**Meet the editors**

Fausto obtained his European PhD with a maximum distinction and earned the distinguished prizes: Runner (2015), Advancement (2013), and Silver (2012) by the International Society of Management Science and Engineering Management (ICMSEM). He works at UCLM, Spain as Senior Lecturer (with tenure, accredited as Full-Time Professor), Honorary Senior Research Fellow

at Birmingham University, UK, and Lecturer at the Postgraduate European Institute. He also acted as Senior Manager in Accenture (2013–2014). He has written over 150 papers (65% ISI, 30% JCR and 92% internationals) and is the author and editor of 18 books and 5 patents. He is also the Editor of 3 international journals, and a Committee Member of over 25 international Conferences. He also acts as Director at www.ingeniumgroup.eu.

Dr Mayorkinos Papaelias (Ph.D. in Metallurgy, Chartered Engineer, Greece) is Senior Lecturer in NDT and Condition Monitoring at the School of Metallurgy and Materials at the University of Birmingham. Dr Papaelias is an expert in NDT and condition monitoring technology. He has been involved as technical coordinator or scientific consultant in several FP6 and FP7 collaborative

research projects. He is the author or co-author of more than 70 journal and conference papers in NDT and condition monitoring. He is also a Member of the International Society for Condition Monitoring. Dr Papaelias regularly authors articles for industrial magazines.

Dr. Noor Zaman is currently working as a Faculty member at King Faisal University, in Saudi Arabia. He headed the Department of Information Technology (IT), and administered the prometric center in the Institute of Business and Technology (BIZTEK) in Karachi, Pakistan. He has worked as a consultant for Network and Server Management remotely in Apex Canada USA base

Software house and call center. Dr. Noor Zaman has authored more than 50 research papers, and several internationally reputed edited books in the field of WSN, Energy Harvesting, Software development, Big data, Signal Processing and Cloud computing. He is an Associate Editor, Regional Editor and Reviewer for a number of reputed international research journals around the world. He has completed several international research grants and is currently involved with different funded projects internationally.

## Contents

### **Preface XI**

## Preface

Chapter 8 **Non-Destructive Techniques Applied to Monumental Stone**

Chapter 9 **Microwave Non‐Destructive Testing of Non‐Dispersive and**

Chapter 10 **Nondestructive Tests for Induction Machine Faults**

**Dispersive Media Using High‐Resolution Methods 215** Cédric Le Bastard, Khaled Chahine, Yide Wang, Vincent Baltazart,

Paulo Cezar Monteiro Lamim Filho, Lane Maria Rabelo Baccarini

Nicolas Pinel, Christophe Bourlier and Xavier Derobert

**Conservation 173** Beatriz Menéndez

**VI** Contents

**Diagnosis 249**

and Robson Pederiva

Non-destructive testing (NDT) is based on inspection methodologies that do not require the change or destruction of the component or system under evaluation. Numerous NDT tech‐ niques are increasingly used, thanks to the recent advances in sensing technologies, data ac‐ quisition, data storage and signal processing. Inspection information is widely employed in order to make effective maintenance decisions based on the defects identified, their location and severity. This book presents the main advances recently made on different NDT techni‐ ques, together with the principal approaches employed to process the signals obtained dur‐ ing inspection.

The first chapter introduces the development of a new remote monitoring technique for the evaluation of corrosion in reinforced concrete structures employing embeddable variations of known ASTM standards and telecommunication technologies. This is a new way for esti‐ mating the rate of mass loss in steel rebars. Corrosion of steel rebars is one of the most com‐ mon causes of structural degradation in civil infrastructure. The technique is based on the creation of an electrochemical half-cell that can be embedded indefinitely into the concrete, providing corrosion rate measurements. The technique uses as an electrode of Copper/ Copper Sulphate, a segment of the same steel of the studied structure as working electrode and an auxiliary electrode made from pure graphite, all covered by mortar.

Chapter 2 considers the mechanical model and control equation for analysing the mechani‐ cal behaviour of marine risers in working conditions. The control equation has been em‐ ploys the weighed residual method, while the analysis model has been verified using finite element analysis (FEA). The deformation and stress distribution within the marine riser are acquired. The simulated experimental system is introduced together with the system com‐ position, functions and operational approach of the experimental setup. A tubular sample has been manufactured to simulate the marine riser. The simulated experiments are carried out considering this setup. Finally, the strain and stress values of the specimen are obtained take into account the analysis of the data obtained.

The next Chapter 3 presents a novel beamforming array technique and probability-based diagnostic imaging method to determine acoustic emission (AE) sources in plate-like struc‐ tures. The technique differs from the common beamforming array techniques as a sensor network instead of a linear sensor array is employed. To reduce uncertainty, avoid the boundary reflection effect and ensure the rationality of the signal superposition, a Hilbert transform–based signal processing is applied before the delay-and-sum algorithm, and a probability-based diagnostic imaging method is developed for AE source localisation. Finite element numerical simulations and Hus-Nielson source tests have been carried out on alu‐ minium plate and a thin-walled cylinder pipe-like structure as part of the development of the proposed method. The results indicate that this method is efficient and capable of visual‐ ising the location results highlighted in the probability images.

Chapter 4 describes guided wave experiments and modelling results for pipeline wall thin‐ ning. Propagation of guided waves and classification of detected features based on signal amplitude are considered in this chapter. The outcome of this interpretation is a decision as to whether the follow-up inspection is classified as high, medium or low priority, and it re‐ quires to be determined. This can be done by analysing the signal amplitude corresponding to a specific level of metal loss. If the resonance can be obtained for specific frequency, the operator can identify the wall thickness loss by interpreting the reflected guided wave ener‐ gy amplitude. The research presented in this chapter identified the suitable way of deploy‐ ing this strategy using thickness resonance. Dispersion curves are evaluated and the thickness loss effect on the dispersion curves are evaluated. The experiments carried out prove the effectiveness of the methodology employed.

Chapter 5 analyses the application of the AE technique to detect crack location in steel and concrete structures. An improved approach, modified from the classical crack source loca‐ tion method, is proposed to provide more reliable data in masonry structures. It is intro‐ duced a new parameter, the degree of inhomogeneity, ξ, that is employed in the case of the modified method considered herewith. This parameter helps to decrease the unavoidable propagation delay related to refraction due to the layers in masonry material. The modified method is successfully applied to the AE source detection during the Hsu-Nielson source test. Tests are done on the central pier settlement of a model bridge to analyse the crack pat‐ tern. The results indicate that the proposed method is a reliable tool for crack source location in masonry structures.

Chapter 6 emphasises the need of a new electromagnetic NDT methodology to provide the basis of the accurate magnetic representation of surface topography. It considers that a con‐ cave-shaped feature produces "positive" magnetic flux leakages, and therefore forms a "raised" signal wave, but a bump-shaped feature generates "negative" magnetic fields, lead‐ ing to a "sunken" signal one. In this case, the corresponding relationships between the wave features and surface topography are presented, and the relevant evaluation system for test‐ ing surface topography (concave, bumped and flat features) is built. The methodology is an‐ alysed and verified by FEA and experiments. The different dimension parameters, height/ depth and width of surface topography, are also studied.

Chapter 7 introduces the metrology and measurement methods applied for NDT investiga‐ tion of electrical discharges occurring in oil insulation systems of high-voltage devices. The main objective is a detailed and multivariate analysis of physical phenomena associated with generation of electrical partial discharges that occurs in oil insulation of electrical equipment. An important cognitive component is the verification whether the form of parti‐ al discharge (PD) has an effect on the energy contribution of the physical phenomena associ‐ ated with their generation. An analysis of physical phenomena associated with the generation in insulating oil is designed and implemented, where the PD is simulated as fol‐ lows: 1) a surface system; 2) needle-needle system in insulating oil and 3) needle-needle sys‐ tem in insulating oil with gas bubbles. The optical signals (IR, UV and visible), ultra–highfrequency electromagnetic and high-energy X-ray radiation, acoustic emission and thermal images are also considered. The signals are studied as multi-variant an in the time and fre‐ quency domains.

Chapter 8 considers the NDT applicability for evaluating cultural heritage buildings because of the high cultural value of the concerned assets and need to preserve them as intact as possible. Different NDT techniques applied for the evaluation of the condition of historical buildings are presented. The selected techniques concern the measurement of some physical properties of the construction materials measured at the surface such as water absorption, permeability, water content, cohesion, hardness, etc.; the actual condition of the building in‐ cluding stress state, deformation, crack growth, etc., and the in-depth physical properties, including mechanical properties, inner structure of walls, damp location and salt content. Some of these techniques are used for inspection of the buildings at a given time; others can be applied for long periods of time to investigate the degradation of the structural integrity with time. The main objective of this review is to focus on the applications, especially to discuss which information can be supplied and to present published results in each case. Some techniques are very simple and require inexpensive equipment, but others, using more sophisticated technology, require post-acquisition treatments based on more complex physical principles. Some examples of combinations of different techniques are presented.

the proposed method. The results indicate that this method is efficient and capable of visual‐

Chapter 4 describes guided wave experiments and modelling results for pipeline wall thin‐ ning. Propagation of guided waves and classification of detected features based on signal amplitude are considered in this chapter. The outcome of this interpretation is a decision as to whether the follow-up inspection is classified as high, medium or low priority, and it re‐ quires to be determined. This can be done by analysing the signal amplitude corresponding to a specific level of metal loss. If the resonance can be obtained for specific frequency, the operator can identify the wall thickness loss by interpreting the reflected guided wave ener‐ gy amplitude. The research presented in this chapter identified the suitable way of deploy‐ ing this strategy using thickness resonance. Dispersion curves are evaluated and the thickness loss effect on the dispersion curves are evaluated. The experiments carried out

Chapter 5 analyses the application of the AE technique to detect crack location in steel and concrete structures. An improved approach, modified from the classical crack source loca‐ tion method, is proposed to provide more reliable data in masonry structures. It is intro‐ duced a new parameter, the degree of inhomogeneity, ξ, that is employed in the case of the modified method considered herewith. This parameter helps to decrease the unavoidable propagation delay related to refraction due to the layers in masonry material. The modified method is successfully applied to the AE source detection during the Hsu-Nielson source test. Tests are done on the central pier settlement of a model bridge to analyse the crack pat‐ tern. The results indicate that the proposed method is a reliable tool for crack source location

Chapter 6 emphasises the need of a new electromagnetic NDT methodology to provide the basis of the accurate magnetic representation of surface topography. It considers that a con‐ cave-shaped feature produces "positive" magnetic flux leakages, and therefore forms a "raised" signal wave, but a bump-shaped feature generates "negative" magnetic fields, lead‐ ing to a "sunken" signal one. In this case, the corresponding relationships between the wave features and surface topography are presented, and the relevant evaluation system for test‐ ing surface topography (concave, bumped and flat features) is built. The methodology is an‐ alysed and verified by FEA and experiments. The different dimension parameters, height/

Chapter 7 introduces the metrology and measurement methods applied for NDT investiga‐ tion of electrical discharges occurring in oil insulation systems of high-voltage devices. The main objective is a detailed and multivariate analysis of physical phenomena associated with generation of electrical partial discharges that occurs in oil insulation of electrical equipment. An important cognitive component is the verification whether the form of parti‐ al discharge (PD) has an effect on the energy contribution of the physical phenomena associ‐ ated with their generation. An analysis of physical phenomena associated with the generation in insulating oil is designed and implemented, where the PD is simulated as fol‐ lows: 1) a surface system; 2) needle-needle system in insulating oil and 3) needle-needle sys‐ tem in insulating oil with gas bubbles. The optical signals (IR, UV and visible), ultra–highfrequency electromagnetic and high-energy X-ray radiation, acoustic emission and thermal images are also considered. The signals are studied as multi-variant an in the time and fre‐

ising the location results highlighted in the probability images.

prove the effectiveness of the methodology employed.

depth and width of surface topography, are also studied.

in masonry structures.

VIII Preface

quency domains.

Chapter 9 discusses the principle and application of two model-based algorithms for proc‐ essing non-dispersive and dispersive ground penetrating radar (GPR) data over layered me‐ dium under monostatic antenna configuration. Both algorithms are selected for their high time resolution capability and reduced computational burden. They allow GPR radar to measure a layer thickness smaller than the fraction of the dominant wavelength. For nondispersive data, the ESPRIT algorithm is generalized to handle different types of data mod‐ els employed in experiments and literature. For dispersive data, the proposed adaptation of the MPM algorithm allows recovering the full-time resolution and jointly estimating the time delays and quality factors of a layered medium with reduced bias. Both processing techniques are applied to probe layered roadways for NDT purposes.

The last chapter presents several methods of NDT for induction motors based on the motor current signature analysis (MCSA), magnetic flux and vibration analysis. The method of analysis is a good alternative tool for destructive tests and fault detection in induction mo‐ tors. Numerical and experimental results demonstrate the effectiveness of the proposed technique. This chapter also presents a model suitable for computer simulation of induction motor in a healthy state and with general asymmetries that can be analysed simultaneously. The model makes it possible to conduct research on different characteristics of engines and outstanding effects produced by the faults.

> **Fausto Pedro Garcia Marquez** UCLM, Spain

> **Mayorkinos Papaelias** University of Birmingham, UK

**Noor Zaman** King Faisal University, Kingdom of Saudi Arabia

## **Remote Monitoring Technique for Evaluation of Corrosion on Reinforced Concrete Structures**

Guillermo Roa Rodríguez and Willian Aperador

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/62314

#### **Abstract**

This chapter presents the development of a new remote monitoring technique for the evaluation of corrosion on reinforced concrete structures, which uses embeddable variations of known ASTM standards and telecommunication technologies as a new way to estimate the rate of loss of the steel used as a component of rebar, since such phenom‐ enon is the main cause of deterioration and degradation of the civil infrastructure. The adaptation of the technique was carried out to obtain an electrochemical half-cell that can be embedded indefinitely into the concrete, which provides the measurements corre‐ sponding to the corrosive state and allows calculating indirectly the rate of corrosion through the linear polarization resistance. The adaptation is based on a reference electrode of copper/copper sulphate, a segment of the same steel of the studied structure as working electrode and an auxiliary electrode made from pure graphite, all covered by mortar.

**Keywords:** Corrosion monitoring, Non-destructive testing on reinforced concrete, Corrosion Rate, Corrosion potential, reinforced concrete, Monitoring technique

## **1. Introduction**

The reinforced concrete structures have a limited service life; such durability depends on the concrete resistance to various physical and chemical factors and its ability to protect the embedded steel against the corrosion processes. The referred processes create products of steel corrosion, which generate a volumetric expansion on the embedded reinforcements, causing extremely high stresses inside the concrete, transforming it into a medium susceptible to the generation of cracks from the position of the reinforcement to the surface or between the rebar. Once the cracks have appeared, the oxygen and moisture diffuse directly up to the reinforce‐

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ment at a greater rate that increments the rate of corrosion [1–3]. Like any natural disaster, earthquakes or severe weather disturbances, corrosion can generate highly risky and costly damage to multiple areas, starting from the automotive, fluid transport systems to the area of infrastructure (bridges, ports, public buildings). As a reference, from 1980 to 2002, the United States suffered 52 major disasters related to climate, which included hurricanes, tornadoes, tropical storms, floods, fires, drought and frost, incurring on losses estimated at US\$ 380 billion (US\$ 17 billion annually). According to the latest study, the direct cost carried by corrosion of metal structures is US\$ 276 billion annually, representing 3.1% of gross domestic product [3,4]. Unlike natural disasters, the phenomenon of corrosion can be monitored and controlled [3,4].

The detection of such corrosive phenomenon is usually performed when the structure clearly shows damage signals which are directly reflected in a rise in cost of corrective maintenance. From the perspective of project managers, there is a marked interest in obtaining information about the states of initiation of degradation processes, to avoid incurring the referred costs. A considerable number of articles and techniques have been published and implemented to perform the monitoring of the corrosive state on reinforced concrete, where some of them not only use a single technique but also use a combination of several evaluation methods that allow to gather information about the condition of the concrete and/or the actual situation of rebar [5,6]. Within those techniques, the standard ASTM C876-91 determines the reinforcement state in terms of probability accordingly to the corrosion potential of rebar (10% of probability of occurrence of the phenomenon, region of uncertainty, 90% of probability of occurrence of the phenomenon) [5,7]. Also a complementary technique could estimate the corrosion rate makes to consider a set of measurements as a more specific evaluation of the corrosion process; according to the aforementioned, the linear polarization resistance method (LPR) rises as the most common procedure, given its ease of interpretation of the results and its high reprodu‐ cibility [5,8]. Although the mentioned techniques are widely applied, its major constraint relies on their flexibility, since they depend at all times on a hardware operated at the site of study (conducted by a user), which increases the costs due to equipment and travel expenses for the specialized personnel [9].

The purpose of this work is to introduce the design of a new remote monitoring technique for the evaluation of corrosion on reinforced concrete structures, which uses embeddable varia‐ tions of known ASTM standards and telecommunication technologies as a new way to estimate the rate of loss of the steel used as a component of rebar which also allows to avoid cost overruns related with specialized technicians.

## **2. Introduction to the electrochemical techniques to assess the corrosive state on reinforced concrete**

The corrosion of steel implies a separation of the anodic and cathodic processes that occur simultaneously on the surface; therefore, corrosion of carbon steel inside the concrete acts as a combined electrode over which the anodic and cathodic reactions take part; at the anode (where the corrosion process is carried out) steel is dissolved and oxidized into steel ions. Due to the electronic balance condition, the ions, which have left the steel, are consumed by the cathodic reaction on the steel surface, where the oxygen is reduced and the hydroxide ions are produced. Depending on the spatial distribution of these reactions and the conductivity of the medium, it can be generated into two kinds of corrosion, uniform corrosion and macrocell corrosion. Uniform corrosion occurs when the anodic and cathodic reactions on the same area are coupled to form microcells. The electrode potential of such coupling is called corrosion potential *Ecorr*. In the case of macrocell corrosion, the anodic and cathodic areas are separated; according to the circumstances of the case, it is presented as a considerable drop of the Ohmic potential that permits to separate the potentials of the cathodic and anodic area. In this process, the corrosion potential varies depending on the evaluated position within the limits of the anodic and cathodic corrosion potential [3].

ment at a greater rate that increments the rate of corrosion [1–3]. Like any natural disaster, earthquakes or severe weather disturbances, corrosion can generate highly risky and costly damage to multiple areas, starting from the automotive, fluid transport systems to the area of infrastructure (bridges, ports, public buildings). As a reference, from 1980 to 2002, the United States suffered 52 major disasters related to climate, which included hurricanes, tornadoes, tropical storms, floods, fires, drought and frost, incurring on losses estimated at US\$ 380 billion (US\$ 17 billion annually). According to the latest study, the direct cost carried by corrosion of metal structures is US\$ 276 billion annually, representing 3.1% of gross domestic product [3,4]. Unlike natural disasters, the phenomenon of corrosion can be monitored and controlled [3,4]. The detection of such corrosive phenomenon is usually performed when the structure clearly shows damage signals which are directly reflected in a rise in cost of corrective maintenance. From the perspective of project managers, there is a marked interest in obtaining information about the states of initiation of degradation processes, to avoid incurring the referred costs. A considerable number of articles and techniques have been published and implemented to perform the monitoring of the corrosive state on reinforced concrete, where some of them not only use a single technique but also use a combination of several evaluation methods that allow to gather information about the condition of the concrete and/or the actual situation of rebar [5,6]. Within those techniques, the standard ASTM C876-91 determines the reinforcement state in terms of probability accordingly to the corrosion potential of rebar (10% of probability of occurrence of the phenomenon, region of uncertainty, 90% of probability of occurrence of the phenomenon) [5,7]. Also a complementary technique could estimate the corrosion rate makes to consider a set of measurements as a more specific evaluation of the corrosion process; according to the aforementioned, the linear polarization resistance method (LPR) rises as the most common procedure, given its ease of interpretation of the results and its high reprodu‐ cibility [5,8]. Although the mentioned techniques are widely applied, its major constraint relies on their flexibility, since they depend at all times on a hardware operated at the site of study (conducted by a user), which increases the costs due to equipment and travel expenses for the

The purpose of this work is to introduce the design of a new remote monitoring technique for the evaluation of corrosion on reinforced concrete structures, which uses embeddable varia‐ tions of known ASTM standards and telecommunication technologies as a new way to estimate the rate of loss of the steel used as a component of rebar which also allows to avoid cost

**2. Introduction to the electrochemical techniques to assess the corrosive**

The corrosion of steel implies a separation of the anodic and cathodic processes that occur simultaneously on the surface; therefore, corrosion of carbon steel inside the concrete acts as a combined electrode over which the anodic and cathodic reactions take part; at the anode (where the corrosion process is carried out) steel is dissolved and oxidized into steel ions. Due

specialized personnel [9].

2 Non-Destructive Testing

overruns related with specialized technicians.

**state on reinforced concrete**

## **2.1. Half-cell potential measuring on embedded reinforcements on concrete (open circuit)**

The corrosion potential is measured as the potential difference according to a reference electrode or half-cell. This measuring is based on the electric and electrolytic continuity between the rebar, the reference electrode and the measuring element (voltmeter), which needs a high input impedance in such a way that the current which flows through the reference electrode does not disrupt the stability of the potential (it is acceptable as an input impedance of 10 MΩ). The connections must to be made such that the reference electrode is over the negative terminal and the reinforcing steel is brought to the positive port of the voltmeter; in this way the readings of the potential will be generally negatives, where the positive meas‐ urements are possibly due to passivated steels on dry concrete [3,10].

As previously mentioned, the half-cell potentials correspond to the corrosive level of steel, influenced by the surrounding environment, which is composed by variables such as the type of concrete cover, concrete resistivity, moisture content, oxygen availability and aggressive agents such as chloride ions and carbon dioxide. In corroded steels at contaminated environ‐ ments, chloride ions can be obtained with potentials within a range between −400 and −600 mV versus an electrode of copper/copper sulphate; furthermore, the passive steel reacts as an oxygen electrode subject to pH variations in the pores of the concrete; hence, potentials on carbonated concrete are less negative. The corrosion potential for passive steels also depends on the oxygen availability and it varies over a great range of voltages [3,10].

The measurement technique is normalized in the standard ASTM C876-91, applicable to the evaluation in situ and is independent of the size of the reinforcement and depth at which it is located inside the concrete paste. This standard allows relating the corrosion potential measured with the probability of corrosion [3,11].

## **2.2. Calculation of the corrosion rate using the linear polarization resistance method (LPR)**

Linear polarization resistance (LPR) is a non-destructive method designed to measure directly the polarization resistance (*Rp*) and indirectly the corrosion rate around the corrosion potential [3].

In order to implement the LPR measurement method, a small disturbance of polarization is applied to the reinforcement steel in the concrete surface, where its response is measured after a proper time delay. Using a potentiostatic method, an overpotential *ΔE*, between 10 and 30 mV, is supplied on the corrosion potential and after a typical time delay of 30 seconds, the response in current *ΔI*, is recorded [3,12]. Although the corrosion of steel is an electrochemical process and does not obey the Ohm's law, it has been demonstrated that if the applied polarization does not exceed ±30 mV, the *Rp* value can be determined from the relation between the potential variation and the current variation and, if the polarization can be confined either to a known area *A* or to a small section isolated from the steel, the corrosion current density (*i corr )* also can be calculated [3,12]. As ASTM G102 indicates, using Eq. 1, the corrosion rate can be directly determined [3,13].

$$\text{Corrosion rate} = \left(\mathbf{B} \cdot K \cdot W\_{\iota}\right) \cdot \left(d \cdot A \cdot Rp\right)^{-1} \tag{1}$$

where the value of *B* corresponds to the slopes of Tafel curves, where typically for the steel embedded in concrete they are assumed with values of 25 mV for steel under active conditions of corrosion and 50 mV for passive conditions, *W <sup>e</sup>* is the equivalent weight in equivalent grams units and *d* is the density of the working electrode (rebar). *K* is the constant that defines the units of the corrosion rate, taking values either of 3272 to configure the units in millimeters per year *mmpy* (its units are ) or a value of 1.288 × 105 for mils penetration per year *mpy* (its units are *mils* ⋅ (*ampere* ⋅ *cetimeter* ⋅ *year*)) [3,13].

## **3. Remote monitoring technique for the evaluation of corrosion on reinforced concrete structures**

The technique allows to adapt the ASTM standards into a remote mode with embeddable instrumentation with which it is possible to avoid movement of personnel to the measuring zone. The overall design allows both half-cell voltages (open circuit potential) and linear polarization resistance values become available and visualizable to the user through a web server.

## **3.1. Design of the embeddable cell**

The reinforcement steels are typically protected by the alkaline nature of concrete. If that alkalinity is compromised at some point, the corrosion in the steel will initiate if oxygen and moisture combine. The corrosion reaction will promote the anodic and cathodic activity across the rebar, thus generating a corrosion cell by the electric difference between the two mentioned regions [14]. The design of the embeddable cell was made with a configuration of three electrodes (reference electrode, *Re*, working electrode, *Wee*, and auxiliary electrode, *Ae*), framed within the norms ASTM C876 and ASTM G-102.

The embeddable cell was designed with a diameter of 15 and 30 cm height. At its center, it was positioned as a segment of structural steel of 0.5 inches diameter and 15 cm height as the working electrode. It was set as the embeddable reference electrode of copper/copper sulphate (Cu/CuSO4) 45 mm next to the segment of steel, and finally at 42 mm of distance from the working electrode and 50 mm from the reference electrode it was embed as a pure graphite electrode (10 cm height), acting as an auxiliary electrode. The electrodes were covered by mortar with a water/binder relation for mortar as 0.65, which produces a porous mix that allows the surrounding medium to penetrate through the mortar up to the three-electrode system. This phenomenon assures that the medium inside the embeddable cell is equal to the medium of the whole structure, thus the measurements provided by the cell are reliable and equivalents. Such configuration allows to obtain an electrochemical half-cell that can be embedded indefinitely into the concrete (**Figure 1**).

**Figure 1.** Design of embeddable half-cell.

In order to implement the LPR measurement method, a small disturbance of polarization is applied to the reinforcement steel in the concrete surface, where its response is measured after a proper time delay. Using a potentiostatic method, an overpotential *ΔE*, between 10 and 30 mV, is supplied on the corrosion potential and after a typical time delay of 30 seconds, the response in current *ΔI*, is recorded [3,12]. Although the corrosion of steel is an electrochemical process and does not obey the Ohm's law, it has been demonstrated that if the applied polarization does not exceed ±30 mV, the *Rp* value can be determined from the relation between the potential variation and the current variation and, if the polarization can be confined either to a known area *A* or to a small section isolated from the steel, the corrosion current density (*i corr )* also can be calculated [3,12]. As ASTM G102 indicates, using Eq. 1, the corrosion rate can

<sup>1</sup> (B ) ( ) *Corrosion rate K W d A Rp <sup>e</sup>*

**3. Remote monitoring technique for the evaluation of corrosion on**

The technique allows to adapt the ASTM standards into a remote mode with embeddable instrumentation with which it is possible to avoid movement of personnel to the measuring zone. The overall design allows both half-cell voltages (open circuit potential) and linear polarization resistance values become available and visualizable to the user through a web

The reinforcement steels are typically protected by the alkaline nature of concrete. If that alkalinity is compromised at some point, the corrosion in the steel will initiate if oxygen and moisture combine. The corrosion reaction will promote the anodic and cathodic activity across the rebar, thus generating a corrosion cell by the electric difference between the two mentioned regions [14]. The design of the embeddable cell was made with a configuration of three electrodes (reference electrode, *Re*, working electrode, *Wee*, and auxiliary electrode, *Ae*),

The embeddable cell was designed with a diameter of 15 and 30 cm height. At its center, it was positioned as a segment of structural steel of 0.5 inches diameter and 15 cm height as the

where the value of *B* corresponds to the slopes of Tafel curves, where typically for the steel embedded in concrete they are assumed with values of 25 mV for steel under active conditions of corrosion and 50 mV for passive conditions, *W <sup>e</sup>* is the equivalent weight in equivalent grams units and *d* is the density of the working electrode (rebar). *K* is the constant that defines the units of the corrosion rate, taking values either of 3272 to configure the units in millimeters

for mils penetration per year *mpy* (its

be directly determined [3,13].

4 Non-Destructive Testing

per year *mmpy* (its units are ) or a value of 1.288 × 105

framed within the norms ASTM C876 and ASTM G-102.

units are *mils* ⋅ (*ampere* ⋅ *cetimeter* ⋅ *year*)) [3,13].

**reinforced concrete structures**

**3.1. Design of the embeddable cell**

server.

#### **3.2. Design of the control system**

The design of the control system allows the equipment to prepare itself to perform the measurements after receiving a start command (the order is sent via a text message, at the discretion of the user). Once the command is received, the system determines the open circuit potential (half-cell potential) between the working electrode (rebar) and the reference elec‐ trode, subsequently, through an integrated circuit for analog to digital conversion (DAC), which guarantees accurate voltage increments up to 75 mV; owing to its resolution of 16 bits, it is supplied as a potential difference between the auxiliary electrode and the working electrode that is varied until it equals the open circuit potential minus 20 mV. To proceed to the start of the voltage sweep, the test is done by varying the half-cell potential 1 mV per second, from −20 mV of the open circuit potential to 20 mV above it [3,14].

With each increase, the half-cell potential and the voltage are measured with a shunt resistance arrangement of 10 Ω, 50 Ω, 100 Ω, 1 KΩ, 5 KΩ and 10 kΩ, which are selected according to the algorithm implemented. The mentioned selection is done to obtain the best measured resolu‐ tion and also to perform de calculus of the current by Ohm's law. At the end of the voltages sweep, the measured values are used to calculate the polarization resistance and the corrosion rate using Eq. 1. Finally, the system sends the stored information in a format of a *.txt* archive to the GSM/GPRS module, which allows the transmission of information to a web server, where the variables are stored in a proprietary database, which gives the user the ability to view the information through a web application (**Figure 2**) [3,14].

**Figure 2.** Design of the control system.

Once the test finishes, it is necessary to provide the information available to the user regardless of the place where comes from; for that reason, the design uses a GSM/GPRS board (Global Systems for Mobile Communications/General Packet Radio Service) which provides the ability to use the mobile network inserting a subscriber identity module for a mobile phone (SIM card), allowing to send and receive text messages, with which the remote command of the equipment is done. The configuration of the module and the control board allows using the file transfer protocol FTP with which it is possible to send the *.txt* file to a web server to query the data generated on the tests.

#### **3.3. Method to assess remotely the corrosive state of rebar**

the start of the voltage sweep, the test is done by varying the half-cell potential 1 mV per second,

With each increase, the half-cell potential and the voltage are measured with a shunt resistance arrangement of 10 Ω, 50 Ω, 100 Ω, 1 KΩ, 5 KΩ and 10 kΩ, which are selected according to the algorithm implemented. The mentioned selection is done to obtain the best measured resolu‐ tion and also to perform de calculus of the current by Ohm's law. At the end of the voltages sweep, the measured values are used to calculate the polarization resistance and the corrosion rate using Eq. 1. Finally, the system sends the stored information in a format of a *.txt* archive to the GSM/GPRS module, which allows the transmission of information to a web server, where the variables are stored in a proprietary database, which gives the user the ability to

Once the test finishes, it is necessary to provide the information available to the user regardless of the place where comes from; for that reason, the design uses a GSM/GPRS board (Global Systems for Mobile Communications/General Packet Radio Service) which provides the ability to use the mobile network inserting a subscriber identity module for a mobile phone (SIM card), allowing to send and receive text messages, with which the remote command of the

from −20 mV of the open circuit potential to 20 mV above it [3,14].

6 Non-Destructive Testing

view the information through a web application (**Figure 2**) [3,14].

**Figure 2.** Design of the control system.

The method to assess remotely the corrosive state of rebar begins with the preparation of the structure to set the embeddable half-cell. First, it is necessary to identify the zone where the structural steel has the major risk of suffering the corrosive phenomenon as a critic represen‐ tation of the whole structure. Once the position is known, and if it is a new construction in progress, it is elemental to locate the embeddable half-cell parallel to the reinforcement. In contrast, if the place to be measured is an existing construction, after identifying the critic zone, it is mandatory to locate the rebar and next to it bore a hole of 22 cm diameter and 40 cm depth, at which the embeddable half-cell can be placed, parallel to the structural steel. Finally, the hole needs to be backfilled with mortar where its water/binder relation is 0.65 (**Figure 3**).

**Figure 3.** Location of the embeddable half-cell.

After placing the half-cell, we proceed to install the control system to perform the measure‐ ments. Once the system receives a text message with the start command, the data acquisition begins where the acquired information corresponds to the half-cell potential and the polari‐ zation potential. Then the system sends the data package to a web server through which a developed web supervisory allows consulting the information of the corrosive state (proba‐ bility of corrosion and corrosion rate) (**Figure 4**).

**Figure 4.** Flowchart for the designed method.

### **3.4. Corrosion monitoring test on concrete specimen**

An embeddable half-cell with the specifications mentioned above was prepared. The probe was allowed to cure for 28 days at a temperature of 25°C at constant moisture (**Figure 5**).

**Figure 5.** Preparation of the embeddable half-cell.

**Figure 4.** Flowchart for the designed method.

8 Non-Destructive Testing

After the curing period, the designed system and a commercial potentiostat (Gamry PCI4) were used in parallel in order to establish a parameter measurement for error values on the measures. Constant monitoring for 192 hours was conducted in an environment free of aggressive agents. These measurements allowed determining the state of the embeddable halfcell prior to set it into the structure object of study [3].

**Figure 6.** Corrosion potential of embeddable half-cell prior to set it into the structure [3].

As shown on **Figure 6**, the corrosion potentials are constants, allowing to calculate an open circuit potential of −52 mV, which corresponds to a 10% or minor probability of corrosion. Also, the data comparison between the proposed design and the commercial equipment over the total time of the test gives a maximum error of 8.4 and 0.03% as minimum where the average error is 3.62% [3].

The linear polarization resistance value for the test was 13 kΩ which when used in Eq. 1 with the values of the steel segment area, *K*, *We*, density and *B* yields a corrosion density of 0.0045 and a corrosion rate of 526.11 × 10−6 *mmpy*, which corresponds to a classification of corrosion as very low, concordant with the obtained corrosion probability, where *B* was assumed as 50 mV because the passive corrosion conditions, *We* takes a value of 27.92 equivalent grams, the density of steel is considered as 7.87 and *K* was assumed as 3272 to establish the units of corrosion rate as millimetre per year *mmpy* [3]. The error values of the linear polarization resistance were found, wherein the maximum gives 6.58%, the minimum error gives 0.019% where the average error is 3.46% (**Figure 7**) [3].

**Figure 7.** Polarization resistance of embeddable half-cell prior to set it into the structure [3].

After determining the error of the half-cell, it was taken to the measuring site, located in the city of Cajicá in the Department of Cundinamarca in Colombia, specifically at the Acoustical Shell of the Universidad Militar Nueva Granada.

As the place of measuring was a new construction in progress, first it was identified as the zone where the structural steel has a major risk of suffering corrosion, the embeddable halfcell was set parallel to the reinforcement as shown in **Figures 8** and **9** and where the place has a high concentration of chloride ions, as the acoustical shell is located 14 km from a mining area of extraction and refining of salt. Finally, the control system was installed.

Remote Monitoring Technique for Evaluation of Corrosion on Reinforced Concrete Structures http://dx.doi.org/10.5772/62314 11

**Figure 8.** Acoustical Shell of the Universidad Militar Nueva Granada.

**Figure 9.** Installation of the embeddable half-cell.

As shown on **Figure 6**, the corrosion potentials are constants, allowing to calculate an open circuit potential of −52 mV, which corresponds to a 10% or minor probability of corrosion. Also, the data comparison between the proposed design and the commercial equipment over the total time of the test gives a maximum error of 8.4 and 0.03% as minimum where the average

The linear polarization resistance value for the test was 13 kΩ which when used in Eq. 1 with the values of the steel segment area, *K*, *We*, density and *B* yields a corrosion density of 0.0045 and a corrosion rate of 526.11 × 10−6 *mmpy*, which corresponds to a classification of corrosion as very low, concordant with the obtained corrosion probability, where *B* was assumed as 50 mV because the passive corrosion conditions, *We* takes a value of 27.92 equivalent grams, the density of steel is considered as 7.87 and *K* was assumed as 3272 to establish the units of corrosion rate as millimetre per year *mmpy* [3]. The error values of the linear polarization resistance were found, wherein the maximum gives 6.58%, the minimum error gives 0.019%

error is 3.62% [3].

10 Non-Destructive Testing

where the average error is 3.46% (**Figure 7**) [3].

**Figure 7.** Polarization resistance of embeddable half-cell prior to set it into the structure [3].

Shell of the Universidad Militar Nueva Granada.

After determining the error of the half-cell, it was taken to the measuring site, located in the city of Cajicá in the Department of Cundinamarca in Colombia, specifically at the Acoustical

As the place of measuring was a new construction in progress, first it was identified as the zone where the structural steel has a major risk of suffering corrosion, the embeddable halfcell was set parallel to the reinforcement as shown in **Figures 8** and **9** and where the place has a high concentration of chloride ions, as the acoustical shell is located 14 km from a mining

area of extraction and refining of salt. Finally, the control system was installed.

As shown in **Figure 10**, monitoring was carried out each 2 hours during 10 days, reaching a maximum potential of −386m V corresponding to a probability of corrosion just over the limit of 90%. Once the pores of the concrete are saturated owing to the high concentration of CO2 and chloride ions, the corrosion potential stabilizes over −305m V on the uncertainty region.

**Figure 10.** Remote monitoring of corrosion potential [3].

The test of linear polarization resistance was carried out after 10 days as shown in **Figure 11** wherein the average value of the linear polarization resistance was 1.98 kΩ when used in Eq. 1. Together with the values of the steel segment area, *K*, *We*, density and *B* (*B* is assumed to be 26 mV, since the corrosion conditions are active) yield a corrosion density of 0.309 and a corrosion rate of 3.592 × 10−3 *mmpy*, which corresponds to a classification of corrosion as low/ moderated, concordant with the obtained corrosion probability, *We* takes a value of 27.92 equivalent grams, the density of steel is considered as 7.87 and *K* was assumed as 3272 to establish the units of corrosion rate as millimetre per year *mmpy*.

**Figure 11.** Remote monitoring of linear polarization resistance [3].

## **4. Conclusions**

Through this study, the feasibility of implementing an embeddable remote monitoring technology for determining the corrosive state of reinforced concrete structures subjected to the carbonation phenomenon following the regulations present in the standards ASTM C876 and ASTM G-102 was verified. Such viability was determined from the given performance of the developed system versus commercial equipment used as a pattern, where the mean error on open circuit potential was 3.62% while the mean error on the test for resistance to linear polarization with respect to the calculations from the polarization resistance was 3.46%. Use of the remote measuring technique and the information provided by the developed system allow diagnosing a reinforced concrete structure identifying the corrosive state of the reinforcing steel structure by determining the corrosion probability and the corrosion rate of the material, avoiding any movement of personnel to the measuring site and any destruction of the structure.

## **Acknowledgements**

The test of linear polarization resistance was carried out after 10 days as shown in **Figure 11** wherein the average value of the linear polarization resistance was 1.98 kΩ when used in Eq. 1. Together with the values of the steel segment area, *K*, *We*, density and *B* (*B* is assumed to be 26 mV, since the corrosion conditions are active) yield a corrosion density of 0.309 and a corrosion rate of 3.592 × 10−3 *mmpy*, which corresponds to a classification of corrosion as low/ moderated, concordant with the obtained corrosion probability, *We* takes a value of 27.92 equivalent grams, the density of steel is considered as 7.87 and *K* was assumed as 3272 to

Through this study, the feasibility of implementing an embeddable remote monitoring technology for determining the corrosive state of reinforced concrete structures subjected to the carbonation phenomenon following the regulations present in the standards ASTM C876 and ASTM G-102 was verified. Such viability was determined from the given performance of the developed system versus commercial equipment used as a pattern, where the mean error on open circuit potential was 3.62% while the mean error on the test for resistance to linear polarization with respect to the calculations from the polarization resistance was 3.46%. Use of the remote measuring technique and the information provided by the developed system

establish the units of corrosion rate as millimetre per year *mmpy*.

**Figure 11.** Remote monitoring of linear polarization resistance [3].

**4. Conclusions**

12 Non-Destructive Testing

To my Grandfather Ramon Rodriguez Martinez and my Parents Guillermo Jose Roa Torres and Carmencita Rodriguez Martinez, for their constant support with this research and its funding.

This research was supported by "Vicerrectoría de investigaciones de la Universidad Militar Nueva Granada" under contract ING 1760 validity 2015.

## **Author details**

Guillermo Roa Rodríguez and Willian Aperador

\*Address all correspondence to<EMAIL_ADDRESS>
School of Engineering, Universidad Militar Nueva Granada, Bogotá, Colombia

## **References**

## **Mechanical Behavior Analysis and Testing of Marine Riser in Deepwater Drilling**

Yanbin Wang, Deli Gao and Jun Fang

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/62315

#### **Abstract**

[5] Romano Pedro; Brito Paulo S.D.; Luiz Rodrigues. Monitoring of the degradation of concrete structures in environments containing chloride ions. Construction and

[6] Otieno Mike; Beushausen Hans; Alexander Mark. Prediction of Corrosion Rate in RC Structures - A Critical Review. In: Andrade Carmen; Mancini Giuseppe, editors. Modelling of Corroding Concrete Structures. Madrid, Spain: Springer; 2011. pp. 15-37.

[7] ASTM. ASTM C876-09, standard test method for corrosion potentials of uncoated

[8] Romano Pedro; Paulo Brito S. D.; Estudo da degradação de estruturas de betão armado expostas ao ataque por sulfatos. Ingenium. 2012;DOI: http://hdl.handle.net/

[9] Rodríguez Guillermo Roa; Chaparro Willian Aperador; Tobón Emilio Delgado. Diseño de sistema de monitoreo remoto para evaluación de la corrosión en estructuras de concreto reforzado sometidas a ion cloruro . Ingeniería Investigación y Tecnología,.

[10] Elsener B.; Andrade C.; Gulikers J.; Polder. R;Raupach M.; Hall-cell potential measure‐ ments—Potential mapping on reinforced concrete structures. Materials and Structures.

[11] Elsener B.; Half-cell potential mapping to assess repair work on RC structures. Con‐ struction and Building Materials. 2001;15(2-3):133-139. DOI: 10.1016/

[12] S.G Millard; Law D; J.H Bungey; Cairns J. Environmental influences on linear polari‐ sation corrosion rate measurement in reinforced concrete. NDT & E International.

[13] ASTM. ASTM G102-89(2010), Standard Practice for Calculation of Corrosion Rates and Related Information from Electrochemical Measurements. In: West Conshohocken, PA:

[14] Roa Rodriguez Guillermo; Aperador Willian; Delgado Tobón Emilio. Desempeño de sonda basada en electrodo de referencia de cobre sulfato de cobre en sistema de monitoreo de corrosión in situ desarrollado para estructuras de concreto reforzado. In:

2001;34(6):409-417. DOI: 10.1016/S0963-8695(01)00008-1

May 19–2, 2014; Fortaleza, Brasil. Fortaleza, Brasil:2014.

reinforcing steel in concrete. In: West Conshohocken, PA:2009.

Building Materials. 2013;47:827-832. DOI: 10.1016/j.conbuildmat.2013.05.042

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14 Non-Destructive Testing

2015;16(4):565-572.

2003;36(7):461-471.

S0950-0618(00)00062-3

ASTM International; 2010.

In this chapter, the mechanical model and control equation have been established to analyse the mechanical behaviour of marine riser in working condition. The control equation has been solved by weighted residual method, and the analysis model has been verified by finite element method (FEM) in ABAQUS framework. Based on this, the deformation and stress distribution of the marine riser have been acquired. Then, a simulation experimental system has been introduced, and the system composition, functions and operational approach of the experimental setup have been stated in detail. After that, a tubular sample has been manufactured to simulate the marine riser, and the simulation experiments have been carried out based on this setup, where the experimen‐ tal procedures, key aspects, difficult points of the experiment and its corresponding solutions have been elaborated. At last, the strain value of the specimen has been measured successfully after the experiment, and the stress state of the specimen has been ob‐ tained based on the analysis.

**Keywords:** Deepwater drilling, Marine riser, mechanical behaviour, Simulation ex‐ periment, Stress state testing

## **1. Introduction**

The exploration and development of offshore oil and gas resources are gradually from shallow to deep sea area. The special sea state conditions and engineering problems in deepwater put forward higher request to the drilling technology, and a higher level of drilling equipment and techniques are urgently need to face the challenges.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Generally, the technical challenges in deep offshore drilling include: (1) water depth—huge drilling platform or drilling ship is needed in deepwater drilling. Moreover, the underwater equipment and tools must be precision, intelligent and flexible with higher reliability. The gravity of drilling riser and the complexity of marine environment increase with water depth. Therefore, the drilling vessel must have sufficient bearing capacity and deck space. (2) Sea wave and current—deviation of drilling vessel will occur under the action of sea wave and current, which will result in riser deformation and stress re-distribution. Riser under dynamic lateral force deduced by sea wave and current will generate vortex-induced vibration (VIV), which puts forward higher requirements on fatigue strength design of offshore pipelines. What's more, during drilling operation, riser is needed to disconnect from subsea wellhead and suspended on the drilling vessel, which will cause dynamic compression and even local instability. (3) Narrow drilling mud density window—the undercompaction of deepwater formation causes narrow drilling mud density window, which will result in frequent drilling accidents, such as lost circulation, well kick, borehole collapse and sticking. Besides, the narrow window will bring about the increase of casing layers even unable to drill to the target stratum. Meanwhile, well control problems always exist in narrow window condition [1]. (4) Geological disasters—geological disasters in deepwater drilling mainly include loose submarine soil and shallow flow. Sinking of subsea wellhead, blowout preventer (BOP) and surface conductor will appear if shallow flow is serious. When gas in shallow flow enters the sea water, the density of sea water and the buoyancy of drilling vessel will decrease, which will cause big accident and even rig capsized. (5) Well control—the well-control risk of drilling equipment, submarine tools and hydrate problems is also remarkable [2].

Various tubulars, such as drilling riser, drilling pipe, production tubulars and subsea tubulars, are indispensable for deepwater exploration and development. These pipelines are subjected to kinds of loads under service condition, and how to ensure the security of them is the foundation of efficiently acquiring oil and gas in deepwater. Taking the drilling riser as example, the operating loads subjecting to the riser include internal pressure, external pressure, axial tension, lateral force generated by sea wave and current and top displacement resulted from floating vessel, which can cause kinds of failure models, such as wear, rupture and collapse. Besides theory analysis, obtaining the mechanical behaviour of these tubulars under service loads through experiment is an effective way to guarantee the safe and efficient of offshore drilling operations [3].

However, few literatures have reported the experimental equipment, which can impose external pressure to tubulars. There is a set of experimental system in the University of Rio De Janeiro, Brazil, which can provide 10 MPa water pressure, and the maximum simulated water depth is 1000 m, and the maximum operating depth of the fifth- and sixth-generation drilling platform (ship) is 3000 m. An experimental system named Mechanics Behaviour Simulation Experimental System for Deep Water Drilling and Production Strings has been developed to provide 30 MPa water pressure and to simulate external pressure of 3000 m water depth [4]. Until now, the system can impose external pressure, internal pressure, axial tension/compres‐ sion load and lateral load to the tubulars, which provide a good platform for exploration and development of offshore oil and gas and can perfect deepwater drilling theory, reduce corresponding operation risk and improve the safety and economy of deepwater oil and gas development.

## **2. Theory analysis of riser mechanical behaviour**

Marine riser is the key equipment connecting subsea wellhead and floating drilling platform (ship) in deepwater drilling and exploration. The main functions of marine riser are to provide channel for drilling mud in the annulus of riser and drill pipe, support auxiliary lines, guide drilling tools and install the BOP. As riser mechanical behaviour has great impact on deepwater drilling engineering, we take the riser in service as example in this chapter. Then, the mechan‐ ical model and control equation have been established. Next, the model validation and sensitivity analysis have been presented. Finally, we get the key parameters to control its mechanical behaviour.

## **2.1. Mechanical model**

Generally, the technical challenges in deep offshore drilling include: (1) water depth—huge drilling platform or drilling ship is needed in deepwater drilling. Moreover, the underwater equipment and tools must be precision, intelligent and flexible with higher reliability. The gravity of drilling riser and the complexity of marine environment increase with water depth. Therefore, the drilling vessel must have sufficient bearing capacity and deck space. (2) Sea wave and current—deviation of drilling vessel will occur under the action of sea wave and current, which will result in riser deformation and stress re-distribution. Riser under dynamic lateral force deduced by sea wave and current will generate vortex-induced vibration (VIV), which puts forward higher requirements on fatigue strength design of offshore pipelines. What's more, during drilling operation, riser is needed to disconnect from subsea wellhead and suspended on the drilling vessel, which will cause dynamic compression and even local instability. (3) Narrow drilling mud density window—the undercompaction of deepwater formation causes narrow drilling mud density window, which will result in frequent drilling accidents, such as lost circulation, well kick, borehole collapse and sticking. Besides, the narrow window will bring about the increase of casing layers even unable to drill to the target stratum. Meanwhile, well control problems always exist in narrow window condition [1]. (4) Geological disasters—geological disasters in deepwater drilling mainly include loose submarine soil and shallow flow. Sinking of subsea wellhead, blowout preventer (BOP) and surface conductor will appear if shallow flow is serious. When gas in shallow flow enters the sea water, the density of sea water and the buoyancy of drilling vessel will decrease, which will cause big accident and even rig capsized. (5) Well control—the well-control risk of drilling equipment, submarine

Various tubulars, such as drilling riser, drilling pipe, production tubulars and subsea tubulars, are indispensable for deepwater exploration and development. These pipelines are subjected to kinds of loads under service condition, and how to ensure the security of them is the foundation of efficiently acquiring oil and gas in deepwater. Taking the drilling riser as example, the operating loads subjecting to the riser include internal pressure, external pressure, axial tension, lateral force generated by sea wave and current and top displacement resulted from floating vessel, which can cause kinds of failure models, such as wear, rupture and collapse. Besides theory analysis, obtaining the mechanical behaviour of these tubulars under service loads through experiment is an effective way to guarantee the safe and efficient

However, few literatures have reported the experimental equipment, which can impose external pressure to tubulars. There is a set of experimental system in the University of Rio De Janeiro, Brazil, which can provide 10 MPa water pressure, and the maximum simulated water depth is 1000 m, and the maximum operating depth of the fifth- and sixth-generation drilling platform (ship) is 3000 m. An experimental system named Mechanics Behaviour Simulation Experimental System for Deep Water Drilling and Production Strings has been developed to provide 30 MPa water pressure and to simulate external pressure of 3000 m water depth [4]. Until now, the system can impose external pressure, internal pressure, axial tension/compres‐ sion load and lateral load to the tubulars, which provide a good platform for exploration and development of offshore oil and gas and can perfect deepwater drilling theory, reduce

tools and hydrate problems is also remarkable [2].

of offshore drilling operations [3].

16 Non-Destructive Testing

The schematic diagram of deepwater drilling riser in service is shown in **Figure 1**.

**Figure 1.** Static analysis model of riser mechanical behaviour.

The analysis model can be regarded as a beam located in the vertical plane and subjected to both non-uniform tension force and lateral force. Both the top and the end of riser are connected with the ball joints, so the boundary conditions are hinge constraints. Take the connection point of drilling ship and riser top as the origin of the coordinate, and the positive direction of *x* axis is vertical to the bottom of the sea, and the positive direction of *y* axis is the same as that of the lateral force. Besides, the following assumptions are applied during equation deduction:

**•** The material of riser is homogeneous, isotropic and linear elastic, and the riser bending stiffness is constant.

The riser differential control equation can be represented as follows [5]:

$$\mathrm{EI}\frac{\mathrm{d}^4y}{\mathrm{d}\mathbf{x}^4} - T(\mathbf{x})\frac{\mathrm{d}^2y}{\mathrm{d}\mathbf{x}^2} - \mathrm{w}\frac{\mathrm{d}y}{\mathrm{d}\mathbf{x}} = F(\mathbf{x})\tag{1}$$

where EI(*x*) is the riser flexural rigidity along the *x* axis (N·m2 ); *T*(*x*) is the riser tension force distribution along the *x* axis (N); *w* is the per unit length weight of riser in sea water (N/m); *F*(*x*) is the total lateral force distribution along the *x* axis (N).

As the top and end of the riser are connected with ball joints, the boundary conditions of Equation 1 can be written as follows:

$$\begin{cases} \left. \mathcal{Y} \right|\_{\boldsymbol{x}=0} = \mathcal{S}; \quad \left. \theta \right|\_{\boldsymbol{x}=0} = 0\\ \left. \mathcal{Y} \right|\_{\boldsymbol{x}=L} = 0; \quad \left. \theta \right|\_{\boldsymbol{x}=L} = 0 \end{cases} \tag{2}$$

#### **2.2. Load calculations**

#### *2.2.1. Tension force*

The main axial loads subjected on riser include gravity and top tension force, and the axial force of riser section at *x* below the sea surface can be represented by the following equation:

$$T\left(\mathbf{x}\right) = T\_{\text{top}} - \mathbf{w}\mathbf{x} \tag{3}$$

where *T*top is the top tension imposed on riser top end (N).

#### *2.2.2. Lateral force*

The main lateral force of riser is generated by sea wave and current. If ignoring the dynamic effects, the combined wave and current force can be calculated by the following equation:

$$F(\mathbf{x}) = C\_\mathrm{D} \rho D \left(\nu\_\mathrm{w} + \nu\_\mathrm{c}\right) \left|\nu\_\mathrm{w} + \nu\_\mathrm{c}\right| / \ 2 + C\_\mathrm{m} \rho \pi D^2 a\_\mathrm{w} / \ 4 \tag{4}$$

where *C*D is the drag force coefficient (a dimensionless quantity); *C*m is the inertia force coefficient (a dimensionless quantity); *ρ* is the density of sea water (kg/m3 ); *D* is the outer diameter of riser (m); *ν*<sup>w</sup> is the horizontal velocity of sea wave particle (m/s); *ν*<sup>c</sup> is the current velocity (m/s); *a*w = d*wt*/d*t* is the horizontal acceleration of sea wave particle (m/s2 ).

Mechanical Behavior Analysis and Testing of Marine Riser in Deepwater Drilling http://dx.doi.org/10.5772/62315 19

**Figure 2.** Riser discretisation model.

**•** The movement direction of sea wave and current is in the same plane.

The riser differential control equation can be represented as follows [5]:

where EI(*x*) is the riser flexural rigidity along the *x* axis (N·m2

*F*(*x*) is the total lateral force distribution along the *x* axis (N).

where *T*top is the top tension imposed on riser top end (N).

rn

4 2 d dd EI d dd

**•** Riser curvature and torsion are small, and the geometric non-linearity is neglected.

( ) ( ) 4 2

distribution along the *x* axis (N); *w* is the per unit length weight of riser in sea water (N/m);

As the top and end of the riser are connected with ball joints, the boundary conditions of

0 0 ; 0 0; 0

q

q

The main axial loads subjected on riser include gravity and top tension force, and the axial force of riser section at *x* below the sea surface can be represented by the following equation:

The main lateral force of riser is generated by sea wave and current. If ignoring the dynamic effects, the combined wave and current force can be calculated by the following equation:

where *C*D is the drag force coefficient (a dimensionless quantity); *C*m is the inertia force

diameter of riser (m); *ν*<sup>w</sup> is the horizontal velocity of sea wave particle (m/s); *ν*<sup>c</sup> is the current

rp

( ) ( ) <sup>2</sup> D w cw c m w *F x C D v v C Da* = + ++

 n/ 2

coefficient (a dimensionless quantity); *ρ* is the density of sea water (kg/m3

velocity (m/s); *a*w = d*wt*/d*t* is the horizontal acceleration of sea wave particle (m/s2

*x x x L x L*

= = = = ìï = = <sup>í</sup> ï = = î

*y S*

*y*

*y yy Tx w Fx x xx* - -= (1)

*T x T wx* ( ) = - top (3)

/ 4 (4)

); *D* is the outer

).

); *T*(*x*) is the riser tension force

(2)

**•** Top tension does not change with time.

18 Non-Destructive Testing

Equation 1 can be written as follows:

**2.2. Load calculations**

*2.2.1. Tension force*

*2.2.2. Lateral force*

The sea current velocity under a certain depth of the sea surface can be calculated by the following equation recommend by American Bureau of Shipping:

$$\nu\_{\mathbf{c}}\left(\mathbf{x}\right) = \nu\_{\mathbf{m}}\left(\mathbf{x}/L\right)^{1/7} + \nu\_{\mathbf{c}}\left(\mathbf{x}/L\right) \tag{5}$$

where *ν*m is the sea surface wind velocity (m/s); *ν*<sup>t</sup> is the sea surface tide velocity (m/s).

The linear wave theory is usually chosen to calculate the horizontal velocity of sea wave particle, and the equation is as follows:

$$\nu\_{\rm w} = \pi H \wedge T\_{\rm w} \exp\left[k\left(\mathbf{x} - L\right)\right] \text{cos}\left(k\mathbf{y} - \alpha\_{\rm w} t\right) \tag{6}$$

where *H* is the wave height (m); *T*w is the wave period (s); *k* is the wave number (a dimensionless quantity); *ω*w is the wave circular frequency (rad/s).

Generally, the maximum of wave current is always used to calculate the maximum value of riser deformation and stress, and the maximum lateral force can be obtained through substi‐ tuting Equations 5 and 6 into Equation 4.

#### **2.3. Model solution**

Equation 1 is very complex and cannot obtain the analytical solutions. In this chapter, we have solved Equation 1 by weighted residual method.

#### *2.3.1. Residual equation*

As shown in **Figure 2**, riser length can be divided into *n* spans. The first node locates at riser top and is marked with No. 1, the last node locates at riser end and is marked with No. (*n* + 1). So, the whole discrete elements have (*n* + 1) nodes and *n* elements.

Because Equation 1 is a fourth-order differential equation, the shape function in weighted residual method can be written as follows [6]:

$$\mathbf{y}\_{i} = \mathbf{C}\_{i,0} + \mathbf{C}\_{i,1}\mathbf{x} + \mathbf{C}\_{i,2}\mathbf{x}^{2} + \mathbf{C}\_{i,3}\mathbf{x}^{3} + \mathbf{C}\_{i,4}\mathbf{x}^{4} + \mathbf{C}\_{i,5}\mathbf{x}^{5}, \ \mathbf{x} \in \left[0, l\_{i}\right], \ \left(i = 1, 2, \cdots, n+1\right) \tag{7}$$

where *yi* is the displacement of discrete nodes; *li* is the length of each span; *Cij* (*j* = 0, 1, 2, 3, 4, 5) is the undetermined coefficients.

The derivative forms of the shape functions are as follows:

$$\begin{cases} y\_i' = C\_{i,1} + 2C\_{i,2}\mathbf{x} + 3C\_{i,3}\mathbf{x}^2 + 4C\_{i,4}\mathbf{x}^3 + 5C\_{i,5}\mathbf{x}^4\\ y\_i'' = 2C\_{i,2} + 6C\_{i,3}\mathbf{x} + 12C\_{i,4}\mathbf{x}^2 + 20C\_{i,5}\mathbf{x}^3\\ y\_i''' = 6C\_{i,3} + 24C\_{i,4}\mathbf{x} + 60C\_{i,5}\mathbf{x}^2\\ y\_i^{(4)} = 24C\_{i,4} + 120C\_{i,5}\mathbf{x} \end{cases}, \quad \mathbf{x} \in [0, l\_i], \ (i = 1, 2, \dots, n+1) \tag{8}$$

Substituting Equations 7 and 8 into Equation 1, the residual equation can be written as follows:

$$R\_i(\mathbf{x}) = \mathbf{E} I\_i \mathbf{y}\_i^{(4)}(\mathbf{x}) - T\_i(\mathbf{x}) \mathbf{y}\_i^{\circ}(\mathbf{x}) - \mathbf{w}\_i \mathbf{y}\_i^{\circ}(\mathbf{x}) - F(\mathbf{x}) \tag{9}$$

As the shape function determined by Equation 7 is fifth order, there are six undetermined coefficients *Cij* (*j* = 0, 1, 2, 3, 4, 5) in each shape function. Besides, there are *n* discrete elements in the system, so there are 6*n* equations that are needed to solve the problem. Generally, two collocation points are needed in weighted residual method. If *li* /3 and 2*li* /3 are chosen as the collocation points, the residual value should be equal to 0 as follows:

$$\begin{split} R\_{i} \left( \frac{1}{3} I\_{i} \right) &= \text{EI}\_{i} \left( 24 C\_{\iota,4} + 40 C\_{\iota,5} I\_{i} \right) - T\_{i} \left( \frac{1}{3} I\_{i} \right) \left( 2C\_{\iota,2} + 2C\_{\iota,3} I\_{i} + \frac{4}{3} C\_{\iota,4} I\_{i}^{2} + \frac{20}{27} C\_{\iota,5} I\_{i}^{3} \right) \\ &- \text{w}\_{i} \left( C\_{\iota,1} + \frac{2}{3} C\_{\iota,2} I\_{i} + \frac{1}{3} C\_{\iota,3} I\_{i}^{2} + \frac{4}{27} C\_{\iota,4} I\_{i}^{3} + \frac{8}{81} C\_{\iota,5} I\_{i}^{4} \right) - F\_{i} \left( \frac{1}{3} I\_{i} \right) = 0, \quad (i = 1, 2, ..., n) \end{split} \tag{10}$$

$$\begin{split} R\_{i} \left(\frac{2}{3} l\_{i}\right) &= \text{EI}\_{i} \left(24C\_{i,4} + 80C\_{i,5}l\_{i}\right) - T\_{i} \left(\frac{2}{3} l\_{i}\right) \left(2C\_{i,2} + 4C\_{i,3}l\_{i} + \frac{16}{3}C\_{i,4}l\_{i}^{2} + \frac{160}{27}C\_{i,5}l\_{i}^{3}\right) \\ &- \text{w}\_{i} \left(C\_{i,1} + \frac{4}{3}C\_{i,2}l\_{i} + \frac{4}{3}C\_{i,3}l\_{i}^{2} + \frac{32}{27}C\_{i,4}l\_{i}^{3} + \frac{80}{81}C\_{i,5}l\_{i}^{4}\right) - F\_{i} \left(\frac{2}{3}l\_{i}\right) = 0, \ (i = 1, 2, ..., n) \end{split} \tag{11}$$

2*n* equations can be obtained through Equations 10 and 11, other 4*n* equations are needed to list according to the boundary conditions and continuity conditions.

### *2.3.2. Continuity conditions*

Because Equation 1 is a fourth-order differential equation, the shape function in weighted

where *yi* is the displacement of discrete nodes; *li* is the length of each span; *Cij* (*j* = 0, 1, 2, 3, 4,

Substituting Equations 7 and 8 into Equation 1, the residual equation can be written as follows:

As the shape function determined by Equation 7 is fifth order, there are six undetermined coefficients *Cij* (*j* = 0, 1, 2, 3, 4, 5) in each shape function. Besides, there are *n* discrete elements in the system, so there are 6*n* equations that are needed to solve the problem. Generally, two

> ( ) 2 3 ,4 ,5 ,2 ,3 ,4 ,5

21 4 5 1 0, ( 1,2,..., ) 3 3 27 81 <sup>3</sup>

( ) 2 3 ,4 ,5 ,2 ,3 ,4 ,5

4 4 32 80 <sup>2</sup> 0, ( 1,2,..., ) 3 3 27 81 <sup>3</sup>

2*n* equations can be obtained through Equations 10 and 11, other 4*n* equations are needed to

2 34

2 34

<sup>æ</sup> ö æö - + + + + - == <sup>ç</sup> ÷ ç÷ <sup>è</sup> ø èø

<sup>2</sup> <sup>2</sup> 16 160 EI 24 80 2 4 3 3 3 27

*R l C Cl T l C Cl Cl Cl*

*i i i i ii i i i ii ii i i*

æ ö æ öæ <sup>ö</sup> = + - ++ + ç ÷ ç ÷ç <sup>÷</sup> è ø è øè <sup>ø</sup>

*w C Cl Cl Cl Cl F l i n*

<sup>æ</sup> ö æö - + + + + - == <sup>ç</sup> ÷ ç÷ <sup>è</sup> ø èø

<sup>1</sup> <sup>1</sup> 4 20 EI 24 40 2 2 3 3 3 27

*R l C Cl T l C Cl Cl Cl*

*i i i i ii i i i ii ii ii*

æ ö æ öæ <sup>ö</sup> = + - ++ + ç ÷ ç ÷ç <sup>÷</sup> è ø è øè <sup>ø</sup>

*w C Cl Cl Cl Cl F l i n*

( ) ( ) ( ) ( ) ( ) <sup>4</sup> EI *R x y x T x y x wy x F x i ii i i ii*

234

*y C Cx Cx Cx x li n*

í Î = ××× +

2 3

2

[ ] ( ) <sup>2345</sup> ,0 ,1 ,2 ,3 ,4 ,5 , 0, , 1,2, , 1 *ii i i i i i i y C Cx Cx Cx Cx Cx x l i n* = + + + + + Î = ××× + (7)

, [0, ], ( 1,2, , 1)

(8)

*i*

² ¢ = - -- (9)

/3 and 2*li*

/3 are chosen as the

(10)

(11)

residual method can be written as follows [6]:

The derivative forms of the shape functions are as follows:

*ii i i i i*

*y C Cx Cx Cx Cx*

,1 ,2 ,3 ,4 ,5

23 4 5

,2 ,3 ,4 ,5

,3 ,4 ,5

( ) ( )

collocation points are needed in weighted residual method. If *li*

,1 ,2 ,3 ,4 ,5

,1 ,2 ,3 ,4 ,5

*i i ii ii ii ii i i*

list according to the boundary conditions and continuity conditions.

*i i ii ii ii ii i i*

collocation points, the residual value should be equal to 0 as follows:

*ii i i i*

<sup>ì</sup> ¢ =+ + + + <sup>ï</sup>

2 6 12 20

,4 ,5

6 24 60

*y C Cx Cx*

ï ¢¢ =+ + +

*ii i i*

24 120

*y C Cx*

*iii*

<sup>ï</sup> ¢¢¢ =+ + <sup>ï</sup>

5) is the undetermined coefficients.

( )

ï

20 Non-Destructive Testing

4

ï = + î

The continuity of geometry and physical properties of riser guarantees the continuity of displacement, deflection angle, bending moment and shear force on the adjacent discrete element as follows:

$$\begin{cases} x\_i(l\_i) = x\_{i+1}(0) \\ \theta\_i(l\_i) = \theta\_{i+1}(0) \\ M\_i(l\_i) = M\_{i+1}(0) \\ Q\_i(l\_i) = Q\_{i+1}(0) \end{cases} (i = 2, 3, \cdots, n) \tag{12}$$

According to the relationship among displacement, deflection angle, bending moment and shear force in mechanics of materials, the following equations can be listed after substituting Equations 7 and 8 into Equation 12 as follows:

$$\begin{cases} C\_{i,0} + C\_{i,1}l\_i + C\_{i,2}l\_i^2 + C\_{i,3}l\_i^3 + C\_{i,4}l\_i^4 + C\_{i,5}l\_i^5 = C\_{i+1,0} \\ C\_{i,1} + 2C\_{i,2}l\_i + 3C\_{i,3}l\_i^2 + 4C\_{i,4}l\_i^3 + 5C\_{i,5}l\_i^4 = C\_{i+1,1} \\ \text{EI}\_i \left( 2C\_{i,2} + 6C\_{i,3}l\_i + 12C\_{i,4}l\_i^2 + 20C\_{i,5}l\_i^3 \right) = 2\text{EI}\_{i+1}C\_{i+1,2} \\ \text{EI}\_i \left( 6C\_{i,3} + 24C\_{i,4}l\_i + 60C\_{i,5}l\_i^2 \right) = 6\text{EI}\_{i+1}C\_{i+1,3} \end{cases}, \quad (i=2,3,\cdots,n) \tag{13}$$

4(*n*–1) equations can be obtained according to Equation 13, and 6*n*–4 equations can be listed through adding 2*n* equation as mentioned above. Other 4 equations can be acquired by boundary conditions.

#### *2.3.3. Boundary conditions*

The boundary conditions of the system are shown in Equation 2. Substituting the shape function and its derivative forms into Equation 2, the boundary conditions can be represented by the following equation:

$$\begin{cases} C\_{1,0} = S; \quad C\_{1,1} = 0\\ C\_{n+1,0} + C\_{n+1,l}I\_{n+1} + C\_{n+1,2}I\_{n+1}^2 + C\_{n+1,3}I\_{n+1}^3 + C\_{n+1,4}I\_{n+1}^4 + C\_{n+1,5}I\_{n+1}^5 = 0\\ C\_{n+1,1} + 2C\_{n+1,2}I\_{n+1} + 3C\_{n+1,3}I\_{n+1}^2 + 4C\_{n+1,4}I\_{n+1}^3 + 5C\_{n+1,5}I\_{n+1}^4 = 0 \end{cases} \tag{14}$$

4 equations can be obtained according to Equation 14, and all of the 6*n* equations have been obtained finally. In other words, the 6*n* undetermined coefficients and the displacement of the riser system can be determined unique. Once the deformation has been obtained, the internal force and strength can be discussed later.

#### **2.4. Model validation**

Taken a real deepwater drilling operation as example, the water depth is 1500 m, the riser outer diameter is 533.4 mm, the riser wall thickness is 15.875 mm, the top tension is 1.3 G, the top displacement of floating vessel is 30 m, the steel density is 7850 kg/m3 , the elastic modulus of steel is 206 GPa, the drilling fluid density is 1200 kg/m3 , the sea water density is 1030 kg/m3 , the wave height is 6.5 m, the wave period is 8 s, the sea surface wind velocity is 2 m/s, velocity of sea tide is 0.5 m/s, the drag force coefficient is 0.8 and the inertia force coefficient is 1.5.

Numerical simulations have been conducted with two-dimensional finite element model using ABAQUS software. The models are completed in the ABAQUS version 6.12-3 software. The computer used is DELL OPTIPLEX-390, and the RAM is 4 GB. Results of analysis calculated by the theoretical method and the numerical simulations are shown in **Figures 3** and **4**.

**Figure 3.** Horizontal displacement.

**Figure 4.** Von Mises stress.

As shown in **Figures 3** and **4**, good consistency has been shown between the calculation results, which validate the availability of the theoretical analysis. In particular, in regard to horizontal displacement, the maximum horizontal displacement calculated by theoretical analysis and ABAQUS software is 36.3 and 35.9 m, which locates at 406 and 383 m below the sea surface, and the maximum calculation error is 1.1% and 5.6%, respectively. However, in regard to stress, the Von Mises stress of the maximum value is 177 and 174 MPa, and both of them appear at 16 m below the sea surface.

## **3. Experimental system**

## **3.1. System compositions**

**2.4. Model validation**

22 Non-Destructive Testing

**Figure 3.** Horizontal displacement.

**Figure 4.** Von Mises stress.

Taken a real deepwater drilling operation as example, the water depth is 1500 m, the riser outer diameter is 533.4 mm, the riser wall thickness is 15.875 mm, the top tension is 1.3 G, the top

the wave height is 6.5 m, the wave period is 8 s, the sea surface wind velocity is 2 m/s, velocity of sea tide is 0.5 m/s, the drag force coefficient is 0.8 and the inertia force coefficient is 1.5.

Numerical simulations have been conducted with two-dimensional finite element model using ABAQUS software. The models are completed in the ABAQUS version 6.12-3 software. The computer used is DELL OPTIPLEX-390, and the RAM is 4 GB. Results of analysis calculated by the theoretical method and the numerical simulations are shown in **Figures 3** and **4**.

, the elastic modulus of

,

, the sea water density is 1030 kg/m3

displacement of floating vessel is 30 m, the steel density is 7850 kg/m3

steel is 206 GPa, the drilling fluid density is 1200 kg/m3

The experimental system is named mechanics behaviour simulation experimental system for deep water drilling and production strings, which has four sub-systems, namely mechanical structure, hydraulic power and control system and data acquisition system. The main system configuration is shown in **Figure 5** [7].

**Figure 5.** System compositions (1) axial piston; (2) end clamp; (3) connection joint; (4) main cylinder; (5) strain gauge; (6) hydraulic cylinder; (7) tubular specimen; (S2) hydraulic power and control system; (S3) data acquisition system.

The mechanical structure, which is the main body of the experimental equipment, is consist of the main cylinder, two axial pistons, two end clamps and two connection joints. The hydraulic power and control system includes proportion booster cylinder, servo booster cylinder and two hydraulic cylinders to apply transverse force. The main parameters of mechanical structure and hydraulic power and control system are shown in **Tables 1** and **2**.

**Table 1.** Main structure parameters of the experimental system.

Note: C1, C2, C3 are proportion booster cylinder, servo booster cylinder and transverse hydraulic cylinders. *D*ip = inner diameter of piston cylinder; *D*p = outer diameter of piston rod; *V*max = maximum output speed; *γ* = Booster ratio; *P*max = maximum output pressure.

**Table 2.** Main parameters of the hydraulic control system.

Besides, the data acquisition system is consist of strain gauges and instruments for displacement, strain, pressure and flow rate measurement.

#### **3.2. System working principle**

## *3.2.1. Determination of simulated condition*

Generally, we do small size simulation experiment, but in some cases, we need to conduct full size simulation experiment. So, the first matter is to decide which kind of the experiment is. Then, the experimental samples are needed to manufacture. However, no matter which kind of experiment is, we must know the loads subjected to the samples before the experiment. So, the simulated conditions are needed to clearly confirm. Next, the internal pressure, external pressure, axial force and lateral force subjected on the samples are in need for precise calcu‐ lation . Finally, we must program the load spectrum and upload into the control system to be called during the experiment. It should be pointed out that, if the experiment is not a destruc‐ tive test, we must limit the load to ensure the safety and integrity of the sample.

#### *3.2.2. Sample installation and load applying*

Once the load spectrum is accomplished, the tubular sample is needed to install into the main cylinder. The installation process should be based on the following procedures: first, the strain gauges should be pasted on the sample, and the test leads should connect to the data acquisition system, then connect the sample with one of the connection joint, the axial piston and the end clamp successively, then put the two lateral hydraulic cylinders into the main cylinder, then connect the hydraulic lines with the hydraulic system and then install the left axial piston and end clamp. When conducting the experiment, the hydraulic power system receives the instructions (pressure and displacement) from the control host, and apply internal pressure, external pressure, axial load and lateral force to the tubular sample. The tubular sample generates displacement and strain under the simulation loads. The displacement and strain signals transmit into the data acquisition system through the teat leads. And finally, the strain and stress state of the sample can be obtained by analysing the data.

## *3.2.3. Pressure relief*

*D***ip (mm)** *D***p (mm) Stroke (mm)** *V***max (m/s)** *γ P***max (MPa)**

C1 180 120 700 0.5 2.25 56

C2 180 120 700 1.0 1.65 46

C3 140 80 100 – – 25

maximum output pressure.

24 Non-Destructive Testing

**3.2. System working principle**

*3.2.1. Determination of simulated condition*

*3.2.2. Sample installation and load applying*

**Table 2.** Main parameters of the hydraulic control system.

displacement, strain, pressure and flow rate measurement.

Note: C1, C2, C3 are proportion booster cylinder, servo booster cylinder and transverse hydraulic cylinders. *D*ip = inner diameter of piston cylinder; *D*p = outer diameter of piston rod; *V*max = maximum output speed; *γ* = Booster ratio; *P*max =

Besides, the data acquisition system is consist of strain gauges and instruments for

Generally, we do small size simulation experiment, but in some cases, we need to conduct full size simulation experiment. So, the first matter is to decide which kind of the experiment is. Then, the experimental samples are needed to manufacture. However, no matter which kind of experiment is, we must know the loads subjected to the samples before the experiment. So, the simulated conditions are needed to clearly confirm. Next, the internal pressure, external pressure, axial force and lateral force subjected on the samples are in need for precise calcu‐ lation . Finally, we must program the load spectrum and upload into the control system to be called during the experiment. It should be pointed out that, if the experiment is not a destruc‐

Once the load spectrum is accomplished, the tubular sample is needed to install into the main cylinder. The installation process should be based on the following procedures: first, the strain gauges should be pasted on the sample, and the test leads should connect to the data acquisition system, then connect the sample with one of the connection joint, the axial piston and the end clamp successively, then put the two lateral hydraulic cylinders into the main cylinder, then connect the hydraulic lines with the hydraulic system and then install the left axial piston and end clamp. When conducting the experiment, the hydraulic power system receives the instructions (pressure and displacement) from the control host, and apply internal pressure, external pressure, axial load and lateral force to the tubular sample. The tubular sample generates displacement and strain under the simulation loads. The displacement and strain signals transmit into the data acquisition system through the teat leads. And finally, the strain

tive test, we must limit the load to ensure the safety and integrity of the sample.

and stress state of the sample can be obtained by analysing the data.

Pressure relief is necessary after the experiment. To ensure the safety of the specimen in pressure unloading, all kinds of loads are needed to be unloaded in proportion.

## **3.3. System main functions**

## *3.3.1. External pressure-withstanding test*

When the external pressure is generated by water pressure in the main cylinder, the axial piston will be pushed towards axially, which will result in axial tension at the tubular sample. In some cases, the axial tension may exceed the maximum allowable load and result in sample damage. So, when external pressure-withstanding tests are done in addition to the water pressure in the main cylinder, the pressure of water must be pumped into the annulus between the end clam and the axial piston to balance the axial force generated by water pressure in the main cylinder. Besides, these two kinds of water pressure must be pumped proportionally.

## *3.3.2. Internal pressure-withstanding test*

Similarly, when the internal pressure is generated by water pressure in the tubular sample, the axial tension will also be appeared. So, when internal pressure-withstanding tests are done, the pressure of water in the sample and the annulus between the end clam and the axial piston must be pumped concurrently and proportionally.

## *3.3.3. Combination test under external, internal and lateral forces*

If we want to study the mechanics performance of tubular under combined internal pressure, external pressure and lateral force, the pressure of water pumped in the main cylinder, tubular sample and the annulus between the end clam and the axial piston must be loaded concurrently and in proportion.

#### *3.3.4. Sealing performance test*

Many devices used in the deepwater engineering require good sealing performance. Since the experiment equipment can provide 30 MPa pressure, it is a good platform to conduct sealing performance test for some special devices.

## **3.4. System performance test**

Through system debugging, the hydraulic power system has presented good performance in receiving and executing the instructions from the control host. Besides, the hydraulic servo valves have excellent performance in regulation of pressure and flow rate according to the feedback signals. No phenomenon of leaking water and oil has been occurred. All of the technical indicators have been reached in the laboratory. After completion of the debugging, the internal and external pressure loading tests have been completed, and the actual value collected by the data acquisition system and the target pressure value is shown in **Figure 6**.

**Figure 6.** System performance test curve.

As shown in **Figure 6**, the pressure can rapidly response and remain unchanged for long time period. After pressure relief, the reload performance is still excellent. During pres‐ sure maintenance phase, the maximum pressure is 31.61 MPa, the minimum pressure is 28.15 MPa, and the average pressure is 29.97 MPa, which indicate that the pressure control system has outstanding performance and can carry out well in accordance with the experimental expectations.

## **4. Simulation experiments**

#### **4.1. Theoretical analysis**

As shown in **Figure 1**, the marine drilling riser in working status is subjected to internal pressure, external pressure, axial tension and bending moment induced by drilling fluid, sea water, top tension and lateral force, respectively. If we choose micro-unit from riser outer wall surface, the stress state is shown in **Figure 7**.

**Figure 7.** Stress state of riser outer wall surface.

As shown in **Figure 7**, the micro-unit is under the stress state of axial stress, radial stress and hoop stress, and all of the stresses are principal stress. The relationship between the stress and the loads is satisfied by the following equation:

$$\begin{cases} \sigma\_{\rm r} = \frac{p\_i a^2 - p\_o b^2}{b^2 - a^2} - \frac{(p\_i - p\_o) a^2 b^2}{(b^2 - a^2) r^2} \\\\ \sigma\_{\rm 0} = \frac{p\_i a^2 - p\_o b^2}{b^2 - a^2} + \frac{(p\_i - p\_o) a^2 b^2}{(b^2 - a^2) r^2} \\\\ \sigma\_{\rm x} = \frac{F\_{\rm a}}{S\_{\rm a}} \pm \frac{M}{W} \end{cases} \tag{15}$$

where *σ*θ is the hoop stress (Pa); *σ*r is the radial stress (Pa); *σ*x is the axial stress (Pa); a and b are the inner diameter and outer diameter of riser, respectively (m); *p*<sup>i</sup> and *p*o are the internal and external pressures, respectively (Pa); *F*a is the axial tension (N); *S*a is the cross-sectional area (m2 ); *M* is the bending moment (N·m); *W* is the bending modulus (m3 ); "+" is selected at the side under tension stress generated by bending moment, whereas "–" is applied at the side under compressive stress generated by bending moment.

Once the stress state has been obtained, the strain value of the micro-unit can be calculated by the generalized Hooke's law as follows:

$$\begin{cases} \mathcal{E}\_r = \frac{1}{E} \left[ \sigma\_r - \mu \left( \sigma\_\vartheta + \sigma\_\chi \right) \right] \\\\ \mathcal{E}\_\theta = \frac{1}{E} \left[ \sigma\_\theta - \mu \left( \sigma\_r + \sigma\_\chi \right) \right] \\\\ \mathcal{E}\_\chi = \frac{1}{E} \left[ \sigma\_z - \mu \left( \sigma\_\vartheta + \sigma\_r \right) \right] \end{cases} \tag{16}$$

where *ε*r, *ε*θ and *ε*<sup>x</sup> are the radial strain, hoop strain and axial strain, respectively, and *E* and *μ* are elastic modulus and Poisson's ratio, respectively.

As shown in **Figure 3**, the riser has the maximum horizontal displacement at about *x* = 400 m. Therefore, we select the riser here as the simulation object, and the theoretical calculation results of loads, stress and deformation are shown in **Table 3**.

**Table 3.** Theoretical calculation results of riser at *x* = 400 m.

**Figure 6.** System performance test curve.

26 Non-Destructive Testing

experimental expectations.

**4.1. Theoretical analysis**

**4. Simulation experiments**

surface, the stress state is shown in **Figure 7**.

**Figure 7.** Stress state of riser outer wall surface.

As shown in **Figure 6**, the pressure can rapidly response and remain unchanged for long time period. After pressure relief, the reload performance is still excellent. During pres‐ sure maintenance phase, the maximum pressure is 31.61 MPa, the minimum pressure is 28.15 MPa, and the average pressure is 29.97 MPa, which indicate that the pressure control system has outstanding performance and can carry out well in accordance with the

As shown in **Figure 1**, the marine drilling riser in working status is subjected to internal pressure, external pressure, axial tension and bending moment induced by drilling fluid, sea water, top tension and lateral force, respectively. If we choose micro-unit from riser outer wall What calls for special attention is that *ε*x and *ε*θ can be obtained after experiment, while *ε*<sup>r</sup> is difficult to be measured directly. However, if we use the theoretical value of radial stress, σx, εx and εθ are known in Equation 16, and σr, σθ and ε<sup>r</sup> can be solved. So, finally, the stress state strength check can be determined by *σ*x, *σ*r and *σ*θ.

## **4.2. Simulation experiment method**

The four-point bending method has been adopted in the simulation experiment, and the mechanical analysis model of the tubular sample is shown in **Figure 8** [8].

**Figure 8.** Simulation experiment method: (a) mechanical analysis model; (b) bending moment diagram of tubular sam‐ ple and (c) shearing force diagram of tubular sample.

Because the two ends of the tubular sample are fixed with the connection joints, this constrain can be regarded as a fixed end. The force outputted by two lateral hydraulic cylinders pushes the sample upward. If both of the two outputted forces equal to *F*, then the bending moment between *L*/2 is constant and equals to *FL*/16. So, the tubular sample between *L*/2 is the real simulation object.

#### **4.3. Key problems**

## *4.3.1. Insulation problem between strain gauges and tubular sample*

Because the strain gauges and its welding wires are working in high water pressure, the insulation between strain gauges and tubular sample must be done to avoid the high water pressure infiltrating into the strain gauge base. Otherwise, the strain gauge will separate from the sample, which will result in rapid drop of insulation resistance and even fall off of the strain gauges. All of these have strong impact on the accuracy of the measurement data. Besides, if the welding wires are exposed to high water pressure directly, the wires would be conductive with water, which will also result in distortion or even failure of the measurement. Therefore, the exposed metal parts in welding wires must be isolated from the water. Generally, the chemical coating method is used in strain measurement under high water pressure. Before the experiment, the sealing protection measures must be adopted after the strain gauges are pasted on the outer wall of the tubular sample.

The measure taken to insulate the strain gauges is shown in **Figure 9**.

What calls for special attention is that *ε*x and *ε*θ can be obtained after experiment, while *ε*<sup>r</sup> is difficult to be measured directly. However, if we use the theoretical value of radial stress, σx, εx and εθ are known in Equation 16, and σr, σθ and ε<sup>r</sup> can be solved. So, finally, the stress state

The four-point bending method has been adopted in the simulation experiment, and the

**Figure 8.** Simulation experiment method: (a) mechanical analysis model; (b) bending moment diagram of tubular sam‐

Because the two ends of the tubular sample are fixed with the connection joints, this constrain can be regarded as a fixed end. The force outputted by two lateral hydraulic cylinders pushes the sample upward. If both of the two outputted forces equal to *F*, then the bending moment between *L*/2 is constant and equals to *FL*/16. So, the tubular sample between *L*/2 is the real

Because the strain gauges and its welding wires are working in high water pressure, the insulation between strain gauges and tubular sample must be done to avoid the high water pressure infiltrating into the strain gauge base. Otherwise, the strain gauge will separate from the sample, which will result in rapid drop of insulation resistance and even fall off of the strain gauges. All of these have strong impact on the accuracy of the measurement data. Besides, if the welding wires are exposed to high water pressure directly, the wires would be conductive with water, which will also result in distortion or even failure of the measurement. Therefore, the exposed metal parts in welding wires must be isolated from the water. Generally, the chemical coating method is used in strain measurement under high water pressure. Before the

mechanical analysis model of the tubular sample is shown in **Figure 8** [8].

strength check can be determined by *σ*x, *σ*r and *σ*θ.

**4.2. Simulation experiment method**

28 Non-Destructive Testing

ple and (c) shearing force diagram of tubular sample.

*4.3.1. Insulation problem between strain gauges and tubular sample*

simulation object.

**4.3. Key problems**

**Figure 9.** Sealing protection measures of strain gauges: (1) outer wall of the tubular sample; (2) strain gauge; (3) sealing glue and (4) test wires.

#### *4.3.2. Sealing problems between test wires and the main cylinder*

As the test leads connect the strain gauges and the strain acquisition instrument, which is put outside of the main cylinder, there must be satisfactory sealing problems between the test wires and the main cylinder. If the sealing measures do not conform to the requirements, the water leakage would happen during pumping water pressure, which would cause pressure fluctu‐ ations in the main cylinder and unstable strain signals. The key to solve this problem is to design reasonable sealing plugs. Design principles of the sealing plug are sealing easy and effective, large capacity of test leads, not complicated machinery manufacturing and installa‐

**Figure 10.** Sealing plug: (1) test wires; (2) sealing plug body; (3) sealing plug core; (4) seal rings and (5) sealing glue.

tion and the possibility to be reused. The comprehensive cleaning of residue and oil stain is necessary and important to ensure that the sealing performance of the plugs after manufacture is completed. In this experiment, sealing glue is used to inject into the plugs to seal them. Moreover, the sealing performance test must be conducted to ensure that the plugs meet the requirements of the pressure in the experiment. Otherwise, the sealing plugs need to be remade. The sealing measure taken to seal the test wires and the main cylinder is shown in **Figure 10**.

#### **4.4. Tubular sample**

The tubular sample is a steel pipe, with a length of 6000 m, outer diameter of 520 mm, inner diameter of 496 mm (wall thickness is 12 mm) and Elastic modulus and Poisson's ratio of 206 GPa and 0.3, respectively.

## **4.5. Pressure loading scheme**

According to **Table 3**, the bending moment subjected to the sample is 1.78e4 N·m, so the force outputted by the lateral hydraulic cylinders is 18.5 MPa based on the experiment equipment shown in **Table 2**. So, there are three parameters needed to be controlled, which are the internal pressure (4.8 MPa), the external pressure (4.0 MPa) and the lateral hydraulic pressure (18.5 MPa). Equal proportion loading scheme has been selected in the experiment, as shown in **Figure 11**.

**Figure 11.** Pressure loading scheme.

As shown in **Figure 11**, the loading scheme of "pressurization–stabilization–pressurization– stabilization…" is adopted. The displacement, pressure and flow rate are collected at all the experimental time, while the strain of the sample is only collected during pressure stabilization period. In each load period, the pressurization duration is 2 min, and the stabilization duration is 2 min. So, the duration of each load period is 4 min. After each load period, the increases of internal pressure, external pressure and lateral hydraulic pressure are about 0.6, 0.5 and 2.31 MPa, and the three kinds of pressure will eventually achieve 4.7, 4.0 and 18.5 MPa, respectively, after 8 load periods. Then, the stress state of the tubular sample reaches that of the marine riser at *x* = 400 m. To acquire more valid data, the duration of stabilization can be extended as expected after 32 min.

#### **4.6. Strain gauges pasted scheme**

tion and the possibility to be reused. The comprehensive cleaning of residue and oil stain is necessary and important to ensure that the sealing performance of the plugs after manufacture is completed. In this experiment, sealing glue is used to inject into the plugs to seal them. Moreover, the sealing performance test must be conducted to ensure that the plugs meet the requirements of the pressure in the experiment. Otherwise, the sealing plugs need to be remade. The sealing measure taken to seal the test wires and the main cylinder is shown in

The tubular sample is a steel pipe, with a length of 6000 m, outer diameter of 520 mm, inner diameter of 496 mm (wall thickness is 12 mm) and Elastic modulus and Poisson's ratio of 206

According to **Table 3**, the bending moment subjected to the sample is 1.78e4 N·m, so the force outputted by the lateral hydraulic cylinders is 18.5 MPa based on the experiment equipment shown in **Table 2**. So, there are three parameters needed to be controlled, which are the internal pressure (4.8 MPa), the external pressure (4.0 MPa) and the lateral hydraulic pressure (18.5 MPa). Equal proportion loading scheme has been selected in the experiment, as shown in

**Figure 10**.

30 Non-Destructive Testing

**Figure 11**.

**4.4. Tubular sample**

GPa and 0.3, respectively.

**4.5. Pressure loading scheme**

**Figure 11.** Pressure loading scheme.

As shown in **Figure 8**, four-point bending method is used in the experiment, and the tubular sample between *L*/2 is the real simulation object. So, the strain gauges are all pasted on this section. The whole scheme of pasting strain gauges is shown in **Figure 12**.

**Figure 12.** Strain gauges pasted scheme of the whole sample.

To acquire more valid data on different section, three sections (A–A, B–B and C–C) have been chosen to paste the strain gauges. One section locates the centre of the sample, and the other two sections symmetrically locate 750 mm from the centre of the sample. On each section, there are four points (1, 2, 3, 4), and the circumference interval of the four points is 90°, as shown in **Figure 12**. To measure the axial strain and hoop strain simultaneously, there are two strain gauges that are pasted at each point, of which one pasting direction is coincidence with the one of the mother lines of the tubular sample, and the other pasting direction is perpendicular to the prior strain gauge. The pasting scheme at each point is shown in **Figure 13**.

**Figure 13.** Pasting scheme at each point.

Therefore, 8 strain gauges are pasted at each section, and 24 strain gauges are pasted at the whole sample, of which 12 strain gauges measure the axial strain, and other 12 strain gauges measure the hoop strain. From theoretical perspective, the hoop strains measured at each point are equal, whereas the axial strains measured at point are unequal (Point 2 > Point 1 = Point 3 > Point 4).

#### **4.7. Pressure acquisition**

According to the experiment purpose, the three kinds of pressure (internal pressure, external pressure and lateral hydraulic pressure) are measured real time. The actual measured value of the pressure during stabilization period is shown in **Figure 14**.

**Figure 14.** Measured pressure value.

As shown in **Figure 14**, good feedback adjustment has been revealed. Although the actual value has fluctuated during pressure loading, they generally increase in the forms of steps. Finally, all of the pressure values have reached the experiment expectation with high consis‐ tency, and the average values of the internal pressure, external pressure and lateral hydraulic pressure are 4.8, 4.1 and 18.5 MPa, respectively. Besides, during the stabilization duration, the strain data have been measured successfully.

### **4.8. Strain acquisition**

**Figure 13.** Pasting scheme at each point.

**4.7. Pressure acquisition**

**Figure 14.** Measured pressure value.

> Point 4).

32 Non-Destructive Testing

Therefore, 8 strain gauges are pasted at each section, and 24 strain gauges are pasted at the whole sample, of which 12 strain gauges measure the axial strain, and other 12 strain gauges measure the hoop strain. From theoretical perspective, the hoop strains measured at each point are equal, whereas the axial strains measured at point are unequal (Point 2 > Point 1 = Point 3

According to the experiment purpose, the three kinds of pressure (internal pressure, external pressure and lateral hydraulic pressure) are measured real time. The actual measured value

of the pressure during stabilization period is shown in **Figure 14**.

The average strain values of the tubular sample under 4.8, 4.1 and 18.5 MPa are shown in **Table 4**.

**Table 4.** Strain data measured by the gauges.

As shown in **Table 4**, all of the strain gauges have collected the strain data during the experiment, which indicates that the key problems (insulation problem between strain gauges and tubular sample and sealing problems between the test wires and the main cylinder) involved in the experiment have been solved effectively, and the strain of the tubular sample can be measured by the experiment method as mentioned above.

## **4.9. Data analysis**

Due to the influence of the bending moment, the axial strain at the same section is different. The average value of the axial strain at Points 1, 2, 3 and 4 are 604, 631, 605 and 578 με, respectively, which verifies the above analysis (Point 2 > Point 1 = Point 3 > Point 4). However, if we take the axial strain (29 με) induced by the bending moment (1.78 × 104 N·m) into consideration, the axial point of the four points can be represented by the following: Point 2 = Point 1 + 29 με = Point 3 + 29 με and Point 1 = Point 3 = Point 4 + 29με. The hoop strain is approximately equal at the 12 measure points, and both of the theoretical value and the average value of the measured value are –143 and –143 με, which verifies the accuracy of the experiment method. The theoretical and measured axial strains are shown in **Figure 15**.

**Figure 15.** Theoretical and measured value of axial strains.

As shown in **Figure 15**, the maximum differences of the four measure points at the three sections are 11, 17, 7 and 17 με. If we take the average of the three sections at the same point, the statistical results can be as presented in **Table 5**.

**Table 5.** Statistical results of the measure axial strain.

#### **4.10. Stress state analysis**

Because the radial strain cannot be measured directly, the stress state can be determined by the theoretical axial stress, the measured hoop strain and axial strain according to Equa‐ tion 16. After analysis, the stress state of the experimental sample under the eight stabilization phases is shown in **Figure 16**.

**Figure 16.** Stress state analysis.

As shown in **Figure 16**, with the increases of internal pressure, external pressure, axial tension and bending moment, the hoop stress, radial stress, axial stress and the Von Mises stress increase gradually. When the loads' state reaches the simulation condition required in the experiment, the Von Mises stress is 121.9 MPa, while the theoretical value is 123.8 MPa. The measurement error is only 1.5%, which verifies the feasibility and validity of the simulation experiment method.

## **5. Conclusion**

**Figure 15.** Theoretical and measured value of axial strains.

**Table 5.** Statistical results of the measure axial strain.

**4.10. Stress state analysis**

phases is shown in **Figure 16**.

Variance (με<sup>2</sup>

34 Non-Destructive Testing

the statistical results can be as presented in **Table 5**.

As shown in **Figure 15**, the maximum differences of the four measure points at the three sections are 11, 17, 7 and 17 με. If we take the average of the three sections at the same point,

Theoretical value (με) 602 631 602 573 Average of the measured value (με) 603 631 605 578 Error (%) 0.2 0 0.5 0.9

) 22 50 18 86

Because the radial strain cannot be measured directly, the stress state can be determined by the theoretical axial stress, the measured hoop strain and axial strain according to Equa‐ tion 16. After analysis, the stress state of the experimental sample under the eight stabilization

**Items Point 1 Point 2 Point 3 Point 4**

Internal pressure, external pressure, axial tension and bending moment are typically loads subjecting on the tubulars in offshore drilling engineering. The mechanical model and control equations have been established to analyse the deformation and stress distribution of the marine riser, and the analysis method has been verified by finite element method (FEM) in the ABAQUS framework.

The experimental system has the ability to provide kinds of loads to simulate the mechanical behaviour of offshore tubulars, which exhibits a good platform to studying the mechanics of tubulars under complicated stress state and can perfect the deepwater drilling from theoretical viewpoint and field practice.

Good solutions must be proposed to solve the key problems in the simulation experiment, and thus, the technique of strain test under high water pressure can be used to measure the strain data effectively. Besides, excellent pressure loading scheme and the strain acquisition scheme are necessary to acquire precise measurement results.

## **Acknowledgements**

The authors gratefully acknowledge the financial support from the Natural Science Founda‐ tion of China (NSFC, 51521063, U1262201)

## **Author details**

Yanbin Wang\* , Deli Gao and Jun Fang

\*Address all correspondence to<EMAIL_ADDRESS>
MOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing, China

## **References**

## **Plate-Like Structure Damage Acoustic Emission Beamforming Array Technique and Probability-Based Diagnostic Imaging Method**

Dongsheng Li, Mengdao Jin and Quanming Feng

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/62413

#### **Abstract**

**Acknowledgements**

36 Non-Destructive Testing

**Author details**

Yanbin Wang\*

**References**

978-7-5636-3598-6.

China

tion of China (NSFC, 51521063, U1262201)

, Deli Gao and Jun Fang

\*Address all correspondence to<EMAIL_ADDRESS>
Field Equipment, Vol. 43, No. 4, pp: 26–29.

Science and Engineering, Vol. 19, pp: 84–90.

ISBN: 978-7-0403-0895-2.

The authors gratefully acknowledge the financial support from the Natural Science Founda‐

MOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing,

[1] Gao Deli. (2011).Optimized Design and Control Techniques for Drilling & Completion of Complex-Structure Wells. China University of Petroleum Press, Beijing, China, ISBN

[2] Lu Baoping. (2014). Key Technologies and Equipment for Deepwater Drilling. China

[3] Robello Samuel & Gao Deli. (2013). Horizontal Drilling Engineering: Theory, Methods and Applications. Sigma Quadrant Publisher, Texas, USA, ISBN: 978-0-615-83770-3.

[4] Wang Yanbin, Gao Deli & Fang Jun. (2014). Development of Mechanics Behavior Simulation Experimental System for Deep Water Drilling and Production String. Oil

[5] Wang Yanbin, Gao Deli & Fang Jun. (2014). Static analysis of deep-water marine riser subjected to both axial and lateral forces in its installation. Journal of Natural Gas

[6] Gao Deli & Zhang Hui. (2012). Mechanical Analysis of Tubes in Deepwater Drilling Operation without Riser. Science & Technology Review, Vol. 30, No. 4, pp: 37–42.

[7] Fang Jun, Wang Yanbin & Gao Deli. (2013). Test Method for the Force Deformation of

[8] Liu Hongwen. (2011). Mechanics of Materials. Higher Education Press, Beijing, China,

Deepwater Riser. China Petroleum Machinery, Vol. 41, No. 12, pp: 53–57.

Petrochemical Press, Beijing, China, ISBN 978-7-5114-2695-6.

A novel beamforming array technique and probability-based diagnostic imaging method are proposed to determine the acoustic emission (AE) source in plate-like structures. The technique that differs from common beamforming array techniques, in particular a sensor network, is used instead of a linear sensor array, to highlight information on the AE source location in one coordinate system as energy distribu‐ tion. To reduce the uncertainty, avoid the boundary reflection effect, and ensure the rationality of the signal superposition, a Hilbert transform-based signal processing is applied before the delay-and-sum algorithm and a probability-based diagnostic imaging method is developed for AE source localization. The finite element numeri‐ cal simulation method and the pencil-lead-broken experiment on aluminum plate are also conducted, and a thin-walled cylinder pipe-like structure is also tested by the pencil-lead-broken experiment to develop the application of the proposed method in various fields. The results indicate that this method is efficient and capable of visually showing the localization results highlighted in the probability images.

**Keywords:** acoustic emission, source localization, beamforming, probability-based di‐ agnosticimaging, plate-like structure, health monitoring

## **1. Introduction**

Plate-like structures are widely used in a variety of fields, such as material, civil, aerospace, and other industries [1–5]. Confirming the health condition of these plate-like structures is a very meaningful assignment for engineers. One of the various non-destructive techniques, acous‐

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

tic emission (AE) monitoring is arguably based on the simplest of physical concepts: the release of transient elastic waves in solid materials as a result of a localized source of damage [2–4]. The process of locating the source of these acoustic waves by capturing the related propagating acoustic signals through various sensors or arrays and properly analyzing them is commonly known as the AE source localization technique [3–8]. Common passive monitoring techni‐ ques are currently applied for AE source localization in isotropic and anisotropic structures, particularly in two-dimensional plate-like structures [9,10].

The techniques for AE source localization, such as triangulation technique, modal AE, and optimization-based technique, are currently performed by accurately determining the exact time of arrival (TOA) or time difference of arrival (TDOA) [8]. An obvious disadvantage of these methods is that the precision of the time difference measurement has a great effect on the location precision. To avoid this problem, McLaskey et al. [11] introduced a novel beam‐ forming method of AE analysis, which is particularly suited for field applications on large plate-like reinforced concrete structures, such as walls and bridge decks. The advantage of the beamforming technique is that it does not require the TOA or TDOA of a specific wave mode; the technique can therefore handle noisy signals if the noise is a Gaussian white noise. He et al. [12] applied the beamforming technique for source localization in a thin steel plate through finite element (FE) simulation and experiment. Nakatani et al. [13] studied AE source locali‐ zation on an anisotropic structure and proved that the technique is simple but effective.

Beamforming has been successfully used in source localization by many researchers, but its limitation as a technique is that it is a velocity-dependent method [11]. As such, its localization accuracy and precision are significantly influenced by the propagation characteristics. The propagation characteristics of an AE signal in plate-like structures are complex because of the signal's repeated reflection in the interface. The wave speed is affected by many factors, such as frequencies, material properties whether isotropic or not, multi-mode, and the dispersion in the propagation process. Xiao et al. [14] proposed a novel beamforming method with two uniform linear arrays in determining the AE source location using an unknown wave speed to reduce the effect of the factors (mentioned earlier) on AE beamforming. However, the accurate two-dimensional position cannot be shown at the same time in one coordinate system, because the localization coordinates are correct along the direction parallel to the array but not along the direction perpendicular to the array.

## **2. Principle of Lamb wave propagation**

The Lamb waves are used to interrogate the whole thickness of the plate-like structures. Either the surface defects or the internal damages can be detected.

## **2.1. The dispersion characteristic of Lamb wave**

Since Lamb waves are waves of plane strain that occur in a free plate, only displacements through the thickness (x3 direction) and in the direction of wave propagation (x1 direction) are taken into consideration (**Figure 1**).

Plate-Like Structure Damage Acoustic Emission Beamforming Array Technique and Probability-Based Diagnostic Imaging Method http://dx.doi.org/10.5772/62413 39

**Figure 1.** Geometric construction sketching of free plate.

tic emission (AE) monitoring is arguably based on the simplest of physical concepts: the release of transient elastic waves in solid materials as a result of a localized source of damage [2–4]. The process of locating the source of these acoustic waves by capturing the related propagating acoustic signals through various sensors or arrays and properly analyzing them is commonly known as the AE source localization technique [3–8]. Common passive monitoring techni‐ ques are currently applied for AE source localization in isotropic and anisotropic structures,

The techniques for AE source localization, such as triangulation technique, modal AE, and optimization-based technique, are currently performed by accurately determining the exact time of arrival (TOA) or time difference of arrival (TDOA) [8]. An obvious disadvantage of these methods is that the precision of the time difference measurement has a great effect on the location precision. To avoid this problem, McLaskey et al. [11] introduced a novel beam‐ forming method of AE analysis, which is particularly suited for field applications on large plate-like reinforced concrete structures, such as walls and bridge decks. The advantage of the beamforming technique is that it does not require the TOA or TDOA of a specific wave mode; the technique can therefore handle noisy signals if the noise is a Gaussian white noise. He et al. [12] applied the beamforming technique for source localization in a thin steel plate through finite element (FE) simulation and experiment. Nakatani et al. [13] studied AE source locali‐ zation on an anisotropic structure and proved that the technique is simple but effective.

Beamforming has been successfully used in source localization by many researchers, but its limitation as a technique is that it is a velocity-dependent method [11]. As such, its localization accuracy and precision are significantly influenced by the propagation characteristics. The propagation characteristics of an AE signal in plate-like structures are complex because of the signal's repeated reflection in the interface. The wave speed is affected by many factors, such as frequencies, material properties whether isotropic or not, multi-mode, and the dispersion in the propagation process. Xiao et al. [14] proposed a novel beamforming method with two uniform linear arrays in determining the AE source location using an unknown wave speed to reduce the effect of the factors (mentioned earlier) on AE beamforming. However, the accurate two-dimensional position cannot be shown at the same time in one coordinate system, because the localization coordinates are correct along the direction parallel to the array but not

The Lamb waves are used to interrogate the whole thickness of the plate-like structures. Either

Since Lamb waves are waves of plane strain that occur in a free plate, only displacements through the thickness (x3 direction) and in the direction of wave propagation (x1 direction) are

particularly in two-dimensional plate-like structures [9,10].

38 Non-Destructive Testing

along the direction perpendicular to the array.

**2. Principle of Lamb wave propagation**

**2.1. The dispersion characteristic of Lamb wave**

taken into consideration (**Figure 1**).

the surface defects or the internal damages can be detected.

Eq. (1) is for the symmetric Lamb wave mode (*Si* , *i* = 0,1,2,3 ⋯.) in which the particle motion of the plate occurs symmetrically about the symmetric axis of the plate. Eq. (2) is for the antisymmetric Lamb wave mode (*Ai* , *i* = 0,1,2,3 ⋯.) in which the particle motion of the plate occurs asymmetrically about the symmetric axis of the plate [15,16].

$$\frac{\tan(qh)}{\tan(ph)} = -\frac{4k^2pq}{(q^2-k^2)^2},\tag{1}$$

$$\frac{\tan(qh)}{\tan(ph)} = -\frac{(q^2 - k^2)^2}{4k^2pq},\tag{2}$$

where the parameters *p* and *q* are defined as follows:

$$p^2 = \frac{f^2}{c\_L^2} - k^2,\\ q^2 = \frac{f^2}{c\_T^2} - k^2,\\ h = \frac{d}{2},$$

Where *cL* and *cT* are the propagation velocities of longitudinal wave and shear wave, respec‐ tively; and wavenumber = *<sup>f</sup> cP* .

The phase velocity dispersion curves can be solved by Eqs. (1) and (2). And, the group velocity dispersion curves can be plotted from the phase velocity dispersion curves using Eq. (3). The group velocity and phase velocity dispersion curves for an aluminum plate are shown in **Figure 2**(**a** and **b**).

$$\mathcal{L}\_g = \frac{\mathcal{L}\_p^2}{\mathcal{L}\_p^2 - fd \frac{\widehat{\mathcal{C}} \mathcal{C}\_p}{\widehat{\mathcal{C}}(fd)}},\tag{3}$$

**Figure 2.** The dispersion curves for an aluminum plate: (a) group velocity dispersion curves and (b) phase velocity dispersion curves.

#### **2.2. Finite element simulation**

Numerical simulation is another main method aside from experimental validation that is used in various fields. Modeling the guided waves conveniently provides modeled data with a high signal-to-noise ratio, which can be used to develop useful advanced signal processing and analysis techniques. A number of numerical methods have been applied to analyze the propagation of elastic waves, such as the finite element method (FEM), finite difference method, boundary element method, and finite strip elements (FSE), all of which have their respective merits and defects. FEM is best understood from its practical application, known as finite element analysis (FEA). FEA is a computational tool for performing engineering analysis. It includes the use of mesh generation techniques for dividing a complex problem into small elements, which in turn represent different areas in the physical system; the technique also uses a software program coded with the FEM algorithm. This study simulates the guided wave signal propagation with FEA in the general three-dimensional domain using the commercial package ABAQUS, which has some advantages and is effective. It easily records the solution results of every element or node by time step and extracts results. In addition, it provides sophisticated pre- and post-processing functions and is user-friendly. Many scholars have demonstrated the possibility of using FEM to solve the guided wave formation and guided wave signal propagation in plate specimens.

#### *2.2.1. Explicit dynamic analysis*

The explicit dynamics analysis procedure, ABAQUS/Explicit, is based upon the implementa‐ tion of an explicit integration rule together with the use of diagonal ("lumped") element mass matrices. The equations of motion for the body are integrated using the explicit centraldifference integration rule.

Plate-Like Structure Damage Acoustic Emission Beamforming Array Technique and Probability-Based Diagnostic Imaging Method http://dx.doi.org/10.5772/62413 41

$$
\dot{\boldsymbol{u}}\_{\left(\iota+\frac{1}{2}\right)} = \dot{\boldsymbol{u}}\_{\left(\iota-\frac{1}{2}\right)} + \frac{\Delta t\_{\left(\iota+1\right)} + \Delta t\_{\left(\iota\right)}}{2} \ddot{\boldsymbol{u}}\_{\left(\iota\right)},\tag{4}
$$

$$
\mu\_{\binom{l+1}{\ell}} = \mu\_{\binom{l}{\ell}} + \Delta t\_{\binom{l+1}{\ell}} \dot{\mu}\_{\binom{l+\frac{1}{2}}{2}},
\tag{5}
$$

Where *u* is a degree of freedom (a displacement or rotation component) and the subscript *i* refers to the increment number in an explicit dynamics step.

The explicit procedure integrates through time by using many small time increments. The central-difference operator is conditionally stable, in order to avoid numerical instability, there are more than 20 points per cycle of the highest frequency. Therefore, the time step can be expressed as follows [17]:

$$
\Delta t = \frac{1}{20f\_{\text{max}}},
\tag{6}
$$

where *fmax* is the highest frequency of interest.

**Figure 2.** The dispersion curves for an aluminum plate: (a) group velocity dispersion curves and (b) phase velocity