First Line of Title Second Line of Title

SEISMOLOGY-BASED APPROACHES FOR THE QUANTITATIVE

ACOUSTIC EMISSION MONITORING OF CONCRETE

STRUCTURES

Lassaad Mhamdi

A dissertation submitted to the Faculty of the University of Delaware in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy in Civil Engineering

Summer 2015

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ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 SEISMOLOGY-BASED APPROACHES FOR THE QUANTITATIVE

ACOUSTIC EMISSION MONITORING OF CONCRETE

STRUCTURES

Lassaad Mhamdi

Approved: Harry W. Shenton III, Ph.D. Chair of the Department of Civil and Environmental Engineering

Approved: Babatunde A. Ogunnaike, Ph.D. Dean of the College of Engineering

Approved: James G. Richards, Ph.D. Vice Provost for Graduate and Professional Education I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy.

Signed: Thomas Schumacher, Ph.D. Professor in charge of dissertation

I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy.

Signed: Harry W. Shenton III, Ph.D. Member of dissertation committee

Signed: Nii O. Attoh-Okine, Ph.D. Member of dissertation committee

Signed: Lindsay Linzer, Ph.D. Member of dissertation committee ACKNOWLEDGEMENTS

In the name of Allah, the Most Beneﬁcent, the Most Merciful

First and foremost, may all praise and glory be to Almighty Allah whom without his blessings and guidance, I would not be able to ﬁnish this thesis. Alhamdulillah, thank you Allah for giving me the patience and the strength.

I would like to express my deepest gratitude and my most considerate acknowledgements to my advisor Thomas Schumacher for his patient guidance, priceless, insightful and knowledgeable advices. His incessant support and help have been of a great importance to me through this work.

Most considerate acknowledgements are also due to Lindsay Linzer for her support and help with the MTI toolbox. Her invaluable knowledge of seismology and Moment Tensor Inversions have been of a great help to me. . Thanks are due to all the wonderful people and colleagues I had the great opportunity to know during the years I spent at the University of Delaware. Without their generous support and help, this work would not be possible.

Finally, my thanks to all my loving family members and all my dearest friends for their encouragements. Words cannot express my gratitude for their continuous emotional support.

iv DEDICATION

To my late mother Bachra Mhamdi. Your words of inspiration and encouragement in pursuit of excellence, still linger on. You will be always remembered.

v TABLE OF CONTENTS

LIST OF TABLES ...... x LIST OF FIGURES ...... xi ABSTRACT ...... xviii

Chapter

1 INTRODUCTION ...... 1

1.1 Introduction ...... 1

1.1.1 Problem Description ...... 3 1.1.2 Principal Objective ...... 3 1.1.3 Methodology ...... 4 1.1.4 Structure of Dissertation ...... 4

2 ELASTIC WAVE PROPAGATION: THEORY AND FUNDAMENTALS ...... 7

2.1 Introduction ...... 7 2.2 Elastic Wave Propagation in Solids and Structures ...... 7

2.2.1 Theory ...... 7

2.2.1.1 Longitudinal waves ...... 8 2.2.1.2 Shear waves ...... 8 2.2.1.3 Rayleigh waves ...... 8 2.2.1.4 Governing equations of elastic waves ...... 9

2.2.2 Interaction of elastic waves with free boundaries ...... 11

vi 3 ACOUSTIC EMISSION TECHNIQUE: HISTORY AND FUNDAMENTALS ...... 15

3.1 Introduction ...... 15

3.1.1 Deﬁnition ...... 17 3.1.2 Historical Review ...... 17 3.1.3 Acoustic Emission versus other NDT techniques ...... 20

3.2 Acoustic Emission Measurement and Instrumentation ...... 22

3.2.1 Measurement Chain ...... 22

3.2.1.1 AE Sensors ...... 23 3.2.1.2 Preampliﬁers ...... 25 3.2.1.3 Data Acquisition System: DAQ ...... 26 3.2.1.4 Storage and Processing of AE Data ...... 28

3.2.2 Acoustic Emission Analysis ...... 29

3.2.2.1 AE Terminology ...... 29 3.2.2.2 Qualitative Parameter-based Analysis ...... 29 3.2.2.3 Quantitative signal-based Analysis ...... 31

3.3 Applications Of Acoustic Emission Methods to Concrete Materials .. 32

4 ACOUSTIC EMISSION SOURCE LOCATION ...... 34

4.1 Introduction ...... 34 4.2 Source Location : Time of Arrival Approach ...... 36

4.2.1 Background and Principle ...... 36 4.2.2 Geiger's Method ...... 38 4.2.3 P-wave arrival time picking ...... 41

4.3 Glaser/NIST Point-Contact Sensors ...... 45

4.3.1 Characteristics of the Glaser/NIST point-contact sensor .... 45 4.3.2 Response of Glaser/NIST sensors on diﬀerent concrete specimens 49

4.4 Source Location Strategy ...... 54

vii 5 MOMENT TENSOR INVERSION INVERSION: THEORY AND FUNDAMENTALS ...... 58

5.1 Introduction and Background ...... 58 5.2 Moment Tensor Inversion: Theory ...... 59

5.2.1 Moment Tensor Source ...... 61

5.2.1.1 Equivalent Force Model ...... 61 5.2.1.2 Moment Tensor of the source ...... 63

5.3 Classiﬁcation Of Moment Tensor Inversion Methods ...... 64

5.3.1 Absolute methods ...... 65 5.3.2 Relative methods ...... 65 5.3.3 Hybrid methods ...... 66 5.3.4 Comparison of diﬀerent Inversion methods...... 66

5.4 MTI toolbox Code ...... 68

5.4.1 MTI Toolbox input parameters ...... 69 5.4.2 MTI Toolbox ouptput parameters ...... 70

6 EXPERIMENTAL INVESTIGATIONS ...... 75

6.1 Introduction ...... 75 6.2 Preliminary Study: Proof of Concept ...... 75

6.2.1 Experimental Setup ...... 75 6.2.2 Results and Discussion ...... 77 6.2.3 Conclusions from the preliminary study ...... 80

6.3 Case Study 1: Small Scale Concrete Beam ...... 80

6.3.1 Experimental Setup ...... 80

viii 6.3.2 Results and Discussion ...... 82

6.4 Case study 2: Large Scale Concrete Beams ...... 87

6.4.1 Concrete beam 1: Flexure beam experiment ...... 87

6.4.1.1 Experimental Setup ...... 87 6.4.1.2 Results and Discussion ...... 88

6.4.2 Concrete beam 2: Shear beam experiment ...... 100

6.4.2.1 Experimental Setup ...... 100 6.4.2.2 Results and Discussion ...... 100

6.4.3 Comparison between the two beams ...... 117

7 CONCLUSIONS ...... 125

7.1 Research Objective ...... 125 7.2 Principal ﬁndings and conclusions ...... 125 7.3 Future Work ...... 127

REFERENCES ...... 129

Appendix

A APPROXIMATE CONVERSION TO AND FROM SI UNITS .. 137

ix LIST OF TABLES

3.1 Characteristics of the KRN AMP-12BB-J Preampliﬁer ...... 27

3.2 Summary of the measurement chain elements ...... 28

3.3 Acoustic Emission Standard Terminology ASTM E1316-05 ..... 30

5.1 Comparison between the diﬀerent MTI techniques [94] ...... 67

5.2 Output Parameters of the MTI Toolbox ...... 72

6.1 Source Contributions From the MTI Inversions[94] ...... 78

6.2 Coordinates of the sensors mounted on The Flexure Beam ..... 90

6.3 Summary of the Events in the Flexure Beam ...... 92

6.4 Classiﬁcation of The Diﬀerent Types of Cracks in The Flexure Beam 95

6.5 Coordinates of the sensors mounted on the shear beam ...... 102

6.6 Summary of The Events in the Shear Beam ...... 103

6.7 Classiﬁcation of The Diﬀerent Types of Cracks in The Shear Beam 113

A.1 *SI Conversion Factors ...... 137

A.2 MTI Results for Cluster N◦1 Events in The Flexure Beam ..... 138

A.3 MTI Results for Cluster N◦2 Events in The Flexure Beam ..... 142

A.4 MTI Solutions for Cluster N◦1 Events in The Shear Beam ..... 146

A.5 MTI Solutions for Cluster N◦2 Events in The Shear Beam ..... 152

x LIST OF FIGURES

2.1 Schematic of the propagation of elastic body waves. (a) P-waves, (b) S-waves and (c) R-waves ...... 9

2.2 Normalized wave phase velocities vs. Poisson's Ratio ...... 11

2.3 Reﬂection and refraction of elastic waves on boundaries (a) P-wave and (b) S-wave (source: Kocur,[23]) ...... 12

2.4 Coupling of P- and S-waves at the boundaries between diﬀerent media (source: Kocur,[23]) ...... 13

2.5 Reflection coefficients for different Poisson's Ratios ...... 14

2.6 Relationship between incident and measured P-wave (source: Kocur,[23]) ...... 14

3.1 Conceptual illustration of a typical AE setup ...... 18

3.2 Acoustic Emission before and after 1950 ...... 20

3.3 AE versus other NDT methods (a) AE technique and (b) Sound-wave based NDT Methods ...... 21

3.4 Acoustic Emission measurement chain. Only one sensor shown for simplicity (source: modiﬁed from Kocur,[23]) ...... 22

3.5 A cut-away of a typical AE Sensor ...... 24

3.6 (a) Spectral response from a Glaser/NIST point-contact AE sensor, (b) Photo of an actual unit (from KRN Services, Inc. website (2014)) 25

3.7 (a)Glaser/NIST point-contact sensor, (b) Plastic ﬁxture for the sensor, (c) Mounting the sensor on a concrete beam ...... 25

xi 3.8 KRN AMP-12BB-J Preampliﬁer (a) Front View, (b) Back Panel. (From KRN Services Website) ...... 26

3.9 (a) TraNET Elsys DAQ, (b) TranAX Software Interface. (From Elsys, Inc) ...... 27

3.10 AE parameters for Qualitative Analysis ...... 31

4.1 Illustration of TOA approach using P-wave arrival times on AE signals. Only three AE sensors are shown for simplicity. (Submitted to the Journal of Nondestructive Evaluation on February 26. In review.) ...... 37

4.2 Flowchart illustrating the computational steps involved in the iterative source location algorithm based on Geiger's method. ... 39

4.3 Typical AE signal recorded in the lab shows the P-wave onset time 42

4.4 Automatic P-wave onset time estimation using an AIC-based algorithm (a) High signal to noise ration and (b) Low signal to noise ratio ...... 44

4.5 (a) Glaser/NIST Point contact sensor versus other typical sensors with aperture ...... 46

4.6 Mounting the Glaser/NIST point-contact sensor on a concrete structure ...... 47

4.7 Mounting the Glaser/NIST point-contact sensor on a concrete structure (a) rough surface with voids (b) smooth surface with perfect contact area ...... 48

4.8 Design issue with the Glaser/NIST point-contact sensor ...... 48

4.9 (a) 3D view of the small beam with the sensor network ...... 50

4.10 AE signals recorded by the sensor network (case 1: Panametrics Actuator) ...... 51

4.11 AE signals recorded by the sensor network (case 2: PLBs) ..... 52

4.12 AE signals recorded by the sensor network (large scale beam) ... 53

xii 4.13 Locating using the best 12 sensors ...... 55

4.14 Locating using the best 5 sensors ...... 55

4.15 Plots of and σ1 versus the number of best sensors used (Diﬀerent events ...... 57

5.1 Propagation eﬀects between the AE source and the recording sensors (source: modiﬁed from Kocur,[23]) ...... 60

5.2 Various force types at a point source: (a) Two equal and opposite forces in tension; (b) Two equal and opposite forces as a torque about the z-axis; (c) Two pairs of forces, where tension and compression are of equal magnitude and are perpendicular to one another; (d) Two pairs of forces with torques about the z-axis of equal magnitude and opposite in direction (Adapted from Andersen[7]) ...... 61

5.3 Actual forces of the physical process and their equivalent force models for (a) A pure explosion and (b) A pure shear in the xy plane ... 62

5.4 Illustration of a single couple with a pair of equal and opposite forces of magnitude F along z-axis ...... 63

5.5 Representation of the nine possible couples Mij. The directions of the force and arm of the couple are denoted by the indices i and j respectively (adapted from[76]) ...... 64

5.6 Example of data ﬁle created by MATLAB for input into the MTI Toolbox ...... 71

5.7 Snapshot of the MTI Toolbox interface ...... 73

5.8 Analogy between Seismology and Acoustic Emission Testing .... 74

6.1 Laboratory specimens: (a) UHMW Polyethylene (b) normal-weight concrete ...... 76

6.2 Comparison of radiation patterns and fault plane solutions for the artiﬁcial AE sources[94] ...... 79

6.3 Small scale concrete beam loaded in a four-point bending scenario . 81

6.4 Sketch of the notched beam ...... 81

xiii 6.5 AE source location estimates for notched concrete beam experiment. Errors are shown in form of principal standard deviations of the location estimate. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively [2] ... 82

6.6 Representation of the MTI solution for Event 300 using the new feature in the MTI code: views from all three directions convenient for engineering laboratory studies. Blue colour represents tension (movement towards the source) and red compression (movement away from the source) [2]...... 83

6.7 Radiation pattern for Event 314 viewed from the top (along X-axis) and side (along Y-axis) for a high-angle shearing crack extending upwards from the notch, with downwards sliding on the down-dip side of the fracture (i.e. normal sense of movement). Blue colour represents tension and red compression [2]...... 84

6.8 Fault plane solutions for selected AE events (elevation view). Blue colour represents tension and red compression. The volume of the stereographs is proportional to the seismic moment. The insert shows a photo of the complex fracture plane of the specimen [2]...... 85

6.9 Radiation patterns for (a) isotropic and deviatoric components and (b)DC components only. Blue colour represents tension and red compression. Stereographs are shown in the XZ plane [2]...... 86

6.10 Test setup: ﬂexure beam ...... 88

6.11 Sketch of the ﬂexure beam - Elevation View ...... 89

6.12 Locations of the Glaser/NIST sensors on the ﬂexure beam ..... 90

6.13 AE source location estimates for the ﬂexure beam. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)1st loading cycle and (b) 2nd loading cycle 91

6.14 AE source location estimates for the ﬂexure beam experiment. Errors are shown in form of principal standard deviations of the location estimate. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)1st loading cycle and (b) 2nd loading cycle ...... 93

xiv 6.15 3D view of the AE source location estimates on the ﬂexure beam. Only the portion of the beam between X=-1m and X=1 m is shown 94

6.16 Clustering operation for the ﬂexural beam. Cracks at mid-span due to high moment M0 can be observed aligned with the clusters events. 95

6.17 Radiation patterns for the events in the first cluster of the flexure beam. Case where the absolute inversion technique was used. From top to bottom and from left to right, the stereographs correspond to the events labeled in the first column of Table A.2. The stereographs are shown in the XZ plane...... 96

6.18 Radiation patterns for the events in the first cluster of the flexure beam. Case where the hybrid inversion technique was used. From top to bottom and from left to right, the stereographs correspond to the events labeled in the first column of Table A.2. The stereographs are shown in the XZ plane...... 97

6.19 Radiation patterns for the events in the second cluster of the ﬂexure beam. Case where the absolute inversion technique was used. From top to bottom and from left to right, the stereographs correspond to the events labeled in the ﬁrst column of Table A.3. The stereographs are shown in the XZ plane...... 98

6.20 Radiation patterns for the events in the second cluster of the ﬂexure beam. Case where the hybrid inversion technique was used. From top to bottom and from left to right, the stereographs correspond to the events labeled in the ﬁrst column of Table A.3. The stereographs are shown in the XZ plane...... 99

6.21 Test setup: shear beam ...... 101

6.22 Sketch of the shear beam - elevation view ...... 101

6.23 Locations of the Glaser/NIST sensors on the shear beam ...... 102

6.24 AE source location estimates for the shear beam. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)1st loading cycle and (b) 2nd loading cycle 104

6.25 AE source location estimates for the shear beam. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)3rd loading cycle and (b) 4th loading cycle 105

xv 6.26 AE source location estimates for the shear beam. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)5th loading cycle and (b) 6th loading cycle 106

6.27 AE source location estimates for the shear beam. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)7rd loading cycle and (b) 8th loading cycle 107

6.28 AE source location estimates for the shear beam experiment. Errors are shown in form of principal standard deviations of the location estimate. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)1st loading cycle and (b) 2nd loading cycle ...... 108

6.29 AE source location estimates for the shear beam experiment. Errors are shown in form of principal standard deviations of the location estimate. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)3rd loading cycle and (b) 4th loading cycle ...... 109

6.30 AE source location estimates for the shear beam experiment. Errors are shown in form of principal standard deviations of the location estimate. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)5th loading cycle and (b) 6th loading cycle ...... 110

6.31 AE source location estimates for the shear beam experiment. Errors are shown in form of principal standard deviations of the location estimate. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)7th loading cycle and (b) 8th loading cycle ...... 111

6.32 Clustering operation for the shear beam. Cracks at the weak region where the stirrups spacing is large. Cracks that are due to high shear V can be observed aligned with the clusters ...... 113

6.33 Radiation patterns for the events in the ﬁrst cluster of the shear beam. Case where the absolute inversion technique was used. From top to bottom and from left to right, the stereographs correspond to the events labeled in the ﬁrst column of Table A.4. The stereographs are shown in the XZ plane...... 114

xvi 6.34 Radiation patterns for the events in the ﬁrst cluster of the shear beam. Case where the hybrid inversion technique was used. From top to bottom and from left to right, the stereographs correspond to the events labeled in the ﬁrst column of Table A.4. The stereographs are shown in the XZ plane...... 115

6.35 Radiation patterns for the events in the second cluster of the shear beam. Case where the absolute inversion technique was used. From top to bottom and from left to right, the stereographs correspond to the events labeled in the ﬁrst column of Table A.5. The stereographs are shown in the XZ plane...... 115

6.36 Radiation patterns for the events in the second cluster of the shear beam. Case where the hybrid inversion technique was used. From top to bottom and from left to right, the stereographs correspond to the events labeled in the ﬁrst column of Table A.5. The stereographs are shown in the XZ plane...... 116

6.37 The ﬁrst cluster from each beam was selected (a) First cluster from the ﬂexure beam (b) First cluster from the shear beam ...... 117

6.38 R-ratio variation for the ﬁrst cluster from the ﬂexure beam ..... 118

6.39 R-ratio variation for the ﬁrst cluster from the shear beam ...... 119

6.40 Frequency plots for the R-ratio for the two beams. Flexure Beam (top plot) and Shear beam (bottom plot) ...... 120

6.41 Logarithmic scale plot of the scalar moment M0 of the events in the ﬁrst cluster of the Flexure beam ...... 121

6.42 Logarithmic scale plot of the scalar moment M0 of the events in the ﬁrst cluster of the shear beam...... 121

6.43 Frequency plots of the scalar moment M0 for the two beams. Flexure Beam (top plot) and Shear beam (bottom plot) ...... 122

6.44 Frequency plots of the %ISO for the two beams. Flexure Beam (top plot) and Shear beam (bottom plot) ...... 123

6.45 Frequency plots of the %ISO for the two beams. Flexure Beam (top plot) and Shear beam (bottom plot) ...... 124

xvii ABSTRACT

Over the last few decades there has been sustained interest in learning about fracture processes to achieve a better understanding of how concrete structures behave and what leads to failure. Such understanding would greatly benefit the concrete industry as it would provide efficient engineering solutions to improve the quality, durability, strength, and behavior of concrete structures and answer more challenging questions such as how, where, and when cracks initiate and propagate. The type of cracking also matters. For example, shear-type failure happens suddenly without warning and means for early detection would be useful. Due to the complex nature of concrete, however, monitoring approaches are challenging to apply and are often subject to significant measurement noise. This PhD research investigated the feasibility of employing moment tensor inversion (MTI), a powerful quantitative seismology-based technique, combined with the capabilities of the acoustic emission (AE) technique for the quantitative monitoring of crack initiation and propagation in concrete materials. The goal was to monitor fracture mechanisms in concrete structures in real time. For this reason a hypothesis was put forth that MTI techniques applied to AE data can produce pertinent information about cracks such as location, type, orientation, and intensity, and thus can distinguish flexural from shear and mixed-mode cracks. The motivation behind using MTI techniques is the strong analogy between AE and seismic events, albeit at different scales. To test the hypothesis identified above, a methodology that capitalizes on the strengths of both the AE technique and the MTI technique was proposed and applied according to which AE waveforms recorded from concrete fracture were inverted using a MTI code, called MTI Toolbox, in order to study the sources of fracture and infer their properties. The MTI Toolbox was applied to estimate source mechanisms

xviii from mining-induced seismicity and was fairly extensively applied to mining research problems. It was used in this research because of the great features it offers that make it applicable to performing inversions on AE data recorded by networks consisting of uniaxial sensors. A number of experiments were performed in the laboratory in a civil engineering environment in order to assess and apply the methodology proposed. In all the experiments, high-fidelity Glaser/NIST point-contact sensors, which represent an important aspect of this research, were used to collect AE data. An algorithm based on the Geiger's location method was implemented in MATLAB and used for all the source location problems. First, a preliminary study was conducted that aimed at evaluating the usefulness of the MTI-based methodology in characterizing AE sources. Artificial AE sources with known location, type, and orientation were produced on two different specimens: a UHMW Polyethylene specimen and a normal-weight concrete specimen. The goal was to establish whether these parameters can be estimated from the recorded AE signals using MTI techniques. The results of this preliminary study were satisfactory as it was possible to reproduce the parameters of the predefined externally applied sources. This proved that the methodology proposed had the potential to be applied in the monitoring of real fractures in critical concrete structures. Second, a case study was conducted on a 6 in × 6 in × 21 in concrete beam. A notch was cut at mid-span to serve as a crack initiator and the beam was loaded to failure. The aim of the experiment was to produce tensile fracture AE sources. An analysis of the results of this experiment showed that 20% of the sources located with high accuracy (= 71) out of a total of 262 sources located were dominantly tensile, 7% were dominantly implosive, and the remaining 73% were dominated by shearing. Even though it was anticipated that a pure flexural crack would produce AE events with high positive isotropic (i.e. opening) components, this was not confirmed and it was speculated that this is due to the heterogeneity of concrete. The methodology however showed potential in dis- tinguishing between the different types of cracks. Third, two large-scale experiments were conducted on two different reinforced normal-weight concrete beams of the same

xix dimensions (12 in × 24 in × 16 ft). One beam was designed to fail in flexure and the second one to fail in shear. The aim of these experiments was to evaluate the ability of the methodology to characterize and monitor fracture in large-scale concrete structures. The MTI results obtained from this experiment showed that the cracks produced from the fracture of the flexure beam are dominantly tensile (%81) while the cracks obtained from the fracture of the shear beam were dominated by shearing (%73). These results satisfied our expectations from the methodology and we were able to prove the hypothesis as we were, in fact, able to (1) distinguish between flexure and shear cracks during the fracture of large concrete structures and (2) answer some of the challenging questions regarding the mechanics of concrete materials.

xx Chapter 1

INTRODUCTION

1.1 Introduction Over the last few decades, there has been sustained interest in understanding failure mechanisms in concrete structures to achieve full insight into ongoing fracture processes. Such understanding would greatly benefit the concrete industry as a whole. The first attempt to study the cracking process in concrete materials dates back to 1961, when Kaplan[1] first applied the theory of Linear Elastic Fracture Mechanics (LEFM) to calculate the fracture parameter KIC in notched three-point and four-point bending of concrete beams. Ever since, there has been an increasing interest in the cracking and fracture mechanisms of concrete materials. A significant amount of work, both theoretical and experimental, has been performed resulting in many scientific contributions that have considerably enhanced the understanding of fracture processes in concrete. Shah[3] investigated the applicability of Griffith theory to concrete specimens with notches of varying lengths, tested in flexure and tension. Higgins and Bailey[4] loaded notched concrete specimens to failure in both flexure and tension and estimated the critical stress intensity factor using LEFM applied to beam geometry. Several other attempts to apply LEFM to concrete have been made. It was subsequently deduced that the theory of LEFM could not predict the fracture resistance of concrete; nonlinear fracture theory, that takes into account the influence of the fracture process zone in concrete, was required. As a result, a number of nonlinear fracture models were developed. For example, Hillerborg et al.[5] proposed a nonlinear finite element based fracture mechanics model to estimate the critical fracture energy. Zdenk et al.[6] developed the crack band model and showed that a fracture in the material

1 could be characterized by only three properties (fracture energy, strength and width of crack band front). Several other nonlinear fracture models for the characterization of concrete fracture mechanics were also proposed.

Despite the extensive research carried out, the application of fracture mechanics to concrete still presents many challenges. For instance, the principles of fracture mechanics are not currently applied in the design of concrete structures because none of the existing code provisions are based on these principles. To address these challenges and gain insight into the ongoing cracking process, the fracture mechanism in real time needs to be fully understood. For this reason, monitoring techniques and methodolo- gies have been proposed as alternatives to the classic theory of fracture mechanics in order to understand the complicated fracture process in concrete materials. Possibly the most important and widely used techniques to study and monitor the formation and growth of cracks in simple and complex structures are AE parameter-based methods. These methods are, however, purely qualitative and cannot provide complete understanding of fracture mechanics in concrete materials. Further developed AE techniques that can provide a more complete understanding of concrete mechanics are needed. As a result, dedicated scientific research programs have been launched to provide the scientific and industrial communities with well-established techniques that can give satisfactory analyses and description of fracture processes in concrete materials. Fortunately, committed researchers have adapted several signal-based AE techniques from seismology and applied them successfully in concrete engineering. These signal- based methods, also known as quantitative methods, are more sophisticated than the traditional parameter-based methods. They provide good tools to answer more challenging questions such as how, where and when cracks initiate and how they propagate. These methods rely on different procedures to analyze the recorded AE waveforms and extract informative parameters to constrain the mechanics of sources of cracks (type, location, orientation, intensity, etc.).

2 1.1.1 Problem Description Concrete, probably the most widely used construction material worldwide, has been used in a myriad of applications thanks to its versatility and its enabling properties (strength, durability, availability, etc.). Concrete, however, is a brittle material that is prone to ﬁssures and cracks due to mechanical, chemical and physical deterioration processes. The understanding of the cracking mechanism in concrete has presented an ongoing challenge and has not, to date, reached a satisfactory level. This lack of insight can be explained by the heterogeneous and complex nature of cementitious materials. As a result, there has been sustained interest, during the last few decades, in understanding failure mechanisms in concrete structures to achieve full insight into ongoing fracture processes

1.1.2 Principal Objective The principal objective of this study is to develop and apply a methodology that combines techniques applied in quantitative seismological analyses with the strong and enabling capabilities of the Acoustic Emission (AE) technique in order to gain full insight into ongoing fracture processes in concrete structures. The proposed methodology exploits the strengths of the technique of Moment Tensor Inversion (MTI), a key analysis tool in seismology and mining seismicity, in order to develop a full understanding of the physics of the source of fracture and infer its properties and characteristics. If the proposed methodology proves to be successful and result in better understanding of the fracturing mechanisms in concrete mechanics, a useful tool will have been added to the existing applied fracture mechanics methods. The methodology will be highly useful in studies of fracture source processes and will enhance the interpretations of the modes of failure in concrete materials, ultimately leading to improved understanding of failure mechanisms. Such understanding would greatly beneﬁt the concrete industry as a whole and help overcoming many challenges complex cementitious materials pose on a daily basis.

3 1.1.3 Methodology To achieve the objective of this research, a set of experiments was performed in the laboratory at the University of Delaware. Concrete specimens of both small and large scales were driven to failure under different loading scenarios. In each experiment, AE activity was generated, recorded in form of AE waveforms using networks of AE uniaxial sensors distributed on the surface of the test specimens. The recorded data was stored in a laboratory computer for later postprocessing. A moment tensor inversion (MTI) code (MTI Toolbox) originally developed by Andersen[7] to compute source mechanisms from mining induced seismicity data was used in the laboratory in a civil engineering research environment to perform moment inversions on the recorded data. In this research, the MTI Toolbox code was used to perform absolute, relative and hybrid inversions on AE waveforms collected from the different set of experiments carried on the concrete specimens. The MTI Toolbox uses input data extracted from the recorded AE waveforms to compute a number of source parameters and plot the radiation patterns and corresponding fault-plane solutions. The main purposes behind using this code are (1) the strong resemblance that concrete mechanics bear to seismology and mining seismicity albeit at different scales and (2) the great features the code offers that make it applicable to performing inversions on acoustic emission data recorded by networks of uniaxial sensors.

1.1.4 Structure of Dissertation In Chapter 1, a general introduction of the context of this research is outlined. The problem description is highlighted and an overview of the principal objective of this study is provided. The general methodology of the research followed and the thesis structure are also outlined.

Chapter 2 reviews the concepts and fundamentals of the elastic wave propagation in solids and structures. The differential governing equations of motion are provided for infinite homogeneous continuum as well as the velocities of the different

4 wave phases. Some illustrative and presentative plots are also provided to establish the link between the different velocities and the elastic constants of the material. Reflec- tion and refraction of p- and s-waves at interface between two media are also defined, sketched and discussed.

Chapter 3 reviews the concepts and fundamentals of the Acoustic Emission technique. Since the technique is of particular interest in this study, an in-depth description of its principles and applications is presented. The most relevant aspects of the technique are covered in this section. A brief comparison between qualitative and quantitative acoustic emission methods is also provided in order to highlight their main advantages and limitations.

An important step in the proposed methodology is the estimation of the spatial and temporal coordinates of the source of AE before applying the moment tensor inversions. Chapter 4 discusses the implementation of traditional time of arrival methods (TOA) for the estimation of acoustic emission source locations. One approach known as the Geiger's method is implemented and discussed in depth. Source location results from laboratory experiments performed on small and large scale concrete specimens are presented and discussed. High-ﬁdelity acoustic emission sensors known as Glaser/NIST point-contact sensors were used in the experiments in order to record the AE activity. These sensors have been developed recently and represent a new aspect of this research since they are applied for the ﬁrst time for the AE monitoring of concrete structures. A detailed description of these sensors is also provided.

Chapter 5 presents an in-depth description of the moment tensor inversion technique. The concepts of the technique are highlighted and explained in details. The diﬀerences between the moment tensor inversion methods available in literature are also provided and discussed. These methods are divided into absolute and relative methods, based on the way the elastodynamic Green's functions, which describe the

5 propagation eﬀects between source and receiver are computed. A considerable amount of attention is given to the hybrid moment tensor inversion. This technique is described in more detail because it capitalizes on the strengths of both the absolute and relative MTI methods. A detailed description of the MTI toolbox and its enabling features is also given.

Chapter 6 presents the results of the experimental investigations carried out in the laboratory at the University of Delaware in order to apply and study the proposed methodology. Laboratory experiments carried out on small and large scale concrete specimens are presented and described. The results of the diﬀerent inversions performed on the AE waveforms using the MTI toolbox are also presented and discussed.

Chapter 7 provides a synopsis of the study. General conclusions from the application of the proposed methodology are drawn. Advantages and limitations of the methodology are also outlined and recommendations on future possible improvements are provided.

6 Chapter 2

ELASTIC WAVE PROPAGATION: THEORY AND FUNDAMENTALS

2.1 Introduction Waves are disturbances (perturbations) that propagate through or on the surface of a medium (solid, liquid and gas) at variable speeds functions of the elastic and internal properties of the medium. They represent ideal means of transportation of the information which made them at the center of preoccupation of many researchers. Waves are classified into different categories based on their nature, their origins and their modes of propagation in elastic media. We distinguish: elastic solid waves, elec- tromagnetic waves, lamb waves and plate waves[63]. Acoustic emission uses low ranges of frequency compared to traditional ultrasonic methods. Therefore the theory of elastic waves in solids and structures is of primary interest in acoustic emission testing. Other types of waves are still of considerable interest since a large fraction of structures are made from steel (pressure vessels, pipes, tanks, etc) and lamb waves would be good candidates for explaining different problems observed when conducting acoustic emission testing (velocity variations, dispersion, etc.). Substantial improvements in the accuracy of AE source location techniques can be achieved through good understanding of Lamb wave propagation. In this study, elastic body waves are of particular interest.

2.2 Elastic Wave Propagation in Solids and Structures 2.2.1 Theory Elastic waves, also known as stress waves, are waves that result from the sudden release of stress within a solid body when it undergoes internal changes. These waves propagate though the solid body and on its surface and represent a mean of transport

7 of the energy released. Elastic waves are classiﬁed into body waves (longitudinal and transversal) and surface waves (Rayleigh and Love).

2.2.1.1 Longitudinal waves These waves represent a common type of elastic stress waves that can propagate through solids, liquids and gases. They are called longitudinal because they induce vibration of particles in the direction of propagation (Figure 2.1.a). They are also known as primary (fastest to reach the sensors), compression, dilatation or pressure waves (result from an alternation of compressions and rarefactions). In this thesis the notation P-waves will be used to refer to longitudinal waves.

2.2.1.2 Shear waves These waves represent another common type of elastic stress waves. A shear wave, or also known as distortion wave, occurs in an elastic medium when it is subjected to a periodic shear which results in alternating transverse motion of particles (displacement of particles is perpendicular to the direction of propagation of the wave) (Figure 2.1.b). In this thesis the notation s-waves will be used to refer to shear waves.

2.2.1.3 Rayleigh waves Rayleigh (R-) waves are a common type of surface wave. The particle motion is elliptical retrograde near the surface, and elliptical prograde further from the surface. The amplitude decreases with distance from the free surface. They are also dispersive i.e. the frequency changes with propagation. Rayleigh waves are typically large in amplitude compared to the p-wave or s-wave from the same source and therefore easier to detect but their travel path can be complicated. The existence of these waves was predicted by John William Strutt (Lord Rayleigh) in 1885[93].

8 Figure 2.1: Schematic of the propagation of elastic body waves. (a) P-waves, (b) S-waves and (c) R-waves

2.2.1.4 Governing equations of elastic waves The governing equations of motions describe the propagation of elastic body waves in diﬀerent material media. For the case of a homogeneous isotropic elastic media, the governing equations are given[63] by:

(λ + µ) uj,ji + µui,jj + fi = ρu¨i (2.1)

If we rewrite Equation 2.1 in terms of rectangular scalar notation we obtain the following equations:

∂2u ∂2u ∂2u ∂2u ∂2u ∂2u ∂2u (λ + µ) 1 + 2 + 3 + µ 1 + 1 + 1 + f = ρ 1 (2.2) ∂x2 ∂x∂y ∂x∂z ∂x2 ∂y2 ∂z2 x ∂t2 ∂2u ∂2u ∂2u ∂2u ∂2u ∂2u ∂2u (λ + µ) 1 + 2 + 3 + µ 2 + 2 + 2 + f = ρ 2 (2.3) ∂x∂y ∂y2 ∂y∂z ∂x2 ∂y2 ∂z2 y ∂t2 ∂2u ∂2u ∂2u ∂2u ∂2u ∂2u ∂2u (λ + µ) 1 + 2 + 3 + µ 3 + 3 + 3 + f = ρ 3 (2.4) ∂x∂z ∂y∂z ∂z2 ∂x2 ∂y2 ∂z2 z ∂t2

9 Where u1, u2, and u3 are the particle displacements in the x, y, and z direction; ρ the mass density per unit volume; fx, fy and fz are the body forces. λ and µ are the Lame's constants and are expressed in terms of the Young's modulus E and the Poisson's ratio ν as follows: νE E Where λ = and µ = (2.5) (1 − 2ν) (1 + ν) 2 (1 + ν)

In the absence of body forces (fx = fy = fz = 0), the propagation velocity cP of the P-wave for a three-dimensional free solid medium, is given by; s λ + 2µ c = (2.6) P ρ

The propagation velocity cS is given by s λ c = (2.7) S ρ

The ratio κ (dynamic material constant) of these two velocities is given by: s c λ + 2µ r2 (1 − ν) κ = P = = (2.8) cS µ 1 − 2ν

The exact relationship between P-wave, S-wave, and R-wave velocity is given by:

2 s 2 s 2 cR cR cR 2 = 2 − 4 1 − 2 1 − 2 (2.9) cS cS cP An approximate expression also called Bergmann Formula for the Rayleigh wave velocity is given in Graﬀ, 1991[63] as:

0.87 + 1.12ν c = c (2.10) R S 1 + ν

From Equations 2.6, 2.7 and 2.10 we also ﬁnd that the following condition is always true:

cP > cS > cR (2.11)

10 Compared to other types a waves (e.g. Lamb waves), the elastic waves are not dispersive i.e. the velocities cP , cS and cR depend only on the material properties E, ν, and ρ but not on the frequency. Figure 2.2 shows a plot of the 3 velocities for diﬀerent values of the Poisson's ratio ν.

Figure 2.2: Normalized wave phase velocities vs. Poisson's Ratio

2.2.2 Interaction of elastic waves with free boundaries Incident waves propagating from inside a medium are subjected to reflection and refraction at the boundaries between the propagating medium and any dissimilar neighboring medium. Consequently, a whole packet of waves is formed consisting of incident, reflected and refracted P- and S-waves. For example, if a P-wave incoming with an initial amplitude (A0) incident on a boundary at an incidence angle θ0 (Fig- ure 2.3.a), a portion of the incident energy is reflected with an amplitude (A1) and an angle of reflection θ1. The remainder penetrates the neighboring medium with amplitude (A2) and an angle of reflection θ2. Similarly an incoming S-wave is reflected and refracted off the boundary (Figure 2.3.b).

11 The reﬂection and refraction of the waves of oﬀ the boundary between two dissimilar media depend only on the angle of incidence θ0 and Poisson's ratio ν.

The angle of refraction, θ2, is function of the angle of incidence, θ0, and the expression that relates these angles to the ratio of the the corresponding phase velocities c1 and c2 of the two media is given by Snell‘s law as follows: sinθ c 0 = 1 (2.12) sinθ2 c2

Figure 2.3: Reﬂection and refraction of elastic waves on boundaries (a) P-wave and (b) S-wave (source: Kocur,[23])

Depending on the incidence angle, however, more waves can be generated. In fact, the interaction with the boundaries couples the P- and S-waves. i.e. when an incident P-wave strikes the boundary between two media, an S-wave is generated and reflected inside the propagating medium with a reflection angle different than the reflection angle

θ1 and an R-wave is generated that propagates on the surface. So an incident P-wave is not only reﬂected and refracted as a p-wave but also gives coupling and giving birth to other phases due to coupling at the interface. (Figure 2.4.a). Similarly for S-waves

12 (Figure 2.4.b). Note that for the case of an incident S-wave the angle of reﬂection θ1

Figure 2.4: Coupling of P- and S-waves at the boundaries between diﬀerent media (source: Kocur,[23])

will always be smaller than the angle of refraction θ2. Since cP > cS and sin(θ1) < 1 the so-called critical angle is: −1 cS θcr = sin (2.13) cP

For the estimation of AE source locations and the application of moment tensor inversions, P-waves are of interest. AE sensors record the surface motion perpendicular to the sensor surface. Therefore, every AE source has a specific distance R and incident angle θ with respect to the sensor. The relationship between the particle displacement up,i due to the incident P-wave, and the resulting surface motion up,m perpendicular to the surface, need therefore to be known. Koppel[64] derived the following relationship in terms of the reflection coefficient Rp.

2 2 2 up,i 2κ cosθ (κ − 2sin θ) Rp = = 2 √ √ (2.14) up,m (κ2 − 2sin2θ) + 4sin2θ 1 − sin2θ κ2 − sin2θ

This relationship was plotted for diﬀerent Poisson's ratios as shown in Figure 2.5. An illustrating schematic of this relationship is shown in Figure 2.6.

13 Figure 2.5: Reflection coefficients for different Poisson's Ratios

Figure 2.6: Relationship between incident and measured P-wave (source: Kocur,[23])

14 Chapter 3

ACOUSTIC EMISSION TECHNIQUE: HISTORY AND FUNDAMENTALS

3.1 Introduction Over the past 20 years, several techniques of nondestructive testing (NDT) have gained large interest throughout the research and industrial communities thanks to their potentials in fast and efficient assessment of materials and structures. These methods offer a lot of advantages that have long been recognized in different fields and sectors (government, private and commercial). They grant the ability to evaluate material properties, characterize structural conditions and detect flaws and defects present in simple and complex structures (metallic, concrete, composite, etc.) without altering the material or disturbing the structure being inspected. In other words, when applied for the inspection of objects, NDT methods do not not impair the usefulness of these objects neither they interfere with their final use. NDT technologies also offer the ability to detect a wide variety of flaws, defects and geometrical discontinuities present in different structures and structural elements. Possible flaws range from small blemishes in the microscopic scale to more visible flaws at larger scales. Such detection capabilities have tremendously helped effectively to reveal on time all the appropriate safety concerns and considerably enhance structural safety and reduce maintenance costs[8].

The principal NDT methods can be classiﬁed into two main categories: electro- magnetic radiation-based methods (Eddy current, magnetic methods, etc) and sound wave-based methods (ultrasonics, etc)[9]. Acoustic Emission technique, an NDT method of particular interest in this study, falls into the second category. A growing

15 interest in this technique and its potential for the use in the nondestructive evaluation of materials and structures has been shown since Joseph Kieser[10] published his pioneering PhD work in 1950. This interest, both from academic and industrial communities, has gained the technique a wide acceptance in the world and a growing momentum in use in myriad of applications. Indeed, AE is an interesting NDT technique because of the wealth of information it oﬀers about sources of energy release that result from various types of damage mechanisms such as fatigue cracks, ﬁber breakage, micro-cracks, etc. As a matter of fact, AE activity accompanies almost all processes when a solid medium undergoes an internal stress change (mechanical, thermal, physical, etc.) which result in a sudden release of stress in the material medium. Acoustic emissions occurs in micro-scale due to the movement of small particles at the microscopic level, as well as in macro-scale due to the failure of structural components (e.g., the failure of assemblies, parts, etc.)[9]. By mounting a set of distributed sensors on the surface of such structural components, one can record AE waveforms that provide valuable information about the details of sources of energy release (position, fracture- type, magnitude, etc.).

Many AE methods have been developed that exploit the information these waveforms provide in order to study AE sources. Most of these methods are purely qualitative parameter-based and do not provide enough feedback about the source of AE. However, they have been applied with diﬀerent degrees of success in many AE-related problems. Other methods, developed by researchers and engineers are the quantitative signal-based methods. Most of these methods are adapted from seismology and mining seismicity and are still under investigation for possible use with diﬀerent materials in much smaller scale than seismology. These methods are more developed and give enough understanding of the AE source mechanism. Each one of them has it own weight, potential and capabilities in the area of nondestructive testing. This put in evidence the importance of the acoustic emission technique as a highly valuable NDT tool. In this chapter, the technique of acoustic emission is described in details and its

16 concepts and fundamentals are presented and explained.

3.1.1 Definition Like many other NDT methods, the AE technique has a basic concept, a distinctive terminology and different characteristic instrumentation, parameters and fundamentals. The general concept of the AE states that a structure, a component or a piece of machinery subjected to an external stimulus (change in load, temperature, pressure, etc) will undergo internal changes in form of stress redistributions that result in sudden release of energy within the material medium. The energy released radiates outward in form of elastic transient waves that propagate through the medium toward the surface of the specimen being tested. By mounting a network of uniaxial sensors on the surface of this specimen, one can listen to audible noise, record acoustic sounds in form of electric signals and perform different types of analyses in order to evaluate the material condition and detect possible flaws and defects. The American Society of Testing Materials (ASTM)[11] defines acoustic emission as ”The class of phenomena whereby transient elastic waves are generated by the rapid release of energy from local- ized sources within a material, or the transient elastic waves so generated”

Figure 3.1 shows a conceptual illustration of a typical acoustic emission setup where a simply supported concrete beam is subjected to a 4-point bending conﬁguration. If an external load is applied to the beam, crack initiation will result in a sudden release of energy that propagates through the specimen to reach the acoustic emission sensors mounted on the surface. Only three sensors are shown here for simplicity.

3.1.2 Historical Review It is commonly known that, only after the leading work of professor Kaiser[10] that modern AE was brought to practice. Historically however, the technique predates the technological era and is as old as thousands of years before recorded history. In fact, it has been known since primeval time that a cracking or breaking material emits sounds

17 Figure 3.1: Conceptual illustration of a typical AE setup

that can be perceived by the human ear (i.e. a breaking branch of a tree, cracking propagation in ice, etc.). These audible sounds often called sounds of the danger, in non-professional terminology, were perceived by primitive man as alert signals for imminent failure[12] (Figure 3.2). Therefore, were effectively used as efficient warning sounds but without any further investigations. Probably the earliest investigation on audible sounds (known today as acoustic emissions) dates back to the Neolithic Period (over 10000 years) when pottery makers used to listen to cracking noise emitted by fired clay vessels that are cooled off too fast and learned that these vessels are defective and will fail when put for their intended use[13]. In metals, the earliest documented observation of acoustic emission dates back to the eighth century when the prominent Arabian polymath Jabir Ibn Hayyan described the crackling sound emitted by pure tin resulting from the mechanical twinning of the metal[13]. By the beginning of the 20th century, more studies have been conducted on the characterization of audible sounds emitted by deformation process and phase transformations in materials and crystals. Czochralski[14] was the first to describe the relationship between tin cry and acoustic emission. Joffe[15], studied the noise emitted from Salt and Zinc crystals under process

18 deformations. Forster and Scheil[16] were able to measure small voltage and resistance variations due to sudden strain change caused by martensite transformations. All these studies and investigations have played a key role in the discovery of modern acoustic emission. The real systematic investigation, however, started after the World War II. In 1948, Mason[17] used the piezoelectric effect in quartz to measure shifts of 0.1nm in the surface of metals. Millard[18] was able to detect twinning on single crystal wires of cadmium using a rochelle salt transducer. Kaiser[10], who is broadly known as the father and founder of modern acoustic emission, performed successful AE measurements during tensile tests on some engineering materials. He culminated his work in a PhD dissertation and published his findings in 1953. His work represents the most important milestone in the history of AE. The most significant result from his investigations was the discovery of the irreversibility phenomenon known as the Kaiser Effect. This effect states that sounds are emitted only when a previous stress level is exceeded. i.e. if a material undergoes repetitive loading scenarios, there is a total absence of acoustic emission at loads not exceeding the previous maximum load level. Only under unprecedented stresses that acoustic emission is emitted. This was thought to work for all materials until Fowler[19] proved in 1989 that the irreversibility phenomenon is not always true and that for some composite materials AE starts at loads lower than the previous maximum load level. The Kaiser Effect, however, is still thought of as one of the major discoveries in the AE measurements field. Soon, after Kaiser published his pioneering work, many researchers showed a great interest and performed extensive research work. Schofield[20] investigated the application of AE in the field of materials engineering and the source of AE. Tatro[21] performed several laboratory experiments and suggested the use of AE as a method to study the behavior of metals. In 1961, the Aerospace industry conducted the first AE test in the United States in order to verify the integrity of the Polaris rocket motor for the U.S Navy. Dunegan[22] suggested the use of AE to assess the integrity of high pressure vessels and founded in 1969 the first company that manufactures AE equipment. Today, owing to the fast advancement in semiconductors technology, the use of AE as an efficient

19 nondestructive testing tool has dramatically increased worldwide.

Figure 3.2: Acoustic Emission before and after 1950

3.1.3 Acoustic Emission versus other NDT techniques Most AE testings involve causing fracture in materials by subjecting structures or structural components to external loads high enough to cause acoustic events. Frac- ture seems then a necessary step in a typical AE test in order to record AE activity. Following the statement, one would, as logical as it would normally be, consider acoustic emission as a destructive or at most, a quasi-nondestructive testing method. The technique is however considered nondestructive and this is generally well accepted in the NDT society. This categorization of AE within the class of NDT techniques does certainly make sense. In fact, AE is used to detect very small-scale defects in structures long before failure. It is also used to monitor structures and detect defect growth in real-time in order to provide warning of impending failure. The AE testing does not in any how alter the behaviour of the material, nor it causes any damage to the structure being tested. Thus, it is obvious to consider the acoustic emission technique as completely nondestructive. It represents, in fact, a good nondestructive testing technique that has a great potential to help taking well-informed decisions about maintenance

20 and repair of structures. Also, AE bears some resemblance to most other NDT techniques, especially in the way signals are recorded during a test. This resemblance is also one of the main reasons why AE is classiﬁed as a nondestructive technique.

Despite the resemblance though, AE is considered unique when compared to most other NDT techniques in that it has some key differences. The first difference pertains to the testing procedure. Unlike other techniques (ultrasonics, etc.) which are applied after or before the damage occurs in the structure, AE is usually applied while the defect propagates in the structure in its full operational mode. This difference is, in fact, a great advantage that the AE technique presents because it a great way to track changes in the structure in real time and reveal all the issues as early as possible. The second difference pertains to the source of energy. In AE testing, the energy released results from a sudden internal change that the material medium undergoes due to external forces. So the source of AE lies within the structure itself and no external sources are applied. In most other NDT techniques, however the source is supplied by an external device and is dictated by the test procedure.

Figure 3.3: AE versus other NDT methods (a) AE technique and (b) Sound-wave based NDT Methods

21 3.2 Acoustic Emission Measurement and Instrumentation 3.2.1 Measurement Chain The measurement process is a fundamental step in every acoustic emission testing. It is performed according to certain standards (ASTM standards, ASME and other codes) in order to record data that contain important information about the sources of emissions. Depending on the objective of the experiment, the data recorded can be in form of complete waveforms or in form of single or multiple parameters such as amplitude, energy, duration in which a speciﬁc event occurs during testing, etc. To record the desired data, elements such as a data acquisition system, a preampliﬁer and a single or a network of recording sensors are required to form a complete measurement chain. Each of these elements plays an important role in the recording process. Figure 3.4 shows a typical measurement chain used in acoustic emission testing.

Figure 3.4: Acoustic Emission measurement chain. Only one sensor shown for simplicity (source: modiﬁed from Kocur,[23])

As described earlier, when a specimen undergoes internal changes (e.g. due to crack formation), energy is released in form of stress waves that propagate from the source where cracking occurred to the surface of the specimen. When the travelling waves reach the surface, they cause the material particles to vibrate which result in

22 small surface displacements. The piezoelectric sensors mounted on the surface con- vert these small mechanical displacements into electrical analog signals that are pre- amplified and then transferred to the data acquisition system. The acquired electric signals are then conditioned and subsequently digitized inside the DAQ and afterwards stored in a computer station. During this journey the signals take to travel from the recording sensors to the computer, many factors that have varying effects on the quality and amount of data collected, come into play. Most of the factors are controlled by the testing environment, the complexity of the propagating medium, the exper- tise of the experimenter and the quality of instrumentation used in the measurement chain. For instance, the selection of the appropriate instrumentation is of great importance in acoustic emission testing because each component of the measurement chain exhibits different sensitivities in different testing setups and applications which may considerably affect the quality of the data.

3.2.1.1 AE Sensors The use of recording sensors is indispensable in acoustic emission applications. These components represent the first link between the host structure being tested and the other components of the recording system. They are frequently used and can be found in the market in different forms and shapes with different properties and prices. Most of the commercially available sensors are made of piezoelectric materials, notably crystals and certain ceramics, that are commonly known for their great inherited ability of electromechanical coupling: a property that allow the conversion of mechanical stimuli to electrical energy and inversely the conversion of electrical stimuli to a mechanical output[8]. Most sensors incorporate a piezoelectric crystal, usually made of Lead-Zirconate Titanate, that converts the small mechanical displacements to electric signals (Figure 3.5) Different AE sensors, available on the market, are designed with different mechanical and physical properties . Some sensors are designed to be more or less sensitive to external stimuli such as ambient noise, cabling, etc. Some others are mechanically

23 Figure 3.5: A cut-away of a typical AE Sensor

designed to resist harsh environments such as high temperature and withstand some abuse such as misuse, dropping, etc. A sensor that performs well in one application will not always produce good results in a different application. Another important factor that comes into play in the design of a sensor is the bandwidth. The bandwidth of a sensor is the range of frequencies in which the sensor performs. Every sensor has a bandwidth and a center frequency that depend on the backing material[23], i.e., a sensor with highly damping backing material will have a broad range of frequencies, and a sensor with less damping material will operate in a narrower range of frequencies. For accuracy purposes, all the experiments listed in this current work were performed using high-fidelity Glaser/NIST point-contact sensors (Figure 3.6.b) that show a flat response for frequencies between 20 kHz and 1 MHz (Figure 3.6.a). One important aspect of the research conducted in this present work is the use of these high-fidelity point-contact sensors. A distinctive feature of the design of a Glaser/NIST point-contact is the quasi-point contact area which minimizes aperture effects that other AE sensors have[2]. This was made possible by using a conical piezoelectric crystal. These novel sensors have recently been absolutely calibrated[24]. In all the experiments, the sensors were mounted on the surface of the host structure using threaded plastic fixture (Figure 3.7) to ensure they remain fixed during testing.

24 Figure 3.6: (a) Spectral response from a Glaser/NIST point-contact AE sensor, (b) Photo of an actual unit (from KRN Services, Inc. website (2014))

Figure 3.7: (a)Glaser/NIST point-contact sensor, (b) Plastic ﬁxture for the sensor, (c) Mounting the sensor on a concrete beam

3.2.1.2 Preamplifiers The mechanical to electrical conversion of the small surface displacements produce relatively weak signals with low voltage amplitudes. AE sensors, usually, do not come with built-in preamplifiers, therefore external pre-amplifiers are required to amplify the recorded voltage signals in order to process them further. The voltage amplification, known as Gain (G), is measured in Decibel (dB) and is obtained by applying the logarithm function to the ratio of the output voltage vout(t) desired for the amplification to the input voltage measured using the sensor vin(t) . Equation 3.1

25 shows the formula used to compute the Gain (G).

v (t) G = 20log out (3.1) vin(t)

The preamplifier used in this study was specially designed to interface the point- contact sensors to the Data Acquisition System for signal capture and analysis. BNC connectors on the rear panel of the preamplifier are used to connect it to the sensors. Both, the sensors and the preamplifier are manufactured by KRN Services, Inc. Figure 3.8 shows a 12-channels preamplifier used in this study.

Figure 3.8: KRN AMP-12BB-J Preampliﬁer (a) Front View, (b) Back Panel. (From KRN Services Website)

The characteristics of the KRN AMP-12BB-J preamp are summarized in Table 3.1

3.2.1.3 Data Acquisition System: DAQ Once the signals are amplified, they are transferred to the Data Acquisition System where they are conditioned, filtered (if required) and then digitized. The digitization process consists of converting the analog signals recorded by the sensors and amplified by the preamp into digital signals that can be easily stored in the memory of a computer’s mainboard. Digitization is very important in acoustic emission testing because of the huge amount of data often recorded (thousands of signals) in a very short time (few seconds). With digital acquisition, fast and efficient collection and

26 Table 3.1: Characteristics of the KRN AMP-12BB-J Preampliﬁer

Electric Properties Values Bandwidth (3dB) 15.4 kHz to 1.8 MHz Bandwidth (3dB) 15.4 kHz to 1.8 MHz Input Noise less than 10mV Input Resistance 453 ohm Input Capacitance DC isolation (10uF 50v) Max Output Voltage 24V Output Impedance 50 ohm Input power 24-28 VDC storage of large amounts of data (in gigabytes) is possible in a very limited time. The data stored in digital format can be easily processed and analysed at any time with no further preparation.

Figure 3.9: (a) TraNET Elsys DAQ, (b) TranAX Software Interface. (From Elsys, Inc)

In this study, we used a high-precision 16-channel Elsys transient recorder designed and produced by Elsys Instruments, LLC (Figure 3.9.a). This Data Acquisition System can operate with up to 128 ms acquisition memory per channel with all the channels recording at the same time. It comes with a user-friendly data acquisition software (Figure 3.9.b) that presents a lot of features and oﬀers a lot of ease in data

27 collection and processing. This product is commercially available and comes under diﬀerent conﬁgurations ( from 4 up to 64 channels).

Table 3.2: Summary of the measurement chain elements

Element Key Characteristics - Point-contact sensor - Conical piezocrystal with built-in JFET Sensors, KRN Services, Inc. - High-fidelity broad-band response - High sensitivity - Wide-band amplification (up to 2MHz) Pre-amplifiers, KRN Services, Inc. - Input noise less than 10 mV - Output voltage up to 22V - 16 channels with 14-bit @ 40 MHz - Up to 128 MS acquisition DAQ, Elsys Instruments, LLC memory per channel - Flexible parallel triggering mode - LAN Ethernet connection - Windows 7 Enterprise - Intel CoreTM i7 CPU 2.93 GHz Personal Computer, Dell Corp. Processor - 8 GB RAM

Table 3.2 summarizes the components of the measurement chain used in all the experiments in this study.

3.2.1.4 Storage and Processing of AE Data Data processing in acoustic emission testing refers to the manipulation of the digitized signals stored in the computer in order to produce meaningful information.

28 Since waveforms represent ideal means of transportation of the information, the analysis of resulting AE signals produces a wealth of information that is very helpful in the interpretation of the different sources of emissions. Today, owing to the technological development in microprocessors and computerized algorithms, it is possible to perform different operations on AE signals such as filtering using digital filters in order to eliminate contaminating signals, converting from the time domain to the frequency domain in order to extract peak frequencies and so on. Several approaches developed for the analysis of AE signals are now available and can be efficiently used to extract different types of parameters from the AE signals.

3.2.2 Acoustic Emission Analysis 3.2.2.1 AE Terminology Table 3.3 summarizes the deﬁnitions, according to the ASTM E1316-05, of some of the most terms used in acoustic emission testing. In Acoustic Emission testing, the acquired AE signals form the basis for any further analysis. Depending on the objective of the testing, two diﬀerent types of analysis can be performed on these signals: qualitative parameter-based analysis and quantitative signal-based analysis.

3.2.2.2 Qualitative Parameter-based Analysis In qualitative analysis, only few characteristic parameters (see Figure 3.10) are extracted from the AE signals and stored for later use. The processing and storage of these parameters is instantaneous and can be performed in real time without the need for large amount of storage space. The main objective of this type of analysis is to produce meaningful information regarding the occurrence in time of AE activity in a giving structure. This can be done by tracking the variation in time of certain key parameters without paying attention to other complex details regarding the AE emissions. Details such how, where and when events occur are challenging and can only be solved using quantitative methods. The

29 Table 3.3: Acoustic Emission Standard Terminology ASTM E1316-05

Term: Definition AE event: Single dynamic process releasing elastic energy AE Source: Local process producing AE event AE Activity: Presence of acoustic emission during a test AE Signal Duration: The time between AE signal start and AE signal end Hit: The detection and measurement of an AE signal on a channel AE energy: The total elastic energy released by an emission event Rise Time: The time between AE signal start and the peak amplitude of that AE signal Count: The number of times the acoustic emission signal exceeds a preset threshold Dead Time: Any interval during data acquisition when the instrument or system is unable to accept new data for any reason Threshold: A voltage level set on by the experimenter so that signals with amplitudes larger than this level are recognized. qualitative analysis also does not take into account neither the influence of the propagating medium on the behavior of the emissions during their journey from the sources where they occurred to the sensors, nor the influence of the different components of the measurement chain on the signals that result from these emissions. Note however that the AE parameters extracted during this type of analysis strongly depend on such influences. For example, the geometry of the specimen, the radiation pattern of the source, the Green's functions of the medium, the location of the sensor relative to the source[25] and the sensor sensitivity[9] are all factors that affect the amplitude of the AE signal. Luckily, these factors are not taken into consideration in qualitative analysis which makes it easier and faster. The only important factor to take into account, however, is the presence of noise in the signals. This factor can be taken care of by

30 Figure 3.10: AE parameters for Qualitative Analysis

setting a well-deﬁned threshold in order to produce signals with high signal to noise (S/N) which allows more eﬃcient extraction of the AE parameters.

3.2.2.3 Quantitative signal-based Analysis Quantitative analysis is far more complex and sophisticated than the traditional qualitative analysis because it is based on the study of the whole waveform and not only some of its key parameters. This type of analysis requires more computational time and eﬀort because of the huge amount of data gathered since waveforms are fully stored. Quantitative analysis, also, attempts to answer challenging questions regarding the physics of the source of emission and the mechanisms behind it. This can be done by fully investigating the recorded waveforms which are far richer in information than the AE Parameters. For instance, the ﬁrst visual examination of a waveform may provide some preliminary information concerning the propagation path of the wave and the frequency content of the resulting signal. Further inspection of

31 the waveform using computerized algorithms also provides valuable information about the sources of emissions. The complexity and tediousness that accompany quantitative analysis, however, makes it far less performed compared to qualitative analysis which has been routinely used in several acoustic emission applications. Quantitative analysis is of particular interest in this study and more details about this type of analysis are provided in chapter4 of this thesis.

3.3 Applications Of Acoustic Emission Methods to Concrete Materials The first investigations on the application of acoustic emission for the study of concrete materials dates as early as 1970, few years after Joseph Kaiser[10] published his pioneering work about acoustic emission activity in metals under tension. His findings mark the beginning of modern acoustic emission. Ever since, a broad spectrum of research has been conducted on the application of Acoustic Emission in cementitious materials. In this section we present a brief summary of the most significant contributions available in literature about the use of acoustic emission for the assessment of plain, reinforced and prestressed concrete. Early experiments started with Green[26] in 1969 when he conducted tests on mortar cylinders for prestressed concrete pressure vessel reactor industry. He concluded that stress wave emission data can be used to determine the onset and progression of failure processes. In 1980, Kobayashi[27] conducted a set of experiments to study de-bonding of reinforcing steel in beam-column joints subjected to cyclic loading. Becoming aware of the capabilities of acoustic emission, several dedicated researchers soon launched intensive research to further investigate the use of this new technique in concrete industry. In reinforcing concrete (RC), Ohtsu[28–30] has been doing a leading work since about 1980. De- bonding as well as crack formation in different RC elements have been extensively studied. Yuyama[31] proposed, in 1998, the concrete beam integrity (CBI) approach for the qualitative assessment of reinforced concrete beams. The results of his observations based on laboratory experiments state that a structural element with a CBI <0.8 can be classified as seriously damaged. Within the same group, Shiotani[32]

32 adapted and improved the b-value approach originally developed in rock mechanics in order to monitor RC structures. Quite simple and efficient, this method has since been in the forefront of the qualitative acoustic emission methods used for the assessment of concrete structures[33, 34]. Colombo[34] and his research group proposed the relaxation ratio method, an approach that can be used to predict the ultimate bending capacity of RC beams. Tinkey[35] performed a set of laboratory experiments on prestressed beams he drove to failure in order to test the feasibility of the acoustic emission technique on large-scale in-service structures. Golaski[36] conducted field experiments on RC structures in order to investigate the applicability of the acoustic emission technique on in-service reinforced and prestressed concrete bridges. Grosse and his team from the University of Stuttgart[37–39] have been conducting a variety of tests to investigate RC and fiber reinforced concrete using the acoustic emission technique. Rebar pull-out experiments were performed on small cubic specimen and Finite Element analysis was conducted for the matter. Several other research studies that contributed enormously to the evolution of acoustic emission in concrete industry can be found in literature. Schumacher[40] provided a rich literature review about the application of acoustic emission in structural concrete.

33 Chapter 4

ACOUSTIC EMISSION SOURCE LOCATION

4.1 Introduction Acoustic emission (AE) has been extensively used for the non-destructive evaluation of different materials because of the wealth of information related to energy release that result from various types of damage mechanisms such as fatigue cracks[41], fiber breakage[42], micro-cracks[43] etc. The technique offers many enabling features, of which the ability to estimate AE source locations is, perhaps, the most useful. That is, for the accurate assessment of an AE source (position, fracture-type, magnitude, etc.) which in this study represents a primary objective, it is required first to locate the source in space and time with the highest accuracy possible. To meet this re- quirement, a whole range of source location schemes[44–50] have been proposed and developed in seismology. The traditional methods based on the time of arrival approach (TOA) are considered among the most successful schemes. They have been routinely applied in seismic and mining related activities for the location of epicenters and mining-induced events. Being aware of the capabilities of these TOA methods in source location problems , scientists and engineers adapted and improved them for the estimation of acoustic emission source locations in other materials. Traditional TOA schemes range from the simple first hit method[51] also known as zonal location to more developed iterative point location methods. All TOA schemes require the prior knowledge of the wave speed in the propagating medium and the arrival times of a particular wave phase, typically the P-wave to a network of recording sensors. Usually, a wave speed is used that represents the average properties of the material. This can lead to errors, particularly in non-homogeneous, non-isotropic, and

34 cracked materials such as concrete[52]. A discussion of traditional TOA schemes, their principles, advantages and limitations is well summarized in Ge's papers[53, 54]. Some recent studies include using non-uniform velocity fields to improve location uncertainties in non-homogeneous materials, see e.g.[55–57]. Finally, probabilistic approaches have been proposed to treat parameters as random variables for a more accurate representation of uncertainties and errors[52]. Several other source location approaches are still under investigation. One approach that does not require picking of a wave phase and that has been implemented successfully for AE source location problems in a variety of materials is called phased array beamforming. The idea was first proposed and demonstrated by the German inventor and scientist Karl F. Braun in 1905[58] to enhance transmission of radio waves in one direction but its application in AE monitoring of engineering structures is relatively new. McLaskey[59] first proposed this approach to locate AE sources in large reinforced concrete slabs. He showed that under far-field conditions, the method can estimate the direction of AE sources up to 3.8 m far from the center of an array of AE sensors. He[60] improved the approach and used it under near-field conditions to locate artificial AE sources placed in close vicinity to a small array of AE sensors in plate-like structures. Nakatani[61] used the approach of phased array beamforming to predict points of impact on a cylindrical structure made of an anisotropic material. They showed that with a linear array of four sensors, it is possible to predict the direction of acoustic sources from randomly chosen point of impacts. Xiao[62] used the approach with two uniform linear arrays of acoustic sensors distributed along x-axis and y-axis directions to locate the acoustic sources on plate-like structures. First, a finite element simulation of the problem was proposed to verify the accuracy and effec- tiveness of the proposed approach. Then, the approach was tested on a plate of carbon fiber reinforced plastics to locate acoustic sources from pencil lead breaks. In this Chapter, we only discuss the implementation of a traditional time of arrival (TOA) approach for the estimation of acoustic emission source locations in concrete materials. This approach is based on Geiger's algorithm[44]. The approach

35 is implemented and discussed in depth. Results of laboratory experiments performed on diﬀerent concrete specimens are presented and discussed for this approach.

4.2 Source Location : Time of Arrival Approach 4.2.1 Background and Principle Time of arrival (TOA) methods represent a set of algorithms that were first proposed in seismology and mining-induced seismicity[53,54]. They utilize arrival time information extracted from the recorded seismograms (seismic waveforms) in order to estimate the location of an earthquake hypocenter or an acoustic emission (AE) source. The arrival times (or onset times) are the instants in time when a specific wave phase (usually P or S) arrives at individual stations (or sensors) in a network at different instances in time. Figure 4.1 illustrates this process for the example of AE in a small material specimen. Often, two phases are identified in seismology, the P phase and the S phase, because seismograms typically show distinct P- and S-wave arrivals allowing both phases to be determined and their arrival times to be picked[2]. In AE testing (similar to seismology albeit at different scales), usually only the P phase is identified and its arrival time picked because AE signals show almost no P-S wave separation which results in the S-wave being hidden in the coda wave and emergent arrivals of the P-wave. Also, AEs are measured on the surface thus contain a strong R-wave component which is barely separated from the S-wave[2]. Figure 4.1 shows an illustration of P-wave picking in AE signals. T1, T2 and T3 represent, respectively, the travel times of the P-wave (= emergent wave front) takes to propagate from the AE source to the AE sensors, S1, S2 and S3. The onset time is marked with the blue vertical line and the picking method that we implemented for this study is discussed in section 4.2.3. In TOA source location schemes, the so-called arrival time function must be established. This function is a deterministic relationship used to describe the time a phase (P, S) takes to travel from a source of unknown location to a recording station

36 Figure 4.1: Illustration of TOA approach using P-wave arrival times on AE signals. Only three AE sensors are shown for simplicity. (Submitted to the Jour- nal of Nondestructive Evaluation on February 26. In review.)

(or sensor) of known location. For the case of a linear, homogeneous and isotropic material, the travel time function can be expressed as follows:

1 q 2 2 2 fi (xs, ys, zs, ts) = (xi − xs) + (yi − ys) + (zi − zs) (4.1) cP,S where xs, ys and zs are the unknown coordinates of the event source; ts is the unknown th origin time of the event source; xi, yi and zi the coordinates of the i sensor and cP,S is the speed of the desired P- or S-wave, respectively. Theoretically, cP,S is unknown and needs to be determined prior to testing. In practice, an estimated value of the average speed in the transmitting medium is usually assigned in order to reduce the number of unknowns and simplify the problem. A typical average value for the P-wave speed, cP in concrete is 4000 m/s. In reality, however, concrete is a very heterogeneous material with complex arrangements of ingredients (cementous materials, aggregates, admixtures, water, steel bars, etc.) and random distributions of voids and cracks. This inhomogeneous nature aﬀects the propagation of stress waves in concrete materials and result in amplitude attenuation of the propagating wave, complex travelling paths

37 and dispersion (wave speed depends on the frequency). Therefore, there is no exact P-wave speed and no exact arrival time functions that perfectly model the behaviour of stress waves in concrete materials. It was justiﬁed, however, through some numerical simulations[65] and experimental investigations that concrete media can be treated as elastic homogeneous materials and a straight propagation path can be assumed. Consequently, a travel time function for a linear, homogeneous and isotropic material can be used. Assuming a travel time function for a linear elastic material, the goal of TOA ap-

0 0 proaches reduces to minimizing the residuals ri between calculated (subscript c ) and observed (subscript 0o0) arrival time at each sensor.

ri = min (ti,o − ti,c) (4.2)

To solve for the unknown spatial coordinates xs, ys and zs and the origin time ts of the AE source, we need a set of four equations, which correspond to the residuals at four diﬀerent sensors. The system of equations obtained represents an inverse non-linear problem that can be best solved using iterative algorithms. The core of an iterative algorithm (see Figure 4.2) consists of generating a sequence of testing and updating of a trial solution by applying a linear least-squares algorithm in order to obtain an optimal estimate of the source location coordinates. A summary of common iterative algorithms can be found in[54].

4.2.2 Geiger's Method For this study we chose to implement a TOA algorithm based on the source location method originally proposed by Geiger[44]. It has been extensively used for AE source location problems (see, e.g.[55],[66],[67], etc.). The method consists of updating a trial solution using a correction vector computed based on the ﬁrst derivatives of the linearized arrival time function using a least-squares approach in order to obtain an optimal estimate of the spatial and temporal source coordinates. That is to say, starting from a trial solution, a ﬁrst set of arrival times, to all sensors, is calculated using Equation 4.1. The calculated arrival times are then compared to the

38 observed arrival times picked from the AE signals and sensor residuals are computed according to Equation 4.2. A correction vector is then computed and used to update the trial solution. The process is repeated until a predeﬁned stopping criterion is fulﬁlled. For each event, an initial solution obtained by averaging the sensors coordinates and the arrival times was used as the trial solution. Figure 4.2 illustrates the computational steps involved in our algorithm.

Figure 4.2: Flowchart illustrating the computational steps involved in the iterative source location algorithm based on Geiger's method.

Geiger's Algorithm:(Source: Ge, [2003][54])

Assume the arrival time function fi(x) given by Equation 4.1 where x denotes the source parameters:

T x = (xs, ys, zs, ts) (4.3)

39 The ﬁrst-degree Taylor polynomial expansion of fi(x) at a nearby location x0, conventionally called trial solution or initial guess gives: ∂f ∂f ∂f ∂f f (x) = f (x + δx) = f (x ) + i δx + i δy + i δz + i δt (4.4) i i 0 i 0 ∂x ∂y ∂z ∂t where:

T x = x0 + δx , x0 = (x0, y0, z0, t0) and δx = (δx, δy, δz, δt) (4.5)

Equation 4.4 can be written in vector notation as follows:

T fi (x) = fi (x0) + δx (Ofi (x)) (4.6)

T where (Ofi (x)) represents the transpose of the gradient Ofi vector and is given by: ∂f ∂f ∂f ∂f f (x) = i , i , i , i (4.7) O i ∂x ∂y ∂z ∂t

The quantity fi (x0) in Equation 4.4 is called calculated arrival time, ti,c, and is always known since the nearby location x0 is always known at the beginning of each iteration as it is assigned by the user at iteration zero and then updated automatically in the algorithm. The quantity fi (x0 + δx) represents the arrival time, ti,o, observed at the th ∂fi ∂fi ∂fi ∂fi i sensor and the quantity ∂x δx + ∂y δy + ∂z δz + ∂t δt called correction factor, γi, represents the channel residual at the ith sensor. Rewriting Equation 4.4, we obtain:

γi = ti,o − ti,c (4.8)

With N sensors used, we obtain the following system of equations:

Aδx = γ (4.9) or in matrix form:       ∂f1 ∂f1 ∂f1 ∂f1 ∂x ∂y ∂z ∂t ∂x γ1        ∂f2 ∂f2 ∂f2 ∂f2       ∂x ∂y ∂z ∂t  ∂y  γ2      =   (4.10)  . .     .   . .  ∂z  .        ∂fN ∂fN ∂fN ∂fN ∂x ∂y ∂z ∂t ∂t γN

40 The least squares solution to the system in Equation 4.9 is deﬁned by:

−1 δx = AT A AT γ (4.11)

And the least squares residual is deﬁned by:

r γT γ Res = (4.12) N − m where N represents the number of equations and m represents the degree of freedom of the system. Now the vector δx can be calculated and added to the previous trial solution to form a new trial solution. The process is repeated until a stopping criterion is fulﬁlled.

End This source location algorithm was implemented in MATLAB and applied to all AE events in our experiments. Three main inputs are required for the algorithm : (1) the spatial coordinates of all sensors, (2) the P-wave speed in the medium and (3) the observed arrival times from the AE event to each sensor. The sensors'coordinates are always known and are measured directly on the test specimen. The P-wave speed is usually determined from pulse velocity experiments using artiﬁcial sources such as Pencil Lead Breaks (PLB). The step that can be challenging, depending on the signal- to-noise ratio (SNR), is the picking of the P-wave arrival times from the recorded AE waveforms. The most accurate and reliable way is to do this is manually, but this can be time-prohibitive if many events have to be evaluated. For all the experiments involved in this research, we used an automatic onset time picking algorithm developed by Maeda[68] based on the Akaike Information Criterion (AIC)[69].

4.2.3 P-wave arrival time picking The first step in quantitative AE analysis is to identify the first onset of the P- wave in time (i.e. pick the P-wave arrival time from the recorded AE signal). This onset time represents the first undisturbed information that arrives at the recording sensor.

41 Subsequent modes such as the shear (S-) wave or the surface (R-) wave can be difficult to observe because AE signals show almost no P-S wave separation which results in the S-wave being hidden in the coda and emergent arrivals of the P-wave. Also, AEs are measured on the surface thus contain a strong R-wave component which is barely separated from the S-wave[2]. Besides, S-wave and R-wave often contain boundary reflections which makes their onset time identification challenging. Figure 4.3 shows a typical AE signal recorded in the laboratory using a Glaser/NIST point-contact sensor. The signal clearly shows the first onset time of the P-wave.

Figure 4.3: Typical AE signal recorded in the lab shows the P-wave onset time

Several onset picking techniques have been proposed in literature, ranging from the simple manual picking technique (very time consuming) to the amplitude threshold- based picking technique to more other developed techniques. Each technique relies on the deﬁnition of the onset time itself and on the margin of acceptable errors. A wide range of pickers, for example, are based on the STA/LTA approach (Short Term Average / Long Term Average) proposed by Baer and Kradolfer[70]. Kurz et al.[71] developed an automatic onset detection algorithm based on the Hinckley criterion and applied it to AE signals recorded during rebar pull-out tests. Many other onset time picking techniques use signal processing approaches based on the modeling of signals

42 as autoregressive processes. Akaike[69] developed an approach called Akaike Informa- tion Criterion (AIC) in which he divides a time series into locally stationary segments and models each segment as an autoregressive process. Maeda[68] later studied the Akaike criterion and developed a formula from which the AIC function can be directly determined from the original signal. The minimum value of the AIC function represents the estimated p-wave arrival. The idea has been used in the AE community for many years and has shown to perform more accurately and reliably compared to other picking schemes[66],[71], etc. In this research, the AIC algorithm was used for the estimation of the p-wave arrival times from the recorded signals. A MATLAB code based on the algorithm was written and implemented for this purpose.

The AIC function is not computed over the whole time series that represents the AE signal but only on a window that contains the P-wave arrival time. This signal window is selected by prearranging the P-wave onset time by a simple threshold. The time, when the amplitude of the signal crosses the threshold, is considered as the prearranged onset time. The window is then obtained by selecting several hundred samples e.g 500 centered on this onset time. Within this signal window, the onset is determined exactly using the AIC. For a window, w, the AIC function is given by:

AIC(ti,w) = ti,w · log (var (w (ti,w, 1))) (4.13) + (Tw − ti,w − 1) · log (var (w (1 + ti,w,Tw))))

Where ti,w represents the current sample of the window w and Tw represents the last sample of the window w. ti,w ranges through all the samples of the window. The term w(ti,w, 1) means that the variance function is only calculated from the current value of ti,w while the term w(1 + ti,w,Tw) means that the variance is calculated from all the samples ranging from 1 + ti,w to Tw. 2 The sample variance var denoted by σN−1 is deﬁned as in[72]:

N 1 X 2 σ2 = (w − w¯) (4.14) N−1 N − 1 k k=1

43 where N denotes the length of the signal, wk the sample k of the time series w andw ¯ is the mean value of the whole time series w.

Figure 4.4 shows the application of the AIC algorithm for the automatic estimation of the P-wave arrival time in two AE signals recorded in the laboratory; one with a high signal to noise ratio (low noise level) and the other with low signal to noise ratio.

Figure 4.4: Automatic P-wave onset time estimation using an AIC-based algorithm (a) High signal to noise ration and (b) Low signal to noise ratio

44 In the estimation of AE source locations, uncertainties in the actual P-wave speed, non-straight travel paths in real complex non homogeneous materials, and arrival time picking errors introduce errors in the estimated source location result[52]. Since the location of a real AE source is unknown, some strategies have to be used to in order to provide source location accuracy.. If at least ﬁve AE signals are available to estimate the source location, the system of equations solved is over-determined (there are four unknowns source coordinates) and the covariance matrix of the solution using the least-squares method can be computed. From that, the standard deviations in the principal directions, σ1, σ2, σ3 can then be obtained by solving for the eigenvalues and eigenvectors of the covariance matrix. These standard deviations are visualized as 3D ellipsoids and represent a measure of inconsistency in the observed arrival times and not the absolute error associated with a certain location result. This inconsistency measure was applied to all the experimental results in this research.

4.3 Glaser/NIST Point-Contact Sensors 4.3.1 Characteristics of the Glaser/NIST point-contact sensor The Glaser/NIST point-contact sensor was briefly discussed in section 3.2.1.1 in chapter 3. Here, we want to give more attention to describing this sensor and exploring its characteristics and features since it represents the main link between the concrete structure and the data acquisition system. This sensor differs from all the other typical acoustic emission sensors by its conical-shaped tip. It has a very small aperture and the contact between the host structure and the sensor is only through the tip. This sensor was developed by Professor Glaser at the NIST laboratories and was only used by very few researchers since it is relatively new. None of the research studies conducted using this sensor, however, shows its application in acoustic emission monitoring of concrete structures. Thus, this research study is the first of its kind that explores the capabilities this sensor offers for the monitoring of concrete structures using the acoustic emission technique. This present section is dedicated to explore

45 Figure 4.5: (a) Glaser/NIST Point contact sensor versus other typical sensors with aperture the Glaser/NIST sensor and highlight its advantages and limitations when used with concrete materials. Glaser/NIST sensors present many advantages over many acoustic emission sensors available in the market. They present a broad-band frequency response characteristics (20 kHz to 1 MHz) with a flat spectrum (within 3 dB) over this frequency range (Figure 3.6). These sensors were selected specifically for this study because of their high-fidelity response characteristics which would ensure that quantitative procedures such as moment tensor inversion (MTI), which rely on unbiased measurements (not contaminated by noise), would be applicable. An important aspect of the a Glaser/NIST point-contact design features is the quasi-point contact area which minimizes aperture effects that other AE sensors have. This was made possible by using a conical piezoelectric crystal. These sensors also do not require the use of a coupling product when they are mounted on the surface of a host structure. To mount a Glaser/NIST point- contact sensor on the surface of a concrete specimen, plastic fixtures with small cutoff windows were designed and produced in the machine shop according to the design of the sensor. The inner surface of the plastic fixture is threaded and the sensor is simply driven inside the fixture similar to a screw-nut mechanism. First the fixture is glued

46 on the concrete structure, then a torque is applied manually to the sensor to drive it inside of the fixture until the tip is in contact with the surface of the structure. The cutoff in the plastic fixture was used as a window through which we check whether the tip of the sensor is in perfect contact with the surface of the concrete structure or not. The sketch in Figure 4.6 shows the procedure described above.

Figure 4.6: Mounting the Glaser/NIST point-contact sensor on a concrete structure

While mounting the sensor, one should pay attention to the surface where the plastic ﬁxture is to be placed. In fact, the surface of a concrete specimen is rough and has a lot of voids of variable sizes. Attention should be payed to tiny voids because the contact between the sensor and the surface is only through the tip of the sensor so it is recommended to make sure this tip is not placed on a tiny void (Figure 4.7). If not, the sensor will not record any displacement and only noise from the surrounding environment will be recorded thus the sensor will be of no utility. This issue is one of the major limitations of using the sensor. In order to avoid such situations, we made

47 sure, in all the experiments we performed, that the contact area was properly chosen and carefully cleaned.

Figure 4.7: Mounting the Glaser/NIST point-contact sensor on a concrete structure (a) rough surface with voids (b) smooth surface with perfect contact area

Figure 4.8: Design issue with the Glaser/NIST point-contact sensor

48 One other major limitation related to the design of the Glaser/NIST point-contact sensor presents, is the inefficiency of the spring-crystal system inside the sensor. In fact, when an excessive amount of rotation is applied to screw the sensor inside the plastic fixture in order to make sure the tip in contact with the concrete surface (Figure 4.8.d) , the concrete surface (harder than the tip of the sensor) pushes the outward indent of the wear plate covering the conical piezoelectric crystal inside the sensor. The problem with the design is that the tip of the sensor does not go back to its original position (Figure 4.8.a) when the sensor is unscrewed from the plastic fixture (Figure 4.8.e). Thus the movement of the tip of the sensor is irreversible and the sensor can be damaged after few applications. A simple comparison between Figure 4.8.a and Figure 4.8.e illustrates this problem.

4.3.2 Response of Glaser/NIST sensors on different concrete specimens Many experiments were conducted in the laboratory using a single or a network of Glaser point-contact sensors. The behavior of the sensors differ from one experiment to another depending on the scale of the experiment, the size and shape and concrete structure and the roughness of the surface of the surface on which the sensors are mounted. For a smaller concrete specimen, the acoustic emission energy released from a source reaches the surface of the specimen in a shorter time and a larger amplitude. Thus, the signal to noise ratio of the recorded signals is usually high which results in better and cleaner signals hence more accurate source locations. An experiment on a 6x6x21 in3 concrete beam was conducted in order to check the quality of the signals recorded by the sensors. A grid of 1x1 in2 was placed on the beam and a Panametrics actuator was used on each grid point to generate artificial acoustic emission sources. A network of 10 Glaser/NIST point-contact sensors were used to record the surface displacements. Figure 4.9 illustrates the experiment performed. The displacements recorded by the sensor network are shown in Figure 4.10. We clearly see that the signals are very clean and noise is almost absent from all of them. All the sensors work properly and all of them show very clear signals with nice P-wave arrivals. The same

49 experiments was repeated with pencil-lead breaks (PLBs) as artiﬁcial sources of acoustic emission. The signals recorded by the sensor network are shown in Figure 4.11.A large scale experiment was also performed on a 192x12x24 in3 beam and a network of 15 sensors was mounted on the beam. Real acoustic emission sources were generated from the initiation of cracks when the beam was subjected to an external loading using a 150 kip hydraulic actuator. Figure 4.12 shows the signals recorded by the sensor network (only the signals recorded by 10 sensors are shown). We clearly see that the network response is diﬀerent from one sensor to another. In some recorded signals the signal to noise ratio is high. This is especially the case when the sensor is close to the source of acoustic emission. In some others signals, the signal to noise ratio is low especially when the sensor is far from the source of acoustic emission. This results in low quality signals contaminated with noise.

Figure 4.9: (a) 3D view of the small beam with the sensor network

50 Figure 4.10: AE signals recorded by the sensor network (case 1: Panametrics Actu- ator) 51 Figure 4.11: AE signals recorded by the sensor network (case 2: PLBs) 52 Figure 4.12: AE signals recorded by the sensor network (large scale beam) 53 4.4 Source Location Strategy This section aims at discussing the strategy we followed in our experiments in order to locate sources of acoustic emission with the best accuracy possible. As it is commonly known, concrete is a very heterogeneous material thus pinpointing a source of acoustic emission in a concrete structure with 100% accuracy in not possible. This is mainly due to systematic errors that are usually very hard to eliminate or control in such experiments. For example, instrumental errors resulting from non-calibrated recording sensors, from preampliﬁers and from other elements in the measurement chain result in source location errors. Theoretical errors due to the assumption of constant p-wave velocity in concrete also result in source location errors. Observational errors in p-wave arrivals can also result in source location errors. To minimize these systematic errors, a source location strategy was applied.

The strategy consists of locating the source of acoustic emission and computing the standard deviations σ1, σ2 and σ3 using the best sensors. To better explain how this works, we are going to use the same 6x6x21 in3 concrete beam in Figure 4.9 where pencil-lead breaks were used on each grid point to generate artiﬁcial acoustic emission sources. Recall that a total number of 12 recording sensors were used in the beam experiment. We ﬁrst use all 12 sensors to estimate the location of the AE source. We assume that the p-wave velocity is variable and we allow for the following iteration process:

1- Assume an initial P-wave speed CP 0. 2- Use the arrival times to all the 12 sensors to locate the source s.

3- Compute the distance di between the estimated source s and each sensor i. 4- Plot the source-sensor distances versus the arrival times to all the sensors. 5- Perform a linear least-mean squares interpolation of the data in the obtained plot.

6- Obtain the slope of the interpolated data. It represents the new p-wave speed. CP i

7- Assume CP i and repeat the steps until a stopping criteria is satisﬁed.

54 Figure 4.13: Locating using the best 12 sensors

Figure 4.14: Locating using the best 5 sensors

At the end of the iteration process, we obtain the plot in Figure 4.13. The magenta line represents the linear least mean squares Interpolation and its slope is equal to a ﬁnal P-wave speed of Cp12 = 4452.27m/s. The next operation consists of locating using the best 11 sensors. This is done by eliminating the sensor that gives the maximum residual between the real and interpolated data. The red star in Figure 4.13

55 indicates the sensor to be eliminated. In this case, the sensor 12 was eliminated. After discarding the outlier sensor, all the steps from 1 to 7 are identically repeated where in each operation the initial speed is assumed to be equal to the speed obtained from the previous operation. This process is repeated identically until we obtain the last ﬁve best sensors (Figure 4.14). At the end of each operation ”N” (N best sensors used to locate, 5 ≤ N ≤ 12) we obtain an estimate of the the source location and we compute the corresponding standard deviations σ1, σ2 and σ3.

A total of 8 source estimates and 8 corresponding values for σ1 are obtained (8 operations performed using, 12 ,11, 10, 9, 8, 7, 6 and 5 best sensors). Since, we used artiﬁcial AE sources from pencil lead breaks, the exact location of each source is known in advance. Thus, for each event an absolute error is computed between the exact location and each of the 8 source estimates. The next step consists of plotting both the absolute error and the standard deviation σ1 as function of the number N of best sensors used. This was done for several acoustic emission events. The results of these plots are shown in Figure 4.15.

We can clearly see that when N decreases, the standard deviation σ1 decreases. The behaviour of the absolute error is, however, not regular but the curve tends to converge to a horizontal plateau between N = 7 and N = 5. In fact the more sensors we use to locate, the more systematic errors and P-wave onset time picking errors we introduce to the ﬁnal solution. Thus, it would be ideal to use a minimum number of sensors to locate the AE source. Since, a minimum of 6 sensors is required for the moment tensor inversions and based on the results shown in Figure 4.15 , we decided to use the best 6 recording sensors for each AE event recorded. This strategy was applied for the large scale experiments we performed in this study (ﬂexural and shear beams). For the other experiments, the strategy was not adopted because the recorded signals were of a high quality and there was no need for eliminating any sensor.

56 Figure 4.15: Plots of and σ1 versus the number of best sensors used (Diﬀerent events

57 Chapter 5

MOMENT TENSOR INVERSION INVERSION: THEORY AND FUNDAMENTALS

5.1 Introduction and Background One ultimate goal in quantitative acoustic emission testing of concrete materials is the detailed understanding and quantification of the physical processes of the acoustic emission source. Such understanding will considerably help addressing challenges related to the lack of knowledge of ongoing cracking processes and fracture mechanisms in concrete mechanics in real-time. Possibly the most important quantitative technique that has been developed that gives enough understanding of the AE source mechanism is the technique of Moment Tensor Inversion (MTI). A well-established quantitative seismological technique, moment tensor inversion has shown great potential in providing a full understanding of the fault mechanisms in seismology (e.g.[74]. The method was pioneered by Dziewonski and Gilbert[75], further developed by Aki and Richards[76] and is now routinely applied by seismologists to study earthquake source mechanisms. Due to the profound analogy between earthquakes and AE, the moment tensor inversion technique is now being adapted to study the fracture of materials and structures. The application of MTI to engineering materials, however, is relatively new and only a few works related to the use of moment tensor inversion in fracture mechanics studies of materials have been published, the reason being that the inversion methods are notoriously tedious and sensitive to noise. Ohtsu[67] was the first scientist who successfully adapted the MTI technique for concrete mechanics. He developed a MTI-based code called SiGMA (Simplified Green's functions for Mo- ment Tensor Analysis), that he used to study cracking mechanisms in concrete at the meso-scale. Ever since his leading work, the MTI technique has been the subject of

58 increasing interest in the ﬁeld of materials science, especially in concrete mechanics, and has been applied by many other authors for the analysis and the study of diﬀerent types of fractures and cracking mechanisms. Grosse has done remarkable work on the quantitative analysis of AE from concrete elements using the MTI technique. He applied a relative MTI code developed by Dahm[77] that computes source mechanisms of clusters of events. Yuyama[78] has used MTI extensively to study the fracture mechanics of concrete beams reinforced with FRP sheets, and reinforced concrete column foundations. The technique is used to invert recorded surface displacements generated within a test specimen due to ongoing rapid internal strain releases to identify and characterize the sources of AE within the specimen

5.2 Moment Tensor Inversion: Theory In 1970, Gilbert[79] introduced the moment tensor concept as a physical representation of an earthquake source and outlined the forward problem, where displacements at the Earth's free surface are expressed as the sum of the moment tensor components multiplied by their corresponding Green's functions. Aki and Richards[76] later proposed a theoretical expression of these seismic displacements. assume a distribution of equivalent body force densities fi within a source volume V . The seismic displacement uk observed at a given position x = (x1, x2, x3) at time t is formulated by Aki and Richards as follows:

Z ∞ Z ∗ ∗ ∗ ∗ ∗ ∗ uk (x, t) = Gki (x, t; x , t ) fi (x , t ) dV (x ) dt (5.1) −∞ V

∗ ∗ where Gki (x, t; x , t ) are the components of the elastodynamic Green's functions, which describe the propagation eﬀects between the source ξ, t0 and the receiver (x, t),

∗ ∗ ∗ ∗ with x = (x1, x2, x3). The subscript k indicates the component of the displacement.

If the coordinate system is placed at a reference point ξ = (ξ1, ξ2, ξ3) within V , the Green‘s functions can be expanded into a Taylor series:

∞ X 1 G (x, t; x∗, t∗) = x∗ − ξ ... x∗ − ξ G (x, t; ξ, t∗) (5.2) ki n! j1 j1 jn jn ki,j1...jn n=0

59 Figure 5.1: Propagation eﬀects between the AE source and the recording sensors (source: modiﬁed from Kocur,[23])

The time dependent force moment tensor can be deﬁned as follows: Z ∗ ∗ ∗ ∗ ∗ Mij1...jn (ξ, t ) = xj1 − ξj1 ... xjn − ξjn fi (x , t ) dV (5.3) V

Using Equations 5.2 and 5.3, the displacement uk given in Equation 5.1 can be expressed as follows:

∞ X 1 u (x, t) = G (x, t; ξ, t∗) ∗ M (ξ, t∗) (5.4) k n! ki,j1...jn ij1...jn n=0 Further simplifications and assumptions (elastic infinite media, point-source, far-field, synchronous source approximation, etc., see Aki and Richards[76] for more details) applied to Equation 5.4 give:

uk (x, t) = Gki,j (x, t) ∗ Mij (5.5)

The linear relationship between the moment tensor and the Green's functions was ﬁrst used by Gilbert[80] to compute moment tensors from recordings of seismic displacements. In this process, Equation 5.5 is written as an inverse problem and solved using matrix algebra methods. Essentially, the moment tensor components are inverted from recorded displacements and estimated Green's functions.

60 5.2.1 Moment Tensor Source 5.2.1.1 Equivalent Force Model In seismology, Aki & Richards[76] showed that, under the assumption of point- source (wavelengths of the seismic waves are large relative to the dimensions of the source, wave periods are longer than to the duration of rupture, non-linear eﬀects in the near-source region are neglected, etc.), the actual forces acting at a seismic source induced from a faulting mechanism can be modeled by equivalent forces that correspond to linear wave equations. These equivalent forces produce displacements at a given point that are identical to the displacements produced by the actual forces of the physical process[7]. Using the same analogy, an acoustic emission source could be modeled by equivalent forces that correspond to the real forces acting on the source. The equivalent force models mostly used to represent a source are summarized in Figure 5.2. The single force model is not illustrated because it is not physically plausible since it implies the application of an external force which is usually not the case in acoustic emission testing.

Figure 5.2: Various force types at a point source: (a) Two equal and opposite forces in tension; (b) Two equal and opposite forces as a torque about the z-axis; (c) Two pairs of forces, where tension and compression are of equal magnitude and are perpendicular to one another; (d) Two pairs of forces with torques about the z-axis of equal magnitude and opposite in direction (Adapted from Andersen[7])

The pair of equal and opposite forces in Figure 5.2.b form an equivalent force model

61 is referred to as single-couple. The more complicated system of forces shown in Fig- ure 5.2.d is an example of a double-couple which consists of two single-couple systems having no resultant torques. Two examples of simple sources are pure explosive and pure shear sources. Figure 5.3 shows the actual forces of the physical process and the corresponding equivalent force models for each one of the two examples.

Figure 5.3: Actual forces of the physical process and their equivalent force models for (a) A pure explosion and (b) A pure shear in the xy plane

62 5.2.1.2 Moment Tensor of the source The moment tensor is one of many important parameters (location, intensity, orientation, etc,) that are used to describe a source. It represents a measure of the irreversible inelastic deformation in the area where the source of emission occurs.

Consider a pair of forces equal in magnitude, separated by a small distance in the x2 direction acting along the positive and negative x3 directions,i.e. two forces (0, 0,F ) 1 1 and (0, 0, −F ) acting at points ξ + 2 e2 and ξ − 2 e2 , respectively, where e2 is a unit vector in the x2 direction (Figure 5.4).

Figure 5.4: Illustration of a single couple with a pair of equal and opposite forces of magnitude F along z-axis

The total displacement ui caused by the two forces is equal to the sum of the displacements caused by each force[81], so that:

1 1 1 u = F ∗ G ξ + e − G ξ − e (5.6) i 13 2 2 13 2 2

Taking the limit of ui as F → ∞, and → 0, in such a way that the product F remains ﬁnite, yields:

∂G13 ∂G13 ui = (F ) ∗ = M32 ∗ (5.7) ∂ξ2 ∂ξ2

63 This pair of forces is known in classical mechanics as a couple, and the quantity M32 as the moment of the couple, which has the dimension of force × length and may be function of time.

Similarly we derive all the components Mij with forces in the xi direction and arm in the xj direction. Nine possible combinations are obtained (Figure 5.5).

Figure 5.5: Representation of the nine possible couples Mij. The directions of the force and arm of the couple are denoted by the indices i and j respectively (adapted from[76])

5.3 Classiﬁcation Of Moment Tensor Inversion Methods A large number of MTI methods have been proposed since the pioneering paper of Dziewonski and Gilbert[75]. The methods are tailored to the available data and diﬀer according to: models of the seismic source; approaches used to evaluate the Green's functions; noise reduction schemes; and, whether the methods are applied in the time or frequency domain, to full waveforms or selected phases. We recognize two broad classes of MTI according to whether the methods are applied to single or clusters

64 of recorded events: absolute methods (e.g. Dziewonski and Gilbert[75]) and relative methods (e.g. Patton[83]).

5.3.1 Absolute methods The absolute methods were the ﬁrst to be developed and applied in moment tensor inversion problems. These methods apply to individual events and require that the Green's function be estimated, either theoretically or empirically from a known point source and a set of observations. The estimation of the Green's functions in absolute methods depends on the model assumed for the material medium in which the wave propagates, the location of the point source, and the position of the sensor used to record the observations [7]. For structurally complex media, with possible inhomogeneities, assuming adequate models always presents a big challenge. Thus, the accurate estimation of the Green's functions complex media is not always possible. As a result, systematic errors will be introduced into the moment tensor elements. This presents one of the major drawbacks associated with absolute inversion methods.

5.3.2 Relative methods In contrast to the absolute methods, the relative inversion methods do not require the calculation of theoretical Green's functions for each event. They apply to spatial clusters of events and assume, using the concept of a common raypath between a cluster of events and a particular receiver, that all the events in the cluster experience the same wave propagation effects to the receiver. This allows for the Green's functions of a reference event from a cluster to be used as estimations for all the other events in the same cluster. A difficulty associated with this approach is that the moment tensor solutions for all the events in the cluster depend on the a priori knowledge of the reference event. Errors in the determination of the radiation pattern of the reference event may lead to biased moment tensor solutions for the other events in the source cluster[7]. Under special conditions, the path effects described by the Green 's functions

65 can be eliminated analytically thereby avoiding the explicit use of Green's functions. This approach is known as the relative method without a reference event[77].

5.3.3 Hybrid methods The hybrid methods are moment tensor inversion approaches developed for high frequency mining-induced data recorded by underground networks. Data recorded in the harsh, deep mining environment is noisy and suﬀers from scattering due to mining- induced fracturing associated with the excavations, and often only one channel of a triaxial sensor is operational. The hybrid methods attempt to compensate for various types of systematic errors (or noise), which inﬂuence seismograms recorded underground. They capitalise on the strengths of both the absolute and relative methods in order to achieve a robust measure of the seismic moment tensor[7]. The hybrid method represents a combination approach that applies the absolute method to individual events in a spatial cluster, and then computes and applies a relative correction to improve the individual solutions. The correction is essentially a weight, based on the statistical distribution of the residuals between the theoretical and recorded displacements, for events in a cluster having common ray paths. Three hybrid methods were developed: (1) the hybrid method using mean corrections, (2) the hybrid method using median corrections and (3) the hybrid method using weighted mean corrections. Detailed description of these inversion methods are fully provided in[7]. In this study, we only used the hybrid method with median correction.

5.3.4 Comparison of different Inversion methods. Table 5.1 summarizes the strengths and limitations of the different MTI methods, according to the broad classification outlined above. The main difference between these techniques is how the Green's functions are evaluated. The accurate evaluation of these functions using theoretical equations is complex for non-homogeneous media or media with changing boundary conditions, i.e. due to cracking in concrete. In addition, assumptions are usually made (use of Taylor series, truncation at the first

66 order, etc.) to simplify the problem and reduce the computational time for numerical techniques.

Table 5.1: Comparison between the diﬀerent MTI techniques [94]

Methods Strengths Limitations - Difficult to apply in non-homogeneous environments. - Tedious evaluation of the Green's Absolute - Applied in single event situations. functions for every AE event. - Requires a dense network of AE sensors. - Noise-sensitive. - Require a cluster of events, i.e. cannot - Green's functions can be estimated be applied in single event situations. from a reference event, either - Events in the cluster must have empirically or theoretically. different radiation patterns. Relative - In special cases, the Green's functions - High-fidelity broad-band response. can be eliminated analytically - Extremely sensitive to noise if source (no need to evaluate them). mechanisms of the cluster events - Applied to clusters of AE events. are very similar. - Capitalize on the strengths of both the Absolute and Relative MTI methods. - Compensate for different types of - Require the evaluation of the Green's Hybrid systematic errors in the AE waveforms. functions. - Achieve accurate and robust measure of the Moment Tensor.

67 5.4 MTI toolbox Code Over a decade ago, a moment tensor inversion (MTI) code was implemented to compute source mechanisms from mining-induced seismicity data[7]. The code, named MTI Toolbox, was fairly extensively applied to mining research problems (e.g. Goldbach et al.[84]; Linzer et al.[85]; Miley et al.[86]). Six different MTI methods are coded in the MTI Toolbox: a single event MTI method based on the far-field for- mulation given by Aki and Richards[25]; two relative methods based on Dahm[77] and three hybrid methods developed by Andersen[7]. The MTI Toolbox was used quite extensively to invert mining-induced data recorded by underground triaxial geophones. Sellers et al.[87] used the hybrid option from the MTI Toolbox to quantify the change in fracture mechanisms of AE recorded during a series of uniaxial compression tests, which were performed on quartzite samples. The MTI Toolbox has also been applied in the field of numerical modelling. Lee[88] implemented a moment tensor source in WAVE3D, a finite-difference modelling code designed for simulating elastic wave interactions with excavations and cracks, for different media (Hildyard[89]; Hildyard et al.[90]). Lee’s work is significant since WAVE3D uses an orthogonal, staggered grid which demands orthogonal input geometries for the source and materials. A moment tensor source allows non-orthogonal source geometries to be modelled. The MTI Toolbox code was used to rigorously test and validate the newly implemented moment tensor source code. A set of experiments for concrete by Finck[91] are closest to the case study in this paper and applied the MTI Toolbox hybrid option. Steel fibre reinforced concrete (SFRC) beams were subjected to cyclic three-point loading fatigue tests and the ongoing damage progression and failure studied. SFRC is an interesting material and even though the basic behaviour is understood, there are open questions regarding the mathematical models and failure processes. The interaction between steel fibres and cementitious matrix is of particular interest. It was observed that the early events, which occurred directly above the notch, had high positive isotropic components. Their nodal planes were mostly aligned with the notch indicating opening of the vertical tensile crack. The later events showed decreasing isotropic components

68 and a larger spread of different source types. The majority of events had only small isotropic but significant deviatoric components. It is speculated that these AE events may be mostly caused by fibre pull-out rather than crack opening (Finck[92]).

In this research, the MTI Toolbox code was used to perform absolute, relative and hybrid inversions on AE waveforms collected from the different set of experiments carried on the concrete specimens. The MTI Toolbox uses input data extracted from the recorded AE waveforms to compute a number of source parameters and plot the radiation patterns and corresponding fault-plane solutions. The main purposes behind using this code are: first, the great resemblance that concrete mechanics bear to seismology and mining seismicity albeit at different scales. An illustrative comparison between seismology and AE is presented in Figure 5.8. Second, the great features the code offers that make it applicable to performing inversions on acoustic emission data recorded by networks of uniaxial sensors. A snapshot of the MTI Toolbox interface is shown in Figure 5.7.

5.4.1 MTI Toolbox input parameters The MTI Toolbox reads the required information from one ﬁle generated in MATLAB. The basic input required by the toolbox consists of: the coordinates and orientations of the uniaxial AE sensors in local coordinates, the event location in local coordinates, the amplitude and the polarity of the P-wave. All these parameters are extracted from the AE signals according to the following steps: 1- Deﬁne a voltage threshold to prearrange a P-wave onset time. 2- Select a signal window centered at this onset time. 3- Apply the AIC picker to the signal window to pick the P-wave arrival time. 4- Extract the P-wave amplitude. 5- Extract the polarity of the P-wave: upward (+1) or downward (-1). 6- Use Geiger's method to estimate the source location (spacial and temporal coordinates of the event source).

69 7- Compute the moment M0 from the P-wave amplitudes (Equation 5.8). 8- Generate the input ﬁle from these parameters.

3 Ω0 M0 = 4πρcP R c (5.8) FθΦ where ρ represents the density of the material, Ω0, the P-wave amplitude, cP the P-wave speed in the medium, R the distance between the event source and the recording sensor

c and FθΦ a parameter that takes into consideration the propagation effects between the events source and the recording sensor. The data file read by the MTI Toolbox consists of a number of fields flagged by various tag identifiers (Figure 5.6). GEO: Text string describes a geophone site (in this case an AE sensor). - Site ID: sensor ID. - Site position: coordinates of the AE sensor (xgeo, ygeo, zgeo). - Site orientation : defined by means of direction cosines (dircxn, dircyn, dirczn). EVC: Text string contains event information: event ID and location (xev, yev, zev). DATA: Text string contains event amplitude data. The fields are: - Event ID - Site ID - Component - Phase - Moment (computed using the P-wave amplitude). - Pol (the polarity of the P-wave),

5.4.2 MTI Toolbox ouptput parameters When used for the inversion, the MTI Toolbox outputs many diﬀerent parameters for each event source. Some of the main parameters are summarized in Table 5.2.

In this study , the condition number, k, the scalar moment M0 and the R-ratio are of main interest. The ﬁrst represents an error estimate of the sensitivity of the system to perturbations in the input data. A value of k larger than 100 means the system

70 Figure 5.6: Example of data ﬁle created by MATLAB for input into the MTI Toolbox is poorly conditioned [2]. For all the inversion performed in this work, solutions with k > 100 were rejected. The R-ratio deﬁnes the nature of the moment tensor (Tensile:

71 R > 30; Shear: -30 <= R <= 30; Implosive: R < -30) and represents the ratio of the volumetric to shear components. The scalar moment M0 represents a measure of the intensity of the emission from the source and is computed directly from the moment tensor components mij as follows [7]:

v u 3 u1 X 2 M0 = t m (5.9) 2 ij i,j=1

Table 5.2: Output Parameters of the MTI Toolbox

Parameters: Deﬁnition Condition number k: Indicates sensitivity of system to perturbations in the input data Low values (<50) = well conditioned; high values (> 100) = poorly conditioned. StdError: Standard Error of the estimate

ScalarMo M0: Scalar moment calculated from the moment tensor components %ISO: Isotropic component of full tensor %DC: Double-couple component of deviatoric tensor R-ratio: Deﬁnes the nature of the moment tensor, ratio of volumetric to shear components (Tensile: R > 30; Shear: -30 <= R <= 30; Implosive: R < -30) DevDC: Deviation of the seismic source from the model of pure double- couple. Ratio of the minimum to maximum deviatoric eigen- value Strike, Dip, Rake: Fault plane solution calculated from deviatoric tensor e1, e2, e3: Eigenvalues of the full moment tensor

72 Figure 5.7: Snapshot of the MTI Toolbox interface

73 Figure 5.8: Analogy between Seismology and Acoustic Emission Testing

74 Chapter 6

EXPERIMENTAL INVESTIGATIONS

6.1 Introduction In this chapter we present and discuss the results of the experimental investigations carried out in the laboratory at the University of Delaware in order to apply and study the proposed methodology. Both small and large laboratory experiments were carried out on diﬀerent concrete specimens and diﬀerent moment (absolute, hybrid) tensor inversions were applied on the recorded AE waveforms. All the inversions were performed using the MTI toolbox written by Andersen[7].

6.2 Preliminary Study: Proof of Concept This preliminary study represents a proof-of-concept that aims at evaluating the usefulness of an MTI-based methodology in characterizing AE sources (fracture, cracks, etc.). The idea was to generate artiﬁcial AE sources with known parameters (type, orientation, intensity, etc.) on diﬀerent material specimens and then assess whether the same (or at least very similar) parameters can be estimated from the recorded AE signals.

6.2.1 Experimental Setup Two specimens of identical dimensions, l × b × h= 12 × 6 × 6 in3 were used in the experiment: a normal-weight concrete specimen (Figure 6.1.a) and a UHMW Polyethylene specimen (Figure 6.1.b). The location of the point of application of the artiﬁcial sources (steel ball drop, shear at 90◦ and shear at 45◦) was the same for both specimens. In addition, the same set of coordinates (axis orientations, directions, etc.) was adopted for both specimens. Two types of artiﬁcial sources were

75 applied: a ball drop using a 1 mm diameter steel ball and an ultrasonic normal incidence shear wave transducer (Panametrics V153-SB). The ball drop was used to imitate an explosion-type source and the transducer was used to generate a shear-type source. Ten high-ﬁdelity Glaser/NIST point-contact sensors were used to record the surface displacements induced by the stress wave that propagates through the specimens due to the application of the artiﬁcial sources. Arrival time picking was performed with high accuracy using the AIC-based algorithm and the source locations were estimated using our own algorithm based on Geiger's method.

Figure 6.1: Laboratory specimens: (a) UHMW Polyethylene (b) normal-weight concrete

The inversions were performed using the MTI Toolbox developed by Andersen[7]. The software was selected for this study (1) because of the analogy between seismicity and concrete fracture mechanics (same phenomena at different scales, same MTI assumptions, etc.) and (2) because the toolbox permits the accurate evaluation of the Green's functions which is an important task for any absolute and hybrid MTI approaches. Also, the tool is flexible as it allows different MTI approaches to be tested (absolute, relative, or hybrid) and the resulting residual errors be compared. The input data can be amplitudes or spectral moments, for a mix of uniaxial and triaxial geophones, un- rotated or rotated into the P-SV-SH system. Radiation patterns, fault plane solutions,

76 various source parameters are calculated from the output moment tensors, which can also be rotated as required.

6.2.2 Results and Discussion We used the MTI Toolbox to compute the Moment Tensor for each of the artiﬁcial sources. We also applied a separate program (that is part of the suite of MTI Toolbox software) to generate synthetic (theoretical) data corresponding to the diﬀerent types of applied sources for comparison.

The output of the MTI consists of the six-component moment tensor computed for each of the sources, from which a number of other parameters describing the source can be calculated, e.g. %ISO, the percentage of isotropic (volume change) component of the full tensor; %DEV, the percentage of deviatoric (no volume change) components of the full tensor; %DC, the percentage of pure double-couple contribution to the deviatoric moment tensor, the R-ratio (ratio of volumetric to shear components) and fault-plane solutions (or orientation of the nodal planes of the radiation pattern).

In the case of an explosive source, the percentage of volume change (%ISO) should be close to 100% and have a positive sign, the percentage of shearing (%DEV) should be close to zero, and the nature of the source as described by the R-ratio should be greater than 30. The fault plane solutions of a purely explosive source are not meaningful, since these are computed from the deviatoric portion of the moment tensor, which should be very low. In the case of a shearing source, the volume change percentage should be very low, the percentage of shearing should be high (close to 100%) and the R-ratio should range between -30 and 30. The fault plane solutions are highly signiﬁcant now and should be consistent between the materials, for the same shear source. The source parameters of the theoretical and artiﬁcial sources are given in Table 6.1. The fault plane solutions are best visualised and are shown in Figure 6.2.

77 Table 6.1: Source Contributions From the MTI Inversions[94]

Source Material %ISO %DEV %DC R-ratio Theoretical explosion 99.8 0.2 71.3 96.2 Steel ball drop Concrete 72.2 27.8 50.4 40.6 Steel ball drop UHMW P. 62.8 37.2 8.5 45 Theoretical shear (90◦) 0 100 99.7 -0.5 Shear wave transducer (90◦) Concrete 0 100 86.9 -0.1 Shear wave transducer (90◦) UHMW P. 0.1 99.9 32.7 3.4 Theoretical shear (45◦) 0 100 91.5 1.2 Shear wave transducer (45◦) Concrete -3.4 96.6 91.4 -18.3 Shear wave transducer (45◦) UHMW P. -0.9 99.1 94.1 -10.8

It is convenient to display the radiation pattern described by the moment tensor as a stereographic projection (beach ball plot). These patterns show the changes in P-wave polarity around the source, where shaded areas represent positive swings of the first-motion. Different types of sources have characteristic patterns related to how the wavefield propagates in 3-D away from the source. For an explosive source, the wavefield propagates spherically outwards in 3-D, and first motions in all directions around the source are positive (or ”away” from the source), creating a beach ball plot dominated by the shaded area (a perfect explosion would create a perfectly shaded beach ball plot). Shearing sources are more interesting, since the wavefront propagates in a four-leafed clover pattern. Alternating quadrants exist around the shearing source where the initial motions of the P-arrival will be either compressional (positive) or dilatational (negative). The orientation of the shear plane and direction of slip will determine which the areas of the beach ball plot will be shaded. Figure 6.2 shows that the results obtained for each of the three artificial sources are very similar (theoretical = similar to UHMW Polyethylene = similar to concrete). For the steel ball source (first row of plots), the shaded areas of the beach balls dominate the theoretical (%ISO=99.8) and UHMW Polyethylene (%ISO=62.8) patterns, indicating completely explosive sources. The beach ball for the UHMW Polyethylene

78 specimen shows that the mechanism is dominantly explosive with a smaller deviatoric component in contrast to concrete: this can be explained by the inhomogeneous nature of concrete. For both shear sources, the mechanism determined by MTI is dominated by shearing (%DEV > 95% for all sources) and the fault plane solutions match (to within a few degrees) the orientations of the artiﬁcial sources. The blue line represents the principal nodal plane and shows the orientation of the source with respect to the x-axis (Figure 6.1). In the second row, the orientation is clearly 90◦ and in the third row the orientation is 45◦ both with respect to the x-axis. The sources are both of shear-type as they were applied but with some small variations in angle possibly due to noise and sensor coupling eﬀects in the recorded AE signals.

Figure 6.2: Comparison of radiation patterns and fault plane solutions for the arti- ﬁcial AE sources[94]

79 6.2.3 Conclusions from the preliminary study The results of this preliminary study were satisfactory as we were able to reproduce the parameters of the predeﬁned externally applied sources. The MTI Toolbox code used was able to predict the source mechanisms well, in both the homogeneous (=UHMW) and the non-homogeneous (=concrete) specimens, and despite the source being applied to the top surface, which represents an outer boundary of the sensor network[94]. This proves at the moment that the methodology we propose in this research for the quantitative acoustic emission monitoring of concrete structures has the potential to be applied in the monitoring of critical civil structures such as concrete bridges.

6.3 Case Study 1: Small Scale Concrete Beam The methodology of moment tensor Inversion applied to AE data was successfully implemented in the preliminary study[2]. The results obtained showed a good potential of the methodology for the characterization of sources of acoustic emissions. The study however was conducted on artiﬁcial sources produced on small scale specimens. In order to fully exploit the potential of the methodology we need to apply it to isolated sources (real acoustic emission sources) that are generated within the material when the specimen is subjected to external loads. In this case study, we present and discuss the results of implementing the MTI-based methodology on a small scale concrete beam.

6.3.1 Experimental Setup This case study represents a further proof-of-concept that aims to evaluate the usefulness of the MTI-based methodology in characterizing real AE sources (fracture, cracks, etc.). The experiment consists of loading a notched concrete beam of dimensions 6 × 6 × 21 in3 in a four-point bending conﬁguration (Figure 6.3). The notch was cut at mid-span with a concrete saw on three sides of the beam (Figure 6.4) and had a depth and width of approximately 12 and 4 mm, respectively. This notch serves

80 as a crack initiator so that the beam fails in a controlled manner in the standard ﬂexural Mode 1 protocol . The goal was to produce tensile fracture AE sources. The beam was loaded to failure very slowly to allow the collection of the maximum number of acoustic emission events to best reproduce the cracking pattern. The beam was equipped with 12 high-ﬁdelity Glaser/NIST point-contact sensors mounted on the six sides. The components required to collect AE data along with key characteristics of the measurement system are summarized in Table 3.2.

Figure 6.3: Small scale concrete beam loaded in a four-point bending scenario

Figure 6.4: Sketch of the notched beam

81 6.3.2 Results and Discussion A total of 262 events were obtained from the experiment. The arrival time picking was performed on the recorded signals using the AIC-based algorithm and the source locations were estimated using the algorithm based on Geiger's method. Out of the 262 events obtained, only 71 events were located with accuracy. The plot in Figure 6.5 shows the estimated locations of these events and their associated location uncertainties (shown in form of ellipsoids).

Figure 6.5: AE source location estimates for notched concrete beam experiment. Er- rors are shown in form of principal standard deviations of the location estimate. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively [2]

Out of the 72 located events, 41 were of high enough quality to apply MTI using MTI Toolbox. The events were grouped into three clusters and a hybrid MTI was

82 performed on each. A new feature that was recently added to the MTI Toolbox code speciﬁcally for materials and civil engineering applications is the option to view the fault plane solutions from any orthogonal projection. An example of one of the events shown in Figure 6.5 is presented in Figure 6.6.

Figure 6.6: Representation of the MTI solution for Event 300 using the new feature in the MTI code: views from all three directions convenient for engineering laboratory studies. Blue colour represents tension (movement towards the source) and red compression (movement away from the source) [2].

An analysis of the MT components showed that 47% of the events had a signiﬁcant isotropic component %ISO (either positive or negative) where %ISO > 10% to a maximum of |%ISO| = 31%. The R-value was also computed. This source parameter describes the nature of the source and is the ratio of volumetric to shear components[82]. If R > 30, the event is considered to be dominantly tensile; if −30 ≤ R ≤ 30, the event is dominantly a shear event; if R <−30 the event is dominantly implosive. 20% of the

83 events were dominantly tensile; 7% were dominantly implosive and the remaining 73% were dominated by shearing. Given the experimental layout and applied stress directions, we expect some fractures to form at a high angle (i.e. steep dip) from the notch to the upper surface of the beam near the loading platen. Idealised radiation patterns for such a fracture are shown in Figure 6.7, for views from the top (along the Z-axis) and side (or elevation) (along the Y-axis) of the beam. Note that radiation patterns shown in Figure 6.9 are viewed from the side (elevation view) of the sample. The ﬁrst set (a) shows the full moment tensor i.e. the volumetric and deviatoric components, whereas the second set (b) only shows the DC sliding components of the moment tensor so that the fracture planes are clear. The nodal planes of about 50% of the events were angled a few degrees from the plane of the notch.

Figure 6.7: Radiation pattern for Event 314 viewed from the top (along X-axis) and side (along Y-axis) for a high-angle shearing crack extending upwards from the notch, with downwards sliding on the down-dip side of the fracture (i.e. normal sense of movement). Blue colour represents tension and red compression [2].

84 Even though it was anticipated that a pure ﬂexural crack would produce AE events with high positive isotropic (i.e. opening) components for events on either side of the notch, this was not conﬁrmed. It is speculated that this is due to the heterogeneity of concrete and the resulting complex curved fracture plane as shown in the insert in Figure 6.8.

Figure 6.8: Fault plane solutions for selected AE events (elevation view). Blue colour represents tension and red compression. The volume of the stereographs is proportional to the seismic moment. The insert shows a photo of the complex fracture plane of the specimen [2].

85 Figure 6.9: Radiation patterns for (a) isotropic and deviatoric components and (b)DC components only. Blue colour represents tension and red compression. Stereographs are shown in the XZ plane [2].

86 6.4 Case study 2: Large Scale Concrete Beams Both the results obtained in the preliminary study and the case study of the small concrete beam showed that the moment tensor based methodology was successfully implemented despite in the case of the small concrete beam the results were not very satisfactory because of the large number shear events obtained. The next goal of this research study is to test the methodology on large scale concrete structures. We wanted to further explore the potential and capabilities of the methodology in monitoring failure of concrete materials. To do so, two large scale concrete beams were designed and tested in two different loading scenarios. One beam was designed to fail in flexure and the second one to fail in shear. The aim was to generate different types of cracks (flexural and shear cracks) in order to (1) evaluate the usefulness of the proposed MTI-based methodology in characterizing real AE sources from large scale structures and (2) test the hypothesis defined earlier.

6.4.1 Concrete beam 1: Flexure beam experiment 6.4.1.1 Experimental Setup The experiment consists in loading a large scale concrete beam of dimensions l × b × h = 16 ft × 12 in × 24in a four-point bending configuration (Figure 6.10). The beam was designed to produce tensile AE sources in a controlled manner in the standard flexural Mode 1 protocol (Figure 6.11). A total number of 29#3 stirrups, 2#8 and 4#4 reinforcing steel bars were used to reinforce the beam. Two loading cycles were applied to the beam using a 150 kip hydraulic actuator available in the laboratory at the University of Delaware. First, the beam was loaded slowly from 0 to 25 kip then slowly unloaded. This allows for the collection of the maximum number of acoustic emission events to best reproduce the cracking pattern. The beam was then loaded, in a second cycle, from 0 to 35 kip in order to produce more flexural cracks. The same loading rate was applied in both cycles and no extra loading cycles were applied because enough AE data was collected. We also did not want to load the beam to failure. The AE events collected from this experiment were recorded and

87 analysed separately for each of the two loading cycles. 15 high-ﬁdelity Glaser/NIST point-contact sensors were mounted on four sides of the beam around the mid-span region where most of the ﬂexural cracks are expected to occur (Figure 6.12). The coordinates of the sensors are summarized in Table 6.2.

Figure 6.10: Test setup: ﬂexure beam

6.4.1.2 Results and Discussion Acoustic emission source locations were performed using the location strategy described in section 4.4 where only the best 6 sensors in each event i were used to locate the source in space and time and to compute the corresponding standard deviations,

σ1i, σ2i and σ3i. The same Geiger's method-based algorithm used in both the preliminary study and the case study of the small concrete beam was used for the AE source location in this experiment. For each of the two loading cycles, the located events were plotted on a sketch of the beam using a color coding that shows the occurrence of the

88 Figure 6.11: Sketch of the ﬂexure beam - Elevation View

events in time due to the propagation of the ﬂexural cracks (Figure 6.13). We can clearly see that all the located events occur at the mid-span region where the sensors were mounted and almost no events were located outside of this region. For the 1st loading cycle (Figure 6.13.a), a total number of 674 events were located and only 216 events were located during the 2nd loading cycle (Figure 6.13.b. In fact, we increased the load by only 10 kip in the 2nd cycle, so the 216 recorded events were mostly generated between 25 kip and 35 kip. Also no visual crack extension was observed during the 2nd loading cycle. Only ﬁve major cracks that occurred during the 1st loading cycle were observed.

89 Figure 6.12: Locations of the Glaser/NIST sensors on the ﬂexure beam

Table 6.2: Coordinates of the sensors mounted on The Flexure Beam

Sensor S1 S2 S3 S4 S5 S6 S7 S8 X,[in] 4.75 -8.75 16.75 -13.25 -6 -2.375 5.5 16.3125 Y,[in] -6 -6 -6 -6 -4.1875 -3.4375 3.5 -0.9375 Z,[in] 3.75 -4 -5.4375 10.25 -12 -12 -12 -12

Sensor S9 S10 S11 S12 S13 S14 S15 X,[in] 15.5 21.75 -5.25 -6.25 4.5 21.125 -21.5 Y,[in] 6 6 6 6 6 -2.125 -2.8125 Z,[in] 7.125 -9.25 -6.5 6.625 10.5 12.25 12.375

90 Figure 6.13: AE source location estimates for the ﬂexure beam. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)1st loading cycle and (b) 2nd loading cycle

In order to select the best events located, the standard deviations which represent a measure of the location uncertainties were computed for each event. Any event with a maximum standard deviation σ1 bigger than 5 cm was rejected. This ﬁltering step is necessary for the moment tensor inversion in order to insure more accurate and stable inversions. This ﬁltering process resulted in only 380 good events for the 1st loading cycle and 117 good events for the 2nd loading cycle (Table 6.3). The best located events for each loading cycle are shown with their corresponding error ellipsoids in

91 Figure 6.14. The same color coding was used to show the occurrence in time during fracture. We can observe in Figure 6.14 that the events which occur outside of the sensor array region usually have larger location uncertainties thus bigger ellipsoids.

Table 6.3: Summary of the Events in the Flexure Beam

Loading cycle Total Number of events located Best located events 1st (0 to 25 kip) 674 380 2nd (0 to 35 kip) 216 117

In view of the large number of events located and since there was no crack extension during the second loading cycle (0 to 35 kip), we will only consider the first loading cycle (0 to 25 kip) for the rest of the analysis. 380 events were located with accuracy during this cycle. We performed a clustering operation in order to associate the events located to the cracks observed. The clustering operation resulted in five main clusters with different number of events. Out of these five clusters, we only consider the two clusters which corresponds to the cracks closer to mid-span (Figure 6.16). The first cluster contains 117 events while the second cluster contains 94 events. Absolute and hybrid (with median correction) inversions were performed, using the MTI Toolbox, on each of the clusters. For the first cluster we ended up with only 92 events out of 117 after we discarded all the events with condition numbers k > 100. For the second cluster we also rejected all the events with k > 100 and we ended up with only 80 events out of 95. The radiation patterns of the p-wave using the absolute and relative techniques, for all these events, are presented in Figures 6.17 and 6.18 for the first cluster and Figures 6.19 and 6.20 for the second cluster, respectively. An analysis of these radiation patterns shows a dominance of the color red which means the events are dominantly tensile. In fact this can be seen in both Tables A.2 and A.3. A simple analysis of the R-ratio, for the case of the absolute technique, shows that, for the first cluster, 80 (87%) events out of 92 (100%) events are tensile since R > 30 and the remaining 12 (13%) events

92 Figure 6.14: AE source location estimates for the ﬂexure beam experiment. Errors are shown in form of principal standard deviations of the location estimate. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)1st loading cycle and (b) 2nd loading cycle

93 Figure 6.15: 3D view of the AE source location estimates on the ﬂexure beam. Only the portion of the beam between X=-1m and X=1 m is shown

94 Figure 6.16: Clustering operation for the ﬂexural beam. Cracks at mid-span due to high moment M0 can be observed aligned with the clusters events.

are dominated by shearing. For the case of the hybrid with median correction method, 84 (91%) events are tensile events while the remaining 8 (9%) events are dominated by shear. No implosive events were obtained using both techniques. A similar analysis for the second cluster shows that, for the absolute inversions, 57 (71%) events out of 80 (100%) events were dominantly tensile while the remaining 23 (29%) events are dominated by shearing. For the hybrid inversions, 68 (85%) events are tensile while the remaining 12 (15%) events are dominated by shearing. Similar, to the ﬁrst cluster, no implosive events were obtained. The results of this classiﬁcation is summarized in Table 6.4. We can clearly see the dominance of tensile events in both clusters. A simple comparison between the two inversions techniques; absolute and hybrid with median correction, shows that the hybrid method has improved the results by increasing the number of tensile events for both clusters.

Table 6.4: Classiﬁcation of The Diﬀerent Types of Cracks in The Flexure Beam

Cluster Total N◦ Absolute Method Hybrid Method

N◦ of events Tensile Shear Implosive Tensile Shear Implosive

1 92 (100%) 80 (87%) 12 (13%) 0 (0%) 84 (91%) 8 (9%) 0 (0%)

2 80 (100%) 57 (71%) 23 (29%) 0 (0%) 68 (85%) 12 (15%) 0 (0%)

95 Figure 6.17: Radiation patterns for the events in the first cluster of the flexure beam. Case where the absolute inversion technique was used. From top to bottom and from left to right, the stereographs correspond to the events labeled in the first column of Table A.2. The stereographs are shown in the XZ plane.

96 Figure 6.18: Radiation patterns for the events in the first cluster of the flexure beam. Case where the hybrid inversion technique was used. From top to bottom and from left to right, the stereographs correspond to the events labeled in the first column of Table A.2. The stereographs are shown in the XZ plane.

97 Figure 6.19: Radiation patterns for the events in the second cluster of the ﬂexure beam. Case where the absolute inversion technique was used. From top to bottom and from left to right, the stereographs correspond to the events labeled in the ﬁrst column of Table A.3. The stereographs are shown in the XZ plane.

98 Figure 6.20: Radiation patterns for the events in the second cluster of the ﬂexure beam. Case where the hybrid inversion technique was used. From top to bottom and from left to right, the stereographs correspond to the events labeled in the ﬁrst column of Table A.3. The stereographs are shown in the XZ plane.

99 6.4.2 Concrete beam 2: Shear beam experiment 6.4.2.1 Experimental Setup The experiment consists in loading a second concrete beam of same dimensions l × b × h = 16 ft × 12 in × 24 in in a four-point bending configuration (Figure 6.21). The beam was designed to produce shear cracks in a controlled manner in the standard shear Mode 2 protocol (Figure 6.22). 22#3 stirrups, 4#8 and 4#4 reinforcing steel bars were used to reinforce the beam. The stirrups were placed unevenly in the beam, with larger spacings at one side (right) and smaller spacings at the other side (left)(Figure 6.22). This aims at creating a weak region in the beam where shear cracks can be generated at small loading values without the need to drive the beam to failure. For the case of this beam, eight loading cycles were applied using the same 150 kip hydraulic actuator. In each cycle, the beam was slowly loaded then unloaded to allow for the collection of the maximum numbers of AE events. Compared to the flexure beam, the shear beam required more loading cycles in order to produce pure shear cracks. It was until we applied 85 kip to the beam that shear cracks started to appear. Similarly, 15 high-fidelity Glaser/NIST point-contact sensors mounted on four sides around the weak region of the beam where the stirrups spacing is large and where shear cracks are expected to occur at early stages of loading (Figure 6.23). The coordinates of the sensors are given in Table 6.5.

6.4.2.2 Results and Discussion Similarly to the ﬂexure beam experiment, acoustic emission source locations were performed using the same location strategy where only the best 6 sensors in each event i were used to locate the source in space and time and to compute the corresponding standard deviations, σ1i, σ2i and σ3i. The same Geiger's method-based algorithm was also used for the AE source location in this experiment. For each of the eight loading cycles, the located events were plotted on a sketch of the beam using the same color coding. The location results for all the loading cycles are shown in Figures 6.24, 6.25, 6.26 and 6.27.

100 Figure 6.21: Test setup: shear beam

Figure 6.22: Sketch of the shear beam - elevation view

101 Figure 6.23: Locations of the Glaser/NIST sensors on the shear beam

Table 6.5: Coordinates of the sensors mounted on the shear beam

Sensor S1 S2 S3 S4 S5 S6 S7 S8 X,[in] 8.1875 -16.125 -29.125 12.75 -4 -24 13.25 5.875 Y,[in] -6 -6 -6 -6 -2.4375 3.125 -1.125 3.5 Z,[in] 7 8.125 -3.25 -8.75 -12 -12 -12 -12

Sensor S9 S10 S11 S12 S13 S14 S15 X,[in] 22.5 10.125 -9.5 -15.5 -4.5 7.875 18.5 Y,[in] 6 6 6 6 1.75 1.5 -4.75 Z,[in] -7.25 0.875 -7.3125 4.875 12 12 12

102 Similarly to the case of the ﬂexure beam, we can see that all the located events occur at the region where the sensors are mounted and almost no events were located outside of this region. In order to select the best events located in this beam experiment, the standard deviations were computed for each event. Any event with a maximum standard deviation σ1 bigger than 5 cm was rejected. The results of this ﬁltering process for all the loading cycles are summarized in Table 6.6.

Table 6.6: Summary of The Events in the Shear Beam

Loading cycle Total Number of events located Best located events 1st (0 to 25 kip) 40 20 2nd (0 to 35 kip) 57 29 3st (0 to 45 kip) 40 24 4nd (0 to 55 kip) 116 53 5st (0 to 65 kip) 89 45 6nd (0 to 75 kip) 107 67 7st (0 to 85 kip) 329 198 8nd (0 to 95 kip) 372 207

The located events for all the loading cycles are shown with their corresponding error ellipsoids in Figures 6.28, 6.29, 6.30 and 6.31. The same color coding was used to show the occurrence of events in time during fracture. We can observe that the events which occur outside of the sensor array region have larger location uncertainties thus bigger ellipsoids.

103 Figure 6.24: AE source location estimates for the shear beam. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)1st loading cycle and (b) 2nd loading cycle

104 Figure 6.25: AE source location estimates for the shear beam. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)3rd loading cycle and (b) 4th loading cycle

105 Figure 6.26: AE source location estimates for the shear beam. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)5th loading cycle and (b) 6th loading cycle

106 Figure 6.27: AE source location estimates for the shear beam. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)7rd loading cycle and (b) 8th loading cycle

107 Figure 6.28: AE source location estimates for the shear beam experiment. Errors are shown in form of principal standard deviations of the location estimate. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)1st loading cycle and (b) 2nd loading cycle

108 Figure 6.29: AE source location estimates for the shear beam experiment. Errors are shown in form of principal standard deviations of the location estimate. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)3rd loading cycle and (b) 4th loading cycle

109 Figure 6.30: AE source location estimates for the shear beam experiment. Errors are shown in form of principal standard deviations of the location estimate. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)5th loading cycle and (b) 6th loading cycle

110 Figure 6.31: AE source location estimates for the shear beam experiment. Errors are shown in form of principal standard deviations of the location estimate. The colours of the events are correlated to the time of occurrence with blue and red early and late, respectively (a)7th loading cycle and (b) 8th loading cycle

111 A similar type of analysis was conducted for the shear beam. Out of 8 loading cycles, we only consider the last loading cycle (0 to 95 kip). In fact for the case of this beam, we could not see shear cracks until we loaded the beam with 85 kip. Only one major shear crack was produced during this loading stage and all the other cracks obtained were vertical ﬂexural cracks. In order to produce more shear cracks, we loaded the beam in an extra cycle from 0 to 95 kip. At this stage we could see two major shear cracks as can be seen in Figure 6.27. Since in this experiment, we are only interested in shear cracks, we neglect all the loading cycles where less than one shear crack was observed. In this case, we ended up with only one loading cycle (0 to 95 kip). During this cycle, 207 events were located with accuracy.

Similarly to the case of the flexure beam, we performed a clustering operation in order to associate the recorded events to the cracks observed. The clustering operation resulted in two major clusters (Figure 6.32. The first cluster contains 166 events and the second cluster contains only 32 events. The inversions results showed that for the first cluster, we only ended up with 125 events from a total of 166 after we discarded the events with condition number k > 100. For each of the two clusters, we used the same approach where absolute and hybrid (with median correction) inversions were performed on the events. The results of the inversions are shown in Figures 6.33, 6.34 and Table A.4 for the first cluster and in Figures 6.35, 6.36and Table A.5 for the second cluster.

An analysis of the results of this experiment shows a dominance of shear cracking for both clusters. In the ﬁrst cluster, out of a 125 (100%) number of events, the absolute inversion method produced 2 (2%) tensile events, 29 (23%) implosive events and the remaining 94(75%) where dominated by shearing. The hybrid method with median correction produced 1 (0.6%) tensile events, 38 (30.4%) implosive events and 86 (69%) shear events. We can see that the hybrid method reduced the number of tensile events by 1% compared to the absolute method. It, however, increased the number of

112 implosive events by 7.4% and only reduced the number of shear events by 8%. For the second cycle, both inversion techniques produced the same number of tensile events 1 (3%), implosive events 5 (16%) and shear events 26 (81%) out of 32 (100%) total number of events. For both cycles, the minimum shear percentage obtained was 68%. A summary of these results is given in Table 6.7.

Figure 6.32: Clustering operation for the shear beam. Cracks at the weak region where the stirrups spacing is large. Cracks that are due to high shear V can be observed aligned with the clusters

Table 6.7: Classiﬁcation of The Diﬀerent Types of Cracks in The Shear Beam

Cluster Total N◦ Absolute Method Hybrid Method

N◦ of events Tensile Shear Implosive Tensile Shear Implosive

1 125 (100%) 2 (2%) 94 (75%) 29 (23%) 1 (0.6%) 86 (69%) 38 (30.4%)

2 14 (100%) 0 (0%) 13 (93%) 1 (7%) 0 (3%) 14 (100%) 0 (0%)

113 Figure 6.33: Radiation patterns for the events in the ﬁrst cluster of the shear beam. Case where the absolute inversion technique was used. From top to bottom and from left to right, the stereographs correspond to the events labeled in the ﬁrst column of Table A.4. The stereographs are shown in the XZ plane.

114 Figure 6.34: Radiation patterns for the events in the ﬁrst cluster of the shear beam. Case where the hybrid inversion technique was used. From top to bottom and from left to right, the stereographs correspond to the events labeled in the ﬁrst column of Table A.4. The stereographs are shown in the XZ plane.

Figure 6.35: Radiation patterns for the events in the second cluster of the shear beam. Case where the absolute inversion technique was used. From top to bottom and from left to right, the stereographs correspond to the events labeled in the ﬁrst column of Table A.5. The stereographs are shown in the XZ plane.

115 Figure 6.36: Radiation patterns for the events in the second cluster of the shear beam. Case where the hybrid inversion technique was used. From top to bottom and from left to right, the stereographs correspond to the events labeled in the ﬁrst column of Table A.5. The stereographs are shown in the XZ plane.

116 6.4.3 Comparison between the two beams This section aims at comparing the results obtained from the experiments on the two large beams in order to see the main differences and draw some conclusions of this case study. To do so, the first cluster from each beam was considered in this section (Figure 6.37). The first cluster from the flexure beam had 92 events and the first cluster from the shear beam had 125 events. Since the hybrid inversion method with median correction produced better results (more tensile events for the flexure beam and more shear events for the shear beam) than the absolute method, we will only focus on the results obtained by this method on each of the clusters selected.

Figure 6.37: The ﬁrst cluster from each beam was selected (a) First cluster from the ﬂexure beam (b) First cluster from the shear beam

When used for the inversion, the MTI Toolbox outputs many parameters (fault plane solution, %ISO,%Dev , condition number k, etc.) that characterize the source. Details about all these parameters can be found in[7]. Some parameters are of importance in this study: (1) the R-ratio which describes the nature (tensile, shear, implosive) of the event and is obtained by dividing the volumetric components to the shear components of the moment tensor (2) the scalar moment M0 which represents a measure of the energy released from the source where the AE event occurred and is computed directly

117 from the moment tensor components. The %ISO parameter which represents the percentage isotropic in the moment tensor and the condition number k which indicates the sensitivity of the system of equations to be inverted to perturbations in the input data. An analysis of these parameters for the two clusters selected is given in Figure 6.38 through 6.45. The color coding shown in some ﬁgures correlates the events to their occurrence in time during fracture with blue and red early and late, respectively.

Figure 6.38: R-ratio variation for the ﬁrst cluster from the ﬂexure beam

In Figure 6.38, which corresponds to the values of the R-ratio in the cluster from the flexure beam, we can clearly see that almost all the events lie in the tensile region where the R-ratio is larger than 30. This tensile dominance satisfies well our expectations that only flexure cracks are generated from the flexure beam. The presence of some shear events is speculated to the heterogeneity of concrete and the presence of noise in the recorded AE data since the moment tensor inversion techniques are sensitive to the noise. Figure 6.39, which corresponds to the values of the R-ratio in the cluster from the shear beam, shows a different nature for the recorded events as almost all of them lie in the region where shear is dominating thus the majority of the events recorded from the shear beam are shear events. This result also satisfies well our expectations

118 Figure 6.39: R-ratio variation for the ﬁrst cluster from the shear beam

that only pure shear cracks are produced from the shear beam even though at the first loading cycles we only recorded events from crack openings due to mode 1 fracture. A frequency plot for the R-values from both clusters is given in Figure 6.40. We can conclude that the methodology proposed was able to differentiate between the two different types of cracks.

A similar analysis was performed on the values of the scalar moment M0 obtained from the two clusters. The results are shown in Figures 6.41, 6.42 and 6.43. The plots do not show a clear difference between flexure and shear cracks in terms of scalar moment. This means that the two types of cracks produce comparable amounts of energy when they propagate. This might not be always the case but at least in this experiment we obtained almost similar behaviour of the scalar moment M0 from the two different beams. A comparative analysis was also conducted on the two beams by comparing the %ISO parameter and the condition number k to see whether we can see any difference or not. The Figures 6.44 and 6.45 show the results of this comparison, respectively. For the case of the %ISO parameter, we clearly see a difference between

119 Figure 6.40: Frequency plots for the R-ratio for the two beams. Flexure Beam (top plot) and Shear beam (bottom plot) the two beams, the values of %ISO are higher for the ﬂexure beam and this makes total sense since the %ISO represents the isotropic components in the moment tensor. For the case of the condition number, k, we only wanted to compare the two beams to see which beam has more stable inversion solutions but we did not see a remarkable diﬀerence and ’k’ showed similar behaviour for the two beams.

120 Figure 6.41: Logarithmic scale plot of the scalar moment M0 of the events in the ﬁrst cluster of the Flexure beam

Figure 6.42: Logarithmic scale plot of the scalar moment M0 of the events in the ﬁrst cluster of the shear beam.

121 Figure 6.43: Frequency plots of the scalar moment M0 for the two beams. Flexure Beam (top plot) and Shear beam (bottom plot)

122 Figure 6.44: Frequency plots of the %ISO for the two beams. Flexure Beam (top plot) and Shear beam (bottom plot)

123 Figure 6.45: Frequency plots of the %ISO for the two beams. Flexure Beam (top plot) and Shear beam (bottom plot)

124 Chapter 7

CONCLUSIONS

In this chapter, a brief overview of this PhD research is given and the principal ﬁndings and conclusions reached at diﬀerent points during this study are summarized.

7.1 Research Objective The aim of this thesis was to investigate the feasibility to employ moment tensor inversion (MTI) for the quantitative acoustic emission monitoring of fatigue crack initiation and propagation in concrete materials. The goal was to monitor fracture mechanisms in concrete structures in real time. An hypothesis was identified that MTI techniques applied to AE data can produce pertinent information about cracks such as location, type, orientation, and intensity, and thus can distinguish flexural from shear and mixed-mode cracks. In line with this hypothesis, the questions this research aimed to answer were (1) how are shear and flexural cracks different using MTI techniques? and (2) What characterizes each of the two?. To test the hypothesis identified and answer the questions above, a methodology that capitalizes on the strengths of both the AE technique and the MTI technique was proposed and applied according to which AE waveforms recorded from concrete fracture were inverted using a MTI code, called MTI Toolbox, in order to study the sources of fracture and infer their properties.

7.2 Principal findings and conclusions A set of experiments were performed in order to apply and study the proposed methodology. Both small and large laboratory experiments were carried out on different concrete specimen and different moment (absolute, hybrid) tensor inversions were applied on the recorded AE waveforms. First, a preliminary study was conducted on

125 two small specimens (UHMW Polyethylene normal-weight concrete) in order to evaluate the usefulness of the proposed methodology in characterizing artificial AE sources with known parameters (type, orientation, intensity, etc.) and assess whether the same (or at least very similar) parameters can be estimated from the recorded AE signals. The results of this preliminary study were satisfactory as it was possible to reproduce the parameters of the predefined externally applied sources. For pure explosive sources generated using a steel ball drop at the top surface of each specimen, the R-ratio values obtained were 40.6% and 45% for the concrete specimen and UHMW Polyethylene specimen,respectively. It was concluded, after inversion of the AE waves, that both events generated are tensile dominated despite the source being applied to the top surface, which represents an outer boundary of the sensor network. For all the cases of external shear sources generated using a Panametrics actuator, it was concluded that the sources obtained from the inversion of the recorded waves using the MTI Toolbox are dominated by shearing. These findings proved that the proposed methodology was in fact useful in characterizing artificial AE sources. Second, a case study was conducted on a small scale concrete beam (6 × 6 × 21 in3) with a predefined notch at mid-span. The aim of the experiment was to produce tensile fracture AE sources. The results of this case study showed that only 7% out of a total of 71 events were dominantly tensile. Most of the events located (73%) were dominated by shearing. It was speculated that this is due to the heterogeneity of concrete. The methodology however showed good potential in characterizing the different types of cracks. Finally, a third case study was conducted on two large-scale concrete beams, one designed to fail in flexure and the second designed to fail in shear. The objective of this case study was to evaluate the ability of the methodology to characterize and monitor fracture in large- scale concrete structures. The results obtained from the experiment conducted on the flexure beam showed that up to 81% of the events resulting from one vertical flexural crack were dominantly tensile which satisfies our expectations that only pure tensile cracks are generated from this beam experiment. For the case of the shear beam, it was shown that up to 73% of the events resulting from a shear crack are dominated by

126 shearing. These results also satisfied our expectations that the events obtained from the shear fracture are dominantly shear. The findings of this case study proved that the proposed methodology is, in fact, very useful for characterizing different types of cracks in large-scale concrete structures. A comparison between the results obtained for the two beams showed a clear tensile dominate for the flexure beam and a clear shear dominance for the shear beam. It was also observed, throughout this comparison, that the scalar moment M0 varied in the same manner for the flexural and shear cracks. This might not be always the case because of the versatility, variability and complexity of concrete materials. To test the efficiency of the proposed methodology, more research studies on different types and geometries of concrete materials are needed.

7.3 Future Work The work presented in this PhD was a research effort to contribute to the quest for a more clear understanding of the complex mechanics of concrete. The MTI- based methodology proposed here, proved efficient for the characterization of cracks in small and large scale concrete structures and satisfactory results were obtained. The complexities that concrete materials entail (variability, versatility, heterogeneity, etc.), however, still represent a challenge for exploiting the full potential of the methodology. To address these challenges, future work will be conducted in order to improve the source location accuracy by (1) developing more robust p-wave onset time picking techniques and (2) developing better source location strategies. Also, since, the recorded waveforms are very rich in information about the sources of AE emissions, it will be very beneficial to invert the whole waveforms instead of only inverting the p-wave amplitudes. This will produce more robust MTI results.

Future work will also include developing an analysis tool (a friendly user software) that incorporates all the steps involved in the proposed methodology (AE source location, moment tensor inversion) in one single package that can characterize cracks in real

127 time and perform preliminary results during experiments. The beneﬁt of this self- developed software is that the user can track the variation of the AE source parameters

(location, scalar moment M0,%ISO, R-ratio, etc) during crack propagation. Also, a more appropriate visualization of the MTI solutions will be developed which will be more convenient than the actual visualization using the stereographes.

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136 Appendix A

APPROXIMATE CONVERSION TO AND FROM SI UNITS

Table A.1: *SI Conversion Factors input unit multiply by output unit / input unit multiply by output unit LENGTH inches, in 25.4 millimeters, mm 0.039 inches, in feet, ft 0.305 meters, m 3.28 feet, ft yards, yd 0.914 meters, m 1.09 yards, yd miles, mi 1.61 kilometers, km 0.621 miles, mi AREA square inches, in2 645.2 millimeters squared, mm2 0.0016 square inches, in2 square feet, ft2 0.093 meters squared, 32 10.764 square feet, ft2 square yards, yd2 0.0836 meters squared, m2 1.196 square yards, yd2 acres, ac 0.405 hectares, ha 2.47 acres, ac square miles, mi2 2.59 kilometers squared, km2 0.386 square miles, mi2 VOLUME cubic feet, ft3 0.028 meters cubed, m3 35.315 cubic feet, ft3 cubic yards, yd3 0.765 meters cubed, m3 1.308 cubic yards, yd3 MASS ounces, oz 28.35 grams, g 0.035 ounces, oz pounds, lb 0.454 kilograms, kg 2.205 pounds, lb

*SI is the symbol for the International System of Measurement

137 Table A.2: MTI Results for Cluster N◦1 Events in The Flexure Beam

Absolute Method Hybrid Method

EvID k M0 %ISO %Dev R k M0 %ISO %Dev R 9 40.2 1.29E+14 10.4 0 28.8 40.2 5.24E+13 10.4 0.1 28.4 22 97.8 4.31E+13 30.8 0.3 41.9 97.8 1.51E+13 49.1 0 53.6 25 64.5 4.29E+14 -0.2 0.1 -5.7 64.5 9.84E+13 0 0.1 2.1 76 18 5.71E+13 38.5 0.1 47.5 18 1.77E+13 46.1 0 53.1 81 50.9 5.63E+13 28.9 0 43 50.9 1.74E+13 30.8 0.1 43.6 94 22 4.6E+13 55.4 0.2 54.8 22 1.79E+13 51.5 0.1 54.1 175 20 2.43E+14 13.6 0.4 29.8 20 1.04E+14 12 0.3 28.4 179 13.1 7.41E+13 44 0 51.8 13.1 2.46E+13 44 0.1 50.7 296 33.3 1.02E+14 31.4 0.2 42.8 33.3 3.25E+13 35.1 0.3 44.4 298 33.3 7.14E+13 40.3 0 49.5 33.3 2.51E+13 41.9 0 50.8 331 20.8 1.29E+14 30.9 0.2 42.2 20.8 3.8E+13 38.2 0.2 46.2 347 18.4 6.17E+13 29.3 0.2 41.5 18.4 2.25E+13 32.4 0.3 42.8 382 95.1 9.96E+13 14.9 0.2 31.4 95.1 3.77E+13 19.9 0.1 36.2 386 32.5 8.18E+13 26.6 0.2 39.7 32.5 2.56E+13 30.2 0.2 41.8 388 29.8 1.06E+14 22 0 38.3 29.8 3.28E+13 31.6 0 44.6 415 91.5 1.26E+14 39 0.1 48.2 91.5 4.53E+13 39.8 0.1 48.3 436 74.8 2.94E+13 52.8 0.2 53.7 74.8 1.01E+13 70.2 0.2 62.5 461 25.7 1.46E+14 21.9 0.1 37.8 25.7 4.69E+13 24.4 0.1 39.4 478 42.9 5.98E+13 55.9 0.3 54.8 42.9 2.2E+13 56.7 0.3 55 517 19.7 8.97E+13 84.1 0.3 71.1 19.7 2.91E+13 83.4 0.4 70.5 519 26 8.9E+13 57.3 0.3 55.4 26 3.32E+13 58.4 0.4 55.7 524 18.5 9.77E+13 65.9 0.3 59.8 18.5 3.91E+13 61 0.4 57.1 Continued on next page

138 Table A.2 – continued from previous page Absolute Method Hybrid Method

EvID k M0 %ISO %Dev R k M0 %ISO %Dev R 528 18 1.21E+14 27.5 0.1 41.3 18 4.59E+13 19.9 0 37.3 536 18.8 4.26E+13 64.5 0 61.9 18.8 1.6E+13 65 0 61.9 549 23.3 6.6E+13 47.1 0.1 51.4 23.3 2.56E+13 43.8 0 50.8 582 34.2 1.17E+14 41 0.3 47.3 34.2 3.96E+13 43.7 0.3 48.6 595 43.1 2E+14 20.2 0.3 35.2 43.1 8.56E+13 18.1 0.3 33.7 603 14.3 5.27E+14 16.2 0.4 31.9 14.3 2.11E+14 15.3 0.4 31.1 619 17.2 9.69E+13 29.1 0.2 41.1 17.2 2.99E+13 31.6 0.2 42.5 679 53 9.01E+13 45.7 0.3 49.8 53 3.37E+13 47 0.3 50.5 680 24 9.33E+13 71.4 0.1 64.1 24 3.28E+13 66.2 0.1 61.6 705 96.3 1.02E+14 51.3 0.3 52.5 96.3 3.41E+13 53.1 0.2 53.7 718 17.2 9.65E+13 71.3 0.3 62.8 17.2 3.44E+13 60.2 0 59.8 722 48.6 5.07E+13 57.7 0.4 55.4 48.6 1.96E+13 56.7 0.4 54.9 726 16.7 1.49E+14 42 0.4 47.4 16.7 4.9E+13 44.8 0.4 48.9 754 23.4 1.65E+14 26.3 0.1 41.1 23.4 7.13E+13 21.8 0 38.8 842 16.4 1.6E+14 24.3 0.1 39.2 16.4 6.71E+13 13.9 0 32.7 846 14 8.57E+13 74.9 0.1 66.3 14 2.73E+13 79.7 0.3 68.2 850 48.6 1.09E+14 31.8 0.1 43.7 48.6 3.74E+13 33.7 0.1 44.6 851 9.2 3.84E+14 70.4 0.1 63.8 9.2 1.44E+14 63.1 0.2 59.4 853 26.4 7.01E+13 31.9 0.2 43.2 26.4 2.2E+13 43.3 0.1 50.2 867 30.1 7.69E+13 51.2 0.4 52.1 30.1 2.66E+13 55.3 0.3 54.3 868 38.7 1.01E+14 48.8 0 54.1 38.7 3.6E+13 46.8 0 52.9 875 22.5 4.7E+14 80.6 0 70.9 22.5 1.66E+14 91 0.2 77.9 925 60.7 1.56E+14 25.9 0.3 39.1 60.7 3.44E+13 44.4 0.3 49.2 936 27.5 5.46E+14 13.6 0.2 30.2 27.5 1.36E+14 49.2 0.1 53.1 Continued on next page

139 Table A.2 – continued from previous page Absolute Method Hybrid Method

EvID k M0 %ISO %Dev R k M0 %ISO %Dev R 940 38.7 1.27E+14 45.3 0.1 51.3 38.7 4.33E+13 43.5 0.1 49.9 1044 26.5 8.71E+13 49.4 0 54.3 26.5 2.98E+13 48.5 0.1 53.1 1132 18.3 1.32E+14 48.3 0.3 50.8 18.3 4.25E+13 56 0.4 54.6 1563 10.7 7.9E+13 63.4 0.2 59 10.7 2.91E+13 62.1 0.2 58.6 1569 32.7 5.26E+13 52.4 0.2 53.4 32.7 1.9E+13 54 0.3 53.8 1573 22.3 5.55E+13 49.5 0.1 52.8 22.3 1.99E+13 50.5 0.1 53.5 1629 15.6 1.19E+14 80.4 0.1 70.2 15.6 4.52E+13 72.4 0 65.8 1637 35.3 5.8E+13 16.6 0 35 35.3 2.08E+13 23.4 0 39.3 1641 23.9 8.55E+13 53.5 0.3 53.4 23.9 3.34E+13 51.9 0.4 52.5 1667 27.7 9.33E+13 23.8 0.1 39.4 27.7 3.47E+13 24.1 0.1 39.3 1682 13.7 2.76E+14 44.8 0.2 50 13.7 9.86E+13 47.7 0 53.2 1826 97.9 1.32E+14 43 0 50.6 97.9 3.01E+13 61 0 59.6 1911 44.8 1.02E+14 40.4 0.3 46.8 44.8 3.12E+13 57.8 0.3 55.7 1976 31.8 1.82E+14 10.5 0 28.8 31.8 4.93E+13 16.2 0 34.8 2146 28.7 8.74E+13 12.5 0 31.5 28.7 3.04E+13 15 0 33 2172 17.7 2.57E+14 26 0.4 38.7 17.7 8.53E+13 28.1 0.4 39.9 2208 17 9.04E+13 47.4 0 52.8 17 2.72E+13 58.1 0 58.8 2312 68.4 2E+14 32.6 0 45.5 68.4 7.46E+13 30.6 0 44.7 2334 70.3 1.12E+14 13 0.2 30 70.3 4.6E+13 10.7 0.1 28 2400 29.1 6.08E+13 46.6 0.1 51.7 29.1 2.48E+13 43 0.2 49.1 2410 59.5 9.82E+13 19 0.2 34.9 59.5 3.07E+13 25 0.2 39.1 2780 29.4 1E+14 31.9 0.1 44.3 29.4 3.38E+13 35.3 0 47.1 2784 73.6 1.56E+14 24.6 0.2 38.5 73.6 6.03E+13 28.8 0.2 41.4 2821 35.9 6.17E+13 39 0.1 47.5 35.9 1.95E+13 54 0.1 54.9 Continued on next page

140 Table A.2 – continued from previous page Absolute Method Hybrid Method

EvID k M0 %ISO %Dev R k M0 %ISO %Dev R 2971 31.5 1.47E+14 10.6 0.1 28 31.5 5.5E+13 11.2 0.2 28.3 3011 49.5 2.81E+14 15.7 0.2 32 49.5 1.08E+14 17.3 0.2 33.6 3224 39.8 6.63E+13 44.2 0.3 48.8 39.8 2.78E+13 42.6 0.4 47.7 3323 12.2 1.41E+14 40 0 49.1 12.2 4.62E+13 38.9 0.1 48.1 3378 18.4 1.10E+15 16.2 0.3 32.1 18.4 4.75E+14 15.9 0.3 31.9 3380 51 1.19E+14 10.3 0 28.5 51 3.73E+13 14.2 0 32.3 3561 39.7 9.99E+13 26.5 0.2 39.7 39.7 3.16E+13 32.8 0.2 43.5 3610 65.4 1.04E+14 21.4 0.2 36.4 65.4 2.74E+13 40.8 0.1 48.6 3780 21.8 9.76E+13 32.9 0.2 43.8 21.8 3.51E+13 34.2 0.2 44.3 3799 25.8 1.36E+14 11.6 0.1 29.5 25.8 4.99E+13 11.8 0.1 29.9 3812 21.8 1.44E+14 10.6 0.1 28.3 21.8 4.08E+13 18.9 0.2 35.1 3833 35.1 1.06E+14 17.4 0 35.2 35.1 3.68E+13 16.3 0 35 3839 28.7 1.16E+14 41.1 0.4 47 28.7 3.83E+13 34.6 0.3 43.7 3888 13.2 5.48E+14 8.8 0.1 26.5 13.2 1.26E+14 12.3 0 30.5 3894 41.5 1.37E+14 4.1 0 19.8 41.5 5.57E+13 1.7 0 13.9 3904 49.6 3.3E+14 16.7 0.3 32.5 49.6 7.4E+13 21.8 0.3 36.1 3932 16 1.46E+14 39.5 0.1 48.1 16 4.95E+13 41.7 0 50.3 3951 23.1 1.36E+14 68.6 0.2 62 23.1 4.25E+13 85.1 0 74.3 4013 34.9 6.49E+13 36.8 0 48.1 34.9 2.55E+13 27.9 0 42.5 4144 55.6 1.08E+14 17.8 0.1 34.6 55.6 3.45E+13 21.9 0.1 37.8 4158 32.5 1.94E+14 18.8 0.2 34.8 32.5 5.75E+13 22.6 0.4 36.5 4233 25.6 6.07E+13 8.4 0.2 25.1 25.6 2.13E+13 10.5 0.1 27.9

141 Table A.3: MTI Results for Cluster N◦2 Events in The Flexure Beam

Absolute Method Hybrid Method

EvID k M0 %ISO %Dev R k M0 %ISO %Dev R 243 31.5 1.53E+14 2 0 15 31.5 5.29E+13 2.7 0 16.8 387 35.5 8.45E+13 23.3 0.2 37.6 35.5 3.36E+13 26.5 0.1 40.6 485 18.6 7.65E+13 21.9 0.1 38 18.6 2.63E+13 36.2 0.3 44.9 571 31.8 1.56E+14 4.2 0.1 19.4 31.8 5.59E+13 5.9 0.1 22.4 693 26.6 9.75E+13 15.5 0.3 31.4 26.6 3.02E+13 24.3 0.3 37.7 694 35.1 1.03E+14 19.1 0.2 35 35.1 3.26E+13 29.7 0.2 41.9 704 35.3 1.73E+14 5.3 0.2 20.6 35.3 5.05E+13 9.4 0.2 26 910 33.5 2.17E+14 15.5 0.2 32.3 33.5 6.69E+13 23.2 0.2 38 923 46.5 1.45E+14 72.7 0 65.8 46.5 5.3E+13 74.6 0 67.5 1002 33.8 3.79E+14 21.9 0 39 33.8 1.37E+14 31.7 0.1 43.9 1009 61.3 2.7E+14 56.7 0.3 55.4 61.3 9.76E+13 75.6 0.1 67.3 1047 33.5 1.53E+14 17.7 0.3 33.2 33.5 5.26E+13 20.3 0.4 34.9 1061 53.9 3.08E+14 31.1 0.2 42.5 53.9 1.18E+14 34.8 0.3 44.2 1072 13.2 1.47E+14 35.7 0.2 45.4 13.2 5.06E+13 46.5 0.1 51.2 1111 40.5 1.58E+15 17.6 0.2 33.5 40.5 5.7E+14 17.9 0.2 33.9 1112 39.4 5.07E+13 47.5 0.1 51.7 39.4 2E+13 50.1 0.2 52.2 1184 46.6 1.49E+14 60.7 0.1 58.6 46.6 4.65E+13 76 0.2 66 1491 55.7 9.03E+13 29.8 0 44.1 55.7 3.24E+13 36.8 0.1 46.5 1537 35.7 8.58E+13 46.7 0 52.9 35.7 2.87E+13 63.9 0.2 59.7 1570 69 1.71E+14 3.4 0.1 17.9 69 5.33E+13 6 0 22.9 1582 25.7 1.05E+14 22.2 0.2 37.4 25.7 3.48E+13 21.7 0.1 37.8 1626 98.9 9.49E+13 51.5 0.2 53.4 98.9 3.42E+13 51.3 0.2 53.2 Continued on next page

142 Table A.3 – continued from previous page Absolute Method Hybrid Method

EvID k M0 %ISO %Dev R k M0 %ISO %Dev R 1652 55 1.12E+14 30.1 0.2 42 55 3.86E+13 34.3 0 45.9 1688 39.8 1.12E+14 30.9 0.1 43.4 39.8 4.55E+13 28.5 0 43.4 1712 21.4 1.02E+14 20.6 0 38.4 21.4 3.47E+13 28.6 0 43.1 1817 31.1 8.97E+13 75 0.3 65.2 31.1 3.48E+13 70.5 0.2 63.2 1867 30.1 1.07E+14 10.7 0.1 28.5 30.1 3.22E+13 25.3 0.2 38.9 1909 18.5 1.15E+14 11.1 0.2 28.3 18.5 3.91E+13 14.8 0.1 32 1912 27.6 6.89E+14 12.4 0.2 29.4 27.6 2.06E+14 20 0.3 35.1 1941 16.2 9.91E+13 73.8 0.2 65.2 16.2 5.19E+13 56.3 0.2 55.7 1952 24 1.73E+14 31.8 0.2 43 24 5.82E+13 36.6 0 47.5 2026 15.3 2.66E+14 40.7 0 49.8 15.3 9.01E+13 46.9 0.1 52.3 2139 14.5 1.32E+14 10.3 0 29.1 14.5 4.55E+13 12.7 0 31.4 2152 26.1 9.89E+13 1.6 0.2 12.3 26.1 3.41E+13 2.6 0.2 15.3 2173 32.6 1.39E+14 10.9 0.1 28.9 32.6 4.54E+13 28.3 0.1 41.7 2192 43.7 1.51E+14 43.2 0.3 48.3 43.7 6.06E+13 35.5 0 46.4 2214 31.1 1.37E+14 23 0.2 37.9 31.1 5.05E+13 25.2 0.2 39.1 2236 70.5 1.64E+14 12.1 0.1 30 70.5 4.35E+13 31.7 0.2 42.6 2255 40.2 7.77E+13 28.2 0 43.3 40.2 2.18E+13 49.8 0.3 52 2259 34.5 7.21E+13 82.6 0.3 70.3 34.5 2.5E+13 91.6 0.3 78 2323 17.9 1.19E+14 35.7 0.1 46.2 17.9 3.34E+13 60.3 0.1 58.4 2424 16.3 1.06E+14 41.8 0.1 49.7 16.3 3.51E+13 47 0.3 50.5 2596 84.1 5.02E+14 2.4 0.3 14.5 84.1 1.37E+14 6.5 0.2 22.4 2620 23.8 1.71E+14 8.7 0.3 25 23.8 4.47E+13 14.4 0.2 31.4 2774 27.1 9.45E+13 33.8 0.3 43.4 27.1 3.24E+13 29.8 0.2 41.8 2810 10.2 5.75E+13 71.3 0.2 63.3 10.2 1.97E+13 77.1 0 68.7 Continued on next page

143 Table A.3 – continued from previous page Absolute Method Hybrid Method

EvID k M0 %ISO %Dev R k M0 %ISO %Dev R 2836 11.9 1.01E+14 26.9 0.2 40.2 11.9 3.22E+13 40.5 0.1 48.5 2842 26.4 1.04E+14 14.9 0.4 30.8 26.4 3.34E+13 16.1 0.3 31.8 2874 20.1 1.2E+14 25.7 0.2 39.1 20.1 3.65E+13 30.3 0.2 42 2944 11.9 1.33E+14 17.8 0 36.1 11.9 3.21E+13 35.8 0 46.9 2945 21.6 9.79E+13 92.7 0 81.1 21.6 3.94E+13 75.8 0 68 3002 22.7 1.56E+14 4.2 0 20.2 22.7 5.03E+13 7.6 0.1 24.9 3025 23.2 8.55E+13 8 0 26.5 23.2 2.88E+13 12.9 0 31.8 3074 9.8 8.27E+13 42.1 0 50.9 9.8 2.3E+13 52.9 0.3 53.2 3107 14.6 2.31E+14 1.2 0 11.8 14.6 7.51E+13 2 0 15 3190 19.1 2.01E+14 66.5 0.1 62.2 19.1 8.11E+13 62.4 0 61.1 3246 89.5 8.79E+13 63.7 0.1 59.9 89.5 3.38E+13 67.8 0.2 61.9 3289 34.3 2.27E+14 0.7 0.2 8.8 34.3 6.41E+13 2 0.3 13.4 3327 63.4 7.34E+13 12.9 0.3 29.3 63.4 2.2E+13 20.2 0.4 34.9 3361 25 7.46E+13 45.8 0 52.4 25 2.46E+13 54.7 0 57.2 3370 29.8 1.67E+14 45.2 0.2 49.8 29.8 7.48E+13 40.4 0 49.1 3400 13.6 1.36E+14 20.4 0 38.3 13.6 4.62E+13 29.8 0 43.6 3429 44.9 1.24E+14 28.6 0.2 41.3 44.9 4.82E+13 26.1 0.2 40 3431 15.2 1.64E+14 32.6 0 45.9 15.2 5.3E+13 41.6 0 50.1 3499 64.2 9.52E+13 49.1 0.4 51 64.2 2.57E+13 60.2 0.2 57.9 3527 32.9 8.26E+13 62.1 0.1 59.7 32.9 3.08E+13 79.7 0 70.4 3594 41.9 1.06E+14 71.2 0 65.7 41.9 3.86E+13 71.3 0 65.6 3753 35 2.09E+14 3.7 0.2 17.8 35 6.24E+13 6.5 0.2 22.5 3762 35.1 2.44E+14 4.5 0.1 20.2 35.1 7.61E+13 6.6 0.1 23.6 3790 37.9 8.94E+13 34.7 0 46.8 37.9 3.54E+13 40.6 0.4 46.7 Continued on next page

144 Table A.3 – continued from previous page Absolute Method Hybrid Method

EvID k M0 %ISO %Dev R k M0 %ISO %Dev R 3852 32.9 1.47E+14 10.4 0.1 28.2 32.9 4.29E+13 19.5 0.1 36.2 3853 29.8 7.51E+13 58.7 0.3 56.3 29.8 2.28E+13 72.3 0.1 65.2 3975 17.3 1.11E+14 8.7 0 26.7 17.3 3.81E+13 13 0.1 30.7 4041 28.5 5.29E+13 48.3 0.2 51.3 28.5 1.68E+13 57.2 0.4 55.2 4043 22.4 1.02E+14 4.7 0.1 20.3 22.4 3.26E+13 9.5 0.1 27.2 4070 28 1.06E+14 13.6 0.2 30.4 28 3.97E+13 16.1 0.1 33 4142 35.8 1.12E+14 33.3 0.1 44.4 35.8 3.47E+13 55.8 0.2 55.5 4203 74.4 1.93E+14 24.5 0 40.5 74.4 5.64E+13 33.4 0.2 43.9 4212 42.4 5.29E+13 24.7 0 40.6 42.4 2.03E+13 20.4 0.1 36.4 4304 33.7 8.74E+13 25.6 0.1 39.8 33.7 2.27E+13 56.8 0 57.9

145 Table A.4: MTI Solutions for Cluster N◦1 Events in The Shear Beam

Absolute Method Hybrid Method

EvID k M0 %ISO %Dev R k M0 %ISO %Dev R 67 57.1 2.11E+14 1.7 0.3 12.4 57.1 5.82E+13 2.2 0.3 13.8 72 31.1 2.1E+14 -13.2 0.1 -30.9 31.1 3.69E+13 -18.5 0 -36.8 90 23.5 5.63E+13 -18.7 0.3 -34.3 23.5 2.13E+13 -21.3 0.1 -37.5 105 86.3 4.38E+14 -1.4 0.1 -12.2 86.3 9.69E+13 -3.1 0 -17.5 144 14.4 1.7E+14 -0.6 0.3 -8.2 14.4 3.37E+13 -4.5 0.3 -19 177 60.6 1.44E+14 16.1 0.2 32.8 60.6 3.27E+13 12.9 0 31.2 188 33.1 9.55E+13 0 0 -0.7 33.1 2.72E+13 -0.7 0.1 -8.9 241 38.6 1.24E+14 0.1 0.2 3.8 38.6 4.25E+13 -1.5 0.4 -11.7 299 23.9 1.08E+14 -6.6 0.4 -22 23.9 3.81E+13 -4.5 0.3 -18.9 306 13.1 3.32E+14 -5 0 -21.2 13.1 7.59E+13 -7.9 0 -25.9 316 18.1 2.38E+14 -4.2 0.1 -19.6 18.1 7.33E+13 -8.2 0 -26.4 338 17.5 2.01E+14 -1.7 0.1 -13.2 17.5 4.2E+13 -4.3 0.2 -19.2 411 28.4 2.06E+14 -8.4 0.1 -25.8 28.4 3.99E+13 -6.5 0 -24.3 439 18.7 2.07E+14 -0.1 0 -4.6 18.7 3.49E+13 -10.3 0.1 -28.2 459 22.6 1.42E+14 -15.5 0.1 -33 22.6 3.24E+13 -25.3 0.2 -39 479 75.6 4.41E+14 5.6 0.3 20.9 75.6 1.66E+14 6.1 0.2 21.8 495 69.7 1.71E+14 0 0.2 0 69.7 2.6E+13 -0.9 0.4 -9.5 513 19.2 2.35E+14 -2 0 -14.3 19.2 5.06E+13 -4.1 0.2 -18.8 575 50.2 4.94E+14 -21.4 0.2 -36.5 50.2 1.57E+14 -28.3 0.3 -40.2 580 9.8 2.03E+14 -8.8 0 -26.7 9.8 4.15E+13 -9.6 0 -28.3 647 50.8 1.41E+14 -18.2 0 -36.1 50.8 4.16E+13 -23 0 -39.5 658 22 5.63E+14 0 0.1 -3 22 1.16E+14 -0.5 0.1 -7.9 Continued on next page

146 Table A.4 – continued from previous page Absolute Method Hybrid Method

EvID k M0 %ISO %Dev R k M0 %ISO %Dev R 681 17.7 1.42E+14 -15.7 0 -34 17.7 2.63E+13 -18.4 0.1 -35.5 693 19.8 1.75E+14 -8 0.2 -24.7 19.8 2.67E+13 -3.6 0.1 -18.1 721 63.5 1.46E+14 0 0.3 -0.1 63.5 3.41E+13 -0.6 0.3 -8.1 741 29.5 2.05E+14 -9.7 0.2 -26.8 29.5 5.25E+13 -3.8 0 -19.1 744 20.6 9.92E+13 0.1 0.3 4.3 20.6 2.97E+13 0 0.3 2.5 748 85.8 4.61E+13 -23.8 0.2 -38 85.8 2.12E+13 -12.2 0.2 -29.1 755 34.1 4.54E+14 -10.5 0 -28.8 34.1 8.3E+13 -19.8 0.3 -34.8 772 34.9 1.08E+14 -0.9 0.2 -9.9 34.9 2.5E+13 -2.5 0.2 -15 785 60.4 1.22E+14 -0.8 0.3 -9.2 60.4 2.47E+13 -2.5 0.3 -14.8 821 37.4 5.71E+14 -6.6 0.3 -22.3 37.4 1.53E+14 -18.3 0.4 -33.5 826 36.1 1.13E+14 -2.8 0.2 -15.8 36.1 3.75E+13 -5.4 0.2 -21 835 97.2 6.36E+14 -1.2 0.4 -10.5 97.2 1.97E+14 -0.3 0.3 -6.3 846 52.3 6.14E+14 -0.7 0 -9.7 52.3 2.91E+14 -3.5 0.1 -18.2 862 69.9 1.49E+14 0 0.3 -0.1 69.9 2.39E+13 -0.8 0.2 -9.4 871 48 1.77E+14 2.6 0 16.6 48 4.7E+13 1.3 0 12.1 880 14.7 2.81E+14 -0.4 0.2 -6.6 14.7 6.48E+13 -1.7 0.3 -12.5 985 25.1 1.11E+14 5.9 0.2 21.4 25.1 2.71E+13 3.5 0.2 17.6 987 30.5 4.1E+14 -1.8 0 -13.9 30.5 6.34E+13 -1.7 0 -13.7 988 73.9 1.94E+15 -30.6 0.1 -43 73.9 3.69E+14 -22.9 0.1 -38.4 996 37.4 1.75E+14 -5.3 0 -22 37.4 6.45E+13 0 0.2 1.6 1006 21.7 1.49E+14 0.4 0.1 7.2 21.7 3.19E+13 0 0.2 -2.3 1032 16.2 1.9E+14 -21.2 0.2 -36.7 16.2 3.96E+13 -21.1 0 -38.7 1039 72.9 3.9E+14 6.3 0.2 22.2 72.9 4.71E+13 6.5 0.3 22 1145 58.2 1.75E+14 -1.3 0.2 -11.4 58.2 4.49E+13 -3.3 0.2 -17.2 Continued on next page

147 Table A.4 – continued from previous page Absolute Method Hybrid Method

EvID k M0 %ISO %Dev R k M0 %ISO %Dev R 1215 60.2 1.41E+14 0 0.2 -1.7 60.2 3.36E+13 -0.1 0.2 -4.5 1234 85.2 1.81E+14 -1 0 -10.8 85.2 5.79E+13 -15 0.3 -31 1272 21 1.67E+14 -10.5 0.1 -28.5 21 3.19E+13 -16.7 0 -35 1280 43.8 1.94E+14 14.9 0.3 31 43.8 4.2E+13 6.1 0 23.1 1294 16.6 2.34E+14 -3.3 0 -18.4 16.6 4.42E+13 -5.7 0 -22.4 1323 64.1 4.95E+14 -29.1 0.4 -40.5 64.1 1.87E+14 -25.6 0.4 -38.3 1337 44.5 2.55E+14 -10.6 0 -28.9 44.5 5.34E+13 -9.8 0.3 -26.3 1338 19.7 1.71E+14 -3.5 0.1 -17.9 19.7 2.61E+13 -6.8 0.2 -23.3 1345 17.6 1.3E+14 0.2 0.3 4.6 17.6 4.05E+13 1.6 0.4 11.9 1353 27 2.56E+14 -18 0.4 -33.3 27 5.39E+13 -14.6 0.3 -30.7 1356 33.4 2.66E+14 1.8 0.4 12.8 33.4 7.32E+13 5 0.2 20 1423 82.7 4.52E+14 4.6 0.2 19.3 82.7 7.82E+13 5.3 0 22 1467 29.9 1.73E+14 -1.3 0 -12.2 29.9 2.62E+13 -7.1 0.1 -24 1469 16.6 1.46E+14 -2.2 0.1 -14.6 16.6 5.3E+13 -1.1 0.1 -10.8 1482 58.3 1.49E+15 -1.3 0.1 -12.1 58.3 4.84E+14 -3.1 0 -17.7 1530 29 1.65E+14 5.6 0.2 21.1 29 3.64E+13 9.5 0.3 25.9 1718 33.6 1.92E+14 0 0.3 0.9 33.6 4.71E+13 0.5 0.4 7.5 1774 27.3 2.29E+14 -6.2 0.3 -21.8 27.3 2.78E+13 -16.8 0.1 -33.6 1790 39.3 9.81E+13 -6.7 0.3 -22.4 39.3 3.87E+13 -0.2 0.1 -5.7 1902 11.2 2.06E+14 -4.8 0.2 -19.7 11.2 3.6E+13 -8 0.2 -24.5 1913 26.3 1.57E+14 -0.9 0 -10.4 26.3 3.44E+13 -1.2 0.1 -11.6 1967 35.1 4.93E+14 -12.1 0.2 -28.9 35.1 6.4E+13 -14 0.3 -30.3 1987 42.1 1.92E+14 -1.1 0.1 -10.7 42.1 4.36E+13 -4.3 0.1 -19.7 2032 80.5 1.7E+14 5.7 0.3 20.9 80.5 4.67E+13 5.6 0.4 20.5 Continued on next page

148 Table A.4 – continued from previous page Absolute Method Hybrid Method

EvID k M0 %ISO %Dev R k M0 %ISO %Dev R 2195 98.7 2.2E+14 -42.5 0.1 -49.9 98.7 5.34E+13 -51.5 0.1 -54.1 2217 74.5 8.58E+13 -5.5 0.3 -20.8 74.5 3.12E+13 -9.2 0.2 -25.9 2269 82.5 1.62E+14 -42.2 0.2 -48.9 82.5 4.72E+13 -48.2 0 -53.9 2307 15.6 4.11E+14 -13.5 0.1 -31.2 15.6 6.75E+13 -34.6 0.1 -45.2 2340 16.4 1.39E+14 -15.4 0.2 -32 16.4 2.86E+13 -20.4 0.1 -36.9 2499 24.9 2.33E+14 -13.4 0.2 -30.4 24.9 5.5E+13 -12.6 0 -31 2546 46.2 8.46E+14 -11.9 0 -30.5 46.2 2.59E+14 -11 0 -29.3 2596 24.1 2.21E+14 -7.4 0 -25.2 24.1 5.48E+13 -9.8 0 -28.5 2682 81.4 1.33E+15 2 0 14.8 81.4 2.81E+14 1.7 0 13.9 2690 88 1.44E+15 2.2 0 15.5 88 2.86E+14 -0.3 0 -6.3 2706 23.2 3.28E+14 0.7 0 9 23.2 8.07E+13 0 0.1 -2 2888 30.5 5.39E+14 -1.7 0.2 -12.9 30.5 6.38E+13 -2 0 -14.4 2961 44 6.63E+13 -0.4 0.2 -6.5 44 1.9E+13 -2.2 0.1 -14.6 2962 22.7 7.82E+13 -25.2 0.1 -39.7 22.7 3.48E+13 -9.7 0 -28 2964 18.8 9.52E+13 0.1 0 4.6 18.8 2.82E+13 0.2 0.2 4.7 3041 16.5 2.68E+14 -6.4 0.2 -22.3 16.5 5.33E+13 -9.2 0.2 -26.3 3096 79.6 1.2E+14 0.2 0.1 5.6 79.6 3.16E+13 2.1 0.2 13.8 3109 48.8 2.23E+14 3.2 0.3 16.3 48.8 6.74E+13 3.9 0.3 17.8 3110 60.1 9.61E+13 -5.9 0.2 -21.6 60.1 1.96E+13 -4.5 0.3 -19.2 3141 28.8 1.45E+14 -1.9 0.1 -13.7 28.8 3.11E+13 -4.5 0 -20.6 3158 35.4 7.79E+13 0.5 0 7.9 35.4 1.68E+13 -4.6 0.1 -20.1 3161 29.5 1.12E+14 -7.6 0.2 -24.2 29.5 3.52E+13 -9.6 0.2 -26.8 3179 56.1 1.78E+14 -34.5 0.1 -45 56.1 6.44E+13 -31.9 0.2 -43.2 3211 20.2 9.15E+13 -1.8 0.1 -13.3 20.2 2.33E+13 -2.3 0 -15.8 Continued on next page

149 Table A.4 – continued from previous page Absolute Method Hybrid Method

EvID k M0 %ISO %Dev R k M0 %ISO %Dev R 3217 30.3 9.9E+13 -40 0.3 -46.9 30.3 3.28E+13 -25.3 0.2 -39.5 3268 32.3 1.42E+14 -9 0 -27.5 32.3 4.06E+13 -14.1 0 -32.7 3336 32.1 2.36E+14 -10.6 0 -28.9 32.1 3.23E+13 -15.2 0.3 -31.4 3381 23.6 1.45E+14 -8.9 0.1 -26.6 23.6 3.5E+13 -8.8 0 -27.4 3413 38.6 1.42E+14 -21.5 0.1 -37.4 38.6 4.25E+13 -19.1 0.1 -35.5 3495 41.1 8.11E+13 -49.6 0.2 -52 41.1 2.41E+13 -28.2 0 -42.8 3637 17.7 1.02E+14 -10.2 0 -29 17.7 3.13E+13 -9.2 0 -27.3 3650 86.3 2.02E+14 -23.5 0.1 -38.4 86.3 6.92E+13 -22.2 0.2 -37 3664 14.5 6.95E+13 0 0 -3.6 14.5 1.71E+13 0 0.2 0.8 3667 31.8 8.64E+13 3.7 0 18.9 31.8 2.07E+13 1.5 0.2 11.8 3676 99.3 6.81E+14 3.3 0 18.1 99.3 2.22E+14 0.4 0 7.5 3712 33.1 3.86E+13 0 0.3 1.8 33.1 1.28E+13 -4 0 -19.5 3715 50.7 7.14E+14 3.9 0 19.5 50.7 1.23E+14 1.9 0 14.4 3738 27.6 1.32E+14 -29.7 0 -43.4 27.6 3.73E+13 -27.6 0 -42.7 3747 69 8.06E+13 0 0.2 1.7 69 2.06E+13 -0.5 0.3 -7 3776 20.6 8.46E+13 -4.9 0.2 -20.2 20.6 1.77E+13 -4.8 0 -21.2 3790 35.8 1.71E+14 -10.7 0.1 -28.7 35.8 3.02E+13 -16.4 0 -34.6 3792 86.3 4.1E+14 0 0 1 86.3 1.57E+14 1.1 0.1 10.8 3858 22.8 8.63E+13 -9 0.3 -25.2 22.8 3.1E+13 -13.5 0.1 -30.9 3880 28.6 2.19E+14 -14.9 0.2 -31.4 28.6 3.68E+13 -17.6 0.1 -34.6 3891 99.8 2.45E+14 7.9 0.2 24.2 99.8 3.61E+13 8.9 0.2 25.8 3937 18 4.88E+13 -18.4 0.2 -34.3 18 1.8E+13 -20.6 0 -37.6 3968 56.3 3.5E+14 -16.6 0.2 -33 56.3 7.22E+13 -13.5 0.1 -31.2 3984 32.1 3.06E+14 -20.1 0.2 -35.6 32.1 1.1E+14 -19.7 0.2 -35.4 Continued on next page

150 Table A.4 – continued from previous page Absolute Method Hybrid Method

EvID k M0 %ISO %Dev R k M0 %ISO %Dev R 4023 23 2.85E+14 -1.4 0 -12.5 23 5.37E+13 -1.9 0.1 -13.9 4041 27.3 6.18E+13 -7.1 0.2 -23.6 27.3 1.25E+13 -1.5 0.1 -12.6 4085 56.2 8.34E+13 0 0.1 -1.9 56.2 1.56E+13 -7.3 0.1 -24.3 4101 23.8 6.89E+13 -5.7 0.3 -21.1 23.8 1.76E+13 -16.3 0.3 -32.1 4116 18.2 8.97E+13 -23.8 0.1 -38.5 18.2 1.51E+13 -46.7 0.2 -50.6 4144 23.6 1.64E+14 -1.6 0 -13.7 23.6 2.56E+13 -17.1 0 -35.6 4148 36.7 1.88E+14 -0.9 0.1 -10.2 36.7 5.04E+13 -1.6 0 -13.2

151 Table A.5: MTI Solutions for Cluster N◦2 Events in The Shear Beam

Absolute Method Hybrid Method

EvID k M0 %ISO %Dev R k M0 %ISO %Dev R 205 9.9 9.86E+13 -4.3 0.3 -18.5 9.9 3.87E+13 -6.8 0.4 -22.3 795 22.9 1.49E+14 -7.9 0.1 -24.7 22.9 6.12E+13 -2.7 0.1 -16.1 1752 39.8 1.45E+14 -0.5 0.2 -7.7 39.8 5.39E+13 -1.2 0.2 -10.7 2172 48.8 1.37E+14 -0.6 0.3 -7.8 48.8 5.11E+13 0 0.4 -2.7 2212 84.5 2.52E+14 6.1 0 23.1 84.5 8.95E+13 5.4 0 22.1 2215 52.5 3.6E+14 -2.3 0.3 -14.1 52.5 1.23E+14 -0.3 0.3 -5.9 2469 50.4 4.07E+14 3.1 0.1 17.2 50.4 1.01E+14 0.7 0 9.4 2655 73.5 1.22E+14 -5.4 0.2 -20.6 73.5 4.99E+13 0 0.2 -2.1 2832 20.5 2.65E+14 -11.4 0.2 -28.2 20.5 6.42E+13 -0.5 0 -7.8 3030 15.3 1.15E+14 -0.3 0.4 -5.5 15.3 4.2E+13 -0.2 0.3 -5.2 3649 65.7 1.92E+14 -0.7 0.2 -8.8 65.7 6.42E+13 -0.7 0.2 -8.9 3702 89 1.53E+14 -15.4 0.1 -33 89 3.61E+13 -9.2 0.3 -25.4 3726 66.9 1.79E+14 0 0.1 1.7 66.9 4.57E+13 -1.3 0.1 -11.8 3908 17.6 1.56E+14 -0.3 0.1 -6.5 17.6 7.07E+13 -0.2 0 -5.7

152