UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Shear modulus and damping properties of sands from cyclic self-boring pressuremeter tests Murthy, R. Thandava 1992

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata


831-ubc_1992_spring_murthy_r_thandava.pdf [ 2.5MB ]
JSON: 831-1.0050508.json
JSON-LD: 831-1.0050508-ld.json
RDF/XML (Pretty): 831-1.0050508-rdf.xml
RDF/JSON: 831-1.0050508-rdf.json
Turtle: 831-1.0050508-turtle.txt
N-Triples: 831-1.0050508-rdf-ntriples.txt
Original Record: 831-1.0050508-source.json
Full Text

Full Text

SHEAR MODULUS AND DAMPING PROPERTIES OF SANDS FROM CYCLIC SELF-BORING PRESSUREMETER TESTS  By  R.THANDAVA MURTHY M.Sc(Engg), I.LSc., Bangalore, India, 1990  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CIVIL ENGINEERING  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA October, 1992  © R.Thandava Murthy,  1992  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  Department of Civil Engineering The University of British Columbia Vancouver, Canada Date1 --  11  ABSTRACT  The thesis considers the problem of assessment of shear modulus and damping properties of cohesionless soils using the self-boring pressuremeter. The self-boring pressuremeter test, which is widely acknowledged as the closest approach to undisturbed in-situ testing, is very frequently used to obtain values of shear modulus in deformation calculations. However, damping calculations from the SBPMT have been rarely attempted. It is understood that both the shear modulus and damping appear to be complex functions of many variables, as a result of which there has been a wide range of values reported in literature making it difficult to choose appropriate values for a particular problem. This thesis presents a study of the influence of various factors such as stress and strain levels, creep, equipment effects and testing procedure on the shear modulus and damping of sands using the SBPMT. The importance of the standardisation of testing procedure and interpretation methods is discussed. The mathematical models that could be used to calculate damping, assuming a visco-elastic model, from the unload-reload loops are presented.  The values of shear modulus were found to depend highly on the testing procedure. Any amount of unloading seemed to yield reasonable unload-reload moduli provided the Wroth (1982) criterion for elastic unloading is adhered to.  However, installation disturbance  affected the obtained moduli in the initial region of the pressure-expansion curve. Comparison of the shear modulus profiles with reference profiles of the modulus from seismic cone penetration tests showed reasonable agreement provided the dominant  111  equipment effects are acknowledged. It was found that reasonable modulus reduction curves can be obtained irrespective of the stress level. Creep seems to have a major effect on the shear modulus.  It appears that cavity strain/minute during the holding phase before  unloading has to be kept extremely low if reasonable results are to be obtained. Interpretation methods are semi-empirical involving elaborate correction procedures. The use of an average stress seems to provide good results when loops are carried out at the similar strains. Equipment effects and calibration of the equipment were the most important factors affecting the results at this stage of the SBPM research.  Damping was found to be affected highly by strain level and creep. No significant effect of stress level on damping was observed.  The intermediate range of rates of inflation or  frequency of loading used in this investigation did not seem to affect damping results. It was observed that average damping curves could be obtained over a strain range for any depth. The equipment effect was the most dominant factor affecting damping as in the case of the shear modulus. Understanding the limitations of the visco-elastic model, it was observed that the model could provide a good calculation technique for damping.  Both the shear modulus and damping seem to be fairly consistent with the reference results from the SCPT and other published results suggesting that the SBPMT could become a popular test to obtain these properties.  V  TABLE OF CONTENTS  ABSTRACT  .  ii  LIST OF TABLES  ix  LIST OF FIGURES  ix  LIST OF SYMBOLS  .xi  ACKNOWLEDGEMENTS  xiii  CHAPTER 1  1  INTRODUCTION  1  1.1. Objectives and Scope of Thesis  1  1.2 Thesis Layout  3  CHAPTER2  4  DYNAMIC CHARACTERISTICS OF COHESIONLESS SOILS  4  2.1 Introduction  4  2.2 ShearModulus  5  2.2.1 Effect of Stress and Strain Levels  8  2.2.2 Effect of Degree of Unloading  14  2.2.3 Effect of h estimation  17  2.2.4 Effectof creep  18  2.2.5 Effect of Disturbance and Anisotropy  18  2.2.6 Effect of Equipment  19  2.3 Damping  20  vi 2.3.1 Complex Oscillator and Viscoelastic Material  22  2.3.2. Oscillator and Stress-Strain Loops  25  CHAPTER 3 EQUIPMENT, CALIBRATION AN]) TEST PROCEDURES  29 29  3.1 Introduction  29  3.2 Details of SBPM Design  30  3.2.1 System Overview  30  3.2.2 Instrumentation  30  3.2.3 Membrane and Lantern Characteristics  32  3.2.4 Jetting System  36  3.3 Calibration of the equipment  38  3.3.1 Strain arms calibration  38  3.3.2 Pressure Transducer calibration  39  3.3.3 Compliance calibration  39  3.3.4 Flow rate and mud pressure calibration  39  3.4 Testing Procedure  40  CHAPTER4  41  TESTING PROGRAMME AND GEOLOGICAL AND GEOTECHNICAL CHARACTERISTICS OF SITE  41  4.1 Introduction  41  vii 4.2 Geology of Lower Mainland  .41  4.3 LaingBridgeSite  43  4.3.1  43  Site Description  4.4 Testing Programme  46  CHAPTER 5  54  SHEAR MODULUS  54  5.1 Introduction  54  5.2 Effect of Various Factors on Pressuremeter Modulus  60  5.2.1 Effect of Stress Level  60  5.2.2 Effect of Strain Level  83  5.2.3 EffectofUnloading  90  5.2.4 Effect of Creep  91  5.2.5 Effect of Equipment  99  5.2.6 Theoretical Models Applied to UBC Data  100 ModulusReductionCurve  100 Gm from the SBPM  104  CHAPTER6  121  DAMPING  121  6.1 Introduction  121  6.2 Visco-Elastic Model and Stress Strain Loops -  125  viii 6.2.lResults  .126 Effect of Confining Pressure and Stress History  126 EffectofStrainLevel  132 Effect of Creep and Repeated Unloading  139 Effect of Equipment  143  6.3 Complex Oscillator and Visco-Elastic Material  145  CHAPTER7  152  CONCLUSIONS  152  ShearModulus  152  Damping  154  BIBLIOGRAPHY  155  APPENDIXA  161  APPENDIX B  178  APPENDIX C  181  BIOGRAPHICAL INFORMATION  186  ix LIST OF FIGURES  Figure 2.1  Variation of shear modulus with shear strain for sands (after Seed & Idriss, 1970)  Figure 2.2  7  Chart for determination of Gm from the measured G* value (after Byrne et al. ,1990)  16  Figure 2.3  Stress-Strain curve for cyclic loading of soil  26  Figure 3.1  Self-boring pressuremeter system overview  .31  Figure 3.2  Self-boring pressuremeter electronics overview  33  Figure 3.3  Lantern designs (after Campanella et al., 1990)  .35  Figure 3.4  Jetting systems (after Campanella et at, 1990)  37  Figure 4.1  Laing Bridge  42  Figure 4.2  Geological cross-section of the Fraser delta  -  South site location  (after Blunden, 1975) Figure 4.3  CPT Sounding (C1VL577 Class  44 -  1991)  45  Figure 4.4.a Grain size distribution, Laing Bridge samples  47  Figure 4.4.b Profile of friction angle  4 7  Figure 4.5  SPT log, Laing Bridge  48  Figure 4.6  Profiles of shear velocities and shear modulus, Laing Bridge  49  Figure 4.7  SBPM sounding locations, Laing Bridge  50  Figure 4.8  SBPM sounding characteristics, Laing Bridge  .51  Figure 4.9  SBPM sounding locations, Laing Bridge  52  x Figure 5.1  Typical SBPM pressure-expansion cue. 55  Figure 5.2  Unload-reload modulus from a typical loop  57  Figure 5.3  Smoothed SBPM pressure-expansion curve  58  Figure 5.4  Comparison of smmoothened and unsmoothened unload-reload loops  59  Figure 5.5  Stress state after pressuremeter loading  Figure 5.6  Variation of unload-reload modulus with effective cavity pressure (SBPO8 sounding, Laing Bridge)  Figure 5.7  62  63  Variation of unload-reload modulus with effective cavity pressure (SBP13 sounding, Laing Bridge)  64  Figure 5.8  Effect of assumed radius of influence on average modulus  65  Figure 5.9  Gur vs. rave’ for 8.6m depth, Laing Bridge  66  Figure 5.10  Gur vs. Loop strain and GurC vs. Loop strain at 7. im depth, Laing Bridge  Figure 5.11  GurC  vs. Depth for SBPO6 sounding,  Laing Bridge Figure 5.12  78  Pressure-Expansion curve at 9.3m depth (SBPO6 sounding), Lainridge  Figure 5.15  77  GuY vs. Depth for SBP1 1 sounding, Laing Bridge  Figure 5.14  76  GurC vs. Depth for SBPO8 sounding, Laing Bridge  Figure 5.13  68  SBPM pressure-expansion curve with Hughes(1977) curve fit  80 81  xi Figure 5.16  Gur’  vs. Shear strain at 5.2m depth, Laing Bridge  84  Figure 5.17  Gur’  vs. Shear strain at 7. im depth, Laing Bridge  85  Figure 5.18  GurC  vs. Shear strain at 10.3m depth, Laing Bridge  86  Figure 5.19  GurC  vs. Shear strain at 11 .5m depth, Laing Bridge  87  Figure 5.20  Gur’  vs. Shear strain at 13.9m depth, Laing Bridge  88  Figure 5.21  Change in  Figure 5.22  Multi-cycle pressure-expansion curves  94  Figure 5.23  Smoothed loops from multi-cycle tests  95  Figure 5.24  Unload strain (AB) vs. Time and Loop strain (BC) vs. Time  vs. Time  (SBP13 sounding), Laing Bridge Figure 5.25  Unload-reload modulus vs. number of ioops  Figure 5.26  Modulus reduction curve from proposed model at 5.2m depth, LaingBridge  Figure 5.27  106  Modulus reduction curve from proposed model at 11 .5m depth, 107  Profile of G ’ vs. depth 0 (SBPO6 sounding-Bellotti et al., 1989, procedure), Laing Bridge  Figure 5.30  110  Profile of G ’ vs. depth 0 (SBPO8 sounding-Bellotti et aL, 1989, procedure), Laing Bridge  Figure 5.31  97  Modulus reduction curve from proposed model at 7. im depth,  Laing Bridge Figure 5.29  96  105  LaingBridge Figure 5.28  93  Profile of  GOthP  vs. depth  111  xli  (SBP1 1 sounding-Bellotti et aL, 1989, procedure), Laing Bdge. 112 Figure 5.32  Profile of G ’ vs. depth 0 (SBPO6 sounding-Byrne et at, 1990, procedure), Laing Bridge  Figure 5.33  Normalised modulus reduction curve (SBPO6 sounding), LaingBridge  Figure 5.34  116  Normalised modulus reduction curve (SBPO8 sounding), LaingBridge  Figure 5.35  114  117  Normalised modulus reduction curve (SBP11 sounding), LaingBridge  118  Figure 6. l.a Spring-Frictioimodel  122  Figure 6. l.b Stress-Strainloopforfrictionmodel  122  Figure 6.2  Spring-mass-dashpot system and free vibration of a viscously damped system  Figure 6.3  Damping vs. Single amplitude loop strain (SBPO6 sounding), Laing Bridge  Figure 6.4  127  Damping vs. Single amplitude loop strain (SBPO8 sounding), Laing Bridge  Figure 6.5  124  128  Damping vs. Single amplitude loop strain (SBP1 1 sounding), LaingBridge  Figure 6.6  Determination of damping from model 1 with raw data  Figure 6.7  Typical smoothed loop for the determination of damping frommodell  129 130  131  xlii  Figure 6.8  Average damping vs. single amplitude loop strain curve (SBPO6 sounding), Laing Bridge  Figure 6.9  134  Average damping vs. single amplitude loop strain curve (SBPO8 sounding), Laing Bridge  Figure 6.10  135  Average damping vs. single amplitude ioop strain curve (SBP1 1 sounding), Laing Bridge  136  Figure 6.11 .a Damping values from SBPO6, SBPO8 and SBP1 1 soundings, LaingBridge Figure 6.11 .b  Comparison of the average damping curves with Seed & Idriss (1970) and Idriss (1990) damping curves  Figure 6.12  138  Comparison of average damping curves with damping vs. shear strain data (SBPO6 sounding), Laing Bridge  Figure 6.13  137  140  Comparison of average damping curves with damping vs. shear strain data (SBPO8 sounding), Laing Bridge  141  Figure 6.14 Comparison of average damping curves with damping vs. shear strain data (SBP1 1 sounding), Laing Bridge  142  Figure 6.15 Damping vs. Number of loops for multi-cycle test  144  Figure 6.16 Comparison of model 2 loop with loop from raw data  150  xiv LIST OF SYMBOLS  CPT SBPM SBPMT SCPT 100 A  D e G Gur G 0 GurC Gave GOSbP  n  I  H  a 1 ‘ave rave’  P 0 ’ 0 p r R R V W aa  13 ave 7  Cone Penetration Test Self-boring Pressuremeter Self-boring Pressuremeter Test Seismic Cone Penetration Test Area of the unload-reload ioop Area of the right triangle between strain axis from origin to point of loop in unload-reload ioop Damping Ratio Void Ratio Shear Modulus Unload-reload Modulus Unload-reload Modulus Shear Modulus at Insitu Stress Level Small Strain Shear Modulus Unload-reload Modulus corrected for Insitu Stress Average Shear Modulus Shear Modulus at Insitu Stress Level from SBPM Transfer Function Magnitude of Transfer Function Modulus Exponent Atmospheric Pressure Small Change in Cavity Pressure Average Cavity Stress Average Effective Cavity Stress Total Cavity Pressure Insitu Horizontal Total Pressure Insitu Horizontal Effective Stress Cavity Radius Initial Cavity Radius Radius of Influence Radius of the Plastic Zone Shear Wave Velocity (mis) Elastic Strain Energy Anisotropy Factor Damping Ratio Cavity Shear Strain Average Shear Strain Elastic Threshold Shear Strain Small Change in Strain Strain Cavity Strain = &ir 0  xv iy) p m 0 0 h o  1 Tave  Tf  Energy Loss Co-efficient Soil Density Mean Normal Stress Mean Normal Effective Stress Insitu Horizontal Effective Stress Insitu Overburden Effective Stress Effective Confining Pressure Effective Radial Stress Effective Tangential Stress Shear Stress Average Shear Strain Failure Shear Strain Friction Angle Plane-Strain Friction Angle Damping Capacity Angular Frequency (rad/sec)  xvi ACKNOWLEDGEMENTS  I am grateful for the financial support provided to me during my two years stay by Dr.R.G.Campanella. In addition I wish to thank Drs.Campanella, Byrne, Fannin and Hughes for the scholarly guidance throughout the MASc program and their critical review of the contents of the thesis. Thanks are due to technicians Harald Schremp and Scott Jackson for their untiring help during the testing program. Discussions with Dr.Pat Stewart and his great source of ideas for the Damping chapter are gratefully acknowledged. Thanks are also due to Renato da Cunha who helped out in the field  .  I wish to thank my wife Mamatha for her untiring help and  understanding throughout the thesis.  1  CHAPTER 1 INTRODUCTION 1.1. Objectives and Scope of Thesis  Soil dynamics problems require that the stiffness properties of the soil, and the attenuation properties, be determined accurately for use in the numerous analytical tools that have been developed for their solution(Seed &Idriss, 1970; Mok et al. 1988;Idriss, 1990). These properties are stress and strain level dependent and will have to be evaluated over a wide range of strain levels (Seed and Idriss 1970; Seed et al. 1986; Sun et al.1988;) especially since free field strain levels during an earthquake exceed 0.01 percent. Numerous attempts have been made in this direction both in-situ and in the laboratory, resulting in the development of a large database. However, the shortcomings of laboratory testing in terms of recreating the natural environment of the soil specimen and complex boundary conditions surrounding most in-situ devices especially in granular media make it necessary that an in-situ tool be developed that  can overcome these shortcomings to a great extent. A very attractive step in this direction would be the pressuremeter. The basis of a pressuremeter test is the expansion of a long, right circular cylinder in the ground, which in theory is a simple boundary value problem  and offers well defined and well controlled stress and strain conditions. Another attraction would be the possibility of evaluating strength and deformation characteristics over a range of stress and strain levels. The Self-boring pressuremeter potentially offers the nearest approach to undisturbed  Chapter 1. introduction  2  testing, and is fast becoming one of the most powerful tools available for site investigation. Though it is routinely used to measure a wide range of soil parameters, it appears that the most frequent application is to provide values of shear modulus in deformation calculations. One reason is that previous experience has indicated the relative insensitivity of modulus measurements from the unload-reload ioops to installation disturbance. However, it is still not obvious as to how these values fit into the framework of soil stiffness dependant on stress and strain level. Also, currently there is no accepted universal standard for carrying out these tests with properly chosen unload-reload loops. Being a sophisticated instrument, equipment effects have to be carefully analysed and corrected for. The testing procedure and method of interpretation have also to be standardised. This thesis attempts to address all these aforementioned factors and also tries to investigate the effects of factors like creep, stress and strain levels on the shear modulus obtained from the tests  conducted in  cohesionless soils. Damping, which is the capacity of soils to absorb energy during cyclic loading, is rarely measured in-situ and has not been well understood. Current attempts at measuring material damping with the seismic cone or other in-situ methods are done by the generation of seismic energy in the form of compression or shear waves at one point and by measuring the amplitude of energy at other points. The unload-reload loops of the pressuremeter, which might offer a simpler way of measuring damping have not been given much attention so far. Getting well defined loops at very small strains, which is extremely difficult, might have been one of the reasons for this neglect. Thus the other main objective of this thesis is to look at the possibility of obtaining damping from the unload-reload loops and the various  Chapter 1. Introduction  3  factors affecting it. These studies were conducted with the UBC self-boring pressuremeter using the UBC in-situ testing truck. The tests were performed at the Laing bridge research site about 4 kilometres from the Vancouver International Airport in Richmond.  1.2 Thesis Layout  A brief literature review emphasising the effects of various factors on shear modulus and damping for cohesionless soils, the theoretical background, methods of analyses and the need for research is discussed in chapter 2. Chapter 3 describes testing equipment and test procedures. The testing programme and site details are provided in chapter 4. Chapter 5 and 6 evaluate the field data, present and discuss the results of the tests conducted along with comparing them with published results. Finally, chapter 7 provides conclusions.  4 CHAPTER 2  DYNAMIC CHARACTERISTICS OF COIJESIONLESS SOILS  2.1. Introduction  Hitherto, numerous researchers have published reports on the dynamic properties of cohesionless soils (Hardin and Black 1968; Seed and Idriss 1970;Hardin and Drnevich 1972a, 1972b; Seed et al. 1986;). This chapter attempts to review the main developments in addition to discussing the general nature of the factors affecting these dynamic properties, with an emphasis on SBPM tests. The growing use of SBPM testing in geotechnical engineering investigations, has stimulated many interpretation procedures, both numerical (Carter et al. 1979; Bannerjee and Fathallah 1979; Baguelin et al. 1986; Lassoudiere and Zanier 1986;) and analytical (Gibson  and Anderson 1961; Ladanyi 1963; Baguelin et al.1972,1978; Palmer 1972; Vesic 1972; Wroth and Windle 1975; Prevost and Hoeg 1975; Hughes et al. 1977; Denby and dough 1980; Jewell et al 1980; Fahey 1986; Juran and Beech 1986) thus aiding in the determination of stress- strain properties and shear strength characteristics from SBPMTs. Testing and interpretation of shear modulus and damping from the unload-reload and reload-unload loops, however, have been limited (Robertson 1982, Robertson and Hughes 1986, Bellotti et at 1989, Byrne et at. 1990).  Chapter 2. Dynamic Characteristics of Cohesionless Soils  5  2.2. Shear Modulus.  The stress-strain relation of soils, being very complex, depends on a large number of parameters that affect the behaviour of soils. Hardin and Black (1968) listed about ten factors that affect the shear modulus of soils. Gm for cohesionless soils primarily depends upon void ratio, effective confining pressure and a small effect of ageing. In the case of cohesive soils, along with the above factors, secondary time effects and clay mineralogy also seem to be of great importance. A comprehensive treatment of dynamic properties of clays can be found in Zavoral (1990).  Hardin and Black (1968) found that for normally  consolidated clays the small strain shear modulus could be expressed as  G  -  K F(e)  [2.1]  in which K  =  dimensionless constant for each soil  F(e)  =  function of void ratio  =  Atmospheric pressure  3c  =  Effective confining pressure  n  =  exponent of about 0.5 to 0.6  Hardin and Drnevich (1972b) confirmed equation 2.1 and also stated that the same expression could be used for sands. They recommended the use of in-situ or laboratory testing to obtain Gm.  Chapter 2. Dynamic Characteristics of Cohesionless Soils  6  Seed and Idriss (1970), discussing parametric effects on shear modulus and damping in sands, have given modulus reduction curves as shown in Fig.2.1. Gm determination from pressuremeter expansion curves has come a long way from the first method of obtaining them from the initial linear portion of the expansion curve. If the pressuremeter is installed without any disturbance it maybe possible to obtain a good estimate of G from the initial portion of the curve which, however, is too small since in sands peak stress ratios are reached next to the membrane at cavity strains of less than 0.1 % (Fahey 1980). Since it is impossible to obtain Gm from the initial linear portion of the expansion curve due to the almost inevitable disturbance, it is generally accepted today that the modulus can be defined from the slope of a small unload  -  reload(IJR) cycle or any loop  performed during the test (Wroth 1982; Hughes 1982; Jamiolkowski et al. 1985) by assuming that -  -  all soil elements follow one unique stress path during loading;  -  upon unloading beneath the current yield surface, the soil  behaves linear elastically with  a unique  modulus, Gur. This necessarily implies that any unload of the expanding cavity brings the stress state of the surrounding soil to a point below the currently expanded yield surface into a zone where strains are small and to a large extent reversible. Thus, if the soil is presumed to behave elastically during unloading, it can be shown that the slope of the loop in the cavity pressure-strain curve is twice the shear modulus, G.  U)  4’  a  0  0  4-  U)  0  L  U)  I-  C 0  0  IO  Fig.2.1. Variation of Shear Modulus With Shear Strain for Sands (from Seed & Idriss, 1970).  Shear Strain, y—percent  102  ‘0-I  p_____  i::  U,  0  4-  0  1  C 4’  4-  1.0  Chapter 2. Dynamic Characteristics of Cohesionless Soils  8  i.e.  2G  -  de  [2.2]  where dP is the amount of unloading and dc the loop strain measured at the wall. Recent developments in the understanding of the deformation behaviour of soils have lead to the potential of converting the cavity stiffness measured in a pressuremeter test to a material stiffness though the cavity stiffness is similar to the average stiffness backfigured from observations of full scale structures. As such it could be safely assumed that shear modulus can be obtained from the unload-reload modulus. Conventionally, it is assumed that the soil behaviour measured at the cavity wall is the behaviour at one point on a unique stress path and that the stiffness measured is identical to the stiffness at all points in the plane of loading. In reality, the soil stiffness varies with effective stress level and strain level (Howie 1990). These variations in stress and strain levels vary the stiffness of the soil element with radial distance. The other effects that have to be studied carefully are those of the amount of unloading, creep, equipment, void ratio and disturbance.  2.2.1. Effect of Stress and Strain Levels  In sands, for a linear-elastic frictional plastic model, with the induction of plasticity, it can be shown (Palmer, 1972) that for pressuremeter loading, the plane strain average stress 2 (r+0)i’  increases as expansion proceeds and varies with radius according to:  Chapter 2. Dynamic Characteristics of Cohesionless Soils  9  / 2sin —  I  [2.3] 1+sin4  where  r a  =  radius of the plastic zone  =  cavity radius  =  Cavity pressure  Thus, as soil stiffness varies with mean normal stress it also varies with radius, and the stress-strain curve for each element is different. This invalidates the assumptions of the Palmer (1972) analysis, which for soil deforming at constant volume assumed identical stress-strain curves for all elements and suggested that the behaviour at the wall was sufficient to define the stress-strain curve of the material (Howie 1990).  Previous  investigators (Robertson 1982; Robertson and Hughes 1986; Bellotti et a!. (1989); Byrne et al 1990) have suggested that Gur should be corrected to account for the average stress and strain level existing around the probe. Robertson (1982) suggested that the modulus should be normalised to the in-situ stress level using the Janbu (1963) expression:  G  -  (a” KPJ—  where 0 K  =  =  =  n  =  modulus number reference atmospheric pressure mean normal stress exponent  “  [2.4]  Chapter 2. Dynamic Characteristics of Cohesionless Soils  10  Clarke and Wroth (1985) showed that the scatter observed by plotting Gur versus depth can be reduced by plotting Gur versus mean effective stress though it is not very clear as to what the relevant stress is. Robertson (1982) suggested a ‘ave  =  0.5 P’ and an average strain of °. 0 where ’Y 45  is approximately twice the cavity strain increment. This assumption suggested a rapid increase in modulus over the course of the test with no theoretical justification given for considering stress level only in the plastic zone. Bellotti et al. (1986) attempted to reduce the effect of strain level by maintaining the strain increment at the cavity wall approximately constant. This meant that the magnitude of unloading must increase as soil stiffens. It seems reasonable to infer that the amount of unloading will decrease as the test proceeds, for a constant strain increment, and Gur will increase as a function of the square root of the cavity pressure. Alternatively, as the test proceeds, by increasing the size of the strain increment, it is possible to obtain a relatively constant value of shear modulus. However, this ignores any effect of stress reversal. Bellotti et al. (1987) suggested the use of the Janbu (1963) expression to get the average stress in the plastic zone by:  -  fc4, dr  [2.5]  fdr  -  x  ‘  [2.6]  Chapter 2. Dynamic Characteristics of Cohesionless Soils  11  where  RN  x-  in which  a  1 l-sincj  [2.7] 2  R —-1 a  R, is the radius of the plastic zone a is the cavity radius  By integrating along a radius this method failed to incorporate the larger volume of soil that came under the influence of increased stresses with the progress of the test (vide Howie 1990). Howie (1990) provided a better expression by considering thin annuli of soil around the cavity.  I  -  R Pc[i a  [2.8]  [(R)2j  He also suggests that if it is assumed that the modulus measured at the cavity wall is an average modulus which is a function of ‘ave” i.e.  (!) /  Ge  -  Kg Pa  0.5  [2.9]  Chapter 2. Dynamic Characteristics of Cohesionless Soils and the modulus at the in-situ level is  12  / 0.5  G 0 -KP a g  [2.101  p  then  -  G0  !.iY  [2.11]  p’o  Bellotti et al. (1989) apply a correction to the Gur value to normalise it to the relevant in-situ effective stress in the soil. This corrected value GuY is obtained from:  G,  -  [2.12]  7 G  This value of Gur’ is then corrected by a factor FN = 1.5 to give the equivalent shear modulus to that obtained after 100 cycles in resonant column tests. Finally, GOSBP is obtained from: G G0  1  SBP  1  +  G 0 SBP  where Yave  =  =  average shear strain amplitude Uho1  2  aw  1  [2.13]  Chapter 2. Dynamic Characteristics of Cohesionless Soils  13  The average effective stress is given by  4dr  R,  f  r  —  /  Oave  [2.14]  fRdr  r  Ja  /  1  —  .1  1+smc  -  2sin4/,  P  (.  2S1fl4),,S  ji”  )  [2.15]  1+sin+’  /  ij P (1 +smP 0 ) 5 /  /  2sine1/  The average elastic shear strain is given by: 2] fR /  i  . L 4 dr  —  —  Yaw  Rdr  1’— a r  i Yc 2  R,,,j  [2.16]  R a  where  —  [2.17]  a  This method seems to take into account all the variations as mentioned earlier though there is no apparent theoretical justification of the assumption that the average stress in the plastic zone is for the relevant strain increment and that an appropriate value of strain increment of 0.2% can be used to reduce the variability between moduli due to strain level effects. As Howie(1990) comments, this really is a semi-empirical correlation which gives a reasonable  Chapter 2. Dynamic Characteristics of Cohesionless Soils  14  agreement between Gur and the strain attenuation relationship of Seed and others. Being a rather theoretical procedure, it fails to reflect a rational basis for such an approach. He emphasised that though this procedure seems to yield good results for that particular program of tests, it might not hold good for tests conducted in different ways. Byrne et al.(1990) conducted a finite element analysis with a plane strain axisymmetric case involving an elastic plastic analysis to determine the stress field caused by pressuremeter expansion and a nonlinear elastic analysis to determine the displacement at the pressuremeter face upon unloading. These are used to obtain an equivalent shear modulus Gur. By linking Gur to the small strain shear modulus Gm, they demonstrate the interdependence of large strain parameters on the initial state of the soil.  Gur being  measured at any particular cavity strain, depends on both the stress and void ratio changes induced in the soil during expansion. By comparing Gur with Gm they have generated a chart to obtain Gm for different unloading conditions at different confining pressures. A detailed analysis considering the complete variation in stress and strain states was presented. The advantage of this method seems to be in the fact that it considers the effects of changes in the average stress (‘ +a’/2), stress ratio 1 r’ O ” and shear induced volume change on the maximum modulus. Results of the analyses are then presented in a chart as shown in fig.2.2.  2.2.2.Effect of Degree of Unloading  Rarely have statements been made about size of loops and programming of such loops  Chapter 2. Dynamic Characteristics of Cohesionless Soils  15  at different depths since the remark made by Wroth(1982) that the loop depth be chosen such that the soil around the pressuremeter did not fail in extension.  During pressuremeter  expansion the soil state at any point in the plastic region is in a state of failure such that:  a  —  l÷sin4’  [2.181  1-sin4’  a  If the pressure is reduced sufficiently reverse failure finally occurs, initially at the cavity wall, with u ’ and 9  0r’  being the major and minor principal stresses, respectively. It has been  proved (Wroth, 1982) that the pressure reduction to reach this state can be given by:  -  1 P ’  [2.19]  i+sincp’f where effective cavity pressure at the start of the loop It has been found that the pressure amplitude has to be kept sufficiently lower than this AP value if excessive hysteresis is to be avoided. As such Fahey (1990) suggested keeping the amplitude at O.5zP to reduce hysteresis to an acceptable level. Ladd et al. (1977) noted that rotation of principal stresses in sands results in considerable change in stiffness values. This would occur when the circumferential stress  ’ exceeds the radial stress 9 u  r’  Thus the amount of unloading becomes very important.  As discussed earlier the problem of assigning the relevant strain arises. Bellotti et al.(1989) in a very large series of calibration tests in sand, set a limit of 0.1% to 0.2% strain in the loops. Based on data published by Dobry et al.(1980) they state that the unload-reload loop will be purely elastic provided the shear strain amplitude in the loop is less than  8 ’ 2 Yt  16 (c,’) Face Foc• GWI Gmoz,  0.0  1.6  0.I 1.4  0.3  1.2  0.4 I. 0.5 0.6  0.8  0.6  0.  0.  0.0 I  2345678  Fig.2.2. Chart for Determination of (from Byrne et al. ,1990)  9101112 (Or)Foc.  from the measured G Value  Chapter 2. Dynamic Characteristics of Cohesionless Soils  17  where ‘y is a low elastic threshold shear strain in real cohesionless soils, below which the soil behaves in a truly elastic manner.  was stated to be approximately i0 3 % thus  limiting the elastic range of the loop to <2x10 3 %.  Actually in sands the shear strain  amplitude of the loops is about one to two times more than this. As such, there will be some hysteresis making the modulus dependant upon the loop depth. Whittle et al (1992) have stated that, provided the ioop depth does not exceed the Wroth limit  ,  practically any reload loop will yield a complete mapping of the variation of  observed Gur against strain increment.  2.2.3. Effect of °h estimation  Robertson (1982), Bellotti et al. (1989) and Byrne et al.(1990) have shown that to relate large strain shear modulus to the small strain shear modulus normalisation of the Gur to the in-situ stress should be done. Hughes(1989) has shown that the influence of the in-situ stress is to define the overall position of the pressuremeter expansion curve referenced to the stress origin. The curve shape and position is also influenced by Gm, which once again depends on the in-situ stress to which the Gur has been normalised. Bellotti et al. (1987) and Sully (1991) have shown the effects of disturbance on the values of in-situ stress. They have shown that most usually the P 0 measured from SBPM tests will be less than the 0 h• Robertson (1982) and Howie (1990) compared the h from various types of pressuremeters and concluded that the scatter in the SBPM data is larger than that from other types of  Chapter 2. Dynamic Characteristics of Cohesionless Soils  18  pressuremeters. Thus it becomes very important that we use oj values that are reliable if reasonable values of Gm are to be obtained.  2.2.4. Effect of creep.  The importance of creep during pressuremeter tests in sands has been briefly alluded to by Robertson (1982), Hughes (1982), Howie et al (1990), however, as Bellotti et al. (1989) conclude, there is a lot of work still to be done in this area. As such, the testing program and procedure should be altered to allow for creep effects. It is observed that as stress level increases there is a significant increase in the amount of creep deformation. This necessitates the incorporation of a holding phase before the commencement of each loop, long enough to reduce the creep rate to such an extent till the effect of creep on shear modulus is minimal.  2.2.5. Effect of Disturbance and Anisotropy  Hughes(1982), Wroth(l982), Robertson andHughes(1986), Howie(1990), have shown that the influence of installation disturbance on the shear modulus from the loops is negligible. But still it is believed that the unload-reload cycles should be carried sufficiently late in the test to ensure that the bulk of the soil being stressed has not been disturbed by installation.  Howie (1990) also suggests that the disturbance effect on  reduced if sufficient time is allowed to elapse before the test begins.  can be  Chapter 2. Dynamic Characteristics of Cohesionless Soils  19  In order to obtain a good agreement between the modulus results obtained from the pressuremeter and that from SCPT or resonant column tests, it becomes necessary that a disturbance factor ad be applied to the values obtained from pressuremeter. Bellotti et al. (1989) and Byrne et al. (1990) suggest ad values of 1.4. Another correction that is to be applied to the Gm values to obtain GVh (resonant column) is the Anisotropy factor aa. Pressuremeter tests involve strains in the horizontal direction whereas resonant column tests involve strains in the vertical direction. Bellotti et al. (1989) suggest a value of 1.2 for aa and Yan and Byrne (1990) suggest a value of 1.1. Thus GVh can be given by:  GVh Gaacd the measured shear modulus, normalised to in-situ stress. —  where  G=  [2.20]  2.2.6. Effect of Equipment  The effect of equipment, calibration, installation, etc has been discussed by many investigators (Campanella et al. 1990; Fahey & Jewell 1990) and shall be alluded to in the coming chapters. The above literature review suggests the following needs for further research: -  -  Effect of test procedure and programming of ioops. Effect of creep, strain and stress amplitudes on the loops programmed.  -  Effect of pressuremeter equipment  Chapter 2. Dynamic Characteristics of Cohesionless Soils -  20  Standardisation of test methods.  2.3. Damping  Damping is the amount of energy dissipated from a vibrating system. categorised into viscous and hysteretic types.  It can be  Damping is viscous when it is frequency  dependent and hysteretic when it is frequency independent. The area of the loop from a stress-strain curve during unloading could give a good measure of the energy loss during unloading. The assumption here is that damping is hysteretic in nature. This was provided by Whitman (1970) while summarising material damping which is the dissipation of energy mainly due to frictional losses. Most authors seem to attribute damping mainly to particle sliding. But, according to Palaniappan and others the free vibration decay envelope in a constant friction model is not a straight line and as such damping might involve not only particle sliding but also rotation and slip. Whitman (1970) expresses the Equivalent viscous damping ratio by:  [2.21]  —  D 41tA,  where A 1 00 Atri  =  =  Area of the ioop Area of the right triangle between strain  axis from origin to point of the loop  Chapter 2. Dynamic Characteristics of Cohesionless Soils  21  Whitman noticed the dependence of damping on shear strain, confining pressure and saturation. Hardin and Dmevich (1972a) found damping to depend primarily on: -  -  -  -  -  Strain amplitude; Effective mean principal stress; Frequency of vibration; Void ratio; Confining time;  They provided equations for Dm in their companion paper (1972b). They showed that damping decreases with the logarithm of the number of cycles of loading and decreased nonlinearly with confining pressure. They also showed the variation of damping with void ratio. Seed and Idriss(1970) provided a general damping versus logarithm of strain curve which they concluded would be adequate for all practical purposes. They assumed that the values were the same for sands and gravelly soils which they confirmed later on (1986). Recently Idriss provided a more conservative curve (1990). Discussing anisotropic effects on damping Lee and Stokoe(1986) and Yan and Byrne(1990), have found that stresses in the direction of propagation (Sa) and particle displacement (Sb) have a very small effect on damping. A number of attempts have been made so far both in the laboratory (Hardin and Drnevich  1 972a, b ;Palaniappan, 1976;  Woods, 1978;  Saxena  and  Reddy, 1989;  Ni, 1987;Zavoral, 1990; Aggour et al. 1982a;) using cyclic triaxial (compression and torsion)  Chapter 2. Dynamic Characteristics of Cohesionless Soils  22  or resonant column testing, and in-situ (Johnson and Toksoz 1981; Tonuchi et al. 1983; Redpath 1982,86; Mok et al. 1988; Stewart 1992).  Stewart (1992) has provided an in-depth summary of the different techniques of measuring damping, formulation for field measurements, etc. The different wave attenuation methods being out of scope of this thesis are not discussed. Two important relations, one between complex oscillator (mass, spring, dashpot) and viscoelastic material and another between oscillator and stress-strain loops that are considered important for analysing damping from pressuremeter loops, are discussed herein.  2.3.1 Complex Oscillator and Viscoelastic Material  Lysmer (1980) developed the concept of the complex oscillator and compared the resulting modulus with that of a viscoelastic material. He used a simple one dimensional model with a spring-mass-dashpot system having the following equation  muII+cuE’+ku_Peit and the relationship between displacement and loading:  [2.22]  Chapter 2. Dynamic Characteristics of Cohesionless Soils P where  H(Z)  =  -  23 [2.23]  u H()  Transfer function H(ø)  -  K  +  iwc —ø m 2  [2.24]  p e  [2.25]  Defining a complex oscillator by mu”  +  k*u  —  with  H()  -  k*  C,  D  =  [2.26]  m 2 c  C  D where  -  [2.27]  2/i&  damping ratio  If we let  —  k(1 —2D  +  i2D/1 —D)  [2.28]  then  111(0)1  —  /(k_o2m)2  +  2 (oc)  [2.29]  Chapter 2. Dynamic Characteristics of Cohesionless Soils [if *(0)I substituting for D  =  —  /(k_co2m)2  +  24  m o 2 4kD  [2.30]  /c/(2. 4 {km})  —  i,/(k_co2m)  2 (oc)  +  [FI(o)  [2.31]  Similarly it caii be shown (Lysmer, 1980) the phase difference ô is given by  2D  84) =  [2.32]  0  (1÷—) 00  Assuming D to be defined at  84=D. öq is ignored if D is small (<10%).  Comparing the complex spring stiffness, K*, to an equivalent complex modulus for solid materials the dashpot models can be approximated as  —  2ii2D _2D / 1 —D G(1 3 ) 2  ) 5 G(1 ÷i2D  [2.33]  Based on the definitions of G and D, it is easy to verify that the real and visco-elastic materials will dissipate the same energy in one cycle of harmonic oscillation with natural  frequency  and amplitude ‘y, if a visco-elastic material verifies eqn. 2.33. The visco  elastic material is then said to be equivalent to the real material, the equivalence being based on the identity of the dissipation properties of the two materials at natural frequency t. This equivalent complex modulus G* is the slope of the major axis of the ellipse representing the r  -  ‘y relationship for one loading cycle. The G*/G ratio is nearly equal to 1 for the  commonly used D values, thus making the slopes of the ellipse and that of the real loop  Chapter 2. Dynamic Characteristics of Cohesionless Soils  25  equal at the first order (Dormieux and Canou, 1990). Thus, the linear complex oscillator allows the reproduction of G and D of the  i-  -  ‘y relationship of the real material. This could  be a very simple approach similar to the Dormieux and Canou (1990) theoretical model to calculate damping from the pressuremeter loops as will be discussed later.  2.3.2. Oscillator and Stress-Strain Loops  Using a simple spring-mass-dashpot model a simple relationship can be developed between a stress-strain loop and damping (Byrne, classnotes CIVL581). A typical loop is shown in fig.2.3.  This development like the earlier one will be restricted to harmonic  loading but at the natural frequency, . 0 The force in a dashpot is given by Fd in  =  Cu’  (where u’ =du/dt). Thus the work done  one cycle of loading is given by the area of the hysteresis loop, A : 1  A 1 00  —  fFd du  —  fcu’  dt  —  2 fc(u’)  dt  [2.341  For sinusoidal displacement: u =U sintt and u’ =Ucost  2 (u”)  =  cos 2 U ( 2 t) 2  =  U22_(1+cos2t)  Substitute in equation 2.27 and integrate over a single period (0-T)  [2.351  26  U) U, I-.  Cd, I  V  C,,  Atrjngie  Shear Strain  100 A  dcp=Ap/Aijang  Fig.2.3. Stress-Strain Curve for Cyclic Loading of Soil (Stewart, 1992)  Chapter 2. Dynamic Characteristics of Cohesionless Soils fT 0  1  cU dt ±(1+cos2t) 22 2  27  1  I  2  120  IT  [2.36]  =  10  For t=Z and using T=2irIZ 0 we get  0 A  =  cU2o2i  =  cU i 0 o 2 c  =  2 i 3 (2D / Jki)U kizir  2 [2.37] 2itDJcU  lOOP  —  D  =  [2.38]  2 2’rrkU As shown in fig 2.3, the area of the right triangle is given by  A  .  =  1 k U2  [2.39]  2  2 k 3 2itD U  AkOP A tn  =  1  [2.40]  2 LkU 2  D  =  [2.41]  Dormieux and Canou (1990) present an analytical method to determine damping based on the viscoelastic interpretation of a low amplitude cyclic pressuremeter test. They use the approach of equivalent viscoelastic modelling to obtain the parameters for use in the Hardin and Dmevich (1972 a,b) model linking the values of G and energy loss co-efficient where ,j  (‘y)  =  D/2irW  i  (‘y):  Chapter 2. Dynamic Characteristics of Cohesionless Soils G  +  G  W  =  28  =1  [2.42]  Timax  2 represents the elastic energy stored l/2G(ym)(’ym) up in one fourth of a cycle by an elastic material with a stiffness GQy)  Gmax and lmax are the maximum values of G  and  i,  functions of material density and the level of stress.  The authors simplified the approach by taking a hyperbolic variation of G/Gmax in function of 71 m and 17 r a reference distortion.  This method being based upon the concept of  equivalence has its own limitations as addressed by Martin (1975), but can be used as a calculation technique as the authors themselves put it.  This being one of the very few  publications that alludes to obtaining damping from the pressuremeter loops, can be used as a base for further studies. Also, no work has been done so far to check the validity of the above said method. Thus it would be very important to explore the possibility of obtaining damping from the pressuremeter loops using the two models and compare the values so obtained to those from established curves as an initial step.  ,  especially Seed and Idriss(1970) and Idriss (1990) curves,  29 CHAPTER 3  EQUIPMENT, CALIBRATION AND TEST PROCEDURES  3.1 Introduction  Pressuremeter testing, introduced by Louis Menard over thirty years ago in France, had been largely based on an empirical approach developed and widely used in France. However, recent advances have relied heavily on attempts towards direct measurements of soil parameters (Mair & Wood, 1987). These depend to a large extent on technological advances in pressuremeter design.  Lately, pressuremeter electronics are getting more  sophisticated leading to a greater need for an understanding of their intricacies.  A  considerable amount of effort, time and money has gone into attempts to improve pressuremeter technology for over a decade.  SBPM research at the UBC first began with the Hughes SBPM, which he designed and developed (Hughes et al, 1977, 1989). Later, to aid further research it was decided to develop an improved version of the Hughes SBPM with major improvements aimed at instrumentation/data processing, membrane corrections, membrane protection and installation methods. The initial design of the UBC SBPM is provided in Campanella et al (1990). Since then a number of changes have been incorporated in the design and instrumentation.  Chapter 3. Equipment, Calibration and Test Procedures  30  3.2 Details of SBPM Design  3.2.1 System Overview  The basic design being much akin to the Hughes SBPM has a overall length of 143 cm with an external diameter of 73 mm. The expandable membrane has a L/D ratio of 6. The bottom of the pressuremeter shows a cutting shoe which simultaneously with drilling mud jetted under high pressure from a central jetting system breaks the soil as the pressuremeter is pushed into the ground. The installation using this combination is done using the UBC in-situ research vehicle. The self-boring pressuremeters with rotating cutters instead of the jetting system create more disturbance thus losing the whole purpose of undisturbed testing. The membrane is inflated by air pressure from an air compressor housed underneath the truck through a 1:3 pressure multiplier. The wires from the transducers and the air line from the compressor pass through a 6.4 mm OD air return line which is taped to the rods as the pressuremeter is pushed in. This is connected to the PC through an interface control box which controls the inflation rate, loading, unloading,etc. The system overview is shown in fig.3.l.  3.2.2 Instrumentation  There are six cantilever type strain arms located at the mid-level of the membrane at  •L tJ1 t [ ‘I  31 Hydraulic System Run Switch Pushing Head  Optical Depth Encod.r  4)  and display dat•  Eie&onicaily Controlled Pressure Regulator (SMC Nfl202) High Pressure Air Source 275 psi Mud Input  Flow Transducer  Pressure Transducer 1:3 Pressure Multiplier (Fairchild)  Airline to Probe 0-250 psi  SBPM2 CHANNELS 6 StraIn Arms • internal Pr.ssum Transducer • Eff.ctlv. Preasur. Transducer .2 Acc.l.rom.t.rs for slop.  NOTES: • PM conol sequence is conaucted on PC and thin downloaded to the Interfac. conoller • 3 dIfferent Data Acquisition Modes  • RID T.mp.ratur. Transdue.r • Front End Load Ciii  Fig. 3.1. Self-Boring Pressuremeter System Overview  1. Sounding 2. Dissipation 3. Pressuremeter  Chapter 3. Equipment, Calibration and Test Procedures  32  60 degree angles in order to monitor membrane expansion.  Each strain arm has a  displacement transducer consisting of a strain gauged bending beam made from beryllium copper and clamped to the pressuremeter body at one end.  To the other end is fixed a  plastic ball that makes point contact with the membrane follower. The effective operating range of each arm is 8 mm corresponding to a radial strain of 22%. There are two pressure transducers to monitor internal air pressure and external pore water pressure. The transducer for measuring pore pressures called the effective pressure transducer is mounted on the SBPM membrane and moves along with it during expansion. A small porous filter in its cavity keeps soil away. An overview of the electronics is shown in fig.3.2. Each of these transducers has a instrumentation amplifier permitting the use of LTC 1290 12-bit AID converter. The amplifiers and AID converter along with voltage regulator circuitry make up the two analog boards. These along with the microcomputer board as shown in fig.3.2 make up the downhole electronics. The interface controller board consists of a 68HC 11 microcontroller along with a 12 bit DIA converter that sends raw data in ASCII format through a RS232 serial link. This is connected to a linear DC power supply. The ASCII signals that are received by the SBPM software in the PC will be converted to engineering units providing real time data with a graphical representation of pressure- radial strain response for two of the six strain arms.  3.2.3 Membrane and Lantern Characteristics  Commercially available gooch rubber tubing of thickness 1 mm and length 58 mm  33 SBPM ANALOG BOARD #1  SBPM MICROCOMPUTER BOARD  Armi  Arm 3  Arm 4  ArmS  Arm  Aco. I  Acc. 2  Tamp  Etf.Pr.  lntPr.  Front Load  RS232 TO P.C.DATA ACQ.  Fig.3.2. Self-Boring Pressuremeter Electronics Overview  Chapter 3. Equipment, Calibration and Test Procedures  34  was used for the membrane. As reported by Campanella et al (1990) and Sully(1991) the expansion in air gave a bilinear envelope with little or no hysteresis. The revised lantern (Campanella et al, 1990, Sully, 1991) was altered subsequently in order to obtain better compliance results. The lantern had to be designed in such a way that it would be as flexible as possible, with a very small compliance correction and be able to expand under plane strain conditions even at high strains. 16 mm stainless steel strips with a uniform curvature were selected and two of those were spot welded with a third overlapping strip. Several of those strips were put together to form the lantern. The other forms used are also similar to this but are without the free overlaps. All the lanterns used were similar to the revised lantern of figure 3.3 without the collar.  The lantern with the stainless steel strips was selected  mainly because of the desire to achieve larger strains. The commercial lanterns available, though flexible with very little compliance effects, are good only for small radial strains of possibly 10%. However, it was doubtful that it might take the rigours of testing in sands. As such, it was decided to use the lantern types that are described above. The initial lantern design suffered frequent blow-outs and also had the problem of sand entering between the strips and the membrane. This would cause a bulging of the probe, resulting in a large amount of disturbance while pushing. One lantern was destroyed during pushing due to the above mentioned reason.  Numerous lanterns of varying overlaps were tried, but the  compliance was too large to obtain reasonable results.  35  ORIGiNAL DESIGN  REVISED DESIGN  Fig.3.3. Lantern Designs (Campanella et a!, 1990)  Chapter 3. Equipment, Calibration and Test Procedures  36  3.2.4.Jetting System  Initially, the self-boring mechanism was through a rotating cutter with drilling mud flushed down to remove the soil.  The method used at the UBC (Hughes et al. 1984),  however, is by jetting drilling mud under pressure to break the soil with minimum disturbance. As Sully (1990) has explained, two types ofjetting systems have been tried out. The showerhead arrangement (fig.3.4.b) has jetting holes about 40 mm from the cutting shoe  and as such might pose problems in stiff/dense soils since there might be a possibility of plugging of the shoe. However, the central jetting arrangement (fig 3.4.a) which is the one used in this investigation, has an advantage wherein, the jet holes can be positioned at various places relative to the edge of the cutting shoe. This helps in the determination of the exact distances of the jetting tip with respect to the edge of the shoe that will be required to attain minimum disturbance in different soils at different densities. This standardisation of the distance between the jetting tip and the edge of the shoe is of extreme importance if good data are to be obtained. The remaining components are: A Flowmeter to monitor flow rates, a swivel through which the drilling mud is flushed into the jetting system, mud pump, a submersible pump to retrieve water from the ditch, barrels, hoses and other hydraulic and electrical connections. transducers are housed in the swivel.  The mud flow and mud pressure  37  CENTRAUZIN WING GUIDE (3 total)  Central jetting system  CHANNEL  (12 total)  Cutting shoe with shower jet  Fig.3.4. Jetting Systems (Campanella et al., 1990)  Chapter 3. Equipment, Calibration and Test Procedures  38  3.3 Calibration of the equipment  Calibration is the most important operation that can be carried out on any equipment that we use for testing. According to Mair and Wood (1987), in the absence of calibration  and hence a reference to any measurement, it is impossible to identify the exact pressure, strain, etc. with sufficient accuracy. Since the performance of the pressuremeter in ideal conditions would not be known, pressuremeter testing would be almost worthless without proper calibrations. Fahey and Jewell (1990) showed that very large errors in evaluating the shear modulus could occur due to system compliance effects. The important calibrations that were carried out were:  3.3.1. Strain arms calibration:  This was achieved using a micrometer to provide a relation between measured displacement and strain arm output voltage. The arms are pushed back to zero strain and the micrometer mounted on each arm by turns is rotated to cause displacement in the arms. The voltages at various displacements are measured and the slope from the graph thus obtained is input in the data acquisition program to obtain real time values. There was no hysteresis in the calibration curves.  Chapter 3. Equipment, Calibration and Test Procedures  39  3.3.2. Calibration of Pressure Transducers:  The probe is placed in a calibration chamber and known increments of pressure are applied to the outside of the probe, as well as inside, and the curves so obtained determine the factors that are to be input into the program. The external pressure is applied using a Druck digital pressure indicator with which precise pressure admissions can be made.  3.3.3. Compliance calibration:  This is done in a split cylinder whose internal dimensions equal the external dimensions of the probe with the lantern. The probe is then inflated and unload-reload loops  are carried out at various pressure levels with varying loop depths and the strain and area corrections in each case are noted.  This is very important since the shear moduli and  damping (area of the loops) are to be corrected for these effects if accurate results are to be obtained.  3.3.4. Flow rate and mud pressure calibration:  The Druck digital pressure indicator (DPI) was used to apply specific pressure on the mud pressure transducer in the swivel, and the pressures from the DPI were compared with those shown by the program simultaneously. Mud flow was checked in the field by allowing water to flow at a specific rate and checking the resulting flow rates in the program with that  Chapter 3. Equipment, Calibration and Test Procedures  40  from the flowmeter. Apart from these calibrations, some of the important checks that have to be carried out are those of proper saturation of the pore pressure element, proper placement of the jetting tip with respect to the shoe edge, proper working of the data acquisition system, making up the command files for the testing program decided and checking whether proper signals are being received by the data acquisition system.  3.4 Testing Procedure  As Bellotti et aI.(1989), Howie (1990), Fahey (1990) and others have reported it is very important how the testing procedure is programmed. However, as Whittle et al.(1992) have rightly noted, precious little has been said about how these loops have to be programmed after the Wroth (1982) suggestion regarding loop depth. As such this thesis concentrates mainly on the effect of testing procedure on the results obtained. As such tests have been carried out with loops of varying amplitudes at strains of 2%, 6% and 10% radial strain mainly. The variation of results with the change in amplitude in terms of whether the loop amplitudes are of descending or ascending order of magnitude is studied. Effect of creep phase on the results is compared with results from tests without the creep phase. Tests have also been carried out to see the effect of continuous cyclic loading at the same cavity pressure in terms of creep and plastic hardening. Tests have been carried out with just the creep phase at various pressures to ascertain the effect of creep with confining pressure. The testing program is given in chapter4.  41 CHAPTER 4 TESTING PROGRAMME AN]) GEOLOGICAL AND GEOTECIINICAL CHARACTERISTICS OF SITE  4.1 Introduction  It is generally accepted that in-situ tests offer the best means of determining many soil properties, especially those of sand which is very difficult to sample and test undisturbed. Even though the self-boring pressuremeter appears to be ideally suited for testing in sands, it is not so well developed in sands as it is in clays. As such the development of the UBC self-boring pressuremeter has concentrated on well documented sites made up of predominantly uniform sands. The Laing bridge-south site is one of the UBC sites that has been the subject of extensive field testing using numerous in-situ tools, eg., CPTU, SCPT, SPT, Field Vane Test, DMT, etc. Previous UBC graduate students working on the UBC self-boring pressuremeter (Howie,J.A. ,1991 ,and Sully,J.P. ,1991) have also used this site for their investigation. The location of the research site is shown in fig.4. 1, and a detailed geological and geotechnical description along with the testing programme is provided below.  4.2 Geology of Lower Mainland  The Vancouver Lower Mainland is a major postglacial alluvial flood plain of the Fraser river and consists of marine deltaic deposits. The Quarternary deposits at the surface that attain depths of 300m were essentially deposited during periods of the most recent glaciation and were affected by isostatic and eustatic fluctuations. At the end of the last glaciation the weight of the ice had depressed the land much below the sea level.  The  submarine delta so formed, had the deeper deposits eroded by waves caused due to isostatic uplift.  Overlain by these deposits are Pleistocene glacial deposits that are made up of a  complex interspersing of sediments from previous glacial ages. Underlying these deposits  (Sully, 1991) Fig.4. 1. Laing Bridge South Site Location  SURREY  Site  MATSOUI  ALOE RGROVE  US- CANADA Border  LANGLEY  S URC Research  SCALEI ‘250000  Chapter 4. Testing Programme and Geological and Geotechnical Characteristics of Site 43 is the bedrock of Tertiary age. This has resulted in a highly heterogeneous delta varying in sediment type and properties both horizontally and vertically. Blunden(1975) has reported that this delta began to develop about 11,000 years ago with the retreat of the ice. Richmond, where the site is located was subject to deposition of fine sediments deposited into the sea by the Fraser River and also large sediments deposited by the retreating ice. This resulted in Richmond attaining its almost present position around 5000 years ago. Since then the sea has risen causing the deposition of shallow water marine delta deposits variations of which have resulted in the formation of organic materials like peat bogs and salt marshes. Annual flooding of the Fraser River has laid down silt and clay overbank deposits. The Holocene soils are generally normally consolidated since they have not been subjected to iceloading. The generalised profile of the Fraser delta is thus fine grained soils overlain by coarse marine, deltaic and tidal flat facies and then by fine levees. A geological cross-section of the Fraser Delta (Blunden, 1975) has been provided in fig. 4.2.  4.3 Laing Bridge Site  4.3.1 Site Description  The site is located on the south-east portion of Sea Island and is bounded by McConnachie Overpass and Airport Way close to the Vancouver International Airport. The topography is simple, with the site being fairly flat and covered with short grass. It is bounded by a drainage ditch, in which the level of water suggests a ground water table level of 0.8m to 1 .4m below the ground level. It has a gate at the north-eastern edge on the Airport road(North). The site also has surface drainage features. During the construction of the overpass, surface regrading and possible fill placement of the site had been done. A stratigraphic profile shows 1 to 2 metres of organic clays and silts. Below this is sand with intermittent silt layers extending down to about 20 metres depth.  A typical  conelog of the site is shown in fig.4.3. A grain size distribution curve along with a profile  1DM  “6.  Pd  £‘rpO3lr5.  a*y lLT  TTAY  f  —  fA41 V MILK5.  vcoi,’w#.  Fig.4.2. Geological Cross-Section of the Fraser Delta (after Blunden, 1975)  ‘e4’  °fY -  /LA.%lb  V74. e7Aa eA7asl.  5o.7w.  —  ‘L’  _TS 100  —  -1000  --oca  -  45  Laing Bridge Site Cone Bearing,Qc (bars)  Friction Ratio  Soil Profile 0-•  Clcyey  SILT with sandy silt. & clay layers  SAND.some silty sand —compact 10—  Silt layers 20—  30-  Fig.4.3. CPT Sounding  -  Laing Biicrg Site (Stewart, 1992)  Chapter 4. Testing Programme and Geological and Geotechnical Characteristics of Site 46 of friction angles is presented in fig.4.4. An SPT log and plots of shear velocity and shear modulus, using the SCPT, with depth are depicted in figs.4.5 and 4.6.  4.4 Testing Programme  Self-boring pressuremeter tests and Seismic cone penetration tests were carried out at various locations on the Laing Bridge site from May 1991 onwards. The location of the soundings and a typical SBPM sounding are shown in figs.4.7, 4.8 and 4.9. The layout of the testing details is provided in table.4. 1.  47  Friction angle, ço(eg.) 10  20 I  0  ,  40 I  •  Lcing Bridge South  50  0.4  2 4  x  I  5  a I 0 0 0 I I I 00  40 ‘I  54.  —  10-  00 00 I I I I I  15- see:. C77—87—2.DT C77—7--3.SCD ““ C77—7—.DA OUT 19!5  ..... DM1 197  cc::  :::: Lc (tt) dc::  .‘  I 00  a  I 0 I CI 0  a  S..  Fig.4.4.b. Profile of Friction Angle  Fig.4.4.a. Grain Size Distrib ution, Laing Bridge Samples (Sully, 1991)  H I •1  48  SPT N volue (blows/3Ocm) 40 20 itil  0  1I11111t  it,,  1111111  hi  I  I  I  I  I I I  I I I  I I I  I I I  I  I I.  I  I  I I I  I I I  I I I  I I I  I  —  60 i-h  1 ——-I.4) -  0  -  is  —  —-I-  I—  -í  20  I I I 25-  I I I  Letng BrLdge South 1ø.Oot.1991. by Foundex ExploretLons.  Fig.4.5. SPT Log, Laing Bridge (CIVL 577, 1991)  49  Shear Velocity (m/s) 1 00  150  200  iiiiiitiiliiiiiitiiliiiiiii  Shear Modulus (MPa) 0 100 50 iiiiiiiiIiiiiii  4-  8-c 0 0  12-  16-  20  Fig.4.6. Protiles of Shear Velocities and Shear Modulus, Laing Bridge  1_ t_  50  souTh  + o  Scile’ 20  4Cm  Fig.4.7. SBPM Sounding Locations, Laing Bridge (Sully, 1991)  F’I’-1  s  _-icj  r —ic  c i—i  Flow Rate and Cutting Velocity  Laing Bridge/12MA92  Pore Pressure (KPa)  ,.  r  .  SBP1 1  Rod  I  Sill to Silty Sind oose La iu Dcnse  ,fht  I •  ----I  Soil Profile  I  Silty Sand to 1 Sidy Silt I  r i cs  (MPa)  ID T E i I  Penetration Rate (cmimin)  Fig.4.8. SBPM Sounding Characteristics, Laiiig Bridge (da Cunha)  i:i II) ]  J  E  Penetration Resistance (KN)  .  5  17  1830JN92 LBSJL92  189JN92  15  . 13  DITCH  14  12  N  Fig.4.9. SBPM Sounding Locations, Laing Bridge  7 8 9 10 11 12 13 14 15 16 17 18  1 2 3 4 5  LB17MAO1 LB1JN9I IB17JL91 IB1AG91 1B27AG91 LB3OAG9I L830CT91 1B240T91 LB5FB92 L820FB92 LB31MR92 LBOAPR92 LB25AP92 L812MA92  Ref. FDPOI FDPO2 FDPO3 SBPO1 SBPO2 SBPO3 SBPO4 SBPO5 SBPO6 SBPO7 SBPO8 SBPO9 SBPIO SBP11 SBP12 SBP13 SBPI4 SBPI5  Test  181 MA91  No.  —‘--  1 •  3  •  •  •q  9  11  .  N  10  7  GAT\  53  I  .  C,,  c  .I el) —  I  I  I  —  S  Ti;fl1)I4hiHH< 4 EC)Q)Z  8  Zz’ .  C,,C  C,)  .  E-  -  LI)  I  :  . ,  co  ,  a) CI•  -  ‘.  0 co  .  I  I  I  I  —  I  -  —  .=  a  .L  —  C  C  ‘oc  —  9  o  0  0  0  C  C C  C,)  C)  C,)  C)  C,)  Cf)  fl  0  a -  r-.  00  C,)  C,)  C  C  0  0  — —  el  c  —  —  .  —  C,)  C,)  C,)  Cl  C,)  C/)  LI)  Cl)  54 CHAPTER 5  SHEAR MODULUS  5.1. Introduction  An attempt is being made in this investigation to study the effects of factors affecting the pressuremeter modulus. The factors examined are: effect of programming of loops or test procedure,stress level, strain level, creep, unloading and repeated unloading. Fig 5.1. shows a typical pressure-expansion curve. The test has been performed at a depth of 13.9m at the Laing Bridge site. The test was stress controlled with the rate of pressure increase being constant throughout the test.  The unload-reload loops were performed at specific  strains of 2%, 6% and 10%. The extent of unloading is defined in terms of percentage of the cavity pressure at the set strain. Loops of various unloads ranging from 10% to 40% of cavity pressure were performed at the set strain as can be seen in the second set of loops in fig.5. 1. Holding phases may be incorporated just before unloading. The present investigation has been based on limited amount of data. The reasons for this were, the delay in procurement of the pressure multiplier (to boost pressures up to a maximum of 1500 kPa) and the compressor, equipment damage and repair, equipment sharing with other students, etc. These limitations resulted in very few soundings, out of which a few had to be discarded due to lantern effects as will be discussed later on. The Table 4.1 shows the number of tests done and the number of tests that were selected for this investigation. The initial tests were only trial installations. There were several problems encountered during installation due to plugging of the shoe, plugging of the jetting tip,etc.  55  2000  20.F.b.1992  L.Ln 6rdg. South  -  —  F—’  1B00  01000 C  I  I  I-s0g  0  RdI  Fig.5.1. Typical SBPM Pressure  Stron  -  Expansion Curve  (%)  S8PØ  56 These resulted in enormous friction on the probe causing the cable or the lantern to break at times. The results from SBPO6 (24.Oct.91), SBPO8 (20.Feb.92) and SBP11 (23.Apr.92) which appeared the best were chosen for analysis. Though SBP12 and SBP13 were successful installations, lantern problems resulted in high values of shear moduli and therefore could not be analysed. The UBC SBPM2 has six strain arms at the centre of the probe (Campanella et aL, 1990). Each of the six arms of the pressuremeter may not show the same strain movement during expansion because of equipment effects and anisotropy. Some arms might show some disturbance due to the presence of a small pocket or a pebble or even due to the immobility of the lantern because of various reasons. As such instead of using only one arm or the average of all the arms, it seems that two of the best opposite arms should be used to get average strain values (Hughes  -  personal communication).  For the purpose of this  investigation such an average strain measurement is used. Typically researchers use the secant modulus of the ioop (line joining the end of the loop with the cross-over point of the unload and reload portions) as shown in fig.5.2 to obtain the 0 ur• Whittle et al. (1992) have proposed that a chord of maximum symmetry be used by dividing the number of points in the loop in order to obtain the modulus. That procedure seems to work well only with high resolution loops. The loops in the following investigation show a great amount of distortion at the smaller levels of unloading. Therefore, smoothing has to be done, if the moduli obtained are to be used. Here, five point smoothing has been used.  Figure 5.3 gives an example of a smoothed curve with a  comparison of smoothed and unsmoothed loops given in Fig.5.4. This smoothing does not  57  C  0  LSBe. D 0 CO 0  -4Bg I  .4-,  B  RedI  Stren (%)  Fig. 5.2. Unload-Reload Modulus from a Typical Loop.  58  1000  24.Oot 1992  —  Letng B tdg. South  —  SSPØ6  —S  C  0 D C’) Ci)  0 L  0 4)  C  90  Rd  I  Stro ln ()  Fig.5.3. Smoothed SBPM Pressure-Expansion Curve.  (_)  •o  •1—’  V  0  —  2.6  11111  I  —  F  Z  —  F—  11111111  2.9  3.0  II 11111111111  Raw Data Smoothened Data  If  I]  ‘I  7  I  2.8 2.7 Strain (z) Radial  —  —  Laing Bridge  11111111111 III  —  ‘F  J  SBPO7  Fig.5.4. Comparison of Smoothened and Unsmoothened Unload-Reload Loops.  500— 2.5  600  700  800  900  1 000  1100  Chapter 5. Shear Modulus  60  seem to affect the larger high resolution loops. For the smaller loops there do not seem to be other ways if the data have to be used because of the distortion. On the whole they seem to show exceedingly good results in that, the loops seem well balanced and even. After using the Whittle et al. (1992) procedure the moduli do not seem to be very different from the secant moduli, therefore the simpler secant modulus is used.  5.2 Effect of Various Factors on Pressuremeter Modulus  5.2.1 Effect of Stress Level  In a pressuremeter test, stresses and strains vary with radial distance from the probe. This causes stiffness of a soil element to vary with radial distance. The complex variation of these stresses and strains cause difficulties for the interpretation of the results which are measured at the walls of the pressuremeter. The changes in stress states due to expansion change the modulus values measured from the Loops. This stress level dependence of moduli is recognised by previous investigators. The obtained moduli have to be normalised to the in-situ stress if Gm has to be calculated. For this purpose a suitable estimate of the stress that the modulus is measured at, should be made. This requires normalising the radius by the cavity radius, cavity pressure by the in-situ horizontal stress and the mean normal stress by the in-situ mean normal stress. It is clear that on expansion the radial stress while the circumferential stress  cQ decreases.  crr’ increases  However, once the failure envelope is reached  and a plastic zone develops, u’ commences to increase in the plastic zone and the average  Chapter 5. Shear Modulus  61  effective stress (Ur’ +0e’12) increases as shown in the figure.5.5 (Hughes et al. 1977). The variation in stress level results in a variation in modulus from a high value close to the wall to the in-situ value at the elastic-plastic interface. As Howie (1991) has reported, the natural variability of sand deposits in the field makes it difficult to use field data to investigate stress and strain level effects and as such it becomes necessary to use results of calibration chamber tests. Bellotti et al.(1987, 1989),  and many others from the U.K. have published results of a large number of tests carried out in the calibration chamber. Therefore, it would be useful to compare the results obtained by using the theoretical formulations that are obtained from these calibration chamber test results and apply them to field tests. Bellotti et al. (1989) and Byrne et al.(1990) have used these data as input for their models. These models have been discussed in chapter 2 and have been used on the data of the present investigation further in this chapter. Plots of Gur versus variation of  P’  are shown in figures.5.6 and 5.7.  Fig. 5.6 shows the  for 40% unloading at different depths. Fig.5.7 shows a similar variation  for different unloads. A close look at the plots shows a trend of increasing modulus with cavity pressure and with decrease in amount of unloading. Though the figures seem to show some trend, it is not very obvious how these rates of increase differ. Fig.5.8 shows the change of radial stress with distance away from the probe. The stress is in-situ stress at the elastic-plastic interface. It is very evident from Figs.5.8 and 5.9 (Gur vs. a 1 ve’) that the SCPT modulus when plotted with respect to  crho’  is much higher suggesting that Gm  measured from the SCPT cannot be tied in with the Gur values unless they are normalised  62  A  —.  —x—. —  Elastic  (0)  a  C ailure Envelope  A  2  (b) Fg.5.5. Stress State after Pressuremeter Loading (Byrne et al, 1990)  200  ,,  52 m m .O...8.6 m k4L* 11.5m a.a.etj.j. 13.9m ethel  —  400  —  600 P’ (KPo)  -  800  1000  40% Unloading  111111111111111111  Loing Bridge  111111  SBPO8  Fig.5.6. Variation of UnlQad-Reload Modulus with Effcctive Cavity Pressure (SBPO8 Sounding Laing Bridge).  0—  20-  40-  80-  100-  1200  0  0—  -  .  t-t,,-,  4.0%  500  G•wa  —  •  1000 P’ (KPa)  -  —  1  i  1500  •  8.8m depth  7  Loing Bridge  33% unload 20%  •,,O 10%  *****  SBP13  2000  -  Fig.5.7. Variation of Unload-Reload Modulus with Effective Cavity Pressure for Different Unloadings (SBP13 Laing Bridge).  0  200-  600  800-  -  -  -  -  0.2-  0.4  0.6  0.8  I—  1.2  1.4  1.6  1.8-  2  2.2-  2.4  2.6  2.8-  3-  I  2  I  Fig.5.8. Effect  0  I  I  I  I  I  I  8  I  Radius of Influence.R/a  6  I  10  I  I  12  14  ll  of Assumed Radius of Influence on Average Modulus(Howje, 1991)  4  Average Modulus for a Given RI/c  Cylindrical Cavity Expansion  0  0  0—  20-  50  avC’  ..  F  —  F  for 8.6m Depth  -  Laing Bridge.  200  4 unload  100 150 P’ (kPa)  —  —  58P07 8.6m SCPT modulus  Fig.5.9. G. vs.  0  60-  80  . ,.  250  A  S  300  Chapter 5. Shear Modulus  67  to the in-situ stress. This signifies the importance of in-situ soil stiffness and also of the trend of increase in moduli with confining pressure. It is now significant that it is very important to determine what stress is to be used when Gur values are normalised to the in-situ stress. As discussed before, many authors have suggested methods for normalisation and the most common is the equation in the form  of eqn. 2.12 0.5 —  G ur  _f_.  [2.12]  ‘ave  where I  and a  =  /  /  I  51  0.2 (from Bellotti et al. 1989). This has been derived from eqn.2. 15.  Since °ur has not been normalised for strain the only way the validity of the above approach could be checked would be by plotting Gur and GurC against the unload-reload loop strain as shown in Fig.5. 10.  The GurC values appear to be have a good trend with the measured  SCPT modulus if a curve were to be drawn through points. However, it should be noted that the trend would also have been good if the moduli values had been lower. Though this method falls to take into account the larger volume of soil that comes under the influence of increased stresses with the progress of the test, by integrating along a radius, with no theoretical justification whatsoever, this method seems to provide reasons to believe that a reasonably good modulus-reduction curve can be obtained with the self-boring pressuremeter.  0)  I I  I  0.001  II•III  —  I  -  I  I.  7.lm  0.1  1111111  —  I  I  IIIIi  vs. Loop Strain at 7.lm  0.01 Loop Strain (%)  I  Loing Bridge  11111111  modulus  SBPO8  Fig.5.IO. Gur vs. Loop Strain and Depth Laing Bridge.  0.0001  6O-  80•  100-  00  Chapter 5. Shear Modulus  69  With this procedure for stress normalisation, the Gur values for the in-situ stress, ave’ are calculated for all the confining pressures at all the depths. beginning of unloading.  P’  is the cavity stress at the  It might be argued that since the pressure disthbution is very  difficult to understand during unloading the pressure at the centre of the loop should be taken as Pa’, however it can be observed that P’ will be different for different unloadings starting at the same confining pressure which then makes it impossible to use eqn.5. 1 for normalisation. Even if this normalisation were to be used, the modulus values would only increase. Since this will complicate the selection of the average stress it is simpler to use the stress at the beginning of unloading as Pa’. Tables 5.1, 5.2 and 5.3 show the unload-reload data from the three soundings selected. They show ho which is calculated by assuming a K 0 value of 0.5 as in Howie (1991) and Sully (1991). The reason for this was the failure in obtaining proper lift-offs due to equipment and installation problems. The tables also show Pa’, the cavity pressure; the amount of unload in terms of kPa; P’/P’ the %age unloading; A the loop strain;  -v’  the loop shear strain;  ‘  the friction angle; ç/min during the holding phase and Gur  the unload-reload modulus. Tables 5.4, 5.5 and 5.6 show results from applying the Bellotti et al. (1989) and Byrne et al. (1990) models to data from the present investigation. They show ave’ the average stress obtained from eqn.2. 12; ‘Yave’ the average loop shear strain; -y the loop shear strain and u 0 r’ the Gur value corrected by using eqn.2. 12. Plots of GurC vs. depth for the three soundings discussed are shown in Figs.5. 11 ,5. 12 and 5.13. A close look at the data for depth 5. 2m in Fig. 5.11 and in Table 5.5, shows that the Gur’ value increases with decrease in strain. The smallest shear strain of 0.087% seems  35  47  66  76  87  97  107  118  128  148  4.1  5.3  7.2  8.2  9.3  10.3  11.3  12.4  13.4  15.4 78  73  64  57  50  45  40  15.4  146  128  114  100  90  80  70  52  26  35  42  34  21  17  V0’  .  •  0.5  0.5  0.5  0.5  0.5  0.5  0.5  0.5  0.5  0.5  0.5  0 K  240  375  502  468  461  315 473  359 367  260 331  195 192  189  138 129 287 275  Gr  -  130  165  188  182  164  116 165  127 69  lii 118  79 38  63  53 25 100 43  ‘c  Table.5.1. Unload-Reload Modulus Data for SBPO6 Sounding Laing Bridge.  u (kPa 23  • Depth (m) 2.9  0.54  0.44  0.37  0.3’)  0.36  0.37 0.36  0.35 0.19  0.43 0.36  0.41 0.2  0.33  0.38 0.19 0.35 0.16  I  0.12  0.08  0.085  0.081  0.084  0.08 0.08  0.081 0.028  0.096 0.084  0.089 0.029  0.062  0.095 0.026 0.094 0.0145  0.24  0.16  0.17  0.162  0.168  0.16 0.16  0.162 0.056  0.192 0.168  0.178 0.058  0.124  0.19 0.052 0.188 0.029  40  40  40  40  40  40  4ô  40  40  40  40  63_  125  110  112  97  72 103  78 123  58 70  44 66  51  28 48 53 148  G.  55  65  65  81  109  136  7.1  8.6  11.5  13.9  130  110  84  70  54  vo’ (KPa)  0.5  0.5  0.5  0.5  0.5  • 0 K  495 801 783 794 800 1101  435 698 710 689 699 941  913 1055 1028 1036 1044 1152  472 570 566 569 570 655  477 487 564 733 750  c  (KPa)  226 363 336 292 141 431  218 294 312 232 127 357  380 442 416 339 199 459  202 247 242 184 114 290  205 258 201 321 350  4c... (KPa)  0.272 0.291 0.257 0.16 0.042 0.252  0.274 0.265 0.268 0.142 0.046 0.248  0.329 0.353 0.3 0.191 0.067 0.347  0.287 0.31 0.278 0.167 0.065 0.33  0.292 0.331 0.174 0.424 0.5  (%)  4c0.  0.544 0.582 0.514 0.32 0.084 0.504  0.548 0.53 0.536 0.284 0.092 0.496  0.358 0.706 0.6 0.382 0.134 0.694  0.574 0.62 0.556 0.334 0.13 0.66  0.584 0.662 0.348 0.848 0.1  (%)  Table.5.2. Unload-Reload Modulus Data for S13P08 Sounding Laing Bridge.  42  35  27  46  °ho (KPa)  5.2  U.  (KPa)  Depth (m)  -  7.62 12.32 12.05 12.2 12.3 16.94  12.5 12.7 12.9 12.5 12.7 17.1  24.7 24.86 27.43 7.9 12.69 12.9  13.5 16.3 18.7 21.74 25.1 24.5  17.67 18 20.9 27.15 27.8  arIlohO’  40  40  40  40  40  4 deg  -  0.11 0.08  -  0.12 0.08  -  0.23 0.2  -  0.17  0.15  0.18  0.17 0.12  Creep 1mm  41.5 62.37 65.37 91.25 167.9 85.5  39.78 55.47 58.21 81.7 138 72  57.75 62.6 69.33 88.74 148.5 66.14  35.19 39.84 43.5 55.1 87.7 43.94  33.34 39 57.76 37.85 35  Gur (MPa)  0.5 0.5  0.5 0.5 0.5  0.5  0.5  74 82  92 100 116  120  130  37  41  46  50  58  60  65  47  58  68  78  88  99  109  7.4  8.4  9.4  10.4  11.5  12.5  ;7c  0.544 0.5 0.15 0.368 0.6 0.094 0.204 0.282 0.556  0.272 0.25 0.075 0.184 0.3 0047 0.102 0.141 0.278  0.44 0.44 0.24 0.36 0.44 0.22 0.34 0.42 0.44  214 215 111 164 207 248 381 465 222  485 490 467 455 464 1133 1116 1119 510  -  0.162  0.081  0.24  100  414  Table.5.3. Unload-Reload Modulus Data for SBP11 Sounding Laing Bridge.  0.72  0.36  0.46  0.44 0.174 0.3 0.68 0.93  148  0.46  0.23  323  0.43  0.2 15  .  ::::4 ...... .  0.22 0.087 0.15 0.34 0.465  0.37  ,.....................  :4P/P  0.38 0.22 0.22 0.35 0.42  82  .....  102 59 147 226 269  .  268 266 660 651 644  ..  4Pe’  0.39  .  101  258  223  ........:..............  6.3  .....  0.5  ø:I  60  I::  30  :9.i  34  ..  U.  ::::Pepth (m) 5.0 ..  40  40  40  40  40  40  40  40  :Gjjr*  35.86 70.58 69.34 41.7 35.3 28.35  0.04 0.02  0.05  -  0.1  -  -  60.7  248 78.9 51.47 539 299 246  61.23 70.05  184  33.4  0.1  -  28.2  -  .  Quifl:  0.081 0.028 0.08 0.08  59.8 59.2  80 94.2  103.8 105.4  101.4 130.6  132.2  139.2  143.6  126.2  106.4  5.3  7.2  8.2  9.3  10.3  11.3  12.4  13.4  15.4  0.06  0.12  -  0.74  70.97  0.2398 52.37  0.66  135.33 0.2103  89.34  0.69  104.33  0.68  0.1774  67.82  0.69  0.75 0.67  0.7 0.84  0.68 0.69  0.7 0.85  0.72  0.7 0.85 0.56 0.81  Gur/GoSbP  86.63  66.78 90.02  69.52 90.55  56.17 62.3  42.1 50.93  43.95  25.77 37.02 46.32 91.31  GbP (MPa)  100.45  0.1873  0.1643  0.1577 0.1577  0.1314 0.1314  0.115 0.115  0.0854 0.0854  0.069  0.0559 0.0559 0.0559 0.0559  Table.5.4. for SBPO6 Sounding (Bellotti et al., 1989 and Byrne Ct al., 1990 Procedures) Laing Bridge.  0.04  0.042  rIliax  (KPa)  71.89  60.03  0.042 0.04  49.88 60.53  48.67 75.91  38.24 42.81  29.26 43.42  31.5  17.92 31.58 26.03 73.81  ‘ur” (MPa)  0.04 0.04  0.04 0.014  0.048 0.042  0.045 0.015  0.031  0.048 0.013 0.047 0.007  (‘°)  0.08  0.085  0.081  0.084  0.096 0.084  0.089 0.029  0.062  54.6  4.1  0.095 0.026 0.094 0.0145  (%)  Y av  41.2 31.4 71 68.6  (KPa)  2.9  Depth (in)  0.55  0.8  1.03  0.92  1.02  0.89 1.1  1.02 1.2  0.87 1.05  0.89 1.1  1.03  0.94 1.1 1.3 1.6  Gur/Oniax  a =  .114  156  106  121  95  81 93.7  76.4 102.5  65.5 66.6  49.8 59.5  49.4  29.6 43.6 40.7 92.5  (Mia  •  151 212 208.6 210.8 212 272  13.9 0.272 0.291 0.257 0.16 0.042 0.252  0.274 0.265 0.268 0.142 0.046 0.248  0.329 0.353 0.3 0.191 0.067 0.347  0.287 0.31 0.278 0.167 0.065 0.33  0.292 0.331 0.174 0.424 0.5  i’av (%)  0.136 0.146 0.129 0.08 0.021 0.126  0.137 0.133 0.134 0.071 0.023 0.124  0.165 0.177 0.15 0.096 0.034 0.174  0.144 0.155 0.139 0.084 0.033 0.165  0.087 0.212 0.25  0.166  0.146  27.26 34.52 36.49 50.67 92.95 41.79  25.78 30.36 31.65 44.93 75.5 35.03  25.45 25.94 29.05 37.06 61.82 26.38  18.8 19.8 21.7 27.37 43.54 20.6  (MPa) 16 18.6 25.9 15.2 13.9  0.2136 0.2136 0.2136 0.2136 0.2136 0.2136  0.1807 0.1807 0.1807 0.1807 0.1807 0.1807  0.138 0.138 0.138 0.138 0.138 0.138  0.115 0.115 0.115 0.115 0.115 0.115  (KPa) 0.0887 0.0887 0.0887 0.0887 0.0887  niax  Byrne et al., 1990 Procedures) -  Laing Bridge.  Table.5 5. G,,,,, for S13P08 Sounding (Bellotti et al.. 1989 and  131 183.6 186 181.8 183.8 232.2  216 244.6 239.2 240.8 242.4 264  8.6 •  11.5  122.4 142 141.2 141.8 142 159  •  as/  (KPa) 117 119 134 168.2 171.6  7.1  5.2  Depth (m)  41.75 65.18 65.06 81.68 113.74 82.44  42.31 54.73 59.66 69.45 93.48 67.46  64.75 77.13 78.86 76.1 88.33 7836  35.48 42.37 45.51 45.42 57.75 50.48  (MPa) 33.87 60.4 52.59 55.13 63.83  sbp 00  0.65 0.53 0.56 0.62 0.82 0.51  0.61 0.55 0.53 0.65 0.81 0.52  0.39 0.34 0.37 0.49 0.7 0.34  0.53 0.47 0.48 0.6 0.75 0.41  0.47 0.31 0.49 0.28 0.22  GurCIGoP  0.85 1.05 1.03 1.15 1.4 1.25  0.82 1.08 1.08 1.2 1.42 1.26  1.33 1.4 1.42 1.39 2 1.3  1.08 1.18 1.17 1.33 1.56 1.22  1.12 1.08 1.43 1.38 1.35  GIjrIOm  .:•..  48.8 59.4 67.4 79.4 119 68  48.5 51.4 53.9 68.1 97.1 57.1  43.5 44.7 48.8 63.8 74 50.8  32.6 34 37.1 41.35 56.2 36  (MPa) 29.8 36.1 40.4 27.4 25.9  max  Table.5.6. G,, for SBP1 1 Sounding (Bellotti et aL, 1989 and Byrne et aL, 1990 Procedures) Laing Bridge.  69.7  0.87  0.44 80.95  0.2136  39.4  0.139  0.278  154  12.5  •  229 83.9 60.4 317 216 195.3  1.08 0.94 0.85 1.7 1.38 1.26 0.38 0.52 0.49 0.4 0.27 0.42  420.7 100.4 68.7 633 521 670 0.1971 0.1971 0.1971 0.1971 0.1971 0.1971  161.8 51.8 33.6 252 141 115.7  0.038 0.092 0.15 0.024 0.051 0.071  0.075 0.184 0.3 0.047 0.102 0.141  141.4 139 140.8 274.6 271.2 271.8  11.5  68 77.7 0.9 0.9  0.44 0.42  87.7 106.3  0.1906 0.1906  38.94 44.4  0.136 0.125  0.272 0.25  143.4 144.4  10.4  165 1.11  0.42  278  0.1643  117.4  0.041  0.081  122.8  9.4  34.6  0.82  0.55  35.03  0.1511  19.1  0.18  0.36  101.4  8.4  41.1 69.9 45.1 32.6 29.7  0.87 1.01 1.53 1.28 1.19  0.6 0.69 0.61 0.47 0.39  41.41 71.12 56.25 44.33 45.94  0.1347 0.1347 0.1347 0.1347 0.1347  24.7 48.7 34.6 20.9 17.8  0.11 0.044 0.075 0.17 0.233  0.22 0.087 0.15 0.34 0.465  86.4 86 164.8 163 161.6  7.4  38  0.88  0.57  39.35  0.1216  22.56  0.115  0.23  81.2  6.3  G* (MPa) 30.3  0.93  Alas  0.59  G:IG:” (MPa) 31.44  (%) 0.215  -  (KPa) 0.0986  Gurc (MPa) 18.65  ..  7 (%) 0.108  (KPa) 68.6  -  Depth (m) 5.0  -4-’  -c a)  0  00000  0  Fig.5. 11. G  -  16-  12-  .1  4-’  0—  a  0  0  I  I  I  40  a  I  a  10  I  °  I  I I  I  0  0  I  —  I  80 I  I  —  a  I  vs. Depth for SBPO6 Sounding  Loin9 5ridge  0  I  24.Oct.91  ———?  I  SCPT moduli SBPO6 moduli  0  I  GurC (MPa) I  I I  -  I  I  120 I I  I  Laing Bridge.  56P06  I I  I I  I  a’  0  -c .4-’  0  •  I  I I  a  I  I  I  a  Lain Srid9e  a  0  I I  —  I I  I  80 I  I I  I  I  I  I I  I  120 I  20Feb.92  0  —  -  Laing Bridge.  SEP08  •.‘.-. SCPT moduli SBPO8 moduli  I  vs. Depth for SBPO8 Sounding  a  I  40  a  I  DU  ma  0  a  GurC  ama  Fig.5. 12.  20  16-  12-  -  4-  0—  CurC (MPo)  0  a  a  —  I  i I I I I I I I I  I  I  23Apr.91  —  -  Laing Bridge.  58P11  a  300  I I I I I I I I I  250  I I I I I I I I I  •..ee SCPT moduli SBP11 rnodulr  I I I I I I I I I  Lain 8rid9e  I  100  I I I I I I I I I  50  Fig.5.13. GurC vs. Depth for SBP11 Sounding  20—  16-  4-  0—  GurC (MPa) 150 200  00  Chapter 5. Shear Modulus  79  to correspond to a GurC of 25.9 MPa and the largest shear strain of 0.25% corresponds to a value of 13.9 MPa. This might suggest that the stress normalisation does not work for all amounts of unloading. However, it becomes difficult to evaluate, since the lantern friction and compliance effects also come into play. The difference in the data obtained from different lanterns can be seen from the three soundings shown earlier on. Fig. 5.10 from sounding SBPO6 using lantern # 3 showed higher moduli than results from SBPO8 with lantern # 7 and SBP1 1 with lantern # 9. The latter two seem to show more sensible results since it is known that the disturbance caused during an SBPMT will tend to reduce modulus values much lower than SCPT Gm values. Fig.5. 14. shows a pressure-expansion curve from SBPO6. The test could be conducted only upto 4% radial strain.  This was due to the fact that the highest pressure that could be  obtained at that time was 800 kPa because of the absence of the pressure multiplier. The yield surface is linear and the curve appears highly disturbed. To understand the disturbance it would be necessary to use a curve fitting technique like that of the Hughes (1977) model to obtain a best fit. Fig.5. 15 shows the Hughes (1977) curve fit as performed on one of the curves from SBPO8 sounding. The reason for using SBPO8 was because a curve performed only upto 4% radial strain cannot be fitted by any model. The flat portion at 2% is the portion where the unload-reload loops were performed. They were removed in order to fit the curve. This figure suggests that the effect of disturbance can be found upto 5% radial strain in the case of the present SBPM. In other words the unload-reload ioops before 5% radial strain should show much smaller values due to disturbance. SBPO6 results on the contrary show higher results.  As such the results from SBPO8 and SBP1 1 seem more  C)  >  0  a)  L  D cL  0.4  Loing Bridge  0.9 1.4 Radial Strain  —  (%)  1.9  —  9.3m  2.4  2.9  iri—i,iiiiiiii.iiiiiiiiii—iiiiii,iiiiii,iiijiii,i,iiiii, .ii  SBPO6  Fig.5. 14. Pressure-Expansion Curve at 9.3ni Depth (SBPO6 Sounding) Laing Bridge.  0— —0.1  200-  400-  600-  800  Fig.5. 15. SBPM Pressure-Expansion Curve with Hughes (1977) Curve Fit.  P:PLOT F:FINISII R:REDRAW lateral stress 45,34,50 friction angle critical friction angle 1 shear Modulus 13000  Go  Chapter 5. Shear Modulus  82  sensible. This shows that the lantern effect is highly pronounced for SBPO6. However, it can be seen that whatever is the lantern type the Gur’ will differ with amount of unloading for the method of correction employed.  Fig.5. 11 and Table. 5.2 show SBPO8 results.  Observing depth 13.9m, it can be seen that the first loop obtained is at 2% where the disturbance is pronounced. As such a low value is obtained. The loop performed at 0.042% loop strain seems to give a Gur” value of 92.95 MPa, a value much higher than the rest. This might suggest that the smaller unloadings definitely are affected by initial friction in the lantern suggesting that if the friction could be eliminated the Gur values for the smaller loops could be used. For the present investigation, neglecting the high results from the smaller loops, the method suggested to obtain 1 ave’ could be used, as it yields values which are in the range of expected GurC values. The above discussion shows the difficulty in deciding what stress has to be used, since in-situ stress is reached at the elastic-plastic interface and the stress at the wall is the cavity stress, it would be simpler to use an average stress. However, it becomes difficult to decide what stress has to be used. This was the essential concern addressed by the Byrne et al. (1990) analysis.  They referenced the in-situ stress state considering the complete  variation in stress and strain states. However, since a reasonable trend was obtained, for calculation purposes the eqn.2. 12 is used, with the more advantageous Byrne et al. (1990) model being discussed further in this chapter. It must also be observed from table 5.1 that stress controlled testing makes it difficult to obtain loops of the same strain for different stresses. As such it becomes difficult to obtain Gur versus depth profile for one particular strain.  Chapter 5. Shear Modulus  83  5.2.2. Effect of Strain Level  The discussion in the previous section showed the importance of correction for stress and strain levels. The strains of concern are the loop strain and the cavity strain. The strain obtained from a pressure  -  expansion curve is the radial strain. To obtain shear strain for  the loop, Yave’ =O. ’ is used as discussed in chapter 2. 5  The use of average strain  calculated over the increasing size of plastic zone means that, for a constant cavity strain increment, the calculated average shear strain over which Gur is measured reduces as cavity stress and hence the radius of the plastic zone increases. The Gur’ values obtained from the soundings discussed in the previous section are plotted versus average shear strain amplitude for the loops. These values seem to fall in the range of 0.02% to 0.45% loop shear strain.  This shows the limits of strain range for  pressuremeter testing. If higher values of loop strain are to be obtained, tests should be conducted at higher confining pressures so that larger unloadings can be obtained. The highest pressure that could be reached with the present system is 1500 kPa. It should also be noted that strains smaller than 0.02% are below the limit of readability of the instruments. Another thing to be noticed is that the pressuremeter can yield results for the modulus reduction curve in the region between 0.01% and 0.5% where the largest change in values of shear moduli are obtained. Moduli below 0.01 % loop shear strain are fairly constant and as such a modulus reduction curve could be drawn using Gm from the SCPT as one of the data points. With the limited data, an attempt was made to obtain modulus reduction curves for the depths shown in figures 5.16,5.17, 5.18, 5.19, and 5.20. These figures seem to yield  0  0  s*s oosø  I  1111111  I  .4-?  I  -  *  Laing Bridge.  ()  *  0.1  1111111  0.001 0.01 Shear Strain Amplitude  —  5.2m sbpO6.sbpO7.sbpl 1 SCPT moduIis  Fig.5.16. GurC vs. Shear Strain at 5.2m Depth  0.0001  0-  .10  -  20  o...30-  40-  5o.  60  S  0  C-,  *.*.s  Fig.5.17.  0.0001  0—  20-  40  60  80  GurC  1111111  vs. Shear Strain at 7.lm Depth  *  -  * *  Laing Bridge.  ()  0.1  1111111  0.001 0.01 Shear Strain Amplitude  —  7.lm sbpll 1 sbpO6sbpO7 SCPT modulus  IFIlI,  Fig.5.18. GurC  •  1111111  •  vs. Shear Strain at 1O.3m Depth  -  Laing Bridge.  0.1  (%)  11,11111  0.001 0.01 Shear Strain Amplitude  —  1O.3m sbpll 1 sbpO6 ••..- SCPT modulus  0.0001  20—  30  60  70  8O  C,  * e ‘. D•ss  Fig.5. 19.  0.0001  0—  20-  40  60-  8O  100  I  1II1I1  I  I  vs. Shear Strain at 11 .5m Depth  -  *  *  Laing Bridge.  ()  0.1  IIIIII  *  0.001 0.01 Shear Strain Amplitude  i•iii.i  Gur’  i  •  11 Sm —sbpO6.sbpO7sbpl 1 SCPT modulus  0  Fig.5.20.  I  ‘s.’ s-....  o$0001  2O  4o.  6O-  8O  1o0.  120  I  I  IIIIIIJ  I  I  e  IIIIIIJ  *  vs. Shear Strain at 13.9m Depth  -  *  a  I  I  Laing Bridge.  0.01 0.1 0.001 Strain Amplitude Shear (%)  1111111  GurC  I  —  139m sbpO6, sbpO7 SCPT modulus  IIIIIb  00 00  Chapter 5. Shear Modulus  89  reasonable results once the high values of moduli from very small unloadings (10%) were removed (as in depth 11 .5m of sounding SBP1 1). The high values obtained for the smaller unloadings might be due to many reasons some of which can be attributed to friction due to overlapping of the strips  ( by the time initial friction is overcome most of the unloading  would have been completed), welding of the strips which might increase lantern stiffness, small sampling rate of the data points which will make it difficult to get a reasonably well defined ioop, etc. All these effects might be found to affect other loops too. However, the effect will be more pronounced on smaller loops. Having taken into account the results from the smaller loops it could be assumed that the SBPM results could possibly provide good modulus reduction curves for any amount of unloading except very small amounts.  The  results from above seem to agree reasonably well with the SCPT data and it can be concluded that a reasonable estimate of the Gm could be obtained from the SBPM data. However, it should be noted that a number of tests were required to obtain these curves. Howie (1991) and many others have reported that once 10% radial strain is reached the expansion will tend to be non-cylindrical. Also, fig.5. 15 shows the effect of disturbance on the initial part of the curve. It can be observed that in all the depths shown in Appendix A when the Hughes (1977) model was fitted to the curves, the installation disturbance might affect the initial 5 % of the pressure-expansion curve. This suggests that the loops should be performed between 5% and 10% cavity strains if disturbance effects are to be taken into account.  This would limit the number of sets of loops that could be performed in a  particular pressure-expansion curve. As such it would be desirable to formulate a method that  Chapter 5. Shear Modulus  90  could yield a good modulus reduction curve from a limited number of data points. One such attempt is briefly discussed in section  5.2.3. Effect of Unloading  Various researchers have discussed the effect of ioop size on the modulus. All the loops in this investigation give reasonably good values of moduli irrespective of the amount of unloading. However, it should be noticed that the Wroth criterion as given in eqn.2. 19  —  2SI114’  ‘lp”  [5.11]  1+sinc’) where P’  =  effective cavity pressure at the start of the ioop,  was not exceeded in any of the unload-reload loops performed. The tables 5.4, 5.5 and 5.6 along with figures 5.10 to 5.13 show that all the points obtained seem to fall fairly close together except for the loops with unloadings around 10% of the cavity pressure. The reason for this might be either the stiffness of the lantern or the resolution because of the limit on the instrumentation with respect to the number of data points that can be sampled per minute. The lantern being made up of many strips will have to overcome the initial friction especially with the sand that might have entered the gaps between the strips. This friction stops the lantern from moving until a sufficient amount of unloading is done. The amount of friction differs with lantern type. The figure 5.5 which shows Gur versus  P’  for lantern # 9 shows  Gur of the magnitude of 600 MPa. Also, table 5.6 shows the same lantern during another test (sbpll  -  ll.5m) reflecting a similar effect. This drawback will affect the smaller loops  Chapter 5. Shear Modulus  91  especially at lower confining pressures. This is because a small loop of say 10% unloading at low confining pressure of around 200 kPa would have to unload by 20 kPa.  When  unloading starts, the friction between the strips restricts movement until the friction is overcome. For small loops of the type mentioned above most of the unloading would be done by the time the friction is overcome. This would result in a very stiff loop. However,  a loop at say 1000 kPa, for 10% unloading would have to unload by 100 kPa. This loop would have a higher resolution than the earlier loop. As such, provided the lantern were to be flexible enough, these loops also might provide good values of the modulus. However, it is of prime importance how these loops are programmed, especially when more than one cycle is performed. This will be discussed in the coming sections.  5.2.4. Effect of Creep  Creep effects in pressuremeter tests are evaluated with tests having holding phases at various confining pressures 100 kPa apart. It has been seen that creep in pressuremeter tests is much higher than the creep in triaxial tests shown by Meija et al.(1988).  The  stresses around the pressuremeter being extremely high with the stress ratios being failure stress ratios it would not be possible to compare the creep from the two. Howie (1990) provided an explanation considering the size of the plastic zone around the cavity. This was illustrated assuming that soil conforms to a model of linear-elastic frictional plastic material. Creep behaviour is out of the scope of this thesis and only the possible effects of creep on the modulus is studied. The creep effect with rate of testing was not studied since only one  Chapter 5. Shear Modulus  92  rate of test was used over the entire test. Jackson et at. (1980) have found that for loading times greater than one millisecond, rate effects had very minor effect. Meija et at. (1988) showed that approximately 2% shear strain occurred in sands in 20 minutes at a stress ratio of 5 and that at high stress ratios creep strains were dilative. Figure 5.21 shows a plot of strain versus time of a test that was conducted with various creep phases at different pressures. The strain has been measured from the start of each holding phase. It can be observed that the creep rate increases with confining pressure. It is also evident that the increase with pressure is logarithmic because of the expanding plastic zone. Hence, higher the pressure, higher will be the holding phase that has to be incorporated before unloading. This makes it necessary to find the exact holding phase that has to be chosen if the moduli are to be unaffected. For this purpose, a test with 11 cycles as shown in figure 5.22 was conducted at a particular confining pressure. The figure 5.23 shows that all the unloading portions were identical, with the unload strains (strain AB during unloading) showing no change with the number of loops.  However, the loop strain  (strain BC) seems to increase with the number of loops and stabilise after a particular amount of strain accumulation. The modulus values also show a similar trend of increasing initially and stabilising as seen in fig.5.24. The modulus and strain do not seem to change when creep rates of less than 0.01 %/min. are reached. A look at the holding phases incorporated would show that, generally, the cavity strain/minute would be around 0.01 %/minute after 10 minutes from the start of the holding phase. The first loop shows a large amount of creep in the reloading portion thus resulting in a rounded loop. The last loop does however show a better defined ioop with all the creep strains eliminated. It has been shown by Howie  93  Time (s)  0.0  0.2  O.4 C  2 “0.6  0.8  1.0  Fig.5.21 Change in  Loing Bridge  c vs.  Time.  —  30. jun. 92 -SBPO14  94  -  -  09.un.1992  —  Letno &tdg. South— SBP13  C  a 4-.  a C  a a a C. 0. S  43  C  RodoI  ..-.320  .un.19 9 0 2  —  Stra.tti C%)  Letng Srtdg. South  —  C  a  4-’296 a C..  a a a 4-,  C  I-,  Fig .5.22 sit’  2.6 2.6 Radtal Stra1n (%) Multi-cycle Pressure-Expansion Curves  SBP13  95  320-  09.un.1992  —  L.Lng Br Ldg. South  —  SBP13  26BC L D 0 C -  . .4)  C  Smoothed date  Dsp th4. 3m  160— 2.4  —E  2.6  RodtI Fig.5.23  2.8  Stren ()  Smoothed Loops from Multi Cycle Tests.  3.0  96  Loing Bridge South  o —-  -  SBPI3  Unload Strom 0•—  ..—.  -S  -.  a  I I Loop Sboin  I  I  0.04  —  0  I1iI1I1IIIIIII1FI1IIIIIl11I1IIIJIJ1jIII1111II1TTF11T1j  6  8 Number of Loops  2  10  Fig.5.24 Unload Strain (AB) vs. Time and Loop Strain (BC) vs. Time (SBP13 Sounding) Laing Bridge. -  12  97  Loing Bridge South  —  SSP1Z  -  20— 0  10 5 Number of loops  Fig.5.25 Unload-Reload Modulus Versus Number of Loops.  15  Chapter 5. Shear Modulus  98  (1990) that stress controlled tests can yield better results in terms of the creep effect on moduli than strain controlled tests. A strain controlled test would have meant that the strain would remain constant and the stress would decrease and the loop would begin in the elastic zone.  The decreasing stress would cause problems with respect to the extent of elastic  unloading. Most of the data that was obtained in all the soundings had fixed amount of creep phases varying from 3 to 7 mins depending on the cavity pressure. As indicated earlier, the fact that the testing was done with loops at set strains (2%, 6% and 10% radial strains), the loops done with and without holding phases could not be compared. This is because when two different soundings are compared at a particular depth the confining pressures could be different for a particular strain. As such the creep studies were done with a test comprising of repeated cycles of load-reload. The result obtained is quite on the contrary to that obtained by Howie, 1990, who suggested that there seems to be little effect on modulus of a small number of cycles. This essentially suggests that all tests done with unload-reload cycles should incorporate holding phases prior to unloading. At creep rates of 0.03-0.02%/mm. or less the effect on moduli is minimal. Very slow tests as done by some investigators might induce effects of creep into the modulus. The creep rate has to nearly zero if a small loop has to be performed at a fast rate. The results of Gur and Gur’ versus depth and versus shear strain for various soundings suggest that the rate of testing does not have any effect in the range tested (3 kPalsec to l0kPalsec). However, the equipment effects are such that this effect is very difficult to discern.  Chapter 5. Shear Modulus  99  5.2.5.Effect of Equipment.  Equipment aspects have been the most important influence in this investigation. The problems of accuracy and compliance have been discussed by many investigators including Fahey & Jewell (1990) and Howie (1990). The major effect here was from compliance and lantern stiffness. It must be observed that the lanterns used in this investigation were made of steel strips that were spot welded and have overlaps as seen in fig.3.3. The lantern with two halves had the problem of more movement at the overlaps and less at the middle of the halves. This resulted in stiffer moduli from strain arms which had lesser movements and smaller moduli in the others showing more movement. Averaging all the arms would mean getting an average stiff value.  As such two opposite arms showing lesser moduli were  selected bearing in mind the error that might be induced. Lantern 9 was made up of many strips that were put together only with overlaps. They were free to move at the overlaps to high strains. But the overlaps resulted in very high friction between the strips during unloading, as discussed in the earlier sections, and as such resulted in stiff loops.  The  results of the soundings which showed very high moduli values can be seen in the figures provided in the Appendix A. The sand entering these overlaps could cause further problems in that it would not allow the strips return easily. The compliance showed similar problems wherein the strips continued to readjust at high pressures thus giving rise to very high corrections. It was also noticed later that the split cylinder used for the calibration test had differences in dimensions with the probe. All the results have been corrected for compliance according to the eqn.  Chapter 5. Shear Modulus  100  1 Gcoected  =  1 Gmered  —  1  [5.12]  G.yem  where =  shear modulus derived from lantern and membrane compression  Gme = shear modulus of the soil along with that of the system Geoff = shear modulus of the soil  5.2.6 Theoretical Models applied to UBC data Modulus Reduction Curve  A model (Hughes  -  personal communication) based on that developed by Hughes,  Wroth and Windle(1977) to obtain the modulus reduction curves using Gur’ and Hughes (1977) curve fitting technique is discussed herein. An attempt is made to obtain the shear modulus at the low strain end and at the high strain end of the modulus reduction curve for  any pressure-expansion curve using the Hughes (1977) curve fitting technique and try to tie them in with the Gc values that are obtained for the unload-reload loops in the same pressure-expansion curve using the method stated in the earlier sections. Assumptions made are that the soil deforms plastically at a constant ratio of principal stresses during failure. Further, during the failure process, the material either contracts or expands depending on the density and stress state of the granular material. The soil is assumed to behave elastically (not restricted to just linear) prior to failure stress ratios being reached. The initial secant  Chapter 5. Shear Modulus  101  shear modulus, 1 (G from zero stress to initiation of failure stress ratio); effective horizontal stress,crh; constant volume friction angle 4k,,’ and friction angle 4)’ are required in the following model. The Hughes (1977) model recognising the similarity between the unload-reload modulus and G 0 the maximum shear modulus at small strains suggests a method to estimate 0 with initial estimates of the above mentioned parameters. They have defined the (3 as G a average constant value of shear modulus when the soil is behaving elastically. This is for a higher magnitude of strain than G 0 and can be defined up to the elastic-plastic boundary.  Assuming the stress-strain behaviour of cohesionless material to follow the hyperbolic model proposed by Kondner (1963), the stress-strain relation can be given by  Y  t  [5.2] 0 G  t  or  1  G=  [5.3]  +  0 G where G 0 is the maximum shear modulus,  Tm  tm  is the maximum shear stress, G=r1 7 is the  shear modulus at any strain. Rearranging the above equation, we obtain Here a mean effective stress need not be used since G 1 is defined within elastic limits.  Chapter 5. Shear Modulus  102 __i__.!._ 0 G  [5.4]  When failure begins (Hughes et al. ,1977) / I / OrO+AOr  155  and the shear stress -  [5.6]  —  2 When the soil behaves elastically, Therefore  Aur’  ‘  2Aa  /  2 Then from Hughes et al (1977)  (c/h3  (az,  -  +  Ac4)  -  [5.81  (+sin4/)  Ac4)  Rearranging,  (-sin4)  /  sifl4)”  [5.9]  In other words the shear stress at which failure stress ratio is reached can be given by  t  where  h  —  %sin4/  =  The maximum shear stress could be given by  [5.10]  Chapter 5. Shear Modulus  103 [5.11]  a’tan  —  The Hughes (1977) model is then fitted to the pressure-expansion curve as shown in fig.5. 15. The initial fit is obtained by a reasonable knowledge of 4’,  lateral stress and (3 as a  first guess. To obtain 1 G Gur is assumed as equal to (3 as a first approximation. In the , absence of Gur, G 0 from any other method can be used and the best fit as seen in fig.5. 15 is obtained from the Hughes (1977) curve fitting program by repeated alterations of the above mentioned parameters. Using eqns.5. 10 and 5.11 in eqn.5.4 one can obtain  4s1n4’  -  -  0 G  [5.12]  4tanp’  G.  1—cos4  [5.13]  (1—cos) G.  [5.14]  — —  0 G or 1 0 G  —  The values of the above mentioned parameters are altered until a good fit is obtained. The final values of these parameters are then used as input into the equation 5.2 to obtain  Y 1—cosc G.  +  y  [5.15]  Chapter 5. Shear Modulus  104  where ‘y is the Ylimit at the boundary between elastic and plastic behaviour. The values of 0 and G at the ‘Ylimit obtained from applying the above equations are plotted along with the G  Gur” got from the UBC SBPM tests. The results are shown in Figures 5.26,5.27 and 5.28 respectively. The results show a reasonably good match with those from UBC SBPM tests. The trend of both the G 0 plotted against ‘Ylimit  0h0’,  the insitu stress, and the G plotted against  seem to suggest that a reasonably good modulus reduction curve could be obtained by  using points obtained from the above model with the SBPM data. The values of the Gm from the model and that from the SCPT also match quite well. Thus it can be shown that the model provides two points, one at low strain end and the other at the high strain end yielding a fairly well defined modulus reduction curve. Gm from the SBPM  Having corrected Gur for the stress and strain levels and having discussed the effect of unloading, creep and equipment effects, it is now of prime importance to link the Gur values with the moduli values required for geotechnical design problems.  The easiest  method to link Gur with Gm would be by using the Hardin and Drnevich (1972) hyperbolic model which for all practical purposes matches the decay of G with increasing ‘y. The model is of the form  C-,  * *  OGOO* acooa  Fig.5.26  0.001 0.01 Shear Strain Amplitude  0.1  (%)  , Gommanm) 1 (C  UBC SBPM —5.3 m —sigma.’—265 KPo SCPT modulus G, from model  Modulus Reduction Curve from Proposed Model at Depth 5.2m Depth -Laing Bridge.  0— 0.0001  10.  20:  a. 30-  40-  5O  60  0  * * *  7 Fig.5.2  o  0.01  *  0.1  11111111  (G Gomr?ia imit)  S  Shear Strain Amplitude (%)  0.001  1I1I11  *  *  UBC SBPM —7.2 m —sigmar’2OO KPa SCPT modulus G, from model  Modulus Reduction Curve from Proposed Model at Depth 7. im Depth -Laing Bridge. .  *000e ooa  0.0001  0—  10.  30:  4O  50  60  0  C.,  4.—  0  i  i  I  I  I  111111  1  I  I  0.1  (%)  IIIII  (G, Gamma  *  a  ——  *  445 kPG  0.001 0.01 Shear Strain Amplitude  IIIII  G,, from model  —  I  *  I  111111  Fig.5.28. Modulus Reduction Curve from Proposed Model at Depth 1 1.5m Depth -Laing Bridge.  0.0001  0—  20  40-  60  -  80  ooooa  100: *. * * UBC SBPM —11 .5m —sig mar’ • •ooo SCPT modulus  C  Chapter 5. Shear Modulus  108  G• 0 G  1 [5.16]  1+ Yr  where G is the shear modulus at strain -y,  m T  is the maximum shear stress and 7 r is the  reference strain. This method was used in the model proposed earlier to obtain the modulus reduction curves. However, it was used to obtain a single value from one whole pressureexpansion curve and did not involve the loops.  An attempt was made by Bellotti et al.  (1989) in this regard when they suggested using  G  1 1+  Y 2t,  ‘-‘a  [  G S bP is the maximum where GurC is the unload-reload modulus normalised to in-situ stress, 0  shear modulus from the SBPM, Yave is the average shear strain and failure  =  Tf  is the shear stress at  P ’ 0 (l +sin’), to convert Gur to the equivalent small strain moduli. However,  the above hyperbolic relationship was based on resonant column data where the number of cycles was large. As such, to fit the same to the hyperbolic relationship Bellotti et al. (1989) used a factor FN = 1.5 to allow for the number of cycles. It is to be noted that there is very little validity for the above assumption. To evaluate the method suggested above, Gur was first corrected for stress level as discussed earlier on, to obtain the normalised modulus Gc at the in-situ mean plane strain stress. It was not corrected for the number of cycles since there is no validity for such an  Chapter 5. Shear Modulus  109  assumption (Negussey, 1985). This was also due to the fact that multi-cycle tests showed no difference in modulus with the number of cycles after creep was eliminated. After this, the eqn. 5.14 is used to obtain  GOSbP.  The results are shown in fig.5.29,5.30 and 5.31. The  soundings are sbpO6,sbp08 and sbpl 1. The lanterns used for each of the soundings were different, thus making the lantern type one of reasons for the difference in the Gm values obtained. The other reasons are soil changes and the resolution of the system. The results from Bellotti et al.(1989) test in Po river sand using a factor of 1.5 for FN are about 0.8 times the SCPT modulus. Results from sbpo8 and sbpl 1 seem to show values that are equal to the SCPT moduli. SbpO6 shows results that are about 1.5 times greater than the SCPT results. This would mean a difference of a factor of 1.85 between the Bellotti results and the results from sbp08 and sbpl 1, the latter two showing higher values. This would be much higher for sbp06.  Since the same method is being used, the difference could only be  attributed to equipment effects. The compliance of the lanterns used being high and the friction between the strips being not easily identifiable, it would be very difficult to decide if the lantern were to be solely responsible for this discrepancy. This difference in the results could be checked to a certain extent by applying another model (Byrne et al., 1990) and comparing the results. The Byrne model is very simple to use and is based on an elastic plastic analysis to determine the stress field caused by pressuremeter expansion and a nonlinear elastic analysis to determine displacements at the pressuremeter face upon unloading. The chart provided by Byrne et al. (1990) was used to an obtain equivalent shear modulus. It should however be noted that the chart is limited to r’o’ values of 12. Any value higher than 12 was extrapolated.  It seems that the obtained  •  •  I  f I  +0  —  150  a  1  J  —  a  0  0  0  +  —  SEP06  *.ses45—5Q  00000 15—20* aaoaa 30—35* 0000035—40*  Degree of unloading  100  200  iiiiilli_iii I I I iiii 11111111  SCPT————  +0  a  Q  I  240ct1991 Loin Brid9e South SCPT 17.Oct.199  *  50  iIIIIIIIII I  -  bP Fig.5.29. Profile of 0 with Depth (SBPO6 Sounding-Bellotti et al., 1989 Procedure) Laing Bridge.  20:  12  8  •  4:  0  Gmax (MPa)  •  20:  12-  :  o  *  —  —  ii  I I  150  II iii I I I I I Ii  0  15—20*  35—40*  —  SBPOB  0OOo*4O—4*  *****  oooaoQ—35  00000  Degree of unloading  100 Ii  I ii lit  SCPT————  +0  i  2O.Fibi92 Loing Bridge South 17.Oct.1991  +  *  4’  I  50  it  SOPT  •  -  Fig.5.30. Profile of GOShP with Depth (S13P08 Sound ing-Bcllotti Procedure) Laing Bridge.  ci)  E  4-  •  0—  Gmax (MPa)  Ct  al., 1989  200  20  15  -  —  SCPT————  —  150  15—20%  —  SBP1 I  s*sss40_45%  0*00035—40%  0000030—35%  00000  Degree of unloading  100  23.Apr.1992 Loin Sndg. South 17.OoLICQ SCPT  0  •  •  *  •  0  50 200  Fig.5.31. Profile of G’ with Depth (SBP11 Sounding-Bellotti et al., 1989 Procedure) Laing Bridge.  11)  •  0-  o  Gmax (MPa)  Chapter 5. Shear Modulus  113  results are the same as SCPT moduli in the case of sbpO8 and sbpl 1 and much higher in the case of sbpo6.  According to Byrne et al. (1990) a factor of 1.4 has to be used as a  disturbance factor.  This would bring about a difference of a factor of 1.4*1.2=1.68  between the present investigation and Byrne model. It appears that the difference in results from the above models is very small. But however, a look at the Hughes-1977 curve fit for  all the pressure-expansion curves shown in Appendix A shows that all the curves seem to have installation disturbance affecting them only up to 5% of the radial strain. As such it might not be necessary to apply a disturbance correction to loops performed beyond 5% strain. In other words, the discrepancy found in the results might be reduced to a great extent. The correction for the initial region could be justified since a problem would arise as to what cavity stress has to be used for normalisation since disturbance would have reduced the cavity stress to a large extent. As such it could be inferred that the lantern rigidity and friction between the strips could be the main reason for the high moduli values. It might be argued that a hyperbolic stress-strain relationship might mean that G’/G’P is not a unique function of strain level but a unique function of stress level and hence a difference in modulus values.  While this assumption might not hold for real soils, the  available experimental evidence on the different G/Gm -y curves derived with different confining stresses tends to support the adoption of this assumption.  Thus it might be  assumed that a big difference in moduli values as is being seen here might not be due to the hyperbolic relationship assumed. If the results using these lanterns are to be compared with those of more flexible lanterns used in Cambridge In-situ camkometers that show very little compliance (Hughes  -  personal communication) we have to use a correction factor that is  I I I  0  I I I I  4  I  I II  I  —  —  I  I I I I I  150 I I I  0  I  I  40—45%  —  I I II  SEP06  +  a*oee45—50%  +++++  DOO03O—35% 0064035—40%  24.Oct.1991 Lain Bridge South SCPT 17.0ct.19Q  SCPT——--  i  Degree of unloading 00000 15—20%  100 I i i  I I  1 10  I  +0  50 I I  I I  200 I  -  Fig.5.32. Profile of G ’ with Depth (SBPO6 Sounding-Byrne et al., 1990 0 Procedure) Laing Bridge.  20-  •  15-  •  •  ci.lO-  •  •  • •  •  0I  GOSbP(M Pa)  Chapter 5. Shear Modulus  115  appropriate for the results. The difference seen earlier suggests that the results from the present investigation have to be corrected by a factor of 1/1.85 which is approximately 0.55. The reason for not using a lantern of the above mentioned type was because of: dimension differences, the penetration and friction resistances recorded at the present site were so high that the lantern could be damaged if very high friction is mobilised at the wall due to various reasons involving installation and also the fact that tests were intended to be conducted to 20% strain and the lantern would tend towards non-cylindrical expansion at strains greater than 10%. The discussion regarding the two models so far have brought out the limitations of the Bellotti et al. (1989) theory and the assumptions that will be involved in the analysis with no proper justification. The Byrne et al.(1990) theory though appearing to yield the same kind of results as the Bellotti et al. (1989) model, takes into account the changes in the average stress, stress ratio and shear induced volume change on the maximum shear modulus. As was said earlier, it also considers the complete variation in stress and strain states. As such, this theory seems to yield much better results than the Bellotti et al.(1989) theory. Having noticed the above discrepancy it would be logical to plot G.jr’/GoP versus shear strain and compare it with the Seed and Idriss (1986) normalised modulus reduction curves. The figs.5.33,5.34 and 5.35 show plots from the three soundings considered. All the results seem to fall on the higher side of the Seed and Idriss curve. However, there is no real scatter evident. If the shear strain were to be taken as 0.15 times the radial strain as suggested by Howie (1991) seems to put the data right on the seed et al (1987) curve shown  E C,  -  -  -  I  I  I  I  0.001  11111  —  I  1  I  IIIIJ  I  -  S  ‘a  111  S  Laing Bridge.  \  \\  0.01 Shear Strom %)  I  •1I.  Fig.5.33. Normalised Modulus Reduction Curve (SBPO6 Soundingj  0.0001  0.0  0.2-  0.6  O.8  1,0  0.1  1II1J  I  I  I  I  tIlT  C,  ——  0.001  -  •  Laing Bridge.  0.01 Shear Strain (%)  i  Fig.5.34. Normajjsed Modulus Reduction Curve (SBPO8 Sounding)  0.000.0001  0.20:  9  -  j  O.6O-  0.4O  C,  -  o.so.1  1.00  S  *  0.1  S  rri  ‘iii  I •  1  I  I  I ** *  •  ___  -i  -  i  0.001  -  0.01 Shear Strain  \  Laing Bridge.  (%)  .*  0.1  NN  \  \  \\  \  \  \  \  \  \. \  \\  N  N  Fig.5.35. Normalised Modulus Reduction Curve (SBP1 1 Sounding)  0.00 0.0001  0.20  0.40  0  £  0.60-  0.80  1.00  Chapter 5. Shear Modulus  119  in fig.5.33. But there is no justification as to why this has to be done. Also, the stiffness of the lanterns used already has given higher values of shear moduli. As such the data are used as shown in figs. 5.33,5.34 and 5.35. It should however be noticed that none of the published studies of the effect of stress  and strain level include calibration and compliance testing procedures adopted. Thus, it is very difficult to assess if the quoted results are of sufficient accuracy to be useful. Thus it  can be concluded that the effect of equipment has to be eliminated if any accurate pressuremeter tests have to be conducted. It is therefore suggested that a lantern of such design be used that would not have any friction effect due to overlaps. This would also remove the effects of compliance that is observed in the UBC tests.  The preliminary  compliance tests on the cambridge camkometer lantern have shown good results. This might suggest that the use of stiff lanterns with overlapping strips as in the present investigation is not recommended. The model 2 that will be formulated in chapter 6 using Lysmer’s equation 2.33 appears to be another way of obtaining Gur. By applying the model to the loop one could get a good approximation of the unload-reload modulus as well as the damping as shall be seen in the next chapter. Summarising the chapter, it can be concluded that the parameters obtained from the self-boring pressuremeter can be used only if the instrument, installation, test procedures and interpretation conform to standard specifications. standardised except for the lantern used.  The instrument seems to be fairly  The installation process not being completely  reliable has to be researched thoroughly since there is no independent check that the  Chapter 5. Shear Modulus  120  instrument is drilled correctly. The installation disturbance results in erroneous values of lift-off and each curve will be highly dependent on this initial disturbance.  Even slight  variations in drilling technique or the rate of drilling seem to yield different shaped test curves.  Thus the interpretation of different tests at different depths and in different  soundings would produce different results. Thus it would be necessary to have a drilling technique that would be able to provide at least consistent results though expecting completely undisturbed tests would be out of question. The parameters will also differ with testing procedures and interpretation can be really subjective since it depends on the installation and testing techniques. It can be concluded that the best method to obtain Gm would be by the Byrne et aL(1990) procedure and that the unload-reload loops should be performed between 5 % and 10% radial strain to remove any effects of initial disturbance. If the loops are to be performed within 5% radial strain the disturbance factor of 1.4 as suggested by Byrne et al (1989) should be used. The loops could be performed for any elastic unloading as specified by the Wroth (1982) criterion. Care should be taken to remove creep as much as possible before the unloading begins. Generally a holding phase of 10 minutes would hold good for all cavity pressures and depths. The normalised profiles of GurC  with respect to shear strain proves that the self-boring pressuremeter is capable of  yielding modulus reduction curves. The use of more flexible lanterns with no overlapping strips could yield extremely good results with the use of the existing theoretical models themselves. The chapter also brings out the need for anlytical procedures that would model the pressure-expansion curve to obtain shear stress-strain curves with the consideration of the unload-reload loops.  121 CHAPTER 6  DAMPING  6.1. Introduction  Material damping describes the energy losses in loaded soil masses caused by interparticle friction at the contacts, interparticle slip and rotation. The pressuremeter being based on the fact that it’s expansion is plane strain would require a model consisting of a spring and a friction component as shown in fig. 6. l.a.  The resultant stress-strain loop  would look like fig.6.1.b. This however would be difficult to model. A look at fig.2.3 would reveal that a visco-elastic model could fill this gap. Apart from this, Hail & Richart (1963), Hardin (1965), Whitman (1977) and many others have demonstrated that hysteretic damping could readily be interpreted in terms of damping of visco-elastic systems. But the main assumption is that the frequency considered is the natural frequency of the system. It can be noticed that due to equipment limitations the rate of loading could not be changed during the test and also the rates of loading available (3 KPa/s to 10 KPa/s) is not sufficient to discern the change in the loop behaviour with the rate of loading. Bearing in mind all the above limitations and understanding the good physical sense that the visco-elastic model might provide by replacing a shear-strain loop by a similar pressure-strain ioop, an attempt is made in this investigation to use the equivalent visco-elastic spring-mass-dashpot model in order to calculate damping from the pressuremeter loops.  122  k  Figure 6.1.a. Spring Friction Model  Figure.6.1 .b. Stress - StraIn Loop for FrictIon Model  Chapter 6. Damping  123  The other assumptions made are that of the stress and the strain levels. It is well known that the stress at the wall does not reflect the stress at any point away from the wall.Thus the average stress assumption is made. The basic model and the ‘logarithmic decrement’ which by illustrating amplitude decay measures damping, are shown in fig.6.2.a. and 6.2.b. The logarithmic decrement is given by: 6  =  in ) 2 / 1 (Z Z =27rD/f(l-D ) 2  =  27rD.  The loss of energy in visco-elastic systems can be described by the strain energy lost during oscillation. As seen in fig 2.3. the ratio of energy lost in one cycle, W, to the elastic energy W, can be given by:  -  w  26  -  47rD  [6.1]  Therefore  D  -  4irW  [6.2]  This equation is used as the basis for damping calculations using the visco-elastic model. The model discussed in section 2.3.2 arrives at the same equation assuming sinusoidal displacements, and attempts to derive damping by calculating the work done in a cycle in terms of area of the loop and the energy stored in terms of the area of the triangle as shown in fig.2.3.  wi  A sin  Fig.6.2. Mass-Spring-Dashpot System and Free Vibration of a Viscously Damped System.  sin  —-  Chapter 6. Damping 6.2. Visco-Elastic Model and Stress  125 -  Strain Loops  As demonstrated in section 2.3.2 a spring  -  mass  -  dashpot model can be used to  develop the relationship between damping ratio and stress-strain loops measured in cyclic triaxial and field pressuremeter tests. Though this development is resthcted to harmonic loading at the natural frequency,cL , it has been assumed to be true for other frequencies as 0 well. Having obtained an expression for damping by evaluating the work done in one cycle of loading assuming sinusoidal displacement, the next step would be to apply this model to field pressuremeter unload-reload loops. The area of the loop is obtained either by a planimeter or by integrating the area using a software with an integration option. As explained earlier, the rates of unload-reload were between 3 kPalsec and 10 kPa/sec. A major limitation was that inflation rate could not be changed during the test. As such, to compare results due to different rates of unloading, different soundings have to used. In other words the effect of frequency on damping could not be discerned. Also, since pressure is boosted three times by the pressure multiplier, there will be stepped loading. Further limitations posed by rate of sampling (resolution) results in distorted loops being obtained at small unloadings (about 10% of cavity pressure) especially at smaller confining pressures. This makes it imperative that we smooth the loops if their areas are to be calculated properly. It has also been shown that for larger loops, smoothing of the loops results in high resolution loops without changes being induced in the values of modulus and damping thus obtained. Since the smaller loops are highly distorted there is no means other than statistical smoothing to get a good quality ioop. In this analysis, 5 point smoothing  Chapter 6. Damping  126  available in Vu-point software was used. The area of the loop is found along with the area of the right triangle from start of the ioop to the centre of the secant modulus (origin) and then input into equation 2.41. to obtain damping. The results thus obtained are presented in figures 6.3,6.4, and 6.5. A typical smoothed loop is shown in figure 6.6 with the method of damping calculation in 6.7. These results are discussed below.  6.2.1. Results  Results of all the tests conducted in one whole sounding are provided in Appendix A for the sake of completeness. This is done, so that the effect of 0 u.,, ’ ,  ur’,  strain, creep,  repeated unloadings, equipment, etc can be studied. As explained in chapter 5 tests at 5 different depths were conducted in the sounding SBPO8 with the last depth being 13.8m corresponding to a u,,, ’ 0  =  128 KPa. Only high amplitude damping ratios are discussed here  since it is not possible to obtain loops < 0.01% cavity strain (R/R, , where R is the radius 0 of the expanded probe and R 0 is the initial radius of the probe) due to equipment limitations. Effect of Confining Pressure and Stress History  A typical high amplitude damping curve is shown in fig.6.3 The effect of confining .  pressure can be evaluated by comparing the damping attenuation curves at different confining pressures. However, since the number of sets of loops are far too few due to the fact that holding phases have to be accommodated before each set of loops, at every pressure level,  127  24.0ct1991  30-  00000  —  SBPO6  52.7  ooooe 70.8  •  +++++ •.*.. *****  20-  0.  Laing Brfdge South  32.1 KPc 42.9  • -F  .9  —  79.8 89.7 98.7 107.7  • •  •  S  •  Oê  10••  +  I  0.0001  11111111  I  IIIIITIj  I  iiiiiq  I  1111111  0.01 0.001 0.1 Single Amplitude Loop Strain (%)  Fig.6.3. Damping vs. Single Amplitude Loop Strain (SBPO6 Sounding)  -  Laing Bñdge  128  20Feb. 1992  3000000  52.8 KPa  •  DbDDO  •  00000  699 KPa 81.4 KPa  •  +++++  —  Laing Bridge South  SBPO 3  —  109.5 KPa •*,ss 128.1 KPc  20•  0  *  00 00  S.—  40  0  .9 E  •0  10  I  0.0001  I  I F Jill]  I  I  I I I liii  I  I  I I I III  0.001 0.01 0.1 Single Amplitude Loop Strain  I  I  I I I III  (%)  Fig.6.4. Dampmg vs. Single Anplitude Loop Strain (SBPO8 Sourciing)  -  Laing Bridge  129  23.Apr.1 992  —  Laing Bridge South  SBP1 1  —  30: ***** 00000 -  60.0 KPa 730 82.0 910  -  •  OG*O  •  +++++  99.0 114.5 xxxxx 120.0 •*..s 129.0  20-  0  E  0  •  0*  •  DHI(  •  *  x  •  10  0—  —  0.0001  1 11 1I  I  I  I I I III  I  I  I  I lI1  0.1 0.001 0.01 Strain Single Amplitude Loop  I  I  I I I ITt  (%)  Fig.6.5. Damping vs. Single Amplitude Loop Strain (SBP11 Sounding)  -  Laing Bridge  130  20.F.b.1992  r 760  — Letng Brtdgo South — SBPGB  2Gur  ci 660-  1  ‘—I  cD L  >  A  trLnIe  Co Ci) cD C  I 460— —>  -1  A  C  0 47) j’A 0 , X 1  360-  2601. 9 I  I  1  I  I  I  I  I  I  I  I  2.1  RedI  I  I  I  I  I  I  I  I  I  I  I  I  I  2.3  Strn  Fig.6.6. Dermination of Damping from Model 1 with Raw Data.  -  (%)  2.6  131  559.8  -  SB?87  —  Za.leI.92  5 .9  Ii) 0  ‘459.9  2.4  2.7 2b 2.5 Radial Strain (i.) -  Fig. 6.7. Typical Smoothed Loop for the Determination of Damping from Model 1.  Chapter 6. Damping  132  the comparisons will have to be made using the attenuation curve for the whole sounding. Another reason for this would be because of stress controlled testing at strains of 2%, 6% and 10% cavity strains common to all the tests, the confining pressures are very difficult to match. A close look at the three attenuation curves provided in the figures 6.3,6.4,6.5 reveals that there is no discernible influence of effective confining pressure on the damping attenuation curves, within the range tested. This is clearly evident since most of the data points from the three curves seem to follow an average attenuation curve which could be passed through them without much effect on the results. It should be noticed that scatter is not very evident especially since a logarithmic scale is used. Thus, this would suggest that a single attenuation curve would suffice to cover a wide range of confining stresses for one particular type of soil. This would generally be good for moderate confining pressures. Low confining pressures could have the effect of disturbance on the damping values. It would seem that in the disturbed zone smaller amounts of work done and higher elastic energy would cause a reduction in damping. Similarly, at high confining pressures, the creep effect will be very high and cannot be eliminated altogether. As such the damping values tend to reduce. The effect of creep on damping is explained later. Effect of Strain Level  The results obtained in this investigation illustrates the difficulty in obtaining low strain damping ratios (<0.01 %) because of equipment limitations. It must be noted that all  Chapter 6. Damping  133  strains mentioned with respect to the loop and damping are those of the loop strains obtained directly from the pressure-expansion curves. At the same time to obtain damping ratios at high strain amplitudes (>0.2%) loops have to be obtained from tests conducted at very high confining pressures. This is so, because adhering to the Wroth (1982) criterion for the limit on unloading if the soil should not fail in extension, only high confining pressures can ensure large unloadings with respect to the amount of pressure unloaded. At the present time the highest confining pressure that can be reached using the available compressor is 1500 kPa. As such loops greater than 0.5% (0.25% single amplitude) cannot be obtained and the ioop strains would be in the range of 0.02% to 0.25%, which on the logarithmic scale would be a very small region. As such it was decided to conduct SCPTs at the Laing Bridge site in order to obtain low amplitude damping ratio and interpolate in order to obtain an average damping curve. The value of damping obtained from the SCPT was 1 %.  The average  damping curves from the three soundings considered are shown in Figs.6.8, 6.9 and 6.10.  Observing the attenuation curves from Fig. 6.11, one might notice that the scatter is very small and the curves seem to show a trend compatible with earlier published results. Consistent with the visco-elastic model, the strain plotted is single amplitude or half loop strain. However, since the probe expansion induces inordinately high strains at the wall along with very high strain gradients, the strains so obtained should be corrected for strain level. To be consistent with previous strain level corrections used in chapter 5 a correction of  134  24.Oct 1991  30-  —  L&ng Brfdge South  —  SBPO6  1/  /  20t  /  C  /  c.  E  o  1  //  10 ‘4 *  / /  1  0.0001  0.1 0.01 0.001 Single Amplitude Loop Strain  (%)  Fig.6.8. Average Damping vs. single Amplituae Loop Strain Curve (SBPO6 Sounding) Laing Bridge. -  135  30  20Feb.1 992  —  Loing Bridge South  —  SBPOS  20  2  0  10  0.0001  0.001 0.01 0.1 Single Amplitude Strain (%)  Fig.6.9. Average Damping vs. Single Amplitude Loop Strain Curve (SBPO8 Sounding) Laing Bridge. -  136  30  23.Apr1992  —  Laing Bridge South  —  SBP1 1  20  E 0  1  0.0001  0.001 0.01 0.1 Single Amplitude Loop Strain  (%)  Fig.6. 10. Average Damping vs. Single Amplitude Loop Strain Curve (SBP11 Sounding) Laing Bridge. -  •1  0.0001  •  •  •  10-  I  —  Idrlss (1990)  —  11111111  I  /  11111111  /  /  /  *11/  /  I  0*1 0,  0.01 0.001 0.1 Single Amplitude Loop Strain (%)  I  /  ad I-  a_o  0  /  1111111  sA®’  *v*  0  SBPOG, SBPO8 and SBP1 1  Seed & Idriss (1970)  11111111  —  Lalng Budge South  Fig.6. 11 .a. Damping Values from SBPO6, SBPO8 and SBP1 1 Soundings Laing Bridge.  .E  20-  30-  -  13.8  E a  0.0001  0.001 0.01 0.1 Single Amplitude Loop Strain  (%)  Fig.6. 11.b. Comparison of me Average Damping Curves with Seed & Idriss (1970) and the Idriss (1990) Damping Curves.  1  Chapter 6. Damping  139  Ye  —  1Yc 3 I  [6.16]  used by Robertson (1982), Robertson & Hughes (1986) and Bellotti et al. (1989) will be employed in this study. The value of L3=O.5 is used here. Figures.6. 12,6. 13 and 6.14 show plots of damping versus single amplitude average shear strain compared with average attenuation curves for single amplitude loop strain. The effect of the correction is to push the curve to the left thus increasing the damping value for any given strain. Since strain is on the logarithmic scale, there is no significant change in the damping values. As such it can be assumed that the same attenuation plot can be used without the correction and still be on the conservative side. It should be noted that the damping has been corrected for compliance effects before the strain correction was applied. This correction for compliance is discussed further in this chapter. All the tests show very similar results with the data falling in a narrow band thus suggesting that a unique curve could be provided if a large number of data points are available. Effect of Creep and Repeated Unloading  Fig 5.22 shows a cyclic pressuremeter test that was performed with eleven loops unloaded to 33 % of the cavity strain at the same confining pressure. As discussed earlier, the unloading portions look surprisingly similar. The strain versus number of loops is presented in fig 5.23. The figure suggests that there is no effect of repeated unloading on the  140  30-i  24.Oct.91  —  Laing Bridge South  —  SBPO6  A //  20j  10  0  0.0001  11 IiJJ  I  0.001  T FVT1TTJ  I  I  I TillEr  0.01 0.1 Sinqie Amplitude Ave. Shear Strain (%)  I  I  1  Fig.6. 12. Lompanson of Average Damping Curve with Damping vs. Shear Strain Data (SBPO6 Sounding) -Laing Bridge.  141  30-  0— 0.0001  20.Feb.92  —  Laing Bridge South  —  0.01 0.1 Singie Ampfltude Ave. 5hear Strain (%)  0.001  SBPO8  1  Fig.6. 13. Comparison of Average Damping Curve with Damping vs. Shear Strain Data (SBPO8 Sounding) -Laing Bridge.  142  30  23Apr.92  —  South  —  SBPO1 1  20  C  E  0  10  0 Ob000l  0.001  0.01 0.1 Single Amplitude Ave. Shear Strain (%)  Fig.6. 14. Comparison of Average Damping Curve with Damping vs. Shear Strain Data (SBP1 1 Sounding) -Laing Bridge.  Chapter 6. Damping  143  unloading portion of the curve. The loop strain versus number of loops however shows a large change in the values from initial unloading to the final reload in the last loop. This suggests that any change in modulus and damping is solely due to the reload portion. The changes in reload strains can only be attributed to creep behaviour of sands. As the cyclic loading is continued accumulation of strains finally removes all the creep and after 8 loops there is no change in the strain. This is also noticeable in the damping versus number of loops plot in figure.6. 15 wherein the initial loops show lesser damping than the loops without creep. In other words the effect of creep is to reduce damping. Since there was no holding phase in this curve the only way to see the creep rate is to plot the strain accumulated during repeated loadings versus time This shows that creep rate was very small at the end of the last loop. To discern the effect of creep at varying confining pressures a test was conducted with various creep phases at different pressures. The strain at the start of the holding phase is plotted against time. This reveals a logarithmic increase in the creep with the confining pressure. The effect of creep on the modulus is discussed in chapter 5. Effect of Equipment  This has proved to be the most important effect on the results in this present investigation. Chapter 5 reflected the drawbacks that the compliance and lantern stiffness posed to modulus measurements. The same could be said of damping too. The reduction in strains due to friction might cause the lantern to yield thinner loops, in other words smaller damping. However, the problem of recognising the correct amount of friction that might be  144  Lalng Bridge South  —  SBPI3  T 15  --__  •1  10-  -...----.----—.—.---—.  1  //  J j 5  -  -  0  -  nTrrrn—nmrrrrrrrrrrrrrrn-rrJ ‘11  2  6 8 4 Number of Loops  i ,  i rrrr  10  Fig.6. 15. Damping vs. Number of Loops for Multi Cycle Test.  I  12  Chapter 6. Damping  145  responsible for a particular amount of strain reduction still exists. However, the larger loops of higher strains which have smaller friction because of larger movements seem to provide good results. This might give a good reason to believe that the pressuremeter loops could give good damping results. The problem of resolution, rate of loading, etc affect damping values also. This is because of the fact that the distorted loops give a very highly variable range of values. It is easily visible that the effect of equipment is more on the damping than on the modulus for very small loops.  6.3. Complex Oscillator and Visco-Elastic Material  Similar to the model in section 6.2, the concept of a complex oscillator could be developed and the resulting modulus and damping compared to that for a visco-elastic material (personal communication with Stewart, 1992). Even this development would be restricted to harmonic loading. The equation for linear elastic loading from (0,0) could be given by:  0w  + —  2Ge  [6.3]  or, incrementally  [6.4]  a=2Ge 2G  Chapter 6. Damping  146  As discussed in chapter 2, we could introduce damping following Lysmer (1980) and sinusoidal loading:  [6.5]  G(1÷i2D)  —  1  a  —  Ae’  A(cosøt  —  [6]  i sinøt)  +  2  A(cosct  =  2G(1  2G(1  +  [(cost ÷ 2Dsmct)  2  +  i sint) (1 (1 i 2D)  +  -  —  +  i  j 2D)  [6.  i 2D)  (smt  4D)  —  cosøt)] [6. 3 2D 8]  Consider only real portions of each expression:  a  —  A 2G(1  1  [6.9]  A cost  2  [cosct  +  2Dsint]  ) 3 4D  +  A similar but more complicated approach is used by Dormieux & Canou (1990) wherein they use an expression:  ) 0 M(ø  -  G(/1_q2  +  ) 1 ir  where M() = slope of the major axis of the ellipse obtained from one unload-reload cycle = energy loss co-efficient G = secant shear modulus  2  [6.10]  A is negative for initial unloading  Chapter 6. Damping  147  However, the actual unload-reload loop obtained from the pressuremeter has loading as a triangular function of amplitude A (negative value) and width T (typically A = -300 kPa,  T= 60 s). This loading can be approximated by a half sine wave or by a full cosine wave. Using a half sine wave, will have an amplitude A and frequency  Co.  2t  it  [6.11]  ==—  2T  T  shift equations 14 and 15 by r/2 radians to start the load change from zero.  ci  €  —  A  —  2G(1  +  t 1 AsirlCo  t 1 [(sin(,.)  [6.12]  —  1 c 5 2D t )] osQ  [6.13]  4D)  This expression gives strains for zero time. It is  necessary to constrain the strain change to  a value of zero until the load decreases a sufficient amount to induce movement. Cosine wave loading has to yield the same results as sine wave loading (personal communication with Hughes, 1992) and as such cosine loading is used as detailed below. Assuming a full cosine wave, will have an amplitude of A/2 and frequency 2• (02  —  A/2(1 —COSG.) t) 2  [6.14]  Chapter 6. Damping  148  A/2  € —  2G(1  The first term shifts  E  A/2 2  +  ) 3 4D  —  2(1  2  +  t+2Dsm 2 [(cosø t )]  ) 5 4D  to a value of zero at zero time. As such if the loop from the model  has to be compared with the pressuremeter loop this shift has to be corrected for. The Vupoint macro written for the preceding analysis is shown in the following page. The loop data obtained from the field tests are input into the model. For the sake of comparison the values of shear modulus and damping obtained from the first model are used as input for this model. The data is input into Vu-point and the macro is run. The pressure  -  strain ellipse  thus obtained is then compared to that obtained from model 1. The results are shown in figure 6.16. and Appendix A  .  The results show a remarkable similarity with that of the  Model 1 and the results seem to match very well. Summarising, provided we understand all the limitations of the visco-elastic model applied to the present case and also of the equipment limitations, it would appear that both the models could provide reasonably good calculation techniques for damping. Though it is well known that the damping values depend on the type of oscillation and that it would be extremely difficult to model dynamic parameters with the present equipment, the fact that we could obtain a very similar loop to replace the shear stress-shear strain loop emphasises the good physical compatibility this method might have with other dynamic methods. This might provide a reasonable basis for further research on damping measurements with pressuremeter loops. It is however recommended that the best solution would be to obtain the shear stress  -  shear strain relationship from the whole pressure expansion curve taking  149  <BEGDEF><CtrlFlO>(?ITLE>Lysmer Damping.1<TITLE> <Esc><Esc><Esc> <Text>Assumes 8 sets, Strain(%) in Seti, Pressure(kPa) (CALC>a= (max2+min2)/2<Enter> c=(max2—min2)/2<Enter> w=4*PI/(abs(tmax2_tmin2)*4) <Enter> b=maxl<Pause><CtzlF9> <ENDDEF>  in Set2<Text>  <BEGDEF><CtrlF9><TITLE>Lysmer Damping. 2<TITLE> <Esc><Esc><Esc><CALC>tr ig=rad<Enter> <Esc> <Text>Enter est. of G(kPa)<Text> <CALC>g=20000<Pause><Esc> <Text>Enter est. of Damping (dec.KText> <CALC>1=O.1<Pause><Esc><CALC>z=100*c/(2*g*(1+4*1*1))<Enter> <Esc><Esc>mmm2mmnow<Enter> c3cs3oc<Enter) oCa]. .Press. <Enter> okPa<Enter> a3oa<Enter> <CtrlF8> <ENDDEF> <BEGDEF><CtrlF8><TITLE>Lysmer Damping. 3<TITLE> <Esc><Esc><Esc>mmm2minnow<Enter> c4cmm2mmnps5ss5o2*1<Enter> oScCos<Enter> okPa<Enter> mj+454oCa1 .Strain<Enter> s4oc/(2*g*(i+4*1*1))<Enter> co%<Enter> s4olOO<Enter> c%a4ob<Enter> <Esc> <Esc>mmid4mm5pa5o—z<Enter> <Esc><Esc> <Text>Calc.Strain in 5, Press, in 3<Text> <ENDDEF>  Macro. 1.  Macro for Damping Cakulation from Model 2  150  55e.e  5.O  Ii) C’, 0  4.8  358.9  3.8  2.4  2.7 2.6 2.5 Radial Strah (i.)  2.8  Fig.6. 16. Comparison of Model 2 Loop with Loop from Raw Data.  Chapter 6. Damping  151  into consideration the unload-reload loops. This would possibly be the best solution since both shear modulus and damping depend solely on the stress-strain relationship. Since the self-pressuremeter has shown the ability of obtaining good data for both shear modulus and damping measurements, research can now be concentrated on modelling the stress-strain curve along with improving the current pressuremeter technology. Also, the damping curve obtained by extrapolating the curve along with the SCPT Gm appears to be very similar to the Seed and Idriss (1970) and the Idriss (1990) curves.  152 CHAPTER 7 CONCLUSIONS  Cyclic testing with the Self-boring pressuremeter in the present investigation could be summarised as follows. SHEAR MODULUS The pressuremeter modulus was found to depend on the instrument, installation, testing procedures and the interpretation techniques used.  The equipment effect was found to be  very highly pronounced in the present investigation. The lantern used being very stiff with a high compliance lead to the conclusion that the lantern has to be quite flexible enough and should have no friction effects as in the present lantern, if good tests are to be obtained. It was observed that between tests conducted with different lanterns the difference in the Gur values was solely because of lantern. Also, after 10% of radial strain since it is observed that cavity expansion might tend to veer away from cylindrical expansion, modulus values obtained from loops at strains beyond 10% cannot be believed.  The installation process is  not very reliable and research is still needed to achieve a drilling method that shall at least provide reasonably consistent results.  Installation and equipment problems result in  erroneous lift-off pressures and even slight variations in drilling technique or rate shall result in diferent shapes of pressure-expansion curves. Interpretation being highly subjective will therefore produce different results for different  soundings and depths.  Interpretation  methods are very few and very subjective. The present investigation has revealed the drawbacks of the Bellotti et al. (1989) procedure because of the various assumptions involved  153 in it.  The Byrne et al. (1990) method provided good values of Gm when disturbance  correction was not applied to the results of loops between 5% and 10% radial strains. This method could be more reliable than the others because it takes into account the complete variation in stress and strain states.  The application of curve fitting techniques like the  Hughes (1977) model showed initial disturbance to affect only the initial 5% of the pressureexpansion curve. This lead to the fact that reliable results of the moduli could be obtained only between 5% and 10% strains. The creep effects tend to decrease modulus values and have to be removed if proper values are to be obtained. It was found that a holding phase of 10 minutes is reasonable to remove most of the creep in general. The creep behaviour could not be studied in detail, however it could be seen that only low amount of creep, possibly lesser than 0.02 %/min. seem to result in modulus values being unaffected by creep. In the presence of creep, the shear modulus was found to increase with the number of cycles until such a stage wherein all the creep effects were eliminated. Further research is needed in this direction. The difficulty in comparing tests at similar depths because of loops conducted at particular strains suggests that the testing procedure should be standardised in such a way that loops should be conducted at the same pressures and at similar unloads. Thus it becomes important to follow consistent testing methodology and the use of similar equipment in order to obtain compatible results. All this suggests that in the order of equipment, test procedure, interpretation methods and tying the obtained results into design everything has to be standardised if the pressuremeter can be used for obtaining moduli.  154 DAMPING Damping seems to be affected by the equipment more than the shear modulus. The rate of sampling data points and the rates of loading have to be significantly improved if well defined loops are to be obtained at lower unloadings. Lanterns should not have overlapping strips if friction effects on smaller unload-reload loops have to be eliminated.  Proper  measurement of strains being a must suggests that strain gauges should be checked for the resistivities periodically to identify offsets in the resistivities.  Even small errors in  measurement of strains can result in large errors in values obtained. Stress level does not seem to influence damping very much. The problems faced in modelling damping as a frictional material resulted in the use of visco-elastic models for obtaining damping. However, the damping values obtained from both the models employed seem to be reasonably good indicating that these models could be used as good calculation methods. Thus, understanding the limitations of the visco-elastic model and the good physical sense that the visco-elastic model puts forth in replacing the shear stress-shear strain loop by a similar pressure-strain loop should be acknowledged in the absence of sufficient information. Based on the limited data , limited theories and interpretation methods and the various equipmental drawbacks as a backdrop, this thesis has attempted to investigate the effects of various factors on pressuremeter moduli and damping. The agreement that the results show with existing results point to the fact that the pressuremeter has a great potential for obtaining the above mentioned parameters.  155  BIBLIOGRAPHY  Aggour, M.S., Tawfiq, K.S. and Amini, F.(1987). “Effects of frequency content on dynamic properties for cohesive soils”. Proc. 3rd Tnt. Conf. on Earthquake Engg. and Soil Dynamics, Princeton, june, Vol. 42, pp. 31-39. Baguelin, F., Jezequel, J.F. and Shields, D.H. (1978). “The pressuremeter and foundation engineering”. Trans Tech Publications, Causthal, Germany. Baguelin, F., Frank, R.A. and Nahra, R.(1986). “A theoretical study of pore pressure generation and dissipation around the pressuremeter”. Proc. ISP2, ASTM STP 950, Texas A&M Univ., College Station, TX. Baguelin, F., Jezequel, J.F., Le Mee, E. and Le Mehaute, A. (1972). “Expansion of cylindrical probes in cohesive soils”. 31. of the Geotech. Engg. Div., ASCE, Vol.98, SM11, Nov. Bannerjee, P.K. and Fathallah, R.C.(1979). “An eulerian formulation of the finite element method for predicting stresses and porewater pressures around a driven pile”. Proc. 3rd Tnt. Conf. on Numerical Methods in Geomech., Aachen, pp. 1053-1060. Bellotti, R., Ghionna, V., Jamiolkowski, M. Lancelotta, R. and Manfredini, G. (1986).”Deformation characteristics of cohesionless soils from insitu tests”. Proc. INSITU’ 86, Blacksburg. -  Bellotti, R., Crippa, V., Ghionna, V., Jamiolkowski, M. and Robertson, P.K.(1987).”Selfboring pressuremeter in pluvially deposited sands”. Final Tech. Rep. to US Army, European Research Office, London. Bellotti, R., Ghionna, V., Jamiolkowski, M., Robertson, P.K. and Petterson,R.W. (1989).”Interpretation of moduli from self-boring pressuremeter tests ii Geotechnique, Vol.39, No.2, pp. 269-292. Blunden, R.H.(1975).”Urban geology of Richmond, British Columbia”. Adventures in Earth Sciences Series No.15, B.C. Govt. Pub. Byrne, P.M., Salgado, F.M. and Howie, J.A.(1990).”Relationship between the shear modulus from the pressuremeter tests and the maximum shear modulus for sands”. Proc. ISP3, Univ. of Oxford, Oxford, U.K. Campanella, R.G., Stewart, W.P. and Jackson, R.S.(1990).”Development of the UBC self boring pressuremeter”. Proc. ISP3, Univ. of Oxford, Oxford, U.K.  Bibliography  156  Carter, J.P., Booker, J.R. and Small, J.C.(1979).”The analysis of finite elasto-plastic consolidation”. Intl. JI. of Num. Methods in Geomech., Vol.3, No.2, PP. 107-129. Clarke, B.G. and Wroth, C.P.(1985).”Discussion of Fahey and Randolph (1984). Geotechnique. Denby, G.M. and Clough, G.W.(1980).”Self-boring pressuremeter tests in clay”. Proc. JGED, ASCE, 106:GT7: pp. 1369-1387. Dobry, R., Powell, B.J., Yokel, F.Y. and Ladd, R.S.(1980).”Liquefaction potential of saturated sand the stiffness method”. Proc. 7th WId. Conf. on Earthquake Engg., Istanbul3, pp.25-32. -  Dormieux, L. and Canou, J.(1990).”Determination of dynamic characteristics of a soil based on a cyclic pressuremeter test”. Proc. ISP3, Univ. of Oxford, Oxford, U.K. Fahey, M.(1980).”A study of the pressuremeter test in dense sand”. Ph.D. thesis, Univ. of Cambridge. Fahey, M. and Randolph, M.F.(1984).”Effects of disturbance on parameters derived from self-boring pressuremeter tests in cohesive deposits”. Geotechnique, 34(1), . 97 81 pp. Fahey, M. and Jewell, R.J.(1990).”Effect of pressuremeter compliance on measuremeter modulus”. Proc. ISP3, Univ. of Oxford, Oxford, U.K. Fahey, M.(1986).”Expansion of a thick cylinder of sand: A laboratory simulation of the pressuremeter test”. Geotechnique, 36(3), . 424 397 pp. Fahey,M.(1990)”Shear modulus of sand measured with the self-boring pressuremeter”. Research Rep. No. GlOb, Geomech. group, The Univ. of Western Australia, Perth, Australia. Gibson, R.E. and Anderson, W.F.(1961).”Insitu measurement of soil properties with the pressuremeter”. Civ. Engg. Pub. Wks. Rev., 56, No.658, May, pp.615-618. Hardin, B.O.(1965).”Nature of damping in sands”. JI. of Soil Mechanics and Foundn. Div., ASCE, Vol.91, No.SM1, Jan., . 97 63 pp. Hardin, B.O. and Black, A.M.(1968).”Vibration modulus of normally consolidated clay”. JI. of the Soil Mechanics and Foundn. Div., ASCE, Vol.98, No.SM2, Mar., pp.353-369.  Bibliography  157  Hardin, B.O. and Drnevich, V.P.(1972a).”Shear modulus and damping in soils: measurement and parameter effects”. JI. of the Soil Mechanics and Foundn. Div., ASCE, Vol.98, No.SM6, June, . 624 603 pp. Hardin, B.O. and Drnevich. V.P.(9172b).”Shear modulus and damping in soils: design equations and curves”. 31. of the Soil Mechanics and foundn. Div., ASCE, Vol.98, No.SM7, July, . 692 667 pp. Howie, J.A.(1991).”Factors affecting the interpretation and anlysis of full displacement pressuremeter tests in sands”. Ph.D. thesis, Univ. of British Columbia, Vancouver, B.C., Canada. Hughes, J.M.O., Wroth, C.P. and Windle, D.(1977).”Pressuremeter sands”.Geotechnique, Dec., No.27(4), . 477 455 pp.  tests  in  Hughes, J.M.O.(1984).”Pressuremeter results obtained using Western Geosystems Inc. selfboring pressuremeter at the McDonald Farm”.Report for the National Research Council of Canada by Western Geosystems Inc., Feb. Hughes, J.M.O.(1982).”Interpretation of pressuremeter tests for the determination of elastic shear modulus”. Proc. of the Conf. on Updating Subsurface Sampling of Soils and Rocks and their Insitu Testing, Santa Barbara, CA. Hughes, J.M.O.(1989).”The pressuremeter materials?” Unpublished notes.  -  Can useful data be obtained for granular  Hughes, J.M.O. and Robertson, P.K.(1985).”Full displacement pressuremeter testing in sands”. Proc. Can. Geot. 31., 22:3:pp.273-289. Idriss, I.M.(1990).”Response of soft soil sites during eathquakes”. Proc. H.B.Seed Mem. Symp., Berkeley, CA. Jackson, J.G.Jr., Ehrgott., 3.0. and Rohani, B.(1980).”Loading rate effects on the compressibility of sands”. JI. of the Geot. Engg. Div., ASCE, Vol.106, No.GT8, pp.839-852. Jamiolkowski, M., Ladd, C.C., Germaine, J.T. and Lancelotta, R.(1985).”New developments in field and laboratory testingof soils”. Proc. IX ICSMFE., San Fransisco, Aug., Vol.1, pp.57-153. Janbu., N.(1963).”Soil compressibility as determined by oedometer and triaxial tests”. Proc. of the European Conf. on Soil Mechanics and Foundn. Engg., Wiesbaden, Germany.  Bibliography  158  Jewell, R.J., Fahey, M. and Wroth. C.P.(1980).”Laboratory studies of the pressuremeter test in sands”. Geotechnique, 30(4), . 531 507 pp. Johnston, D.H. and Toksoz, M.N.(1981).”Definitions and terminology in seismic wave attenuation”. Geophysics Reprint Series No.2, Soc. Exp. Geophy., pp.1-5. Juran, I. and Beech, J.F.(1986).”Effective stress analysis of soil response in a pressuremeter test”. Proc. ISP2, ASTM STP 950, Texas A&M Univ., College Station, TX. Ladanyi, B.(1963).”Evaluation of pressuremeter tests in granular soils”. Proc. of the 2nd Pan Am. Conf. on Soil Mechanics and Foundn. Engg., Brazil, Vol.1, . 20 3 pp. Ladd, C.C, Foott, R., Ishihara, K.,Schlosser, F. and Poulos, H.G.(1977).”Stress deformation and strength characteristics”. SOA Report, IX ICSMFE., Tokyo. Lassoudiere, F.M. and Zanier, F.B.(1986).”Numerical analysis of pressuremeter tests by the finite element method”. Proc. ISP2, ASTM STP 950, Texas A&M Univ., College Station, TX. Lee, H.F.S. and Stokoe, K.H.IL(1986).”Investigation low amplitude shear wave velocity in anisotropic material”. Geot. Engg. Report, GR86-6, Civil Engg. Dept., The Univ. of Texas at Austin, TX. Lysmer, J.(1980).”Foundation vibrations with soil damping”.Proc. 2nd ASCE Conf. on Civil Engg. and Nuclear Power, Knoxville, TN., Vol.11, paper 10-4, . 18 1 pp. Mair, R.J. and Wood, D.M.(1987).”Pressuremeter testing : Metods and Interpretation”. CIRIA, Butterworth. Martin, P.P.(1975).”Non-linear methods for dynamic analysis of ground response”. Ph.D. thesis, Univ. of California, Berkeley, CA. Meija, C.A., Vaid, Y.P. and Negussey, D.(1988).”Time dependent behaviour of sand”. Soil Mechanics Series No. 122, Dept. of Civil Engg., The Univ. of British Columbia, Vancouver, B.C. Mok, Y.J., Sanchez-Salinero,I, Stokoe, K.H.,II, and Roesset, J.M.(1988).”Insitu damping measurements by crosshole seismic method”. Earthquake Engg. and Soil Dynamics II, ASCE Spec. Conf., Park City, Utah.  Ni, S-H.(1987).”Dynamic properties of sand under true triaxial stress states from resonant column/torsional shear tests”. Ph.D. thesis, The Univ. of Texas at Austin.  Bibliography  159  Palaniappan, E.(1976).Shear modulus and damping characteristics of soils”. Ph.D. thesis, Georgia Institute of Tech. Palmer, A.C.(1972).” Undrained plane-strain expansion of a cylindrical cavity in clay: a simple interpretation of the pressuremeter test”. Geotechnique, Sept., 22(3), pp. 45 1457. Prevost, J.H. and Hoeg, K.(1975).”Analysis of pressuremeter in strain softening soil”. 31. of the Geotech. Engg., ASCE, Vol.101, No.GT8, pp.717-731. Redpath, B.B., Edwards, R.B., Hale, R.J. and Kintzer, F.C.(1982).”Development of field techniques to measure damping values for near surface rocks and soils”. Prepared for NSF Grant No. PFR-7900192. Redpath, B.B. and Lee, R.C.(1986).”Insitu measurements of shear wave attenuation at a strong motion recording site”. Prepared for USGS Contract No.14-08-001-21823. Robertson, P.K.(1982).”Insitu testing of soil with emphasis on its application to liquefaction assessment”. Ph.D. thesis, The Univ. of British Columbia, Vancouver, B.C. Robertson, P.K. and Hughes, J.M.O.(1986).”Determination of properties of sand from selfboring pressuremeter test”. Proc. ISP2, ASTM STP 950, Texas A&M Univ., College Station, TX. Saxena, S.K. and Reddy, K.R.(1989).”Dynamic moduli and damping ratios for monterrey no.0 sand by the resonant column method”. Soils and Foundations, Vol.29, No.2, June, 5 1. 37 pp. Seed, H.B. and Idriss, (1970).”Soil moduli and damping factors for dynamic response analysis of cohesionless soils”. Report No. UCB?EERC-70/10, Univ. of Cal. Berkeley, CA. Seed, H.B., Wong, R.T., Idriss, I.M. and Tokimatsu, K.(1986).”Moduli and damping factors for dynamic analysis of cohesionless soils”. JGED, ASCE, Vol.112, No.11, Nov., pp.1016-1032. Stewart, W.P.(1992).”Insitu measurement of dynamic soil properties with emphasis on damping”. Ph.D. thesis, The Univ. of British Columbia, Vancouver, B.C. Stewart, W.P. and Campanella, R.G.(1991).”Insitu measurement of damping in soils”. Proc. 2nd Tnt. Conf. on Geot. Eathquake Engg. and Soil Dynamics, St. Louis, Mar. Sully, J.P.(1991).”Measurement of insitu lateral stress during full displacement tests”. Ph.D. thesis, The Univ. of British Columbia, Vancouver, B.C.  Bibliography  160  Sun, J.I., Golesorkhi, R. and Seed, H.B.(1988).’Dynamic moduli and damping factors for cohesive soils”. Report No. UCB/EERC-88/15, Univ. of Cal., Berkeley, CA. Tonouchi, K., Takayama, T. and Imai, T.(1983).”S wave velocity and the damping factor”. Bull. mt. Assoc. Eng. Geol. No. 26-27, Paris, pp.327-333. Vesic, A.S.(1972).”Expansion of cavities in infinite soil masses”. 11. of the Soil Mechanics and Foundn. Div., ASCE, Vol.98, SM3, pp.265-290. Whitman, R.V.(1970).”Site evaluation and dynamic analysis of nuclear power plants”. M.I.T. press. Whittle, R.W., Dalton, J.C.P. and Hawkins, P.G.(1992).”Shear modulus and strain excursion in the pressuremeter test”. Unpublished Notes, Cambridge Insitu. Woods, R.D.(1978).”Measurement of dynamc soil properties”. ASCE, GED Spec. Conf. on Earthquake Engg. and Soil Dynamics, Pasadena, CA., Vol.1, . 178 91 pp. Wroth, C.P.(1982).”British experience with the self-boring pressuremeter test”. Proc. of the Symp. on pressuremeter and its marine applications, Paris. Wroth, C.P. and Windle, (1975).”Analysis of the pressuremeter test allowing for volume change”. Geotechnique, Vol.25, No.3, . 604 598 pp. Yan, L. and Byrne, P.M.(1990).”Simulation of downhole and crosshole seismic tests on sand using the hydraulic gradient similitude method”. Can. Geot. 31., Vol.27, No.4, Aug., pp.441-4.60. Zavoral, D.(1990).”Dynamic properties of an undisturbed clay from resonant column tests”. M.A.Sc. thesis, Dept. of Civil Engg., The Univ. of British Columbia, Vancouver, B.C.  161  APPENDIX A  -  Modulus and Damping from Theoretical Models  162  oee.e  4-.  7.8  0 0  688.8  590.0  13.1  132  13.3  13.4  13.5  Radial Strain  136  13.?  (x)  Fig.A. 1. Damping from area of the smoothened loop, 5.2m depth, SBPO8, Laing Bridge  163  Cl)  6.8  13.1  13.2  13.3  13.4  115  13.6 Radial Strain ()  13.7  Fig.A.2. Damping and Shear Modulus from Lysmer Model, 5.2m depth, SBPO8, L.aing Bridge  164  S1P7  -  2LFth.92  596.8  4 .8  Th .0 2.2 2.1 Radial Strain (‘.)  2.3  Fig.A.3. Damping from area of the smoothened loop, 7. im depth, SBPO8, Laing Bridge  165  559.8  5.9  45LO  18L8  359.9  398.8  2.8  2.1 2.2 Radial Strain (i.)  2.3  Fig.A.4. Damping and Shear Modulus from Lysmer Model, 7. lm depth, SBPO8, Laing Bridge  166  6.9  cf 5OU  48L9  Radial Strain (i.) Fig.A.5. Damping from area of the smoothened loop, 7. im depth, SBPO8, Laing Bridge  167  a) 1)  a)  4.8  4.9  s.e  5.1 Radial Strain (i.)  5.Z  Fig.A.6. Damping and Shear Modulus from Lysmer Model, 7 .lm depth, SBPO8, Laing Bridge  168  650.0  0  550.0  5.0  450.0  5.2  5.25  5.3  Radial Strain ( Fig.A.7. Damping from area of the smoothened loop, 7. im depth, SBPO8, Laing Bridge  169  e.e  4-’  0)  550.8 0 0)  525 5.3 Badial Strain (‘.)  Fig.A.8. Damping and Shear Modulus from Lysmer Model, 7. im depth, SBPO8, Laing Bridge  170  1180.0  a)  1880.0  Ce) C’s 0)  [Os  •  880.0  780.0  Radial Strain Cx) Fig.A.9. Damping from area of the smoothened loop, 8.6m depth, SBPO8, Laing Bridge  171  n.e  0.•i 0 0  7.8 61 6.0 Radial Strain  6.2  (x)  Fig.A.1O. Damping and Shear Modulus from Lysmer Model, 8.6m depth, SBPO8, Laing Bridge  172  11.50.0  -  11.0  1950.0  .—  c  959.0  6.4  6A?  6.45  Radial Strain  &4?5  Cx)  Fig.A. 11. Damping from area of the smoothened loop, 8.6m depth, SBPO8, Laing Bridge  173  1158.0  -  11.e  1858.8 (4)  1.e  6.375  6.4  6.425  6.45  6.475  Radial Strain (x) Fig.A. 12. Damping and Shear Modulus from Lysmer Model, 8.6m depth, SBPO8, Laing Bridge  174  880.0  780.0 Ct, ‘1,  c. 180.0  500.0  4.1  .Z  4.)  1.4  Radial Strain Cx) Fig.A. 13. Damping from area of the smoothened loop, 11 .5m depth, SBPO8, Laing Bridge  175  L8  C., C.,  6.8  4.1  4.2 4.3 Radial Strain fyj  4.1  Fig.A. 14. Damping and Shear Modulus from Lysmer Model, 11 .5m depth, SBPO8, Laing Bridge  176  %L8  b-F  LI (1) C?)  798.8  4.5  4.55  1.6  4.65  4.7  Radial Strain Cx) Fig.A. 15. Damping from area of the smoothened loop, 13.9m depth, SBPO8, Laing Bridge  177  7OO.G  4.5  4.55  1.6 4.15 Radial Strain (i.)  4.7  Fig.A. 16. Damping and Shear Modulus from Lysmer Model, 13.9m depth, SBPO8, Laing Bridge  178  APPENDIX B  -  Calibration Curves  179  800  Spilt Cylinder Compliance Calibration for Lantern  B  Li.  D C’) Ci)  4)  > C  C)  Radial Strain (x)  Fig.B. 1. Compliance Calibration for Lantern#8 with Split Cylinder  180  Split Cylinder Compliance Calibration for Lantern  9 15—Apr—92  Radial Strain (s)KPa)  Fig.B.2. Compliance Calibration for Lantern#9 with Split Cylinder  181  Appendix C  182 SCPT DETAILS  Introduction  Any soil property assessment has to be done by comparison of the obtained results with results from existing techniques. In this research, the shear moduli and damping results were validated by comparison with SCPT results. The SCPT has been used extensively since 1980 (Robertson et al. ,1986). The SCPT methods yielding small strain moduli and damping measurements have been fairly well established (Campanella and Robertson,1984; Campanella and Stewart, 1990; Stewart, 1992). The SCPT involves striking a weighted beam at the ground surface by a standard drop hammer thereby producing a shear wave that is picked up by an accelerometer at the tip of the cone. The accelerometer record is recorded on a Nicolet oscilloscope. This procedure is repeated at a metre depth intervals and the accelerometer records for all these depths stored. The shear wave velocity and damping measurements are made from these records.  Shear Wave Velocity  The plot for shear wave velocity is shown in figure.4.8. The cross-correlation method (Campanella and Stewart, 1990) is used wherein the shear waves from two consecutive depths are matched and the shift in time of arrival of the two shear waves obtained. This time taken for the wave to travel between two consecutive depths. The profile of shear velocity with depth shows the velocity to vary from 35 m/s at a depth of 5m to 110 m/s at 15m depth. The  183 shear strains that are associated with these velocities are in the range of 0.001 % to 0.0001 %, a range in which soil behaviour is linear elastic. The moduli obtained by this method is compared to that from the pressuremeter since both the tests are in-situ and can be carried out at similar locations and depths. The fact that the SCPT is well established gives further impetus to the above comparison. It has also been noted by Zavoral (1990) and Stewart (1992) that the agreement between laboratory and SCPT results is quite good. After obtaining  the shear wave velocity V the shear modulus is obtained by : where  p  =  G  2 pV  In-situ density  A profile of the shear modulus is also shown in figure.4.8.  Damping  The most usual methods of obtaining damping measurements are from the laboratory. However, since the SCPT was established, several methods have been available to calculate the in-situ damping ratio from the SCPT. Stewart and Campanella (1990) and Stewart (1992) suggest that the spectral ratio slope method developed by Redpath et al. (1982) gives consistently meaningful results. The SRS method (Stewart and Campanella, 1990) is based on the equation  (A 1 ,J 2 dfdR  =-z  184 where A2/A1 dR Z  =  =  =  Ratio of signal amplitudes in frequency domain from successive depths.  Depth derivative a/f, where a is an attenuation co-efficient  This is solved using Vu-point digital signal processing program. The fast fourier transforms of all the signals and then the negative of the natural logarithm of the ratio is obtained. The slope of this ln ratio versus the frequency plot for each depth is calculated. The slope of this plot yields Z. Damping can then be obtained by  zv  S  2t  This was found to be 1 % for small strains. This was used as an input in the damping results along with the SBPMT results to obtain an average damping curve.  


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items