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In all cases we have film ed the best available copy. University Microfilms International 300 N. ZEEB RD., A N N ARBO R, Ml 48106 8202441 G o i t o m ,T esfai CHARACTERISTICS OF MICHIGAN COHESIVE SUBGRADE SOILS U N D E R CYCLIC LOADING PH.D. 1981 Michigan State University University Microfilms International 300 N. Zeeb Road, Ann Arbor, M I 48106 PLEASE NOTE: In all cases this material has been filmed in the best possible way from the available copy. Problems encountered with this docum ent have been identified here with a check mark V . 1. Glossy photographs or pages______ 2. Colored illustrations, paper or p rin t______ 3. Photographs with dark background______ 4. Illustrations are poor copy______ 5. Pages with black marks, not original copy______ 6. Print shows through as there is text on both sides of page______ 7. Indistinct, broken or small print on several pages______ 8. Print exceeds margin requirem ents______ 9. Tightly bound copy with print lost in spine______ 10. Computer printout pages with indistinct print______ 11. P age(s)_____________ lacking w hen material received, and not available from school or author. 12. Page(s) 13. Two pages n u m bered____________ . Text follows. 14. Curling and wrinkled pages______ 15. Other_______________________________;___________________________________________ 322 seem to be missing in numbering only as text follows. University Microfilms International CHARACTERISTICS OF MICHIGAN COHESIVE SUBGRADE SOILS UNDER CYCLIC LOADING By Tesfai Goitom A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Civil Engineering 1981 ABSTRACT CHARACTERISTICS OF MICHIGAN COHESIVE SUBGRADE SOILS UNDER CYCLIC LOADING by Tesfai Goitom In this study, the plastic and elastic characteristics of Michigan cohesive subgrade soils are evaluated using repeated load triaxial tests on undisturbed samples. The results of the investigation led to the development of a normalized predictive model of the plastic strain. The model have demonstrated its ability to evaluate and predict the plastic behavior of several materials sub­ jected to cyclic loadings. The input parameters of the model consist of the static strength and the correspond­ ing total strain of the material in question. The model was tested and evaluated using five different materials ranging from gravel, sand, clay and clayey silt. The developed normalized predictive model neutralizes the effects of several sample and test variables. The model was found to be unique for each class of soil and independent of compaction, density, water content and stress-level. Further, the model was used to develop a new approach and understanding of the soil support value of the AASHTO INTERIM GUIDE FOR THE DESIGN OF FLEXIBLE PAVEMENT. TO MY PARENTS ACKNOWLEDGMENT The author is grateful to the Michigan Department of Transportation and the Federal Highway Administration for their support which made this report possible. The author wishes to express his gratitude to Dr. Gilbert Baladi for his personal and professional discus­ sion and guidance throughout the course of these investi­ gations. The interests and comments expressed by the members of the research committee, Messrs. K. Allemeir, J. Burge, C. Mainfort, E. Novak and Dr. S. Kou are acknow­ ledged. To Drs. 0. B. Andersland, W. A. Bradley, R. K. Wen, and N. Altiero special thanks and deep appreciation for serving on his guidance committee and reviewing this thesis as well as for the many inspiring classes which they pro­ vided him as a student. The efforts expended by Mr. J. Brichta for his help in reducing some of the data, and Ms. Nancy Hunt and Ms. Vicki Brannan for typing the figures and tables are greatly acknowledged. To the Division of Engineering Research personnel for typing this thesis, the author expresses his appreciation. Very special thanks go to his fiancee Selamawit G/Michael for her support, encouragement and love provided a special source of inspiration and incentive which in large measure sustained his efforts throughout his educa­ tion. TABLE OF CONTENTS PAGES LIST OF TABLES vii LIST OF FIGURES viii LIST OF SYMBOLS XXV CHAPTER I : INTRODUCTION 1 CHAPTER II: REVIEW OF LITERATURE 4 2.1 General 4 2.2 Design Methodologies 5 2.2.1 Deformation-Failure Approach 2.2.1.a Laboratory or Field Index 6 Test Procedure 2.2.1.b Limiting Subgrade Strain Procedure 2.2.2 Prediction of Cumulative Deformation 7 9 Approach 10 2.2.2.a Quasi-Elastic Approach 11 2.2.2.b Viscoelastic Approach 12 2.2.2.b.l Primary Response Model 12 2.2.2.b.2 Damage Model 14 2.2.2.b.3 Performance Model 15 2.3 Cyclic Loadings 16 2.3.1 Behavior of Cohesive Soils Subjected to Cyclic Loadings 18 2.3.1.1 Factors Affecting the Plastic Deformations of Cohesive Soils 21 2.3.1.1.a Number of Load Applications 2.3.1.1.b Magnitude of Loadings 21 23 2.3.1.1.C Effect of Thixotropy 25 2.3.1.1.d Effect of Stress History 25 2.3.1.1.e Effect of Frequency and Duration 27 2.3.1.2 Factors Affecting the Resilient or Elastic Characteristics of Cohesive Soils 27 2.3.1.2.a Number of Load Applications 30 2.3.1.2.b Confining Pressure 30 2.3.1.2.c Stress-Level 30 2.3.1.2.d Load Duration and Frequency 31 2.3.1.2.e Compaction Density and Water Content 34 2.3.1.2.f Thixotropy 36 PAGES 2.4 Correlations of Soil Support Values to Material Characterization (SSV) 38 2.4.1 Correlations Between California Bearing Ratio (CBR) and Soil Support Values (SSV) 38 2.4.2 Correlations Between Modulus of Deformation and SSV 40 2.4.3 Correlation Between SSV and Resilient Modulus CHAPTER III: FIELD AND LABORATORY INVESTIGATIONS 40 47 3.1 Field Investigations 47 3.1.1 Site Selection 47 3.1.2 Scope of Sampling Techniques 47 3.2 Laboratory Investigation 53 3.2.1 Test Material 53 3.2.2 Laboratory Tests 62 3.2.2.1 Static Triaxial Tests 62 3.2.2.1.a Incremental Creep Test (ICT) 62 3.2.2.1.b Ramp Test (RT) 3.2.2.2 Cyclic Triaxial Tests 63 (CTT) 3. 2. 2. 3 Conventional Consolidation Test 63 (CCT) 3.2.3 Test Procedures 68 69 3. 2.3.1 Cyclic Triaxial Test 69 3.2.3.2 Ramp Triaxial Test 70 3.2.3.3 Incremental Creep Test 70 3.2.4 Test Parameters 70 3. 2.4.1 Number of Load Repetitions 70 3.2.4. 2 Confining Pressure 71 3.2.4.3 Cyclic Principal Stress Difference 72 3.2.5 Sample Preparation 72 3.3 Data Reduction 73 CHAPTER IV: TEST RESULTS 77 4.1 General 77 4.2 Lower Peninsula Test Sites 86 4.2.1 Static Triaxial Tests 86 4.2.2 Cyclic Triaxial Tests 93 4.2.2.1 Consolidated Cyclic Triaxial Tests- 93 4.2.2.2 Unconsolidated Cyclic Triaxial Tests 93 iv PAGES 4.3 Upper Peninsula Test Sites 106 4.3.1 Static Triaxial Tests 106 4.3.2 Consolidated Cyclic Triaxial Tests 106 4.3.3 Unconsolidated Cyclic Triaxial Tests 120 CHAPTER V: DISCUSSION , 125 5.1 General 125 5.2 Static Triaxial Tests 128 5.2.1 Incremental Creep Tests Versus Ramp Tests 128 5.2.2 Sample Failure and Failure Mode 129 5.2.3 Strength Parameters 135 5.2.4 Stress-Strain Relationship 140 5.3 Cyclic Triaxial Tests 142 5.3.1 Effect of Test and Sample Variables on the Axial Plastic Response 145 5.3.1.1 Number of Load Repetitions 145 5.3.1.2 Confining Pressure 154 5.3.1.3 Stress Level 157 5.3.1.4 Stress History 161 5.3.1.5 Water Content and Consolidation 164 5.4 Stress-Strain Relationship 166 5.5 Soil Support Value 184 5.6 Limiting Stress and Strain Criterion 195 5.7 Implementation 196 5.7.1 General 196 5.7.2 Numerical Example 197 CHAPTER VI: CONCLUSIONS AND RECOMMENDATIONS 201 6.1 Conclusions 201 6.2 Recommendations 2 02 BIBLIOGRAPHY 203 APPENDICES APPENDIX A: EQUIPMENT 213 A . 1 The Cyclic Triaxial Test (MTS) System ' 213 A . 1.1 The MTS Electrohydraulics Closed Loop Test System 213 A . 1.2 The MTS Servovalve Controller Model 406.11 217 A . 1.3 The MTS Controller Model 436.11 222 v PAGES A. 1.4 Control Box 224 A. 1.5 Output Recording Equipment 224 A . 2 Minicomputer System 226 A.2.1 Waveform Shaper Circuit 226 A . 2.1.a Characteristics of the MTS 436 Signal Generator 226 A.2.1.b Triggering the Circuits on the MTS 436 Rear Panel 229 A.2.1.C Circuits Used to Generate the Signals Previously Mentioned 232 A.2.1.d Software 236 A.2.1.e Procedure to Run the Program 247 A. 3 Figure Conditioning Box 248 APPENDIX B: CALIBRATION INFORMATION 252 B.l Load Cell 252 B.2 Linear Variable Differential Transducers B.3 Strip Charp Recorder - (LVDT) 252 253 APPENDIX C: TEST RESULTS OF THE LOWER PENINSULA TEST SITES 254 APPENDIX D: TEST RESULTS OF THE UPPER PENINSULA TEST SITES 298 LIST OF TABLES PAGE TABLE General Information Concerning the Test Sites, Upper Peninsula 49 General Information Concerning the Test Sites, Lower Peninsula 50 Specific Gravity, Atterberg Limits, and Average Natural Moisture Content of the Subgrade Materials at the Test Sites 60 3.4 Consolidation Data of the Test Sites 67 4.1 Information Pertaining to the Test Samples of the Lower Peninsula Test Sites 78 Information Pertaining to the Test Samples of the Upper Peninsula Test Sites 84 3.1 3.2 3.3 4.2 5.1 5.2 5.3 5.4 C.l C.2 C .3 D.l Strength Parameters and Regression Constants of the Static Tests for the Lower Peninsula Test Sites 137 Strength Parameters and Regression Constants . of the Static Tests for the Upper Peninsula Test Sites 138 Regression Parameters for Least Squares Fit of Equation 155 The Values of the Regression Constants an /t>n / a ,b for Five Different Materials m m 197 List of the Radial Permanent Strain for Consolidated Samples, Sites 1, 3, and 4, Lower Peninsula 293 List of Axial Permanent Strain for Uncon­ solidated Samples 296 List of Radial Permanent Strain for Uncon­ solidated Samples 297 List of the Radial Permanent Strain for Test Sites 1, 2, 3, Upper Peninsula 323 vii LIST OF FIGURES FIGURE PAGE 2.1 Modular Structure of VESYS IIM (18). 13 2.2 Load History Used in "Incremental Static Dynamic" Test (18). 17 No. of Load Applications versus Ratio of Cyclic Stress to Static Strength (40). 19 Shear Stress versus Shear Strain for Cyclic Loading (27). 21 Permanent Strain versus Number of Load Repetitions for Silt Clay (46). 21 Effect of Deviatoric Stress on Deforma­ tion of Silty Clay under Repeated Loading (22). 24 Strength Regain in a Thixotropic Material (24). 26 Effect of Thixotropic in Three Clay Minerals (24). 26 Variation of Equivalent Vertical Stress Pulse Time with Vehicle Velocity and Depth (64). 28 Variation of Equivalent Principle Stress Pulse Time with Vehicle Velocity and Depth (64). 29 Secant Modulus and Poisson's Ratio of Clay Subgrade as a Function of Repeated Axial Stress and Depth Beneath Pavement Surface (58). 32 Effect of Stress Intensity on Resilient Characteristics for AASHO Road Test Subgrade Soil (50). 33 Water Content-Dry Density-Resilient Modulus Relationship for Subgrade Soil (73) . 35 Effect of Thixotropy on Resilience Char­ acteristics, AASHO Roadtest Subgrade Soil (61). 37 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 viii FIGURE 2.15 PAGE Effect of Storage Period on Resilience Characteristics of Compacted Subgrade Material (69). 39 Correlation Between Soil Support Value (SSV) and California Bearing Ratio (CBR) (57). 41 Design Chart for Terminal Serviceability Index of 2.5 (Based on AASHO Interim Guide Except for Addition of Modulus of Deformation Scale) (57) . 42 Correlation Chart for Estimating Soil Support Value (SSV) (22). 43 Resilient Modulus Versus Soil Support Value for Recompacted and Undisturbed Cohesionless Soils for First Stress Invariant 0 = 15 psi (7). 44 Resilient Modulus Versus Soil Support Value for Recompacted and Undisturbed Cohesionless Soils for First Stress Invariant 0 = 20 psi (7). 45 Resilient Modulus Versus Soil Support Value for Recompacted and Undisturbed Cohesionless Soils for First Stress Invariant 0 = 30 psi. 46 3.1 General Location of Test Sites. 48 3.2 Pavement Cross-Sections at the Test Sites Lower Peninsula. 51 Pavement Cross-Sections at the Test Sites Upper Peninsula. 52 Samples and Shelby Tubes Numbering Technique. 54 Grain Size Distribution Curves for Site 1 and Site 2, Lower Peninsula. 56 Grain Size Distribution Curves for Site 3 and Site 4, Lower Peninsula. 57 Grain Size Distribution Curves for Site 1 and Site 2, Upper Peninsula. 58 2.16 2.17 2.18 2. 19 2.20 2.21 3.3 3.4 3.5 3.6 3.7 ix FIGURE PAGE Grain Size Distribution Curves for Site 3 and Site 4, Upper Peninsula. 59 3.9 Typical Varved-Clay Cross-Section. 61 3.10 Typical Dual-Reading Versus Logarithm of Time Curve for One Load Increment, Site 3. 64 Typical Consolidation Curve, Void Ratio vs. Logarithm of Pressure, Site 2. 65 Typical Void Ratio Versus Pressure Curve, Site 3. 66 3.13 Typical Displacement and Load Records. 74 3.14 Brackets Used to Hold the Horizontal LVDT's. 76 Void Ratio Versus the Logarithm of Time for Samples Consolidated Under the Designated Confining Pressure Prior to the Commencement of the Incremental Creep Tests, Site 2, Lower Peninsula. 87 Principal Stress Difference Versus Total Axial Strain from Incremental Creep Tests, Site 2, Lower Peninsula. 88 Mohr Circles and Failure Envelopes from Incremental Creep Tests, Site 1, Lower Peninsula. 89 Mohr Circles and Failure Envelopes from Incremental Creep Tests, Site 2, Lower Peninsula. 90 Mohr Circles and Failure Envelopes from Incremental Creep Tests, Site 3, Lower Peninsula. 91 Mohr Circles and Failure Envelope from Incremental Creep Tests, Site 4, Lower Peninsula. 92 Typical Void Ratio Versus the Logarithm of Time for Three Samples Consolidated Under a Confining Pressure of 5 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 2, Lower Peninsula. 94 3.8 3.11 3.12 4.1 4.2 4.3 4.4 4.5 4.6 4.7 x PAGE FIGURE 4.8 4.9 4.10 4.11 4 .12 4.13 4.14 Typical Axial Permanent Strain Versus Number of Load Applications for Samples Consolidated Under Confining Pressure of 5 psi and Tested Using Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 95 Typical Axial Permanent Strain Versus Number of Load Applications for Samples Consolidated Under a Confining Pressure of 25 psi and Tested Using Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 96 Typical Axial Permanent Strain Versus Number of Load Applications for Samples Consolidated Under a Confining Pressure of 50 psi and Tested Using Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 97 Typical Resilient Modulus Versus Number of Load Applications for Samples Consoli­ dated Under a Confining Pressure of 5 psi and Tested Using Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 98 Typical Resilient Modulus Versus Number of Load Application for Samples Consoli­ dated Under a Confining Pressure of 25 psi and Tested Using Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 99 Typical Resilient Modulus Versus Number of Load Application for Samples Consoli­ dated Under a Confining Pressure of 50 psi and Tested Using Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 100 Typical Radial Permanent Strain Versus Number of Load Applications for Samples Consolidated Under Confining Pressure of 5 psi and Tested Using Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 101 Typical Radial Permanent Strain Versus Number of Load Applications for Samples Consolidated Under Confining Pressure of 25 psi and Tested Using Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 102 xi FIGURE 4.16 4.17 4.18 4.19 4.20 4.21 4.22 4. 23 PAGE Typical Radial Permanent Strain Versus Number of Load Applications for Samples Consolidated Under Confining Pressure of 25 psi and Tested Using Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 103 Typical Radial Permanent Strain Versus Number of Load Applications for Samples Consolidated Under Confining Pressure of 50 psi and Tested Using Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 104 Typical Radial Permanent Strain Versus Number of Load Applications for Samples Consolidated Under Confining Pressure of 50 psi and Tested Using Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 105 Typical Axial Permanent Strain Versus Number of Load Applications for Uncon­ solidated Samples Tested Under a Con­ fining Pressure of 5 psi and Different Stress Ratio, Site 2, Lower Peninsula. 107 Typical Axial Permanent Strain Versus Number of Load Applications for Uncon­ solidated Samples Tested Under a Con­ fining Pressure of 25 psi and Different Stress Ratio, Site 2, Lower Peninsula. 108 Typical Resilient Modulus Versus Number of Load Applications for Unconsolidated Samples Tested Under a Confining Pressure of 5 psi and Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 109 Typical Resilient Modulus Versus Number of Load Applications for Unconsolidated Samples Tested Under a Confining Pressure of 25 psi and Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 110 Typical Radial Permanent Strain Versus Number of Load Applications for Uncon­ solidated Samples Tested Under a Con­ fining Pressure of 5 psi and Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 111 xii FIGURE 4.24 4.25 4.26 4.27 4.28 4.29 4. 30 4.31 4.32 4.33 4.34 PAGE Typical'Radial Permanent Strain Versus Number of Load Applications for Uncon­ solidated Samples Tested Under a Con­ fining Pressure of 5 psi and Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 112 Typical Radial Permanent Strain Versus Number of Load Applications for Uncon­ solidated Samples Tested Under a Con­ fining Pressure of 25 psi and Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 113 Typical Radial Permanent Strain Versus Number of. Load Applications Samples Tested Under a Confining Pressure of 25 psi and Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 114 Principal Stress Differences Versus Total Axial Strain from Ramp Tests, Site 4, Upper Peninsula. 115 Mohr Circles and Failure Envelopes from Ramp Tests, Site 1, Upper Peninsula. 116 Mohr Circles and Failure Envelopes from Ramp Tests, Site 2, Upper Peni n s u l a . 117 Mohr Circles and Failure Envelopes from Ramp Tests, Site 3, Upper Peninsula. 118 Mohr Circles and Failure Envelopes from Ramp Tests, Site 4, Upper Peninsula. 119 Typical Axial Permanent Strain Versus Number of Load Applications for Uncon­ solidated Samples Under a Confining Pressure of 5 psi and Different Cyclic Stress Ratio, Site 4, Upper Peninsula. 121 Typical Resilient Modulus Versus Number of Load Applications for Unconsolidated Samples Tested Under a Confining Pressure of 5 psi and Different Cyclic Stress Ratio, Site 4, Upper Peninsula. 122 Typical Radial Permanent Strain Versus Number of Load Applications for Uncon­ solidated Samples Tested Under a Confining Pressure of 5 psi and Different Cyclic Ratio, Site 4, Upper Peninsula. 123 xiii FIGURE 4.35 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 PAGE Typical Radial Permanent Strain Versus Number of Load Applications for Uncon­ solidated Samples Under a Confining Pressure of 5 psi and Different Cyclic Stress Ratio, Site 4, Upper Peninsula. 124 Principal Stress Difference Versus Total Axial Strain for Incremental Creep and Ramp Tests, Site 2, Lower Peninsula. 130 Mohr Circle Diagrams and Failure Envelopes for Incremental Creep and Ramp Tests, Site 2, Lower Peninsula. 131 Schematic Representation of Sample Failures. 133 Schematic Representation of Sample Failure by Squeezing-Out of the Silt Layers. 134 Stress-Strain Curves for Vertical and Inclined Varved Clay Samples Tested Under the Designated Confining Pressure. 139 Mohr Circle Diagrams and Failure Envel­ opes for Vertical and Inclined Varved Soil Samples, Site 4, Upper Peninsula. 141 Regression Constants m and n of Equation 5.1 versus Confining Pressure, Site 1, Lower Peninsula. 143 Typical Plot of Permanent Strain Versus Number of Load Cycles Under Confining Pressure of 5 psi, Site 2, Lower Peninsula. 146 Typical Plots of Permanent Strain Versus Number of Load Cycles Under Confining Pressure of 5 psi, Site 2, Lower Peninsula. 148 Typical Axial Permanent Strain Versus Number of Load Applications for Samples Consolidated Under a Confining Pressure of 5 psi and Tested Using Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 150 xiv PAGE FIGURE 5.11 5.12 .5.13 5.14 5.15 5.16 5.17 5.18 5.19 5.20 5.21 Axial Permanent Strain Versus Number of Load Applications for ( a i- a 3)d / a 3=1.0 for Different Confining Pressures, Site 1, Lower Peninsula. 153 Cyclic Principal Stress Difference as Percent of Sample Strength Versus Time for Samples Tested at the Same Cyclic Stress Ratio and Different Confining Pressure. 154 Effect of Stress Level on Permanent Strain for Samples Tested Up to 30,000 Load Applications, Site 3, Lower Peninsula. 158 Principal Stress Difference Versus the Regression Constants a. and a, n„ of Equation 5.4, Site 3, Lower Peninsula. 159 Principal Stress Difference Versus the Regression Constants b. and b, 0Q of Equation 5.4, Site 3, Lower Peninsula. 160 Axial Permanent Strain Versus Number of Load Applications for Consolidated Samples Tested Under Different Stress Path, Site 2, Lower Peninsula. 162 Axial Permanent Strain Versus Number of Load Applications for Unconsolidated Soil Samples Tested Under Two Different Stress Paths, Site 3, Lower Peninsula. 163 Axial Permanent Strain Versus Number of Load Applications for Unconsolidated and Consolidated Samples Under a Confining Pressure of 5 psi, Site 4, Lower Peninsula. 165 Normalized Cyclic Principal Stress Difference Versus Normalized Permanent Strain (After 23). 168 Typical Principal Stress Difference Versus Strain From Incremental Creep Test. 169 Normalized Stress Ratio Versus Nor­ malized Strain Ratio at 30,000 Cycles. 170 xv FIGURE 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.30 5.31 5. 32 5. 33 PAGE Normalized Cyclic Stress-Strain Data for Subbalast Materials Subjected to 10.000 Load Repetitions (After 106). 172 Normalized Cyclic Stress-Strain Data for Under Tie Materials Subjected to 10,000 Load Repetitions (After 106). 173 Average Grain Size Distribution Curves for Lorraine and Aberdeen Subballast and Under-Tie Materials (After 106). 175 Normalized Cyclic Stress-Strain Data for A-6 AASHTO Subgrade Soils Subjected to 10.000 Load Repetitions (After 23). 176 Normalized Stress-Strain Data for Clay Subgrade Materials from Four Different Test Sites Subjected to 10,000 Load Repetitions. 177 Normalized Cyclic Stress-Strain Data for A-6 AASHTO Subgrade Soils Subjected to 10,000 and 1,000,000 Load Repetitions. 178 Normalized Stress-Strain Data for Clay Subgrade Materials from Four Different Test Sites Subjected to 10,000 and 1,000,000 Load Repetitions. 179 Normalized Cyclic Stress-Strain Data for Subballast Materials Subjected to 10.000 and 1,000,000 Load Repetitions. 180 Normalized Cyclic Stress-Strain Data for Compacted Sand Subgrade Materials Subjected to 10,000 and 1,000,000 Load Repetitions. 181 Normalized Cyclic Stress-Strain Data for Under Tie Materials Subjected to 10.000 and 1,000,000 Load Repetitions. 182 Normalized Stress-Strain Data for Clay Subgrade Materials from Four Different Test Sites Subjected to Different Load Repetitions. 183 Soil Support ValuS Versus 18 kips Equi­ valent Single Axle Load for Regional Factor of 2.0, Terminal Serviceability of 2.5 and Different Structural Numbers. 186 xvi PAGE FIGURE Soil Support Value Versus Structural Number for Regional Factor of 2.0, Terminal Serviceability of 2.5 and Different Numbers of 18 Kips Equivalent Single Axle Load. 187 Structural Number Versus 18 Kips Equi­ valent Single Axle Iioad for Regional Factor of 2.0, Terminal Serviceability of 2.5 and Different Soil Support Values. 188 Structural Number Versus Soil Support Value for Regional Factor of 1.0, A Terminal Serviceability of 2.5 and Different Numbers of 18 Kips Equivalent Single Axle Load. 189 Normalized Cyclic Stress-Strain Ratio for Five Different Materials Subjected to 1,000,000 Load Repetitions. 191 Typical Relationship Between Number of Load Applications and the Parameters n and m of Equation (5.5) for Subballast Materials. 193 5.39 Flow Chart of the Implementation. 198 A.l Schematic of Cyclic Triaxial Test Equivalent. 214 A.2 Test Set-up. 215 A.3 Schematic of MTS Electrohydraulic Closed Loop Test System. 216 A.4 MTS Servovalve Controller Model 406.11. 218 A.5 Grain and Stability Adjustment. 220 A.6 The MTS Control Unit Model 436.11. 223 A.7 Front Panel of the Control Box. 225 A.8 . Front Panel of the Minicomputer. 227 5.34 5.35 5.36 5.37 5.38 A.9 Generated Waveforms. 228 A . 10 Start and Stop Generator's Outputs. 228 A. 11 Triggered Time. 230 xvii FIGURE A . 12 PAGE General Signal Output from the MTS System. 230 Typical Signals for Triggering the Circuits. 230 Schematic Electrical Diagram of the Driving Circuit. 231 Typical Output of the Monostables and Transistors. 233 A . 16 Connection Diagram Between the Apparatus. 234 A . 17 Connection Daigram in the Waveshaper Box. 235 A . 18 Program Flow Chart. 237 A . 19 Inverters Location. 250 A.20 Offsets Location. 250 A. 21 Electrical Circuits of the Inventers in the Signal Conditioning Box. 251 Electrical Circuits of the Offset in the Signal Conitioning Box. 251 Consolidation Curve, Void Ratio Versus Logarithm of Pressure, Site 1, Lower Peninsula. 255 Consolidation Curve, Void Ratio Versus Logarithm of Pressure, Site 2, Lower Peninsula. 256 Consolidation Curve, Void Ratio Versus Logarithm of Pressure, Site 4, Lower Peninsula. 257 Void-Ratio Versus the Logarithm of Time for Samples Consolidated Under the Designated Confining Pressure Prior to the Commencement of Incremental Creep Tests, Site 1, Lower Peninsula. 258 A.13 A.14 A . 15 A. 22 C.l C .2 C. 3 C. 4 C. 5 \ Void-Ratio Versus the Logarithm of Time for Samples Consolidated Under the Des­ ignated Confining Pressure Prior to the Commencement of the Incremental Creep Tests, Site 3, Lower Peninsula. xviii 259 PAGE FIGURE C .6 C .7 C. 8 C .9 C.10 C.ll C .12 C. 13 C.14 C. 15 C. 16 C .17 Void-Ratio Versus the Logarithm of Time for Samples Consolidated Under the Designated Confining Pressure Prior to the Commencement of the Incremental Creep Tests, Site 4, Lower Peninsula. 260 Principal Stress Difference Versus Total Strain from Incremental Creep Tests, Site 1, Lower Peninsula. 261 Principal Stress Difference Versus Total Strain from Incremental Creep Tests, Site 3, Lower Peninsula. 262 Principal Stress Difference Versus Total Strain from Incremental Creep Tests, Site 4, Lower Peninsula. 263 Principal Stress Difference Versus Total Axial Strain from Ramp TEst, Site 1, Lower Peninsula. 264 Principal Stress Difference Versus Total Axial Strain from Ramp Test, Site 2, Lower Pensinula. 265 Principal Stress Difference Versus Total Axial Strain from Ramp Test, Site 3, Lower Peninsula. 266 Mohr Circles and Failure Envelopes from Ramp Test, Site 1, Lower Peninsula. 267 Mohr Circules and Failure Envelopes from Ramp Test, Site 2, Lower Peninsula. 268 Mohr Circles and Failure Envelopes from Ramp Test, Site 3, Lower Peninsula. 269 Void Ratio Versus the Logarithm of Time for Samples Consolidated Under a Confining Pressure of 5 psi Prior to the Commence­ ment of the Triaxial Cyclic Load, Site 1, Lower Peninsula. 270 Void Ratio.Versus the Logarithm of Time for Samples Consolidated Under a Con­ fining Pressure of 25 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 1, Lower Peninsula. 271 xix PAGE FIGURE C. 18 C .19 C. 20 C. 21 C. 22 C. 23 C.24 C. 25 C .26 Void Ratio Versus the Logarithm of Time for Samples Consolidated Under a Con­ fining Pressure of 50 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 1, Lower Peninsula. 272 Void Ratio Versus the Logarithm of Time for Samples Consolidated Under a Con­ fining Pressure of 25 psi Prior to the Commencement of the Traiaxial Cyclic Load, Site 2, Lower Peninsula. 273 Void Ratio Versus the Logarithm of Time for Samples Consolidated Under a Con­ fining Pressure of 50 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 2, Lower Peninsula. 274 Void Ratio Versus the Logarithm of Time for Samples Consolidated Under a Confining Pressure of 5 psi Prior to the Commence­ ment of the Triaxial Cyclic Load, Site 3, Lower Peninsula. 275 Void Ratio Versus the Logarithm of Time for Samples Consolidated Under a Con­ fining Pressure of 25 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 3, Lower Peninsula. 276 Void Ratio Versus the Logarithm of Time for Samples Consolidated Under a Con­ fining Pressure of 5 psi Prior to the Commencement of the Traxial Cyclic Load, Site 4, Lower Peninsula. 277 Void Ratio Versus the Logarithm of Time for Samples Consolidated Under a Con­ fining Pressure of 25 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 4, Lower Peninsula. 278 Axial Permanent Strain Versus Number of Load Applications for Samples Consoli­ dated Under a Confining Pressure of 5 psi and Tested Unsing Different Cyclic Stress Ratio, Site 1, Lower Peninsula. 279 Axial Permanent Strain Versus Number of Load Applications for Samples Consoli­ dated Under a Confining Pressure of 2 5 psi and Tested Using Different Cyclic Stress Ratio, Site 1, Lower Peninsula. 280 xx PAGE FIGURE C. 27 C. 28 C. 29 C. 30 C .31 C. 32 C. 33 C. 34 C. 35 Axial Permanent Strain Versus Number of Load Applications for Samples Consoli­ dated Under a Confining Pressure of 50 psi and Tested Using Different Cyclic Stress Ratio, Site 1, Lower Peninsula. 281 Axial Permanent Strain Versus Number of Load Applications for Samples Consoli­ dated Under a Confining Pressure of 5 psi and Tested Using Different Cyclic Stress Ratio, Site 3, Lower Peninsula. 282 Axial Permanent Strain Versus Number of Load Applications for Samples Consoli­ dated Under a Confining Pressure of 25 psi and Tested Using Different Cyclic Stress Ratio, Site 3, Lower Peninsula. 283 Axial Permanent Strain Versus Number of Load Applications for Samples Consoli­ dated Under a Confining Pressure of 5 psi and Tested Using Different Cyclic Stress Ratio, Site 4, Lower Peninsula. 284 Axial Permanent Strain Versus Number of Load Applications for Samples Consoli­ dated Under a Confining Pressure of 25 psi and Tested Using Different Cyclic Stress Ratio, Site 4, Lower Peninsula. 285 Resilient Modulus Versus Number of Load Applications for Samples Consolidated Under a Confining Pressure of 5 psi and Tested Using Different Cyclic Stress Ratio, Site 1, Lower Peninsula. 286 Resilient Modulus Versus Number of Load Applications for Samples Consolidated Under a Confining Pressure of 25 psi and Tested Using Different Cyclic Stress Ratio, Site 1, Lower Peninsula. 287 Resilient Modulus Versus Number of Load Applications for Samples Consolidated Under a Confining Pressure of 50 psi and Tested Using Different Cyclic Stress Ratio, Site 1, Lower Peninsula. 288 Resilient Modulus Versus Number of Load Applications for Samples Consolidated Under a Confining Pressure of 5 psi and Tested Using Different Cyclic Stress Ratio, Site 3, Lower Peninsula. 289 xxi PAGE FIGURE C .36 C. 37 C .38 D. 1 D. 2 D. 3 D. 4 D. 5 D.6 D. 7 D.8 Resilient Modulus Versus Number of Load Applications for Samples Consolidated Under a Confining Pressure of 25 psi and Tested Using Different Cyclic Stress Ratio, Site 3, Lower Peninsula. 290 Resilient Modulus Versus Number of Load Applications for Samples Consolidated Under a Confining Pressure of 5 psi and Tested Using Different Cyclic Stress Ratio, Site 4, Lower Peninsula. 291 Resilient Modulus Versus Number of Load Applications for Samples Consolidated Under a Confining Pressure of 25 psi and Tested Using Different Cyclic Stress Ratio, Site 4, Lower Peninsula. 292 Average Pavement Deflection Versus Distance from Wheel Load, Upper Peninsula 300 Standard Deviation Versus Distance from the Wheel Load, Upper Peninsula. 301 Consolidation Curve, Void Ratio Versus Logarithm of Pressure, Site 1, Upper Peninsula. 302 Consolidation Curve, Void Ratio Versus Logarithm of Pressure, Site 2, Upper Peninsula. 303 Consolidation Curve, Void Ratio Versus Logarithm of Pressure, Site 3, Upper Peninsula. 304 Consolidation Curve, Void Ratio Versus Logarithm of Pressure, Site 4, Upper Peninsula. 305 Void Ratio Versus Logarithm of Time for Sample Consolidated Under Confining Pressure of 25 psi Prior to the Commence­ ment of the Incremental Creep Test, Site 1, Upper Peninsula. 306 Principal Stress Difference Versus Total Axial Strain Consolidated Sample Under 25 psi Prior to Incremental Creep Test, Site 1, Upper Peninsula. 307 xxii PAGE FIGURE D. 9 D.10 D.ll D .12 D. 13 Void Ratio Versus Logarithm of Time for Sample Consolidated Under Confining Pressure of 10 psi Prior to the Commence­ ment of the Ramp Tests, Site 2, Upper Peninsula. 308 Principal Stress Difference Versus Total Axial Strain Consolidated Sample Under 10 psi Prior to Ramp Test, Site 2, Upper Peninsula. 309 Principal Stress Difference Versus Total Axial Strain from Ramp Tests, Site 1, Upper Peninsula. 310 Principal Stress Difference Versus Total Axial Strain from Ramp Tests, Site 2, Upper Peninsula. 311 Principal Stress Difference Versus Total Axial Strain from Ramp Tests, Site 3, Upper Peninsula ' D. 14 D. 15 D. 16 D. 17 D. 18 . ■ 312 '- Void Ratio Versus the Logarithm of Time for a Sample Consolidated Under a Con­ fining Pressure of 10 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 1, Upper Peninsula. 313 Void Ratio Versus the Logarithm of Time for Three Samples Consolidated Under a Confining Pressure of 10 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 2, Upper Peninsula. 314 Void Ratios Versus the Logarithm of Time for Two Samples Consolidated Under a Confining Pressure of 10 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 3, Upper Peninsula. 315 Axial Permanent Strain Versus Number of Load Applications for Consolidated.Sam­ ples Tested Under a Confining Pressure of 10 psi and at Cyclic Stress Ratio of 1.0, Site 1, Upper Peninsula. 316 Axial Permanent Strain Versus Number of Load Applications for Consolidated Sam­ ples Tested Under a Confining Pressure of 10 psi and Different Cyclic Stress Ratio, Site 2, Upper Peninsula. 317 xxiii PAGE FIGURE D. 19 D. 20 D. 21 D.22 D. 23 D. 24 Axial Permanent Strain Versus Number of Load Applications for Consolidated Samples Tested Under a Confining Pressure of 10 psi and Different Cyclic Stress Ratio, Site 3, Upper Peninsula. 318 Resilient Modulus Versus Number of Load Applications for Consolidated Sample Tested Under a Confining Pressure of 10 psi and Cyclic Stress Ratio of 1.0, Site 1, Upper Peninsula. 319 Resilient Modulus Versus Number of Load Applications for Consolidated Sample Tested Under a Confining Pressure of 10 psi and Different Cyclic Stress Ratio, Site 2, Upper Peninsula. 320 Resilient Modulus Versus Number of Load Applications for Consolidated Sample Tested Under a Confining Pressure of 10 psi and Different Cyclic Stress Ratio, Site 3, Upper Peninsula. 321 Axial Permanent Strain Versus Number of Load Applications for Unconsolidated Sample Tested Under a Confining Pres­ sure of 10 psi, Site 1, Upper Peninsula. 324 Resilient Modulus Versus Number of Load Applications for Unconsolidated Sample Tested Under a Confining Pressure of 10 psi, Site 1, Upper Peninsula. 325 xxiv LIST OF SYMBOLS A l' A 100' a l' a 100 Permanent strain at N=1 and N=100 respectively. a . b , a , b n' n' m' m Regression constants. Coefficient of compressibility. v B l' B 100' b l' b 100 Slope of the straight lines. C Crack index C Consolidated. and C 2 (in Chapter 2 o n l y ) . Cohesion. Slope of the field compression curve. Average coefficient of secondary com­ pression. v Coefficient of consolidation. CCT Conventional consolidation test. CTT Cyclic triaxial tests. 1 o Initial calculated void ratio. F Fall sample. G s Specific gravity. ICT Incremental creep test. LL Liquid limit. MR Resilient modulus. m and n Normalized model's parameters or regression constants. N Number of axle load repetitions. P Patched area. P p o p Effective overburden pressure. Preconsolidation pressure. PSI Present serviceability index. PL Plastic limit. P, Terminal serviceability index. xxv Regional factor. R a d i u s of the sample. C o e f f i c i e n t of c o r r e l a t i o n . M o m e n t a r m f r o m the h i n g e to t h e m i d d l e of the plate. Radius of the brackets holding the hori­ zontal LVDT(s). Average rut depth. Ramp test. S p r i n g sample. Principal stress difference. Soil support value. Slope variance. Site number - Lower Peninsula. Site number - Upper Peninsula. Unconsolidated. Initial natural water content. Final water content. Number of equivalent 18-kip single axle load Permanent deformation response parameters. Total deformation. Axial elastic strain. Radial elastic or permanent strain. Total axial vertical strain. Axial strain at 95% of the sample strength. Initial dry density. Angle of internal frictions. xxvi a i and a 3 (°l-°3)d Principal stresses. Cyclic principal stress. xxvii CHAPTER I .INTRODUCTION The complexity and variability of pavement sub­ grade materials and their interactive mechanisms make the design of flexible pavements a major task. Present design procedures call for material characterization techniques whereby several parameters and/or scaling factors are measured or estimated. These factors and/or parameters are then used in pre-established relationships to correlate performance, structural thickness and traffic loadings and frequency. Further, it is generally recognized that any material characterization technique should take cognizance of the fact that pave­ ment materials are subjected to continuous series of rapidly applied and released stresses of varying magni­ tudes and frequencies [1,2*]. The duration** of these stresses depends upon the speed of the moving vehicles; the interval between two consequent applications depends on the frequency of traffic and gear configurations [3], and their magnitudes depend on the vehicle weight, gear configurations and tire pressure [4,5,6]. A laboratory test that closely simulates the traffic action in the field is the repeated-load triaxial test [2,7,8]. In this test, samples of paving materials are placed in a chamber and subjected to radial and axial stresses, as in the conventional triaxial test. just The difference, however, is that the application of stresses to the sample in the cell is cycled or repeated. The sample responses, from the repeated-load triaxial tests, are measured and characterized under different parameters and ** Figures in brackets indicate reference number in the bibliography. Also see references [56, 92 and 93). 1 moduli and then used in a related design method. Recently, several design procedures adopted a design criterion whereby the magnitude of the vertical strain at the surface of the subgrade material is limited to some tolerable amount associated with a specific number of load repetitions [9,10,11,12,13]. The use of this limiting strain criterion has been based on empirical and theoretical considerations of the magnitude of soil deformation and stress intensity which are related to vehicle speeds, traffic frequency and tire pressure [5,6]. An important factor in any overall pavement design system, whether it be empirical or rational, is the consideration and limitation of perma­ nent deformation of the subgrade material [14,15,16]. Consequently, the general practice is to design pavement layers of such thickness and strength that the stresses transmitted to the subgrade are low enough relative to the strength of the soil so that permanent deformation in the subgrade materials are minimized or eliminated [13]. Furthermore, the strength and the plastic behavior of the subgrade should be evaluated and characterized prior to design. Different design methods call for different strength-scaling factor using several evaluation tech­ niques such as California bearing ratio support value modulus (CBR), soil (SSV) , resilient modulus (E),...etc. (M_.) , elastic K The AASHO design method in partic­ ular uses a subgrade strength factor called soil support value (SSV). This factor was assigned a scale of 3 to 10 depending on the type of subgrade. The values of this scale, however, are limited by the condition under which it was assigned [17]. Consequently, the AASHO interim guide for design of pavement structures points out that it is the responsibility of local highway departments to establish a correlation between soil support values and the subgrade materials that are suitable for the partic- 2 u l a r l o c a t i o n arid e n v i r o n m e n t a l condit i o n s . n e c e s s a r y to d e v e l o p soil s u p p o r t v a l u e s Thus, it is for e a c h of the soil t e x t u r e s e n c o u n t e r e d in the S t a t e of M i c h i g a n p r i o r to th e a p p l i c a t i o n of the A A S H O d e s i g n method. Thi s r e s e a r c h p r o j e c t d e a l s w i t h c h a r a c t e r ­ i z a t i o n of s u b g r a d e c o h e s i v e soils highway pavements t r i a x i a l testing. 1) found under Michigan t h r o u g h the u s e of r e p e a t e d load T h e o b j e c t i v e s of this s t u d y include: e s t a b l i s h m e n t of r e l a t i o n s h i p s b e t w e e n m a t e r i a l c h a r a c t e r i s t i c s of c o h e s i v e soils and the soil v a l u e s c a l e using, the r e p e a t e d support load t r i a x i a l tests u n d e r d i f f e r e n t t e s t a n d s a m p l e conditions; 2) e s t a b l i s h m e n t of a l i m i t i n g str e s s a n d / o r s t r a i n c r i t e r i o n that c o u l d be u s e d in d i f f e r e n t d e s i g n m e t h o d s d e s i g n meth o d , the V E S Y S This the A A S H O s t r u c t u r a l s u b s y s t e m for a predictive design procedure d e s i g n meth o d . such as: [18] and the e l a s t i c la y e r s l i m i t i n g c r i t e r i o n w i l l be b a s e d u p o n t he b u i l d u p of the d i f f e r e n t c o m p o n e n t s of the v e r t i c a l c o m p r e s s i v e s t r a i n in the s u b g r a d e layer as m e a s u r e d in the r e p e a t e d load test. The s c o p e of the s t u d y p r e s e n t e d in this r e p o r t i n c l u d e s a b r i e f d e s c r i p t i o n of the c y c l i c t r i a x i a l s y s t e m an d the e x p e r i m e n t a l tes t t e c h n i q u e s e m p l o y e d to e v a l u a t e d y n a m i c p r o p e r t i e s of s u b g r a d e c o h e s i v e soil. A l s o i n c l u d e d is a d i s c u s s i o n o f the e x p e r i m e n t a l r e s u l t s a n d c o m p a r i s o n of r e s u l t s of the p r e s e n t s tudy to t h o s e r e p o r t e d b y o t h e r in v e s t i g a t o r s . 3 CHAPTER II REVIEW OF LITERATURE 2.1 General The principal objective of any pavement design procedure is to provide a structural system which will be suitable in a specific regional area and be able to sus­ tain the anticipated traffic loading and frequency 8,14]. [13, It is generally accepted that pavement deteriorates or looses serviceability with time due to load repetitions and environmental conditions. Existing design methods attempt to control or limit this loss in serviceability by minimizing the factors contributing to the different distress modes such as fatigue, rutting, excessive deflec­ tion, temporary excessive rebound in the subgrade and base materials and lack of stability in the wearing course [20,24]. Thus, the design of a pavement-section is not simply a matter of guessing or estimating the thickness of the surface, base, subbase and subgrade of the pavement structure. Rather it embraces a more detailed study of each pavement component through the investigation of their physical properties and interaction mechanism. These properties are looked at, in general, through three differ­ ent aspects. The first of these is the stress-strain characteristics (mechanistic model) of the different materials used in the various layers of the pavement structure. The second, is the most likely failure mode of the various pavement components. Finally the third aspect is the interaction between the different materials and their integrated behavior under traffic loadings and environmental conditions. Current pavement-design proce­ dures use different design criteria and call for different 4 material characterization techniques using one or more of these three aspects. Consequently, it may be beneficial at this time to look briefly at several different design methods. 2.2 Design Methodologies The strength of a flexible pavement is the result of building up thick layers and thereby distribut­ ing the load over the subgrade rather than by the bending action of the slab [6]. Historically, pavement design has been approached from two broad differing points of view. First, the practicing engineer often approaches the prob­ lem solely from the standpoint of pavement performance. In contrast researchers and educators approach the problem largely from theoretical concepts. Neither of the above approaches is satisfactory within itself. Complete reliance upon pavement performance represents a lengthy process. Thus, one m u s t w a i t a relatively new concepts can be proven. long p e r i o d of time b e f o r e On the other hand, theoretical equations are generally based upon simplified assumptions and many times do not apply to conditions as they exist in the field. For comprehensive and ideal pavement design, both approaches must be integrated and used properly [19]. For any pavement design procedure to be completely rational, total consideration must be given to three elements. These elements are: 01. th e t h e o r y u s e d to p r e d i c t the f a i l u r e Or d i s t r e s s parameter, 02. the determination of the relationship between the magnitude of the parameter in question to the failure or performance level desired, and 03. the evaluation of the pertinent material properties necessary for the theory selected. A great deal of research and analysis has been devoted toward development of a fundamental rational design system for flexible pavement based on the above stated e l ements. E v e n t h o u g h all of the d e s i g n e l e m e n t s hav e b e e n 5 recognized by many pavement engineers, differences exist a m o n g t h e m in a d a p t i n g t h e s e d e s i g n factors. Therefore, the d e s i g n m e t h o d s t h a t t h e y a d o p t for a g i v e n s e t of c o n d i t i o n s are a l s o d i f f e r e n t . The design of flexible pavement has changed rather significantly in the past several years. Generally speaking, flexible pavements were classified as pavement structures having a relatively thin asphalt-wearing course with layers of granular base and subbase used to protect the subgrade from being overstressed. This type of pavement design was primarily based upon empiricism or experience, with theory playing only a subordinate role in the pro­ cedure. Presently, highway engineers are faced with the need to provide remedial measures to upgrade existing pavements to meet today's traffic loadings and frequencies. Also, they have recognized that various independent distress modes, such as rutting, shoving, cracking, etc..., contrib­ ute to pavement structural and/or functional failure. These needs and knowledge have brought about several changes in pavement design and have led many investigators to search for a more comprehensive pavement design analyses based on theroetical and experimental considerations. Today, there is no one fundamental or rational design procedure that is widely accepted in the pavement design industry. Witczak Yoder and [13,19] described two broad categorical approaches to the problem of pavement design based upon the limitation of subgrade overstress. The first category is based on empirical correlations of excessive deformations related to some predefined failure condition of the pavement. The second category is based on the prediction of the cumulative deformations (cumulative damage) of the pavement system under consideration. These two categories will be discussed further below. 2.2.1 Deformation-failure approach: This c a t e g o r y is f u r t h e r s u b d i v i d e d into two procedures: 6 2.2.1. a Laboratory or field index test procedure: In this design procedure, laboratory or field index tests (CBR, stabilometer. ..) are used to categorize the strength of the subgrade materials. It is one of the most widely accepted design procedures for control of repetitive shear deformations used to date [19,18,22]. Generally the fundamental approach is to control pavement layer thickness and material quality based upon some of the above mentioned index tests. It is inherently assumed that the primary source of deformation occurs in the subgrade provided that the thickness and material quality controls are met [19,3,14]. Consequently, allowable deformations are controlled by adjustment of the pavement thickness to reduce the stresses on the subgrade to a level such that actual deformation will not exceed the allowable deformation within the design life of the pave­ ment [19,8]. One such design method is presented in the AASHO interim guide for design of pavement structures [14]. A brief review of this method is presented below. In the early 1950's, the highway engineers were confronted with the need to predict the performance of pavement systems subjected to greater wheel loads and frequencies than they had ever before experienced [19] and to establish an equitable policy for vehicle sizes and weights. This need has led the American Association of State Highway and Transportation officials (AASHTO) to develop the AASHO-Interim Guide design procedure to alle­ viate the above-mentioned problem. The procedure is based on an extensive road test that was conducted in Ottawa, Illinois. The test site consisted of six loops loops and four large o n e s ) . (two small The first AASHO Interim Guide [14] was published in 1961 and all recommendations for the design procedure were based on the result obtained through a period of 25 months of testing. of the AASHO Road tests were: 7 The primary objectives a. To establish relationships between the number of load repetitions and the performance of different pavement systems of known subgrade soil characteristics. b. To determine the effect of different loadings, repre­ sented by the magnitude and frequency of axle loads. c. To establish instrumentation, test procedures, data charts, graphs and formulas which would be helpful in future highway design, for both rigid and flexible pavements of conventional design. In general, the AASHO interim guide is used to determine the total thickness of the pavement structure, as well as the thickness of the individual pavement compo­ nents. It should be noted that the main assumption of the procedure is that most subgrade soils can be adequately represented, for pavement design purposes, by means of their soil support value (SSV) for flexible pavements or by their modulus of subgrade reaction ments. (K) for rigid pave­ In special cases when poorer soils (frost suscepti­ ble, highly organic, etc.) are encountered, adequate pavement performance is achieved by increasing the thickness of the pavement structure, or by using special precautions. The term "pavement performance" is defined in the AASHO interim guide as follows: "a pavement which maintains a high level of ability to serve traffic over a period of time is superior in performance to one whose riding quality and general conditions deteriorate at a more rapid rate under the same traffic conditions." The term pavement service­ ability was adopted to represent the ability of a pavement to perform under the given traffic. Thus, pavement perfor­ mance is assigned a value from zero to five and it is called pavement serviceability index. Prediction of the present serviceability index of a pavement system can be achieved by using a combination of different physical me a ­ surements and is given by the following relationships PSI = 5.03-1.91 log (1+SV)-1.38 RD2 -0.01 (C+P)1^ 2 (14). (2.1) where SV = slope variance, a measure of longitudinal roughness 8 RD = average rut depth C+P = area of class 2 and 3 cracking plus patching per 1000 ft2 (92.9 m 2) This serviceability-performance concept is the basic philosophy of the AASHO interim guide. Thus,a pavement section may be designed for the level of serviceability desired at the end of the selected traffic analysis or after exposure to a specific total traffic volume. The basic flexible pavement design equation, developed from the results of the AASHO Road test, uses a traffic equiv­ alency criterion which convert mixed-traffic to 18-kip equivalent single-axle load. log W = 9,36 log 0 l o g [4.2-P.)/(4.2-1.5)] (SN+l)-0.20+ — -------- -— — --- e- T q— 0.40+[1094/(SN+1)->*iy ] + log (^) + 0.372 I\ (SSV-3.0) (2.2) where W . , 8 = number of equivalent 18-log single axle loads expected in time t SN = structural number of Pfc = the terminal serviceability index or serviceability index at time t R = regional factor SSV = soil support value The soil support value the pavement system the (SSV) of any given soil ranged from 3.0 for A-6 materials to 10.0 for A-l materials. The objectives of this research project include a study of the (SSV) scale as related to some physical characteristics of the subgrade soil in question. 2.2.1.b Limiting subgrade strain procedure This, design approach as described by Yoder and Witczak [13] uses the elastic layered theory to limit the vertical subgrade strain. Concepts for designing flexible 9 pavements using multilayer elastic analysis were presented by Dorman and Metcalf in 1965 [9]. The principles outlined by these investigators were based upon limiting strains in the asphalt surface and permanent deformation in the subgrade. The use of multilayered elastic theory in conjunction with a limiting strain criteria for design involves the consideration of three factors: the theory used, the material characterization technique, and the development of failure criterion for each mode of distress. In the development of the procedure, use was made pf computer solutions to solve stresses, strains and displace­ ments within a multilayered [24,25,261 . (elastic) pavement system Most elastic layered design procedures, considers both permanent deformation (rutting) of subgrade as well as fatigue cracking of the asphalt-bound layer as the two most significant failure mechanisms. Dissatisfaction has been expressed by many high­ way agencies concerning the use of these conventional procedures, because both design procedures are based on empirical relationships derived from experience and observa­ tions. Furthermore they are applicable only to a defined range of pavement materials, traffic loads and environ­ mental conditions for which experience is available 27,16]. [19,8,18, Also both procedures failed to predict the amount of anticipated deformation after a given number of load applications. 2.2.2 Prediction of cumulative deformation approach Yoder and Witczak [19] described this category as representative of procedures that are based upon the prediction of accumulated deformations in pavement systems using quasi-elastic or viscoelastic approaches. These approaches, however, are not presently refined to the point where this can be accomplished with a level of confidence needed for adequate design methods [19,8,28,29]. Despite this disadvantage, the methodology is the most preferred for use in a more advanced or rational design 10 method due to its capability of obtaining cumulative deformations of any pavement system 31,3]. [19,28,29,18,27,30, Many investigators have suggested that research should be directed towards developing better material characterization techniques for use in such rational design methods [19,8,18,27,30,3,32,33]. A comprehensive literature review of the quasi-elastic and viscoelastic approaches may be found in reference [23] , a part of which is repeated here for the benefit of the reader. 2.2.2.a Quasi-elastic approach The quasi-elastic approach as described by Yoder and Witczak [19] is based upon the use of elastic theory and the results of plastic strains determined by repeated load laboratory tests on pavement materials. This approach was initially introduced by Heuklom and Klomp [34]. Since then, research has been conducted by others such as Monismith [35] and Barksdale [29] for soils, granular materials and asphalt concrete. The fundamental concept of the analysis is the assumption that the plastic strain [e ] is functionally proportional to the elastic state of stress (or strain) and number of load repetitions. This constitutive deformation law is considered applicable for any material type and at any point within the pavement system. The response of any material must be experimentally determined from laboratory tests for conditions (time, temperature, stress state, density, moisture, etc.) to occur in situ. The elastic theory nonlinear) expected (either linear or is then used to determine the expected stress state within the pavement provided that the plastic defor­ mation is known. thicknesses Subdividing each layer into convenient (AZj) and determining the average stress state at each layer increment, the permanent deformation of the pavement may be computed using [13,10,14] 4t = J , ep- (Azj’ 3=1 3 J (2-3) 11 where = total deformation n = number of layers Ep = permanent strain Az = thickness j = the layer in question 2.2.2.b Viscoelastic Approaches A pavement design method employing the visco­ elastic approach has been developed under the direction of the Office of Research, Federal Highway Administration, (FHWA) [18]. The procedure is based on a mechanistic structural subsystem known as VESYS IIM computer program. This computer program predicts the performance of a pavement in terms of its present serviceability index, PSI, derived from the American Association of State Highway Officials (AASHO) Road Test analysis [19,18]. Inputs to the program must be in the form of statistical distributions describing material properties, geometry of the pavement section being analyzed, traffic and environment. Program outputs are presented in terms of means and variances of the damage indicators - cracking, rutting, roughness and serviceability. The VESYS IIM computer program consists of three models shown diagramatically in Figure 2.1. These models are: 2.2.2.b.l Primary Response Model The Primary Response Model represents the pavement system by a three layer semi-infinite continuum such that the upper two layers are finite in thickness while the third layer is infinite in extent. Each layer is infinite in the horizontal directions and may have elastic or viscoelastic behavior. The model constitutes a closed form probabilistic solution to the three layers linear viscoelastic boundary value problem. 12 It is valid for a MATERIAL RESPONSE PROPERTIES PRIMARY RESPONSE MOOEL PAVEMENT SYSTEM GEOMETRY P*««m«nt S riu m Piimwy A.tpoffM MATERIAL DISTRESS PROPERTIES TRAPFlC CONDITIONS DAMAGE RESPONSE MOOEL ENVIRONMENT Omium Irtdiuton: C iM fc in 9 S. Roufhntii ^v^Runin*-/ DESIGN CRITERIA PERFORMANCE m ooel S*»icubilitv lntf» USER FIGURE 2.1 Modular Structure of VESYS IIM 13 (18). single stationary circular loading at the pavement surface. Stochastic inputs to the model are in terms of the means and variances of the creep compliances for viscoelastic materials, and elastic or resilient moduli for elastic materials. The output from the Primary Response Model, in the form of statistical estimates of stresses, strains and deflections, is used as input to the Damage Model. 2.2.2.b.2 Damage Model The Damage Model consists of three separate models each designed to predict distress accumulation in the pavement. 01. The Rut Depth Model uses the results from the Primary Response model along with laboratory determined permanent deformation characteristics of the pavement and subgrade materials to compute the mean and variance of the rut depth accumulated over any incremental analysis period. 02. The Roughness Model uses the rut depth output from the Rut Depth Model, along with the assumption that rut depth at any time along the wheel path will vary due to material variability and non-uniform construc­ tion practices, to compute the roughness in terms of slope variance as defined by AASHO [14]. 03. The Fatigue Cracking Model is a phenomenological model which predicts the extent of cracking of the asphalt layer based on Miner's hypothesis. This cracking is due to fatigue resulting from tensile strain at the bottom of the asphalt concrete layer. A crack index is computed after any number of load applications using the viscoelastic radial strain amplitude at the bottom of the asphalt concrete layer along with laboratory determined fatigue properties of the asphalt concrete. The radial strain amplitude is found at the peak of a haversine load pulse of specified duration applied to the pavement surface. From this crack index the expected area of cracking is computed in square yards per 1000 square yards. The output from the above three parts of the Damage Model, i.e., rut depth, slope variance, and crack index, as input to the Performance Model. 14 is used 2.2.2.b.3 Performance Model The Performance Model computes a Serviceability Index, Pavement Reliability and Expected Life of the Pavement. The serviceability index, PSI, is defined ac­ cording to the PSI = a + AASHO Interim Guide 1972[14] b log10 as (1 + SV) + c / c " T T + dR 2 (2.4) where a = 5.03, b = 0.01, c = 1.91, d = 1.38 are multiple regressions constants SV = Slope C = Crack Variance (Roughness) Index R = Rut depth P = Patched area The expected value and variance of the PSI is then calcu­ lated at any time. The reliability of the serviceability index at any time is defined as the probability that the PSI is above some unacceptable level, PSI^, which has been established beforehand. The distribution of PSI's is obtained assuming a Gaussian distribution. The expected life of the pavement is the time for the Serviceability Index to reach the unacceptable level, PSI^. Two categories of mechanical properties are required for the VESYS IIM structural analysis, primary response properties, and distress properties. The primary response properties define the response of layer materials to the given loads and environments. These properties are in the form of elastic or viscoelastic characteristics which may exhibit non-linear behavior because of previous load histories, plastic effects, and stress dependencies. The distress properties are those properties defining the capability of the materials to withstand the imposed loads. The Rut Depth Model in the current version of VESYS IIM [18] assumes a permanent deformation accumulative 15 damage law of the form F(N) = y± Nai (2.5) where N = Number of axle load repetitions ou and y^ = Permanent deformation response parameters for material in layer i. One method for determining ou y^ for equation 2.5 is to use the result's of the Dynamic Series of an "Incremental Static-Dynamic" test described by the load program shown in Figure 2.2. For more detailed information the reader is referred to reference t11 J. A sensitivity analysis of the VESYS IIM struc­ tural model [29] determined that calculated responses of the system were: a) insensitive to variations of the parameter y for base and subgrade; b) insensitive to variations of parameter a for base materials; c) sensitive to variations of a for subgrade material. Researchers have indicated that one of the most urgent research needs in material characterization is the development of simplified tests which decrease the total number of tests, shorten the amount of time required for each test, and simplify the test methods and instrumen­ tation requirements 2.3 [30,27,18,3,32]. Cyclic Loadings Timoshenko [36] credits Poncelet as being the first to consider the strength of materials under repeated loadings and to introduce the term "fatigue" to describe the resulting strength-deterioration characteristics. Timoshenko also credits Wohter for conducting the most extensive and the earliest experimental repeated load tests, Wohter found that the number of load cycles to failure increased as the cyclic stress intensity increased. Other investigators [37,38,39] concerned themselves with fundamental aspects of fatigue and developed hypotheses to 16 INCREMENTAL STATIC SERIES DYNAMIC SERIES STRESS (psi) 1000 Cm p 2m 2m 2m 4m 8m .9* Time t FIGURE 2.2 Load History Used in "Incremental StaticDynamic" Test (18). explain their experimental data. They postulated the formation of crystalline or intergranular structure during cyclic loading. These studies are still continuing with many theories proposed each satisfying one or more aspects of the fatigue phenomenons and yet none being adequate for all cases. In general, all materials including soils lose strength or stiffness, or both, with increasing number of cyclic stress [40] as shown in Figure 2.3. Most of the early studies, and indeed most of the more recent studies have used uniform repeated load intensity rather than irregular one to study the effects of traffic loading on the pavement system in question. This is so because a uniform repeated load intensity test machine is easier and cheaper to build and operate than an irregular loading apparatus. Generally, the loading patterns are likely to vary from vehicle to vehicle or from case to case even within the same problem area. Thus, irregular or variable cyclic loading tests will better simulate the traffic action. However, this requires the evaluation of each possible load pattern to be expected throughout the lifetime of the pavement structure [41,42]. A review of literature concerning the behavior of cohesive soils subjected to cyclic loading is presented in the next paragraph. The background information for cohesionless soils, on the other hand, may be found in Reference 2.3.1 [1]. Behavior of Cohesive Soils Subjected to Cyclic Loadings A qualitative measure of the behavior of soils subjected to cyclic loadings, such as that induced by earthquakes, has been widely recognized since .they were examined by Casagrande in 1936 [43]. Over the past several years, considerable advances have been made in our under­ standing of soil behavior during cyclic loading and in our ability to reasonably predict this behavior. Idriss and Ricardo According to [27], the stress-strain characteristics of soils subjected to cyclic loadings is nonlinear and 18 Reference Stress Conditions (2) Material (1) Cyclic Stress Conditions (3) Metals Static tensile strength Reversing compression/ extension Clays Static Com­ pressive strength Reversing compression/ extension Sands Cyclic stress to fail in N = 1 cycle Reversing compression/ extension Asphalt and Treated Soil Cyclic stress to fail in N = 1 cycle One-directional beam bending 120 o ■H i—( O a O o\o •H ' E +J u ra O -P C W +J •h \ cr> c CO c D tn a> Shear Strain FIGURE 2.4 Shear Stress vs Shear Strain for Cyclic Loading (2 7). Number of Stress Applications 10 8) , using 24,000 load appli­ cations, found that the resilient modulus decreased with 2 increasing applied stress up to 25 psi (0.176 Kg/cm ), above which the resilient modulus increased slightly. Seed et al. [5 0] had also found that the resilient modulus decreased rapidly with a variation of 300 to 400 percent . as the principal stress difference increased from 3 to 15 2 psi (0.21 to 1.05 Kg/cm ). Above this range the resilient modulus was observed to increase slightly, as shown in Figure 2.12. 2.3.1.2.d Load Duration and Frequency Most researchers agree that the effect of stress duration on the resilient response of cohesive soils is negligible. In general, the resilient modulus tends to increase slightly as the time of load duration decreases, this effect is considered insignificant for the range of load durations encountered in pavement structures [59]. Conflicting findings concerning the effects of frequency on the resilient response are reported in the literature. Coffman [71] stated that the resilient modulus increases as the load frequency increases. This increase was on the order of 50 to 400 percent depending on the water content and density of the sample. and Nishi Tanimoto [69], on the other hand, reported a decrease in resilient modulus with an increase in load frequency. 31 Ratio Poisson's Resilient Sustained Radial Stress, 2 psi 4 8 T T" 10 Q 1.33 to 2.35 0 2.35 to 3.30 A 3.30 to 4.33 V 4.33 to 5.30 15 (xlO ), (psi) Depth,- Feet Resilient Modulus (1 psi = 0.07 kg/cm2 ) -L 4 6 Repeated Axial Stress FIGURE 2.11 JL 8 (psi) 10 Secant Modulus and Poisson's Ratio of Clay Sub­ grade as a Function of Repeated ’xial Stress and Depth Beneath Pavement Surface (58) *2 ■H W Or m o i —( 12 After 200 Stress Repetitions (1 psi = 0.07 kg/cm2 ) U] P rH P Tl 0 s •p c 0) •rH H ■H to a) Pi 0 10 20 30 Deviator Stress 40 J___I 50 (psi) •rH w 00 o After 100,000 Stress Repetitions 12 rH P 2 -P C *- 15 min Modulus Resilient 14 d >11c P. C/5 C/5 0) 3 r-t cd > cd •H e M UO -l u cd o o 00 JS m 3 3 ft cd cri PQ > «S 90 C/5 4-> e CJ yu 1100 10 ■ ■70 o X X 3 cu CU O .CJX cd 3 Cu cn 3 ft 3 "O CJ a •H Cu C/5 09 a o u cd X (U ft M H T3 c C o 6 40 10 • 0 . 10,000 ■5 30 50 4 •10 .4,000 •15 ■10 .10 '20 ? -1 2,000 1 psi = 0.07 kg/cm2 FIGURE 2.18 Correlation Chart for Estimating Soil Support Value (SSV) (22) . 43 io r CO •P u o a a b w •H o w / / / / Recompacted Samples & Undistributed Samples 0 = 15 psi (1 psi = 0.07 kg/cm2) X 0 O X 10 X 20 25 3 Resilient Modulus x 10 , (psi) FIGURE 2.19 Resilient Modulus vs SSV for Recompacted and Undisturbed Cohesionless Soils for First Stress Invariant. 0 = 15 psi (7). 7 r CO +j Undisturbed Samples 5-4 / O Qa 3 / Ck 3 CO 9 / rH / / / •H o co Recompacted Samples =20 psi (1 psi = 0.07 kg/cm2) / / 10 Resilient Modulus x 10 FIGURE 2.20 20 25 (psi) Resilient Modulus Vs SSV for Recompacted and Undisturbed Cohesionless Soils for First Stress Invariant 6 = 20 psi (7). 7 r CO 0) 3 rH d / > / +> u o a a 3 CTi / / Zi Undisturbed Samples O Recompacted Samples 0= 3 0 psi (1 psi = 0.07 kg/cm2 ) CO •H o CO / / r 20 40 50 3 Resilient Modulus x 10 , (psi) FIGURE 2.21 Resilient Modulus vs SSV for Recompacted and Undisturbed Cohesionless Soils for First Stress Invariant 0 = 3 0 psi (7) CHAPTER III FIELD AND LABORATORY INVESTIGATIONS 3.1 Field Investigations 3.1.1 Site Selection The field phase of this study had as its objec­ tives the selection of several test sites; where the highway pavements showed different signs of distress and the subgrade materials were of different compositions. The investigations were conducted at eight different sites. Four sites were located in the lower Peninsula of the State of Michigan and four sites in the upper Peninsula as shown in Figure 3.1. general information Tables 3.1 and 3.2 provide concerning location, topography and pavement conditions at the test sites, while Figures 3.2 and 3.3 show their cross-sections. The subgrade materials of the lower Peninsula sites were Brookston and Blount clays (pedological soil classifications) ent composition, [79] with differ­ gradation and properties. All the upper Peninsula test sites had Ontanagon Rudyard or Ontonagon Bergland varved clay as subgrade materials. 3.1.2 Scope of Sampling Techniques Generally, for all the test sites, the investi­ gations were designed and samples were obtained to accom­ plish several objectives. These include: 01. The determination of the resilient and permanent Characteristics of the subgrade materials, 02. the determination of the grain size distribution curves, Atterberg limits and specific gravities of the subgrade soils, and 03. the reconstruction of the pavement cross-sections. 47 LAKE SUPERIOR Sl-UP iarquette S4-UP S3-UP S2-UP Sl-LP S3-LP S2-LP LAKE MICHIGAN S4-LP etroit FIGURE 3.1 General location of test sites. TABLE 3.1 Test-Sites General information concerning the test sites, upper peninsula. General - Description Pavement - Conditions General Location Sl-UP Gently undulating glacial deposits of boulder and ontonagon clay. Surfaces are generally rough and broken Predominantly transverse with some longitudinal cracks. With 0.025 "to 0.050" rut depth North bound, about 8 miles on US-4 5 south of Ontanogon City S2-UP Level to gently undulating ontonagon clay Discrete longitudinal and transverse cracks. Some longitudinal cracks in outer wheel path. With 0.05" - 0.1" rut depth West bound, about 3 miles on M-28 west of Ewen S3-UP Hilly deposits of boulder and varved clay, surfaces rough and broken. Ontonagon clay Same as S2-UP except the rut depth is in between 0.025" to 0.40" East bound, about 6/10 of a mile on M-28 east of Kenton City S4-UP Level to gently undulating Esabella clay Newly resurfaced, no major distresses, with the rut depth varies from 0100 to 0.05" South bound, near Saulte Ste. Marie on M-129 TABLE 3.2 Designation of Test Site General information concerning the test sites, lower peninsula. General - Description Pavement - Conditions Approximate Location SI - LP Level to nearly level till plain, mainly deposits of Brookston clay soils Discrete longitudinal and transverse cracks West bound, about 1.5 miles from the county line of Tuscona County on M-138 S2 - LP Level to gently undu­ lating Brookston clay soils Predominantly transverse but not as severe as Sl-LP North bound, about 1-2 miles from Elmer Village on M-19 S3 - LP Same as Sl-LP Same as Sl-LP South bound, about 5 miles from Unionville on M-138 S4 - LP Hilly deposits of Blount clay soils No major distresses West bound, about 3.5 miles from Lake Odessa City on M-50 2.5" > 3" / / / / ; / / y : * / -7 v -7 6" t o ' / ' / / B 4" A 12" D SITE-1 SITE-2 3" 4" 4" 6" T T v SITE-3 SITE-4 (1 inch = 2.54 cm) LEGEND A = Asphalt-Bituminous Concrete B = Gravel Base C = Sand Subbase D = Brookston Subgrade Soil E = Blount Subgrade Soil FIGURE 3.2 Pavement cross-sections at the test sites, Lower Peninsula. 51 SITE-2 SITE-1 A 4 6" 16" B - B 12 22 13" E \ \\ \\\ \ \ \ A \ 48 D SITE-3 LEGEND A = Asphalt-Bituminous Concrete B = Gravel Base SITE-4 (1 inch = 2.54 cm) C = Sand Subbase D = Rock Fill E = Ontonagon Rudyard F = Ontonagon Bergland FIGURE 3.3 Pavement cross-section at the test sites Upper Peninsula. To accomplish these objectives, the following sampling techniques were used. 01. A circular section, of the pavement surface, approxi­ mately six inches (15.3 cm) in diameter was cut and removed from the existing pavement (along the outer traffic wheel path) and a hole through the pavement structure was drilled using an auger. The base and subbase materials were collected in separate bags and the thickness of each pavement structure (pave­ ment surface, base and subbase) was measured. This information was used to reconstruct the pavement cross-section of the upper Peninsula test sites that are shown in Figure 3.3. The cross-sections of the lower Peninsula test sites shown in Figure 3.2 were drawn using information supplied by Michigan Department of Transportation (MDOT). After collec­ tion of the base and subbase materials, the hole was then cleared and shelby tubes were driven to obtain subgrade samples. 02. A test pit along the ditch of the road was excavated and prepared as shown in Figure 3.4(a) and an undis­ turbed box samples were obtained using the same sampling techniques that was previously used by Boker (74]. Shelby tubes were then driven through the bottom of the test pit to obtain more represen­ tative subgrade samples. The numbering technique of the shelby tubes and of the samples obtained from these tubes is shown in Figure 3.4. It should be noted that part a of the sampling technique and the box samples were used for the upper Peninsula test sites only. 3.2 Laboratory Investigation 3.2.1 Test Material The test materials of these investigations consisted of four different subgrade soil deposits encoun­ tered in some parts of the State of Michigan [79,91]. These deposits are: 01. Brookston soils at test sites Sl-LP, S2-LP and S3-LP 02. Blount soils at test site S4-LP 03. Ontonagon Rudyard soils at test sites Sl-UP, S2-UP and S3-UP 04. Ontonagon Bergland soils at test site S4-UP 53 20'center line of the road a) test -- ■*« pit o o o a b c o o o d e f tm Numbering of Shelby Tubes in the Test Pit UPPER-END #4 UPPER-MIDDLE END #3 LOWER-MIDDLE-END #2 BOTTOM-END #1 (1 inch = 2.54 cm) b) Numbering of Samples in the Shelby Tube FIGURE 3.4 Samples and Shelby tubes numbering technique The grain size distribution curves of these materials are shown in Figures 3.5 through 3.8. Their specific gravi­ ties, atterberg limits and average natural moisture contents are listed in Table 3.3. In general, Michigan cohesive soils are the result of glaciofluvial and glacial-lake deposits. The glaciofluvial soils are generally unstratified and primarily composed of silt, clay, sand and gravel. Such cohesive soils in the lower peninsula of the State of Michigan are Brookston and Blount soil desposits. Con­ struction and/or excavation in these materials is not generally difficult. In wet periods, however, the materials are slippery and difficult to haul over. The surface will crust and become hard in periods of pro­ longed hot dry weather. Seepage may be encountered but not extensive enough to be a serious construction problem [79]. The glacial-lake deposits on the other hand exhibit silt and clay stratification which are the characteristics of varved clay [80,81,82,84,85,86]. subgrade of the upper peninsula test sites soil deposits) The (ontanagon exhibit such characteristics. Figure 3.9 shows a cross section through a varved clay specimen. These materials have very low permeability and because of high moisture content excavation by means of scraper equipment is generally difficult [79]. Hauling over this material is difficult due to its slippery and soft condi­ tions and to its adhesion characteristics. Also, com­ paction of this material for embankments or any other purpose is often difficult due to its high moisture content. Further, it was reported [80] that glacial-lake deposits often exist as normally consolidated clays. Such clays with low shear strength and high compress­ ibility often are not suitable for use as subgrade material. Near the ground surface, however, desiccation due to seasonal fluctuations in the water table has 55 100 Percent Finer by Weight 1 inch = 54 cm 80 60 40 SITE #2 20 SITE #1' 0 10 1 0.1 0.01 0.001 Equivalent Grain Diameter, mm FIGURE 3.5 Grain size distribution curves for site 1 and site 2, Lower Peninsula. 100 Weight 60 Percents Finer 80 by 1 inch 2.54 cm SITE #4 SITE #3 40 20 0 10 1 0.1 0.01 0.001 Equivalent Grain Size Diameter, mm FIGURE 3.6 Grain size distribution curves for site 3 and site Lower Peninsula. 100 -p X! tn ■H <1> s 80 SITE #1 >1 X! P d) 60 C •H SITE #2 1 inch fa 40 20 10 1 0.1 0.01 0.001 Equivalent Grain Size Diameter, mm FIGURE 3.7 Grain size distribution curves for site 1 and site Upper Peninsula. 80 60 Finer by Weight 100 1 inch = 2.54 cm Percentage 40 20 Equivalent Grain Size Diameter, mm FIGURE 3.8 Grain Size Distribution curves for site 3 and site 4, Upper Peninsula. TABLE 3.3 Specific gravity, Atterberg limits and average natural moisture content of the subgrade materials at the test sites. Sites Water Content (%) Sl-LP 17. 56 2.700 30.75 15.05 S2-LP 20.51 2.716 33.0 19. 56 Se-LP 15.35 2.720 25.0 16.28 S4-LP 20.83 2.700 23.5 16. 39 Sl-UP 20.12 2.694 26.4 16.12 S2-UP 21.83 2. 700 23.2 16. 52 S3-UP 22.45 2.689 28.1 15. 74 S4-UP 18.23 2.705 29.4 15.02 G Legend: LP = Lower peninsula UP = Upper peninsula G s = Specific gravity LL = Liquid limit PL = Plastic limit 60 s LL (%) PL (%) FIGURE 3.9 Typical varved clay cross section. 61 resulted in a slightly overconsolidated condition. The subgrade samples of the upper peninsula test sites are normally consolidated to slightly overconsolidated varved clay deposits as shown in the next section. 3.2.2 Laboratory Tests 3. 2.2.1 Static Creep Tests Conventional triaxial test equipment (ASTM specification D-2850) which utilizes the same size speci­ mens as that used in the repeated load triaxial tests were not available to this project. Thus, to provide the best possible correspondence between static and dynamic test conditions, the static tests were performed in the dynamic triaxial cell. This equipment and the way they were setup (stress control mode) precluded loading the sample at a constant deformation rate as is usually done in the conventional triaxial test. Rather, the axial load was applied incrementally and consequently the test is called incremental creep test (ICT), or it was applied at a constant rate for the ramp test (RT). A brief discussion of both tests is presented in the following subsections: 3. 2.2.1.a Incremental Creep Test (ICT) The axial load for the ICT was applied gradually in small increments using the load control mode of the MTS system (for more information, the reader is referred to reference number 13 in the bibliography). The size of the load increment at the beginning of the test was approximately ten percent of the estimated sample strength as suggested by Bishop and Henkel [87] . The size of the load increment however, was reduced as the failure stress was approached to allow for a reliable determination of strength. Each load increment was maintained on the sample until the rate of strain decreased to a value less than 0.02 percent per minute. 62 At that time, the sample deformation and the magnitude of the load were recorded. Using these data, stress strain curves were plotted and the strength parameters were determined as explained in Chapter 4. It should be noted that, only the peak sample strength could be determined from these tests. This is so because the load control mode of the MTS system did not allow the load to decrease to the ultimate strength level as the sample deformed* 3. 2 .2.1.b Ramp Test (R.T.) The axial load for the ramp test was applied on the sample at a constant rate. This was accomplished using the triangular loading pattern of the MTS system at a frequency of 0.01 Hertz. The maximum principal stress difference which corresponds to the peak of this triangular loading was set at a value higher than the estimated sample strength by 25 percent. This high principal stress difference value insured that failure will occur before the end of the first loading cycle. 3.2.2.2 Cyclic Triaxial Tests (CTT) Cyclic triaxial tests were performed to study the elastic and plastic characteristics of clay soils subjected to repeated loadings under different test and sample parameters. These parameters include: a. number of load repetitions (N), b. Confining pressure c. cyclic principal stress difference d. stress history, e. moisture content, and f. density (c?^) » (a^-cr^d, All samples were tested up to thirty thousand load repetitions (unless failure occurred) under constant confining pressure and maximum cyclic principal stress difference. Several tests, however, were conducted up to 63 1470 Dial-Reading-Inch (xlO (1 inch 54 cm) 1450 50 1420 100 10(7 Ca 1410 3 10° Time FIGURE 3.10 (sec) Typical Dial-Reading versus Logarithm of Time Curve for One Load Increment, Site 3. p o (psf) c P P (psf) C a P o P c V (in2/lb) Sl-LP 491 1375 0.00101 0.181 0.00049 0.0023 S2-LP 859 1187 0.00083 0.139 0.00050 0.00156 S3-LP 661 1310 0.00092 0.231 0.00044 0.00218 S4-LP 559 896 0.00110 0.19 3 0.00036 0.00127 Sl-UP 960 2149 0.00098 0.283 0.000-53 0.00227 S2-UP 860 2005 0.00072 0.19 8 0.00067 0.00210 S3-UP 737 1494 0.00088 0.201 0.00059 0.00212 S4-UP 986 1166 0.00078 0. 300 0.00056 0.0020 - LEGEND P C A 2V (in /sec) = Effective Overburden Pressure = Preconsolidation Pressure = Average Coefficient of Secondary Compression 1 inch = 2.54 cm 1 psi = 0.07 kg/cm2 C /"i = Slope of the Field Compression Curve Cv = Average Coefficient of Consolidation A = Coefficient of Compressibility 1 psf = 1 kg/cm: n i n e t y t h o u s a n d load r e p e t i t i o n s . The r e s u l t s of t hese tests h e l p e d to v e r i f y the v a l i d i t y of th e d e v e l o p e d r e l a t i o n s h i p b e y o n d t h i r t y t h o u s a n d c y c l e s a n d to s tudy the e f f e c t s of s t r e s s h i s t o r y on the s a m p l e b e h a v i o r . The c y c l i c t r i a x i a l t e s t s w e r e c o n d u c t e d u s i n g two d i f f e r e n t proced u r e s . In t h e first, the samp l e s w e r e consolidated u n d e r the c o n f i n i n g p r e s s u r e p r i o r to th e a p p l i c a t i o n of c y c l i c loading. In the s e c o n d p r o c e d u r e , th e samp l e s w e r e c o n f i n e d and t h e n s u b j e c t e d to c y c l i c loading w i t h ­ o u t a l l o w i n g a n y t i m e for c o n s o l i d a t i o n . 3.2.2.3 Conventional Consolidation Test On e c o n s o l i d a t i o n tes t (CCT) ( A S T M - d e s i g n a t e d D-2435) w a s c o n d u c t e d for e a c h t e s t site to s t u d y the c o m p r e s s i o n c h a r a c t e r i s t i c s of t h e t e s t m a t e r i a l s . r e s u l t s p l o t t e d as d i a l r e a d i n g v e r s u s tim e for on e s i n g l e 3.10. ation Typical test t h e l o g a r i t h m of i n c r e m e n t of l oad is s h o w n in F i g u r e F r o m this c u r v e th e tim e to 100 p e r c e n t c o n s o l i d ­ (t^gg) and the d i a l r e a d i n g at this and the coefficient of consolidation for the load increment in question. time (R ^gg) (C ) were determined' v Figure 3.11 shows a typical consolidation curve, void ratio versus logarithm of pressure for site 2. curve The characteristics of this (the preconsolidation pressure (ap) anc^ the slope of the estimated field virgin compression curve obtained. The coefficient of compressibility the sample was obtained using Figure 3.12. (Cc ) were (av ) of The consolid­ ation data of the test sites are listed in Table 3.4. It should be noted that the test materials at the test sites are covered with varying thicknesses of overburden mate­ rial and, in general, they were subjected in the past to pressure higher than the existing overburden pressure [88,89]. Consequently, the soils are said to be over­ consolidated. The overconsolidation ratio (OCR) of the materials at the test sites are listed in Table 3.4. 68 3.2.3 T e s t P ro ced u res The f o l l o w i n g t e s t s a n d t e s t i n g p r o c e d u r e s w e r e use d to p r o v i d e i n f o r m a t i o n p e r t a i n i n g to th e tes t materials 3.2.3.1 a. s t u d i e d in this investigation. C y c l i c T r i a x i a l Test The MTS hydraulic pump, the minicomputer and the signal monitoring and recording equipment were turned on at the beginning of sample preparation to allow enough time to warm up. b. The minicomputer was programmed and left on the stop position until testing (see Appendix A ) . c. The stylus of the load channel of the strip chart recorder was adjusted to the zero position before loading the sample. d. The loading plate of the triaxial cell was put in place and carefully adjusted so that it was exactly parallel to the top of the sample cap. The loading plate was then secured in place. e. The triaxial cell was assembled around the sample and the desired confining pressure was then applied. f. The stylus of the deformation channel of the strip chart recorder was then adjusted to the zero position. g. The required initial axial sustained stress (one psi) was applied to the sample by moving the actuator of the MTS system (using the set point dial as described in A p p e n d i x A) . This sustained stress was carefully controlled through its read-out signal on a voltmeter. h. The span dial of the MTS system was then adjusted to the proper setting for the desired principal stress difference. i. The function generator was set to the desired frequency (one hertz for all tests in these investigations) and the cycle counter was set to zero. j . The run button on the minicomputer was engaged to conduct the cyclic test. k. The load and deformation output were recorded on a strip chart recorder for the desired number of cycles. All cycles from cycle number one to cycle number two hundred were recorded continuously, after which only segments of about ten cycles before and after the desired cycle number were recorded. Recordings were stopped between readings for economical reasons. 69 1. At the end of test, all final values pertaining to diameter, length, deformation and load were recorded and the cell was then dismantled. A part of the sample was then used to determine its final moisture content. 3.2.3.2 Ramp Triaxial Test The testing procedure for the ramp tests was the same as steps a through h for the cyclic triaxial tests. After setting the spin dial of the MTS system at a principal stress difference value of 25 percent higher than the estimated sample strength at the particular con­ fining pressure, the following steps were taken: i. The function generator was set to the minimum frequency of 0.01 hertz. j. The run button on the minicomputer was engaged to con­ duct the cyclic test. k. The output was continuously recorded on a strip chart recorded until the sample failed. 1. Same as step 1 of the cyclic triaxial test procedure. 3.2.3.3 Incremental Creep Test The test procedure for the incremental creep test was the same as steps a through f for the cyclic triaxial tests. chart recorder, After positioning the stylus of the strip the following steps were then taken: g. The first increment of load which is equivalent to about ten percent of the estimated sample strength was then applied by adjusting the span dial set of the MTS system. This increment of load was maintained on the sample until the rate of strain of the sample decreased to less than 0.02 percent per minute. At this time a second increment of load was then applied. It should be noted at this time that the size of the load incre­ ment was decreased as the failure stress was approached to allow more accurate determination of the sample strength. h. Same as step 1 of the cyclic triaxial test procedure. 3.2.4 3.2.4.1 Test Parameters Number of Load Repetitions A reasonable estimate of the number of eighteen thousand pounds equivalent single axle load, that traffic 70 a highway pavement throughout its life cycle, is not possible. However, it is believed that a typical pave­ ment section may be subjected thousand to ten to about one hundred million load repetitions of eighteen thousand pounds equivalent single axle load [90]. The application of ten million or even one hundred thousand load repetitions on soil samples, at a frequency of one hertz, in the laboratory would require a constant data monitoring of up to 28 hours per test. This is impracti­ cal due to lack of automatic monitoring devices. other researchers such as Brown Further, [57] reported that both elastic and plastic characteristics of soil samples changed very little after ten thousand cycles. quently, Conse­ it was decided that for the purpose of this study, most soil samples be tested up to thirty thousand load cycles and few to ninety thousand cycles for verifi­ cation and study of stress history purposes. 3. 2. 4.2 Confining Pressure The determination of lateral stress in high­ way subgrade materials is not an easy task. researchers [76,79,74] Several indicated that the value of this stress may vary from as low as a fraction of the applied axial stress (corresponding to at rest conditions) high as a fraction of the compaction stresses. to as Boker [79] used the existing Chevron computer program and calculated the lateral stress in the subgrade in the vicinity of four to six pounds per square inch (psi) (0.28 to 42 Kg/cm ) depending on the pavement thickness. Others estimated this stress at sixty to seventy psi (4.2 2 to 4.9 Kg/cm ) due to locked stress during compaction. In these investigations, it was decided to use different values of confining pressures fifty psi) (five, twenty-five and 2 (0.35, 1.76 and 3-5 Kg/cm ) to study its effects on the sample behavior. 71 3.2.4.3 C y c lic P rin c ip a l S tre s s D iffe re n c e The elastic and plastic characteristics of soil samples are dependent on the level of cyclic principal stress difference [74]. Consequently, it was decided that for each confining pressure samples be tested at several values of principal stress differences These values ranged from 0.25 to 0.90 of the soil strength. 3.2.5 Sample Preparation Throughout the course of these investigations, the soil samples, for all tests, were prepared using the following procedure: 01. Shelby-tubes were cut to a length of approximately seven inches and the soil was extracted using a hydraulic jack. 02. The sample was placed on a trimmer and trimmed to a diameter close to that of the trimmer head (about 5^40 cm), using a wire cutter. 03. The sample was then removed and placed in a specially designed steel sleeve for end trimming. After end trimming the following measurements were taken. a. Four sample height measurements were taken at approximately 90° apart. The average value of these readings was used as the initial specimen height. b. Two diameter readings 90° apart were taken at each of the following locations: top (dt), midheight (dm) and bottom (db) of the sample. The average diameter of the sample at these locations was computed. The sample's average diameter was computed using equation 3.1. dt + 2dm_._ + db = — av------ av----- av av 4 v where dtav - average diameter at the top of the sample dm a v = diameter at the middle height of the sample db „ = average diameter at the bottom of the sample. O.V 04. The sample was then placed on the sample base of the MTS system and the sample cap was positioned on top of the sample. 72 ' 05. The sample cap and base were then seated in place using membrane (two membranes were used to avoid leakage), rubber strips and O-rings. 06. The sample with the cap and to the loading frame of the 3.3 Data Reduction base was then attached triaxial equipment. In all triaxial cyclic tests, a sustained stress of one psi was applied on the samples at the beginning of the test. This was felt to be a large enough stress to have seated the top cap firmly on the top of the sample without causing significant deformation in the sample. The cyclic principal stress difference was applied in a wave form shown in Figure 3.13. This was thought to closely duplicate the stress applied to the subgrade in the field due to a moving tandum axle truck. The wave form shown in Figure 3.13 was obtained using the sinusoidal wave form of the MTS modified by coupling a minicomputer and a function generator. Also, ing insured that the sample was at rest (under the con­ fining pressure and sustained stress) cation of the cyclic stress. this coupl­ prior to the appli­ The LVTD's output correspond ing to rest condition was selected as the datum for defor­ mations. The axial permanent and elastic strains of the sample were calculated as the permanent or elastic change in distance between the sample cap and sample base divided by the original sample length, respectively. This change in distance was calculated as the average reading of two vertical LVDT(s) mounted on the sample at 180° from each .other, multiplied by the appropriate calibration factors (see Appendix B ) . The radial permanent and elastic strains on the other hand were calculated using the following formula: R_ Displacement /-VJVrV-ATA \ _______ Datum Point for Displacement I______________ i_____________ l________ t 0 3 6 Number of Load Repetitions a) Displacement-Record Number of Load Repetitions 6 3 O' Vertical Load Jt— cf a s = Sustained Loading = Principal Stress Difference b) FIGURE .13 Load-Record Typical Displacement and Load Records 74 where eR = elastic or permanent strain of the sample R^ = moment arm from the hinge to the middle of the plate as shown in Figure 3.14 R2 = the average radius of the brakets holding the horizontal LVDT(s) as shown in Figure 3.14 r = radius of the sample, and A = the elastic or permanent deflection of the sample Throughout this investigation, the resilient modulus was calculated using the following formula Mr = (al " ° 3 )d - £' Q (3.3) where M R = resilient modulus ^al_a3^d = cyclic Principal stress difference ee = elastic strain corresponding to a parti­ cular number of stress repetition 75 > < ■ Plate Hinge JC fP~ ■rji" Section A-A . were obtained using test data at confining pressures of 2 5 and 25 psi (0.35 and 1.76 Kg/cm ). Mohr circles at 2 confining pressures of 25 and 50 psi (1.76 and 3.5 Kg/cm ) were used to obtain the second failure envelope with strength parameters of c2 and 2 . The data for the upper peninsula test sites were plotted and the figures are shown in Appendix C. 86 Sample 3d-S 0.66 4c-F Void Ratio 0.62 2b-F 0.58 0.54 10 10 10 10 10 10 Time (sec) FIGURE 4.1 Void Ratio versus the Logarithm of Time for Samples Consolidated under the Designated Confining Pressure Prior to the Commence­ ment of the Incremental Creep Tests, Site 2, Lower Peninsula. (psi) Sample 3d-S 2b-F 1 psi = 0.07 kg/cm 40 Principal Stress Difference 60 20 4c-F 10 Total Axial Strain (%) FIGURE 4.2 Principal Stress Difference versus Total Axial Strain from Incremental Creep Tests, Site 2, Lower Peninsula. = 24 p s i <}>^ = 31° 50 1 psi = 0.07 kg/cm Shear Stress (psi) 40 30 20 10 sample 2c-F - ld-F- la-F 20 FIGURE 4.3 40 60 Normal Stress (psi) 80 100 120 Mohr Circles and Failure Envelopes from Incremental Creep Tests, Site 1, Lower Peninsula. c^ = 6.2 ^=28° c 2 = 17.3 2 = 14° Stress sample 4d-S Shear (psi) 1 psi = 0.07 kg/cm 2b-F 4c-F 20 40 Normal Stress FIGURE 4.4 80 60 100 (psi) Mohr Circles and Failure Envelopes from Incremental Creep Tests, Site 2, Lower Peninsula. 120 c, 100 Shear Stress tpsi) 80 =4 p si =35 2 “ 23 psi cp2 "16 1 psi = 0.07 kg/cm 60 40 sample 4e-S 20 •3b-F -3c-F 20 40 60 80 Normal Stress FIGURE 4.5 100 120 140 160 (psi) Mohr Circles and Failure Envelopes from Incremental Creep Tests, Site 3, Lower Peninsula. 180 3 psi 15° 1 psi = 0.07 kg/cm 15 10 ' sample 4e-F 2a-F a 10 20 CT Normal Stress FIGURE 4.6 30 40 50 (psi) Mohr Circles and Failure Envelope from Incremental Creep Tests, Site 4, Lower Peninsula. 4.2.2 Cyclic Triaxial Tests Cyclic triaxial tests were performed on consoli­ dated and unconsolidated samples to study the elastic and plastic characteristics of the test materials. All tests were conducted up to thirty thousand load repetitions unless failure occurred. The maximum cyclic principal stress difference and the cell pressure were kept constant throughout each test. 4. 2.2.1 Consolidated Cyclic Triaxial Tests The samples were isotropically consolidated under the confining pressure. Plots of typical time dependent consolidation curves for site 2, are shown in Figure 4.7. A sustained deviatoric stress of one psi 2 (0.07 Kg/cm ) was applied to the samples after one hun­ dred percent consolidation was reached. The cyclic tri­ axial test was then commenced and the output was record­ ed. Typical plots of the logarithm of accumulated axial permanent strain as a function of the logarithm of number of load cycles for site 2, lower peninsula are shown in Figures 4.8 through 4.10. sample number figures. The confining pressure and the (see Table 4.1) are indicated in the Plots of the logarithm of resilient modulus versus the logarithm of number of load cycles for the same samples are shown in Figures 4.11 through 4.13. Finally, the radial permanent strain versus the logarithm of number of load repetitions of the same samples are shown in Figures 4.14 through 4.18. It should be noted that the straight lines in Figures 4.8 through 4.18 were obtained using a least squares fitting technique. intercepts, slopes and the correlation coefficients The 2 (r ) of these lines are listed in Table 5.3. 4. 2.2.2 Unconsolidated Cyclic Triaxial Tests The unconsolidated soil samples were subjected to the confining pressure first after which, an additional 93 0.66 sample 4f-F Void Ratio 0.62 A A--4 2f0.58 0.54 10 10 10 10 Time FIGURE 4.7 (sec) Typical Void Ratio versus the Logarithm of Time for Three Samples Consolidated Under a Confining Pressure of 5 psi Prior to the Com­ mencement of the Triaxial Cyclic Load, Site 2, Lower Peninsula. 10 sample 4f-F (%) 10 Strain 2 f-F Axial Permanent -1 lf-F 10 -2 10 10 4 10 Number of Load Applications FIGURE 4.8 Typical Axial Permanent Strain versus Number of Load 10 3f-F 10 Axial Permanent Strain (%) sample 3e—F ~~ 3c-F 10 10 -I -2 10 10 10 10 10 10 Number of Load Applications FIGURE 4.9 Typical Axial Permanent Strain versus Number of Load Applica­ tions for Samples Consolidated under a Confining Pressure of 25 psi and Tested using Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 10 Strain dP 10 Axial Permanent sample 4c-S 2c-S 10 10 -1 10 10 10 10 10 10 Number of Load Applications FIGURE 4.10 Typical Axial Permanent Strain versus Number of Load Applications for Samples Consolidated under a Confining Pressure of 50 psi and Tested using Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 10 4 2f-F Resilient Modulus (psi) Sample 4f-F jaJS. I 2c-S — v l.-- 9 - -- 1 ^ © ® -1 -2 10r 31 10 FIGURE 4.18 10 10 10 10 10 Typical Radial Permanent Strain versus Number of Load Applications for Samples Consolidated under a Confining Pressure of 50 psi and Tested under Different Cyclic Stress Ratio, Site 2, Lower Peninsula. sustained axial stress of one psi applied. 2 (0.07 Kg/cm ) was The cyclic test was then started without giving a time for the sample to consolidate. The logarithm of the axial permanent strain, the logarithm of the resil­ ient modulus and the logarithm of the radial permanent strain were all plotted against the logarithm of the number of load applications. These plots are shown in the following Figures 4.19 - 4.20, 4.21 - 4.22, and 4.23 through 4.26 respectively. As in the case of consolidated samples, the straight lines in the figures were obtained using least square fitting technique. The intercepts, slopes and the correlation coefficients are listed in Table 5.3. 4.3 4.3.1 Upper Peninsula Test Sites Static Triaxial Tests At least three unconsolidated static triaxial tests (ramp tests) were performed on three different samples from each test site using confining pressures of 0, 10 and 25 (0, 0.7 and 1.76 Kg/cm^) or 0, 5 and 25 psi 2 (0, 0.35, 1.76 Kg/cm ). Figure 4.27 displays typical plots of stress-strain curves obtained from these tests for site number 4. The data for the other three sites are shown in Appendix D. Figures 4.28, 4.30 and 4.31 show Mohr circle diagrams and the resulting failure envelopes for sites 1, 2, 3 and 4 respectively. 4.3.2 Consolidated Cyclic Triaxial Tests Few consolidated cyclic triaxial tests were executed on samples obtained from sites 1, 2 and 3 as shown in Table 4.2. in Appendix D. The data from these tests are listed It should be noted that the results obtained from the consolidation part of the tests were highly variable due to the nature of the samples. is so because all test samples contained alternate layers of clays and sandy silts which made the test 106 This 10 le-F 2c-F 10 -1 Axial Permanent Strain (%) sample lc-F 10 -2 10 0 10 1 2 10 3 10 4 10 5 Number of Load Applications FIGURE 4.19 Typical Axial Permanent Strain versus Number of Load Applica­ tions for Unconsolidated Samples Tested under a Confining Pressure of 5 psi and Different Stress Ratio, Site 2, Lower Peninsula. 3a-S Sample 3c-F 10 Axial Permanent Strain (%) 10 10 -1 10 10 10 10 10 10 Number of Load Applications FIGURE 4.20 Typical Axial Permanent Strain versus Number of Load Applications for Unconsolidated Samples Tested under a Confining Pressure of 25 psi and Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 10“ * 10 ------*-- -A— A Modulus (psi) sample 2e-F t - > ft # * '— A • A•(* ft — d j&' Ar -A"---¥ = i— a— .— * | . . . . ^ j p j H "fl | a —B B B 2 = 3 : ■ B ]-C-F Resilient le-F id3 1 psi = 0. 07 kg/cm2 10 +2 10 10 ' 10^ 10° 10 10 ' Number of Load Applications FIGURE 4.21 Typical Resilient Modulus versus Number of Load Applications for Unconsolidated Samples Tested Under a Confining Pressure of 5 ps and Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 10- 104 — — ►— Resilient gi . -Q ~ *— — ^3 — &• Modulus (psi) sample 3c-F 3a-F \ _ la-F 10 ' 1 psi = 0. 07 kg/cm2 ' 10 +2 10 ' 10 10 10 10 10 ' Number of Load Applications FIGURE 4.22 Typical Resilient Modulus versus Number of Load Applications for Unconsolidated Sample Tested under a Confining Pressure of 25 psi and Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 10 10 Radial Permanent Strain (%) LVDT was located at the middle of the sample length sample lc-F 10 le-F 2e-F lo"1*10 10 10 10 10 10 Number of Load Applications FIGURE 4.23 Typical Radial Permanent Strain versus Number of Load Applications for Unconsolidated Samples Tested under a Confining Pressure of 5 psi and Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 10 sample lc-F 10 ■le-F -2e-F 10 Radial Permanent Strain (%) LVDT was located at 1/3 of the sample length from the bottom 10 10 10 10 10 10 10 Number of Load Applications FIGURE 4.24 Typical Radial Permanent Strain versus Number of Load Applications for Unconsolidated Samples Tested under a Confining Pressure of 5 psi and Different Cyclic Stress Ratio, Site 2, Lower Peninsula. LVDT was located at the middle of the sample length 10 sample la-F Permanent Strain 10 3a3c-F 10 Radial 38.— 10 -1, 10 10 10 10 Number of Load Repetitions FIGURE 4.25 Typical Radial Permanent Strain versus Number of Load Applica­ tions for Unconsolidated Samples Tested under a Confing Pressure of 25 psi and Different Cyclic Stress Ratio, Site 2, Lower Peninsula. 10 10 10 sample la-F -1 3c-F Radial Permanent Strain (%) LVDT was located at 1/3 of the sample length from the bottom 10 3a-F -2 10 10 10 10 10 10 Number of Load Applications FIGURE 4.26 Typical Radial Permanent Strain versus Number of Load Applica­ tions Samples Tested under a Confining Pressure of 25 psi and Different Cyclic Stress Ratio, Site 2, Lower Peninsula. Sample 3a-s 2a-s 40 Stress Difference (psi) 60 4c-s Principal 20 la-s 1 psi = 0.07 kg/cm2 2 4 6 Total Axial Strain Figure 4.27 8 10 (%) Principal Stress Difference versus Total Axial Strain from Ramp Tests, Site 4, Upper Peninsula. 60 9,5 psi 40 Shear Stress (psi) psi 12 ° 1 psi = 0.07 kg/cm 20 3C-S sample 2C-S 1C-S 0 20 40 Normal Stress FIGURE 4.28 60 80 100 (psi) Mohr Circles and Failure Envelopes from Ramp Tests, Site 1, Upper Peninsula. 20 40 Shear Stress (psi) 60 1 psi = 0.07 kg/cm 20 lb-F sample 4B-F 2b-F 0 20 40 Normal Stress FIGURE 4.29 60 80 100 (psi) Mohr Circles and Failure Envelopes from Ramp Tests, Site 2, Upper Peninsula. 60 6.0 psi 40 (psi) 1 psi = 0.07 kg/cm' 20 Shear Stress 12 5.8 psi 3b-S 20 lb-S sample 2b-S 40 Normal Stress FIGURE 4.30 60 80 100 (psi) Mohr Circles and Failure Envelopes from Ramp Tests, Site 3, Upper Peninsula. 1 psi = 0.07 kg/cm 40 Shear Stress (psi) = 15 psi 20 Sample 3a-s la-s 4c-s Cl C2 2a-s 0 20 40 Normal Stress Figure 4.31 60 80 (psi) Mohr Circles and Failure Envelopes from Ramp Tests, Site 4, Upper Peninsula. 100 results highly variable and dependent upon the sequence and thickness of these layers. Consequently, the efforts in the testing program were shifted to unconsolidated samples and to the lower peninsula test sites. 4.3.3 Unconsolidated Cyclic Triaxial Tests Figures 4.32, 4.33, 4.34 and 4.35 show plots of the axial permanent strain, the resilient modulus, the radial permanent strain measured at the middle of the sample and the radial permanent strain at 1/3 of the sample length from the bottom respectively, all plotted against the logarithm of the number of load applications for site number four. The data pertaining to the other test sites are listed in Appendix D. 120 10 Strain sample 2b-S Permanent lb-S Axial -1 10 -2 10 0 10 1 10 2 10 3 10 4 10 5 Number of Load Repetitions FIGURE 4.32 Typical Axial Permanent Strain versus Number of Load Applications for Unconsolidated Samples under a Confining Pressure of 5 psi and Different Cyclic Stress Tested Ratio, Site 4, Upper Peninsula. (psi) --- #— •--- -- ♦~~g \ 9 1 4 9 Resilient Modulus, ----- sample lb-S 1 psi = 0. 07 kg/cm2 10° 101 102 103 104 105 Number of Load Applications FIGURE 4.33 Typical Resilient Modulus versus Number of Load Applications for Unconsolidated Sample Tested under a Confining Pressure of 5 psi and Different Cyclic Stress Ratio, Site 4, Upper Peninsula. LVDT was located at the middle of the sample length -{ 10 sample 2b-S lb-S 10 Radial Permanent Strain C?P 10 10 10 10 10 Number of Load Applications FIGURE 4.34 Typical Radial Permanent Strain versus Number of Load Applica­ tions for Unconsolidated Samples Tested under a Confining Pressure of 5 psi and Different Cyclic Stress Ratio, Site 4, Upper Peninsula. -----LVDT was located at 1/3 of the sample length from the bottom i i l (%) sample 2b-Sj Strain ! Permanent ; lb-S / / / — $— • "... • ► 10° 101 10 103 104 105 Number of Load Applications FIGURE 4.35 Typical Radial Permanent Strain versus Number of Load Applications for Unconsolidated Samples Tested under a Confining Pressure of 5 psi and Different Cyclic Stress Ratio, Site 4, Upper Peninsula. CHAPTER V DISCUSSION 5.1 General It was hypothesized herein that there exists a relationship between the behavior of subgrade materials under traffic loadings and their characteristic values as measured in the repeated load cyclic tests. Further, it was assumed that the in-situ stresses induced by vehicular loadings could be approximated by a stress spectrum applied during the course of the cyclic test. These characteristic values could be used as follows: 01. As indicators of the performance and. conditions of the subgrade soils and pavement system. 02. As measures of the elastic and plastic behavior of the test materials. 03. To study the effects of different stress conditions on the cumulative compressive permanent strain. 04. To establish a limiting design criterion whereby the cumulative damage could be minimized. The test procedures for obtaining the sample characteristic values were outlined in Chapter III. Analyses of the data included: 01. Modeling the stress-strain characteristics of the test materials using a hyperbolic relationship. 02. Modeling the resilient and permanent characteristics at any number of load applications using exponential functions. 03. Convoluting the models in 1 and 2 above to yield a general predictive model whereby the plastic strain at any number of load repetitions could be predicted using typical triaxial test data. 04. Incorporating other investigators' 3 above. 05. Correlating the material characteristics to the soil support values as defined by the AASHO interim guide for design of asphaltic pavements. 125 data in 1, 2, and Item 1 was accomplished using the test data from the incre­ mental creep tests and/or ramp tests (see Chapter III ) . The data from the triaxial cyclic tests were used in Item 2. Items 3, 4 and 5 were necessary to investigate the validity of the working hypothesis and to contribute to the state of the art. Throughout the course of these investigations, the tests were designed and the analyses were performed to accomplish the following objectives. 01. Obtain disturbed and undisturbed clay samples from beneath existing Michigan highways. 02. Define a sample preparation technique whereby disturbed samples will be compacted so as to show similar behavior to the undisturbed samples when tested in a repeated load triaxial test. 03. Conduct repeated load triaxial tests on recompacted and undisturbed samples of the clay materials to evaluate the resilient stress-strain characteristics, and the cumulative compressive strain under different test conditions. 04. Establish a correlation equation between the material characteristics and the soil support values, and consequently generalize this correlation for sand and clay using data obtained from tests on both materials. 05. Use the cumulative permanent strain data to establish a limiting stress and/or strain criterion that could be used to minimize the cumulative damage due to a desired number of load applications. To accomplish the above mentioned objectives, shelby tube and bag samples were collected from the test sites. How­ ever, only the shelby tube samples were used in the test­ ing program due to the nature of the clay and varved clay soils encountered at the test sites. It was found, as expected, that the soil behavior and conditions did dras­ tically change in the disturbed bag samples relative to those which existed in the field or in the shelby tube sam­ ples. This is so because the overburden and lateral pres­ sures decrease during sampling causing the soil to expand. The tendency for expansion is resisted, the capillary pressure. to some extent, by Also, the shear stresses on the 126 samples are different than those which existed in the field and may vanish depending on the stress state. turbed (bag samples) Although dis­ and relatively undisturbed (shelby tube samples) were subjected to the above mentioned behavior during sampling, the undisturbed samples, however, tend to retain the soil mass structure as it existed in the field. Bag samples on the other hand, are unlikely to preserve the structure. Generally speaking, soil samples inherit the same or similar strength characteristics that the soil structure had attained in the field. This behavior is known to be more pronounced in undisturbed samples of natural deposits than in compacted soils [93]. Further, the shear strength of a soil mass is highly dependent on the effective stress, the stress path, the soil type, and the soil structure and moisture that were attained either through natural deposition or compaction processes. Cohesive soil, in its natural state in the ground, may have single grained structure or compound structure. In the single grained structure, each particle is supported by contact with several of the grains. In the compound struc­ ture large voids are enclosed in a skeleton of arches of individual fine grains (honeycomb structure) or of aggrega­ tions of colloidal sized particles into chains or rings (flocculent structure) [94]. Casagrande [94] reported that the compound structure is the result of sedimentation of particles which are small enough to exhibit appreciable surface activity. Soils with compound structure are usually of low density, but may have developed considerable strength due to compression of the arches in the soil skeleton. these soils are recompacted, their structure is changed When [94] and consequently their strength characteristics may not re­ flect those which existed in the field. at the test site are of these kind. The cohesive soils Thus, it is extremely hard to impossible to recompact bag samples so as to achieve structural composition similar to those existing in the 127 field. Therefore, objective number 2, which calls to define a sample preparation technique whereby disturbed samples will be compacted so as to have similar soil structure to the undisturbed samples, was not feasible for this project (cohesive soils). This objective, however, was accomplished for sand materials in a previous research project 5.2 [7,8,77]. Static Triaxial Tests 5.2.1 Incremental Creep Tests Versus Ramp Tests As noted in Chapter III, conventional triaxial test equipment utilizing the same specimen size as that used in the MTS triaxial cell was not available. Thus, to provide the best possible correspondence between static and dynamic (cyclic) test conditions, the static tests were performed in the MTS triaxial cell using two differ­ ent procedures: a) the load was incremented at ten percent of the estimated sample strength, the test was called an incremental creep test (ICT), and b) the load was applied at a constant rate, the test was called ramp test Both of the above tests (RT). (ICT and RT) are referred to herein as static triaxial tests to differentiate them from the cyclic tests. The purposes of the static triaxial tests include: 01. to model the static stress-strain relationship of the test materials, and 02. to provide a data base whereby the cyclic triaxial test data could be compared to and convoluted with, to yield a general predictive model of the plastic behavior of the materials. Kholsa and Wu [95] were the first to use the incremental creep tests to study the stress-strain behavior of sand. Recently, Baladi and Lentz [23] used the ICT results to normalize the plastic behavior of sand sub­ grade materials and developed a permanent strain predictive model. They concluded that the model was successful and independent of the sample and test variables (water content, confining pressure, compaction efforts and stress level). 128 The main disadvantage of the ICT relative to the RT is that two independent investigators cannot duplicate the stress rate. The strain rate, however, is controlled . by the soil type and sample behavior. In the ICT a new increment of loading is added when the strain rate due to the previous increment decreases to a certain level Chapter III). (see To alleviate this problem and after a brief discussion with the Federal Highway Administration person­ nel, Kenis [96] suggested that ramp tests (constant stress rate) be performed to check the ICT results and possibly to standardize the test. Figure 5.1 shows typical results of the ICT and RT for three different confining pressures. Examination of the figure indicated that at any strain level, the RT samples were subjected to a higher stress level than those of the ICT samples. This was expected because the stress rate of the ramp test was higher than that of the incremental creep test. The values of the strength parameters from both tests, however, modest variations, as indicated in Figure 5.2. showed very As it was expected, the stress-strain relationship and the strength parameters of sand subgrade materials, showed very little to no variations. from both tests, It should be noted herein that when the results from both tests were used to normalize and study the plastic behavior of the test materials the resulting model showed 1) a small variation for the clay materials and 2) no change at all for the sand subgrade materials. These observations along with the normalization process will be discussed in detail in Section 5.4 below. 5.2.2 Sample Failure and Failure Mode Throughout the course of this study, sample failure was defined as follows: "the sample was considered to fail when the vertical deformations reached the maximum range of the vertical LVDT(s)". 129 This corresponds 120 sample 4d-s i 17.5 (psi)22.0 (psi) C z (psi) 14° 14° 2 co a 01 LEGEND Symbols 80 01 a) P -p oi p (d a) X! 01 40 . 11 ^Ci 80 120 Normal Stress 140 i 160 (psi) FIGURE 5 . 2 'Mohr Circle Diagrams and Failure Envelopes for Incremental Creep and Ramp Tests, Site 2, Lower Peninsula. to about 8 percent strain and it is dependent on the ini­ tial seating of the LVDT (datum). Also, all tests were performed using the stress controlled mode of the MTS system. This mode did not allow the load to drop after the peak sample strength was reached and consequently the sample continued to deform causing a system shut-off which was automatically activated when the maximum LVDT deflection range was reached. This could be restated as; the stress controlled mode of the MTS system did not allow the determination of the sample ultimate and/or residual strength. until shut-off. Rather, the vertical stress increased The shut-off mode was designed in the system as a safety precaution to prevent the MTS actuator from moving against some sensitive equipment parts inside the cell and eventually destroying them. Observations of the test samples at failure revealed the following failure modes: 01. Michigan's Lower Peninsula test sites: Most of the cohesive soil samples obtained from the lower penin­ sula test sites characteristically exhibited general bulging failure rather than the formation of a distinct failure plane. This is so because of the high water content of the samples and the end effects of the upper and lower platens. 02. Michigan's Upper Peninsula test sites: Basically, three types of shear failure were noticed for soil samples obtained from the upper peninsula test sites. These failure types are: a) Bulging out of the clay layers, as shown schematically in Figure 5.3a, b) shear strength failure in the silt layer as shown in Figure 5.3b, c) squeezing out of the silt layers as shown in Figure 5.4. The bulging out of the clay layers occurs when the samples were composed of a thick clay layer than 1 inch (2.54 cm)] thin silt layer. Lo [97]. [greater alternating with a relatively This observation was also reported by The squeezing out of the silt layers on the 132 clay silt Sample Before Testing a) Sample After Testing Bulging-Out of the Clay Layer clay silt Sample Before Testing b) Sample After Testing Shearing of the Silt Layer FIGURE 5.3 Schematic Representation of Sample Failures 133 silt clay Sample After Testing Sample Before Testing FIGURE 5.4 Schematic Representation of Sample Failure by Squeezing-Out of the Silt Layers. 134 other hand was found to be the dominating failure mode when the samples were composed of alternating thick horizontal layers of silt and clay. with findings by Metcalf This is consistent [98], Milligan [99] and Lo [97]. The third test failure mode was observed and reported when the samples were composed of: a) horizontal thin clay and silt layers, b) thick clay layers and thin inclined silt layers, or c) discontinuity in the layers. 5.2.3 Strength Parameters In all tests (ICT, RT, and cyclic triaxial tests) the interior of the sample was connected to a saturated water line which in turn could be connected either to a pore pressure transducer atmosphere (route 2). (route 1) or to the For all samples, route 2 was used to check membrane leakage after the application of the confining pressure on the sample. Also, this route was used during the consolidation phase of the test for all samples consolidated under the confining pressure prior to shear or cyclic loading tests. The interior of the sample was connected to the pore pressure transducer, using route 1, and the pore water pressure was measured throughout the ICT, RT and cyclic triaxial tests. measurement, as expected, This showed very little development in the pore water pressure. Typical values were on the 2 order of 0.1 to 0.3 psi (.007 to .021 Kg/cm ) for con2 fining pressures of 5 to 50 psi (.35 to 3.5 Kg/cm ) respectively. These low values could be attributed to the unsaturated conditions of the test samples. Based on the pore pressure data, it was decided to use total stress analyses rather than effective stress analyses. The difference between the two analyses were negligible. It should be noted that the interested reader may obtain the data for the pore water pressure from the author upon request. 135 The data from the incremental creep tests and ramp tests were reduced and plotted as shown in Chapter IV and Appendix C. The peak sample strength data and the corresponding confining pressures were used to draw Mohr's circle diagrams from which the failure envelopes were con­ structed and the strength parameters were determined. These parameters are listed in Table 5.1 for the lower peninsula and Table 5.2 for the upper peninsula test sites. As shown in Table 5.1, two sets of strength param­ eters are given (c^, ()>^, and c 2 , 2 ) • The first set (c^, was obtained from tests using confining pressures of 5 and 25 2 psi (0.35 and 1.75 kg/cm ). The second set (c2 , <}>2) was ob­ tained from confining pressures of 25 and 50 psi 2 and 3.5 kg/cm ). (1.75 kg/cm2 It is common practice to use a curved failure envelope to express the strength parameters of the soils. For this study, however, the induced lateral stresses in the sub­ grade materials due to a moving wheel load varies considerably and it is a function of tire pressure and pavement thickness. Consequently, it was felt that two sets of strength parameters may serve the user better than one single failure envelope. The strength parameters c^ and (J>^ should be used for all pave­ ments where the lateral stress in the subgrade materials is expected to be in between 5 and 25 psi 2 (0.35 and 1.75 kg/m ). The second set of strength parameters should be used for higher lateral stresses. The soil samples from the upper peninsula test sites were tested using unconfined as well as confined ramp tests. All samples, except two from site 4, were obtained and tested orientation. (sheared) perpendicular to the varve The latter two samples were obtained at an angle to the varves using an inclined shelby tube during sampling. Figure 5.5 shows the stress-strain curves of two inclined and two vertical varved clay samples. Examination of the figure indicated that the vertical samples were subjected to higher stress at failure than 1 36 TABLE 5 . 1 Test-Site Number -Location S t r e n g t h P a r a m e t e r s a n d R e g r e s s io n C o n s t a n t s o f th e Low er P e n in s u la T e s t S i t e s . Ci * (psi) n C2 * i 9.5 0* n ^ (X10 ) m 3 (XiO" ) 0 10 13.20 3.31 -2.36 0.101 0.064 -30.45 -13.33 - 0.82 0.474 0.148 0.035 0.826 25.80 18.85 12.55 0.326 0.092 0.084 0.981 0.993 0.995 7° 5 25 50 -1.67 4.83 1.71 -0.54 0.071 0.044 0.032 0.028 0.880 0.859 0.847 0.836 6° 25 50 -9.7 -13.94 0.137 0.129 0.513 0.5663 12 ° 25 0 S2-UP 8.5* 7.5 6.0 S3-UP 5.8 0* 0* 20 ° 12 ° 5 25 0 10 25 0* 16* S4-UP 15 16.5 9 8.0 S4-UP T e s ts c3 (psi) (psi) 9.0* S ta tic 0 0.190 r2 0.976 0.976 0.904 0.666 °3= c o n f i n i n g p r e s s u r e i a n d the data will follow a straight line. n is the i n t e r c e p t , while m The parameter is the s l o p e o f the stress-strain data were m o d e l e d using equation l east square f i t t i n g t e c h n i q u e . (5.1) The and Th e r e g r e s s i o n c o n s t a n t s n a n d m and the c o e f f i c i e n t of c o r r e l a t i o n r in Tables 5.1 a n d 5.2 line. 2 are l i s t e d for th e l o w e r a n d u p p e r p e n i n s u l a t e s t sites r e s p e c t i v e l y . E x a m i n a t i o n of the curves of A p p e n d i x C i n d i c a t e d that, stress-strain in all tests, the h i g h e r the c o n f i n i n g p r e s s u r e the h i g h e r the p r i n c i p a l stress d i f f e r e n c e a t f a i lure. sistent with results T h i s w a s e x p e c t e d an d c o n ­ r e p o r t e d in the l i t e r a t u r e . the values of the r e g r e s s i o n c o n s t a n t s (n an d m) S t u d y of indicated tha t the h i g h e r th e c o n f i n i n g p r e s s u r e the l o w e r the v a l u e s of n and m. This lower peninsula. is s h o w n in F i g u r e 5.7 for s i t e 1 of th e Attempts were made to m o d e l n an d m as a fu n ction of the c e l l p r e s s u r e a n d t h e r e b y be a b l e to r e ­ write equation attempts, 5.1 in t e r m s of c o n f i n i n g p r e s s u r e . however, did not Th e gene r a l c o n s e n s u s , con f i n i n g p r e s s u r e the l e a d to c o n c l u s i v e results. however, for a c o n s t a n t p r i n c i p a l These i n d i c a t e d that, stress difference in g e n e r a l , the h i g h e r the l o w e r the t o t a l a x i a l v e r t i c a l strain. 5.3 Cyclic T r i a x i a l T e s t s Th e a p p l i c a t i o n of by moving wheel stress to p a v e m e n t m a t e r i a l s l oads is t r a n s i e n t in nature. any m a t e r i a l c h a r a c t e r i z a t i o n t e c h n i q u e w h i c h the l oads a p p l i e d t o s p e c i m e n s Consequently, s h o u l d b e o n e in are a l s o trans i e n t . T h e r e p e a t e d l o a d t r i a x i a l t e s t is o n e s u c h t e s t 142 in w h i c h 6 .L E G E N D • = ICT RT 8 unconsolidated open symbols - Regression i n d i c a t e m va l u e s closed symbols indicate n values 6 - 4 - 2 . Constant Constant n (X10 I CM I consolidated (X10 - m 10 1 ps i = 0.07 k g / c m *<» 0 L 10 0 20 30 Confining Pressure FIG U R E 5 .7 40 50 (psi) T h e R e g r e s s io n C o n s t a n t s m a n d n o f E q u a t io n C o n fin in g P r e s s u r e , S i t e 1 , Low er P e n in s u la . 5 -1 V e rs u s Regression — samples of the soils or paving materials are placed in the cell and subjected to confining and axial stresses, just as in the static triaxial test* The difference, however, is that application of the axial stress to the sample in the cell is cycled or repeated. The repeated application of axial stress does not duplicate applied stresses in the field, but more realistically represent the form of stress applied to roadbed materials by moving traffic. In this research project, the cyclic loads were applied using a MTS closed loop electrohydraulic system (see Appendix A ) . Also, the sinusoidal wave form of the system was selected, which closely duplicates the applied stresses in the field [7, 23, 50]. The capability of the MTS system in simula­ ting the transient nature of the traffic loading was rec­ ognized by several researchers [19, 23, 29, 30] who have been using the cyclic triaxial test for studying dynamic properties of pavement and s.ubgrade materials. It should be noted that the MTS system did not produce exactly the same load input on every cycle; also reported by Lentz stress difference hundred cycles) [23]. this characteristic was The variation in principal (ai - a 3)d (especially in the first one ranged from approximately two to five per­ cent of the average principal stress difference. After the' first one hundred cycles, the magnitude of the cyclic load was more consistent, although there was some variation from cycle to cycle throughout each test. These variations of the principal stress difference are mainly a function of the system's pump and fluid and the accuracy of the load cell. The cyclic test program of this project calls for three cyclic triaxial tests to be performed on each test material and for each designated confining pressure. The purpose of these tests were 1) to provide information needed to study the cumulative nature of the axial and radial permanent deformations and the axial and radial resilient response of the subgrade soils, and 144 2 ) to study the effects of stress level on item (1) above. In the next two sections, an investigation and study of the factors which affect the plastic and elastic responses of the test materials will be presented. a. number of load repetitions b. confining pressure These factors include: (N), (a3), c. cyclic principal stress difference d. moisture content e. stress history, f. consolidation. 5.3.1 (ai - 03 )^, (w), Effect of Test and Sample Variables on the Axial Plastic Response Examination of Figures through C.13 and analyses of the 4.8 through 4.16and C.7 data listed in Tables C.2 have directed that the axial permanent strain is influenced by the following test variables. 5.3.1.1 Number of Load Repetitions Before any attempt can be made to establish a limiting subgrade stress and/or strain criterion to be used in different pavement design methods, it is necessary to be able to predict the effect of number of load repetitions on permanent deformation. To accomplish this, the results from the cyclic triaxial tests were reduced. Typical data of permanent strain versus number of load applications plotted on arithmetic scales are shown in Figure 5.8. It should be noted that most of the cyclic tests were conducted up to thirty thousand cycles (unless failure occurs). In Figure 5 .8 , however, only the first one thousand cycles are plotted to show greater detail at low number of load repetitions. Examination of Figure 5.8 showed that the rate of accumula­ tion of permanent strain is high in the first one hundred load applications and decreases as the number of load repe­ titions continue to increase. This observation can be e x ­ plained by considering the general mechanisms of soils under 145 14 sample 4f-F 12 (X10 CO 10 2f-F Strain 10 psi Permanent lf-F 5 psi (1 psi = 0.07 kg/cm2) 0 200 400 600 800 1000 Number of Load Applications FIGURE 5.8 Typical Plot of Permanent Strain Versus Number of Load Cycles Under Confining Pressure of 5 psi, Site 2, Lower Peninsula. dynamic loading. The energy applied to the sample during a loading cycle is partly stored as elastic strain energy and partly dissipated within the material causing plastic de­ formation, which is the result of crushing the grains at the particle contact points and intraparticle sliding. When the load is applied, the elastic and plastic components of the deformation will take place simultaneously until the rear­ rangement of particles results in a structural equilibrium. During unloading, the elastic strain energy stored during compression will be released, causing the soil skeleton to expand. This expansion will again cause some particles to slide over one another causing further particle rearrange­ ments. It should be noted that a part of the energy input is lost as heat is generated by particle movements during loading and unloading. Also, during unloading, a part of the strain energy is not recovered, which results in a net permanent strain at the end of the load cycle. When the new particle arrangements are subjected to a second load cycle, elastic and plastic compression will again occur. This time the compression will commence from more stable conditions of the soil skeleton than existed during the first application of load. Thus, less crushing and sliding will occur to reach an equilibrium condition than took place during the first cycle. Therefore, the net permanent strain during the second cycle is less than that of the first cycle. Further­ more, each subsequent load cycle results in further rearrange­ ment of particles into a more and more stable structure. This process is manifested by a large permanent strain during the first cycle of load followed by smaller increments of permanent strain due to each succeeding load cycle. data were also reported by several investigators Similar [7, 8, 23, 57, 101, 102] . Further examination of Figure 5.8 suggested that the relationship between permanent strain and the number of load repetitions can be described by some forms of loga­ rithmic functions [23, 19]. Figure 5.9 shows typical 147 12 sample 4f-F 10 Axial-Permanent Strain (X10 3) 14 2f-F lf-F 10° Number of Load Cycles FIGURE 5.9 (N) Typical Plots of Permanent Strain Versus Number of Load Cycles Under Confining Pressure of 5 psi. Site #2, Lower Peninsula. permanent strain data plotted, on arithmetic scale, against the logarithm of the number of load repetitions. Figure 5.10, on the other hand, shows the same data plotted as the logarithm of permanent strain versus the logarithm of the number of load repetitions. Studies of Figures 5.9 and 5.10 revealed that both plots displayed certain characteristics. These include: 1) the relationship between permanent strain and the number of load applications can be expressed by log­ arithmic functions representing two discontinued straight lines, and 2) number 100. the two straight lines intersect around cycle Equations 5.3 and 5.4 were used to model the data in Figures 5.9 and 5.10 respectively. ep = u(100-N) (A1+B1log N) + u(N-100) (A100+ B 10()logN) (5.3) ^1 ^100 ep = u(100-N)(a1N x) + u(N-100)(a1 0 0 ,N (5.4) where ep = cumulative permanent strain N = number of load repetitions A l fA100 = t*le values of ep at N=1 and 100 respectively (semi-log plot) B 1'B 100 = t*ie sl°Pes °f the straight lines between N=1 and 100 and N>100 respectively (semi-log plot) a l'a 100 = t*le values of the logarithm of ep at N=1 and 100 respectively (log-log plot) ^l'^lOO = s^-m ilar to B^ and plot but for the log-log u(100-N) = a step function the value of which is defined as u (100-N ) = I 0 ’ 0 £or (1.0 for U O O -N X O .O (100-N)>0.0 u(N-100) = a step function the value of which is defined as u(N-100) = i ° * ° for (1.0 for {N“100)< 0 -° (N-100)>0.0. The straight lines in Figures 5.9 and 5.10 were determined using least square fitting technique. The re­ gression parameters and the coefficient of correlation are 149 5 & AA A (%) 1(T Strain 2f-F $ sample 4f-F -1 Permanent 10 t ■ T § #ss lf-F Axial 6 10 -2 10 -3 10v 10 10 10 10 10 ' Number of Load Applications FIGURE 5.10 Typical Axial Permanent Strain versus Number of Load Applications for Samples Consolidated Under a Confining Pressure of 5 psi and Tested Using Different Cyclic Stress Ratio, Site 2, Lower Peninsula. listed in the figures. Examination of the values of the re­ gression parameters indicated that Equation (5.4) appears to model the data slightly better than Equation 5.3. This is due to a higher coefficient of correlation of Equation 5.4. These results were found to be consistent with those reported by Lentz [23] and Yoder and Witman [19]. Consequently, all other analyses in this study will be based on Equation 5.4. Table 5.3 provides a summary of the values of the regression constants of all the test data for the lower pen­ insula test sites. The angle 3 in the table indicates the angle of intersection of the two straight lines as shown in Figure 5.10 and Appendix C. A study of the values of the angle 3 listed in Table 5.3 indicates that 3 decreases as the principal stress ratio increases. of 1.0, For a stress ratio 3 reaches its limiting value of 180°. For this case, both slopes b^ and b^^^ assume one limiting value which is proportional to the coefficient of consolidation of the sam­ ple. The significance of the angle 3 may be revealed by con­ sidering the cumulative rate of permanent strain during the first 100 load cycles cycles (£p^oo^ * (ep j) relative to the rate beyond 100 T^e ^ower t^le an,?le 6, the higher the ratio of epi/£pioo an<^ t*le t h e damage delivered to the sam­ ple during its initial loading phase. One hundred cycles may not be significant when considering the life period of a pavement section which may be subjected to 100,000 or 1,000,000 load repetitions. However, for a pavement section newly opened to traffic, the first 100 load repetitions will set the initial border of the rut channel on the pavement surface. Consequently, the traffic distribution over the pavement will be narrowed and directed toward the rut channel which will accelerate pavement rutting. The permanent strain data of the upper peninsula test sites are shown in Figures 4.32 through 4.35. The data show a behavior similar to that of the lower penin­ sula test sites; the cumulative axial permanent strain in­ creases as the number of load repetitions increases. 151 Due S2-LP L e a s t S q u a re s F i t o f E q u a t io n 5 . 4 (XL0_1*) (X10“ ) (X10~) 10.90 189.15 6.450 57.90 25.026 28.94 158325 13.41 110.25 2.220 299.01 18.66 32.25 3.8526 3.9717 4.1604 2.9158 4.3428 3.6355 7.523 2.894 2.6704 5.3192 0.9057 3.950 1.2319 b io o 1 Sl ~ a io ° i-p fo r s CO Sl-LP P a ra m e te rs 1 Sitea Number Sample 3 location timber (psi) - 2a-F 4a-S 2b-F lc-F 2d-F 3d-F 4d-F le-F 2e-S lf-F 2f-S 3f-S 5 50 5 5 25 5 25 5 25 5 25 25 2.0 0.5 1.0 3.0 1.0 2.0 2.0 3.0 1.5 1.0 1.5 1.0 la-F 3a-S lb-S 3b-S 4b-S 4b-F lc-F 2c-F 3c-F 4c-S 2d-S le-F 2e-F 3e-F 25 25 5 25 5 25 5 5 25 50 5 5 5 25 * 2.0 183.0 * 1.5 127.3 1.0 3.6708 5.715 1.0 3.790 26.326 1.0 3.0745 5.714* * 1.5 122.02 3.0 3.694 48.640 1.0 3.0744 5.715 32.8 1.0 148.0 * 0.70 99.20 2.0 27.58 114.17 2.0 5.744 19.064 1.0 0.1528 8.501 * 2.0 L83.01 — 25.910 124.13 137.4 94 74.37 — 15.61 — 6.160 404.06 * X R e g r e s s io n ! TABLE 5 . 3 9.3128 5.1379 3.025 6.0064 3.41520 2.9144 2.0783 3.4152 2.845 2.802 3.589 4.1623 5.963 0.9313 2 rj 0.9784 0.98423 0.02591 0.9402 1.4318 0.9889' 0.8224 0.91256 1.4909 0.9709 — 0.99053 3.098 0.9459 — 0.97961 2.4993 0.97537 0.1195 0.8100 * 0.9957 — * * 1.939 1.9292 1.9393 * 1.609 1.9393 2.824 * 1.058 1.280 6.592 * 1.000 0.9541 0.9398 0.9738 0.9557 0.9796 0.9321 0.9557 0.9650 1.000 0.850 0.9382 0.8226 1.000 y. 2 r 10 0 0.9806 — 0.8953 0.9365 0.8989 0.9873 — 0.9716 6 165° ** 163° 172° 163° 170° ** 178° — 0.9593 166° 0.9187 175° * * * 0.9954 0.9488 0.9954 * 0.9938 0.9954 0.9871 * 0.9882 0.9896 0.9656 * ** * * 169° 167° 170° 176° 171° 168° 165° 177° 168° Test Mode (CT) C C C C C U c u u u c u u u c c c c u c u c c u u c TABLE 5 . 3 C o n tin u e d SiteNumber Sample location Number a 3 (psi) f x - a % Sl (X10 " ) aioo (X10 bl (X10~) bi o o (X10" ) 3 r 2 i 5 5 25 5 1.0 2.0 1.5 3.0 1.990 10.506 18.341 14.22 S3-LP la-F 2a-F 3a-F 2b-F 4b-F 2c-F 2e-S 5 25 25 5 25 5 5 3.0 1.5 2.0 2.0 1.0 1.0 2.0 55.2065 132.953 90.001 279.323 99.065 117.497 27.2111 33.054 92.05 78.012 6.075 2.810 95.13 59.11 S4-LP la-F 4a-F 2d-F 2e-F 3e-F 5 5 25 25 5 1.0 3.646 1.162 3.460 0.50 41.056 64.401 1.0 15.155 2.0 153 S2—LP lf-F 2f-F 3f-F 4f-F 21.41 46.843 * 73.29 18.871 3.460 97.131 162.552 82.554 r 2 10 0 6 Test Mode (CT) 5.1429 3.796 9.534 4.322 1.320 0.7673 * 0.6647 0.9384 0.9966 0.9812 0.9821 0.8680 163° 0.9701 164° * 0.9632 165° C C C C 3.3236 3.0955 2.0699 0.9636 4.3214 2.039 1.91203 1.6117 0.7032 1.8047 0.6091 0.673 1.068 0.86736 0.9774 0.9706 0.9954 0.9550 0.9816 0.9541 0.9724 0.9686 0.9877 0.9704 '0.9528 0.9776 0.9771 0.9850 177° 173° 179° 178 ° 173° 172° 176° C C C C C C U 5.269 4.859 3.245 4.353 5.747 2.219 2.075 1.863 2.551 2.334 0.9951 0.9832 0.9947 0.9837 .0.9589 0.9275 0.9463 0.9072 0.9914 0.8980 167° 168° 172° 170° 167° C C C C C * samples failed at less than 30,000 number of load applications ** samples failed at less than 100 number of load applications to the nature and variability of the varved clay samples, however, two similar samples from the same test site did not show similar behavior when tested under the same confining pressure and cyclic load. Consequently, no further studies were performed and the test data were judged as erratic. 5.3.1.2 Confining Pressure For the same cyclic stress ratio (ai-a3)^/a3, the higher the confining pressure the higher the cumulative per­ manent strain. Figure 5.11 shows plots of the logarithm of permanent strain versus the logarithm of the number of load repetitions for two samples tested under the same cyclic stress ratio and different confining pressures. It can be seen that the higher the cell pressure the higher the per­ manent strain. Recall that the results of incremental creep tests and/or ramp tests have indicated that the higher the confin­ ing pressure the lower is the ratio of sample strength to con­ fining pressure. For example, if two samples were tested under confining pressures of 5 and 25 psi then the strength ratio at failure 2 (.35 and 1.75 kg/m ), (ai-a3)^/a3 for the first sample is higher than that of the second sample. Further, if two identical samples were confined as above and then subjected to the same cyclic stress ratio (tfi-a3)£/a3 and if the cyclic principal stress difference (Oi-a3)^ is expressed as a percent of the sample strength, then this percentage will be lower for the sample with low confining pressure than that with high con­ fining pressure. This is shown in Figure 5.12. The dashed curve in the figure is for samples tested under higher con­ fining pressures than those represented by the solid curve. The cyclic stress ratio (Oi~o3)^/a3 , however, is the same for both curves. The above noted observations could also be seen by studying the permanent strain of the test samples after one single load application. This is represented by the values of the parameter a1 in Table 5.3. 1 54 Examination of 2d-F 10 Permanent S t r a i n (%) 3 = 25 psi Axial sample lc-F (1 psi = 0.07 kg/cm2) _ 2 10 10° 101 102 103 10“ 10s Number of Load Applications FIGURE 5.11 Axial Permanent Strain Versus Number of Load Applications for (°i “ a3 )d/°3 = 1.0 and Different Confining Pressures, Site 1, Lower Peninsula. T3 i CO “ t—i too aj — p Xi -p ■p CO h 1.0 3 = 25 psi tr> c CT 1 u (U o m c o 0) p o o -H ip -p

d 03 1 1.5 2.0 10° datum Symbols • ■ A 101 Ep at cycle number one for sample 2e-S was measured as .0591%. 102 103 10“ 105 Number of Load Applications FIGURE 5.17 Axial Permanent Strain Versus Number of Load Applications for Unconsolidated Soil Samples Tested Under Two Different Stress Paths, Site 3, Lower Peninsula. should be subjected to relative to the expected traffic load throughout the life cycle of the pavement. Study of the stress history of laboratory samples indicated that the dam­ age (in form of permanent strain) could be minimized if the applied stresses were small and they increased gradually. Consequently, in the field, and as far as the pavement de­ formation is concerned, a newly constructed pavement should be opened to light traffic (light tire pressure) prior to trafficking the pavement indiscriminantly. This process, however, may prove to be either expensive or to cause higher user cost. Further, the lateral stress in a newly construct­ ed pavement is a function of the pavement materials, ness, and method of compaction. thick­ If, however, the lateral stress in a pavement section at the end of construction is taken as a datum, then the lateral stress at any time after * opening the pavement to traffic is greater than the datum. The increase in lateral stress is due mainly to the pavement section being seated by the action of traffic. Increasing the lateral stress will permit higher load and thus less damage. It should be noted that (see section 5.3.1.2) in­ crease in the lateral stress should not be interpreted as unlimited license to substantially increase the axial load on the pavement. 5.3.1.5 Water Content and Consolidation The variation of water contents of samples for the same site was not significant to influence the plastic characteristics of the sample. Consequently, this section will be restricted to the effect of consolidation. Figure 5.18 shows plots of permanent strain versus the number of load repetitions for two samples. Sample 2b-f was consolidated under a confining pressure of 5 psi (.35 2 kg/cm ), then subjected to cyclic principal stress difference 2 of 5 psi (.35 kg/cm ). Sample lf-f was subjected to the * Assuming that the pavement does not heave or deform radially. 164 10 Permanent Strain (%) sample lf-F Azial 2b-F 10 10° Number of Load Applications FIGURE 5.18 Axial Permanent Strain Versus Number of Load Applications for Unconsolidated and Consolidated Samples Under a Confining Pressure of 5 psi, Site 1, Lower Peninsula. same confining pressure and principal stress difference with no consolidation allowed. From the figure, it is apparent that the unconsolidated sample experienced much higher per­ manent strain than the consolidated sample. Indeed, the permanent strain of sample lf-f was in order of magnitude greater than that of sample 2b-f. The effects of consolidation on the plastic behav­ ior of the samples appears to decrease as the cyclic princi­ pal stress difference increases. 'This was expected because the sample, during the consolidation phase, did some particle reorientation which resulted in a more stable structure to resist the consolidation pressure. As the sample was sub­ jected to a larger virgin load due to axial load that it had never experienced before, new particle reorientation and a higher order of stable structure are required. result in increased plastic deformation. This will This could be re­ written as follows: the higher the ratio of virgin pressure to the consolidation pressure of a sample, the lower the effects of consolidation on the sample deformation due to that virgin load. 5.4 Stress-Strain Relationship Lentz [23] and Lentz and Baladi [8,77] provided the technical guidance for the early phase of this work. They reported that the plastic strain of sand subgrade mate­ rials could be predicted using triaxial test results. They concluded that the prediction model is dependent on the num­ ber of load applications and independent of the test vari­ ables (confining pressure, stress level) and sample variables (compaction effort and moisture content). They observed that the cyclic and static tests are highly dependent on the same test and sample variables. Consequently, they rationalized that the data from both tests could be normalized to mini­ mize the effects of the sample and test variables. Their normalization process could be summarized as follows: 01. The cyclic principal stress difference (Oi-a3) , was expressed in terms of the peak static strength (S^) 166 of an identical soil sample tested under the same con­ fining pressure using incremental creep tests. (It was shown later that the normalization results did not change when the incremental creep test was substituted by the ramp tests.) 02. The cumulative permanent strain at the desired number of load repetitions (e ) was normalized relative to the axial strain at 95% of the sample strength (e ) of an identical sample tested under the same con-* d fining pressure using incremental creep test. Figure 5.19 shows their normalized data for natural sand de ­ posit as well as manufactured sand. For more informa­ tion on their data and normalization procedure, the reader is referred to reference [23] in the biblio­ graphy. The above normalization procedure was also used in this research project. The sample strength and the strain at 95% of sample strength were determined using the incremen­ tal creep test. Figure 5.20 displays typical stress-strain 2 data of a sample tested under 5 psi (.35 kg/m ) confining pressure using incremental, creep test,, As illustrated in the figure, the value of the strain at failure (peak strength) could not be determined because the stress-strain curve b e ­ comes asymptotic to the strain axis. Consequently, the strain at 95% strength was used as shown in the figure. Figure 5.21 shows a plot of the normalized stressstrain data at 30,000 load repetitions for the four test sites of the lower peninsula. Examination of the figure indicated that the normalized data could be expressed in one single-hyperbolic function that expresses the normalized strain ratio in terms of the normalized stress ratio or vice versa. This function (Equation 5.5) is independent of con­ fining pressure, principal stress difference, density, and water content. — £ *95Sd d where e p = -2 (5.5) Sa = cumulative permanent strain at the desired number of load repetitions, 167 1.0 _ 0) o a 00 0) n a) m xi

1 u indicates two data points data pts were normalized relative to ICT and FT I I I________ I________ I________ I________ J _______ Permanent Strain_____________ Static Strain at 0.95 Peak Static Strength FIGURE 5.19 Normalized Cyclic Principal Stress Difference Versus Normalized Permanent Strain. (After 23). » •H CO 30 sample strength S Q. CO ^-- 0.95 S a) 20 o c a) n 0) m •H Q ca 01 a) M 10 4J 26.0 psi e0. 95S ,= 5.55X10 CO 1 psi = 0.07 kg/cm 0 2 4 Axial Strain FIGURE 6 8 (X10~2) 5.20 Typical Principal Stress Difference Versus Strain From Incremental Creep Test. 10 1.2 LEGEND 1.0 'O w •a ■ = site 1 closed symbol 3= 5 •= site 2 open symbol = ▲ = site 3 partially open symbol a3 = 50 psi site 4 .8 ° 3 psi 25 psi * data normalized using ramp test Ratio .4 Stress .6 .2 A O A □ (1 psi = .07 kg/cm2) j____________ 1_____________1____________ L 0.0 0.2 0.4 Strain Ratio FIGURE 5.21 0.6 0.8 1.0 (ep/e Qro ) * d Normalized Stress Ratio Versus Normalized Strain Ratio at 30,000 Cycles e qc._ d = axial strain at 95% of the strength, static = static strength, n,m = regression parameters, (ai—a 3)^ = cyclic principal stress difference. Indeed, the same hyperbolic function describes the data from test site 4 as well as test sites 1, 2, and 3, which are several hundred miles apart. Lentz [23] and Lentz and Baladi [8,77] found a similar function for natural sands as well as for manufactured sand. The differences between the sand and clay functions, however, are the values of the parameters n and m. These findings suggested that during the normali­ zation procedure the effects of the test and sample variables are minimized or even eliminated. thought that if soils, Consequently, it was in general, could be classified into, say, six different types (silty clay, clay, sandy clay, sand, sandy gravel, and gravel) then a set of six different param­ eters could be found to be used in Equation 5.5. It should be noted that ramp test data were also used to check the normalization process and the resulting general relationship. terisks. This is shown in Figure 5.21 by as­ It can be seen that the normalized data follow the same general relationship (curve) as that obtained using the incremental creep test as a base for normalization. At this time and in order to check the validity and generality of the normalization process, a call for data was initiated and mailed to several independent researchers. The call inquired static and dynamic data for all type soils. The response was overwhelming and encouraging. Unfortunately, a substantial part of the received data consisted of either dynamic or static stress-Strain curve. As noted above, both cyclic and static data of some kind are required to initiate the normalization process. Figures 5.22 and 5.23 show the nor­ malized data of subballast and under-tie materials respec­ tively. The data were received from Dr. Sileg at the Univer­ sity of Massachusetts, Amherst 171 [106]. The gradation curves 1.0 0.8 Stress Ratio 0.6 .4 3 psi .2 1 psi = 0.07 kg/cm 0 0 0.2 0.4 Strain Ratio 0.6 0.8 (ep/eg ^ d FIGURE 5.22 Normalized Cyclic Stress-Strain Data for Subbalast Materials Subjected to 10,000 Load Repetitions (After 106). 1.0 1.0 co \ m o •H +J Oh (0 0) (D S-4 -P 0 ct3 = 12 psi CO (1 psi = 0.07 kg/cm2) 0 0.2 0.4 Strain Ratio FIGURE 5.23 0.6 0.8 (ep/eQ g5g ) Normalized Cyclic Stress-Strain Data for Under Tie Materials Subjected to 10,000 Load Repetitions. (After 106). 1.0 of the subballast and under-tie materials are presented in Figure 5.24. Figure 5.25 shows the normalized data for the AASHTO A-6 materials; the tests were conducted under the direction of Dr. Baladi during the course of a previous re­ search project sponsored by the Michigan Department of Trans­ portation. Figure 5.26, on the other hand, shows the normal­ ized data for the clay subgrade materials of the lower penin­ sula test sites. It should be noted that the data for the curves in Figures 5.19, 5.22, 5.23, 5.25, and 5.26 indicated that each type of soil could be represented by one single and unique curve. Finally, it is appropriate to note that other data received from Penn State, the National Crushed Stone Association, Rensselaer Polytechnic Institute, Japan, and the Federal Highway Administration showed similar nor­ malized curves. Recall that Equation 5.4 was used in this re­ search to model the permanent strain as a function to the number of load repetitions. It was found that the same equation could be used to model all the received data. At this point in time it was suggested that the normalization process be repeated at a higher number of load repetitions. i Consequently, the plastic strain at one million load cycles for each material was calculated and normalized relative to the corresponding static data. Figures 5.27 through 5.31 show plots of normalized curves at ten thousands and one million load applications for AASHTO A-6 subgrade soils, the clay subgrade soils, the subballast, the sand subgrade, and the under-tie materials respectively. Examination of the figures indicated that the values of the parameters m and n which control the position of the curve are dependent on soil type and number of load applications. Figure 5.32 shows different plots of the normal­ ized stress and strain ratio for different numbers of load repetitions. It can be observed that the curves tend to shift and rotate downward as the number of load repetitions increases. This shift in the curve is reflected in a change in the value of the parameters n and m of Equation 5.5. 174 100 £ O' •H 0) £ >1 80 60 u 0) g •H P4 o •H +» nJ Ctj 0.4 to to a> M co -P (1 psi = 0.07 kg/cm2.) 0.2 0.2 0.6 0.4 Strain Ratio 0.8 (e p /E q ) d F ig u r e 5 . 2 5 N o r m a liz e d C y c l i c S t r e s s - S t r a i n D a ta f o r A - 6 AASHTO S u b g ra d e S o i l s S u b je c t e d t o 1 0 , 0 0 0 L o a d R e p e t i t i o n s . (A fte r 2 3 ). 1.0 1.0r 0.8 'd co \ 'd 0.6 0 -H -P m a 01 in (ep / e 0>95s ) d O tvj O •' • o o rt* n 0 CD Oi o AASHTO, A-6 _ subgrade soils (type 6) o H O O O Stress ■» H* o cn r+ t-* n Jd cn CD r t tl H (l Michigan subgrade clay soils, lower peninsula (type 5) ._ Ratio o O j CO rt H- H- 3 H- Sd O P> 3 rt* co H- Q j i-h H- cn O. subballast material (type 3) ___ H- Hi Hi 00 H- Michigan sub­ grade sand (type 2) / under tie material (type 1) o 0.76 for the subballast materials, 0.85 for Michigan sand subgrade, and 0.98 for under-tie materials. It should be noted that both the subballast and under-tie materials were classified as A-l-a according to the AASHTO soil classification (106). If the predesignated soil support value is superimposed on the above data (SSV=3.0 for A-6 and SSV^IO.0 for the under-tie), it follows that the SSV can be expressed using the following equation SSV = 10 where the subscript (CTi-03) , s d (f, N=1 0 ) (5.7) g (f, N=10 ) indicates failure at one mil­ lion load applications. Equation (5.7) can be generalized as follows: (ai-a3) , SSV = a --d (f, N) (5.8) where a is constant depending on the number of load repeti­ tions (N) and the subscript (f, N) indicates failure at N number of load applications. Recall that (see section 5.4 above) the normalized model (equation 5.5) is a function of the number of load applica­ tions (N) and soil type. These observations suggested that (for each soil type) the parameters n and m of equation 5.5 can be expressed in terms of (N). Figure 5.38 shows a typical plot of the parameters n and m as function of (N). This functional relationship was found to be of the following form. n = a„ + b An N (5.9) m = a^ + b An N m m The values of the regression constants a , b , a , and b n n m m are summarized in Table 5.4 for five different soil types. 192 1.14 O fH >< c u a) 0) 6 (0 u (d .0 1.12 .8 1.10 .4 1.08 ■p u Q) +J 0) e m u (d Q) Eh > XI 1.02 2 .8 10 10 10 10 10 10 Number of Load Applications FIGURE 5.38 Typical Relationship Between Number of Load Applications and the Parameters n and m of Equation (5.5) for Subbalast Materials. TABLE 5.4 Soil The Values of the Regression Constants a , b , a and b for Five Different Materials n n m m Soil Type n m an (X10"Z bn (X10"2) am (X10-2) b (X10-2) mV ' 194 Undertie 1 -3.69700 1.74370 88,35894 -0.45769 Sand 2 -4.50225 2.26355 101.40517 -0.72966 Subballast 3 -4.82732 2.25408 111.57562 -0.46162 4 No data avai lable Clay 5 -12.66488 2.52718 283.89983 -7.44985 A-6 6 -13.05600 6.97645 331.63359 -7.91234 < Substituting equations a E_ e .95S n (5.9) into equation + b n (5.5) yields S-n N (5.10) d (ai-a3)d (am + bm N) which expresses the strain ratio as a function of the stress ratio and soil type. It should be noted that equation (5.10) is independent of confining pressure, water content and state of compaction. 5.6 Limiting Stress and Strain Criterion The significance of the normalized model and the SSV correlation is that the model itself could be used for three different purposes. These purposes are: 01. To predict the cumulative permanent strain of the sub­ grade materials due to dynamic loadings once the static stress-strain characteristic is known. 02. To be able to calculate and better understand the soil support value of the materials. 03. To establish a limiting stress criteria that could be used in the pavement design. Item 1 above was discussed in detail in references 77]. Item 2 was discussed in Section 5.5. accomplished using the normalized model. [8,23, Item 3 could be For example, assume that a pavement section is to be constructed using Michigan clay soils as subgrade materials and to be sub­ jected to one million 18 kip equivalent single axle load. What are the limiting conditions, so that at the end of the life cycle the subgrade will experience rut depth (permanent strain) equal to 50% of the static strain at failure? The answer, using Figure 5.36, is that the limit­ ing condition of the design should be that the traffic in­ duced stress in the subgrade be no more than 40% of its static strength. This limiting condition could be related to the pavement thickness and consequently to the struc­ tural number. 195 The benefits of this limiting strain criteria could be maximized if it is incorporated into a pavement management system computer program. Such a program could then analyze current construction costs for the limiting condition versus future maintenance and rehabilitation costs. 5.7 5.7.1 Implementation General Assume that a pavement section is to be constructed on clay or sand subgrade soil. The highway engineer is in- ested to know the following information: (a) estimate of the soil support value, (b) estimate of the rut depth of the subgrade materials, (c) the relative conditions of the subgrade at the end of the pavement life cycle, and (d) alternative design options so as to maximize bene­ fits at the lowest cost. This information could be obtained by the highway engineer, prior to design and construction, using the follow­ ing steps: (1) Collect undisturbed as well as bag samples of the subgrade materials in question according to the AASHTO soil classifications using the bag samples. (2) Classify the subgrade materials. (3) Estimate the soil support value of the materials using Figure 5.36 and equation 5.7. (4) Select the desired life cycle of the pavement. (5) Conduct a conventional triaxial test using the undisturbed soil samples with the proper density and water content. (6) Select a trial pavement section and the appropriate parameters of equation 5.6 if the AASHTO design procedure is to be used. Otherwise, select the proper parameters for the desired design procedure. (7) Calculate, using any available computer program such as the Chevron program, the induced and sustained 196 stresses in the subgrade due to the 18 kips single axle load and the pavement weight respectively. These stresses shall include the vertical and lateral stresses. (8 ) Calculate the stress ratio which is equal to the difference between the total vertical lateral strength (di) and (03 ) stresses divided by the sample (S^) obtained in Step 5 above. The total vertical and lateral stresses herein include the traffic induced stresses as well as the stresses caused by the pavement section above the subgrade. (9) Use the results of Steps 5 and 8 above and the appro­ priate parameters from table 5.4 as an input to equation 5.10 and calculate the strain ratio as well as the estimated rut depth of the subgrade materials. (10) If the strain ratio (the ratio of permanent strain of the subgrade to the static strain obtained in Step 6 above) is high (close to 1.0) then select another trial section (thicker base and subbase) and go to Step 6 . Otherwise, the subgrade is ex­ pected to fail at the end of the life cycle. (11) Use the estimated SSV and the parameters of Step 6 above as input to the AASHTO design equation or charts to back calculate the life cycle of the pave­ ment section in question. (12) If the calculated life of the pavement section in question is not compatible to the estimated life then go to Step 5. The above implementation steps are summarized in a flowdiagram that is presented in Figure 5.39. 5 . 7 . 2 Numerical Example . Assume that a clay soil classified as type 5 material is to be used as subgrade for a three feet thick flexible pavement section. The estimated applied vertical 197 undisturbed samples collect undisturbed and bag samples bag samples classify the subgrade materials conduct a conven­ tional triaxial test __ select the desired life cycle of the pavement estimate the SSV using Fig. 5.36 calculate the strength parameters select a trial pavement section calculate the total stresses in the subgrade ________ calculate the stress ratio = °i ~ 0 3 no calculate the strain ratio using eq. 5.5 no is the strain ratio acceptable? STOP FIGURE 5.39 yes calculate the life cycle of the pavement is the calculated life cycle acceptable?______ FLOW CHART OF THE IMPLEMENTATION. 198 and lateral stresses on the subgrade, due to the weight of the pavement section and an 18 kips equivalent single axle load, were found to be 7 and 3 psi respectively. A conven­ tional triaxial test on representative sample of the com­ pacted subgrade was conducted using a confining pressure of 3 psi (equal to the estimated lateral stress). The strength of the sample was found to be 13 psi and the strain at 95 percent strength was measured as 7.2%. (a) The estimated soil support value of this material using Figure 5.36 is 4.92. calculated as This also could be where n and m are the parameters of equation 5.10 calculated for N = 1,000,000 using the appropriate constants from Table 5.4. (b) The stress ratio that the material will be subjected to in the field is q^ -a3 = d = 0.308 (c) Calculate the strain ratio for different number of load applications using equation 5.10 with the proper parameters from Table 5.4 and a stress ratio of 0.308. N Strain Ratio 100,000 .143 1,000,000 .174 10,000,000 .198 (d) Calculate the cumulative permanent strain the subgrade. (ep ) of e = e g5g x (strain ratio) ^ d ■ 100,000 !e !!1 1.03 1,000,000 1.25 10,000,000 1.43 199 (e) Calculate the rut depth (RD) of the subgrade assuming that the stressed zone is 3 feet deep. The depth of the stressed zone could be calculated using any available computer program such as the Chevron program. N RD (inch) 100,000 371 1,000,000 450 10,000,000 515 (f) If the rut depth is high then select thicker pave­ ment section and recalculate steps b, c, d, and e. (g) Calculate the number of 18 kips equivalent of the pavement section using the AASHTO design equation, the SSV of step a above and the estimated structural number of the different pavement components. Assume the calculated 18 kips equivalent is 7,000,000. This means that at 7,000,000 load repetitions a rut depth of 0.5 inch should be expected. If this rut depth is high, then the rut model controls the pavement performance. Different distress mode controls the pavement section in question for low rut depth value. 200 CHAPTER VI CONCLUSIONS AND RECOMMENDATIONS 6.1 Conclusions On the basis of the test results of this study and in the range of the test and sample variables, the following con­ clusions were drawn: (1) The cumulative permanent strain of Michigan cohesive subgrade materials was found to be a function of several variables. These include the stress level and stress path, moisture content, density and confining pressure. (2) For a given set of sample and test variables, Equation 5.4 was found to model the cumulative permanent strain at any number of load applications. (3) At any confining pressure and number of load repe­ titions, the relationship between the cyclic principal stress difference and the cumulative permanent strain of one sample was represented by a hyperbolic function. (4) The effect of the test and sample variables, mentioned in conclusion 1 above, on the cumulative permanent strain was minimized or eliminated using a normalization procedure di s ­ cussed in Section 5.4. This procedure calls for the normaliza­ tion of the cyclic principal stress difference with respect to the static strength and of the cumulative permanent strain relative to the static strain at ninety-five percent of the static strength. (5) The normalized procedure yielded a normalized pre­ dicted model which was found to be unaffected by the type of test (incremental creep or ramp test) from which the normal­ izing parameters were obtained. (6) A general predictive model of the plastic behavior of the test materials was developed using the normalization procedure. The input parameters of the model consisted of the static strength and the corresponding total strain of the material in question. 201 (7) The normalized predictive model shown in Figure 5.36 was found to be a function of s6il type and number of load applications only. (8) A correlation between the soil support values and the normalized predictive model of the material was developed. This correlation was based on a single point related to the AASHTO A-6 material and its assigned soil support value of 3. (9) It was demonstrated that the normalized predictive model could be used to establish a limiting stress and strain criterion of the pavement materials under consideration. 6.2 Recommendations The results of this investigation has led to the develop­ ment of a normalized predictive model of the plastic strain of pavement materials. The model has demonstrated its abil­ ity to evaluate and predict the plastic behavior of several materials subjected to cyclic loadings. The input parameters of the model consisted of the static strength and the corres­ ponding total strain of the material in question. The model was tested and evaluated using five different materials rang­ ing from gravel and sand to clay and clayey silt. Further, a correlation was developed between the soil support value and the normalized predictive model of the materials. It should be noted that no knowledge was available at the time of the soil support value of the test materials. Rather, the correlation was based on a singular point related to the AASHTO A-6 material and its assigned soil support value of 3. Consequently, it is recommended that studies be continued so that the singularity point of the correlation is eliminated and wider base is established. The development of the normalized predictive model offers a new understanding of the plastic behavior of the test materials. This model is based on relatively rapid static tests and it eliminates the need for a long and time con­ suming cyclic tests. However, the model was not checked or validated against some variables. 202 It is recommended that efforts be expended to check the validity of the predictive model for soils subjected to freeze-thaw cycles and to verify its predicting capability using measured rut depth data in the field. The interaction mechanism between the different pavement layers and its effects on the plastic strain should be investigated and incorporated into the normalized predictive model. 203 BIBLIOGRAPHY BIBLIOGRAPHY 1. Wen-Kuh-Luo, "The characteristics of soils subjected to repeated loads and their applications to engineering practice." Japanese Society of Soil Mechanics and Foundation Enginering, Vol. 13, No. 1, 1973. 2. Seed, H. B. and Chan, C. K . , "Effect of Duration of Stress Application on Soil Deformation Under Repeated Loading." 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N. and Addo-Abedi, "Repeated Compressive Loading of Leda Clay," Canadian Geotechnical Journal, Vol. 16, No. 1, 19 79. 50. Seed, H. B., Chan, C. K . , and Lee,lC. E . , "Resilience Characteristics of Subgrade Soils and Their Relation To Fatigue Failures in Asphalt Pavements," Proceed­ ings of International Conference on Structural Design of Asphalt Pavements, University of Michigan, 1962. 51. Finn, F. N . , Nair, K . , and Monismith, C. L . , "Appli­ cations of Theory in the Design of Asphalt Pavements," Proceedings of the 3rd International Conference on the Structural Design Asphalt Pavements, London, England, 19 72. 52. Cannon, R. H. Jr., "Dynamic of Physical System," McGraw-Hill Book Company, 19 67. 53. Chou, Vu T., "Engineering Behavior of Pavement Materials State of the Art," U.S. Army Engineer Water­ ways Experiment Station CE, Vicksburg, Miss, Techni­ cal Report S-77-9, 1977. 207 54. Monismith, C. L., Seed, H. B., Mitry, F. G., and Chan, C. K., "Prediction of Pavement Deflections from Labora­ tory Tests." Proceedings of the 2nd International Conference on Structural Design of Asphalt Pavements, U.M., 1967. 55. Seed, H. B., McNeill, R. L. and De Guenin, J., "In­ creased Resistance to Deformation of Clay caused by Repeated Loading," Journal, Soil Mechanics Division A.S.C.E. 84 SM2, 19 58. 56. Seed, H. B., .and Chan, C. K., "Effect of Stress History and Frequency of Stress Application on Deformation of Clay Subgrade under Repeated Loading," Proceedings H R B , Vol. 37, 1958. 57. Chou, Vu T., "Analysis of Permanent Deformation of Flexible Airport Pavements," U.S. Army Engineer Water­ ways Experiment Stateion, CE, Vicksburg, Miss., Tech­ nical Report S-77-8, 1977. 58. Mitchell, J. K., Shen, C. K . , and Monismith, C. L. , "Background equipment, preliminary investigation, re­ peated compression and flexure tests on cement treated silty clay". Report No. 1, University of California, Berkeley, December 1965. 59. Young, M. A. and Baladi, G. Y . , "Repeated Load Triaxial Testing of the Art," Division of Engineering Research, Michigan State University, 19 77. 60. Moretto, O., "Effect of Natural Hardening on the Un­ confined Compression Strength of Remolded Clays," Proceedings, 2nd International Conference of Soil Mechanics,"Vol. 1, 1948. 61. Seed, H. B. and Chan, C. K., "Thixotropic Characteris­ tics of Compacted Clays," Journal, Soil Mechanics and Foundations Division, A.S.C.E. Vol. 83 SM4, 1957. 62. Humphries, W. K., and Wahls, H. E., "Stress History Effects on Dynamic Modulus of Clay," Journal of Soil Mechanics and Foundation Division, Proceedings ASCE, Vol. 94, No. SM2, 19 68. 63. Seed, H. B., McNeil, R. L. and De Guenin, Jacques, "Clay Strength Increase caused by Repeated Loading," Journal, Soil Mechanics A.S.C.E. Transactions, 19 58. 64. Barksdale, R. D., "Compressive Stress Pulse Times in Flexible Pavements for use in Dynamic Testing," HRB Record 34 5, 19 71. 65. Allen J. and Thompson, M. R . , "Resilient Response of Granular Materials Subjected to Time-Dependent Lateral Stresses," TRB, NAS, Transportation Research Record No. 510, 1974. 208 66. Hicks, R. G. and Monismith, C. L . , "Prediction of the Resilient Response of Pavements Containing Granular Layers using Non-Linear Elastic Theory," Proceedings, 3rd International Conference on the Struct. Design of Asph. Pavement, London, England, 19 72. 67. Seed, Mirty, Monismith, Chan, "Prediction of Flexible Pavement Deflections from Laboratory Repeated Load Tests," NCHRP Report No. 35, 1967. 68. Dehlen, "Test Procedures for Characterizing Dynamic Stress Strain Properties of Pavements Materials," Transportation Research Board, Special Report 162, Washington, D.C., 1975. 69. Tanimoto, K. and Nishi, M . , "On Resilience Character­ istics of Some Soils under Repeated Loading." Soil and Foundation Vol. 4, 1970. 70. Seed, H. B. and Monismith, C. L . , "Some Relationships between Density and Stability of Subgrade Soils." HRB Highway Research Records, Bulleton No. 93, 19 54. 71. Coffman, B. S., Kraft, D. C., and Tamayo, J., "A Comparison of Calculated and Measured Deflections for the AASHO Road Test," Proceedings, Association of Asphalt Paving Technologists, Vol. 33, 19 34. 72. Seed, H. B., Mitry, F. G . , Monismith, C. L . , and Chan, C. K . , "Factors Influencing the resilient deformations of untreated aggregate base in two-layer pavements subjected to repeated loading," HRB, Highway Research Record No. 190, Washington, D.C., 1967. I 73. Finn, F. N., Nair, K . , and Monismith, C. L., "Applica­ tions of Theory in the Design of Asphalt Pavements," Proceedings of the 3rd International Conference on the Structural Design of Asphalt Pavements, London, England, 19 72. 74. Baladi, G. Y., and Boker, T. D., "Resilient Charac­ teristics of Michigan Cohesionless Roadbed Soils in Correlation to the Soil Support Values," Final Report, Grant 75-1679, Division of Engineering Research, Michigan State University, 1978. 75. Highway Research Board "The AASHO Road Test" National Academy of Sciences - National Research Council Wash­ ington D.C. Publication 954 Special Report 61E 1962'. 76. Hicks, R. G. and Monismith, C. L., "Factors Influenc­ ing the Resilient Response of Granular Materials," Highway Research Board, Highway Research Record No. 345, 1971. 209 74. Baladi, G. Y., et al, "Shear Strength of Cohesionless Soils, ASTM Special Publication STP 740, September 1981. 75. Highway Research Board "The AASHO Road Test" National Academy of Sciences — National Research Council Wash­ ington D.C. Publication 954 Special Report 61E 1962. 76. Hicks, R. G. and Monismith, C. L., "Factors Influenc­ ing the Resilient Response of Granular Materials," Highway Research Board, Highway Research Record No. 345, 1971. 77. Lentz, R. and Baladi, G. Y., "Permanent Deformation of Cohesionless Subgrade Material under Cyclic Loading." Proceedings of the International Symposium of Soil under Cyclic and Transient Loading, Swansea, 1980. 78. Casagrande and Fadum, R. E., "Notes on Soil Testing for Engineering Purposes," Harvard University Graduate School of Engineering Publication 268. 79. "Field Manual of Soil Engineering, Fifth Edition by Michigan Department of State Highways, Lansing, Michi­ gan, 1970. 80. Tien-Hsing, Wu, "Properties of Soil Deposits," Soil Mechanics and Foundation Design, Second Edition, 1976. 81. Suzanne M. Lucasse and Charles Ladd, "Undrained Be­ havior of Embankments on New Liskeard Varved Clay," Canadian Geotechnique, January, Vol. 14, 1977. 82. Stermac, A. G. and Lo, K. Y., "The Performance of an Embankment on a Deep Deposit of Varved Clay," Canadian Geotechnical Journal, Vol. 4, No. 1. 83. Metcalf, J. B. and D. L. Townsend, "A Preliminary Study of the Geotechnical Properties of Varved Clay," as Reported in Canadian Engineering Case Records. 84. Milligan, V. M . , ASCE, Soderman, L. G. and Rutka, A., "Experience with Canadian Varved Clays," Journal of the Soil Mechanics and Foundation Division Proceed­ ings, of the A.S.C.E., 1962. 85. James D. Parsous, "New York Glacial Lake Foundation of Varved Silt and Clay," Journal of the Geotechnical Eng. Div., Vol. 103. 86. Bishop, A. W. and Henkel, D. J., "The Measurement of Soil Properties in the Triaxial Test," Second Edition, Edward Arnold (Publishers) Ltd., London, 1962. 210 87. Simons, N. E., "The effect of overconsolidation on the shear strength characteristics of an undisturbed Oslo clay," A.S.C.E. Research conference on shear strength of cohesive soils, 1960. 88. Peterson, R., et al., "Limitations of laboratory shear strength in evaluating stability of highly plastic clays," A.S.C.E. Research conference on shear strength of cohesive soils, 1960. 89. Barksdale, R. D. and Hicks, R. G . , "Evaluation of Materials for Granular Base Courses," presented at the Third Interamerican Conference on Materials Tech­ nology, Rio de Janero, Brazil, August 14-17, 19 72, pp. 134-143. 90. Wonder, C. H., Veatch, J. 0. and Jones, L. R . , "Soil Survey of Michigan Counties, Michigan," United State Department of Agriculture, Bureau of Chemistry and Soils (1919-1977). 91. Seed, H. B., Chan, C. K. and Monismith, C. L . , Effects of Repeated Loading on the Strength and De­ formation of Compacted Clay," Proceedings, Highway Research Vol. 34, 19 55. 92. Seed, H. B., and McNeill, R. L . , "Soil Deformation under Repeated Stress Applications, Conference on Soils for Engineering Purposes, Mexico City, A.S.T.M. Special Technical Publication 232, 1957. 93. Gibbs, H. J . , and al, "Shear Strength of Cohesive Soils" ASCE Research Conference on Shear Strength of Cohesive Soils, 1980. 94. Casagrade, A., "The Structure of Clay and Its Impor­ tance in Foundation Engineering", Journal of the Boston Society of Civil Engineering, 1932. 95. Khosla, R. L . , and Wu, T. H . , "Stress-Strain Behavior of Sand", Journal of the Geotechnical Engineering Divi­ sion, ASCE, Vol. 102, 1976. 96. Personal Communication with Mr. Ben Kenis, DOT, FHA. 97. Lo, K. Y . , and Victor Milligan, "Shear Strength Pro­ perties of Two Stratified Clays", Journal of the Soil Mechanics and Foundation Division, ASCE, Vol. 93, No. SMI, 1967. 211 98. Metcalf, J. B . , and D. L. Townsend, "A Preliminary Study of the Geotechnical Properties of Varved Clays as Reported in Canadian Engineering Case Records", Proceedings of the Fourteenth Canadian Soil Mechanics Conference, Associate Committee on Soil and Snow Mechanics, National Research Council of Canada, Ottawa, 1961. 99. Milligan, V . , L. G. Soderman, and A. Rutka, "Experience with Canadian Varved Clays", Journal of the Soil Mechan­ ics and Foundation Division, ASCE, Vol. 88, No. S M 4 , 1962. 100. Murphy, O. J . , G. Wayne Clough, and Robert S. W. "Temporary Excavation in Varved Clay", Journal of the Geotechnical Engineering Division, ASCE, Vol. 101, NO G T 3 , 1975. 101. Konder, R. L . , "Hyperbolic Stress Strain Response: Cohesive Soils", Journal of the Soil Mechanics and Foundation Division, ASCE, Vol. 89, No. SMI, Proceedings Paper 3429, 1963. 102. Konder, R. L . , and Zelasko, J. S., "A Hyperbolic Stress Strain Formulation for Sands," Proceedings, Second International Pan-American Conference of Soil Mechanics and Foundation Engrg. Vol. 1, Brazil, 1963. 103. Konder, R. L . , and Zelasko, J. S., "Void Ratio Effects on the Hyperbolic Stress Strain Response of a Sand", Laboratory Shear Testing of Soils, ASTM STP No. 361 O h a w a , 1963. 104. Duncan, James M . , and Chan, Chin-Yung, "Nonlinear Analysis of Stress and Strain in Soils," Journal of the Soil Mechanics and Foundation Division, ASCE, Vol. 96, No. SMS, 1970. 105. Chan, Chin-Yung and Duncan, J. M . , "Nonlinear Analy­ sis of Stress and Strain in Soils," Journal of the Soil Mechanics and Foundation Division, ASCE, Vol. 96, No. SM5, 1970. 106. Thomas J. Siller, "Properties of Railroad Ballast and Subballast for Track Performance Prediction" University of Massachusetts, Project Report Concrete Tie Correlation Study, Amberst, Massachusetts, 1980. 107. AASHTO Interim Specifications and Methods of Sampling and Testing Adopted by the AASHTO subcommittee of materials, 1980. 212 APPENDIX A EQUIPMENT A. 1 The Cyclic Triaxial Test (MTS) System A schematic diagram of the cyclic triaxial test equipment is shown in Figure A.I. The test set up is shown in Figure A.2; it consisted of the following components: 01. An MTS electrohydraulic closed loop test system which consisted of the actuator, servovalve, hydraulic power supply, servo and hydraulic controllers. (These ap­ plied the cyclic axial stress to the sample.) 02. A triaxial cell which contained the sample, load cell, and LVDT's. 03. A control box for interfacing the MTS closed loop to the output recording equipment. 04. Output recording equipment which monitored the load (stress) and displacement (strain) during the tests. 05. Minicomputer (digital) loading system. A.1.1 system, which modified the The MTS Electrohydraulics Closed Loop Test System A schematic representation of the MTS electro- hydraulic closed loop test system is shown in Figure A . 3. The system consists of: 01. An MTS hydraulic power sypply, Model 506.02, per minute at 3000 psi. 6.0 gal 02. An MTS hydraulic control unit, Model 436.11, with a function generator. 03. An MTS servovalve controller, Model 406.11, with and DC feedback signal conditioning. 04. An MTS actuator, Model 204.52, capacity with a Model 252.23A-01 servovalve. 05. of AC 5.5kips A Strainsert load cell, Model FL5U-2SGKT, maximum capacity 5000 pounds. The system operates as follows: 01. A command signal (voltage) from the function generator in the 425.11 (see Figures A . 2 and A . 3) or other exter­ nal source is input to the 406.11, where it is com­ pared to the feedback signal (voltage) from a trans­ ducer (e.g., a load cell or LVDT) monitoring the re­ sponse of the specimen in the closed loop. 213 Strip Chart Recorder Digital Multimeter Oscilloscope Function Generator Hydraulic Power Supply Servo Controller Hydraulic Controller Switching Panel -Load Frame Triaxial Cell Load Cell M in i­ computer' 214 □ Actuator Servovalve FIGURE A.l Schematic of Cyclic Triaxial Test Equipment. FIGURE A. 2 Test Set-Up. 215 z z / ^ z /.// / / / / Summing Jun ction LVDT Command Signal 406.11 Control 1er Load ■+ Cell Function Generator 436.11 Hydraulic Control 1er A m p l i fi e a Di f f e r e n c e Between Signals 506.02 DoubleSided Piston Servoval ve Hydraulic Power Supply A ctu at or FIGURE A . 3 Schematic of MTS Electrohydraulic Closed Loop Test System. 216 APPENDICES APPENDIX A 02. The difference error between the two signals is ampli­ fied and applied to the torque motor in the servovalve coupled to the actuator. 03. The torque motor drives a pilot stage which in turn drives a power stage of the servovalve which directs hydraulic fluid under pressure to one side or the other of the double-sided actuator piston to cause the actuator to move. 04. The movement of the actuator causes the specimen to respond in such a way that the transducer monitoring the specimen "feeds back" a signal which is equal to the command signal. The speed at which these steps are executed causes the sample, for all practical purposes, to be subjected to a loading equal to the command signal. A more complete treat­ ment of closed loop testing theory is given by Johnson A.1.2 [58]. The MTS Servovalve Controller Model 4 06.11 The front panel of the 406.11 controller is shown in Figure A . 4. The controls indicated by the circled num­ bers are discussed in order below. 01. The panel voltmeter has two functions. First, it can be used to indicate the error between the command sig­ nal and the feedback transducer. Second, it can be used to indicate the voltage output of feedback trans­ ducer XDCRl, XDCR2, or the servovalve drive. (The servovalve regulates the flow of hydraulic pressure between the hydraulic power supply and the actuator.) For the cyclic triaxial tests a negative error means compression and positive error means tension to the specimen. The panel voltmeter was most often used to monitor the error between the command signal and the feedback transducer before applying the hydraulic pressure. To insure that the actuator does not move when hydraulic pressure is applied, the'error signal must be zero. 02. The Set Point control provides a static command signal (voltage). There are 1000 divisions on the Set Point dial. Each division is equivalent to 20 mv. A posi­ tive command signal (Set Point between 500 and 000) produces actuator piston compression; a negative com­ mand signal (Set Point between 500 and 1000) produces actuator piston extension. When the feedback signal is from the LVDT in the actuator, Set Point is used to move the actuator up or down even with no specimen in the loop. When the feedback is from any other trans­ ducer, the Set Point control establishes a static level 217 zito fXCiTAVION 218 FOBS SHICT IKII.it•atIII FIGURE A. 4 MTS Servovalve CONTROLLER Model 406.11. of response of the specimen. With feedback from the load cell, Set Point was used to apply static compres­ sive loads for the static triaxial tests. Set Point was also used to apply static load of one-half a, for the cyclic triaxial tests. 03. The Span control established the amplitude of a com­ mand signal waveform during cyclic loading. The am­ plitude is about the Set Point level. There are 1000 divisions on the Span control dial. Each division is equivalent to an amplitude of 10 mv. The Span was used to set the load amplitude during cyclic triaxial testing. 04. The Gain control establishes the rate and accuracy of response of the actuator ram to the command signal. The Gain control is therefore used to improve the re­ sponse of the closed loop test system, which includes the specimen. To set the system at optimum Gain, the sample was subjected to a low frequency, low amplitude square wave loading. The feedback signal was monitored with an oscilloscope. The Gain control was turned clockwise until small oscillations were observed at the peak of the square wave, as shown in Figure A.5b. At this point, the Gain was reduced until the oscilla­ tions stopped, as shown in Figure A.5c. The Rate (de­ scribed below) was adjusted to eliminate "overshoot" at the corner of the peak of the square wave, as shown in Figure A.5c. 05. The Rate control helps prevent "overshoot" at high Gain settings. The Rate was adjusted after the Gain had been set as described above. 06. The AP control is operative only when the 406 is equipped with option B. Provides added stability in some systems by addition of the signal from a differ­ ential pressure (AP) transducer across the actuator cylinder. 07. The DITHER trimmer controls the amplitude of a small cyclic signal applied to the servovalve coil to pre­ vent servovalve silting. 08. The Error Detector (ED) trimmer adjusts the percentage of error at which the Error Detector circuit sets, turning on the ERROR indicator and opening the fail­ safe interlock. When ERROR lights, all other limit and error detecting circuits, including those on any other channels, automatically become inoperative. 09. The Cal factor, Zero, and Fine/Coarse controls provide adjustment of the signal for transducer XDCRl. In general, the transducer used with XDCRl was an LV D T . Cal Factor was used to adjust the voltage output from the LVDT. The Cal Factor was adjusted to obtain ± 10 volts when the core of the LVDT moved 0.100 inch. The 219 \ y i) Overdamped, Gain too low r w i n )) Underdamped, Gain to high n — :) Optimum Gain FIGURE A .5 Gain and Stability Adjustment. 220 Zero control introduces an electrical offset to the signal from the LVDT. It has 1000 divisions on the dial. A Zero control setting of 500 corresponds to zero voltage offset. The Zero control provides nega­ tive electrical offset when it is between (000) and (500) and positive offset when it is between (500) and (1000). The Fine/Coarse switch determines the operating range for the Zero control. When it is selected to Fine, the electrical offset from the Zero control per division is lower than when it is selected to Coarse. In this experiment, high electrical offset is necessary; therefore, the switch was selected to Coarse. 10. Program is used to input an external source of com­ mand s i g n a l . . 11. The Excitation, Zero, and (xl/xlQ) switch provides adjustment of the signal for transducer XDCR2. In general, the transducer used with XDCR2 was a load cell. The Excitation was used to adjust the voltage output from the load cell. It has 1000 divisions on the dial. The Excitation was adjusted to obtain 20 mv per pound of loading using a 5 Kip load cell. The Zero control introduces an electrical offset to the signal from the load cell. It has (100) divisions on the dial. A Zero control setting of (500) corresponds to zero voltage offset. It provides positive electri­ cal offset when it is between 500 and 1000. The xl/xlO switch determines the operating range for the signal from the load cell. When in the (xlO) position, the signal from the load cell is amplified 10 times that of the xl position. The xlO position was used in the laboratory investigations phase of this research pro­ gram. By selecting the xlO position, the 5000 pound load cell functioned effectively as a 500 pound load cell. This was desirable because of the relatively small loads used in the testing program. High output signals could thus be obtained without the danger of the load cell being overstressed. 12. The Feedback Select position determines which feedback signal will be used in the closed loop test circuit. This may be the signal from Transducer Conditioner 1 (XDCRl), Transducer Conditioner 2 (XDCR2), or from an external transducer conditioner (EXT). For the current research it was desired to control the load amplitude. Therefore, Feedback Select was placed in position XDCR2 to feedback the signal from the load cell to use in the closed loop circuit. 13. The Limit Detector determines which transducer condi­ tioner (XDCRl or XDCR2) signal will be monitored in the "failsafe" circuit. If the switch is set on INTKL^ 221 the failsafe interlock circuit will turn off the hy­ draulic power supply when the signal voltage is greater or lower than a selected range of voltage. If the switch is set on IND, the Limit Detector will indi­ cate, by the upper or lower red light on the panel, when the signal voltage is greater or lower than a selected range of voltage. 14. The Upper and Lower limit controls are used to select the range of acceptable voltage. The Upper limit is set at the most positive or least negative limit. The Lower limit is set at the most negative or least positive limit. Each limit dial has 1000 divisions corresponding to 10 volts. 15. The Reset is used to extinguish the indicator light when the signal voltage level is within the selected voltage range. If the light for the Limit Detector is still lit with the failsafe interlock circuit in operation, the hydraulic power supply cannot be en­ gaged. Therefore, before applying the hydraulic power supply, the light has to be extinguished with the Re­ set button. If the switch is in the off position, the failsafe circuit is inoperative. A . 1.3 The MTS Controller Model 436.11 The front panel of the 436.11 is shown in Figure A.6. The controls indicated by the circled number are dis­ cussed in order below. 01. The Power control applied AC operating voltage to the control unit. 02. The HYD Pressure Low or High or Hydraulic Off control is used to turn the hydraulic power supply on and off. 03. The Program Stop or Run control is used to start or stop generation of a command signal waveform. 04. The HYD INTLK (hydraulic interlock) switch indicator is associated with abnormal condition sensors, such as the failsafe circuits in the controller and the over­ temperature and low fluid level conditions of the hy­ draulic power supply. The indicator will light when any such condition occurs. At the same time, the hy­ draulic pressure is automatically removed from the servovalve and the programmer stop. When the abnormal condition has been removed, the HYD INTLK should be extinguished by pushing it and holding it to allow the system to be restarted without removing the abnormal condition, unless that condition is related to the hydraulic fluid overheating (overtemperature) or is at low level. 222 Optional mtmtu m SSm SSm itt FUNCTION GENERATOR MTS ^.3B C Q i •FREQUENCY- COUNTER INTLK hop 223 POWER EMERGENCY STOP COUNT MRUT WAVEFORM— * A, iT I r\ t j i COUM' FIGURE A. 6 The MTS Control Unit Model 4 36.11. 05. Emergency Stop is used to stop the hydraulic power supply and generation of the command signal waveform. Emergency Stop and Hyd Off have the same effect. 06. The Count Input control is used to select the method of controlling the number of cycles during a test. If Program is selected, the duration of the test must be present. 07. The Counter indicates the number of elapsed cycles in increments of ten. 08. The End Count indicator lights when the 'upper counter register reaches the preset count. 09. The Counter INTLK switch determines whether an END COUNT causes complete system shutdown, including re­ moval of hydraulic pressure (STOP-HYD OFF position), or only program stop (STOP position) After the re­ quired number of cycles has been reached, the pro­ gram will automatically stop and the End Count will light up. If the Off position is selected, the pro­ gram will run either until the operator pushes Stop or until the Failsafe system is triggered. A.1.4 Control Box The control box was built at Michigan State Uni­ versity. The front panel of the box is shown in Figure A . 7. The control box allows for switching between two complete MTS electrohydraulic closed loop systems so that output re­ cording equipment, can be shared. Also, electronic circuits are incorporated which can be used to offset and amplify output signals so that they are compatible with the input requirements of a minicomputer. Provision is also made for recording the unadultrated output signals. Voltage offsets are also provided to offset large constant voltages so that amplitudes of cyclic signals can be recorded with better resolution. A . 1.5 Output Recording Equipment The following equipment was used to monitor the load cell and LVDT during the testing program (see Figure A.2). 01. A Sanborn Model 150 strip chart recorder with two DC Coupling Preamplifiers, Model 150-1300. Both load and deformation were recorded directly on the strip chart recorder. 224 FIGURE A . 7 Front Panel of-the Control Box. 225 02. A Simpson Model 460 digital voltmeter. The voltmeter was used to monitor both load cell output and LVDT output during the experimental set up. The voltmeter was also used to monitor both load and deformation during the static triaxial tests and to monitor load as static load of one-half was being applied. 03. A Tektronic Model D13 dual beam storage oscilloscope with two 5A18N dual trace amplifiers. A. 2 Minicomputer System The LSI-2 minicomputer system shown in Figure A. 8 was used to control the signal and frequency output of the MTS controller. A detailed description of the system and program is discussed below. A . 2.1 Waveform Shaper Circuit An interface between the LSI-2 minicomputer from Computer Automation and the MTS 436 Control Unit was designed to generate waveforms of the shape shown in Figure A . 9. The frequency range of this signal varies from 0.01 Hz up to 20 Hz. The waveforms are generated by means of the generator associated with the control circuits of the MTS 436 Control Unit. This generator is triggered "on" and "off" by means of the minicomputer and under complete software control. All information required by the computer is typed on a tele­ type during an initialization phase. A . 2.1.a Characteristics of the MTS 436 Signal Generator The signal generator delivers triangular, rectan­ gular, or sinusoidal signals with peak amplitudes of 10V. No attenuation circuits are provided to adjust the ampli­ tudes to different levels. Frequencies ranging from 2 KH2 down to 0.01 Hz are available. When triggering the "run" switch (either on the front panel or by means of the pro­ grammed input on the rear panel), the generator begins de­ livering a signal that starts at zero volt and stops at zero volt at the end of the last half-cycle during which the "stop" switch (either on the front panel or under program control on the rear panel) has been triggered. 226 Figure A . 10 FIGURE A. 8 F r o n t P anel of the M i n i c o m p u t e r . 227 i«— I n I .'A A A A A jA A A j IDelay 1 1 J 1 j f ------------- 4s------------ 4»----- m ------> 1 N, half cycle I | One Delay 2 N2 n ( half cycles cycle J FIGURE A.9 Generated Waveforms. N cycles IIRun" is triggered here The signal stops here if "stop" is triggered at any time during At — 1>)At !*— FIGURE A. 10 Start and Stop Generator's Outputs. 228 illustrates this mode of operation. The same operation holds, whatever the shape of the signal, and/or rectangular signals. for the triangular A selector on the front panel allows the user to select positive-starting loading or neg­ ative-starting unloading signals. To generate the type of signal represented in Figure A.11 from the previously mentioned considerations, it is obvious that a positive-starting signal in this case) (sinusoidal should be selected and that the generator's "Run" and "Stop" circuits should be triggered at the times indicated in Figure A . 11. It should be noted that: 1) if the stop is not triggered the generator goes on delivering a sinusoidal sig­ nal, the frequency of which, in this case, is that read on the frequency selector on the front panel; 2) the word "frequency" herein is referred to as the frequency of the equivalent sinusoidal periodic signal even if the generated signal is not periodic. Also, this frequency is equal to (1/T) where T is the period, as shown in Figure A . 12. Fur­ ther, this frequency should be distinguished from the "fre­ quency of repetition," which is the rate at which the signal frames repeat in time. The "Run" and "Stop" circuits in Figure A . 11 will be triggered under program control. A.2.1.b Triggering the Circuits on the MTS 436 Rear Panel Figure A.13 shows the typical signals that should be applied to the triggering circuits. "Run" and "Stop" may be triggered as follows: 01. The user has access to the Run triggering circuit by means of connectors T15A, T15B, and T15C on the rear panel. On any of these connectors, plus C and F have to be used to trigger the "Run," i.e., start generating a half-cycle (see Figure A . 14). It should be noted that pin F is ground (signal ground) and pin C is nor­ mally open, and so is the connection to the "Run" switch on the front panel. The voltage, when pin C is open, is around 11 volts (measured with a voltmeter). In order to trigger the "Run," one has to short-circuit 229 / w \ / v 4 - 4 \ _ _ t trigger t/2 "RUN" -> > -------trigger "STOP" / v v \ L U 4 \ ' k Jt . 1 1i 4i 4i j. FIGURE A . 11 Triggered Time. t/2 1 T frequency = f FIGURE A . 12 General Signal Output from the MTS System. 2 microseconds +11 volts r---------- 1 i . "Run" circut signal between C and F on J15A (or J15B or J15C) +11 volts "Stop" circuit signal between A and B on J14A or J14B 2 microseconds FIGURE A. 13 Typical Signals for Triggering the Circuits. 230 +5v Computer 370 ft SEL:12,1 RUN +5v +5v 390 ft MTS 290 ft mono­ stable > 560 ft — W— J15A CL 7406 :18 twists/ , foot (or 7416) 330 ft 7404 74121 'MTS R 50K +5v 390 ft +5v 390 coihputer I +5v r r 220 ft nono3table SEL:12,6 STOP ma I 56K 7406 (or 7416) J]_330 ft |18 twists/i foot , 7404 74121 manual computer R 50K FIGURE A . 14 Schematic Electrical Diagram of the Driving Circuit. J14A C and F during a time t. whose minimum value is only limited by the time-constant of the network-(R17, C5, R16, C4) . Experimental tests have proven that this time should not be less than 2 microseconds to ensure that triggering occurs. 02. The user has access to the "Stop" triggering circuit by means of connectors T14A and T14B on the rear panel of the MTS 436. As can be seen in Figure A . 14 on both of these connectors, pins A and B are normally shortcircuited and connected to ground through the front panel "Stop" switch. Pushing the front panel "Stop" switch, as well as breaking the short-circuits between A and B, will cause T14A and T14B connectors to trigger the "Stop" circuit. Due to the time-constant of the network (RI1, Cl, R12, C 2 ) , the circuit must be kept open for at least 2 y '2 to ensure "Stop" triggering. It should be noted that when triggering the "Run" and "Stop" citcuits under program control, the program must be written is such a way that the "Run" and "Stop" triggering signals never overlap. In other words, "Stop" should only be triggered after the "Run" signal has returned to 11 volts. This requires a software delay in the program. A.2.1.C Circuits Used to Generate the Signals Previously Mentioned The output stages of the driving circuits are made of 2N 222 transistors. These transistors are triggered by monostables with adjustable output pulse widths. As men­ tioned before, pulse widths of at least 2 y's are needed to ensure that triggering always occurs. Here they have been adjusted to 5 y's by means of the internal elements R and C. Figure A.15 gives the typical signals at the outputs of the monostables and the corresponding transistors. Figure A . 15 gives the complete electrical diagram of the driving cir­ cuits. The two functions are driven at the SELECT lines of the computer, available on connector Tl. Figures A . 16 and A . 17 show the different connec­ tions between the apparatus. foot cable is used. For all connections, 18 twists/ As can be seen on these figures, a DPDT switch is used to switch from Program-Control Mode puter Mode) to MANUAL MODE. (or Com­ This allows the user to trigger 232 1+ 5V A + 11V B " I / + 5V a _____c + 11V r \ D software delay LEGEND A Output of "RUN" Monostables B Output of "RUN" transistor C Output of "STOP" monostable D Output of "STOP" transistor FIGURE A. 15 Typical Output of the Monostables and Transistors. 233 + 5v L *+ 5 v 18 twists/ft Q\ purple ::^xmxxoxcl J1 +5v 390 n i 'oxue the j' zDoc11 oho&pooc!::: r blac 7406 (or 7416) 7406 (or 7416) !! II iI -» I DRIVING CIRCUIT Diagram blacjc J I< Ii orange _ _l >I ii i igreen Dcocwoooocxjoocxooc^ ^ i Towards 1i ii Box ■ir7wc: blue ti . !kfl-uei* ^00 ii i ii jgrey orang Spurple black green L_ " D O O O C C ~ J15A (or J15B or J15C) 2=21 RUN CTB STOP MTS SYSTEM 234 J14A (or J14B) Connection A26 >.. ,+ 5v Apparatus. blue w Eh D eu a o u 7406 (or 7416) 7406 (or 7416) Between black A . 16 black FIGURE SEL: 12,1 >• SEL:12,6 390 390 n A31 orange grey +5v 280 ft mono-■ stable green 560 £2 50K 330 n purple 2N2222 RUN 74121 7404 computer "Tblue manual. manual +bv computer 280 fi 2yF 330 .monostable 2N2222 50K 56K 0, 7404 74121 STOP FIGURE A . 17 Connection Diagram in the Waveshaper Box. the "Run" and "Stop" on the front panel of the NTS 436, without disconnecting the computer from the T14A and T15A connectors. A.2.1.d Software The program has been written in the assembly lan­ guage of the LSI-2. It has been stored on diskette by means of the SIGMA Loader. SIGMA is also on diskette and is loaded into the minicomputer by means of the "autoload" feature. The program has been called WVSHPR (standing for "waveform shaper"). After switching the computer on, to execute WVSHPR, SIGMA must be loaded from diskette into the mini­ computer by means of autoload. Then SIGMA is used to load WVSHPR from diskette and to link it with TUP package). (the utility When the program is loaded, to begin the exe­ cution, one must input the starting address (normally taken as X ,0200') by means of the console register into the P register. When putting the minicomputer into the "Run" mode, the initialization phase starts and the user has to input all the required values (Nl, Delay 1, N2, Delay 2, frequency of the "equivalent periodic signal"). The pro­ gram then computes the delay D corresponding to the given frequency, by means of two different algorithms, one for the frequencies above 1000 mHz, the other for those under 1000 mHz. These algorithms are needed because no floating point routines are available. The execution then continues by giving the user a few instructions. The program then waits for the user to input a "Go" message. This message starts the triggering of the MTS system, i.e., the signal to be generated. The execution can be stopped at any time by push­ ing the "Stop" switch on the console and then can be re­ sumed by switching the computer from the "Stop" mode into the "Run" mode. Figure A . 18 shows a flow-chart of the program. A listing of the program is given hereafter. 236 ENTRY POINT I " INITIALIZATION INPUT Nl,DELAY1, N2, DELAY2 r 7 INPUT FREQUENCY YES FREQUENCY 1000 m H z ^ > i DO APPROPRIATE FREQUENCY TRANSFORMATION INTO DELAY D DO APPROPRIATE FREQUENCY TRANSFORMATION INTO DELAY D T GIVE INSTRUCTIONS TO USER NO "GO" SIGNAL RECEIVED? YES N=N1 TRIGGER "RUN" 3 H N=N-1 DELAY OF 3 S TRIGGER "STOP" DELAY D NO r__ < £ ° 2 > YES YES ---- !' ------------------ V WAS ET Nl? NO t DELAY Dl DELAY D2 N=N2 FIG U RE A . 18 P r o g ra m F lo w C h a r t . 237 > ceei £002 0003 0004 £00 5 £006 0007 0006 £009 £010 001 1 CO 12 0013 001 4 £015 £016 001 7 0016 0019 0020 0021 £022 G023 0024 002 5 0026 £027 £026 0029 £030 0031 £022 £033 £034 £2 3 5 0036 0037 £038 £039 QieAZ £0 41 ££42 , 00 0 G - 000 G 400 5 0A00 £116 0F00 F90O 81 A D C6BD ££05 £0 0 6 £F££ F900 0££7 blAb 00 F F . 0006 0009 0FG0 F900 £00 A 61AA 00£E EADC 000C 0F££ F9 S 0 0£0 D 8 1A D 0110 000 E 000F C6BD 0010 0F00 001 1 F900 81 A S 0012 0101 0F00 0013 0014 F900 6 1AA EAD4 001 5 0F00 001 6 £017 F900 61 A D 0018 0110 C6BD 0019 00 1A ’ 0 F 0 0 £0 1B F90G 81A8 00 1C 0112 001 D 0F00 G0 1 E F900 81AA EAC9 C01F 0e2G 0F00 0021 F900 8 1A D 0022 0110 £023 C6ED 0024 CF00 F900 ££2 5 6 1A 8 0114 0026 0000 £001 0002 0003 £004 NAM PEL VVSHPR EQU INIT CIE E1N ZAX SUM JST LAP SVM JST VVSHPR e .s *CRLF •s « LOCI STX SVM JST Nl •s • ASK F O R K2 ASK FOF. D E L A Y 2 DELAY 1 *0TL STX SUM JST DELAY1 * I DEC *CRLF •a • *0TL DATA SV M JST LOC3 STX SVM JST N2 * I DEC *CRLF 1S * sum 238 FOR -*CRLF L0C2 ZAR La p ASK * 1D EC DATA SVM JST ZAR LAP SVM JST FOR Nl *0TL DATA SUM JST ZAR LAP SVM JST ASK - JST *0TL DATA L0C4 CC 43 0044 0327 0028 G0 4 5 £04 6 0647 0629 002A 602B 00 48 0049 G0 50 0051 602C 062D 602E 662F 00 52 60 53 30 54 6036 6631 0632 00 55 80 56 00 57 005 8 00 59 6068 8061 0062 0063 0033 6634 0035 0036 0037 0038 0039 G03A 663E 003C 0G3D 663E G03F 60 46 06 41 8042 0043 0644 0045 6846 0847 6648 60 49 004A 804B 004C 004D 004E ■C04F 00 58 00 51 00 52 00 53 06 54 00 55 0656 0057 00 64 006 5 06 66 6067 0068 0069 0670 6671 0072 6673 0074 0075 0676 0077 0078 6079 0080 0081 0082 0083 0084 008 5 0066 CFC0 F986 81AA EAC1 6F00 F900 8 1A C 6110 C6BD 0F60 F900 81A8 6 195 6F00 F900 81AA EABA G036 D2C2 F201 F210 0118 E2 C 0 1E G G 1970 00 EE 6110 1960 0GF6 1560 6030 92B2 9Aa E C719 9AAB 9AA9 F216 6118 E2A4 1E00 1970 00F7 EAA1 0118 E2A9 1B00 1970 60 EF 61 16 1960 00F6 1B86 0C30 SVti JST STX SVM JST ZAR LAP S VM JST X2 1 DELAY2 *CP>LF •*s • - *0TL DATA SVM JST L0C9 STX TXA CMS JMP JMP ZAX LDX' LLL DVD FREQ ZAR MPY XI *1 DEC LLR TICA SUB STA LAM STA STA JMP ZAX LDX LLL DVD STX .ZAX LDX LLL DVD ZAR MPY LLR TXA * I DE C TH X2 XI TTH 1 FR E Q . TEN 1 EIGHT TCNT 25 TFwTC TRTC6 A FR EQ 1 HUN NFR FTH 1 NFR TEN 1 0087 0088 0089 O09C 0091 0092 0093 809 4 0058 00 59 00 5A 00 5E ease 005D 00 5E 005F 009 5 8096 00 6 0 0061 .0097 08 56 .8099 0100 0062 0063 0864 00 65 0101 0182 0103 0866 0067 00 6 8 01 04 0105 0106 0107 0069 806A 00 6E 006 C 8108 0109 81 10 ee6D 0Q6E 206F 81 1 1 81 12 8113 81 14 0070 0071 0072 0S73 81 15 811 6 81 17 0074 0075 2076' £1 18 01 19 8128 2121 0877 0078 0079 0G7A 0122 0123 012 4 S87E 007C 007D 812 5 81 26 0127 0128 0E7E 007F £080 £081 92A2 0318 9A95 9A9 5 B297 9A94 0F00 F900 61AD 0F08 F900 81 A D 0110 C6E5 0F00 F900 81A8 0125 0F00 F90 6 8 IAD 0110 C6AE 0F0O F900 8 IAS 013F 0F00 F5G0 8 1A D 8118 C6AE CF00 F90 B 61A8 01 54 0FG0 F980 81AD 0110 C6AE 0F08 F9B0 81A8 G16E CFC0 F90 0 8 1AD' 8110 C6AE 0 F 80 F9 08 81A8 A SUEs NAP. STA STA LDA STA S VM JST *CRLF SVM JST *CRLF ZAP LAP SV M JST DATA S VM JST ZAP. LAP SVM JST DATA SVM JST ZAR LAF SVM J-ST DATA SV M JST ZAR LAP SVM JST DATA s ™ JST ZAR LAP SV M JST 240 P S D EL TF.TCG TRTC ONE TCNT ; •; • *0TL LCC5 *CP.LF *0TL L0C6 *CPLF •• • ' **OTL L0C7 *CRLF •. » *OTL L0C7A *CRLF «• • *OTL 0129 01 30 0131 0282 2083 0084 0132 Cl 33 013 4 0085 0086 0087 0135 0136 0137 0088 0089 008A 01 38 0139 Cl 40 0141 0142 008B 208C 208D 028E 028F £143 0144 £1 45 0146 0147 01 48 0149 2150 01 51 01 52 21 53 01 54 015 5 01 56 21 57 0158 £159 2160 2161 2162 2163 2164 ei65 £1 66 0167 6168 0169 0170 0171 .2172 017 3 01 7 4 £175 0176 0177 0290 0091 2292 •0293 2094 0095 0096 2397 £098 0399 009A O09B 009C 009D 009E G09F 00A0 60A 1 00A2 20m 3 2CA4 00A5 00A6 0CA7 00A8 -G0A9 20AA 02A8 00AC 02AD 00AE 00AF 00E2 02E1 00B2 0164 2F20 F9 C 0 81AD C6AE 0F00 F900 81AB 01AE 4006 B 100 01AE D271 F62E F62F 0F20 F922 81 A C B2S7 9A53 E26 1 9A53 4091 E24F 00 00 9A4D C 7 50 9A52 E2 61 9A4A B257 F221 4296 C752 9A4E B244 01 50 9A42 B24F F219 B24A 9A48 9A43 E23C 01 50 9A3A E245 F21 I B236 D243 F6 1 C F61D B233 DATA - SVM JST LAP SVM JST DATA CI D LDA A2 Al B , 51 E2 B3 • L0C8 •* C R L F «• • FOR INPVT * IKL BFR1 BF R1 CMS JMP JMP S VM JST GO A A LDA STA LDA STA S EL LDA DAR STA LAM STA LDA STA LDA JMP SEL LAM STA LDA IAR STA LDA JMP LDA STA STA LEA IAR STA LDA JMP LDA CMS JtlP JMP LDA N1 N ONE N0 : 12/1 N 241 WAIT IS IT "G O" ? NO NO YES *CRLF N 80 RTCCT BEG NN ONE C2 : 12, 6 80 RTCCT NN. NN ONE C2 TRTC TRTC0 RTCCT NN NN TCNT C2 N ZERO B E NN NO;CONTINUE NO;CONTINUE Cl 78 2179 £186 ciei 2162 0183 0184 0185 0186 0187 0188 0169 C190 0191 0CB3 GGE4 60E5 6626 60E7 00B8 00E9 00EA 00BE 0CBC 00ED C0BE 00BF 00C0 ei92 S6CI C0C2 0193 0194 06C3 0195 S0C4 06C5 0196 0197 00C6 0198 6GC7 0199 00C8 0200 06C9 0201 00CA 02 0 2 00CB 00CC 02 6 3 0204 00CD 00CE 020 5 02CF 020 6 60 D 0 0207 0208 00D1 0269 00D2 G210 60D3 021 1 GCD4 0212 00C5 62 1 3 • 0 G D 6 0214 60 D 7 02 1 5 e£D8 0216 00D9 60 DA 6217 £2 1 8 66CE £219 £6 DC £220 00DD 0221 00DE 0222 60DF 02 2 3 00 E0 00E1 0224 0225' 00 E2 0226 00E3 0227 00E4 02 2 8 00E5 0229 0£E6 £230 0 0 E7 CI S C 9a 3 1 C764 9A39 9A34 B22E D239 F2 0 3 F2 0 2 B22E F2C 1 E22E 9A2D 4606 4044 46 4 2 40 4 0 0A00 F600 .F60 6 F31E F62A F623 F6 1 C E21E D22 6 F2 0 2 F20 1 F63F 00D0 9A15 £216 9A1 1 F640 0800 E219 9A14 32 14 06D0 9A12 D2 1 7 F204 F203 B609 0150 F201 B60C 0150 9E0E F70F IAR STA LAM STA STA LDA CMS JMP JMP LDA JMP Cl LDA C2 STA DC C ID SEL - SEL SEL EIN WAIT JMP JMP BR JMP JMP JMP D2 LDA CMS JMP ■ JMP JMP DAR E STA LDA STA JMP CLK ENT LEA STA LDA DAR > STA CMS JMP JMP LCA IAR JMP CL1 LDA CL2 IAR STA RTN N RES NN RES N0 RES 242 NN 106 TP.TCC RTCCT IJ0 ZERO Cl Cl DELAY2 C2 DELAY1 COUNT 6* 4 8*2 6* 0 I N I T I A L I Z E F.TC D0 *NN B1 B2 B3 N0 ZERO E E WAS IT D E L A Y 1? Al N0 • N2 N £ TRTC0 RTCCT COUNT COUNT ZERO CL1 CL1 CLK CL2 CLK „• CLK CLK 1 1 1 IS C O U N T - 0 ? 6231 £232 0233 0234 023 5 02 3 6 0237 0238 0239 0240 0241 C242 02 43 2244 G245 2246 0247 0248 2249 0250 0251 0252 0253 0254 02 55 RES RES RES RES RES RES RES RES RES RES RES DATA DATA DATA DATA DATA DATA DATA DATA DATA DATA TEXT TEXT TEXT L0C2 TEXT 1 1 1 1 1 1 1 1 1 1 G 1 8 16 106 1060 50 0 0 2G000 :069E 3R •GO' *I N ' *N1 * ' • LOC4 TEXT - II TEXT - -9 L0C3 CM 0257 0000 0601 £008 606A 00 64 03E8 1388 4E20 669E 60C8 C7CF C9CE C EB 1 AGED C4C5 CCC1 D9EI A0C9 CEA0 C8D5 CEC4 D2C5 C4C4 CSD3 A0CF C6A0 C1A0 D3C5 C3CF CEC4 A8BD CEE2 A0ED C4C5 CCCi D9 B2 A0C9 CEA0 C6D5 CEC4 D2C5 C4D4 N1 N2 DELAY1 DELAY2 P.TCCT COUNT FR E Q NFR TRTC0 TFITC TCNT ZER O ONE EIGHT TEN HUN TH FTH TTH R5DEL BR0 GO IN LOCI' ' • 02 56 06 E8 £6 L9 00 EA 00 EB 06EC 00ED 00 E E 00 EF C0F0 Q0FI 8GF2 C0F3 • Z0F4 66 F5 v 00F6 00F7 00F8 00F9 00 FA £6FB 00FC 00FD 00FE 00FF 0100 0101 0102 0103 0104 0105 0106 0107 0108 0109 010A 010B 010C 610D 0 10 E 01GF 6110 01 1 1 0112 0113 6114 6115 6116 0117 0118 0119 0 1 1A 01 IE 0 11C £261 £262 G263 £ 1 52 Cl 53 Cl 54 0155 fc1 56 0157 0158 0159 01 5A 0 1 SB G15C 015D 015E 01 5 F 0160 01 61 0162 0163 0164 0165 0166 0167 0168 0169 016A G16E 016C 016D 016E 016F 0170 0171 0172 0173 0174 0175 0176 0177 0178 0179 017A 017E 017C 017D C17E 017F 0180 01 81 0182 0183 0184 0185 0186 CCC5 ACAE D4CF A0D2 C5D3 D4C1 D2D4 ACA0 DCD5 D4 A 0 A2E0 E2E0 ECA2 A0C9 CEE4 CFA0 C3CF CED3 CFCC C5A0 D2C5 C7C9 D3C4 C5D2 A0AE D3D7 C9D4 C3C8 A0AA D7D2 C9D4 C5AA A0CF CEEE A0C0 D2C5 D3D3 A0AA D0AA EEA0 D3D7 C9D4 C3C8 ACAA D7D2 C9D4 C5AA A0CF C6C6 A0AE D0D2 C5D3 D3A0 L0C7 TEXT L0C7A TEXT L0C8 . TEXT 244 02 64 0265 0266 0267 02 6 8 02 69 0270 0271 0272 0273 e27 4 027 5 027 6 \ 0277 £278 0279 0000 0187 0166 '0169 016A 6 1S B 0 18C 818D 018E &18F 0190 01 9 1 0192 0193 0194 0195 0196 0197 0198 ei99 C19A 019E 019C 019D 019E 019F 01A0 01A1 01A2 G 1A 3 01A4 01A5 01A6 01A7 01A8 01A9 01AA 01AE 0 1A C 0 1A C G1AE Cl EG £0 1 E 00 IE 0018 £016 001A £01A AAE2 C5D3 C5C4 AABB D3D7 C9D4 C3C8 A0AA D3D4 CFD0 AAA0 CFC6 C 6EE A0D0 D2C5 D3D3 A0AA D2D5 CEAA A0AE C6C2 C5D1 D5C5 CEC3 D9A0 C9CE A£CD C9CC CCC9 ADC 8 C5D2 D4CA A0BD v L0C9 TEXT-. OTL OTT 1 DEC no. IK B CRLF BFRl BFR2 REF REF REF REF REF REF RES R ES ABS JMP 50 50 : IE INIT ABS IMS : 16 RTCCT ABS JST : 1A CLK FI 00 0000 C90G 08 EC F9 0 0 00 D5 - EN D ERRORS 245 A BFP.2 El CL1 Cl D0 FREQ I DEC IN L0C4 L0C7A NFR TJ1 OTT TEN TTK ZERO 005E 01E6 669E O0E1 60BE 00 C 0 00 EE 01AA S2FE 0114 0.165 O0EF 00 E8 01A9 O0F6 00 FA 00F3 AC­ 006E ER 0OC8 52 60A6 CL2 60E2 C2 665F D2 06C5 FT H 00 F9 IKE 01 AC LOCI 60FF L0C5A 012F LOC'7 0154 NN 0£E6 N2 00 E 9 R S D E L ' ££ F5 Tri 00 F 8 00 0 6 WVSKPR A1 . . BF.0 53 COUNT DELAYI EIGHT GO IKL L0C2 L0C5 L0C6 N ONE RTCCT TP-TC XI 6090 00 FC 00AE 06 ED 66EA, E0F5 6GFD ' 01A5 6 101 0125 £164 66 £5 ££ F4 06 EC G6F1 £048 EFF1 E CLK CRLF DELAY2 E h UN INIT L0C3 L0C6 ' . L0C 9 ' NG QTL TCNT TF.TC6 X2 SIAE £094 OSES 6 1A D £ 0 EE 6GD6 S£F7 £060 £112 Gl3r 6195 '06 E7 £1a 2 6£F2 62 F £ 0638 246 A.2.1.e Procedures to Run the Program 01. Turn Main Power Switch on. 02. Turn MTS 436 on. 03. Press Stop switch on the computer's console to put the computer into the Stop mode. Make sure light indicator is on. 04. Load Waveshaper program from diskette into memory by doing the following steps: a. Make sure computer is still in Stop mode Stop light indicator is o n ) . b. Press SREG/DATA switch on the right of the con­ sole until the corresponding light indicator is on. c. Put "6" in the sense register. "0110" should appear in the four least significant bits of the console data register light indicators. d. Press SREG/DATA switch off should be o f f ). e. Press SENSE switch on computer). f. Press RESET switch momentarily. g. Press Stop switch off off). h. (i.e., (the light indicator (on the left side of the (light indicator should go Press AUTO switch on and wait. The teletype will then write: SIGMA CR (CR means push the Car­ riage Return). Note: Each time a line is drawn under a teletype message in this explanation note, it means that the message has been printed on the teletype in­ dependently from any user's action. If the line does not appear, it means the user has to type in these characters on the teletype's keyboard. The user must type in "L" after the previous message, which means that he wants to enter the load pro­ cedure. This complete operation can be summarized as: SIGMA CR L. CR loader link. The computer then performs a few Carriage Returns and the following message will appear on the tele­ type : REL ADR (AR) = 200. CR BASE PG (XR) = 0. CR (SR) = 2. CR MODE/PRN 247 CR WYSHPR CR TUP CR CR CR WYSHPR 0200 CR E .00F5 0478 CR CR CR Start program execution by doing the following steps: a. Put computer into the Stop mode, i.e., press Stop switch on. b. Make sure SREG/DATA switch is off. c. Press WRITE/READ switch on. d. Put '0200' into the Console Data register. e. Press P switch momentarily. f. Press WRITE/READ switch off. g. Press RESET momentarily. h. Press STOP switch off. i. Press RUN switch on. j. Enter all data the computer asks, DELAY 1, N2, DELAY 2, FREQUENCY. k. While the computer prints out the procedure mes­ sage, adjust the frequency of the generator from the MTS system to the value you have given to the computer. 1. Type GO; the whole procedure starts. namely Nl, 06. To stop at any time, put the computer into the Stop mode and repeat (5) to restart the process. 07. At the end, just put the computer into Stop mode and switch the Main Power Switch off. A.3 Figure Conditioning Box 01 . Two inverters have been installed into Signal Condi­ tioning Box #2. Only one is needed, namely to invert the signal delivered by the generator. The reason for this is that in order to have a positive-going (upwardgoing) movement of the sample, one should take a nega­ tive-starting signal on the generator. But, by only using negative half-cycles, the internal counter is not incremented. Therefore, to have at the same-time 248 counter incrementing and upward-going movement of the sample, the signal which goes from the MTS-436 to the MTS-416 is inverted, as shown in Figure A . 19. 02. Three offset circuits have also been installed (OFF­ SET 1, OFFSET 2, OFFSET 3) to apply an offset to the signals which come from the sample and arrive at the chart recorders. This is shown schematically in Fig­ ure A . 20. The electric diagrams of the above circuits are shown in Figures A . 21 and A . 22, respectively. 249 inverter 1 or 2 :onnector Signal Vout Conditioning Box #2 Vi MTS-4 36 FIGURE A . 19 from sample . . 1 , signal amplifier Inverters Location. IN Signal Conditioning Box #2 $ 1 2 & OUT 3 OFFSETS FIGURE A . 20 MTS-416 Offsets Location. Chart Recorders FIGURE A . 21 Electrical Circuits of the inventers in the signal conditioning box. FIGURE A . 22 Electrical circuits of the offset in the signal conditioning box. 251 APPENDIX B A P PE N D IX B CALIBRATION INFORMATION B.l. Load Cell In these investigations, a five kips maximum ca­ pacity load cell was used. The calibration of this load cell was accomplished by applying known loads to the cell and adjusting the excitation setting to produce the desired voltage outputs. The load was applied using lead bricks which had been previously weighed to the nearest one-hun­ dredth of a pound. The excitation setting was adjusted to produce the desired calibration factor of twenty millivolts per pound. factor. The switch on the MTS controller was set to X10 This amplified the output signal so that the full output signal of ten volts corresponded to a load of five hundred pounds, or ten percent of the load cell capacity. This was chosen to permit higher resolution and accuracyand because the applied axial loads were less than five hundred pounds. B.2 Linear Variable Differential Transducers (LVDT) Axial and radial sample deformations were measured using two vertical and two radial LVDT's. The calibration of these LVDT's was performed using a micrometer which read to the nearest 0.0001 inch. The LVDT's were mounted in a bracket holding the micrometer. Movement of the LVDT core was measured with the micrometer, and the calibration factor of the different signal conditioners was adjusted to pro­ duce the desired voltage outputs. These calibration factors were: 01. The main axial LVDT, which was calibrated to produce ±10 volts output for a full range deflection of ± two tenths of an inch. 02. The second axial LVDT was calibrated to produce +10.0 volts output for a full range deflection of ± twentyfive hundredths of an inch. 252 03. Both radial LVDT's were calibrated to produce +10.0 volts output for a full range deflection of ± one tenth of an inch. B.3 Strip Chart Recorder The calibration of the strip chart recorder was checked before each test using the built-in cal button, which applies a one hundred millivolt input signal to pro­ duce an output movement of the stylus of .787 inch (20 mm). The static response was also checked by comparing the strip chart reading with the voltage reading on the Simpson 460 voltmeter for the same output signal. Lentz determined that the dynamic response of the strip chart recorder was unaffected by frequency up to fifty hertz. He used a func­ tion generator and a power supply to simultaneously apply and compare the signal to the strip chart recorder and to an oscilloscope. For each loading frequency the proper paper speed and stylus temperature of the strip chart re­ corder are marked on the recorder. 25 3 APPENDIX C APPENDIX C TEST RESULTS OF THE LOWER PENINSULA TEST SITES This appendix summarizes all the test results in the form of figures and tables as follows: 01. The conventional consolidation curves of the lower peninsula test sites are presented in Figures C.l through C.3. 02. The Incremental Creep Tests 03. 04. 05. a. The results of the consolidation tests performed prior to the commencement of the incremental creep tests are presented in Figures C.4 through C.6. b. The incremental creep test results are shown in Figures C.7 through C.9. Unconsolidated Ramp Tests a. The results of the ramp tests are plotted in Fig­ ures C.10 through C.12. b. Mohr's circle diagrams obtained from the ramp tests are shown in Figures C.13 through C.15. Consolidated Cyclic Triaxial Tests a. The data of the consolidation tests performed prior to the commencement of the cyclic loading tests are plotted in Figures C.16 through C.24. b. The axial permanent strain curves are shown in Fig­ ures C.25 through C.31. c. The resilient Modulus data are plotted in Figures C.32 through C.38. d. The radial permanent strain data are listed in Table C.l. Unconsolidated Cyclic Triaxial Tests a. The axial permanent strain and the resilient modu­ lus data are tabulated in Table C.2. b. Table C.3 provides a list of the radial permanent strain data. 254 0.68 0.181 0.56 Void Ratio 0.62 (1 tsf = 1.07 kg/cm?) 0.50 10 -2 10 -1 10 Pressure FIGURE C.l 0 1 10 (tsf) Consolidation Curve, Void Ratio versus Logarithm of Pressure, Site 1, Lower Peninsula. 2 0.65 0.139 o •H +> td 0.58 a 0.51 10 -2 10 -1 10 Pressure FIGURE C .2 0 10 1 10 2 (psf) Consolidation Curve, Void Ratio versus Logarithm of Pressure, Site 2, Lower Peninsula. 0.580 0.19 3 0.52 0.46 Void Ratio (1 psf = 1 kg/cm2) 0.40 10 -2 10 -1 10 0 Pressure FIGURE C .3 10 1 10 2 (psf) Consolidation Curve, Void Ratio versus Logarithm of Pressure, Site 4, Lower Peninsula. 0.38 sample la-F 0.33 Ratio 2c-F Void ld-F 0.28 101 102 103 Time FIGURE C.4 104 105 106 (sec) Void-Ratio versus the Logarithm of Time for Samples Consolidated under the Designated Confining Pressure Prior to the Commencement of the Incremental Creep Tests, Site 1, Lower Peninsula. 0.36 sample 3c-F Ratio 0.30 3b-F Void 0.24 4e-S 0.18 10 10 Time FIGURE C.5 (sec) Void Ratio versus Logarithm of Time for Sample Consolidated under the Designated Confining Pressure Prior to the Commencement of the Incremental Creep Tests, Site 3, Lower Peninsula. sample 2a-F Ratio 0 Void 4e-F 0 0 10 10 10 10 Time FIGURE C.6 10 10 (sec) Void Ratio versus the Logarithm of Time for Samples Consolidated under the Designated Confining Pressure Prior to the Commencement of the Incremental Creep Tests, Site 4, Lower Peninsula Difference (psi) 70 sample 2c-F 60 50 ld-F Principal Stress 40 (1 psi = 0.07 kg/cm2 ) 30 20 la-F 10 0 2 4 Total Axial Strain (xlO FIGURE C.l 8 6 10 -2 ') Principal Stress Difference versus Total Axial Strain from Incremental Creep Tests, Site 1, Lower Peninsula. Difference (psi) 120 sample 4e-S 100 80 3b-F Principal Stress 60 (1 spi = 0.07 kg/cm2) 40 20 8 12 Total Axial Strain (10 ^) FIGURE c.8 Principal Stress Difference versus Total Axial Strain from Incremental Creep Tests, Site 3, Lower. Peninsula. 20 -Difference (psi) 28 24 20 sample 4e-F Stress 16 12 Principal (1 psi = 0.07 kg/cm2) 2a-F 0 4 8 12 16 20 Total Axial Strain (10 FIGURE C.9 Principal Stress Difference versus Total Axial Strain from. Incremental Creep Tests, Site 4, Lower Peninsula. (psi) Principal Stress Differences 50 sample 4f-S 30 3a-S (1 psi = 0.07 kg/cm2) 10 0 2 4 Total Strain FIGURE C.10 6 8 10 (%) Principal Stress Difference versus Total Axial Strain from Ramp Test, Site 1, Lower Peninsula. (psi) 50 30 4f-S Stress Difference sample 2f-S Principal 10 psi = 0.07 kg/cm2 ) 0 2 4 6 8 10 Total Strain (%) FIGURE- C.ll Principal Stress Difference versus Total Axial Strain from Ramp Tests, Site 2, Lower Peninsula. 60 r 40 3c-S 20 ‘ (1 psi = 0.07 kg/cm2) Principal Stress Difference (psi) sample le-S 0 2 4 Total Strain FIGURE C.12 6 8 10 (%) Principal Stress Difference versus Total Axial Strain from Ramp Tests, Site 3, Lower Peninsula. 14.5 psi (1 psi = 0.07 kg/cm2) 30 Shear Stress_(psi) 50 sample 3c-S 10 4f-S 0 20 40 Normal Stresses FIGURE C.13 60 80 (psi) Mohr Circles and Failure Envelopes from Ramp Test, Site 1, Lower Peninsula. 50 15 30 (1 psi = 0.07 kg/cm2 ) Shear Stress (psi) 10.5 psi 10 sample 2f-S 4f-S 0 20 40 Normal Stress FIGURE c.14 60 80 100 (psi) Mohr Circles and Failure Envelopes from Ramp Test, Site 2, Lower Peninsula. Shear Stress (psi) (1 psi = 0.07 kg/cm2 ) 30 sample le-S 10 3c-S 0 20 40 Normal Stress FIGURE C.15 60 80 (psi) Mohr Circles and Failure Envelopes from Ramp Test, Site 3, Lower Peninsula. Void Ratio sample Ic-F 2b-F I 2a-F 0 0 10 1 10 2 10 3 Time FIGURE C.16 10 4 10 5 10 6 (sec) Void Ratio versus the Logarithm of Time for Samples Consolidated under a Confining Pressure of 5 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 1, Lower Peninsula. 0.53 sample ' 2d-F Void Ratio. 0.47 2f-S 0.41 4d-F 0.36 10 10 10 10 10 10 Time (sec) FIGURE C .17 Void Ratio versus the Logarithm of Time for Three Samples Consoli­ dated under a Confining Pressure of 25 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 1, Lower Peninsula. 0.44 sample 4a-S I Void Ratio 0.42 0.40 0.38 10 1 10 2 10 3 10 4 10 5 10 6 Time (sec) FIGURE C.18 Void Ratio versus the Logarithm of Time for Three Samples Consolidated under a Confining Pressure of 50 psi Prior to the Commencements of the Triaxial Cyclic Load, Site 1, Lower Peninsula. 0.48 sample 3f-F 0.42 Ratio -3c-F Void •3e-F 0.36 0.30 10 Time FIGURE C.19 (sec) Void Ratio versus Logarithm of Time for Three Samples Consolidated under a Confining Pressure of 25 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 2, Lower Peninsula. 0.44 sample 2c-S I Void Ratio 0.40 0.36 0.32 1 10 2 10 3 Time FIGURE C .20 10 4 10 5 10 6 (sec) Void Ratio versus the Logarithm of Time for Three Samples Consoli­ dated under a Confining Pressure of 50 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 2, Lower Peninsula. 0.68 sample 2c-F 0.62 Void Ratio 2b-f 0.56 M m __ -la-F 0.50 ] 10X 10 7 Time FIGURE C.21 4 10J 104 5 10° 6 10° (sec) Void Ratio versus Logarithm of Time for Three Samples Consolidated under a Confining Pressure of 5 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 3, Lower Peninsula. 0.28 sample■ 4b-F Ratio 0.26 Void I 2a-F 0.24 3a-F 0.22 101 102 103 Time FIGURE C . 2 2 104 105 106 (sec) Void Ratio versus Logarithm of Time for Three Samples Consolidated under a Confining Pressure of 25 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 3, Lower Peninsula. 0.66 sample 4a-F Void Ratio 0.60 3e-F 0.54 la-F 0.48 101 10 2 10 3 10 4 10 5 6 Time (sec) FIGURE C.23 Void Ratio versus Logarithm of Time for Three Samples Consolidated under a Confining Pressure of 5 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 4, Lower Peninsula. 0.50 Ratio 0.44 Void sample 2d-F 2e-F 0.38 0.32 10 1 10 2 10 3 Time FIGURE c . 2 4 10 4 10 5 10 6 (sec) Void Ratio versus Logarithm of Time for Three Samples Consolidated under a Confining Pressure of 2 5 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 4, Lower Peninsula. sample 2b-F 10 2a-F lc-F 10 -1 Axial Permanent Strain (%) 10 10 -2 10 10 2 3 10 4 10 5 Number of Load Applications FIGURE C.25 Axial Permanent Strain versus Number of Load Applications for Samples Consolidated under a Confining Pressure of 5 psi and Tested Using Different Cyclic Stress Ratio, Site 1, Lower Peninsula. 10 10 2f-S 2d-F 10 Axial Permanent Strain (%) sample 4d-F 10 -1 10 10 2 10 3 10 4 10 5 Number of Load Applications FIGURE c.26 Axial Permanent Strain versus Number of Load Applications for Samples Consolidated under a Confining Pressure of 25 psi and Tested Using Different Cyclic Stress Ratio, Site 1, Lower Peninsula. 10 sample 4a-S 10 Axial Permanent Strain (%) 10 -B 10 10 10 10 10 10 Number of Load Repetitions FIGURE c .27 Axial Permanent Strain versus Number of Load Cycles for Samples Consoli­ dated under a confining Pressure of 50 psi and Tested using Different Cyclic Stress Ratio, Site 1, Lower Peninsula. (%) 10 2b-F 10 Axial Permanent Strain sample la-F 2c-F 10r 2 10 10 10 10 10 Number of Load Applications FIGURE C.28 Axial Permanent Strain versus Number of Load Applications for Samples under a Confining Pressure of 5 psi and Tested Using Different Cyclic Stress Ratio, Site 3, Lower Peninsula. 10 sample 3a-F £ « 10 L •P •H CO +) C (1) C td g L -1 £ 10 2a-F 4b-F 10 -2 10 0 10 1 10 2 10 3 Number of Load Repetitions FIGURE C.29 10 4 5 (N) Axial Permanent Strain Versus Number of Load Cycles for Samples Consolidated under, a Confining Pressure of 25 psi and Tested Using Different Cyclic Stress Ratio, Site 3, Lower Peninsula. 10 10 la-F 10 -1 Axial Permanent Strain (%) sample 3e-F 4a-F 10 -2 10 10 * 10 10 10 Number of Load Applications FIGURE C . 30 Axial Permanent Strain versus Number of Load Applications for Samples Consolidated under a Confining Pressure of 5 psi and Tested Using Different Cyclic Stress Ratio, Site 4, Lower Peninsula. (%) Strain sample 2e-F • • 2d-F 10 Axial Permanent 10 10 -1 10 10 2 10 3 10 4 10 5 Number of Load Applications FIGURE C . 31 Axial Permanent Strain versus Number of Load Applications for Samples Consolidated under a Confining Pressure of 25 psi and Tested Using Different Cyclic Stress Ratio, Site 4, Lower Peninsula. 105 / sample 2b-F |— lc-F -HHi 1 M l __ = — ^ — =#5=1 1— .A--- # 4 Ml \--- 1-*-*■-- \ • wrf 4— — --i ■ ■"— 2a-F Resilient Modulus, (psi) ■ 1 (1 psi = 0.07 kg/cm2) 10° 101 102 103 104 Number of Load Applications FIGURE C.32 Resilient Modulus versus Number of Load Applications for Samples Consolidated under a Confining Pressure of 5 psi and Tested using Different Cyclic Stress Ratio, Site 1, Lower Peninsula. 105 4d-F Resilient Modulus, (psi) sample 2e-S 2d-F 103 (1 psi = 10 10 10 10 10 10 Number of Load Applications FIGURE C.33 Resilient Modulus versus Number of Load Applications for Samples Con­ solidated under a Confining Pressure of 25 psi and Tested using Different Cyclic Stress Ratio, Site 1, Lower Peninsula. 10' Resilient Modulus, (psi) 10 - * V ^sample 4a-S 10' (1 psi = 0.07 kg/cm2 ) 10 +2 10 10 ' 10 10 10 10 ' Number of Load Applications FIGURE C .34 Resilient Modulus versus Number of Load Applications for Samples Con­ solidated under a Confining Pressure of 50 psi and Tested using Different Cyclic Stress Ratio, Site 1, Lower Peninsula. 10 (psi) sample la-F 10 Resilient Modulus, • • 4Ip 2c-F 2b-F 10 (1 psi = 0.07 kg/cm2) 10 +2 10° 101 102 103 Number of Load Applications FIGURE C.35 Resilient Modulus ( M r ) versus Number of Load Applications for Consolidated Samples Consolidated Under a Confining Pressure of 5 psi and Tested Using Different Cyclic Stress Ratio, Site 3, Lower Peninsula. (psi) ■ ■ ■ ft* "” ■ r * 1i a ■ ; ■■■■.. a i Modulus, .. » - » i ........... Resilient ■ (1 psi = 0.07 kg/cm2) 10° 101 102 103 104 105 Number of Load Applications FIGURE C.36 Resilient Modulus versus Number of Load Applications for Samples Con­ solidated under a Confining Pressure of 25 psi and Tested using Different Cyclic Stress Ratio, Site 3, Lower Peninsula. sample 4a-F Resilient — \ 10‘ — — | --- e— € Modulus, (psi) 10' J— ------- . — A ■ » — * r* •* A** i --- 9 O .aj S X * * * — V * la-F 3e-F 10(1 psi = 0.07 kg/cm2 ) i+2f 10' 10' 1 10 10^ 10J 10 10 Number of Load Applications FIGURE C . 37 Resilient Modulus versus Number of Load Applications for Samples Consolidated under a Confining Pressure of 5 psi and Tested Using Different Cyclic Stress Ratio, Site 4, Lower Peninsula. - 10 sample 2e-F to VO NO co 3 fH 3 T3 O 2d-F S +J C a) •H i —I 1C 3 •rH CO a) £ (1 psi = 0.07 10 +2 10 10 10 10 10 10 • Number of Load Applications FIGURE C . 38 Resilient Modulus versus Number of Load Applications for Samples Consolidated under a Confining Pressure of 25 psi and Tested using Different Cyclic Stress Ratio, Site 4, Lower Peninsula. TABLE C.l List of the Radial Permanent Strain for Consolidated Samples, Sites 1, 3 and 4, Lower Peninsula. RADIAL PERMANENT STRAIN AT MIDDLE OF SAMPLE (xl0~4 ) RADIAL PERMANENT STRAIN AT 1/3 FROM THE SAMPLE BOTTOM (xlO 4 ) SAMPLE SITE NUMBER 2b-F 3.72 293 2d-F 25 2e-S 4d-F 50 4a-S 1,000 4.00 10,000 15.2 3.50 1.01 9.28 19.6 13.7 7.29 31 10.8 142 44 4.37 3.13 84. 2 37.8 51.8 102 155 87.2 85.1 84.8 61.2 60.2 58.2 154 22.1 60.8 17.0 109. 25.3 87.2 47.6 20.0 15.2 21.8 20.1 67.9 10.2 19.6 23.1 21.7 1.29 30,000 10.3 1.02 2a-F lc-F 100 10 N=1 155 157 48.4 TABLE C.l (Continued) RADIAL PERMANENT STRAIN AT MIDDLE OF SAMPLE (xlO- 4 ) SITE a3 SAMPLE NUMBER RADIAL PERMANENT STRAIN AT 1/3 FROM THE SAMPLE BOTTOM (xlO- 4 ) (01-a3)d 03 294 5 .x"" 2c-F 1.0 2b-F 2.0 la-F 3.0 4b-F 1.0 2a-F 1.5 3a-F 2.0 N=1 10 5.13 6.75 * 1,000 100 8.19 10.2 9.13 1.81 L. 08 10,000 7.05 30,000 31.4 3.15 ^ ^ 2 1 . 2 9.18 10.5 .^2.78 81.2 111. 21.3 51.6 ^ ^ 8 . 34 12.1 .^50.7 ^ ^ ^ 9 0 . 1 15.7 26.1 4.72 ^ ^ 6 . 1 9 86.9 1 8 0 . ^ ^ 1 7 0 . ^ - ^ 181. 55.7 ^ ^ " 1 2 5 . ^ ^ i . 4 0 . .^25. 6 3 25 54.3 .^13.2 78.2 ^^28.1 103. ^^87.2 9.02 12.3 3.18 ^ ^ 8 . 6 9 19.1 ^/"12.8 40.8 65.6 86.8 28.8 ^ ^ 2 9 . 9 10.2 .^6.83 25.2 .^10.8 88.3 1 6 4 . 6 ^ ^ 1 7 4 . 0 / " ^ 183.4 12.2 ^ ^ 1 7 . 8 ^ - ^ 3 4 . 0 ^ ^ 3 5 . 8 6.84 1.02 27.8 1 0 2 . ^ ^ 105. ^^^30.5 ^ ^ 3 2 . 2 TABLE C.l (Continued) RADIAL PERMANENT STRAIN AT MIDDLE OF SAMPLE (xl0~4) SITE a3 SAMPLE NUMBER (0 l”a3) d a3 295 5 4 RADIAL PERMANENT STRAIN AT 1/3 FROM THE SAMPLE BOTTOM (xlO- 4 ) 4a-F 0.7 la-F 1.0 3e-F 2.0 2d-F 0.5 2e-F 1.0 N=1 10 1.24 1.08 * 2.01 8.73 5.74 5.24 37.8 .^11.8 10.4 7.29 .^21.2 112. .--'52.5 58.9 115. 2.38 30.9 8.41 14.3 10,000 30,000 4.82 2.85 4.40 1.69 1.84 2.10 / l . 39 2.21 .^1.16 1.82 9.82 1,000 100 29.7 31.5 3.10 41.6 48.7 17.7 . ^ jL6.5 159. 147. ^^32.1 ^^^33. 3 25 13.8 22.6 9.79 51.8 15.0 ^ - ^ 4 6 . 2 * Measurements were less than the accuracy of the LVTD. Blank space indicates sample failed before the designated number of load repetitions was reached TABLE C.2 List of Axial Permanent Strain for Unconsolidated Samples AXIAL PERMANENT STRAIN (xlO“ 4) RESILIENT MODULUS (xl()3) (psi) SAMPLE NUMBER SITE 10 N=1 lf-F 3d-F 296 le-F 3f-S 3.37 8.16 2.60 37.6 69.6 140 219 2.96 325 296 2.71 2.73 149 57.0 30,000 3.47 3. 73 2.71 26.0 19.1 10,000 64.1 31.1 21.8 2.98 3.02 1,000 100 321 330 4.02 3.09 21.1 13.9 54.0 37.8 2.40 53 25 2e-S 4c-S 2e-S 25 3e-S 35.2 21.2 78.0 2.44 51.0 70. 5 150 120 1.74 1. 89 5.11 5.42 2. 37 132. 68.4 176 235 210 13.6 5. 39 5.63 55.4 50.1 13.4 2.57 3.04 5.79 14.5 13. 7 200 . 178 3.09 12.2 11.8 TABLE C.3 List of Radial Permanent Strain for Unconsolidated Samples RADIAL PERMANENT STRAIN AT MIDDLE OF SAMPLE (xlO- 4 ) SITE SAMPLE NUMBER a3 5 . RADIAL PERMANENT STRAIN AT 1/3 FROM THE SAMPLE BOTTOM (xl0“ 4) (Uf-a 3)d a3 3d-F 1.0 lf-F 2.0 10 N=1 100 11.8 7.56 23.7 L. 81 12.6 10,000 1,000 40.2 21.0 7.13 94.3 30,000 92.0 61.5 . x ^ 32.0 .x-^58.0 187. 161. ^^L32. ^ ^ 9 8.2 1.28 24.8 /^3.84 3.27 210 . 73.5 31.5 1 4 7 . ^ ^ 172. .-^6.54 9.81 ^ ^ 5 2 . 3 .^114. ^ ^ ^ 1 4 4 . \ § 1 . s ^ 15.2 ^ ^ 7 1 . 4 s' 1 3.0 3f-S 1.0 27.8 .^19.8 2e-S 1.5 1 3 8 . ^ ^ 274. 312. .^191. 117. 84.0 4c-S 1.0 2e-S 2.0 3e-S 1.5 297 C D 3 25 21.0 le-F 21.0 * 88.4 112 . 1 3 7 . ^ ^ 53.0 ^ - " ' 6 7 . 0 72.0 80.6 56.1 .-^9.34 ^ - ^ 1 3 . 8 94.6 87.6 85.9 .^26.4 ^'•"38.9 ^ ^ ^ " 5 4 . 8 - 42.1 119. 70.1 38.4 31.0 10.8 37.3 2.07 L12 . 1 8 9 . ^ ^ 217. L40 . ^ ^ 1 7 2 . 135. 58.4 90.9 ^ ^37.2 51.6 ./"19.2 10 .3 *Measurements were less than the accuracy of the LV T D . 231. ^^189. 154. ^ ^ ^ 4 8.4 APPENDIX D APPENDIX D TEST RESULTS OF THE UPPER PENINSULA TEST SITES This appendix summarizes all the laboratory and field test results of the Upper Peninsula test sites in forms of figures and tables as follows: (1) The pavement deflection curves that were measured using a highway truck and a Benkelman beam of all the Upper Peninsula test sites are presented in Figure D.l. (2) The standard deviation of the pavement deflection curves of all the Upper Peninsula sites are shown in Figure D.2. (3) The conventional consolidation curves of the Upper Peninsula test sites are presented in Figure D.3 through D.6. (4) Consolidated Incremental Creep Tests (a) The results of a consolidation test performed prior to the commencement of the incremental creep test is presented in Figure D.7. (b) The incremental creep test results are shown in Figure D.8. (5) Consolidated Ramp Tests (a) The results of the consolidation test performed prior to the commencement of the ramp test is presented in Figure D.9. (b) The ramp test results are shown in Figure D.10. (6) Unconsolidated Ramp Test (a) The results of the unconsolidated ramp tests are plotted in Figures D.ll through D.13. (7) Consolidated Cyclic Triaxial Tests (a) The time dependent consolidation curves of the consolidation tests performed prior to the commencement of the cyclic loading tests are plotted in Figures D.14 through D.16. (b) The axial permanent strain curves are shown in Figures D.17 through D.19 as a function of the number of load repetitions. 298 (c) The resilient modulus of the Upper Peninsula test sites data are plotted in Figures D.20 through D.22 as a function of the number of load repetitions. (d) The radial permanent strain data are listed in Table D.l. (8) Unconsolidated Cyclic Triaxial Tests (a) The axial permanent strain from the unconsolidated cyclic triaxial tests data are shown in Figure D.23. (b) The resilient Modulus data are plotted and shown in Figure D.24. (c) The radial permanent strain data are listed in Table D.l. 299 (inch), (XlO Deflection Pavement 4 3 site 3 2 site 2 (1 inch = 2.54 cm) site 4 1 Average site 1 0 0 2 4 6 Distance FIGURE D.l 8 10 (ft) Average Pavement Deflection Versus Distance from Wheel Load, Upper Peninsula. Standard Deviation (inch), (XlO 4 3 site 4 2 site 3 inch = 2.54 cm) site 2 1 site 0 0 2 4 6 Distance FIGURE D.2 8 (ft) Standard Deviation Versus Distance from the Wheel Load, Upper Peninsula. 10 0.540 0.283 0.480 0.420 Void Ratio (1 tsf = 1.07 kg/cm2) 0.360 10 _2 10 _1 10 Pressure 10 10 (tsf) FIGURE D. 3 Consolidation Curve, Void Ratio Versus Logarithm of Pressure, Site 1, Upper Peninsula 0.760 0.198 0.700 0.640 Void Ratio (1 tsf = 1.07 kg/cm2) 0.580 _l _2 10 10 10 10 Pressure 10 (tsf) FIGURE D.4 Consolidation Curve, Void Ratio Versus Logarithm of Pressure, Site 2, Upper Peninsula 0.740 0.201 0.680 (1 tsf = 1.07 kg/cm2) o •H ■P (0 T3 ■H O > 0.620 0.560 -2 10 _1 10 0 ' 10 Pressure 1 10 2 10 (tsf) FIGURE D.5 Consolidation Curve, Void Ratio Versus Logarithm of Pressure, Site 3, Upper Peninsula 0.660 0. 300 0.610 Void Ratio (1 tsf = 1.07 kg/cm2) 0.560 0.510 10 -2 FIGURE D.6 _ 10 i 0 10 Pressure (tsf) 10 1 10 Consolidation Curve, Void Ratio Versus Logarithm of Pressure, Site 4, Upper Peninsula 2 Ratio 0.58 Void sample 2b-F 0.54 0.50 10 10 10 10 Time FIGURE D .7 10 10 (sec) Void Ratio Versus Logarithm of Time for Sample Consolidated Under Confining Pressure of 25 psi Prior to the Commencement of the Incremental Creep Test, Site 1, Upper Peninsula. Principal Stress Difference (psi) 70 60 50 sample 2b-F 40 30 20 10 4 6 8 10 Total Axial Strain FIGURE D . 8 Principal Stress Difference Versus Total Axial Strain Consolidated Sample Under 25 psi, Prior to Incremental Creep Test, Site 1, Upper Peninsula 0.640 0.058 • Void Ratio sample lc-F 0.52 0.46 10 10 10 10 Time 10 10 (Sec) FIGURE D. 9 Void Ratio Versus Logarithm of Time for Sample Consolidated Under Confining Pressure of 10 psi Prior to the Commencement of the Ramp Tests, Site 2, Upper Peninsula. 40 sample lc-F (psi) Principal Stress Difference 60 20 2 4 6 8 10 Total Axial Strain FIGURE D.10 principal Stress Difference Versus Total Axial Strain Consolidated Sample Under 10 psi, Prior to Ramp Test, Site 2, Upper Peninsula 40 sample 2c-S lc-S 20 Principal Stress Difference (psi) 60 3c-S 10 1 psi = 0.07 kg/cm 10 Total Axial Strain (%) FIGURE D .11 Principal Stress Difference Versus Total Axial Strain from Ramp Tests, Site 1, Upper Peninsula (psi) 40 2b-F Principal Stress Difference sample 4b-F 20 lb-F 1 psi = 0.07 kg/cm 2 4 6 Total Axial Strain FIGURE D.12 8 10 (%) Principal Stress Difference Versus Total Axial Strain from Ramp Tests, Site 2, Upper Peninsula lb-S 20 2b-S 10 3b-S Principal Stress Difference (psi) 30 (1 psi = 0.07 kg/cm2) 0 2 4 6 Total Axial Strain 8 10 (%) FIGURE D.13 Principal Stress Difference Versus Total Axial Strain from Ramp Tests, Site 3, Upper Peninsula. 0.94 0.88 o •H ■P (0 tt sample lb-F 0.82 0.76 Time FIGURE D.14 (Sec.) Void Ratio Versus the Logarithm of Time for a Sample Consolidated Under a Confining Pressure of 10 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 1, Upper Peninsula. 0.92 0.86 Ratio 2a-F Void la-F 0.80 sample 3a-F 0.74 10 Time FIGURE D.15 (Sec.) Void Ratio Versus the Logarithm of Time for Three Samples Consolidated Under a Confining Pressure of 10 psi Prior to the Commencement of the Triaxial Cyclic Load, Site 2, Upper Peninsula. 0.78 sample la-F Void Ratio 0.72 2a-F 0.64 0.58 Time FIGURE D.16 (Sec.) Void Ratio Versus the Logarithm of Time for Two Samples Consolidated Under a Confining Pressure of 10 p s i }Prior to the Commencement of the Triaxial Cyclic Load, Site 3, Upper Peninsula. (%) sample Ib-f Permanent Strain 10° Axial 10 10 -2 10 0 FIGURE D.17 10 1 2 3 10 10 Number of Load Repetitions 10 if 10 Axial Permanent Strain Versus Number of Load Applications for Consolidated Samples Tested Under a Confining Pressure of 10 psi and at Cyclic Stress Ratio of 1.0, Site 1, Upper Peninsula 5 (%) Strain Permanent Axial Number of Load Applications FIGURE D.18 Axial Permanent Strain Versus Number of Load Applications for Consolidated Samples Tested Under a Confining Pressure of 10 psi and Different Cyclic•Stress Ratio, Site 2, Upper Peninsula 10 ° sample 2a-F - 10 1 Axial Permanent Strain (%) 10 la-F 2 10 10 ° Number of Load Applications FIGURE D.19 Axial Permanent Strain Versus Number of Load Applications for Consolidated Samples Tested Under a Confining Pressure of 10 psi and Different Cyclic Stress Ratio, Site 3, Upper Peninsula. 6 Modulus (psi) 10 — Resilient U 10 sample lb-F • • 3 10 ° Number of Load Applications FIGURE D.20 Resilient Modulus Versus Number of Load Applications for Consolidated Sample Tested Under a Confining Pressure of 10 psi and Cyclic Stress Ratio of 1.0, Site 1, Upper Peninsula sample la-F 10 Modulus (psi) 10 3a-F — 2a-F Resilient — 10 10 ° Humber of Load Applications FIGURE D.21 Resilient Modulus Versus Number of Load Applications for Consolidated Samples Tested Under a Confining Pressure of 10 psi and Different Cyclic Stress Ratio, Site 2, Upper Peninsula sample la-F Resilient Modulus (psi) 10 2a-F 10 10 10 10 10 10 10 10 Number of Load Applications FIGURE D.22 Resilient-Modulus Versus Number of Load Applications for Consolidated Samples Tested Under a Confining Pressure of 10 psi and Different Cyclic Stress Ratio, Site 3, Upper Peninsula. TABLE D.l List of the Radial Permanent Strain for Test Sites 1, 2, 3 Upper Peninsula °3 SlUP 10 lb-F 1.0 10 3b-S 1.0 10 la-F 1.0 10 2a-F 2.0 10 3a-F 3.0 10 la-F 1.0 10 2a-F 2.0 323 Site Sample Number 32UP 33UP Radial Permanent Strain at Middle of Sample (X10" ) / (0l- CT3)d °3 10 100 2.4£/ 3.3/ ^ 1000 10000 5 . 1 / ^ 6.44/" 6 . 4 / ^ * / 1 . 6 1 /^1.82 s ' * * * 9.4/" 1 0 . 4 / " 4../'"" 5.8^/" 3.5^^ s ' * / " " l . 0 4 /""2 . 0 1 / " 3 . 4 3 / / 5 1 ^ ^ 3 ^ 6 1 7 . 4 £ / 8.]/" 8.87/" 5.60^/ 1.37/ 3.6j/" * ^/lT42 . / I . 81 / f . 9 3 ^ / 2 T o 5 * 1.42/ 5.46^-^ 6 . 9 6 / " 1 0 . 9 / " 1 8 . 5 / 2 0 . 5 / s ' * /^l7o9 / / 2 4 ^ / 1 . 6 8 / 1 . 9 4 ^/2To8 4./-^ 2.37/ 6.9J^/ 1 5 . 7 . / 19. 8 / ' 22.4/" / ' I . 61 / l . 83 / ^ 1 . 9 4 / / 0 1 / 1 . 15 / ^ 3 2 5.0/"" 6 . 6 3 ^ ^ 6.63/ 6.67^/ 2.18/ 2.59/" * 3.55/ * * 5.46/ * * 5.*// ^/USl * / l . 15 / l T 4 3 9 . 5 / / 15* > ^ 1 8 - 2 / " /"1.97 Test Mode 30000 s ' _5 ♦Readings are smaller than 10 N=1 Radial Permanent Strain at 1/3 From the Sample Bottom (Xl0-£t) / 2 . 17 / " 2 . 3 5 C U c c c c c 10 10 Permanent Strain (%) sample 3b-S 10 10 -1 -2 10 10 10 10 10 10 Number of Load Applications FIGURE D.23 Axial Permanent Strain Versus Number of Load Applications for Unconsolidated Samples Tested Under a Confining Pressure of 10 psi, Site 1, Upper Peninsula . . .. 1sample 3b-S ••A A - • • 10° 101 io2 io3 104 105 Number of Load Applications FIGURE D.24 Resilient Modulus Versus Number of Load Applications for Unconsolidated Sample Tested Under a Confining Pressure of 10 psi, Site 1, Upper Peninsula