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- Permanent Link:
- http://digital.auraria.edu/AA00003193/00001
## Material Information- Title:
- Stress path effect on the static behavior of Monterey no. 0/30 sand
- Creator:
- Goldstein, Barry
- Publication Date:
- 1988
- Language:
- English
- Physical Description:
- 217 leaves : illustrations ; 28 cm
## Subjects- Subjects / Keywords:
- Sand -- Testing ( lcsh )
Soil mechanics ( lcsh ) Sand -- Testing ( fast ) Soil mechanics ( fast ) - Genre:
- bibliography ( marcgt )
theses ( marcgt ) non-fiction ( marcgt )
## Notes- Bibliography:
- Includes bibliographical references (leaves 195-198).
- General Note:
- Submitted in partial fulfillment of the requirements for the degree, Master of Science, Department of Civil Engineering.
- Statement of Responsibility:
- by Barry R. Goldstein.
## Record Information- Source Institution:
- |University of Colorado Denver
- Holding Location:
- Auraria Library
- Rights Management:
- All applicable rights reserved by the source institution and holding location.
- Resource Identifier:
- 19782988 ( OCLC )
ocm19782988 - Classification:
- LD1190.E53 1988m .G64 ( lcc )
## Auraria Membership |

Full Text |

STRESS PATH EFFECT ON THE STATIC BEHAVIOR
OF MONTEREY NO. 0/30 SAND by Barry R. Goldstein B.S., Colorado State University, 1983 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Master of Science Department of Civil Engineering 1988 This thesis for the Master of Science degree by Barry R. Goldstein has been approved for the Department of Civil Engineering by Z- Date Goldstein, Barry R. (M.S., Civil Engineering) Stress Path Effect on the Static Behavior of Monterey No. 0/30 Sand. Thesis directed by Professor Nien-Yin Chang Two of the most important characteristics of soil behavior are stress-path dependency and principal stress rotation effect. Actual field conditions often result in soil elements following different stress paths. When a structure is subjected to axial and lateral loading, the resulting transfer of load will cause the soil elements to undergo different stress paths. The theory of isotropic linear elasticity is sometimes applied in the analysis of soil mechanics problems. It is well known, however, that soils do not behave as an isotropic linear elastic material. Thus, the influence of different stress paths on the behavior of soil should be of importance. The rotation of principal stress directions can occur under in-situ conditions, such as during slope movements, excavations and cyclic loading. Soil behavior is significantly affected by the rotation of the principal stress direction. Behavior which is affected includes the maximum deviatoric stress, internal angle of friction, pore pressure generation-volume change characteristics and plastic deformation. In this study, Monterey No. 0/30 sand was used and nineteen static triaxial tests on seven different stress paths were con- ducted. The test results were used to analyze the behavior of Monterey No. 0/30 sand on different stress paths in the Rendulic plane. Also, using the results from the isotropic compression test, conventional triaxial compression test, and the reduced triaxial iv compression test, were calculated, behavior of soils the soil parameter for Lade's elasto-plastic model These parameters can be Used to predict the under other stress paths on the Rendulic plane can be simulated. ACKNOWLEDGEMENTS This study was conducted in the Department of Civil En- gineering at the University of Colorado at Denver. The author wishes to express his sincerest appreciation to his advisor, Professor Nien-Yin Chang, for his guidance and support. Gratitude is also extended to Dr. Tzong-H. Wu for his insightful discussions. The author is grateful to his fellow graduate students, Mr. Hsing-Cheng Liu, Dr. Jing Wen Chen, Mr. Z. X. You and Ms. Elaheh Kheirkhahi for their help during this study. I would also like to thank Mr. Joseph Cesare for his support over the last several years. Finally, I would like to express my gratitude to Carol McAmis for her patience and assistance in the typing and Ms. Pauline LeBlanc for finalizing this thesis. Finally, I would like to thank my parents for all their continued support and encouragment. LIST OF TABLES Table 11.1 Stress Paths on the Rendulic Plane (after Das, 1983)........................................16 11.2 The Parameters M and N in Equation 11.34 (after Naylor, 1978).....................................42 III.3 Parameters for Lade's Model..............................63 IV. 1 Proposed Testing Program.................................65 IV. 2 Stress Paths Conducted for Study.........................66 IV. 3 Physical Properties for Monterey No. 0/30 Sand...........69 V.l Sample b-Parameters Prior to Testing.....................88 VII. 1 Initial Conditions of Triaxial Samples..................100 VII.2 Elastic Moduli of Monterey No. 0/30 Sand from Hydrostatis Compression Tests Dr = 43.2) 103 VII.3 Initial Young's Moduli determine from CTC Tests .... 113 VII.4 Initial Young's Moduli determined from TC Tests .... 121 VII.5 Initial Young's Moduli determined from RTC Tests. . . 130 VII.6 Initial Young's Moduli determined from RTE.C Tests. . 138 VII.7 Initial Young's Moduli determined from TC Tests .... 146 VII.8 Initial Young's Moduli determined from CTE Tests. . . 154 VII.9 Initial Young's Moduli determined from TC Tests .... 163 VII.10 Initial Young's Moduli determined from TC Tests. . 164 VII.11 Volume Change Characteristics Drained Triaxial Tests 166 vii Table VIII.1 Parameters for Lade's Model Monterey No. 0/30 Sand CTC Stres Path.....................................185 VIII.2 Parameters for Lade's Model Monterey No. 0/30 Sand RTE Stress Path....................................189 LIST OF FIGURES Figure 1.1 Orientation of Stress Directions at Failure.............3 11.1 Cambridge Stress Field (Roscoe, et al., 1958) Illustrating Principal Stresses.........................7 11.2 Mohr Stress Circle Defining Stress Parameters t' and s' (after Atkinson and Bransby, 1978)............9 II.3 Stress Paths for (a) Drained and (b) Undrained Loading Tests (after Atkinson and Bransby, 1978) . .12 11.4 Stress Field for Axial Symmetry (after Henkel, 1960).....................................................13 11.5 Rendulic Diagram (after Das, 1983)....................... 15 11.6 Results of Drained Triaxial Tests on (a) Dense Sand and (b) Loose Sand (after Bishop and Henkel, 1962).............................................18 11.7 Results from Undrained Triaxial Tests and (a) Medium Dense and (b) Loose Sand (after Bishop and Henkel, 1962).........................................19 11.8 Deviatoric Stress-Strain Curve for Triaxial Test Showing Alternate Shear Moduli (after Naylor, 1978)..............................'.............30 11.9 Flow Rule in Three-Component Space (after Naylor, 1978).............................................37 11.10 Yield Surface in Principal Stress Space (after Naylor, 1978)......................................38 11.11 Yield Surfaces; 1 = Mohr-Coulomb, 2 = Extended VonMises, 3 = Compromise Cone, 4 = Axial Extension Cone, and 5 = Drucker-Prager (after Naylor, 1978).................40 11.12 General Static Failure Criteria (after Horita, 1983) 45 IX Figure 11.13 General Static Failure Criteria (after Horita, 1983)............................................46 11.14 (a) Classical Failure Criteria in Principal Stress Space and (b) Cross-Sections of Mohr-Coulomb Failure Criterion Shown for Three Different Friction Angles (after Bishop, 1966).............................................47 111.1 Strain Components in Lade's Model (after Lade, 1977)...............................................53 111.2 Ultimate Strength and Yield Surface in Lade's Model (after Lade, 1977)...........................55 111.3 Yield Surface and Plastic Potential Surface in Triaxial Plane of Lade's Model.........................59 IV.1 Grain Size Distribution of Monterey No.0/30 Sand (after Muzzey, 1976).................................18 IV.2 Material Testing System Equipment Used in Study.....................................................72 V.l Plot of Internal Pressure Against Volumetric Polyethylene Tube Expansion...............................90 VII.1 Isotropic Consolidatiron Triaxial Test Results .... 102 VII.2 CTC Stress Paths in p':q' Stress Space .................. 106 VII.3 Mohr Stress Circles at Failure for CTC Triaxial Tests ......................................... 107 VII.4 CTC Triaxial Test Data for 30 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Against Ea ............................... 108 VII.5 CTC Triaxial Tests Data for 60 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Against Ea ............................... 109 VII.6 CTC Triaxial Tests Data for 90 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Against Ea ............................... 110 VII.7 Stress-Strain Curves for CTC Triaxial Tests Conducted at Different Effective Confining Stress Levels 111 X Figure VII.8 TC Stress Paths in p':q' Stress Space...................114 VII.9 Mohr Stress Circules at Failure for TC Triaxial Tests ....................................... 116 VII.10 TC Triaxial Test Data for 30 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Against Ea...........................117 VII.11 TC Triaxial Test Data for 60 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Against Ea...........................118 VII.12 TC Triaxial Test Data for 90 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Against Ea...........................119 VII.13 Stress-Strain Curves for TC Triaxial Tests Conducted at Different Effective Confining Stress Levels................................120 VII.14 RTC Stress Paths in p':q' Stress Space ................ 123 VII.15 Mohr Stress Circles at Failure for RTC Trixial Tests..........................................124 VII.16 RTC Triaxial Test Data for 30 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Against Ea..................... 126 VII.17 RTC Triaxial Test Data for 60 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Against Ea ....................... 127 VII.18 RTC Triaxial Test Data for 90 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Against Ea...............................128 VII.19 Stress-Strain Curves for RTC Triaxial Tests Conducted at Different Effective Stress Levels.................................................129 VII.20 RTE Stress Paths in p':q' Stress Space ................ 132 VII.21 Mohr Stress Circles at Failure for RTE Triaxial Tests ....................................... 133 VII. 22 RTE Triaxial Test Data for 30 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Against Ea .................... 134 XI Figure VII.23 RTE Triaxial Test Data for 60 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Against Ea..............................135 VII.24 RTE Triaxial Test Data for 90 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Against Ea ............................. 136 VII.25 Stress-Strain Curves for RTE Triaxial Tests Conducted at Different Effeective Confining Stress Levels..................................................137 VII.26 TE Stress Paths in p':q' Stress Space..................140 VII.27 Mohr Stress Circles at Failure for TE Triaxial Tests ....................................... 141 VII.28 TE Triaxial Test Data for 30 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Against Ea...........................142 VII.29 TE Triaxial Test Data for 60 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Sgainst Ea ............................. 143 VII.30 TE Triaxial Test Data for 90 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Against Ea...............................144 VII.31 Stress-Strain Curves for TE Triaxial Tests Conducted at Different Effective Confining Stress Levels..................................................145 VII.32 CTE Stress Paths in p':q' Stress Space ................ 148 VII.33 Mohr Stress Circles at Failure for CTE Triaxial Tests ....................................... 149 VII.34 CTE Triaxial Test Data for 30 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Against Ea...........................150 VII.35 CTE Triaxial Test Data for 60 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Against Ea ............................. 151 VII.36 CTE Triaxial Test Data for 90 psi Effective Confining Pressure (a) q Against Ea and (b) Volume Change Against Ea..........,...................152 Xll Figure VII.37 Stress-Strain Curves for CTE Triaxial Tests Conducted at Different Effective Confining Stress Levels...................................................153 VII.38 Stress Paths for 30 psi Effective Confining Pressure................................................157 VII.39 Stress Paths for 60 psi Effective Confining Pressure................................................158 VII.40 Stress Paths for 90 psi Effective Confining Pressure............................................... 159 VII. 41 Failure Envelope Defined in p':q' Space...............160 VIII. 1 Plot of Elastic Modulus Against Confining Pressure to CTC Stress Path.............................170 VIII.2 Plot of Volumetric Strain Against Effective Confining Pressure From an Isotropic Consolidation Triaxial Test.............................172 VIII.3 Plot of Plastic Collapse Work, Wc, and fc Parameter...............................................174 VIII.4 Determination of the Parameters and m for the CTC Stress Path.................................175 VIII. 5 Plot of tj2 Aagainst fp of Various a'3 Levels for CTC Stress Path.....................................178 VIII. 6 Plot of Intercept Against a3 for CTC Stress Path....................................................179 VIII.7 Plot of Plastic Work Against fp for Various cr3 Levels for CTC Stress Path..........................182 VIII. 8 Plot of q against a3 for determining a and /3 parameters for the CTC Stress Path...................183 VIII.9 Plot of Wppeak Against a3 for Determining 1 and p Parameters for the CTC Stress Path..............184 TABLE OF CONTENTS ABSTRACT.........................................................iii ACKNOWLEDGEMENTS...................................................v LIST OF TABLES............................................... .vi LIST OF FIGURES.................................................viii CHAPTER I. INTRODUCTION ............................................. 1 1.1. Purpose............................................1 1.2. Scope..............................................4 II. BACKGROUND AND LITERATURE REVIEW ......................... 6 II.1. Stress paths on the Rendulic plane ............... 6 11.2 Static Behavior of Granular Materials.............14 11.3 Factors Affecting Triaxial Testing................20 11.3. a Introduction.............................20 11.3. b Inherent Soil Properties.................21 11.3. c Initial Void Ratio.......................23 11.3. d Confining Pressure.......................24 11.3. e Loading Conditions.......................25 II. 3. f Rate of Loading..........................25 11.4 External Effects on the Triaxial Test.............25 II.4.a Introduction 25 xiv CHAPTER II. 4.b Rubber Membrane...........................26 II. 4. c Piston Friction..........................27 II. 5 Stress-Strain Laws for Soil.......................27 11.5. a Introduction.............................27 II. 5.b Linear Elastic Laws......................28 II. 5. c Variable Elastic Laws....................31 11.5. C.1 Hyperbolic Model................31 11.5. C.2 Differential Models.............31 11.5. d Elastic-Plastic Laws.....................33 11.5. d.l Yield Surface...................34 11.5. d.2 Strain Hardening................35 II. 5 d. 3 Flow Rule....................35 11.5. d.4 Specific Forms of Yield Surface.........................36 II. 6 Failure Criteria..................................43 11.6. a Classical Failure Criteria................44 11.6. b Three-dimensional Failure Criteria . .48 III. LADE'S ELASTO-PLASTIC MODEL..............................50 III. l Introduction....................................50 111.2 Strain Components...............................51 III. 2. a Elastic Strains........................52 111.2. b Plastic Collapse Strains................54 111.2. C Plastic Expansive Strain................57 111.3 Summary of Stress-Strain Parameters.............62 XV CHAPTER IV. MATERIALS AND TESTING APPARATUS............................64 IV. 1 Test Program......................................64 IV.2 Monterey No. 0/30 Sand..............................64 IV. 3 Test Equipment....................................67 IV.3.a Triaxial Test...............................67 IV. 3.b MTS Loading Machine.......................71 IV.4.c Data Acquisition Systems....................77 V. SAMPLE PREPARATION ....................................78 V. l Relative Density Control..........................78 V.2 Sample Preparation................................79 V.3 Flusing...........................................84 V.4 Connecting Pore Pressure Transducer...............85 V.5 Saturation........................................86 V.6 Determining B-Parameter...........................86 V. 7 Consolidation.....................................87 VI. TEST PROCEDURES............................................92 VI. 1 MTS Operation.....................................92 VI.2 Connecting Loading Ram to Top Cap...................93 VI.3 Conducting Tests with a Constant Radial Stress .94 VI.4 Conducting Tests with Changing Radial Stress . .95 VI. 5 Conducting High Pressure Tests....................98 VII. RESULTS AND DISCUSSION OF LABORATORY RESULTS ............ 100 VII. 1 Introduction...................................100 VII.2 Hydrostatic Compression (HC) Test................100 VII.3 Conventional Triaxial Compression (CTC) Tests . 104 xvi CHAPTER VII.4 Triaxial Compression (TC) Tests ............. 112 VII.5 Reduced Triaxial Compression (RTC) Tests. . 122 VII. 6 Reduced Triaxial Extension (RTE) Tests...........125 VII.7 Triaxial Extension (TE) Tests .............. 131 VII.8 Conventional Triaxial Extension (CTE) Tests . 147 VII. 9 Summary..........................155 VIII. STRESS PATH EFFECT ON LADE'S PARAMETERS....................168 VIII. 1 Introduction ...................... 168 VIII. 2 Soil Parameter Calibration ............... 168 VIII.2.a Calibration of the CTC stress path parameters......................169 VIII.2.b Calibration of the RTE Stress Stress Path Parameters ............. 181 IX. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER STUDY.........................................190 IX. 1 Summary........................................190 IX. 2 Conclusions......................................193 IX.3 Recommendation for Further Study ............... 194 BIBLIOGRAPHY.....................................................195 APPENDIX.........................................................199 A. TEST DATA 200 CHAPTER I INTRODUCTION I.1 Purpose Soils, in a geotechnical sense, can be regarded as engineer- ing materials. Their physical characteristics can be determined by experiment, and the application of methods of analysis enables these properties to be used to predict their likely behavior under defined working conditions. Unlike other engineering materials such as metals and concrete, over which control can be maintained during manufacture, soils are naturally occurring materials which most often must be used in their natural condition. Even when some type of processing is possible, soil can be modified only to a limited extent and by relatively simple procedures. The main problems associated with soil mechanics are generally divided into two catagories: deformation and stability. The former are considered to be governed by stress-strain and strain-time relationships and the latter by the shear-strength properties. The extent and accuracy to which an analysis to determine stability and/or deformation can be achieved is often limited by the practical problem of sampling and testing to deter- mine inherent characteristics and that of understanding soil behavior. In general, much emphasis has been placed on refinements 2 in sampling techniques and testing procedures. Even with these refinements, accurate solutions can be obtained only if the soil strata are for practical purposes, homogeneous and continuous in a spacial aspect. To obtain more certain engineering characteristics based on quantitative measurements of relevant soil properties to predict and/or determine the subsequent performance of the actual structure, further understanding of basic soil behavior under in- situ conditions is necessary. Two of the most important characteristics of soil behavior are stress-path dependency and principal stress rotation effect. Actual in-situ conditions often subject soil elements to different stress paths. When a structure is subjected to axial and lateral loading, the resulting transfer of load will cause the soil elements to undergo different stress paths. The theory of isotropic linear elasticity is sometimes applied in the analysis of soil mechanics problems. It is well known, however, that soils do not behave as an isotropic linear elastic material. Thus, the influence of different stress paths on the behavior of soil should be of importance. The rotation of principal stress directions can occur under in-situ conditions, such as during slope movements, excavations and cyclic loading (see Figure 1.1). Soil behavior is significantly affected by the rotation of the principal stress direction. Behavior which is affected includes the maximum deviatoric stress, internal angle of friction, pore pressure generation volume change characteristics and plastic deformation. Fig. 1.1 Orientation of Stress Directions at Failure 4 In summary, soil behavior is stress-path dependent and is significantly affected by the rotation of the principal stress direction. The purpose of this study is four-fold. 1. To determine the stress-strain relationships and volume change characteristics of Monterey No. 0/30 sand on different stress paths and at varying effective stress levels on the Rendulic plane. 2. To determine the influence of stress paths on the characteristics of soil behvior and soil parameters. 3. To develop the parameters necessary to apply Lade's elasto-plastic model. To perform triaxial tests on different stress paths such that these tests can be used as actual comparison with the predicted behavior generated by Lade's constitutive model. 4. To perform triaxial tests so that a comparison of the behavior of a solid cylindrical sample tested in a standard triaxial cell and that of a hollow cylindrical sample tested in a large diameter triaxial cell, developed by the University of Colorado at Denver, can be made. I.2 Scone The scope of this thesis is to evaluate the stress-strain characteristics of Monterey No. 0/30 sand on varying stress paths on the Rendulic plane. Triaxial tests on the following stress paths were conducted: CTC Conventional Triaxial Compression RTC Reduced Triaxial Compression TC Triaxial Compression 5 CTE Conventional Triaxial Extension RTE Reduced Triaxial Extension TE Triaxial Extension IC Isotropic Compression Testing was conducted at three different effective stress levels; 30 psi, 60 psi and 90 psi. Sample density used in the testing program was the same as that used in the testing program with the hollow cylinder triaxial cell conducted at the University of Colorado at Denver. This would allow for more complete com- parison of the soil behavior under two triaxial systems. Upon completion of the laboratory testing, stress-strain, volume change-strain and p:q plots were developed for each stress path. Using the HC, CTC and RTE triaxial test data, the soil parameters for Lade's elasto-plastic constitutive model were evaluated. Results from this study will be used to further understand soil behavior on the Rendulic plane, and soil behavior as it relates to stress path dependency. Finally, this study will also assist in the continued development of the University of Colorado at Denver's hollow cylinder triaxial cell. CHAPTER II BACKGROUND AND LITERATURE REVIEW II.1 Stress Paths on the Rendulic Plane In a general cubical element of material, there are six independent stresses; three shear stresses arid three normal stres- ses. If the element is rotated such that the faces become principal planes, the shear stresses of the face become zero and the normal stresses become principal stresses. For a soil, the state of stress is completely defined by three principal total stresses (and their directions) and the pore water pressure. The three principal effective stresses may be calculated based on Terzaghi's effective stress equation. To define an effective (or total) stress space, a three- dimensional plot with a1 element may be plotted as a point in the effective stress space and the line joining all points of instantaneous states of stress is defined as the effective stress path. The points represent only the magnitude of the principal stresses. The stress path does not indicate direction nor does it indicate any rotation of the prin- cipal planes. 7 Fig. II.1 Cambridge Stress Field (Roscoe, et al, 1958) Illustrating Principal Stresses 8 It may be at times, convenient to plot effective stress paths in the two-dimensional effective stress plane o'1:o3 ignoring the intermediate principal stress, az . The instantaneous two-dimensional state of stress may be represented by a Mohr's circle of stress, as shown in Figure II.2. From the geometry of the Mohr circle, and noting that rxz = tzx; t' = 1/2[(ctx-ctz)2+4txz]1/2 s' = 1/2(ctx-ctz) or, in terms of principal effective stresses; t' = 1/2 (ct-l -a3 ) s = 1/2 (o^+CTg) II.1 II.2 II. 3 II.4 The parameters t' and s', their magnitudes for a given state of stress are independent of the choice of reference axes, and are known as stress invariants. Octahedral normal stress, uQct> an<3 t^ie octahedral shear stress, roct-, are invariants and defined as; ^oct 1/3 (x y *" CTz) II.5 T Fig. II.2 Mohr Stress Circle Defining Stress Parameters t' and s(after Atkinson and Bransby, 1978) 10 ('oct)2 = V9 [ (o^-ap2 + (ffy-a^)2 + (&2 ax)2 + 6(r2xy + r2yz + r2xy)] II.6 or in terms of principal stress: CToct = 1/1(CTi + ^2 + 117 rOCt = 1/1 [ (CT1 "a2 )2 + (*2"a3 )2 + (^-Oi)2] 11 8 For the case where ag = cr^ and where a = 0 (a = angle of rotation); a^t = l/3(a{+2^) II. 9 r^ct = II.10 To avoid the recurring 1/372 term, the following in- variants are defined, where a'z = o'z\ For a general three-dimensional state of stress, q* and p* become; p' = l/3(a[+2a^) = crÂ£ct II. 11 q' = (ol+2ai) = 3 1/72 r'ct 11.12 For a general three-dimensional state of stress, q' and p' become: 11 p' = 1/3(a{+a^+a^) 11.13 q' = 1/J2[ (cr^ -CTg )2 + (cr^ -erg )2 + (erg -cr^ )2 ]1 /2 11.14 and the third invariant a, will be non-zero. Roscoe, Schofield and Wroth (1958) at the University of Cambridge, England, developed the use of the mean of the three prin- cipal effective stresses (cr^ a^, 03) instead of the mean major and minor principal stresses. This method of plotting, which will be used throughout this text, is known as the Cambridge stress path plot. To distinguish between triaxial compression and extension, since in both cases q is positive (by definition , the parameters of stress (and strain) can be redefined as; q' = 11.15 p' = l/3+2a;) 11.16 where cr' is the effective axial stress and oL is for effective a r radial stress. The stress paths shown in Figure II.3 are plotted using p,p':q,q' space. A method of representing the stress path for triaxial tests is the plot suggested by Rendulic (1937) and later by Henkel (1960). The Rendulic plot is a diagram of the results of triaxial tests for the condition of axial symmetry, as shown in Figure II.4. The equal h'b 12 P,P' P
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