The Hilbert transform can be implemented in a complex framework as follows (as in the Matlab software): let X(t) the real valued process; let Y(t) = H(X(t) its real Hilbert transform. Then the complex Hilbert transform of signal X(t) is defined as Z(t) = X(t)+**i**.Y(t) where **i** is the pure imaginary

The Hilbert transform is implemented numerically for discrete time signals in MATLAB.

+∞ +∞

−∞ −∞

*t*

 τ

π

 τ

Wavelets can also be used in different ways for cross-analyses of two signals like atmospheric and pore pressure. For instance:

The latter alternative may be viewed as a "*simplified cross-wavelet approach***".** It is a way to combine two "simple wavelet analyses" to finally obtain a simplified but practical crossanalysis of the two signals at the selected scale. In this work, we will use this type of approach *to identify semi-diurnal earth tide effects* in pore pressure data, leading to an estimate of the elastic "Ss" as the ratio of tidal strain / pore pressure amplitudes in terms of semidiurnal wavelet components.9

In *Sections 4 & 5*, this simplified cross-wavelet approach will be applied to obtain a constant global "Ss" and also to quantify the effect of excavation on a more local estimate of Ss(t). To achieve this, we will need to characterize the time varying amplitude of a semi-diurnal wavelet component (time scale of moon induced earth tides). In his way, we will be able to "see" the effect of the moving excavation front on the semi-diurnal wavelet "signal".

For this task, we need a new tool that can evaluate statistically the "time-modulated amplitude" of a signal. This tool is available already (although we apply it in an unusual way, in combination with wavelets): it is the theory of "*statistical envelopes"*, presented in the next sub-section below.

#### **3.5 Statistical envelope analysis of a signal ("modulated amplitude")**

The *Cramer-Leadbetter* theory10 and the related *Hilbert Transform11*, are the theoretical tools that enable us to define, mathematically and statistically, the "modulated amplitude" (or the

 9 In fact, our current implementation of this general idea to the Mont Terri site is further simplified, using constant tidal amplitude because of the lack of direct earth dilatation record at the site. 10 Cramer-Leadbetter theory in a nutshell: see *Box N°1*.

"envelope") of a fluctuating and evolutionary pressure process. The theory of statistical envelopes is well established for zero mean stationary random processes (*Vanmarcke 1983; Veneziano 1979*). This theory, together with the associated Hilbert Transform, is particularly useful for characterizing relatively narrow-band signals, e.g. ocean & coastal waves *(Huang et al. 1999)*.

But the present study (see *Section 5*) suggests that the "statistical envelope" can also be useful in a variety of other cases in geophysics, provided it is combined with carefully selected "components" of the signals (e.g., here, the semi-diurnal wavelet component of pore pressure). In fact, the mathematical theory of statistical envelopes is established only for stationary processes, but as will be seen in *Section 5*, using wavelets, we will get rid of the strong non stationary mean trend due to excavation. This is naturally accomplished by using multi-resolution wavelets at specific dyadic scales. The dominant scale of the mean trend is ∼11days, while the wavelet scale selected for analysis is semi-diurnal (scale ≈ 12hours). The effects of the 11 day trend due to excavation are still "visible" as a time varying "modulated" amplitude in the semi-diurnal wavelet component C12HOURS(t), which we capture using envelope theory. Thus, our use of the theory of envelopes and Hilbert Transform in the present context, with semi-diurnal pressure fluctuations superimposed on a strong nonlinear trend due to excavation, seems rather new in the literature.

#### **Cramer-Leadbetter theory in a nutshell**.

For a zero mean (detrended) stationary random process X(t), one defines first a dephased "sister" process S(t). Based on X(t) and S(t), one obtains a symmetric double envelope ±R(t) such that:

R(t)=(X2(t)+S2(t))1/2.

402 Radioactive Waste

• One can study the "*detail"* or (perhaps more interestingly) the "*residual*" of a signal X(t) at any selected dyadic scale "m". The analysis can be performed for several signals X(t), Y(t). One can compare for instance the details of air and pore pressure at scale 24h. • One can select dyadic components from one or several signals, and these can be studied and compared as a function of dyadic scale (2m\*Δt) across the whole spectrum of available scales, from finest scale Δt to largest dyadic scale (which is never smaller than

Wavelets can also be used in different ways for cross-analyses of two signals like

• It is possible to develop a somewhat sophisticated approach for orthogonal crossanalyses of signals based on the theory of wavelet spectra and cross-spectra (see for

• Yet another practical approach is to compare directly the amplitudes of the wavelet

The latter alternative may be viewed as a "*simplified cross-wavelet approach***".** It is a way to combine two "simple wavelet analyses" to finally obtain a simplified but practical crossanalysis of the two signals at the selected scale. In this work, we will use this type of approach *to identify semi-diurnal earth tide effects* in pore pressure data, leading to an estimate of the elastic "Ss" as the ratio of tidal strain / pore pressure amplitudes in terms of semi-

In *Sections 4 & 5*, this simplified cross-wavelet approach will be applied to obtain a constant global "Ss" and also to quantify the effect of excavation on a more local estimate of Ss(t). To achieve this, we will need to characterize the time varying amplitude of a semi-diurnal wavelet component (time scale of moon induced earth tides). In his way, we will be able to

For this task, we need a new tool that can evaluate statistically the "time-modulated amplitude" of a signal. This tool is available already (although we apply it in an unusual way, in combination with wavelets): it is the theory of "*statistical envelopes"*, presented in the

The *Cramer-Leadbetter* theory10 and the related *Hilbert Transform11*, are the theoretical tools that enable us to define, mathematically and statistically, the "modulated amplitude" (or the

9 In fact, our current implementation of this general idea to the Mont Terri site is further simplified,

using constant tidal amplitude because of the lack of direct earth dilatation record at the site.

"see" the effect of the moving excavation front on the semi-diurnal wavelet "signal".

**3.5 Statistical envelope analysis of a signal ("modulated amplitude")**

10 Cramer-Leadbetter theory in a nutshell: see *Box N°1*.

components of the two signals X(t) and Y(t) at the same dyadic scale "m".

instance *Labat 2005* and references therein), but this theory will not be used here. • Simpler analyses can be developed by studying the cross-correlation between atmospheric pressure (Patm) and pore pressure (P). The wavelet component of interest is treated as a signal, and cross-component correlation analysis can be conducted at the chosen time scale: see *Labat et al. (1999 a,b*); *Wang et al. (2010); Möri et al. (2011);* for applications of cross-wavelet analyses in karst hydrology, beach hydrodynamics, and

half the record length).

diurnal wavelet components.9

next sub-section below.

atmospheric and pore pressure. For instance:

clay rock hydrogeology, respectively.

The envelope is usually much smoother than the original process X(t).

In the special case where X(t)=sin(ωt), we obtain S(t)=cos(ωt), and then R(t) = sin2(ωt)+cos2(ωt) = 1, as one may expect. Indeed, it should be obvious that the envelope of the sinusoïdal signal X(t)=sin(ωt) is just a pair of horizontal lines of ordinates -1 and +1.

#### **Hilbert transform in a nutshell.**

The Hilbert transform is an integral transform of the form:

$$\hat{X}(t) = H(X(t)) = (h \otimes X)(t) = \int\_{-\infty}^{+\infty} X(t)h(t-\tau)d\tau = \frac{1}{\pi} \int\_{-\infty}^{+\infty} \frac{X(t)}{t-\tau}d\tau \dots$$

For a real-valued signal X(t), H(X(t) is essentially the convolution of the signal X(t) by the kernel, or transfer function, h(t) = 1/(πt). Note: X(t) = sin(t) H(X(t)) = -cos(t).

The Hilbert transform can be implemented in a complex framework as follows (as in the Matlab software): let X(t) the real valued process; let Y(t) = H(X(t) its real Hilbert transform. Then the complex Hilbert transform of signal X(t) is defined as Z(t) = X(t)+**i**.Y(t) where **i** is the pure imaginary number (**i** = √-1). The above defined envelope of X(t) is then obtained as:

$$R(t) = \pm \sqrt{X(t)^2 + H\left(X(t)\right)^2} \\
= \pm \sqrt{X(t)^2 + Y(t)^2} \\
= \pm \left| Z(t) \right|.$$

The Hilbert transform is implemented numerically for discrete time signals in MATLAB.

Box 1. Envelope theory in a nutshell

11 Hilbert transform in a nutshell see *Box N°1*.

Statistical Analyses of Pore Pressure Signals in

φ

ε

 δ

and δH is total head variation, with head H defined by: *ATM*

*P MP REL*

where Δ

( ) ( ) 2

*Takeuchi (1950)* gives: Δ= ×

( ) 1 [ ] *Sm V V H S MP MP* δ

8 33

( ) ( ) ( ) 1 [ ] *S g Pa V V p t S M* ρδδ

( ) 1 *S w w B W Sg g K K*

 βρ

( ) ( )

 δ

ρα

 δ

δε

δ

 εω*t t* =Δ + .sin *M*

ε

ε

Claystone During Excavation Works at the Mont Terri Underground Research Laboratory 405

The purpose of this "box" is to summarize the simplified, but physically-based, hydro-mechanical models. These models are used in combination with statistical analyses in order to interpret pressure signals in terms of rock properties (elastic storativity Ss, effective elastic porosity Φ).

Astronomic movements of Earth, Moon, Sun, induce fluctuations of the gravimetric field g(t), which has an impact on deformations of the earth crust (displacements, strains). Focusing on the M2

Concerning M2, it is the principal lunar earth tide, and its period is more precisely 12h 25 mn.

the earth, and "g" is gravity. One may take W2/g ≈ 10 for M2. The constant 0.5 was computed by Takeuchi from earth crust mechanics data (Lamé stiffness moduli, Love number). At the scale of a

2 10 [ / ] *m m* − Δ≈× (value adopted *in this work* in the absence of direct measurements).

− = where VMP is the volume of deformable bulk Porous Matrix,

Using Terzaghi's 1936 effective stress concept, assuming constant total stress, and assuming elastic

The *Bredehoeft (1967)* model relates tidal strain to relative pressure fluctuations (or �H) via Ss:

Without going into details (see *Freeze and Cherry 1979*), we present the result obtained with the effective stress hypothesis (*Terzaghi 1936*), in the case where the total stress is held constant, and assuming here also that our hydro-geologic unit behaves like a (*partially*) confined aquifer:

*pREL t Bp t* =− × *ATM* , with the barometric efficiency B given by: *B* =Φ +Φ

Using the previous expression for Ss in terms of (α,β) compressibilities *B Sg* = Φ

In this work, barometric efficiency is re-interpreted statistically as the spectral gain at frequency 1/24h. The above equation shows that barometric efficiency B, specific elastic storativity Ss, and effective elastic porosity Φ are interrelated (the compressibility β=1/Kw of water is known).

 ≈ = ρ ρδ

compressibility of water (β=1/Kw) and of the bulk porous matrix (α=1/Kb…) leads to:

*TIDAL S* ≈ *S H* , or equivalently: *TIDAL S* ( ) *S g gH S g p* ( ) ( ) *S* ( ) *REL*

δε

Box 2. Summary of physically based hydro-mechanical models

**Barometric efficiency B - classical model (***compressibility & effective stress***)**

= +Φ = + Φ (where Kw � 2 GigaPa for water).

− = , with *pREL* ( )*t pt p t* = − ( ) *ATM* ( ) (relative pressure).

is the tidal strain amplitude [m3/m3].

0.5 *W a* 2 ( ) *g* , where W2 is the tidal potential of M2, "a" is the radius of

*w p p H z* ρ*g*

− = + . Equivalently:

 ρ δ.

β

β

 ( ) α β.

> ρ( ) *s* ( ) .

**Tidal strain - astronomic and global earth (the semi-diurnal component)**

ε

harmonic (Moon semi-diurnal), the volumetric strain fluctuations take the form:

geologic unit (as opposed to the global scale of the earth), *Melchior (1978)* estimates

**Tidal strain and elastic specific storativity Ss of a geologic unit - the** *Bredehoeft* **model**  Specific storativity Ss : Ss is in units of [m-1] ↔ Ss/(ρg) is in units of [(m3/m3)/Pa].

Rather than present here the full theory of statistical envelopes, we refer the reader to the *abovecited references* for the theory, and to the *summary* presented here in Box *N°1.* The reader who is not directly interested in the theory can move on to *Section 5* for application of statistical envelope + wavelet analysis, to the non stationary evolution of semi-diurnal fluctuations of (relative) pore pressure during the excavation of Mont Terri gallery Ga98 ("*mine by test"*).

As mentioned earlier, the final objective and result of this analysis is to estimate the evolution of specific storativity "Ss(t)" in the EdZ of the clay rock. This is done by using the tidal dilatation model of Bredehoeft relating tidal strain / relative pore pressure. The originality of this "envelope" approach should be emphasized. The amplitude of the semidiurnal wavelet component is estimated as a modulated envelope, which varies more smoothly than the signal itself. The resulting storativity coefficient is therefore a timevarying coefficient, Ss(t), which reflects the mechanical disturbance due to the evolving excavation front, over short time scales (days, weeks).

#### **3.6 Physically-based hydro-mechanical models to characterize the clay rock from pressure signals (earth tides and barometric effect)**

The statistical methods of signal analysis are complemented or combined with physically based, but "*simplified" hydro-mechanical models.* These are used for hydrogeologic interpretation of the pressure signals (pore pressure and atmospheric pressure), and they are also related to inferred earth tide strain fluctuations, with the aim of characterizing quantitatively some of the hydrogeologic properties of the porous clay rock (Ss, Φ).

Specifically, the simplified hydro-mechanical models used here relay on assuming both water and the prous matrix (bulk) to be elastically compressibility, and on accepting Terzaghi's 1936 effective stress concept. The corresponding models can be traced back to *Jacob (1940)* for the barometric efficiency model; and to *Bredehoeft (1967)* for the earth tides model (also *Jacob 1940* and *Cooper 1966)*. These physically-based models both assume that the total stress can be decomposed additively into effective stress between grains, and pressure (fluid stress), according to the Terzaghi concept. This implies that the grains of the claystone are "incompressible". The more general Biot poroelasticity theory can account for the case where individual grains are compressible (see for instance *Hsieh et al. 1988* concerning specific storativity).

In this work we use Terzaghi based hydro-mechanical models. They are outlined below in *Box N°2*, where the final results are expressed in terms of:

#### **4. Long time scales: statistical structure of pressure signals and characterization of time averaged properties (specific storativity Ss; elastic porosity** φ**)**

This section is devoted to the analysis of long records (months to years) of observed air pressure and relative pore pressure signals, for the purpose of characterizing global and average hydro-geologic properties of the clay stone (global in space, and also, average in time)…Statistical analyses based on correlations, spectra, and wavelets, will enable us to detect and characterize in particular the diurnal relation between relative pore pressure and air pressure (leading to a "barometric efficiency"), and the half-diurnal effect of earth tides (leading to a characterization of compressibility and/or specific storativity).

The purpose of this "box" is to summarize the simplified, but physically-based, hydro-mechanical models. These models are used in combination with statistical analyses in order to interpret pressure signals in terms of rock properties (elastic storativity Ss, effective elastic porosity Φ).

#### **Tidal strain - astronomic and global earth (the semi-diurnal component)**

404 Radioactive Waste

Rather than present here the full theory of statistical envelopes, we refer the reader to the *abovecited references* for the theory, and to the *summary* presented here in Box *N°1.* The reader who is not directly interested in the theory can move on to *Section 5* for application of statistical envelope + wavelet analysis, to the non stationary evolution of semi-diurnal fluctuations of (relative) pore pressure during the excavation of Mont Terri gallery Ga98 ("*mine by test"*).

As mentioned earlier, the final objective and result of this analysis is to estimate the evolution of specific storativity "Ss(t)" in the EdZ of the clay rock. This is done by using the tidal dilatation model of Bredehoeft relating tidal strain / relative pore pressure. The originality of this "envelope" approach should be emphasized. The amplitude of the semidiurnal wavelet component is estimated as a modulated envelope, which varies more smoothly than the signal itself. The resulting storativity coefficient is therefore a timevarying coefficient, Ss(t), which reflects the mechanical disturbance due to the evolving

**3.6 Physically-based hydro-mechanical models to characterize the clay rock from**

quantitatively some of the hydrogeologic properties of the porous clay rock (Ss, Φ).

compressible (see for instance *Hsieh et al. 1988* concerning specific storativity).

**time averaged properties (specific storativity Ss; elastic porosity** φ**)**

(leading to a characterization of compressibility and/or specific storativity).

*Box N°2*, where the final results are expressed in terms of:

• The effective (elastic or dynamic) porosity Φ [m3/m3].

• The specific (elastic) storativity Ss [m-1];

The statistical methods of signal analysis are complemented or combined with physically based, but "*simplified" hydro-mechanical models.* These are used for hydrogeologic interpretation of the pressure signals (pore pressure and atmospheric pressure), and they are also related to inferred earth tide strain fluctuations, with the aim of characterizing

Specifically, the simplified hydro-mechanical models used here relay on assuming both water and the prous matrix (bulk) to be elastically compressibility, and on accepting Terzaghi's 1936 effective stress concept. The corresponding models can be traced back to *Jacob (1940)* for the barometric efficiency model; and to *Bredehoeft (1967)* for the earth tides model (also *Jacob 1940* and *Cooper 1966)*. These physically-based models both assume that the total stress can be decomposed additively into effective stress between grains, and pressure (fluid stress), according to the Terzaghi concept. This implies that the grains of the claystone are "incompressible". The more general Biot poroelasticity theory can account for the case where individual grains are

In this work we use Terzaghi based hydro-mechanical models. They are outlined below in

**4. Long time scales: statistical structure of pressure signals and characterization of**

This section is devoted to the analysis of long records (months to years) of observed air pressure and relative pore pressure signals, for the purpose of characterizing global and average hydro-geologic properties of the clay stone (global in space, and also, average in time)…Statistical analyses based on correlations, spectra, and wavelets, will enable us to detect and characterize in particular the diurnal relation between relative pore pressure and air pressure (leading to a "barometric efficiency"), and the half-diurnal effect of earth tides

excavation front, over short time scales (days, weeks).

**pressure signals (earth tides and barometric effect)**

Astronomic movements of Earth, Moon, Sun, induce fluctuations of the gravimetric field g(t), which has an impact on deformations of the earth crust (displacements, strains). Focusing on the M2 harmonic (Moon semi-diurnal), the volumetric strain fluctuations take the form:

( ) ( ) 2 ε εω *t t* =Δ + .sin *M* φ where Δεis the tidal strain amplitude [m3/m3].

Concerning M2, it is the principal lunar earth tide, and its period is more precisely 12h 25 mn. *Takeuchi (1950)* gives: Δ= × ε 0.5 *W a* 2 ( ) *g* , where W2 is the tidal potential of M2, "a" is the radius of the earth, and "g" is gravity. One may take W2/g ≈ 10 for M2. The constant 0.5 was computed by Takeuchi from earth crust mechanics data (Lamé stiffness moduli, Love number). At the scale of a geologic unit (as opposed to the global scale of the earth), *Melchior (1978)* estimates 8 33 ε2 10 [ / ] *m m* − Δ≈× (value adopted *in this work* in the absence of direct measurements).

**Tidal strain and elastic specific storativity Ss of a geologic unit - the** *Bredehoeft* **model**

Specific storativity Ss : Ss is in units of [m-1] ↔ Ss/(ρg) is in units of [(m3/m3)/Pa].

( ) 1 [ ] *Sm V V H S MP MP* δ δ− = where VMP is the volume of deformable bulk Porous Matrix,

and δH is total head variation, with head H defined by: *ATM w p p H z* ρ *g* − = + . Equivalently:

( ) ( ) ( ) 1 [ ] *S g Pa V V p t S M* ρδδ *P MP REL* − = , with *pREL* ( )*t pt p t* = − ( ) *ATM* ( ) (relative pressure).

Using Terzaghi's 1936 effective stress concept, assuming constant total stress, and assuming elastic compressibility of water (β=1/Kw) and of the bulk porous matrix (α=1/Kb…) leads to:

$$S\_S = \rho\_w g (\alpha + \Phi \beta) = \rho\_w g \left( \bigvee\_{K\_B} + \bigvee\_{W\_{W}} \right) \text{ (where } \text{Kw } \sqcap 2 \text{ GigaPa for water)}.$$

The *Bredehoeft (1967)* model relates tidal strain to relative pressure fluctuations (or �H) via Ss:

$$\boldsymbol{\delta\mathcal{E}}\_{\text{TIDAL}} = \mathbf{S}\_{\text{S}} \boldsymbol{\delta\mathcal{H}} \text{ , or equivalently: } \boldsymbol{\delta\mathcal{E}}\_{\text{TIDAL}} = \left(\mathbf{S}\_{\text{S}} \Big/ (\rho \, \mathbf{g})\right) \rho \mathbf{g} \boldsymbol{\delta\mathcal{H}} = \left(\mathbf{S}\_{\text{S}} \Big/ (\rho \, \mathbf{g})\right) \boldsymbol{\delta\mathcal{p}}\_{\text{REL}} \dots$$

**Barometric efficiency B - classical model (***compressibility & effective stress***)**

Without going into details (see *Freeze and Cherry 1979*), we present the result obtained with the effective stress hypothesis (*Terzaghi 1936*), in the case where the total stress is held constant, and assuming here also that our hydro-geologic unit behaves like a (*partially*) confined aquifer:

( ) ( ) δ δ *pREL t Bp t* =− × *ATM* , with the barometric efficiency B given by: *B* =Φ +Φ β ( ) α β.

Using the previous expression for Ss in terms of (α,β) compressibilities *B Sg* = Φβ ρ( ) *s* ( ) .

In this work, barometric efficiency is re-interpreted statistically as the spectral gain at frequency 1/24h. The above equation shows that barometric efficiency B, specific elastic storativity Ss, and effective elastic porosity Φ are interrelated (the compressibility β=1/Kw of water is known).

Box 2. Summary of physically based hydro-mechanical models

Statistical Analyses of Pore Pressure Signals in

• the absolute mean deviation ("*norm 1*" or 1

( ) 1 ( ) *p p p Xi X*

**1420**

**1425**

 **relative p ressu re in kP a**

signal: Δt = 30 min (and k=1).

**1430**

**1435**

**1440**

*N*

σ

(C8H(t)+C16H(t))/2.

the Δε(t) signal.

Note:

Claystone During Excavation Works at the Mont Terri Underground Research Laboratory 407

Note that the site specific signal of volumetric strain Δε(t) is not available, so its amplitude is only estimated indirectly (from data surveys in the literature). However, our method can be extended to the case where Δε(t) is available, by applying a semi-diurnal wavelet analysis on

The amplitude of relative pressure head Δh(t) is obtained from multi-resolution wavelet analysis of P(t)-PATM(t). The wavelet component with dyadic time scale close to semi-diurnal

*Figure 12* shows the evolution of the components according to time and scale. The goal is to isolate the component corresponding to earth tides (the semi-diurnal component): as indicated on this figure, we have chosen the component of dyadic scale T = 8h (close to 12h). Note: in other calculations, we have attempted to improve the accuracy of semi-diurnal scale selection by computing the mean of the dyadic 8h and 16h wavelet components:

**03 August 08 August 14 August 20 August 26 August 01 Sept**

Fig. 10. Signal of the raw relative pore pressure PP1(t) (kPa) at Mont Terri

(from 02/08/2002 to 04/09/2002). Time span: 15 month. Time step of raw pressure

**Time(days)**

).

 = − and ( )2 (2) 1 *Xi X* ( ) *N* σ

; or else

= − (20)

is isolated, and its amplitude is evaluated using either of the following "norms":

• the RMS (Root-Mean-Square) standard deviation: "*norm 2*" or 2

1

= − (1) 1 *Xi X* ( ) *N*

σ

Long records with many time steps (tens of thousands or much more) usually have non stationary structures at various scales. In this section, the undesired non stationary structures are partially eliminated by the selection of specific peak frequencies (in Fourier spectra), and/or by the selection of pertinent dyadic "scales" via multi-resolution wavelet analysis. We seek here only global characteristics of the signals (global amplitudes, etc.).

As explained earlier in the methodology *Section 3*, in order to achieve these goals (hydrogeologic characterization), we use simplified hydro-mechanical "models" to account for the porosity "Φ", the compressibility of water, and the compressibility of the bulk porous matrix. This leads also to the related concept of elastic specific storativity "Ss", based on Terzaghi's decomposition of total stress into effective stress+pressure. The "Ss" coefficient represents an equivalent elastic coefficient for the water filled poro-elastic rock. See the "outlook" comments in *Section 6* for a discussion on the limitations and possible extensions of these hydro-mechanical models.

#### **4.1 A first example: statistical analyses and interpretations of "clean" records of raw (un-processed) pressure signals over**∼**1 month**

The above-mentioned statistical techniques are first illustrated here using only relatively short sections of the pore pressure signal PP1(t) at Mont Terri, with constant time step and no data gaps (no reconstitution required): see *Figures 10, 11, 12, 13*.

The unprocessed pore pressure signal is analysed in terms of:

#### **4.1.1 Specific storativity from earth tides (using semi-diurnal wavelets)**

We estimate in this subsection the month-scale specific storativity "Ss" from semi-diurnal wavelet component of relative pore pressure (strain/pressure -- earth tide effect).

The specific storage coefficient quantifies the volume of water stored per unit volume of porous domain and per unit variation of hydraulic head. It can be estimated from earth tide amplitude using the relation of Bredehoeft (1967), based on a simplified model that takes into account bulk deformation effects due to earth tides in the poro-elastic water filled porous medium:

$$S\_s = \frac{\left| \Delta \mathcal{E} \right|}{\left| \Delta h \right|} \tag{19}$$

where **SS** is specific storativity (m-1), |*Δε*| is the amplitude of volumetric strain fluctuations related to the M2 semi-diurnal earth tide**,** and |*Δh***|** is the amplitude of relative pressure head fluctuations (estimated from the semi-diurnal wavelet component of relative pressure). The strain amplitude |*Δε*| was estimated by *Takeuchi (1950)* based on astronomic earth tides and earth elasticity*,* then later on (in the 1960's) by Melchior and others for hydro-geologic formations: see *Melchior (1978) (*originally in *1960), Bredhoeft (1967),* and others*:* **|Δε***| = 2*×*10-8 m3/m3*.

Note that the site specific signal of volumetric strain Δε(t) is not available, so its amplitude is only estimated indirectly (from data surveys in the literature). However, our method can be extended to the case where Δε(t) is available, by applying a semi-diurnal wavelet analysis on the Δε(t) signal.

The amplitude of relative pressure head Δh(t) is obtained from multi-resolution wavelet analysis of P(t)-PATM(t). The wavelet component with dyadic time scale close to semi-diurnal is isolated, and its amplitude is evaluated using either of the following "norms":

Note:

406 Radioactive Waste

Long records with many time steps (tens of thousands or much more) usually have non stationary structures at various scales. In this section, the undesired non stationary structures are partially eliminated by the selection of specific peak frequencies (in Fourier spectra), and/or by the selection of pertinent dyadic "scales" via multi-resolution wavelet analysis. We seek here only global characteristics of the signals (global amplitudes,

As explained earlier in the methodology *Section 3*, in order to achieve these goals (hydrogeologic characterization), we use simplified hydro-mechanical "models" to account for the porosity "Φ", the compressibility of water, and the compressibility of the bulk porous matrix. This leads also to the related concept of elastic specific storativity "Ss", based on Terzaghi's decomposition of total stress into effective stress+pressure. The "Ss" coefficient represents an equivalent elastic coefficient for the water filled poro-elastic rock. See the "outlook" comments in *Section 6* for a discussion on the limitations and possible extensions

**4.1 A first example: statistical analyses and interpretations of "clean" records of raw**

The above-mentioned statistical techniques are first illustrated here using only relatively short sections of the pore pressure signal PP1(t) at Mont Terri, with constant time step and

We estimate in this subsection the month-scale specific storativity "Ss" from semi-diurnal

The specific storage coefficient quantifies the volume of water stored per unit volume of porous domain and per unit variation of hydraulic head. It can be estimated from earth tide amplitude using the relation of Bredehoeft (1967), based on a simplified model that takes into account bulk deformation effects due to earth tides in the poro-elastic water filled

> *Ss h* Δε

where **SS** is specific storativity (m-1), |*Δε*| is the amplitude of volumetric strain fluctuations related to the M2 semi-diurnal earth tide**,** and |*Δh***|** is the amplitude of relative pressure head fluctuations (estimated from the semi-diurnal wavelet component of relative pressure). The strain amplitude |*Δε*| was estimated by *Takeuchi (1950)* based on astronomic earth tides and earth elasticity*,* then later on (in the 1960's) by Melchior and others for hydro-geologic formations: see *Melchior (1978) (*originally in *1960), Bredhoeft (1967),* and others*:*

= Δ (19)

2. its wavelet component at nearly semi-diurnal time scale (shown in *Figure 13*).

wavelet component of relative pore pressure (strain/pressure -- earth tide effect).

**4.1.1 Specific storativity from earth tides (using semi-diurnal wavelets)**

etc.).

of these hydro-mechanical models.

porous medium:

**|Δε***| = 2*

×

*10-8 m3/m3*.

**(un-processed) pressure signals over**∼**1 month**

no data gaps (no reconstitution required): see *Figures 10, 11, 12, 13*.

The unprocessed pore pressure signal is analysed in terms of:

1. its frequency spectrum (shown in *Figure 11*), and

$$\sigma^{(p)} = \left(\frac{1}{N} \sum \left| \mathbf{X}(\mathbf{i}) - \overline{\mathbf{X}}\right|^p \right)^{\frac{1}{p}} \Rightarrow \sigma^{(1)} = \frac{1}{N} \sum \left| \mathbf{X}(\mathbf{i}) - \overline{\mathbf{X}} \right| \text{ and } \sigma^{(2)} = \sqrt{\frac{1}{N} \sum \left( \mathbf{X}(\mathbf{i}) - \overline{\mathbf{X}} \right)^2} \tag{20}$$

*Figure 12* shows the evolution of the components according to time and scale. The goal is to isolate the component corresponding to earth tides (the semi-diurnal component): as indicated on this figure, we have chosen the component of dyadic scale T = 8h (close to 12h). Note: in other calculations, we have attempted to improve the accuracy of semi-diurnal scale selection by computing the mean of the dyadic 8h and 16h wavelet components: (C8H(t)+C16H(t))/2.

Fig. 10. Signal of the raw relative pore pressure PP1(t) (kPa) at Mont Terri (from 02/08/2002 to 04/09/2002). Time span: 15 month. Time step of raw pressure signal: Δt = 30 min (and k=1).

Statistical Analyses of Pore Pressure Signals in

 **relative pressure in kP**

 **a**

**-0.8 -0.58 -0.4 -0.2 0 0.2 0.4 0.58 0.8 1 1.2**

Δh(norm 1)=**0.058 m**; Ss(norm 1)= **3.4**×**10-7 m-**1 Δh(norm 2)=**0.064 m** ; Ss(norm 2)=3.1×**10-7 m-**1

"barometric efficiency" (B or BE).

relation*):*

relative pore pressure and air pressure (barometric efficiency).

Claystone During Excavation Works at the Mont Terri Underground Research Laboratory 409

Δ**P(kPa)** Δ**H(m)**

**4 August 8 August 13 August 18 August 22 August**

 **Time (days)**

Fig. 13. Multiresolution wavelet analysis : dyadic time scale component 8h (near 12h) for the

*Figure 13* shows the evolution of the selected wavelet component (in this case, C8H(t)). We have determined numerically the amplitude of the fluctuations of this wavelet component, e.g., its absolute mean deviation. The result can be expressed in terms of relative pressure head: for instance it was found that the absolute mean amplitude ("norm1") of semi-diurnal pressure head is Δh = 0.058 m. We can then calculate specific storativity Ss by applying the previous

raw signal of relative pore pressure PP1(t) at Mont Terri. Duration: 02/08/2002 to 22/08/2002. Time step: Δt = 30 min (k=1). Amplitude of fluctuations: Δh = 0.058 m.

relation (*Eq. 19*). The results are the following, using either "norm1" or "norm2" for Δh:

**4.1.2 Effective elastic porosity** Φ **from barometric efficiency (using spectral gain)**

We now estimate month-scale effective porosity from the diurnal frequency gain between

The diurnal (and other) components would be due in part to barometric pressure effects. The effect of barometric pressure fluctuations on observation wells in closed, confined aquifers, is well known. The piezometric head in the aquifer is related linearly to atmospheric pressure (assuming linear poro-elastic behavior) via a coefficient named

Although the geometry, boundary conditions, and hydraulic configuration of the Mont Terri claystone appear quite different from those of a confined aquifer, we nevertheless propose to retain the same linear relationship. This makes it possible to calculate effective porosity, according to the relations described in *Section 3.6* and Box N°2 (the following is *Jacob's 1940*

Fig. 11. Reduced spectrum of ΔPP1(t), the first difference of relative pore pressure (kPa), at Mont Terri. Time span: ~1 month (from 02/08/2002 to 04/09/2002). Time step of raw pressure signal: Δt = 30 min (and k=1).

Fig. 12. Multiresolution wavelet analysis : several dyadic time scale components are shown for the raw relative pore pressure PP1(t) at Mont Terri. Duration: 02/08/2002 to 22/08/2002. Time step: Δt = 30 min (and sampling step: k=1).

**0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0**

**Normalized frequency(ADIM)**

**02 August 07 August 11 August 15 August 19 August 24 August**

 **Time(days)**

Fig. 12. Multiresolution wavelet analysis : several dyadic time scale components are shown for the raw relative pore pressure PP1(t) at Mont Terri. Duration: 02/08/2002 to 22/08/2002.

Fig. 11. Reduced spectrum of ΔPP1(t), the first difference of relative pore pressure (kPa), at Mont Terri. Time span: ~1 month (from 02/08/2002 to 04/09/2002). Time step of raw

**1**

**1h**

Time step: Δt = 30 min (and sampling step: k=1).

**2h**

**4h**

 **scale of the com**

 **ponents**

**8h**

**16h**

**32h**

**64h**

pressure signal: Δt = 30 min (and k=1).

**2**

**3**

**4**

**Normalized spectrum(ADIM)**

**5**

**6**

**12h**

**24**

**7**

**8**

**9**

Fig. 13. Multiresolution wavelet analysis : dyadic time scale component 8h (near 12h) for the raw signal of relative pore pressure PP1(t) at Mont Terri. Duration: 02/08/2002 to 22/08/2002. Time step: Δt = 30 min (k=1). Amplitude of fluctuations: Δh = 0.058 m.

*Figure 13* shows the evolution of the selected wavelet component (in this case, C8H(t)). We have determined numerically the amplitude of the fluctuations of this wavelet component, e.g., its absolute mean deviation. The result can be expressed in terms of relative pressure head: for instance it was found that the absolute mean amplitude ("norm1") of semi-diurnal pressure head is Δh = 0.058 m. We can then calculate specific storativity Ss by applying the previous relation (*Eq. 19*). The results are the following, using either "norm1" or "norm2" for Δh:

Δh(norm 1)=**0.058 m**; Ss(norm 1)= **3.4**×**10-7 m-**1 Δh(norm 2)=**0.064 m** ; Ss(norm 2)=3.1×**10-7 m-**1

#### **4.1.2 Effective elastic porosity** Φ **from barometric efficiency (using spectral gain)**

We now estimate month-scale effective porosity from the diurnal frequency gain between relative pore pressure and air pressure (barometric efficiency).

The diurnal (and other) components would be due in part to barometric pressure effects. The effect of barometric pressure fluctuations on observation wells in closed, confined aquifers, is well known. The piezometric head in the aquifer is related linearly to atmospheric pressure (assuming linear poro-elastic behavior) via a coefficient named "barometric efficiency" (B or BE).

Although the geometry, boundary conditions, and hydraulic configuration of the Mont Terri claystone appear quite different from those of a confined aquifer, we nevertheless propose to retain the same linear relationship. This makes it possible to calculate effective porosity, according to the relations described in *Section 3.6* and Box N°2 (the following is *Jacob's 1940* relation*):*

Statistical Analyses of Pore Pressure Signals in

**pre-processing)**

*January 2004 to 12 April 2005).*

Claystone During Excavation Works at the Mont Terri Underground Research Laboratory 411

The same techniques illustrated in the previous *Section 4.1* are now being applied to a much longer - but *pre-processed* - joint record of absolute pore pressure and atmospheric pressure (p(t), pATM(t)). The time span of the processed pair of signals is about 15 months *(from 29*

Note that, initially, only shorter pieces of "clean" signals were available during that time window. Note also that the pre-processing procedures (reconstructing, homogenizing, etc.) must be implemented jointly on p(t) and on pATM(t) over the same time window, since the relative pressure signal must be obtained from pREL(t) = p(t)-pATM(t), and cross-analysis of (pREL(t), pATM(t)) must be implemented to identify the barometric effect. A flow-chart depicting

The results of statistical analyses of the 15 month long pre-processed pressure signals (pREL(t), pATM(t)) are shown below in *Figures 15, 16, 17, 18* for the PP1 pore pressure sensor. *Figure 15* shows pREL(t) over the entire 15 month time span. Similarly to the previous *Section 4.1*, we analysed the cross-spectral gain of (pREL(t), pATM(t)) at frequency 1/24h (*not shown here*), and the wavelet component at nearly semi-diurnal time scale (*Figure 17*). In addition, *Figure 16* shows the spectrum of *Δp*REL*(t),* the first order difference of *p*REL*(t).* Differencing enhances the peak frequencies, and allows one to detect a dominant 1/24h frequency, and a somewhat less dominant 1/12h frequency (subdominant but still visible). We see that these two characteristic frequencies can be detected in spite of the obvious non stationarity (large

**3 Feb 1 Apr 29 May 26 Jul 22 Sept 19 Nov 16 jan 14 March**

Fig. 15. Signal of the relative pore pressure PP1(t) (kPa) at Mont Terri Time span: 15 month (29/01/2004 to 12/04/2005 ). Time step of pre-processed signal: Δt = 30 min, and sampling

 **Time(days)**

pre-processing tasks and methods was shown earlier in *Sub-Section 2.2.1* (*Figure 2***)**.

scale non linear trend) of the 15 month pore pressure signal (*Figure 15*).

step k=1 (i.e. no under-sampling).

 **relative pressure in kPa**

**4.2 Long term analysis of pressure signals over more than 1 year (after**

$$\Phi = \frac{E\_w \times B}{\rho \times g} \times S\_S \tag{21}$$

where Φ or ΦEFF is the effective elastic porosity (m3/m3), B the barometric efficiency which expresses the elastic response of the system, ρ the density of water, g the acceleration of gravity, EW (or KW) is the stiffness modulus of water (EW = KW ≈ 2.05 GigaPascals).

In order to calculate barometric efficiency B, a statistical cross-spectral analysis of the relation between atmospheric pressure and relative pressure was developed, with 30 minute time steps, to determine the reality of the effect of barometric pressure. We carried out the cross-spectral analyses between barometric pressure and relative pressure in borehole BPP-1 (from the PP niche, which contains two rooms, PP1 and PP2).

The estimated spectral gain function (in frequency space) was finally used to determine barometric efficiency (B) by looking at the value of the spectral gain at diurnal frequency, as shown in *Figure 14*. From this spectral gain, barometric efficiency is determined, and porosity is calculated with *Eq. 21* just above, using the previous estimate of specific storativity (Ss) from semi-diurnal wavelet analysis. We obtain in this fashion the following results:

φ**EFFECTIVE (**norm 1) ≈ 6%; φ**EFFECTIVE** (norm 2) ≈ 5.4%

Recall that this procedure to obtain "Φ" (by spectral analysis of barometric gain at diurnal frequency) is combined with the previous procedure to estimate "Ss" (by wavelet analysis of semi-diurnal earth tide effects). In fact, the two procedures do not need to be implemented sequentially. They can be viewed as a system of two equations (*Eq. 19* and *Eq. 21***)** with two unknowns (Ss, Φ). The two unknowns could have been determined both at once (alternative approach).

Fig. 14. Reduced spectral gain *vs.* normalized frequency f×Δt (the maximum value of f×Δt is 0.5, in agreement with Shannon's sampling theorem). This spectral gain function was obtained by cross-spectral analysis of the raw signals of atmospheric pressure Patm(t) [kPa] and relative pore pressure PP1(t)-Patm(t) [kPa]. Signal duration: about 1 month (from 02/08/2002 to 04/09/2002). Time step: 30 mn. The gain at diurnal frequency (1/24h) is indicated by the arrow; it is used to estimate barometric efficiency.

#### **4.2 Long term analysis of pressure signals over more than 1 year (after pre-processing)**

410 Radioactive Waste

where Φ or ΦEFF is the effective elastic porosity (m3/m3), B the barometric efficiency which expresses the elastic response of the system, ρ the density of water, g the acceleration of

In order to calculate barometric efficiency B, a statistical cross-spectral analysis of the relation between atmospheric pressure and relative pressure was developed, with 30 minute time steps, to determine the reality of the effect of barometric pressure. We carried out the cross-spectral analyses between barometric pressure and relative pressure in borehole BPP-1

The estimated spectral gain function (in frequency space) was finally used to determine barometric efficiency (B) by looking at the value of the spectral gain at diurnal frequency, as shown in *Figure 14*. From this spectral gain, barometric efficiency is determined, and porosity is calculated with *Eq. 21* just above, using the previous estimate of specific storativity (Ss) from

φ**EFFECTIVE (**norm 1) ≈ 6%; φ**EFFECTIVE** (norm 2) ≈ 5.4% Recall that this procedure to obtain "Φ" (by spectral analysis of barometric gain at diurnal frequency) is combined with the previous procedure to estimate "Ss" (by wavelet analysis of semi-diurnal earth tide effects). In fact, the two procedures do not need to be implemented sequentially. They can be viewed as a system of two equations (*Eq. 19* and *Eq. 21***)** with two unknowns (Ss, Φ). The two unknowns could have been determined both at once (alternative

**24h; G=0.8267**

**0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0**

 **Normalized frequency (ADIM)**

Fig. 14. Reduced spectral gain *vs.* normalized frequency f×Δt (the maximum value of f×Δt is 0.5, in agreement with Shannon's sampling theorem). This spectral gain function was obtained by cross-spectral analysis of the raw signals of atmospheric pressure Patm(t) [kPa] and relative pore pressure PP1(t)-Patm(t) [kPa]. Signal duration: about 1 month (from 02/08/2002 to 04/09/2002). Time step: 30 mn. The gain at diurnal frequency (1/24h) is

gravity, EW (or KW) is the stiffness modulus of water (EW = KW ≈ 2.05 GigaPascals).

semi-diurnal wavelet analysis. We obtain in this fashion the following results:

(from the PP niche, which contains two rooms, PP1 and PP2).

**0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1**

indicated by the arrow; it is used to estimate barometric efficiency.

 **Reduced gain (ADIM)**

approach).

*w S E B S* ρ *g* × Φ= × ×

(21)

The same techniques illustrated in the previous *Section 4.1* are now being applied to a much longer - but *pre-processed* - joint record of absolute pore pressure and atmospheric pressure (p(t), pATM(t)). The time span of the processed pair of signals is about 15 months *(from 29 January 2004 to 12 April 2005).*

Note that, initially, only shorter pieces of "clean" signals were available during that time window. Note also that the pre-processing procedures (reconstructing, homogenizing, etc.) must be implemented jointly on p(t) and on pATM(t) over the same time window, since the relative pressure signal must be obtained from pREL(t) = p(t)-pATM(t), and cross-analysis of (pREL(t), pATM(t)) must be implemented to identify the barometric effect. A flow-chart depicting pre-processing tasks and methods was shown earlier in *Sub-Section 2.2.1* (*Figure 2***)**.

The results of statistical analyses of the 15 month long pre-processed pressure signals (pREL(t), pATM(t)) are shown below in *Figures 15, 16, 17, 18* for the PP1 pore pressure sensor.

*Figure 15* shows pREL(t) over the entire 15 month time span. Similarly to the previous *Section 4.1*, we analysed the cross-spectral gain of (pREL(t), pATM(t)) at frequency 1/24h (*not shown here*), and the wavelet component at nearly semi-diurnal time scale (*Figure 17*). In addition, *Figure 16* shows the spectrum of *Δp*REL*(t),* the first order difference of *p*REL*(t).* Differencing enhances the peak frequencies, and allows one to detect a dominant 1/24h frequency, and a somewhat less dominant 1/12h frequency (subdominant but still visible). We see that these two characteristic frequencies can be detected in spite of the obvious non stationarity (large scale non linear trend) of the 15 month pore pressure signal (*Figure 15*).

Fig. 15. Signal of the relative pore pressure PP1(t) (kPa) at Mont Terri Time span: 15 month (29/01/2004 to 12/04/2005 ). Time step of pre-processed signal: Δt = 30 min, and sampling step k=1 (i.e. no under-sampling).

Statistical Analyses of Pore Pressure Signals in

pressure fluctuations:

(or Standard Deviation).

Claystone During Excavation Works at the Mont Terri Underground Research Laboratory 413

Fig. 18. Multi-resolution wavelet analysis: graph of the 8h dyadic scale component (near 12h) of the pre-processed relative pore pressure, PP1(t) or pREL(t). Record length ∼15 months (from 29/01/2004 to 12/04/2005); Δt = 30 min, k=1 (no sub-sampling). The amplitude of

The methods used here are again the same as those applied in the first example of *Section 4.1* where we analysed shorter, unprocessed pressure signals. We obtain here successively the specific storativity "Ss" and the effective elastic porosity "Φ". The final results are shown below for two different methods of quantifying the amplitude of semi-diurnal wavelet

where "*norm 1*" stands for the absolute mean, and "*norm 2*" stands for the Root Mean Square

**5. Short time scale effects of gallery excavation on the evolution of pore pressure and**

**5.1 Excavation of a gallery: observed effects on the evolution of pore pressure (syn-**

We focus here on a total duration of ∼5 months, corresponding to the syn-excavation period of gallery Ga98 (17th of November 1997 to 23rd of April 1998). The pre- and post-excavation periods were also analysed for comparison (*Fatmi 2009*), but it is sufficient to treat here the 5 month "syn-excavation" period. Furthermore, we will also focus, within this 5 month period,

semi-diurnal pressure fluctuations is Δh ≈ 0.06 m equivalent water height.

**|Δh|** (*norm 1*) ≈ **0.06m**; **Ss** (*norm 1*) ≈ **3.3**×**10-7m-1** Φ (*norm 1*) ≈ **1.0% |Δh|** (norm 2) ≈ **0.08m** ; **Ss** (norm 2) ≈ **2.6**×**10-7m-1** Φ (*norm 2*) ≈ **0.9%**

**of elastic properties (specific storativity Ss; elastic porosity)**

on a shorter phase of about 2 weeks of "fast" pressure changes (*see below*).

**excavation phase, Mont Terri gallery Ga98)**

Fig. 16. Reduced spectrum of ΔPP1(t) (ΔpREL(t)), first difference of relative pore pressure PP1(t) [kPa] at Mont Terri. Time span ∼15 months (29/01/2004 to12/04/2005). Time step of pre-processed signal: Δt=30 min (no sub-sampling).

Fig. 17. Multi-resolution wavelet scale-time plot. Several dyadic components are shown here for the signal of relative pore pressure PP1(t) or pREL(t) (pre-processed) at the Mont Terri site. Signal duration: from 29/01/2004 to 12/04/2005; time step Δt = 30 min; no subsampling (k=1).

**0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0**

 **Normalized frequency (ADIM)**

**29 Jan 18 Apr 19 Jul 20 Oct 10 Jan 12 Apr 0**

 **Time(days)**

Fig. 17. Multi-resolution wavelet scale-time plot. Several dyadic components are shown here for the signal of relative pore pressure PP1(t) or pREL(t) (pre-processed) at the Mont Terri site. Signal duration: from 29/01/2004 to 12/04/2005; time step Δt = 30 min; no sub-

Fig. 16. Reduced spectrum of ΔPP1(t) (ΔpREL(t)), first difference of relative pore pressure PP1(t) [kPa] at Mont Terri. Time span ∼15 months (29/01/2004 to12/04/2005).  Multi-resolution wavelet analysis: graph of the 8h dyadic scale component (near 12h) of the pre-processed relative pore pressure, PP1(t) or pREL(t). Record length ∼15 months (from 29/01/2004 to 12/04/2005); Δt = 30 min, k=1 (no sub-sampling). The amplitude of semi-diurnal pressure fluctuations is Δh ≈ 0.06 m equivalent water height.

The methods used here are again the same as those applied in the first example of *Section 4.1* where we analysed shorter, unprocessed pressure signals. We obtain here successively the specific storativity "Ss" and the effective elastic porosity "Φ". The final results are shown below for two different methods of quantifying the amplitude of semi-diurnal wavelet pressure fluctuations:

**|Δh|** (*norm 1*) ≈ **0.06m**; **Ss** (*norm 1*) ≈ **3.3**×**10-7m-1** Φ (*norm 1*) ≈ **1.0% |Δh|** (norm 2) ≈ **0.08m** ; **Ss** (norm 2) ≈ **2.6**×**10-7m-1** Φ (*norm 2*) ≈ **0.9%**

where "*norm 1*" stands for the absolute mean, and "*norm 2*" stands for the Root Mean Square (or Standard Deviation).

#### **5. Short time scale effects of gallery excavation on the evolution of pore pressure and of elastic properties (specific storativity Ss; elastic porosity)**

#### **5.1 Excavation of a gallery: observed effects on the evolution of pore pressure (synexcavation phase, Mont Terri gallery Ga98)**

We focus here on a total duration of ∼5 months, corresponding to the syn-excavation period of gallery Ga98 (17th of November 1997 to 23rd of April 1998). The pre- and post-excavation periods were also analysed for comparison (*Fatmi 2009*), but it is sufficient to treat here the 5 month "syn-excavation" period. Furthermore, we will also focus, within this 5 month period, on a shorter phase of about 2 weeks of "fast" pressure changes (*see below*).

Statistical Analyses of Pore Pressure Signals in

diurnal earth tide component (*as will be seen*).

**extraction of earth tide semi-diurnal component**

(*not shown*), whence: pREL(t) = p(t)-pATM(t).

impact on pore pressure).

*p.93, for more details*).

point).

Claystone During Excavation Works at the Mont Terri Underground Research Laboratory 415

A study of the signal on longer time scales (*not shown in this text*) confirms in fact that the pore pressure disturbance was indeed reversible (hence the name "Excavation *disturbed* Zone", as explained earlier). Indeed, a slow relaxation of pore pressure was observed during a long period, somewhat less than two years, subsequent to the end of excavations works (there are almost two years counting from the start of excavation till the end of pressure relaxation: 30/11/1997-18/02/2000). The pore pressure at the end of this period reached approximately the value it had at the beginning of the period (pre-excavation) and it continued to decrease to reach finally the pre-pumping test value (*see Fatmi 2009, Fig.28,*

These observations justify our initial assumption and remark on the distinction between "EDZ" (*irreversibly damaged* "Excavation Damaged Zone"), and "EdZ" (*Excavation disturbed Zone*): the latter is thought to be a *reversibly disturbed* zone due to quasi-elastic hydromechanical variations of pressure and stress. These reversible variations occurred in the zone of our pressure sensor, and they caused the observed variations of pressure during the passage of the excavation front (which came within 4 m of the pressure sensor at the closest

Now, looking at the short and fast rise period of 11 days in *Figure 19*, it may seem "impossible" at first sight to detect a pattern of semi-diurnal pressure fluctuations due to earth tides, and even less, to follow possible changes in these fluctuations during the phase of rapid pressure change. Yet, although earth tides are partially masked, they can still be detected indirectly using proper filtering techniques. For example, applying differential filters can enhance subdominant frequencies, moving average filters can be used to look at residuals, and multi-resolution *wavelet* analysis can be used to extract precisely the semi-

Below, we will take advantage of the precise way in which multi-resolution wavelets can capture the semi-diurnal component of the original signal, and we will then analyse the new "12h" signal using envelope techniques, to finally obtain time-varying hydraulic parameters of the claystone during the passage of the excavation front nearby the pore pressure sensor.

**5.2 Multi-resolution wavelet analysis of relative pressure signals during excavation:**

First, we obtain the relative pore pressure pREL(t) from the absolute pore pressure signal p(t) [*shown in Fig. 19 above as "PP1(t)"*] by subtracting the atmospheric pressure signal pATM(t)

Obviously, one should not expect pATM(t) to be influenced by excavation works (rather, pATM(t) contains barometric fluctuations, with peak frequency 1/24h, part of these having an

The procedure to identify the elastic specific storativity Ss is then similar to that illustrated in *Section 4.1*, except that here, after extracting the semi-diurnal wavelet component "C12H(t)" from the relative pore pressure signal pREL(t), we perform an additional analysis of

Note, from now on, the semi-diurnal wavelet component "C12H(t)" is treated as a signal. The wavelet signal C12H(t) and its statistical envelope are now presented and analysed in the

the modulated amplitude, or "envelope" of C12H(t), in a statistical framework.

Upon inspection of *Figure 19*, it is clear that the pore pressure signal in sensor PP1 exhibits a strong response to the passage of the excavation front. This indicates the existence of a moving EdZ ("Excavation disturbed Zone") as the excavation front passes near the pressure sensors. Pressure rises gradually at first, then very rapidly ("fast" 11 day period). After this rise, pressure seems to reach a stable value but in fact, it starts a long and slow relaxation process (confirmed from analyses of longer records). The sharp rise of pore pressure can be explained as a hydro-mechanical disturbance of the geologic porous formation due to excavation works.

More precisely, *Figure 19* shows the pore pressure data from the PP1 sensor, in comparison with the evolving distance D(t) of the excavation front. The pre- and post-excavation phases are not shown. The 5 month "syn-excavation" phase was determined to run from the 17th of November 1997 to the 23rd of April 1998, and it is shown entirely in this figure (*see caption for other details and comments*). Clearly, within the 5 month syn-excavation phase, there is a remarkable sub-phase of "fast" pressure rise, lasting about two weeks only (∼11 days). Similar effects were observed for the other sensor PP2 in the same borehole (*not shown here*).

Fig. 19. Comparison of pore pressure and excavation front versus time over a 5 month period (syn-excavation). The green curve "PP1(t)" represents the time evolution of absolute pore pressure p(t) in sensor PP1. The blue curve with circles represents the distance D(t) between measurement chamber PP1 and the excavation front of gallery Ga98. The arrow at left indicates the minimal distance achieved (4 m), after which excavation was stopped for about a month (February/March 1998), before restarting around the 2nd week of April 1998. The sharp rise of pressure PP1(t) from 2250 to 2800 kPa (Δp ≈ +5.5 bars) indicates the "fast" part of the syn-excavation phase, which lasted only 11 days (or roughly two weeks).

Upon inspection of *Figure 19*, it is clear that the pore pressure signal in sensor PP1 exhibits a strong response to the passage of the excavation front. This indicates the existence of a moving EdZ ("Excavation disturbed Zone") as the excavation front passes near the pressure sensors. Pressure rises gradually at first, then very rapidly ("fast" 11 day period). After this rise, pressure seems to reach a stable value but in fact, it starts a long and slow relaxation process (confirmed from analyses of longer records). The sharp rise of pore pressure can be explained as a hydro-mechanical disturbance of the geologic porous formation due to

More precisely, *Figure 19* shows the pore pressure data from the PP1 sensor, in comparison with the evolving distance D(t) of the excavation front. The pre- and post-excavation phases are not shown. The 5 month "syn-excavation" phase was determined to run from the 17th of November 1997 to the 23rd of April 1998, and it is shown entirely in this figure (*see caption for other details and comments*). Clearly, within the 5 month syn-excavation phase, there is a remarkable sub-phase of "fast" pressure rise, lasting about two weeks only (∼11 days). Similar effects were observed for the other sensor PP2 in the same borehole (*not shown here*).

**~11days PP1**

**PP1(t)**

**30 Nov 97 24 Dec 16 Jan 10 Feb 04 March 30 March 19 April 98**

Fig. 19. Comparison of pore pressure and excavation front versus time over a 5 month period (syn-excavation). The green curve "PP1(t)" represents the time evolution of absolute pore pressure p(t) in sensor PP1. The blue curve with circles represents the distance D(t) between measurement chamber PP1 and the excavation front of gallery Ga98. The arrow at left indicates the minimal distance achieved (4 m), after which excavation was stopped for about a month (February/March 1998), before restarting around the 2nd week of April 1998. The sharp rise of pressure PP1(t) from 2250 to 2800 kPa (Δp ≈ +5.5 bars) indicates the "fast" part of the syn-excavation phase, which lasted only 11 days (or roughly two weeks).

**D(t)**

**Time (days)**

**2100**

**2200**

**2300**

**2400**

**2500**

**Absolute Pressure PP1 (kPa)**

**2600**

**2700**

**2800**

**Distance**

**2900**

excavation works.

**0 4**

**19**

**37**

**54.5 Distance (m)**

A study of the signal on longer time scales (*not shown in this text*) confirms in fact that the pore pressure disturbance was indeed reversible (hence the name "Excavation *disturbed* Zone", as explained earlier). Indeed, a slow relaxation of pore pressure was observed during a long period, somewhat less than two years, subsequent to the end of excavations works (there are almost two years counting from the start of excavation till the end of pressure relaxation: 30/11/1997-18/02/2000). The pore pressure at the end of this period reached approximately the value it had at the beginning of the period (pre-excavation) and it continued to decrease to reach finally the pre-pumping test value (*see Fatmi 2009, Fig.28, p.93, for more details*).

These observations justify our initial assumption and remark on the distinction between "EDZ" (*irreversibly damaged* "Excavation Damaged Zone"), and "EdZ" (*Excavation disturbed Zone*): the latter is thought to be a *reversibly disturbed* zone due to quasi-elastic hydromechanical variations of pressure and stress. These reversible variations occurred in the zone of our pressure sensor, and they caused the observed variations of pressure during the passage of the excavation front (which came within 4 m of the pressure sensor at the closest point).

Now, looking at the short and fast rise period of 11 days in *Figure 19*, it may seem "impossible" at first sight to detect a pattern of semi-diurnal pressure fluctuations due to earth tides, and even less, to follow possible changes in these fluctuations during the phase of rapid pressure change. Yet, although earth tides are partially masked, they can still be detected indirectly using proper filtering techniques. For example, applying differential filters can enhance subdominant frequencies, moving average filters can be used to look at residuals, and multi-resolution *wavelet* analysis can be used to extract precisely the semidiurnal earth tide component (*as will be seen*).

Below, we will take advantage of the precise way in which multi-resolution wavelets can capture the semi-diurnal component of the original signal, and we will then analyse the new "12h" signal using envelope techniques, to finally obtain time-varying hydraulic parameters of the claystone during the passage of the excavation front nearby the pore pressure sensor.

#### **5.2 Multi-resolution wavelet analysis of relative pressure signals during excavation: extraction of earth tide semi-diurnal component**

First, we obtain the relative pore pressure pREL(t) from the absolute pore pressure signal p(t) [*shown in Fig. 19 above as "PP1(t)"*] by subtracting the atmospheric pressure signal pATM(t) (*not shown*), whence: pREL(t) = p(t)-pATM(t).

Obviously, one should not expect pATM(t) to be influenced by excavation works (rather, pATM(t) contains barometric fluctuations, with peak frequency 1/24h, part of these having an impact on pore pressure).

The procedure to identify the elastic specific storativity Ss is then similar to that illustrated in *Section 4.1*, except that here, after extracting the semi-diurnal wavelet component "C12H(t)" from the relative pore pressure signal pREL(t), we perform an additional analysis of the modulated amplitude, or "envelope" of C12H(t), in a statistical framework.

Note, from now on, the semi-diurnal wavelet component "C12H(t)" is treated as a signal. The wavelet signal C12H(t) and its statistical envelope are now presented and analysed in the

Statistical Analyses of Pore Pressure Signals in

Claystone During Excavation Works at the Mont Terri Underground Research Laboratory 417

Fig. 21. Temporal zoom of the previous figure, shown over a time window of approximately 1 month (instead of 5 months in the previous figure). The (blue) curve designated as "PP1 (12h)" is the wavelet component signal C12H(t) extracted from PP1 relative pressure. The envelope is the (red) curve designated as "R(t)". The ∼ 11 day period of fast pressure change

Comparing *Figure 21* to *Figure 19*, it is now clear (and remarkable) that the 11 day phase of rapidly increasing pore pressure (*Figure 19)* corresponds to a significant increase of the *amplitude* of the semi-diurnal component of pore pressure (*Figure 21)*. Recall, from *Fig. 19*, that this 11 day phase corresponds to the approach of the excavation front nearest to the PP1

**5.4 Calculation of specific storage Ss(t) as a function of time based on Bredehoeft's**

again, we invoke the Bredehoeft earth tide strain/pressure model (see *Eq. 19* earlier).

×

By analogy with the procedure described in *Section 4.1*-*4.1.1***,** we estimate again the elastic specific storativity Ss from the semi-diurnal wavelet component C12H(t) of relative pore pressure (using now the average of the 2 components at dyadic scales 8h and 16h, respectively). And

Only, this time, instead of taking a constant amplitude for C12H(t), we use instead the time-modulated amplitude of C12H(t) represented by its statistical envelope "R(t)". On the other hand, since we still do not have direct *in situ* measurements of the volumetric strain Δε(t), we must replace Δε(t) by an indirect estimate of its amplitude based on data surveys:

> ( ) ( ) *S t S R t* Δε

*10-8 m3/m3* (as in *Sections 4.1 and 4.2*). In this way, we

=(19b)

occurs between the dates of 7th and 19th of February 1998.

pressure sensor (distance D(t) ∼ 4 m at the closest point).

**simplified hydro-mechanical model (strain / pressure)**

accordingly, we use again **|**Δε*| = 2*

obtain, instead of *Eq. 19*:

next section below (*Section 5.3*), in order to derive, from that information, the time-varying specific storativity "Ss(t)" during the syn-excavation phase.

#### **5.3 Statistical envelope of semi-diurnal wavelet of relative pressure during excavation (Hilbert transform & method of maxima)**

In this section, we present the wavelet component signal "C12H(t)" of relative pore pressure, and we analyse its modulated amplitude by computing its Cramer-Leadbetter statistical envelope using MATLAB's Hilbert Transform (Section 3.5: Statistical envelope analysis...).

In addition, in some cases, we compare this theoretical envelope with an empirical one computed by our own "method of maxima". Briefly, the latter method generates an empirical envelope that has irregular time steps. The result of the empirical method agrees generally with the theoretical envelope except for isolated discrepancies (this is a minor point, but the interested reader can consult Fatmi 2009 for more details).

Figure 20 shows (in blue) the semi-diurnal signal "C12H(t)", i.e. the 12h wavelet component of relative pressure in sensor PP1, and it shows also (superimposed in red) the statistical Cramer-Leadbetter envelope of "C12H(t)" (envelope computed with the Hilbert Transform). Recall our gal is to analyse the effects of excavation of gallery Ga1998. Here, the entire "synexcavation" phase of 5 months is shown (approximately from mid-november 1997 to midapril 1998).

Figure 21 shows a temporal zoom of Figure 20 over a much shorter period. The time window is approximately one month, and it is centered around the "fast" sub-phase of synexcavation, which lasts only 11 days.

Fig. 20. Semi-diurnal wavelet component C12H(t) of relative pore pressure in PP1 (blue curve) and its envelope (red curve) during the "syn-excavation" phase of gallery Ga98 at Mont Terri (5 months, from 17 Nov 1997 to 23 April 1998, with Δt=30 mn time steps).

next section below (*Section 5.3*), in order to derive, from that information, the time-varying

**5.3 Statistical envelope of semi-diurnal wavelet of relative pressure during excavation**

In this section, we present the wavelet component signal "C12H(t)" of relative pore pressure, and we analyse its modulated amplitude by computing its Cramer-Leadbetter statistical envelope using MATLAB's Hilbert Transform (Section 3.5: Statistical envelope analysis...).

In addition, in some cases, we compare this theoretical envelope with an empirical one computed by our own "method of maxima". Briefly, the latter method generates an empirical envelope that has irregular time steps. The result of the empirical method agrees generally with the theoretical envelope except for isolated discrepancies (this is a minor

Figure 20 shows (in blue) the semi-diurnal signal "C12H(t)", i.e. the 12h wavelet component of relative pressure in sensor PP1, and it shows also (superimposed in red) the statistical Cramer-Leadbetter envelope of "C12H(t)" (envelope computed with the Hilbert Transform). Recall our gal is to analyse the effects of excavation of gallery Ga1998. Here, the entire "synexcavation" phase of 5 months is shown (approximately from mid-november 1997 to mid-

Figure 21 shows a temporal zoom of Figure 20 over a much shorter period. The time window is approximately one month, and it is centered around the "fast" sub-phase of syn-

Fig. 20. Semi-diurnal wavelet component C12H(t) of relative pore pressure in PP1 (blue curve) and its envelope (red curve) during the "syn-excavation" phase of gallery Ga98 at Mont Terri (5 months, from 17 Nov 1997 to 23 April 1998, with Δt=30 mn time steps).

point, but the interested reader can consult Fatmi 2009 for more details).

specific storativity "Ss(t)" during the syn-excavation phase.

**(Hilbert transform & method of maxima)**

excavation, which lasts only 11 days.

april 1998).

Fig. 21. Temporal zoom of the previous figure, shown over a time window of approximately 1 month (instead of 5 months in the previous figure). The (blue) curve designated as "PP1 (12h)" is the wavelet component signal C12H(t) extracted from PP1 relative pressure. The envelope is the (red) curve designated as "R(t)". The ∼ 11 day period of fast pressure change occurs between the dates of 7th and 19th of February 1998.

Comparing *Figure 21* to *Figure 19*, it is now clear (and remarkable) that the 11 day phase of rapidly increasing pore pressure (*Figure 19)* corresponds to a significant increase of the *amplitude* of the semi-diurnal component of pore pressure (*Figure 21)*. Recall, from *Fig. 19*, that this 11 day phase corresponds to the approach of the excavation front nearest to the PP1 pressure sensor (distance D(t) ∼ 4 m at the closest point).

#### **5.4 Calculation of specific storage Ss(t) as a function of time based on Bredehoeft's simplified hydro-mechanical model (strain / pressure)**

By analogy with the procedure described in *Section 4.1*-*4.1.1***,** we estimate again the elastic specific storativity Ss from the semi-diurnal wavelet component C12H(t) of relative pore pressure (using now the average of the 2 components at dyadic scales 8h and 16h, respectively). And again, we invoke the Bredehoeft earth tide strain/pressure model (see *Eq. 19* earlier).

Only, this time, instead of taking a constant amplitude for C12H(t), we use instead the time-modulated amplitude of C12H(t) represented by its statistical envelope "R(t)". On the other hand, since we still do not have direct *in situ* measurements of the volumetric strain Δε(t), we must replace Δε(t) by an indirect estimate of its amplitude based on data surveys: accordingly, we use again **|**Δε*| = 2*×*10-8 m3/m3* (as in *Sections 4.1 and 4.2*). In this way, we obtain, instead of *Eq. 19*:

$$S\_S\left(t\right) = \frac{\left|\Delta\varepsilon\right|}{R\left(t\right)}\tag{19b}$$

Statistical Analyses of Pore Pressure Signals in

**0**

**0.2**

**0.4**

**0.6**

**0.8**

**1**

**1.2**

**Specific storage Ss (m-1)**

**1.4**

**1.6**

**1.8**

**2 x 10-6**

Claystone During Excavation Works at the Mont Terri Underground Research Laboratory 419

Fig. 23. Evolution of the decimal logarithm of Ss(t), on the same time window as the previous figure (1.5 month). Here, the red curve shows Ss(t) calculated from the theoretical envelope (Hilbert Transform, Cramer-Leadbetter envelope), applied to the semi-diurnal dyadic

component of relative pore pressure PP1 during excavation of gallery Ga98. The distance D(t) of the excavation front from the PP1 pressure sensor is shown as the black curve with circles "o".

**~11days**

*Syn-excavation Ga98*

**3.6 3.62 3.64 3.66 3.68 3.7 3.72**

corresponding to the approach of the excavation front of gallery Ga98 to the pressure sensor.

Fig. 24. Zoomed view of the evolution of Ss(t) on a cartesian ordinate (rather than logarithmic). The plot is centered on the 11 day period of fast pressure change,

**Time(s)**

**x 107**

*Figure 22* shows the time evolution of log10 Ss(t), where Ss(t) was estimated using the empirical envelope R(t) computed by the method of maxima, rather than the theoretical Cramer-Leadbetter envelope computed by the Hilbert Transform. The evolution of the excavation front distance D(t) is also shown on the same graph.

*Figure 23* shows the time evolution of log10 Ss(t), using the theoretical Cramer-Leadbetter envelope (computed by the Hilbert Transform) to estimate Ss(t). The evolution of the excavation front distance D(t) is also shown on the same graph.

Comparing *Figure 22* and *Figure 23*, it is somewhat re-assuring that the two methods of estimating the wavelet envelope yield approximately the same results. Thus, we focus mostly on results obtained with the Hilbert Transform method for the remaining plots and analyses.

The time scale of *Figure 23* is about 1.5 month, including the interesting 11 day window of fast changes. It can be seen that the specific storativity *Ss(t*) decreases by one to two orders of magnitude during just *a few days*, as the excavation front approaches within roughly *6 m* to the PP1 pressure sensor (before reaching an even closer distance of *4 m*).

*Figure 24* shows a zoomed view of Ss(t) with a cartesian ordinate rather than semi-log. The zoomed time window is only about 2 weeks or so, to see more details in the 11 day period of fast change.

Finally, *Figure 25* gives a broader picture, depicting the time evolution of log10 Ss(t) over the entire "syn-excavation" phase of 5 months (including, again, the 11 day period of fast changes).

Fig. 22. Evolution of the decimal logarithm of Ss(t). The time window here is about 1.5 month or so, and it includes the 11 day period of fast change (*double arrow*). Here, Ss(t) is calculated from an empirical envelope (estimated with the lethod of maxima rather than the Hibert transform) of the semi-diurnal dyadic component of relative pore pressure PP1 during excavation (gallery Ga98, excavation from 17/11/1997 to 23/04/1998, time step Δt=30min).

*Figure 22* shows the time evolution of log10 Ss(t), where Ss(t) was estimated using the empirical envelope R(t) computed by the method of maxima, rather than the theoretical Cramer-Leadbetter envelope computed by the Hilbert Transform. The evolution of the

*Figure 23* shows the time evolution of log10 Ss(t), using the theoretical Cramer-Leadbetter envelope (computed by the Hilbert Transform) to estimate Ss(t). The evolution of the

Comparing *Figure 22* and *Figure 23*, it is somewhat re-assuring that the two methods of estimating the wavelet envelope yield approximately the same results. Thus, we focus mostly on results obtained with the Hilbert Transform method for the remaining plots and analyses.

The time scale of *Figure 23* is about 1.5 month, including the interesting 11 day window of fast changes. It can be seen that the specific storativity *Ss(t*) decreases by one to two orders of magnitude during just *a few days*, as the excavation front approaches within roughly *6 m*

*Figure 24* shows a zoomed view of Ss(t) with a cartesian ordinate rather than semi-log. The zoomed time window is only about 2 weeks or so, to see more details in the 11 day period of

Finally, *Figure 25* gives a broader picture, depicting the time evolution of log10 Ss(t) over the entire "syn-excavation" phase of 5 months (including, again, the 11 day period of fast changes).

Fig. 22. Evolution of the decimal logarithm of Ss(t). The time window here is about 1.5 month or so, and it includes the 11 day period of fast change (*double arrow*). Here, Ss(t) is calculated from an empirical envelope (estimated with the lethod of maxima rather than the Hibert transform) of the semi-diurnal dyadic component of relative pore pressure PP1 during excavation (gallery Ga98, excavation from 17/11/1997 to 23/04/1998, time step Δt=30min).

excavation front distance D(t) is also shown on the same graph.

excavation front distance D(t) is also shown on the same graph.

fast change.

to the PP1 pressure sensor (before reaching an even closer distance of *4 m*).

Fig. 23. Evolution of the decimal logarithm of Ss(t), on the same time window as the previous figure (1.5 month). Here, the red curve shows Ss(t) calculated from the theoretical envelope (Hilbert Transform, Cramer-Leadbetter envelope), applied to the semi-diurnal dyadic component of relative pore pressure PP1 during excavation of gallery Ga98. The distance D(t) of the excavation front from the PP1 pressure sensor is shown as the black curve with circles "o".

Fig. 24. Zoomed view of the evolution of Ss(t) on a cartesian ordinate (rather than logarithmic). The plot is centered on the 11 day period of fast pressure change, corresponding to the approach of the excavation front of gallery Ga98 to the pressure sensor.

Statistical Analyses of Pore Pressure Signals in

**6. Summary, conclusions, and outlook**

**6.1 Summary and conclusions**

Terri's LP 14 experiment.

Claystone During Excavation Works at the Mont Terri Underground Research Laboratory 421

We have presented in this chapter a set of statistical methods for pre-processing and analysing multivariate hydro-geo-meteorological time series, and we have developed hydro-mechanical interpretations, in order to infer hydro-geological properties such as Ss and Φ. The aim of this study is to quantify some of the properties of the clay rock in terms of elastic response to barometric and earth tides fluctuations, both *globally* and *locally* in spacetime. We focused on atmospheric and pore water pressure signals measured in Opalinus clay stone, at the Mont Terri underground rock laboratory (URL), in the framework of Mont

Pre-processing methods were developed in order to detect and correct some defects common to most time series data, like aberrations or outliers, variable time steps, and missing data. These pre-processing steps are necessary, in most cases, to obtain signals that are both "clean" and long enough for useful analyses. Durations of a couple of weeks to a few months are needed for short scale analyses related to excavation works.  Once the pressure signals were pre-processed (reconstructed), statistical analyses were performed with cross-correlation functions and cross-spectra, and with multi-resolution wavelet analyses. These techniques were then used to determine "globally" some hydromechanical parameters of the Opalinus clay: elastic specific storativity (Ss), and effective elastic porosity (Φ). The values compare favourably with data from the literature, obtained independently with completely different methods. In particular, the simplified hydromechanical model of *Bredehoeft* relating pREL(t) to earth tides was applied to the "12h" dyadic component of pREL(t), leading to a global estimated Ss value of 10-6 m-1 (1E-6 m-1) in

excellent agreement with that deduced from hydraulic tests at the Mont Terri site.

D(t) (or of the "EdZ" around and ahead of the front).

hydro-mechanical variations of pressure and stress.

during the passage of the excavation front.

After this "global" characterization of the clay from long term pore pressure measurements, we turned our attention to the (significant) impact of excavation works on pore pressure signals. We devised an original method to infer the time evolution of clay rock properties (Ss(t)) due to the excavation disturbance. The pressure disturbance coïncides (with some lead time or negative delay) with the arrival near the pressure sensor of the excavation front

Indeed, pressure signals recorded in the PP1 chamber of the BPP-1 borehole during excavation of the Ga98 gallery, have shown a net increase of absolute pressure (+5.5 bars) over the 11 day period of fast change (or as much as +7 bars over the total 5 month "*synexcavation*" phase). This is evidence of a direct hydro-mechanical disturbance of the rock

A study of the signal on longer time scales (from pre- to post-excavation stages, *not shown in this text for lack of space*) confirmed that the disturbance due to excavation was indeed reversible. A slow relaxation of pore pressure was observed during a period of about two years (or somewhat less) subsequent to the end of excavation, reaching approximately the value it had before excavation. This observation appears to justify our initial remark on the distinction between "EDZ" (*irreversibly damaged* "Excavation Damaged Zone"), and "EdZ" (*Excavation disturbed Zone*). The latter "EdZ" is a *reversibly disturbed* zone due to quasi-elastic

Fig. 25. A broader view of the evolution of log Ss(t) (red curve, computed with the Hilbert Transform envelope). Here the time window is the entire "syn-excavation" phase of 5 months (including, again, the 11 day period of very fast changes). The black curve with circles "o" represents the distance D(t) of the excavation front from the PP1 pressure sensor.

#### **5.5 Calculation of elastic porosity** Φ**(t) from barometric effect (diurnal gain pREL/pATM) and from the previously estimated Ss(t)**

Finally, from the previously estimated evolution of Ss(t), and using the spectral barometric gain at 1/24h frequency (*as in Section 4.1.2*), it is possible to apply again the simplified hydro-mechanical model of *Eq. 21,* in order to estimate the time-varying elastic porosity Φ(t):

$$\Phi(t) = \frac{E\_w \times B}{\rho \times g} \times S\_S(t) \tag{21b}$$

where *Ss(t)* is the time varying specific storativity obtained earlier from the strain/pressure envelope (**Eq.11b,** *Section 5.4*).

It should be observed that, in this analysis, the elastic porosity Φ(t) varies in time proportionally to Ss(t). It can be seen that a constant barometric efficiency "B" is assumed; the diurnal gain "g" between atmospheric and relative pore pressure is assumed constant during excavation. But, because pore pressure is influenced by excavation (even if air pressure is not), the assumption of constant barometric gain ("B" or "g") during excavation is debatable and should be verified.

In conclusion, a revised version of the procedure should be to analyse the diurnal barometric gain, like the semi-diurnal earth tide effects, in a wavelet framework rather than in a Fourier spectral framework. This would provide a tool to either capture or eliminate, depending on purpose, any non stationary / evolutionary phenomena.

#### **6. Summary, conclusions, and outlook**

#### **6.1 Summary and conclusions**

420 Radioactive Waste

Fig. 25. A broader view of the evolution of log Ss(t) (red curve, computed with the Hilbert Transform envelope). Here the time window is the entire "syn-excavation" phase of 5 months (including, again, the 11 day period of very fast changes). The black curve with circles "o" represents the distance D(t) of the excavation front from the PP1 pressure sensor.

**5.5 Calculation of elastic porosity** Φ**(t) from barometric effect (diurnal gain pREL/pATM)**

Finally, from the previously estimated evolution of Ss(t), and using the spectral barometric gain at 1/24h frequency (*as in Section 4.1.2*), it is possible to apply again the simplified hydro-mechanical model of *Eq. 21,* in order to estimate the time-varying elastic porosity

> ( ) ( ) *w S E B t St* ρ *g* × Φ= × ×

where *Ss(t)* is the time varying specific storativity obtained earlier from the strain/pressure

It should be observed that, in this analysis, the elastic porosity Φ(t) varies in time proportionally to Ss(t). It can be seen that a constant barometric efficiency "B" is assumed; the diurnal gain "g" between atmospheric and relative pore pressure is assumed constant during excavation. But, because pore pressure is influenced by excavation (even if air pressure is not), the assumption of constant barometric gain ("B" or "g") during excavation is

In conclusion, a revised version of the procedure should be to analyse the diurnal barometric gain, like the semi-diurnal earth tide effects, in a wavelet framework rather than in a Fourier spectral framework. This would provide a tool to either capture or eliminate,

depending on purpose, any non stationary / evolutionary phenomena.

(21b)

**and from the previously estimated Ss(t)**

envelope (**Eq.11b,** *Section 5.4*).

debatable and should be verified.

Φ(t):

We have presented in this chapter a set of statistical methods for pre-processing and analysing multivariate hydro-geo-meteorological time series, and we have developed hydro-mechanical interpretations, in order to infer hydro-geological properties such as Ss and Φ. The aim of this study is to quantify some of the properties of the clay rock in terms of elastic response to barometric and earth tides fluctuations, both *globally* and *locally* in spacetime. We focused on atmospheric and pore water pressure signals measured in Opalinus clay stone, at the Mont Terri underground rock laboratory (URL), in the framework of Mont Terri's LP 14 experiment.

Pre-processing methods were developed in order to detect and correct some defects common to most time series data, like aberrations or outliers, variable time steps, and missing data. These pre-processing steps are necessary, in most cases, to obtain signals that are both "clean" and long enough for useful analyses. Durations of a couple of weeks to a few months are needed for short scale analyses related to excavation works.

Once the pressure signals were pre-processed (reconstructed), statistical analyses were performed with cross-correlation functions and cross-spectra, and with multi-resolution wavelet analyses. These techniques were then used to determine "globally" some hydromechanical parameters of the Opalinus clay: elastic specific storativity (Ss), and effective elastic porosity (Φ). The values compare favourably with data from the literature, obtained independently with completely different methods. In particular, the simplified hydromechanical model of *Bredehoeft* relating pREL(t) to earth tides was applied to the "12h" dyadic component of pREL(t), leading to a global estimated Ss value of 10-6 m-1 (1E-6 m-1) in excellent agreement with that deduced from hydraulic tests at the Mont Terri site.

After this "global" characterization of the clay from long term pore pressure measurements, we turned our attention to the (significant) impact of excavation works on pore pressure signals. We devised an original method to infer the time evolution of clay rock properties (Ss(t)) due to the excavation disturbance. The pressure disturbance coïncides (with some lead time or negative delay) with the arrival near the pressure sensor of the excavation front D(t) (or of the "EdZ" around and ahead of the front).

Indeed, pressure signals recorded in the PP1 chamber of the BPP-1 borehole during excavation of the Ga98 gallery, have shown a net increase of absolute pressure (+5.5 bars) over the 11 day period of fast change (or as much as +7 bars over the total 5 month "*synexcavation*" phase). This is evidence of a direct hydro-mechanical disturbance of the rock during the passage of the excavation front.

A study of the signal on longer time scales (from pre- to post-excavation stages, *not shown in this text for lack of space*) confirmed that the disturbance due to excavation was indeed reversible. A slow relaxation of pore pressure was observed during a period of about two years (or somewhat less) subsequent to the end of excavation, reaching approximately the value it had before excavation. This observation appears to justify our initial remark on the distinction between "EDZ" (*irreversibly damaged* "Excavation Damaged Zone"), and "EdZ" (*Excavation disturbed Zone*). The latter "EdZ" is a *reversibly disturbed* zone due to quasi-elastic hydro-mechanical variations of pressure and stress.

Statistical Analyses of Pore Pressure Signals in

be determined both at once.

used a fixed value, **|Δε***| = 2*

relative pore pressure pREL(t).

not straightforward and requires further analyses.

to better interpret the effects of these signals.

compressible hydrogeologic medium.

future:

enhanced:

Claystone During Excavation Works at the Mont Terri Underground Research Laboratory 423

The multi-cross analysis of these signals will also serve as a complement to physically based models, with some of the signals considered as inputs, and others considered as outputs of the models. It will be very useful to link the statistical approaches with physically-based models that can account for the hydro-mechanical coupling between pore pressure and *exogeneous* fluctuations (piezometric variations in adjacent aquifers, barometric fluctuations, and earth tides). In addition, some aspects of the procedures developed in this work could be modified in

• Thus, we developed a sequential procedure to estimate first "Ss" then "Φ". First, we estimated "Ss" from wavelet analysis of semi-diurnal earth tide effects, and secondly, we estimated "Φ" from spectral analysis of barometric gain at diurnal frequency (given the previously estimated "Ss"). In reality, these 2 steps need not be implemented sequentially: they can be viewed as a system of 2 equations with 2 unknowns (Ss, Φ) to

• To estimate the global "Ss" and (also) the evolutionary "Ss(t)" during excavation, we

Another extension worth considering concerns the simplified hydromechanical "models" which we have used so far for interpreting the pressure signals. These models need to be

• Thus, it was noted that "Ss" represents an equivalent elastic coefficient for the water filled poro-elastic rock. However, this concept rests on a simplified view of poro-elastic deformations, usually applied to confined aquifers. Its interpretation for the hydrogeologic configuration and boundary conditions of the claystone at Mont Terri is

• Also, a more "physical" hydromechanical approach based on Biot's poro-elastic theory (*Biot 1956*) could be developed, as in the coupled T-H-M models developed in *Ababou et al. (2005)* and *Canamon (2009).* Such models should be upgraded with explicit coupling of pore pressure to external "forcing" functions (air pressure, earth tides, etc.), in order

• Finally, the hydro-mechanical model could be constructed to predict space-time propagations explicitly. Thus, *Mallet et al. (2007, 2008*) developed a simple model to illustrate pore pressure fluctuations and propagation under boundary forcing in a

In summary, the simplified hydro-mechanical models used in this study can be replaced, in future, with models based on PDE systems. The statistical "interpretations" of pressure signals presented in this text will then appear as the solution of PDE inverse problems (in a statistical setting). This point of view sheds a new light on the coefficients (Ss, Φ) obtained in the present study. They can be viewed as the solution of an inverse problem based on

related to the M2 semi-diurnal earth tide (*based on Melchior 1978, Bredhoeft 1967, and others*). This is because the site specific signal of volumetric strain Δε(t) was not available, so we had to estimate its amplitude indirectly from data surveys. Nevertheless, our method can be extended to the case where the strain signal Δε(t) is available. The new procedure would be to apply semi-diurnal wavelet analysis, then envelope analysis, to the Δε(t) signal, in a way similar to that already implemented for

*10-8 m3/m3*, for the amplitude of the volumetric strain

×

In summary, the signal analysis and processing methods applied at various (long/short) time scales, exploit the influence of natural "forcings" like earth tides and barometric fluctuations on pore pressure signals. Combining multi-resolution wavelet and he Cramer/Hilbert envelope analysis reveals a time modulation (disturbance) of the "12h" dyadic wavelet component, suggesting a modification in time of the specific storativity Ss(t) during the excavation of gallery passing nearby the pressure sensor. During the passage of excavation, there is a net decrease of Ss(t) by almost two orders of magnitude, from 10-6 (1E-6) m-1, down to 10-8 (1E-8) m-1. This minimum occurs during a short period of just a few days, corresponding to front crossing (actually, in advance of front crossing by a couple of meters).

This result demonstrates how statistical analyses on pore pressures can be a valuable tool in the assessment of potential clay repositories for the purpose of high level radioactive waste disposal in deep, isolating geologic formations.

#### **6.2 Outlook**

A useful extension of this work would involve the development of a multivariate or "*multi-cross* analysis" of time series data {Xi(t), i = 1 , 2, …, K}, where the Xi's are either reconstructed or raw signals, involving possibly a number of pore pressures measured in different boreholes at different measurement sections, as well as other types of signals such as air pressure, air temperature, air humidity (relative or absolute), wall crack displacements, and moisture contents in the rock.

Accordingly, in multi-cross analysis, the results would be expressed in matrix form *MXiXj(s)* where "s" is the relevant parameter (time lag, frequency, etc.): thus *MXiXj(s)* may represent a K×K matrix of cross-correlation functions, or of Fourier cross-spectra, and/or, of multiresolution cross-wavelets (or their cross-correlations at given scales). These analyses will be useful for assessing the added value of *all* signals collected at the site, in terms of the "information" gained concerning the hydro-geologic properties of clay rock at different time scales (hourly, daily, yearly).

The purpose of such multi-cross analyses might be to integrate the complete set of all available signals in order to solve an *inverse problem*, namely, the identification of hydrogeologic properties from observations of state variables. Thus, in the work presented here, the state variables were the pore pressure at different sensors, atmospheric pressure, and (indirectly) tidal strain. The properties to be identified were (Ss, Φ) - but this set of unknown coefficients could be extended in future, in a generalized treatment of the "hydro-geologic identification problem".

For instance, techniques to estimate the hydraulic conductivity "K" from natural signals sampled at different positions might be developed as a complement to classical well pumping tests (*e.g. pulse tests*). Indeed "K" is an important property for a geologic radioactive waste repository, as "K" must be low to efficiently isolate radioactive waste from the environment. Furthermore, it is well known that "K" may vary greatly in geologic media, depending on the spatial scale of analysis (e.g. *Ababou 2008, Sahimi 1993*, *Gelhar 1993, Ababou et al. 1990,*). With the "multi-cross" concept, the spatial scales of analysis can be associated with the distances between sensors.

In summary, the signal analysis and processing methods applied at various (long/short) time scales, exploit the influence of natural "forcings" like earth tides and barometric fluctuations on pore pressure signals. Combining multi-resolution wavelet and he Cramer/Hilbert envelope analysis reveals a time modulation (disturbance) of the "12h" dyadic wavelet component, suggesting a modification in time of the specific storativity Ss(t) during the excavation of gallery passing nearby the pressure sensor. During the passage of excavation, there is a net decrease of Ss(t) by almost two orders of magnitude, from 10-6 (1E-6) m-1, down to 10-8 (1E-8) m-1. This minimum occurs during a short period of just a few days, corresponding to front crossing (actually, in advance of front crossing by a couple of

This result demonstrates how statistical analyses on pore pressures can be a valuable tool in the assessment of potential clay repositories for the purpose of high level radioactive waste

A useful extension of this work would involve the development of a multivariate or "*multi-cross* analysis" of time series data {Xi(t), i = 1 , 2, …, K}, where the Xi's are either reconstructed or raw signals, involving possibly a number of pore pressures measured in different boreholes at different measurement sections, as well as other types of signals such as air pressure, air temperature, air humidity (relative or absolute), wall crack

Accordingly, in multi-cross analysis, the results would be expressed in matrix form *MXiXj(s)* where "s" is the relevant parameter (time lag, frequency, etc.): thus *MXiXj(s)* may represent a K×K matrix of cross-correlation functions, or of Fourier cross-spectra, and/or, of multiresolution cross-wavelets (or their cross-correlations at given scales). These analyses will be useful for assessing the added value of *all* signals collected at the site, in terms of the "information" gained concerning the hydro-geologic properties of clay rock at different time

The purpose of such multi-cross analyses might be to integrate the complete set of all available signals in order to solve an *inverse problem*, namely, the identification of hydrogeologic properties from observations of state variables. Thus, in the work presented here, the state variables were the pore pressure at different sensors, atmospheric pressure, and (indirectly) tidal strain. The properties to be identified were (Ss, Φ) - but this set of unknown coefficients could be extended in future, in a generalized treatment of the "hydro-geologic

For instance, techniques to estimate the hydraulic conductivity "K" from natural signals sampled at different positions might be developed as a complement to classical well pumping tests (*e.g. pulse tests*). Indeed "K" is an important property for a geologic radioactive waste repository, as "K" must be low to efficiently isolate radioactive waste from the environment. Furthermore, it is well known that "K" may vary greatly in geologic media, depending on the spatial scale of analysis (e.g. *Ababou 2008, Sahimi 1993*, *Gelhar 1993, Ababou et al. 1990,*). With the "multi-cross" concept, the spatial scales of analysis can be associated

meters).

**6.2 Outlook**

disposal in deep, isolating geologic formations.

displacements, and moisture contents in the rock.

scales (hourly, daily, yearly).

identification problem".

with the distances between sensors.

The multi-cross analysis of these signals will also serve as a complement to physically based models, with some of the signals considered as inputs, and others considered as outputs of the models. It will be very useful to link the statistical approaches with physically-based models that can account for the hydro-mechanical coupling between pore pressure and *exogeneous* fluctuations (piezometric variations in adjacent aquifers, barometric fluctuations, and earth tides).

In addition, some aspects of the procedures developed in this work could be modified in future:

Another extension worth considering concerns the simplified hydromechanical "models" which we have used so far for interpreting the pressure signals. These models need to be enhanced:

In summary, the simplified hydro-mechanical models used in this study can be replaced, in future, with models based on PDE systems. The statistical "interpretations" of pressure signals presented in this text will then appear as the solution of PDE inverse problems (in a statistical setting). This point of view sheds a new light on the coefficients (Ss, Φ) obtained in the present study. They can be viewed as the solution of an inverse problem based on

Statistical Analyses of Pore Pressure Signals in

"m")

spectra)

ρδ

*K* Hydraulic conductivity [m/s]

**MATHEMATICAL SYMBOLS: LATIN**

*CXY* ( ) τ

*RXY* ( ) τ

Claystone During Excavation Works at the Mont Terri Underground Research Laboratory 425

A**m**(t) Wavelet approximation of order "m" (multi-resolution dyadic scale

(relative pressure / atmospheric pressure effects)

*C t m* ( ) Wavelet component of dyadic scale "m" (time scale = 2**m**��t)

 Cross-covariance function of X(t) and Y(t), versus time-lag [units of Cxy] = [units of X(t)] � [units of Y(t)] D(j) or D(τ(j)) Tuckey-2 filter function of time-lag (used for estimation of Fourier

D**m**(t) Wavelet "detail" at dyadic scale "m" (*see also: wavelet component Cm(t)*)

*g f XY* ( ) Reduced spectral gain *vs.* frequency, obtained from cross-spectrum. The complex-valued reduced gain is defined as:

"f" is related to angular frequency "ω" by: f = ω /2π.

*f* Frequency "f" in [Hz] or [Number of cycles / second];

*H* Total hydraulic head [m], related to relative pressure by:

(sometimes unduly called "permeability")

*REL p* Relative pore pressure [Pa], defined as : *p pp REL ATM* = − (**\*)**  *R t*( ) Statistical envelope of a signal (the envelope is in fact ±R(t)).

Cross-correlation function of X(t) and Y(t), versus time-lag;

*s f XY* ( ) Reduced cross-spectrum of signals X(t) and Y(t), *vs.* frequency "f".

Rxy is the normalized version of Cxy: [units of Rxy] =

It is equal to the cross-spectrum *S f XY* ( ) divided by ( )

The cross-spectrum is complex-valued (even if the signals are real-

σ σ*X Y* × .

2 *M*2, *M* Moon semi-diurnal component of astronomic tides (here, earth tides)

*g f s fs f XY XY XX* () () () = .

*REL*

*k* Permeability (intrinsic Darcy permeability) in [m2]

, *ABS p p* Pore pressure (or "absolute" pore pressure), [Pa]. (**\*)**

*pATM* Atmospheric pressure (or air pressure), [Pa]. (**\*)**

 δ*gH p* =

[dimensionless]

valued).

, , *B BE BE* Barometric efficiency, [dimensionless] or [Pa/Pa]

*C t* 12*H* ( ) Wavelet component of scale 12h (semi-diurnal)

spectral gain (pREL/pATM) and on wavelet amplitude ratio (|Δε|/|ΔpREL|). For this reason, it is thought that the statistical methods used here can be adapted for solving an inverse problem involving a hydro-mechanical PDE model forced by pressure signals and other measurements (humidity, temperature, etc.).

#### **7. Acknowledgments**

This chapter presents data analyses developed within Mont Terri's LP 14 experiment (Long term Pressure monitoring project, phase 14), as part of the international research programs of the MONT TERRI CONSORTIUM on the properties of claystone as a potential geologic repository for radioactive waste. The authors acknowledge the support of institutions participating in the LP 14 project at Mont Terri (ANDRA, NAGRA, IRSN, NWMO, SWISSTOPO). In addition, the authors gratefully acknowledge the help and advice provided by the following persons: Paul Bossart (SWISSTOPO); Martin Cruchaudet (ANDRA); David Jaeggi (SWISSTOPO); Herwig Mueller (NAGRA); Eric Sykes (NWMO). The authors wish also to thank Alain Mangin (CNRS-UPS Toulouse, Laboratoire Souterrain de Moulis) who initiated some of the statistical tools and methods used in this project, and others who provided scientific advice on various issues (cracks, geophysics, signals, hydrogeology, porous media): Andrea Möri (SWISSTOPO); Jacques Delay (ANDRA, LSM/HM Bure); Israel Cañamón Valera (Universidad Politecnica de Madrid); Moumtaz Razak (Université de Poitiers, HYDRASA); and Michel Quintard (IMFT, Toulouse).

#### **8. Appendix: Symbols and abbreviations**

#### **MATHEMATICAL SYMBOLS: LATIN**

424 Radioactive Waste

spectral gain (pREL/pATM) and on wavelet amplitude ratio (|Δε|/|ΔpREL|). For this reason, it is thought that the statistical methods used here can be adapted for solving an inverse problem involving a hydro-mechanical PDE model forced by pressure signals and other

This chapter presents data analyses developed within Mont Terri's LP 14 experiment (Long term Pressure monitoring project, phase 14), as part of the international research programs of the MONT TERRI CONSORTIUM on the properties of claystone as a potential geologic repository for radioactive waste. The authors acknowledge the support of institutions participating in the LP 14 project at Mont Terri (ANDRA, NAGRA, IRSN, NWMO, SWISSTOPO). In addition, the authors gratefully acknowledge the help and advice provided by the following persons: Paul Bossart (SWISSTOPO); Martin Cruchaudet (ANDRA); David Jaeggi (SWISSTOPO); Herwig Mueller (NAGRA); Eric Sykes (NWMO). The authors wish also to thank Alain Mangin (CNRS-UPS Toulouse, Laboratoire Souterrain de Moulis) who initiated some of the statistical tools and methods used in this project, and others who provided scientific advice on various issues (cracks, geophysics, signals, hydrogeology, porous media): Andrea Möri (SWISSTOPO); Jacques Delay (ANDRA, LSM/HM Bure); Israel Cañamón Valera (Universidad Politecnica de Madrid); Moumtaz Razak (Université de

ANDRA Agence Nationale pour la gestion des Déchets RAdioactifs (*France*)

EdZ Excavation disturbed Zone (reversibly disturbed zone around an

EDZ Excavation Damaged Zone (irreversibly damaged, fissured and fractured zone around an excavation in rock)

IRSN Institut de Radioprotection et de Sûreté Nucléaire (France) LP14 Long term Pressure monitoring project - phase 14 (Mont Terri

NAGRA National Cooperative for the Disposal of Radioactive Waste

URL Underground Rock Laboratory (*or:* Underground Research

PP Pore Pressure, i.e., absolute pore water pressure (*Mont Terri site*) SWISSTOPO Swiss Federal Office of Topography (*and Mont Terri Project*)

NWMO Nuclear Waste Management Organization (*Canada*)

T-H-M or THM Thermo-Hydro-Mechanical (coupled models)

excavation in rock, elastic hydro-mechanical disturbance)

BPP Borehole instrumented for Pore Pressure measurements

measurements (humidity, temperature, etc.).

Poitiers, HYDRASA); and Michel Quintard (IMFT, Toulouse).

(*Mont Terri site*)

Project)

(*Switzerland*)

Laboratory)

**8. Appendix: Symbols and abbreviations**

**ABBREVIATIONS, ACRONYMS**

**7. Acknowledgments**

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(**\*)** Pressures "p" are sometimes denoted with a capital "P" within the text.

#### **MATHEMATICAL SYMBOLS: GREEK**

#### **9. References**

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Time-lag or "delay", used in correlation function analyses:

(**\*)** Pressures "p" are sometimes denoted with a capital "P" within the text.

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**1. Introduction**

Among the most severe sources of potential concern in terms of natural environment contamination with antropogenic radionuclides, a huge potential is associated to the radioactive waste resulting from the processing of the nuclear fuel used for energy generation purposes and from military and medical actvities. Although it represents about 3% of the total radioactive waste existing nowadays in the world, its total radioactivity amounts to more than 95% of that of the low & intermediate level and high-level radioactive waste taken together (Hu et al., 2010). By the present time, deep geologic disposal is considered to be the safest method for isolating highly radioactive and long-lived waste over millennia (Acero et al., 2010; Kim et al., 2011; Kurosawa & Ueta, 2001), while for the low and intermediate radioactive waste management, near surface storage is, for economic reasons, the preferred

**Particulate Phases Possibly Conveyed from**

**Nuclear Waste Repositories by Groundwater**

*"Emil Racovit¸Ć" Institute of Speleology of the Romanian Academy,*

Constantin Marin

*Bucharest Romania*

**18**

It is a well-known fact that groundwater represents the most effective agent by which radionuclides stored in repositories could be transferred to the adjacent environment (Altmann, 2008; Baik et al., 2009; Geckeis & Rabung, 2008; Wersin et al., 2011). This is the reason why, each time when the issue of the radioactive waste repositories is addressed, irrespective of the repository type or of its inventory of stored radionuclides, the primary

Radionuclides may be conveyed by groundwater in a dissolved state, but especially in association with particles of various origins that are carried along with water. Those particles may have various structures and chemical compositions, their possible natures being: inorganic, organic or even micro-organisms. The inorganic particles genesis is closely related to the geochemistry of the environment with which groundwater is in contact, while particles

Particles dimensions may be very different, ranging from those of the colloids, up to microscopic particles, generically designated as "suspended particulate matter". Their reactivity and their ability of binding and conveying contaminants is to a certain extent controlled by their dimension, namely their reactivity is progressively enhanced as the particulate phase is more finely dispersed (Kersting & Zavarin, 2011; Wigginton et al., 2007).

option (Dogaru et al., 2010; IAEA, 2004; Niculae et al., 2009).

concern is to assess the local groundwater contamination risk.

of organic and biological nature are, as a general rule, allochtonous.

### **Particulate Phases Possibly Conveyed from Nuclear Waste Repositories by Groundwater**

Constantin Marin

*"Emil Racovit¸Ć" Institute of Speleology of the Romanian Academy, Bucharest Romania*

#### **1. Introduction**

430 Radioactive Waste

Schaeren, G.and Norbert, J. (1989): Tunnels du Mont Terri et du Mont Russelin. La traversée

Takeuchi, H (1950): On the earth tide of the compressible earth of variable density and elasticity. *Transactions American Geophysical Union*: 31, 651-689, 1950. Terzaghi, V.K. (1936): "The Shearing Resistance of Saturated Soils and the Angle between

Thury M. & Bossart P. (1999): "Mont Terri rock laboratory. Results of hydrogeological,

Vanmarke E. (1983): *Random Fields Analysis and Synthesis*. The MIT Press, Cambridge MA,

Veneziano D. (1979): Envelopes of Vector Random processes and their Crossing Rates. *The*

Wang Y., R. Ababou, M. Marcoux (2010): "Signal Processing of Water Level Fluctuations in a

Yevjevich V., (1972): *Stochastic Processes in Hydrology*. Water Resources Publications, Fort

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Geochemical and geothechnical Experiments Performed in 1996 and 1997". *Swiss National Hydrological and Geological Survey*. Geologic Report N°23. Bern,

Sloping Sandy Beach Modeled in a Laboratory Wave Canal", in: *Experimental & Applied Modeling of Unsaturated Soils GSP202* (Proc.2010 GeoShanghai International Conference, Part II: Applied Modeling and Analyses. L. R. Hoyos, X. Zhang, A. J. Puppala, eds.). American Society of Civil Engineers: *ASCE Geotech. Special Publi. (GSP):* Vol.376, No.41103, pp.204-210. http://dx.doi.org/10.1061/41103(376)26 Yaglom, A. M. (1987). *Correlation Theory of Stationary and Related Random Functions: Basic*  Among the most severe sources of potential concern in terms of natural environment contamination with antropogenic radionuclides, a huge potential is associated to the radioactive waste resulting from the processing of the nuclear fuel used for energy generation purposes and from military and medical actvities. Although it represents about 3% of the total radioactive waste existing nowadays in the world, its total radioactivity amounts to more than 95% of that of the low & intermediate level and high-level radioactive waste taken together (Hu et al., 2010). By the present time, deep geologic disposal is considered to be the safest method for isolating highly radioactive and long-lived waste over millennia (Acero et al., 2010; Kim et al., 2011; Kurosawa & Ueta, 2001), while for the low and intermediate radioactive waste management, near surface storage is, for economic reasons, the preferred option (Dogaru et al., 2010; IAEA, 2004; Niculae et al., 2009).

It is a well-known fact that groundwater represents the most effective agent by which radionuclides stored in repositories could be transferred to the adjacent environment (Altmann, 2008; Baik et al., 2009; Geckeis & Rabung, 2008; Wersin et al., 2011). This is the reason why, each time when the issue of the radioactive waste repositories is addressed, irrespective of the repository type or of its inventory of stored radionuclides, the primary concern is to assess the local groundwater contamination risk.

Radionuclides may be conveyed by groundwater in a dissolved state, but especially in association with particles of various origins that are carried along with water. Those particles may have various structures and chemical compositions, their possible natures being: inorganic, organic or even micro-organisms. The inorganic particles genesis is closely related to the geochemistry of the environment with which groundwater is in contact, while particles of organic and biological nature are, as a general rule, allochtonous.

Particles dimensions may be very different, ranging from those of the colloids, up to microscopic particles, generically designated as "suspended particulate matter". Their reactivity and their ability of binding and conveying contaminants is to a certain extent controlled by their dimension, namely their reactivity is progressively enhanced as the particulate phase is more finely dispersed (Kersting & Zavarin, 2011; Wigginton et al., 2007).