscillatory component. Hence, anisotropic HCS may be interpreted to
indicate the influence of a unidirectional component of a combined flow under conditions that would otherwise form
isotropic HCS.


The debate over the origin of HCS continues and has become more perplexing over the same period that
new evidence for a wave-induced origin. Work by Rust and Gibling (1989) and Prave and Duke (1990) provided
examples of cross-stratification that appears like HCS but was produced by three-dimensional in-phase waves. Now
we have an HCS-look-alike. The paleoenvironmental interpretation of each structure is radically different; HCS
formed by in-phase waves is definitely indicative of unidirectional flows whereas the shallow marine forms of HCS
appear to have been largely influenced by waves. The most promising approach to distinguishing the two forms
is through detailed studies of grain fabric and this research is on-going and the general debate continues.

APPENDIX 1: Standard procedure for sieve analysis of sand

One of the fundamental problems encountered by a sedimentologist is in the description of the size of
particles which make up sediments and sedimentary rocks. A good description of particle size is important for
a number of reasons: (1) description provides a basis for comparison with other deposits, (2) size and/or
sorting (in part) will control the porosity and permeability of a rock, and (3) size, sorting, etc., reflect the
processes that were active in the depositional environment.

This appendix illustrates the standard procedure for determining the size distribution of particles in an
unconsolidated sediment by passing them through stacks of nested sieves with square openings of known


Note that samples that include a considerable amount of silt and clay size sediment (i.e., <4 φ) should
normally be wet-sieved, that is, washed through a 4φ screen to remove all particles finer than 4 φ. The size
distribution of the material that passes through that screen can be determined by the pipette method or by
analyzing the mixture with a sedigraph.

Step 1. Using a sample splitter obtain approximately 30 to 50 g of sample for sieving. Weigh a beaker on the
scale and record that weight on the Sieve Data Sheet. Pour the portion of the sample to be sieved into the
beaker and determine the combined weight of the sediment plus beaker. Record this weight on the Sieve Data
Sheet. Determine the absolute weight of sediment to be sieved and record this weight on the Data Sheet. Save
the remaining portion of the sample in a labeled sample bag.

Step 2. Select sieves to be used (in this case -1.0φ to 4φ at 0.5φ intervals) and nest them in their proper order,
coarsest at the top, pan at the bottom. Hand sieve, for three minutes, a small stack consisting of the coarsest
sieves, down to 0φ. The remaining sand should be poured onto the top sieve in the remaining stack for sieving
on the sieve shaker.

Step 3. Place the stack of sieves onto the sieve shaker and place the three-armed bracket on the lid of the stack.
Lower the straight-arm bracket and make sure that the end pins are penetrating appropriate holes on the frame
so that the stack is secure. Set the timer to 15 minutes and turn the power switch to the “on” position.

Step 4. When the shaker has turned itself off empty the contents of each sieve, one at a time, onto a piece of
glazed white paper. Invert the sieve and strike it sharply on the paper to dislodge any sand grains that are lodged
in the mesh. With the soft brush, gently, wipe the bottom of the screen so that all of the relatively loose grains
fall back through the mesh and onto the paper. Never wipe the top of the screen with the brush as this may force
grains that are too large to pass through the screens, damaging the mesh. Carefully pour all of the sand from
that size fraction into the appropriate plastic beaker and place the beaker into the beaker holder. If the finest
screen in your stack is not 4φ then pour the contents of the pan into the top screen on a second stack. If the
finest screen is 4φ then pour the contents of the pan into the appropriate plastic beaker.

Step 5. Weigh the sediment in each size fraction (recording the weight on the Sieve Data Sheet) and return the
sieved fraction to the original sample bag. (Note that you would normally store the sand from that sieve
fraction in a labeled plastic bag; e.g., Sample 1, .5φ to 1.0φ .) Repeat the procedure for each of the sieve
fractions and the contents of the pan.

Step 6. Determine the weight of sediment in each size fraction and the proportion of sample that was lost
during sieving (from the total summed on the sieve data sheet and the total initially poured into the sieves).
Calculate the percentage (by weight) for each fraction and the cumulative weight (%) for the sample. Save this
data for Laboratory two. Hand in your final sieve data sheet with Laboratory 2.

Note: The sample supplied should be almost aggregate-free (i.e., it contains little or no cemented clumps of

sand). Normally a “step 7” would involve using a hand lens to briefly examine each of the size fractions to
determine if there are significant quantities of aggregates. The approximate proportion aggregates, as a per-
centage of the total number of grains in the fraction would be estimated and entered into an appropriate column
on the data sheet. This information would be used to “correct” the percentages calculated for each sieve


Note that a summary of symbols is given at the end of Appendix 2.

1. Flow Reynolds’ Number (R):

2. Froude Number (F):

3. Boundary shear stress (τo): τo = ρgDsinθ

4. Shear velocity (U*):

5. Law of the wall for rough boundaries:

Note that for closely packed spheres of uniform size yo=d/30. Mean velocity of a turbulent flow
occurs at a height of 0.4D above the bed.

6. Boundary Reynolds’ Number (R*):

R* is used to classify boundaries of turbulent flows based on the relationship between the rough-
ness of the boundary (grain size of the sediment comprising the bed material) and the thickness of
the viscous sublayer (δ), where:

When R*< 5 the boundary is smooth (δ > d), when 5 < R*T < 70 the boundary is transitional, and
when R* > 70 the boundary is rough (δ < d).

7. Shields’ criterion for sediment movement:


and find the corresponding value of β on Shields’ diagram (Fig. 4-17, a copy will be supplied for
tests), where:

and solve for

8. Middleton’s criterion for suspension: A particle will go into suspension when U* > ω. The
settling velocity of quartz grains with mean size equal to or finer than 0.1 mm may be calculated
using Stoke’s Law of settling:

For quartz grains coarser than 0.1 mm Fig. 4-20 may be used.

Summary of symbols

D flow depth;
d grain size;
F flow Froude Number;
g acceleration due to gravity;
R flow Reynolds’ Number
R* boundary Reynolds’ Number
θ slope of water surface and boundary for uniform, steady flow;
U flow velocity (usually mean flow velocity in the downstream direction);
U* shear velocity;
u mean flow velocity at some height (y) above a boundary;
y some height above a boundary;
yo the height of the roughness elements on a boundary;
β Shields’parameter;
δ thickness of the viscous sublayer;
µ dynamic viscosity;
ν kinematic viscosity (ν=µ/ρ);
ρ fluid density; Note that in one instance, on page 23, p is a logarithmic transformation of
ρs density of a sediment particle;
τo boundary shear stress;
κ von Karman’s constant (normally assume κ=0.4);
ω settling velocity.

References Cited

ALLEN, J.R.L., 1984a, Parallel lamination developed from upper-stage plane beds: a model based on the larger
coherent structure of the turbulent boundary layer: Sedimentary Geology, 39, p. 227-242.

ALLEN, J.R.L., 1984b, Sedimentary structures, their character and physical basis. Vol. 1. Elsevier, New York, 593

ALLEN, J.R.L., 1970, Physical Processes of Sedimentation. George Allen and Unwin Ltd., London, 248 pp.
ALLEN J.R.L., 1968, Current Ripples. Amsterdam, North-Holland Publishing Company, 433 pp.
ALLEN, J.R.L., 1966, On bedforms and paleocurrents: Sedimentology, 6, p. 153-190.

ALLEN, J.R.L., 1964, Primary current lineation in the Lower Old Red Sandstone (Devonian), Anglo-Welsh basin:
Sedimentology, 3, p. 89-108.
ALLEN, P.A., 1985, Hummocky cross-stratification in not produced purely under progressive gravity waves:
Nature, 313, p. 562-564.
ALLEN, P.A., & UNDERHILL, J.R., 1989, Swaley cross-stratification produced by unidirectional flows, Bencliff Grit
(Upper Jurassic), Dorset, U.K.: Journal of the Geological Society of London, 146, p. 241-252.

ALLEN, P.A., & POUND, C.J., 1985, Conference Report: Storm Sedimentation: Journal of the Geological Society of
London, 142, p. 411-412.
ANSTEY, R.L., & CHASE, T.L., 1974, Environments through time. Burgess Publishing Company, Burgess, Minneapolis,
ARNOTT, R.W.C., & HAND, B.M., 1989, Bedforms, primary structures and grain fabric in the presence of suspended
sediment rain: Journal of Sedimentary Petrology, 59, p. 1062-1069.
ARNOTT, R.W.C., & SOUTHARD, J.B., 1990, Exploratory flow-duct experiments on combined flow bed configurations
and some implications for interpreting storm-event stratification: Journal of Sedimentary Petrology, 60, p.

ASHLEY, G.M. (Symposium Chairperson), 1990, Classification of large-scale subaqueous bedforms: a new look at
an old problem: Journal of Sedimentary Petrology, 60, p. 160-172.

BARWIS, J.H., & HAYES, M.O., 1985, Antidunes on modern and ancient washover fans: Journal of Sedimentary
Petrology, 55, p. 907-916.
BEARD, D.C., & WEYL, P.K., 1973, The influence of texture on porosity and permeability of unconsolidated sand:
Bulletin of the American Association of Petroleum Geologists, 57, p. 349-369.
BEST, J.L., & BRIDGE, J.B., 1992, The morphology and dynamics of low amplitude bedwaves upon upper stage
plane beds and the preservation of planar lamination: Sedimentology, 39, p. 737-752.

BLATT, H., MIDDLETON, G.V., & MURRAY, R., 1982, Origin of Sedimentary Rocks. (Second edition) Prentice-Hall, New
Jersey, 782 pp.
BOGGS JR., S., 1987, Principles of Sedimentology and Stratigraphy. Merril Publishing Company, Toronto, 784 pp.
BOURGEOIS, J., 1983, Hummocks - Do they grow? Bulletin of the American Association of Petroleum Geologists,
67, p. 428.

BOURGEOIS, J., 1980, A transgressive shelf sequence exhibiting hummocky cross-stratification: the Cape Sebastian
Sandstone (Upper Cretaceous), southwestern Oregon: Journal of Sedimentary Petrology, 50, p. 681-702.
BRENCHLEY, P.J., 1985, Storm influenced sandstone beds: Modern Geology, 9, p. 369-396.

BRENCHLEY, P.J., NEWALL, G. & STANISTREET, I.G., 1979, A storm surge origin for sandstone beds in an epicontinental
platform sequence, Ordovician, Norway: Sedimentary Geology, 22, p. 185-217.
BRIDGE, J.S., 1978, Origin of horizontal lamination under turbulent boundary conditions: Sedimentary Geology,
20, p. 1-16.
BRIDGE, J.S. & BEST, J.L., 1988, Flow, sediment transport and bedform dynamics over the transition from dunes to
upper-stage plane beds: implications to the formation of planar laminae: Sedimentology, 35, p. 753-763.

BRIDGE, J.S. & BEST, J.L., 1990, Flow, sediment transport and bedform dynamics over the transition from dunes to
upper-stage plane beds: implications to the formation of planar laminae: Reply: Sedimentology, 37, p. 551-553.
CAMPBELL, C.V., 1966, Truncated wave-ripple laminae: Journal of Sedimentary Petrology, 36, p. 825-828.

CHEEL, R.J., 1991, Grain fabric in hummocky cross-stratified storm beds: genetic implications: Journal of Sedimentary
Petrology, 61, p. 102-110.

CHEEL, R.J., 1990a, Horizontal lamination and the sequence of bed phases and stratification under upper flow
regime conditions: Sedimentology, 37, p. 517-530.

CHEEL, R.J., 1990b, Flow, sediment transport and bedform dynamics over the transition from dunes to upper-stage
plane beds: implications for the formation of planar laminae: Discussion of paper by J.R. Bridge and J. Best.
Sedimentology, 37, p. 549-551.

CHEEL, R.J., 1984, Heavy mineral shadows, a new sedimentary structure formed under upper flow regime conditions:
its directional and hydraulic significance: Journal of Sedimentary Petrology, 54, p. 1173-1180.

CHEEL, R.J., and LECKIE, D.A., 1992, Coarse-grained storm beds of the Upper Cretaceous Chungo Member (Wapiabi
Formation), southern Alberta, Canada: Journal of Sedimentary Petrology, 62, p. 933-945.

CHEEL, R.J. and MIDDLETON, G.V., 1986, Horizontal lamination formed under upper flow regime plane bed conditions:
Journal of Geology, 94, p. 489-504.

CLIFTON, H.E., 1976, Wave-formed sedimentary structures - a conceptual model. In: Beach and nearshore
sedimentation (Ed. by Davis Jr., R.A., and Ethington, R.L.) Society of Economic Paleontologists and
Mineralogists, Special Publication No. 24, p. 126-148.
DOBKINS JR., J.E. & FOLK, R.L., 1970, Shape development on Tahiti-Nui: Journal of Sedimentary Petrology, 40, p.

DOTT JR., R.L., 1964, Wacke, graywacke and matrix - What approach to immature sandstone classification? Journal
of Sedimentary Petrology, 34, p. 625-632.

DOTT JR., R.H. & BOURGEOIS, J., 1983, Hummocky stratification: significance of its variable bedding sequences:
Reply: Geological Society of America Bulletin, 94, p. 1249-1251.

DOTT JR., R.H. & BOURGEOIS, J., 1982, Hummocky stratification: significance of its variable bedding sequences:
Geological Society of America Bulletin, 93, p. 663-680.

DUKE, W.A., 1990, Geostrophic circulation or shallow marine turbidity currents? The dilemma of paleoflow patterns
in storm-influenced systems: Journal of Sedimentary Petrology, 60, p. 870-883.

DUKE, W.A., 1987, Hummocky cross-stratification, tropical hurricanes, and intense winter storms: Reply:
Sedimentology, 34, p. 344-359.

DUKE, W.A., ARNOTT, W., AND CHEEL, R.J., 1991, Shelf sandstones and hummocky cross-stratification: New insights
on a stormy debate: Geology, 19, p. 625-628.

FOLK, R.L. & WARD, W.C., 1957, Brazos River Bar: a study of the significance of grain size parameters: Journal of
Sedimentary Petrology, 27, p. 3-26.

FRIEDMAN, G.M., 1967, Dynamic processes and statistical parameters for size frequency distribution of beach and
river sands: Journal of Sedimentary Petrology, 37, p. 327-354.

GILBERT, G.K., 1914, The transportation of debris by running water: U.S. Geological Survey Professional Paper 86,
263 pp.

GOLDRING, R. & LANGESTRASSEN, F., 1979, Open shelf and nearshore clastic facies in the Devonian: Special Papers
in Palaeontology, 23, p. 81-97.

GUPTA, G.D., PARKASH, B., & GARDE, R.J., 1987, An experimental study of fabric development in plane-bed phases:
Sedimentary Geology, 53, p. 101-122.

GUSTAVSON, T.C., 1974, Sedimentation on gravel outwash fans, Malspina Glacier Foreland, Alaska: Journal of
Sedimentary Petrology, 44, p. 374-389.

HAMBLIN, A.P. & WALKER, R.G., 1979, Storm dominated shallow marine deposits: the Fernie-Kootenay (Jurassic)
transition, southern Rocky Mountains: Canadian Journal of Earth Sciences, 16, p. 1673-1690.

HAND, B.M., WESSEL, J.M. & HAYES, M.O., 1969, Antidunes in the Mount Toby Conglomerate (Triassic), Massa-
chusetts: Journal of Sedimentary Petrology, 39, p. 1310-1316.

HANDFORD, C.R., 1986, Facies and bedding sequences in shelf-storm-deposited carbonates - Fayetteville Shale
and Pitkin Limestone (Mississippian), Arkansas: Journal of Sedimentary Petrology, 56, p. 123-137.

HARMS, J.C., 1969, Hydraulic significance of some sand ripples: Geological Society of America, Bulletin, 80, p.

HARMS, J.C., SOUTHARD, J.B. & WALKER, R.G., 1982, Structures and sequences in clastic rocks. Society of Economic
Paleontologists and Mineralogists, Short Course, No. 9, 401 pp.

HARMS, J.C., SOUTHARD, J.B., SPEARING, D.R. & WALKER, R.G., 1982, Depositional environments as interpreted from
primary sedimentary structures and stratification sequences. Society of Economic Paleontologists and
Mineralogists, Short Course, No. 2, 161 pp.

HJÜLSTROM, F., 1939, Transportation of detritus by moving water. In Recent marine sediments (Ed. by P.D. Trask).
American Association of Petroleum Geologists, Tulsa, Oklahoma, p. 5-41.

HOWARD, J.D., 1971, Comparison of the beach-to-offshore sequence in modern and ancient sediments. In Recent
advances in paleoecology and ichnology: Short course Lecture Notes (Ed. by J.D. Howard, J.W. Valantine
and J.E. Warme). American Geological Institute, Washington, B.C., p. 148-183.

HOWARD, J.D., 1972, Trace fossils as criteria for recognizing shorelines in the stratigraphic record. In Recognition
of Ancient Sedimentary Environments (Ed. by J.K. Rigby and W.K. Hamblin). Society of Economic
Paleontologists and Mineralogists, Special Publication No. 16, p. 215-255.

HSÜ, K.J., 1977, Ventura Basin: Bulletin of the American Association of Petroleum Geologists, 61, p. 137-191.

HUMBERT, F.L., 1968, Selection and wear on pebbles on gravel beaches. Unpublished dissertation. University of
Groningen, The Netherlands.

HUNTER, R.E. & CLIFTON, H.E., 1982, Cyclic deposits and hummocky cross-stratification of probable storm origin in
Upper Cretaceous rocks of the Cape Sebastian area, southwestern Oregon: Journal of Sedimentary Petrology,
52, p. 127-143.

JOHANSSON, C.E., 1965, Structural studies of sedimentary deposits: Geol. Föreningens Stockholm Förhandlingar,
87, p. 3-61.

JOHANSSON, C.E., 1975, Structural studies of frictional sediments: Geografiska Annaler, 58A, p. 201-300.

JOPLING, A.V. & WALKER, R.G., 1968, Morphology and origin of ripple-drift cross-lamination, with examples from
the Pleistocene of Massachusetts: Journal of Sedimentary Petrology, 38, p. 971-984.

KENNEDY, J.F., 1963, The mechanics of dunes and antidunes in erodible-bed channels: Journal of Fluid Mechan-
ics, 16, p. 521-544.

KOMAR, P.D., 1987, Selective grain entrainment by a current from a bed of mixed sizes: a reanalysis: Journal of
Sedimentary Petrology, 57, p. 203-211.

KOMAR, P.D., 1976, Beach processes and sedimentation. Prentice-Hall Inc., Englewood Cliffs, New Jersey, 429 pp.

KOMAR, P.D. & MILLER, M.C., 1973, The threshold of sediment movement under oscillatory water waves: Journal
of Sedimentary Petrology, 43, p. 1101-1110.

KRUMBEIN, W.C., 1934, Size frequency distribution of sediments: Journal of Sedimentary Petrology, 4, p. 65-77.

KUENEN, P.H., 1964, Experimental abrasion of pebbles 4: Eolian Action: Journal of Geology, 68, p. 427-449.

LANGFORD, R. & BRACKEN, B., 1987, Medano Creek, Colorado, a model for upper-flow-regime fluvial deposition:
Journal of Sedimentary Petrology, 57, p. 863-870.

LECKIE, D.A. & KRYSTINIK, L.F., 1989, Is there evidence for geostrophic currents preserved in the sedimentary
record of inner to middle-shelf deposits? Journal of Sedimentary Petrology, 59, p. 862-870.

LECKIE, D.A. & WALKER, R.G., 1982, Storm- and tide-dominated shorelines in Cretaceous Moosebar-Lower Gates
interval - outcrop equivalents of Deep Basin gas trap in Western Canada: American Association of Petroleum
Geologists Bulletin, 66, p. 138-157.

LEEDER, M.R., 1982, Sedimentology: process and products. George Allen and Unwin, London, 344 pp.

MCBRIDE E.F., SHEPHERD, R.G. & CRAWLEY, R.A., 1975, Origin of parallel near-horizontal laminae by migration of bed
forms in a small flume: Journal of Sedimentary Petrology, 45, p. 132-139.

MIDDLETON, G.V., 1976, Hydraulic interpretation of sand size distributions: Journal of Geology, 84, p. 406-476.

MIDDLETON, G.V., 1965, Antidune cross-bedding in a large flume: Journal of Sedimentary Petrology, 35, p. 922-927.

MIDDLETON, G.V. & SOUTHARD, J.B., 1984, Mechanics of sediment movement. Society of Economic Paleontologists
and Mineralogists, Short Course Notes No. 3, 401 pp.

MYROW, P.M. & SOUTHARD, J.B., 1991, Combined flow model for vertical stratification sequences in shallow marine
storm-deposited beds: Journal of Sedimentary Petrology, 61, p. 202-210.

NAGTEGAAL, P.J.C., 1978, Sandstone-framework instability as a function of burial diagenesis: Journal of the
Geological Society of London, 135, p. 101-106.

NÖTTVEDT, A. & KREISA, R.D., 1987, Model for combined-flow origin of hummocky cross-stratification: Geology,
15, p. 357-361.

PAOLA, C., WIELE, S.M. & REINHART, M.A., 1989, Upper-regime parallel lamination as the result of turbulent
sediment transport and low amplitude bedforms: Sedimentology, 36, p. 47-60.

PETTIJOHN, F.J., POTTER, P.W., & SIEVER, 1973, Sand and sandstone. Springer-Verlag, New York, 618 pp.

POTTER, P.E., MAYNARD, J.B. & PRYOR, W.A., 1980, Sedimentology of shale. Springer-Verlag, New York, 549 pp.

POWER, W.R., 1961, Backset beds in the Coso Formation, Inyo County, California: Journal of Sedimentary Petrology,
31, p. 603-607.

POWERS, M.C., 1953, A new roundness scale for sedimentary particles: Journal of Sedimentary Petrology, 23, p.

PRAVE, A.R. & DUKE, W.L., 1990, Small-scale hummocky cross-stratification in turbidites: a form of antidune
stratification: Sedimentology, 37, p. 531-539.

ROSENTHAL, L.R.P. & WALKER, R.G., 1987, Lateral and vertical facies sequences in the Upper Cretaceous Chungo
Member, Wapiabi Formation, southern Alberta: Canadian Journal of Earth Sciences, 24, p. 771-783.

RUST, B.R. & GIBLING, M.A., 1989, Three-dimensional antidunes as HCS mimics in a fluvial sandstone: the
Pennsylvanian South Bar Formation near Sydney, Nova Scotia: Journal of Sedimentary Petrology, 60, p. 540-

SELLEY, R.C., 1982, An introduction to sedimentology. Academic Press, New York, 417 pp.

SHERMAN, D.J. & GREENWOOD, B., 1989, Hummocky cross-stratification and post-vortex ripples: length scales and
hydraulic analysis: Sedimentology, 36, p. 981-986.

SHIELDS, A., 1936, Anwendung derhnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung
Preuss. Versuchsanstalt fur Wasserbau und Schiffbau. Berlin, Mitt. 26, 26 pp. (English translations are also

SIMONS, D.B. & RICHARDSON, E.V., 1961, Forms of bed roughness in alluvial channels: American Society fo Civil
Engineers, Proceedings, 87, No. HY3, p. 87-105.

SNEED, E.D., & FOLK, R.L., 1958, Pebbles in the Lower Colorado River, Texas, a study in particle morphogenesis:
Journal of Geology, 66, p. 114-150.

SOUTHARD, J.B. & BOGUCHWAL, L.A., 1990, Bed configurations in steady unidirectional water flows, Part 2. Synthesis
of flume data: Journal of Sedimentary Petrology, 60, p. 658-679. (Note: This paper is accompanied by two
companion papers by Southard and his students, in the same issue of the journal.)

SOUTHARD, J.B., LAMBIE, J.M., FEDERICO, D.C., PILE, H.T. AND WEIDMAN, C.R., 1990, Experiments on bed configura-

tions in fine sands under bidirectional purely oscillatory flow, and the origin of hummocky cross-stratification:
Journal of Sedimentary Petrology, 60, p. 1-17.

SUNDBORG, A., 1956, The river Klaralven, a study in fluvial processes: Geografiska Annaler, 38, p. 125-316.

SWIFT, D.J.P., FIGUEIREDO, A.G., FREELAND, G.L. AND OERTEL, G.F., 1983, Hummocky cross-stratification and megaripples:
a geological double standard?: Journal of Sedimentary Petrology, 53, p. 1295-1317.

SWIFT, D.J.P., HUDELSON, P.M., BRENNER, R.L., AND THOMPSON, P., 1987, Shelf construction in a foreland basin: storm
beds, shelf sandstones, and shelf-slope depositional sequences in the Upper Cretaceous Mesaverde Group,
Book Cliffs, Utah: Sedimentology, 34, p. 423-457.

THURMAN, H.V., 1988, Introduction to Oceanography. Merril Publishing Company, Toronto, 515 pp.

UDRI, A., 1991, An experimental study of antidunes on a bed of 0.18 mm sand: bedform behavior, internal
stratification and fabric. Brock University, Unpublished B.Sc. Thesis, 113 pp.

WADEL, H., 1932, Volume, shape, roundness of rock particles: Journal of Geology, 40, p. 443-451.

Walker, R.G., Duke, W.L. & Leckie, D.A., 1983, Hummocky stratification: significance of its variable bedding
sequences: Discussion: Geological Society of America Bulletin, 94, p. 1245-1249.

Weedman, S.D. & Slingerland, R., 1985, Experimental study of sand streaks formed in turbulent boundary layers:
Sedimentology, 32, p. 133-145.

Zingg, T., 1935, Beiträge zur Schotteranalyse: Schweiz. min. pet. Mitt., 15, p. 39-140.