THE DYNAMIC PROPERTIES OF FROZEN SOILS UNDER- GYCLIC {RENAL Lflfiufilfifi BQNWIUNS THESIS ran we DEGREE or v.5. MICHIGAN sure unmasm ammo LEO cmxnwsm 1977 ll LII mu; 1%"ij fill (Ill 1m l“ 1” mm (11 ”Lung II L ABSTRACT THE DYNAMIC PROPERTIES OF FROZEN SOILS UNDER CYCLIC TRIAXIAL LOADING CONDITIONS By Ronald Leo Czajkowski Cyclic triaxial tests were conducted on laboratory prepared samples of frozen silt and clay to evaluate the dynamic properties of frozen silt and clay under simulated earthquake loading conditions. The testing apparatus consisted of an MTS electrohydraulic closed-loop test system, a triaxial cell, a refrigeration unit, and output record- ing devices. Two silts - Hanover silt and Alaska silt - and a kaolinite clay were used in the research program. All soils were generally prepared at two water contents to assess the influence of water content on the dynamic properties of frozen silt and clay. The samples were 3 tested at axial strain amplitudes from approximately 2 x 10' to 8 x l0-2%, temperatures from -l to —l0°C, frequencies from 0.05 to l0.0 cps, and confining pressures from 0 to 200 psi. Values of dynamic 5 5 _Young's modulus obtained ranged from l x l0 to 35 x l0 psi for Hanover silt, from T x 105 to 22 x 105 psi for Alaska silt, and from 1 x lo5 to l4.5 x l05 psi for kaolinite. The test results indicate that dynamic Young's modulus decreases with increasing strain ampli- tude and increases with increasing frequency and decreasing Ronald Leo Czajkowski temperature. The relationship between dynamic Young's modulus and water content varies; in some cases dynamic Young's modulus increases with increasing water content and in other cases it decreases. Dynam- ic Young's modulus is apparently not affected by confining pressure. Values of damping ratio obtained ranged from .02 to .36 for Hanover silt, from .02 to .32 for Alaska silt, and from .01 to .22 for kaolin- ite. The test results indicate that damping ratio generally increases with increasing axial strain amplitude and decreases with increasing frequency and decreasing temperature. For frozen silt damping ratio decreases with increasing water content; for frozen clay there is only a slight influence of water content on damping ratio. Damping ratio is generally not significantly influenced by confining pressure. The dynamic properties of frozen silt and clay obtained in the present study were compared to those obtained in previous studies. Values of dynamic Young's modulus for silt obtained in the present study were generally somewhat lower than the values obtained in pre- vious studies while values of damping ratio were somewhat higher. Values of dynamic Young's modulus and damping ratio for clay obtained in the present study compared favorably with the values obtained in previous studies. The variation in the dynamic properties in the different studies may be due to differences in frequency, strain ampli- tude, and material characteristics between the present and previous studies. THE DYNAMIC PROPERTIES OF FROZEN SOILS UNDER CYCLIC TRIAXIAL LOADING CONDITIONS By Ronald Leo Czajkowski A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Civil Engineering ACKNOWLEDGEMENTS The author wishes to extend his appreciation to Dr. Ted S. Vinson for his guidance during the course of this project. The author also wishes to acknowledge the contribution of Geraldine Wright, Ruth Wise, Charlene Burns, John Contrady, Sheila Eddington, and Ellen Kehoe, Under- graduate Research Aides in the Division of Engineering Research at Michi— gan State University, who assisted in the data reduction, and the manage- ment and staff of Woodward-Clyde Consultants in New Orleans and Houston, who provided valuable typing and reproduction services. The work covered by this project was done under Grant ENG74-13506 of the National Science Foundation. ii TABLE OF CONTENTS iii Page ACKNOWLEDGEMENTS ...................... .. . ii LIST OF TABLES ......................... vi LIST OF FIGURES ......................... vii LIST OF SYMBOLS ............... ' .......... xviii Chapter 1. INTRODUCTION ........................ l l.l. Statement of the Problem ................ l 1.2. Purpose and Scope of Studies .............. l 1.3. Distribution of Frozen Soil Deposits in Alaska. . . . . 3 l.3.l. Northern Alaska ................ 3 1.3.2. Central Alaska ................. 6 1.3.3. Southern Alaska ................ 7 1.4. Structure of Frozen Soil Deposits ........... 7 2. DYNAMIC PROPERTIES OF FROZEN SILT AND CLAY ......... 9 2.1. General ........................ 9 2.2. Previous Research on the Dynamic Properties of Frozen Soils ...................... 9 2.3. Dynamic Elastic Properties of Frozen Silt ....... 10 2.3.1. Effect of Void Ratio .............. 10 2.3.2. Effect of Ice Saturation ............ 12 2.3.3. Effect of Temperature ............. 12 2.3.4. Effect of Frequency .............. 16 2.3.5. Effect of Dynamic Stress or Strain ....... 16 2.4. Damping Properties of Frozen Silt ........... l6 3. SAMPLE PREPARATION, SAMPLE INSTALLATION, TRIAXIAL CELL ASSEMBLY. AND TEST PROCEDURE .............. 21 3.l. General ........................ 2l 3.2. Preparation of Frozen Silt Sample ........... 21 3.3. Preparation of Frozen Clay Sample ........... 27 3.4. Sample Installation and Triaxial Cell Assembly ..... 31 3.5. Test Procedure ..................... 35 4 DYNAMIC PROPERTIES OF FROZEN SILT UNDER CYCLIC TRIAXIAL LOADING CONDITIONS ................. 37 4.l. General ........................ 37 4.2. Testing Sequence .................... 37 4.3. Dynamic Young's Modulus of Frozen Silt ......... 40 Chapter Page 4.3.1. Effect of Strain Amplitude .......... 43 4.3.2. Effect of Frequency .............. 43 4.3.3. Effect of Temperature ............. 48 4.3.4. Effect of Water Content ............ 58 4.4. Damping Ratio of Frozen Silt ............. 62 4.4.1. Effect of Strain Amplitude .......... 63 4.4.2. Effect of Confining Pressure ......... 75 4.4.3. Effect of Frequency. . ........... . 75 4.4.4. Effect of Temperature ............. 84 4.4.5. Effect of Water Content ............ 93 5. DYNAMIC PROPERTIES OF FROZEN CLAY UNDER CYCLIC TRIAXIAL LOADING CONDITIONS ..... . ............... 101 5.1 General ........................ 101 5.2. Testing Sequence ............. . . . . 101 5.3 Dynamic Young's Modulus of Frozen Clay ........ 101 5.3.1. Effect of Strain Amplitude .......... 102 5.3.2. Effect of Frequency .............. '105 5.3.3. Effect of Temperature ............. 105 5.3.4. Effect of Water Content ............ 110 5.4. Damping Ratio of Frozen Clay ............. 110 5.4.1. Effect of Strain Amplitude .......... 112 _ 5.4.2. Effect of Confining Pressure ......... 113 5.4.3. Effect of Frequency .............. 113 5.4.4. Effect of Temperature ............. 122 5.4.5. Effect of Water Content ........ . . . . 122 6. COMPARISONS OF DYNAMIC PROPERTIES OF FROZEN SILT AND CLAY ........................ 129 6.1. General .................... . . . . 129 6.2. Comparison of Dynamic Properties of Frozen Silt. . . 130 6.2.1. Longitudinal and Compression Nave Velocity . 130 6.2.2. Damping Ratio ................. 135 6.3. Comparison of Dynamic Properties of Frozen Clay . . . 138 6.3.1. Longitudinal and Compression Nave Velocity. . . 138 6.3.2. Damping Ratio ........... . . . . . . 143 7. SUMMARY AND CONCLUSIONS ................... 147 APPENDIX A. CYCLIC TRIAXIAL TEST RESULTS - DYNAMIC YOUNG'S MODULUS OF FROZEN SILT ................... 158 B. CYCLIC TRIAXIAL TEST RESULTS - DAMPING RATIO - OF FROZEN SILT. . ...... . . ...... . . . . . . 192 C. CYCLIC TRIAXIAL TEST RESULTS - DYNAMIC YOUNG'S MODULUS OF FROZEN CLAY ................... 226 iv Appendix Page D. CYCLIC TRIAXIAL TEST RESULTS - DAMPING RATIO OF FROZEN CLAY ...................... 242 LIST OF REFERENCES ...................... 258 LIST OF TABLES Table Page 2.1 FIELD MEASUREMENTS OF WAVE VELOCITY IN FROZEN SILT .................... 11 3.] SUMMARY OF SAMPLES MADE AND TESTED ........ 32 vi Figure 1.] LIST OF FIGURES PHYSIOGRAPHIC REGIONS OF ALASKA (after Lovell and Roberts, 1975) .................... GENERALIZED SOILS MAP OF ALASKA (after Woods et al, 1962) ...................... COMPLEX SHEAR MODULUS VERSUS VOID RATIO FOR FROZEN SILTS (after Stevens, 1973) .......... EFFECT OF ICE SATURATION ON COMPLEX SHEAR MODULUS OF FROZEN MANCHESTER SILT (after Stevens, 1973) . . . LONGITUDINAL WAVE VELOCITY VERSUS TEMPERATURE FOR FROZEN NEW HAMPSHIRE SILT, FAIRBANKS SILT, AND YUKON SILT (after Kaplar, 1969) ........... S-WAVE VELOCITY VERSUS TEMPERATURE FOR FROZEN HANOVER SILT (after Nakano and Froula, l973) ..... EFFECT OF TEMPERATURE ON COMPLEX MODULI OE FROZEN MANCHESTER SILT (after Stevens, l973) ....... . COMPLEX SHEAR MODULUS VERSUS FREQUENCY FOR FROZEN HANOVERrNEW HAMPSHIRE SILT (after Stevens, 1973). . . COMPLEX SHEAR MODULUS VERSUS DYNAMIC STRESS FOR FROZEN MANCHESTER SILT (after Stevens, 1973) ..... EFFECT OF TEMPERATURE ON TAN 6 OF FROZEN MANCHESTER SILT (after Stevens, 1973) ........ EFFECT OF FREQUENCY ON TAN 6 OF FROZEN MANCHESTER SILT (after Stevens, l973) .............. EFFECT OF DYNAMIC STRESS ON TAN 6 OF FROZEN MANCHESTER SILT (after Stevens, 1973) ........ GRADATION CURVES FOR SOILS .............. TYPICAL FROZEN KAOLINITE SAMPLE .......... . DISTRIBUTION OF WATER CONTENT OVER LENGTH OF HIGH WATER CONTENT FROZEN SILT SAMPLES .......... vii Page 4 5 13 13 14 15 ' 15 17 17 18 18 20 22 24 26 DISTRIBUTION OF WATER CONTENT OVER LENGTH OF HIGH WATER CONTENT FROZEN CLAY SAMPLE ............ FROZEN SAMPLE WITH ANTI-TILT DEVICE AND LVDT CONNECTED ....................... DIAGRAM OF TEST HISTORY FOR FROZEN SILT AND CLAY. . . . TYPICAL HYSTERESIS LOOPS OBTAINED DURING CYCLIC TRIAXIAL TESTING .................... DYNAMIC YOUNG'S MODULUS VERSUS CONFINING PRESSURE FOR ALASKA SILT AT AN AXIAL STRAIN OF 5.0 x 10-31 . . DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HANOVER SILT AT 21.4% WATER CONTENT .......... DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HANOVER SILT AT 21.4% WATER CONTENT .......... DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HANOVER SILT AT 35.5% WATER CONTENT .......... DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR HANOVER SILT AT 35.5% WATER CONTENT .......... DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR ALASKA SILT AT 20.5% WATER CONTENT ........... DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR ALASKA SILT AT 20.5% WATER CONTENT ........... DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR ALASKA SILT AT 29.2% WATER CONTENT ........... DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR ALASKA SILT AT 38.9% WATER CONTENT ........... DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR ALASKA SILT AT 38.9% WATER CONTENT ........... DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR HANOVER SILT AT AN AXIAL STRAIN OF 3.15 x 10’3% . . . . DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR HANOVER SILT AT AN AXIAL STRAIN OF 3.16 x lO'2% . . . . DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR HANOVER SILT AT AN AXIAL STRAIN OF 3.16 x 10'3% . . . . DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR HANOVER SILT AT AN AXIAL STRAIN OF 3.16 x 10’2% . . . . viii Page 30 34 38 41' . 42 42 44 44 45 45 46 46 47 47 49 49 SO 50 Figure 4.17 4.26 DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR ALASKA SILT AT AN AXIAL STRAIN OF 3.16 x 10'3% . . DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR ALASKA SILT AT AN AXIAL STRAIN OF 3.16 x 10'2% . . DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR ALASKA SILT AT AN AXIAL STRAIN OF 3.16 x 10‘3% . . DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR ALASKA SILT AT AN AXIAL STRAIN OF 3.16 x 10'2% . . DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR ALASKA SILT AT AN AXIAL STRAIN OF 3.l6 x 10'3% . . DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FOR ALASKA SILT AT AN AXIAL STRAIN OF 3.16 x 10-2% . . DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE Fog HANOVER SILT AT AN AXIAL STRAIN OF 3.16 x 10‘ % DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE F05 HANOVER SILT AT AN AXIAL STRAIN OF 3.16 x 10' % DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FOR HANOVER SILT AT AN AXIAL STRAIN OF 3.16 x 10-3% 'DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FO§% HANOVER SILT AT AN AXIAL STRAIN OF 3.16 x 10' DYNAMIC YOUNG'S MODULUS ALASKA SILT AT AN AXIAL DYNAMIC YOUNG'S MODULUS ALASKA SILT AT AN AXIAL DYNAMIC YOUNG'S MODULUS ALASKA SILT AT AN AXIAL DYNAMIC YOUNG'S MODULUS. ALASKA SILT AT AN AXIAL VERSUS TEMPERATURE Fgg STRAIN OF 3.16 x 10' VERSUS TEMPERATURE FQQ STRAIN OF 3.16 x 10" VERSUS TEMPERATURE Fgg STRAIN OF 3.16 x 10' VERSUS TEMPERATURE F8§ STRAIN OF 3.16 x 10" DYNAMIC YOUNG'S MODULUS VERSUS WATER CONTENT FOR HANOVER SILT AT A TEMPERATURE OF -1°C ....... DYNAMIC YOUNG'S MODULUS VERSUS WATER CONTENT FOR HANOVER SILT AT A TEMPERATURE OF -4°C ....... DYNAMIC YOUNG'S MODULUS VERSUS WATER CONTENT FOR HANOVER SILT AT A TEMPERATURE OF -TO°C ...... ix Page 51 51 52 52 53 54 54 55 55 56 56 57 57 59 59, 60 Figure 4.34 4.35 4.36 4.38 4.39 4.40 4.41 4.42' 4.43 4.44 4.45 4.46 4.47 4.48 4.49 4.50 DYNAMIC YOUNG'S MODULUS VERSUS WATER CONTENT FOR ALASKA SILT AT A TEMPERATURE OF -1°C ........ DYNAMIC YOUNG'S MODULUS VERSUS WATER CONTENT FOR ALASKA SILT AT A TEMPERATURE OF -4°c ........ DYNAMIC YOUNG'S MODULUS VERSUS WATER CONTENT FOR ALASKA SILT AT A TEMPERATURE OF -lO°C ...... DAMPING RATIO VERSUS AXIAL STRAIN FOR HANOVER SILT AT 0.05cps FREQUENCY AND 21.4% WATER CONTENT . DAMPING RATIO VERSUS AXIAL STRAIN FOR HANOVER SILT AT 0.3cps FREQUENCY AND 21.4% WATER CONTENT. . DAMPING RATIO VERSUS AXIAL STRAIN FOR HANOVER SILT AT 1.0 cps FREQUENCY AND 21.4% WATER CONTENT . DAMPING RATIO VERSUS AXIAL STRAIN FOR HANOVER SILT AT 5.0 cps FREQUENCY AND 21.4% WATER CONTENT . DAMPING RATIO VERSUS AXIAL STRAIN FOR HANOVER SILT AT 10.0 cps FREQUENCY AND 21.4% WATER CONTENT. DAMPING RATIO VERSUS AXIAL STRAIN FOR HANOVER SILT AT 0.05 cps FREQUENCY AND 35.5% WATER CONTENT. DAMPING RATIO VERSUS AXIAL STRAIN FOR HANOVER SILT AT 0.3 cps FREQUENCY AND 35.5% WATER CONTENT. . . . DAMPING RATIO VERSUS AXIAL STRAIN FOR HANOVER SILT AT 1.0 cps FREQUENCY AND 35.5% WATER CONTENT. . . . DAMPING RATIO VERSUS AXIAL STRAIN FOR HANOVER SILT AT 5.0 cps FREQUENCY AND 35.5% WATER CONTENT. . . . DAMPING RATIO VERSUS AXIAL STRAIN FOR HANOVER SILT AT 10.0 cps FREQUENCY AND 35.5% WATER CONTENT . . . DAMPING RATIO VERSUS AXIAL STRAIN FOR ALASKA SILT AT 0.05 cps FREQUENCY AND 20.5% WATER CONTENT . . . DAMPING RATIO VERSUS AXIAL STRAIN FOR ALASKA SILT AT 0.3 cps FREQUENCY AND 20.5% WAHER CONTENT. . . . DAMPING RATIO VERSUS AXIAL STRAIN FOR ALASKA SILT AT 1.0 cps FREQUENCY AND 20.5% WATER CONTENT. . . DAMPING RATIO VERSUS AXIAL STRAIN FOR ALASKA SILT AT 5.0 cps FREQUENCY AND 20.5% WATER CONTENT. . . . Page 6O 61 61 64 64 65 65 66 66 67 67 68 68 69 69 70' 7O Figure 4.51 DAMPING RATIO VERSUS AXIAL STRAIN FOR ALASKA SILT AT 10.0 cps FREQUENCY AND 20.5% WATER CONTENT . . . DAMPING RATIO VERSUS AXIAL STRAIN FOR ALASKA SILT AT 29.2% WATER CONTENT ............... DAMPING RATIO VERSUS AXIAL STRAIN FOR ALASKA SILT AT 29.2% WATER CONTENT ............... DAMPING RATIO VERSUS AXIAL STRAIN FOR ALASKA SILT AT 0.05 cps FREQUENCY AND 38.9% WATER CONTENT . . . DAMPING RATIO VERSUS AXIAL STRAIN FOR ALASKA SILT AT 0.3 cps FREQUENCY AND 38.9% WATER CONTENT. . . . DAMPING RATIO VERSUS AXIAL STRAIN FOR ALASKA SILT AT 1.0 cps FREQUENCY AND 38.9% WATER CONTENT. . . . DAMPING RATIO VERSUS AXIAL STRAIN FOR ALASKA SILT AT 5.0 cps FREQUENCY AND 38.9% WATER CONTENT. . . . DAMPING RATIO VERSUS AXIAL STRAIN FOR ALASKA SILT AT 10 cps FREQUENCY AND 38.9% WATER CONTENT . . . . DAMPING RATIO VERSUS CONFINING PRESSURE FOR HANOVER SILT AT A WATER CONTENT OF 21.4% ...... DAMPING RATIO VERSUS CONFINING PRESSURE FOR HANOVER SILT AT A WATER CONTENT OF 35.5% .......... DAMPING RATIO VERSUS CONFINING PRESSURE FOR ALASKA SILT AT A WATER CONTENT OF 20.5% .......... DAMPING RATIO VERSUS CONFINING PRESSURE FOR ALASKA SILT AT A WATER CONTENT OF 29.2% .......... DAMPING RATIO VERSUS CONFINING PRESSURE FOR ALASKA SILT AT A WATER CONTENT OF 38.9% .......... DAMPING RATIO VERSUS FREQUENCY FOR HANOVER SILT AT AN AXIAL STRAIN 0F 3.16 x 10'% .......... DAMPING RATIO VERSUS FREQUENC; FOR HANOVER SILT AT AN AXIAL STRAIN OF 3.16 x 10'% .......... DAMPING RATIO VERSUS FREQUENCE FOR HANOVER SILT AT AN AXIAL STRAIN OF 3.16 x 10'% .......... DAMPING RATIO VERSUS FREQUENCE FOR HANOVER SILT AT AN AXIAL STRAIN OF 3.16 x 10’% .......... xi Page 71 71 72 72 73 73 74 74 '76 76 77 77 '78 78 79 79_ 80 Figure 4.68 DAMPING RATIO VERSUS FREQUENCY FOR ALASKA SILT AT AN AXIAL STRAIN OF 3.16 x 10’3% .......... DAMPING RATIO VERSUS FREQUENCY FOR ALASKA SILT AT AN AXIAL STRAIN OF 3.16 x 10' % .......... DAMPING RATIO VERSUS FREQUENCE FOR ALASKA SILT AT AN AXIAL STRAIN 0F 3.16 x 10' % .......... DAMPING RATIO VERSUS FREQUENCY FOR ALASKA SILT AT AN AXIAL STRAIN 0F 3.16 x 10- % .......... DAMPING RATIO VERSUS FREQUENC§ FOR ALASKA SILT AT AN AXIAL STRAIN 0F 3.16 x 10' % .......... DAMPING RATIO VERSUS FREQUENC; FOR ALASKA SILT AT AN AXIAL STRAIN 0F 3.16 x 10' % .......... DAMPING RATIO VERSUS TEMPERATURE FOR HANOVER SILT. AT AN AXIAL STRAIN OF 3.16 x 10-33 ......... DAMPING RATIO VERSUS TEMPERATURE FOR HANOVER SILT AT AN AXIAL STRAIN OF 3.16 x 10'3% ......... DAMPING RATIO VERSUS TEMPERATURE FOR HANOVER SILT AT AN AXIAL STRAIN OF 3.16 x 10'3% ......... DAMPING RATIO VERSUS TEMPERATURE FOR HANOVER SILT AT AN AXIAL STRAIN OF 3.16 x 10'2% ......... DAMPING RATIO VERSUS TEMPERATURE FOR HANOVER SILT AT AN AXIAL STRAIN OF 3.16 x 10’2% ......... DAMPING RATIO VERSUS TEMPERATURE FOR HANOVER SILT AT AN AXIAL STRAIN OF 3.16 x 10'31 ......... DAMPING RATIO VERSUS TEMPERATURE FOR HANOVER SILT AT AN AXIAL STRAIN OF 3.16 x 10'3% ......... DAMPING RATIO VERSUS TEMPERATURE FOR HANOVER SILT AT AN AXIAL STRAIN OF 3.l6 x 10-31 ......... DAMPING RATIO VERSUS TEMPERATURE FOR HANOVER SILT AT AN AXIAL STRAIN OF 3.16 x 10'2% ......... DAMPING RATIO VERSUS TEMPERATURE FOR ALASKA SILT AT AN AXIAL STRAIN OF 3.16 x 10-31 ......... DAMPING RATIO VERSUS TEMPERATURE FOR ALASKA SILT AT AN AXIAL STRAIN OF 3.16 x 10-3% ......... xii Page 80 8l 81 82 82 83 83 - 85 85 86 86 87 87 88 ' 88 89 89 Figure Page 4.85 DAMPING RATIO VERSUS TEMPERATUREZFOR ALASKA SILT AT AN AXIAL STRAIN OF 3.16 x 10' % and 0.05 cps . FREQUENCY .................... 90 4.86 DAMPING RATIO VERSUS TEMPERATURE FOR ALASKA SILT AT AN AXIAL STRAIN OF 3.16 x l0‘2% AND 0.3 cps FREQUENCY .................... 90 4.87 DAMPING RATIO VERSUS TEMPERATURE FOR ALASKA SILT AT AN AXIAL STRAIN OF 3.16 x 10‘2% AND l.O cps FREQUENCY .................... 91 4.88 DAMPING RATIO VERSUS TEMPERATURE FOR ALASKA SILT AT AN AXIAL STRAIN OF 3.16 x lO'2% ........ 91 4.89 DAMPING RATIO VERSUS TEMPERATURE FOR ALASKA SILT AT AN AXIAL STRAIN OF 3.16 x 10-31 ........ 92 4.90 DAMPING RATIO VERSUS TEMPERATURE FOR ALASKA SILT AT AN AXIAL STRAIN OF 3.16 x 10-2% ........ 92 4.91 DAMPING RATIO VERSUS WATER CONTENT FOR HANOVER . ' SILT AT A TEMPERATURE OF -1°C .......... 94 4.92 DAMPING RATIO VERSUS HATER CONTENT FOR HANOVER SILT AT A TEMPERATURE OF -I°C .......... 94 4.93 DAMPING RATIO VERSUS HATER CONTENT FOR HANOVER SILT AT A TEMPERATURE OF -1° ........... 95 4.94 DAMPING RATIO VERSUS HATER CONTENT FOR HANOVER SILT AT A TEMPERATURE OF -1°C .......... 95 4.95 _. ‘DAMPING RATIO VERSUS HATER CONTENT FOR HANOVER SILT AT A TEMPERATURE OF -4°C .......... 96 4.96 DAMPING RATIO VERSUS HATER CONTENT FOR HANOVER SILT AT A TEMPERATURE OF -lO°C .......... 96 4.97 DAMPING RATIO VERSUS HATER CONTENT FOR ALASKA SILT AT A TEMPERATURE OF -1°C .......... 97 4.98 DAMPING RATIO VERSUS HATER CONTENT FOR ALASKA SILT AT A TEMPERATURE OF -I°C .......... 97 4.99 DAMPING RATIO VERSUS WATER CONTENT FOR ALASKA SILT AT A TEMPERATURE OF -1°C .......... 93 xiii Figure 4.100 4.101 4.102 DAMPING RATIO VERSUS WATER CONTENT FOR ALASKA SILT AT A TEMPERATURE OF -1°C .......... DAMPING RATIO VERSUS WATER CONTENT FOR ALASKA SILT AT A TEMPERATURE OF -4°C .......... DAMPING RATIO VERSUS WATER CONTENT FOR ALASKA SILT AT A TEMPERATURE OF -10°C .......... DYNAMIC YOUNG' S MODULUS VERSUS CONFINING PRES URE FOR KAOLINITE AT AN AXIAL STRAIN 0F 5. 0 x 10' %. DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR KAOLINITE AT 28.1% WATER CONTENT ......... DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR KAOLINITE AT 71.3% WATER CONTENT ........ DYNAMIC YOUNG'S MODULUS VERSUS AXIAL STRAIN FOR KAOLINITE at 71.3% WATER CONTENT ......... ' DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FgR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10' % DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FBR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10' % DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FgR KAOLINITE AT AN AXIAL STRAIN 0F 3.16 x 10' % DYNAMIC YOUNG'S MODULUS VERSUS FREQUENCY FgR KAOLINITE AT AN AXIAL STRAIN 0F 3.16 x 10' % DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FOR KAOLINITE AT AN AXIAL STRAIN 0F 3.16 x 10'3%. . . DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10'2%. DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE 3FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10"3 %. DYNAMIC YOUNG'S MODULUS VERSUS TEMPERATURE FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10'2%. . . DYNAMIC YOUNG'S MODULUS VERSUS HATER CONTENT FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10-31. . . xiv Page 98 99 99 103 103 104 104 -106 106 107 107 108 108 109 '109 111 Figure 5.14 DYNAMIC YOUNG'S MODULUS VERSUS HATER CONTENT FOR 16 x 10-21. KAOLINITE AT AN AXIAL STRAIN OF 3. DAMPING RATIO VERSUS AXIAL STRAIN AT 28.1% WATER CONTENT .............. DAMPING RATIO VERSUS AXIAL STRAIN AT 28.1% WATER CONTENT .............. DAMPING RATIO VERSUS AXIAL STRAIN AT 28.1% WATER CONTENT .............. DAMPING RATIO VERSUS AXIAL STRAIN AT 28.1% WATER CONTENT .............. DAMPING RATIO VERSUS AXIAL STRAIN AT 28.1 WATER CONTENT .............. DAMPING RATIO VERSUS AXIAL STRAIN AT 71.3% WATER CONTENT .............. DAMPING RATIO VERSUS AXIAL STRAIN AT 71.3% WATER CONTENT .............. DAMPING RATIO VERSUS AXIAL STRAIN AT 71.3% HATER CONTENT -------------- DAMPING RATIO VERSUS AXIAL STRAIN AT 71.3% WATER CONTENT .............. DAMPING RATIO VERSUS AXIAL STRAIN AT 71.3% WATER CONTENT .............. FOR FOR FOR FOR FOR FOR FOR FOR FOR FOR KAOLINITE KAOLINITE KAOLINITE KAOLINITE KAOLINITE KAOLINITE KAOLINITE KAOLINITE KAOLINITE KAOLINITE DAMPING RATIO VERSUS CONFINING PRESSURE FOR KAOLINITE AT A WATER CONTENT OF 28.1% . DAMPING RATIO VERSUS CONFINING PRESSURE FOR KAOLINITE AT A WATER CONTENT OF 71.3% ...... DAMPING RATIO VERSUS FREQUENCY FgR KAOLINITE % ........ AT AN AXIAL STRAIN OF 3.16 x 10‘ DAMPING RATIO VERSUS FREQUENCY FQR KAOLINITE %. . .' ..... AT AN AXIAL STRAIN 0F 3.16 x 10' DAMPING RATIO VERSUS FREQUENCY FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10-31 ........ XV Page 111 113 113 114 .114 115 115 116 116 117 117 119 119 120 120 121 Figure Page 5.30 DAMPING RATIO VERSUS FREQUENCY FQR KAOLINITE % ........ AT AN AXIAL STRAIN OF 3.16 x 10' 121 5.31 DAMPING RATIO VERSUS TEMPERATURE FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10-31 ........ 123 5.32 DAMPING RATIO VERSUS TEMPERATURE FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10'2% ........ 123 5.33 DAMPING RATIO VERSUS TEMPERATURE FOR KAOLINITE . AT AN AXIAL STRAIN OF 3.16 x 10'3% ........ 124 5.34 DAMPING RATIO VERSUS TEMPERATURE FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10-21 ........ . 124 5.35 DAMPING RATIO VERSUS HATER CONTENT FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10’3% ........ 125 5.36 DAMPING RATIO VERSUS HATER CONTE T FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10- z ........ 125 5.37 DAMPING RATIO VERSUS HATER CONTENT FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10'3% ........ 125 5.38 DAMPING RATIO VERSUS HATER CONTENT FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10-23 ........ 125 5.39 DAMPING RATIO VERSUS HATER CONTENT FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10'3% ........ 127 5.40 DAMPING RATIO VERSUS HATER CONTENT FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10'2% ........ 127 6.1 HAVE VELOCITY VERSUS TEMPERATURE OF FROZEN SILT . 13] 6.2 LONGITUDINAL HAVE VELOCITY VERSUS FREQUENCY OF FROZEN SILT AND CLAY, .............. 132 6.3 LONGITUDINAL HAVE VELOCITY VERSUS AXIAL STRAIN AMPLITUDE OF FROZEN SILT AND CLAY ........ 134 6.4 DAMPING RATIO VERSUS TEMPERATURE OF FROZEN SILT . 136 6.5 DAMPING RATIO VERSUS FREQUENCY OF FROZEN SILT AND CLAY ..................... 137 6.6 DAMPING RATIO VERSUS AXIAL STRAIN AMPLITUDE OF FROZEN SILT AND CLAY ............... 139 xvi Figure Page 5.30 DAMPING RATIO VERSUS FREQUENCY FQR KAOLINITE % ........ AT AN AXIAL STRAIN OF 3.16 x 10' 121 5.31 DAMPING RATIO VERSUS TEMPERATURE FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10-31 ........ 123 5.32 DAMPING RATIO VERSUS TEMPERATURE FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10-21 ........ 123 5.33 DAMPING RATIO VERSUS TEMPERATURE FOR KAOLINITE . AT AN AXIAL STRAIN OF 3.16 x 10-3z ........ 124 5.34 DAMPING RATIO VERSUS TEMPERATURE FOR KAOLINITE - AT AN AXIAL STRAIN OF 3.16 x 10'2% ........ . 124 5.35 DAMPING RATIO VERSUS HATER CONTENT FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10-3% ........ 125 5.36 DAMPING RATIO VERSUS HATER CONTENT FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10-21 ........ 125 5.37 DAMPING RATIO VERSUS HATER CONTENT FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10-31 ........ 125 5.38 DAMPING RATIO VERSUS HATER CONTENT FOR KAOLINITE AT AN AXIAL STRAIN 0F 3.16 x 10-21 ........ 125 5.39 DAMPING RATIO VERSUS HATER CONTENT FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10-31 ........ 127 5.40 DAMPING RATIO VERSUS HATER CONTENT FOR KAOLINITE AT AN AXIAL STRAIN OF 3.16 x 10-2% ........ 127 6.1 HAVE VELOCITY VERSUS TEMPERATURE OF FROZEN SILT . 13] 6.2 LONGITUDINAL HAVE VELOCITY VERSUS FREQUENCY OF FROZEN SILT AND CLAY, .............. 132 6.3 LONGITUDINAL HAVE VELOCITY VERSUS AXIAL STRAIN AMPLITUDE OF FROZEN SILT AND CLAY ........ 134 6.4 DAMPING RATIO VERSUS TEMPERATURE OF FROZEN SILT . 136 6.5 DAMPING RATIO VERSUS FREQUENCY OF FROZEN SILT AND CLAY ..................... 137 6.6 DAMPING RATIO VERSUS AXIAL STRAIN AMPLITUDE OF FROZEN SILT AND CLAY ............... 139 xvi Figure 6.7 (5.8 WAVE VELOCITY VERSUS TEMPERATURE OF FROZEN CLAY ....................... LONGITUDINAL WAVE VELOCITY VERSUS LIQUID LIMIT OF FROZEN CLAY ................... DAMPING RATIO VERSUS TEMPERATURE OF FROZEN CLAY . xvii Page 140 142 144 LIST OF SYMBOLS confining pressure damping ratio dynamic Young's modulus complex Young's modulus frequency complex shear modulus liquid limit plasticity index plastic limit shear wave velocity loss factor longitudinal wave velocity compression wave velocity water content .lag angle between stress vector and strain vector Poisson's ratio density dynamic stress xviii H}- u: CHAPTER 1 INTRODUCTION 1.1 Statement of the Problem Much attention has been focused in recent years on the evalua- tion of the dynamic properties of frozen soils. Such information is most appropriate when considering the future development of Alaska, where the design of structures may require knowledge of the mechanical properties of permafrost deposits on which structures may be founded. Since southern Alaska lies within one of the worlds major seismic zones, engineers should especially consider the dynamic properties of the frozen soil deposits under earth— quake loading conditions. While some field and laboratory work has been done to evalu- ate the dynamic properties of frozen soils, most of the work has been done over ranges of test parameters which might be inappro- priate for use in a seismic analysis of a structure founded on a frozen soil deposit. Test strain amplitudes, for example, have generally been much lower than those associated with strong-motion earthquakes, while test frequencies have generally been much higher. Thus, an engineer might be unable to predict ground motions for a design earthquake in a permafrost region since the necessary dynamic properties of the soils have not been determined. 1.2 Purpose and Scope of Studies The purpose of this research program is to: (1) Evaluate the dynamic Young's modulus and damping ratio of frozen silt and clay over ranges of test condition parameters that would be useful for ground motion predictions of permafrost deposits during earthquakes. (2) Investigate the influence of various parameters that might affect the dynamic Young's modulus and damping ratio of frozen silt and clay. ’ The scope of this research program includes a description of sample preparation and experimental techniques used in evaluating the dynamic properties of frozen silt and clay, a discussion of the experimental results, and a comparison of the results obtained in this program with the results obtained by previous investi- gators. Information on the thermal and mechanical properties of ice and frozen soils and the dynamic properties of unfrozen soils - which is essential to an understanding of the dynamic properties of frozen soils - has been summarized by Chaichanavong (1976). To better understand the extent and nature of the soils tested in naturally occurring frozen deposits, the remainder of this chapter provides information on the distribution and structure of the various soil deposits in Alaska. Chapter 2 summarizes the results of previous research to evaluate the dynamic properties of frozen fine-grained soils. Chapter 3 provides information On the pre- paration of the frozen soil samples used in the research program, installation of the samples in a triaxial cell, and the test pro— cedure employed. The test results for silt and clay are discussed in Chapters 4 and 5, respectively. The relationships between dynamic Young's modulus and damping ratio of the soils tested and confining pressure, strain amplitude, temperature, frequency, and water content are also presented in these chapters. Chapter 6 R .- X‘r f h '5 provides a comparison between the results obtained in this research and the results obtained by previous investigators. A summary of the results obtained in the research program is provided in Chapter 7. 1.3 Distribution of Frozen Soil Deposits in Alaska The unconsolidated surficial deposits in Alaska consist of soils of all types and of all origins. They have been described and mapped by many investigators and are summarized by Woods et al (1962) and Williams and Waller (1963). An evaluation of the various soil deposits in Alaska is best made on a regional basis; the basic physiographic regions of Alaska and corresponding soil deposits associated with each region are summarized in Figures 1.1 and 1.2. 1.3.1 Northern Alaska Northern Alaska as discussed here includes three physiographic regions: the Arctic Rockies, the Arctic Foothills, and the Arctic Coastal Plain. The Arctic Rockies - loosely synonymous with the Brooks Range — is generally a mountainous area with little or no soil cover. The Arctic Foothills lie between the Arctic Rockies to the south and the Arctic Coastal Plain to the north and are characterized by erosional rather than depositional features; soil deposits are thin and generally consist of sand and silt, with some gravel associ- ated with streams. The Arctic Coastal Plain is the northernmost region and contains extensive deposits of fluvial and marine sedi— ments up to 150 feet thick. The sediments consist primarily of sands and silts with occasional gravel, clay, and peat. The soils are generally permanently frozen over their entire depth, with permafrost extending from 600 to 1300 feet beneath the ground surface. —-J —-l A —4c>u>a:\40101¢-01n9-a Coast Range Alaska Basins Alaska Range Seward-Peninsula Bering Shelf Ahklun Mountains Western Alaska Northern Plateau Arctic Rockies Arctic Foothills Arctic Coastal Plain Figure 1.1 PHYSIOGRAPHIC REGIONS OF ALASKA (after Lovell and Roberts, 1975) Clay shale (with some limestone) - ‘.’ ‘ Metamorphic ond intrusive rocks (schist. gneiss, slate, granite. etc.) ’ [Intrusive rocks (basalt and low) Gloclol Soils \. \§ Yoimg dritt (Wisconsin and Iowan Ages) .\\ Water-deposited Soils Gravel ond sand Valley till. Consolidated to unconsolidated % sands. silts, grovels. clays, tufts, volcanic ash Sand-clay; Interbedded and intermixed sands. clays, grovels. and silts oi the Coastal Plain (includes semigrsonulor deposits in the interior of A to filth muskeg cover) Miscellaneous ' : Glacial Ice Nonsoll oreos (locations in which the soil is very 111111 or otherwise has little e l- neering significance because at rouo fiapoqroohy or euposed rock; Including mountains. conpns. scoblonds, or _ tbodlonds and Ice-scoured areas olthe Loonntion upload) Figure 1.2 GENERALIZED SOILS MAP OF ALASKA (after Woods et al, 1962) 1.3.2 Central Alaska Central Alaska as discussed here includes the area of Alaska between the Brooks Range in the north and the Alaska Range in the south and between the Canada-Alaska boundary in the east and the Bering Sea in the west. The area can be divided into the following physiographic regions: Northern Plateau, Western Alaska, Seward Peninsula, Bering Shelf, and Ahklun Mountains. The most extensive soil deposits in Central Alaska are alluvial deposits associated with the Yukon and Kuskokwim drainage basins in the Northern Plateau, Western Alaska, and Bering Shelf regions. The deposits are generally thick and consist primarily of silt, gravel, and sand. The soil deposits generally occur in flood plains and terraces of valleys and outwash plains and alluvial fans fronting the mountains. The Yukon-Kuskokwim delta in the Bering Shelf region con- sists of silt, sand and gravel to a depth of almost 1000 ft. Coastal plain deposits occur over the entire Bering Sea coast; on the Seward Peninsula the deposits consist primarily of gravel on the southern coast and silt on the northern coast. Additional soil deposits which occur in local areas include 1acuStrine deposits, glacial drift in mountainous areas which had been glaciated, and eolian deposits of silt and sand, generally less than 60 ft. thick, over alluvial de- posits and upland areas. Central Alaska is generally an area of discontinuous permafrost. The depth of permafrost varies considerably throughout the area; de- posits in the Yukon-Kuskokwim delta are frozen to depths of 350 to 600 ft. while deposits bordering Bristol Bay farther south are frozen in some places to depths of 150 ft. Alluvial deposits in Central Alaska are generally unfrozen beneath river and stream channels and oxbow lakes and are frozen to depths ranging up to 300 ft. and more elsewhere. The depth and areal extent of permafrost is generally greater in higher flood-plain deposits than in lower deposits and is also greater in northern regions than in southern regions. 1.3.3 Southern Alaska Southern Alaska includes the Alaska and Coast Ranges and the Alaska Basins. The Alaska and Coast Ranges consist of rugged mountainous topography and contain little or no soil cover except in low places, where gravelly glacial outwash occurs. The Alaska Basins lie between the Alaska and Coast Ranges and include the Copper River Valley in the eastern section and the Matanuska Valley in the western section. The Copper River Valley contains deposits of granular material up to several hundred feet in thickness; silt and sand cover the granular material in the flood plain and silty glacial till occurs in areas closer to mountains. The Matanuska Valley contains thick deposits of granular outwash covered in many places by thin deposits of fluvial and eolian silt. Southern Alaska is near the southern boundary of the perma- frost zone; permafrost in the area is thus discontinuous and gen- erally thin. In the Matanuska Valley permafrost is sporadic; in the center of the Copper River Valley, sediments are frozen to depths of 100 to 200 ft. 1.4 Structure of Frozen Soil Deposits Frozen soil deposits can occur in several forms determined by the amount and structure of interstitial ice. The structure of ice in frozen ground is dependent on soil type, availability of moisture, and other factors and can be classified as disseminated ice, ice gneiss, and massive ice. Disseminated ice typically occurs as ice uniformly distributed through a soil mass, resulting in a homogeneous appearance; the frozen soil may be saturated or unsaturated with ice generally taking up less volume than soil particles. Ice gneiss is characterized by foliated layers of ice and soil, with ice typically taking up from 30% to 90% of the total volume; ice gneiss is especial- ly common in permafrost with a high silt content. Massive ice typi- cally occurs as thick deposits containing relatively little soil, with ice contents ranging up to 1000% over depths of several tens of feet. Massive ice may be associated with variable soil types but is often found overlying sand and gravel deposits. CHAPTER 2 DYNAMIC PROPERTIES OF FROZEN SILT AND CLAY 2.1 General This chapter provides information on the results of previous investigations to evaluate the dynamic properties of frozen silt and clay. The dynamic properties that have been evaluated by various investigators using different testing techniques fall into two cate- gories: (1) dynamic elastic properties and (2) damping properties. Dynamic elastic properties are given in terms of dynamic Young's and shear moduli, complex Young's and shear moduli, sound velocity, and compression, dilatational, longitudinal, irrotational, primary, bulk, or "P" and shear, transverse, secondary, rotational, or "S" wave velocities. Damping properties are expressed in terms of angle of phase lag, attenuation coefficient, damping coefficient, loss factor, quality factor, log decrement, and damping ratio. Con- version equations between the various terms can be used to allow direct comparisons to be made between the results obtained by dif- ferent investigators. These equations are given by Chaichanavong (1976). 2.2 Previous Research on the Dynamic Properties of Frozen Soils A summary of the results from previous investigations to evalu- ate the dynamic properties of frozen clays has been presented by Chaichanavong (1976). The remainder of this chapter will concentrate culthe results of investigations to evaluate the dynamic properties of frozen silts. Field techniques have been widely used to evaluate the dyna- rnic elastic properties of frozen soils. The most common method lJSEd is the seismic method, which involves the measurement of com- ;Dressional and shear wave velocities in naturally frozen soil depos- ‘its. A summary of wave velocities in frozen silt deposits obtained lay several investigators is given in Table 2.1. The dynamic properties of frozen silts have been investigated EJsing various laboratory techniques by Kaplar (1969), Nakano and [Froula (1973), and Stevens (1973). Silt samples tested in the labo- sratory have generally been artificially prepared; Stevens (1973), Fiowever, has tested silt which had been cored in a naturally frozen estate. Kaplar (1969) and Stevens (1973) used a resonant frequency Tnethod in their testing programs; Nakano and Froula (1973) used an tJltrasonic method. The apparatus and experimental technique used buy each investigator is described in detail by Chaichanavong (1976). ELL; Dynamic Elastic Properties of Frozen Silt The influence of various parameters on the dynamic elastic prop- Eirties of frozen silt has been investigated by Kaplar (1969), Nakano aaid Froula (1973), and Stevens (1973). The parameters considered iliclude stress or strain amplitude, frequency of loading, tempera- tJJre, void ratio or water content, and degree of ice saturation. 2.3.1 Effect of Void Ratio The effect of void ratio on the dynamic elastic properties of 'frozen silt has been investigated by Stevens (1973) and is summarized 10 umm\Ex m.~ mmmcmr mxmm_< oom.P- op o.~ 66? ;p_z Seem .ma< campmcu Amum_v cesopm omm\sx mm.m uo~.3- op mo.~ 332m mxcanccua A3No_v capes: 665\E¥ N.N 66? new p_wm . Amkmyy uwm\sx m.P Ame zucmm ucmFmH mLmEmmPFM Lopez: ucm mcmmo wmzpAHoosm> m><3 SHOW oneqooe muzwmmdum 4HHu04m> m><3 do mhzmzmm2mf= frozen silt has been investigated by Stevens (1973). As shown in F‘i gure 2.2, the complex shear modulus increases significantly as the cieaggree of ice saturation in the voids increases. The complex shear nic> b ‘ / . s - ' - ‘ . § 11 .. ‘ _ _‘ .a _ O Q ' _1 5 / - . _ 1- g L- a .. t; to u .. . g - . . . .1 , New Hampshtte sm .. ,1 n, I‘LL _LL 1 u 1_l 1 l 14 1 l 1 1 e I 1 1.1 ‘ so 20 10 o —10 ~ 20 TEMPERATURE ,’F ' IZI10‘ 1 ‘I j T' i 7 T 1 f Y T TV T a U I V V T I I I T )- ' 4 _4 F- i ‘ 4 3 L : ,rf 1 :1 ll A J >_‘ P- “! 1 I " L- r e/ i 1 8 - , I «' 3 F :5 1 9 : i > 'c T i 3+ f > P “I. I I ' ‘ -1 3 ‘ 5"- ‘ | f I . .J 7 l , ' IL " 2 ’ . I I T 3 ~ -' . ‘ A . . -‘ ': ~ I Fairbanks Silt . o __ i 3 . I l .1 T , t l I -( ,4 r i l - P- : ' 4 7 L L l 1 J 1 I 1 44 1 J J 1 L J I I 1 I 1 I I 1 A 30 20 IO 0 -IO -20 TEMPERATURE .‘F l2 s to. I Y I T 1' Y T I I I Y 1 T 7 Y Y T T 1 T F- .4 I- -1 3 ' ' ‘ Y— 1‘ / "l :1 ll LL. . F' t' . T E 1- Y‘ ‘ q » -i 8 b g .1 s I ' 3 3 . . ~ 1 i ' A g -1 __ Yukon slit 4 g .. . I ". 1 f - 1 l l j l 1 l A L L l l l 1 l A LJ 20 -IO -20 nuetnawnefr F‘ . 'gure 2-3 LONGITUDINAL HAVE, VELOCITY VERSUS TEMPERATURE FOR FROZEN NEH HAMPSHIRE SILT. FAIRBANKS SILT, AND YUKON SILT (after Kaplar, 1969) 14 Figure F'gUre 2.6 I I T y. 2.4 1- '1 e I . 5 2-2 ’ Hanover sm 3" T ‘ . ' . - - . (P"-33 o/CM’I « 15 2.0 - " > 1.8 - ‘ F l 1.6 1 1 1 1 ‘ ‘ -16 -12 -a '4 0 Temperature. 'C Figure 2.4 S-WAVE VELOCITY VERSUS TEMPERATURE FOR FROZEN HANOVER SILT (after Nakano and Froula, 1973) 3! s. . Des 11 $5 a 97.2 - 0.13 E. " 3m 0‘ - 914 0.73 _ .._. E 97.2 - 0.73 . *— ‘ F-M- u st SH 6' - 914—10131 G W" " ' j T f Y I V Y 7 fi I Y r V V T 1 .1 b "4—\ 5.,6. ‘ 1— ‘ (016' ~ ‘\ tO’L— E i N "' \ '1 E b 2 ’- .1 z , . 3‘ L '5 1 i 1.0.? _1 . ‘ 2 T 1 i I ‘ F 1 U r- .9 .0 F J .3 Y- 4 u I . a 4 107 -: F . . :- E'——-—o': 1 ‘-20‘-F6 -12 -a :4 ‘ o 4 8 {2 l6 Temperolufl. 'C Figure 2.5 EFFECT OF TEMPERATURE ON COMPLEX MODULI OF FROZEN MANCHESTER SILT (after Stevens, 1973) 15 1m resuit decree 1011. “1‘ CC!” (T) D.) C)- to 5.5 lr\.> In) >—-4 Stevens (1973) has studied the influence of temperature on the dynamic complex Young's and shear moduli of Manchester silt. The results are shown in Figure 2.5. The dynamic complex Young's modulus decreases from 2.5 x 103 MN/m2 at -18°C to 1.9 x 103 MN/m2 at ~4°C and to 11.0 MN/m2 in the unfrozen state. The dynamic complex shear modulus decreases from 9.5 x 102 PIN/m2 at -18°C to 7.5 x 102 MN/m2 at -4°C and to 5.5 MN/m2 in the unfrozen state. 2.3.4 Effect of Frequengy The influence of frequency on the dynamic elastic properties of frozen silts has been studied by Stevens (1973). As shown in Figure 2.6, the complex shear modulus of frozen Hanover-Manchester silt increases slightly with increasing frequency between 1.0 kHz and 1000 kHz, with much of the increase occurring in the 1-5 kHz range. Stevens suggests that a significant decrease in shear modulus might result if testing was done at much lower frequencies. L215 Effect of Dynamic Stress or Strain Information on the effect of dynamic stress on the dynamic elastic properties of frozen silts is given by Stevens (1973). As shown in Figure 2.7, the complex shear modulus of Manchester silt decreases slightly with increasing dynamic stress between 0.7 kN/m2 and 34.5 kN/mz. In general, the influence of stress is greater at higher temperatures, lower frequencies, and higher stress levels. W119 Properties of Frozen Silt The damping properties of frozen silt have been studied by St ° ' evens (1973). The influence of temperature on damang (1n terms of ta" 5) for Manchester silt is shown in Figure 2.8. The overall 16 5': fit 1 I V'Y'Yl Y foIY—Iv' I ‘—T I VIVTVI ’ fl. N V _1_ Hanover - Manchester Silt 6' Complex Shear Modulus. GN/mz - -|7.7°C er 8%. r ——-o- '3.9°C 4 I 34.111Il 1 IIIIIIJ I .JIIIIJI 10° 10' 1o2 10’ Frequency. kHz Figure 2.6 COMPLEX SHEAR MODULUS VERSUS FREQUENCY FOR FROZEN HANOVER-MANCHESTER SILT (after Stevens, 1973) I 'I'r'l I I I V‘Ijv' r T e=0.73 10L ~ ea °C no. ............................ E _I7 7{ eeeeeee v eeeeeeeeeeeeeeeeeeeeeeee 0.. 5 ’ ' 73L- ---------- ‘°'---—--—-9- ‘ o 2 a" 9" Q. 3 mmwummmmuuuweflu.wuou_.guuu. ”.0; 3 '9.4 ““v ‘5 ” de— 2 A a e- 2 m L x b _: F-3.9{I3:.u.u.u.wm.g.‘u.;.g...o..='.:—...—..£m23:61. 6 7~ - ‘ fl. 0 0 ‘0, '- Manchester Silt. saturated ‘ 6 1 s 1 L14] 1 a l A j e 1 Al J J j 10° to' 05 Dynamic Stress kN/m’ Flgure 2.7 COMPLEX SHEAR MODULUS VERSUS DYNAMIC STRESS FOR FROZEN MANCHESTER SILT (after Stevens, 1973) 17 IQUTE .\ FF - 5- . Design. % I 8 Manchester Silt 95.8 0J2 V I I 1 .2 3 0.08r O :3. 0.04» B O c >- O '— 920 4‘5 40 -5 o 5 lb 15 20 Temperature °C Tan 8 (Torsional) .0 O b i I j, o l l l L 1 A -20 ~15 -10 -5 0 5 10 IS 20 Temperature 'C Figure 2.8 EFFECT OF TEMPERATURE ON TAN 6 OF FROZEN MANCHESTER SILT (after Stevens, 1973) T F T T I ' 0.06~ ~ 8 F i .9 fl 3 .I— ~— o.04- ~ so 8 1.. 1- d 0-02" Manchester Silt '1 J leJJlel 4 11411111 1 I 11111 10° 10' IO FrequenCy kHz Figure 2.9 EFFECT OF FREQUENCY 0N TAN 6 OF FROZEN MANCHESTER SILT (after Stevens, 1973) 18 relationship between damping and temperature is not entirely clear; it appears that longitudinal damping in frozen silt is less than in unfrozen silt and decreases with increasing temperature while tor- sional damping in frozen silt is greater than in unfrozen silt and increases with increasing temperature. The influence of frequency on damping has been studied by Stevens (l973). As shown in Figure 2.9, damping of frozen Manchester silt decreases with increasing frequency between 1 and l0 kHz. The influence of dynamic stress on damping of frozen silt has been1 studied by Stevens (1973) and is shown in Figure 2.10. Damping of"frozen Manchester silt increases slightly with increasing dynamic strwass between 0.7 kN/m2 and 34.5 kN/mz; the influence of dynamic stress on damping is generally greater at higher stress levels than at Tower stress levels. 19 —lkHz —---5kHz --------- lOkHz 00000-000." 006r O‘OIOOOOIHIOIOOO000000000000... Tan 87 ”‘my J —————— _o._.._..——-- —o ______ 0.04 l- - d I l l l l L l l l l Io° Io' 0", Dynamic Stress lTN/m2 °-—9.4 oc T‘I'l T fl l fI'T‘] I ' T 0.08' / .T Tan 81. 0.06» . F '0 ——————————— o--—-—"""'.':: .. on... O o 04 l A 141 l A l 1 l A l 1] L 1 l ' uo° . Io‘ 2 05 Dynamic Stress kN/rn b. - 3.9 '6 Figs}. 2.10 EFFECT OF DYNAMIC STRESS 0N TAN 5 OF FROZEN MANCHESTER SILT (after Stevens, l973) 20 l‘” ce' pr: rel dea CHAPTER 3 SAMPLE PREPARATION, SAMPLE INSTALLATION TRIAXIAL CELL ASSEMBLY AND TEST PROCEDURE 3.1 General This chapter deals with the laboratory preparation of frozen silt and clay samples, installation of the samples in a triaxial cell, triaxial cell assembly, and the test procedure used in the program. A basic knowledge of the components of the test system is assumed. The MTS electrohydraulic closed-loop test system, the refrigeration unit, the triaxial cell, and the output recording devices used in the testing program are described in detail by Chaichanavong (1976). 3.2 Preparation of Frozen Silt Sample Two types of silt were used in the testing program: Hanover silt, termed HS, and Alaska silt, termed AS. Physical properties of both silts are given in Figure 3.1. Samples were prepared at two water contents for each of the two silts to assess the influence of water content and dry density on the dynamic properties of silts. All samples were formed and frozen to aluminum coupling devices in a hollow cylindrical teflon mold 30.5 cm high, 7.1 cm in inside dia- meter, and 1.3 cm thick. The high density (low water content) samples for both Hanover silt and Alaska silt were prepared as follows: (1) A silt slurry with a water content of approximately 36% was made by adding distilled water to oven-dried silt and mixing thorough- ly. The slurry was then placed in a triaxial cell and consolidated 21 AIV Bully DU 6 u.£.w..03 \fiQ LUC~R UCOULOQ Design. Soil LL PL PI _ 1 HS Hanover Silt 22 -- NP AS ATaska SiTt 28 23 5 K ' Kaolinite 40 23 T7 SANS SILT CLAY 100’ :1 T T‘T T"T 1 TTT T l 14*: 1 iii gaob '8 3 >, .- .0 S- 1 cc, 1 [sop K 4.) C Q, 8 r- £3 40— 20 - \ \ O -J ' LJJJ 11 .L 1 L111] 4,; J 111 0.1 .OT .00] Grain Size (mm) Figure 3.1 GRADATION CURVES FOR SOILS 22 EF‘C 13.": ‘11 (It :- (r; isotropically under a cell pressure of 40 psi for 24 hours. (2) The sample was removed from the consolidation cell and trimmed to a diameter approximately equal to the inside diameter of the mold. Material trimmed from the sample was packed tightly around the couplings on the caps; the sample and the caps were then placed in the mold. The caps were then hammered vigorously to assure a good bond between the main portion of the sample and the material around the couplings and to allow any entrapped air to escape. A small hole near the top of the mold facilitated the removal of air. The mold was then placed in a freezer at -30°C and left for 24 hours. (3) The mold was then removed from the freezer. The sample was extruded from the mold as quickly as possible, weighed, trans— ferred to a freezer, and jacketed with two rubber membranes. The sample was now ready for installation in the triaxial cell. A typical frozen sample is as shown in figure 3.2. The high density frozen silt samples were uniform in appearance with occasional ice lenses in the outer portion of the sample and were classified as ML, an (Linell and Kaplar, 1966). The water content was reasonably uniform over the length of the sample, with a slight- ' ly higher water content in the vicinity of the caps. Average water contents were 21.4% for Hanover silt and 20.5% for Alaska silt. The low density (high water content) samples for both Hanover silt and Alaska silt were prepared as follows: (1) A silt slurry with a water content of 51% was made by add- ing the appropriate amount of distilled water to oven-dried silt 23 Figure 3.2 TYPICAL FROZEN KAOLINITE SAMPLE 24 and mixing thoroughly. The slurry was stored at a temperature slightly above 0°C for 24 hours. (2) The teflon mold and aluminum caps were precooled to -30°C. The slurry was mixed again and poured into the mold with the bottom cap in place. Additional slurry was packed around the coupling of the top cap, which was then set in the mold and hammered to remove any entrapped air. The mold was then placed on its side in a freezer at -30°C for 24 hours. In order to prevent settlement of the silt particles before freezing, the sample was rotated 180° every 10 minutes for the first three hours after being placed in the freezer. (3) The mold was removed from the freezer and the sample was extruded, weighed, and jacketed with membranes as described above. The resulting low density frozen silt samples were classified ML, Nbe. They contained a layer approximately .1" thick consisting of silt with ice lenses around the entire sample. While the interior of the sample appeared to be uniformly frozen with no ice lenses, the water content varied significantly from the center to the ends of the sample. The distribution of water content over the effective length of the sample (between top and bottom coupling) for both Hanover silt and Alaska silt is shown in Figure 3.3. It is apparent that the permeability of both silts was great enough to allow significant migration of water in both a radial direction and along the length of the sample during the freezing process. This movement occurred despite efforts to freeze the sam- ple as quickly as possible by precooling the slurry, mold, and caps. Since a uniform water content could not be obtained, the water con- 25 Hanover silt Alaska Silt Figure 3.3 DISTRIBUTION OF WATER CONTENT OVER LENGTH OF HIGH WATER CONTENT FROZEN SILT SAMPLE 26 m' H as fr fn ple dur sil the UlOr Has ‘ tent was taken as the weighted average water content of the material over the effective length of the sample excluding the silt-ice layer around the outside of the sample. Average water contents determined using this technique were 35.5% for Hanover silt and 38.9% for Alaska silt. ' Two samples of Alaska silt were prepared at water contents intermediate between high and low water contents. The procedure used was similar to the method used in preparation of the high water content samples, with the major difference being the use of a slurry with a water content of 36%. The frozen sample was similar in appearance to the high water content sample and had an average water content of 29.2%. 3.3 Preparation of Frozen ClayiSample The clay used in the testing program was a commercial kaoli- nite, termed K. Physical properties of the kaolinite are given in Figure 3.1. Clay samples were prepared at two water contents to assess the influence of water content on the dynamic properties of frozen clay. The same mold and caps used in the preparation of frozen silt samples were used in the preparation of frozen clay sam- ples. The low water content clay samples were prepared with a proce- dure similar to that used in the preparation of high density frozen silt samples. A clay slurry of 50% water content was made by adding the appropriate amount of distilled water to dry clay and mixing thoroughly. After setting for a minimum of three days, the slurry was consolidated isotropically under a cell pressure of 40 psi for 27 24 hours; the final water content after consolidation was 35%. The sample was then removed from the consolidation cell, trimmed, placed in the mold, and frozen as described previously. The resulting low water content frozen clay samples were classified CL, an. They contained a layer approximately .1" thick consisting of ice and clay with ice lenses around the entire sample. The interior of the sample had few apparent ice lenses and a rea- sonably uniform water content over the effective length of the sam- ple. The average water content of the sample excluding the clay-ice layer in the outer portion was 28.1%. It was found that high water content clay samples could not be prepared in the same way as low density silt samples due to the re- sulting large degree of non-uniformity in both structure and water content over the length of the frozen sample. Significant migra- tion of water during the freezing process resulted in a sample which had a uniformly frozen structure with a water content of about 30% in the central part and a structure consisting of horizontal layers of ice and frozen clay with a total water content of about 110% near the outer portions of the sample. To alleviate this problem, high water content clay samples were prepared by adding clay slurry in layers, with each layer added after the previous layer had frozen. The high water content clay samples were prepared with the following procedure: (1) A clay slurry with a water content of 75% was made by adding the appropriate amount of distilled water to dry clay and mixing thoroughly. The slurry was stored for a minimum of two days and precooled to a temperature slightly above 0°C before use. 28 (2) The aluminum caps were precooled to -30°C. Clay slurry was packed around the coupling on the bottom cap, which was then placed in the mold. Additional slurry was poured into the mold to the top of the coupling and the mold was placed in the freezer at -30°C. The mold in this case was not precooled and was surrounded radially by additional insulation; the purpose of this was to assure that the sample would freeze vertically rather than radially. (3) After the slurry above the coupling had formed a crust, a second layer of slurry was added to a depth of approximately 3/4". Additional 3/4" layers of slurry were added in succession after a crust had formed on each previous layer. After the last layer was in place, slurry was packed around the coupling of the top cap; the top cap was then set in the mold and hammered as described previously. (4) After 24 hours, the mold was removed from the freezer and the sample was extruded, weighed, and jacketed with membranes as described earlier. The resulting high water content frozen clay sample was classi- fied CL, Vs and had a structure consisting of predominantly hori- zontal layers of ice and clay throughout. Ice lenses, which varied from .02" to .04" in thickness, were generally non-uniformly distri- buted over the length of the sample, resulting in a water content which varied over the length of the sample; a typical water content dis- itribution is as shown in Figure 3.4. The average water content of the sample obtained using a weighted average technique was 71.3%. 29 Kaolinite 60.2% 54.0% 83.8% 78.2% 78.l% ER“ If Figure 3.4 DISTRIBUTION OF WATER CONTENT OVER LENGTH OF HIGH HATER CONTENT FROZEN CLAY SAMPLE 3O co at ti Sal Ei‘u’il lb A summary of all silt and clay samples made and tested is given in Table 3.1. 3.4 Sample Installation and Triaxial Cell Assembly_ The base clamp of the anti-tilt device was fastened to the bot- tom cap of the frozen silt or clay sample which had been previously jacketed with rubber membranes. The sample was then placed in the cold bath of the testing apparatus and connected to the load cell at the bottom. A spring-loaded LVDT was then attached to the anti- tilt device. An anti-tilt ring was fastened to the top cap of the sample; one end of the anti-tilt ring was fastened to a spring steel clip which extended from the base of the anti-tilt device and the opposite end contained a flat-headed bearing screw which bore di- rectly on the core of the LVDT. The voltage output from the LVDT was then adjusted close to zero by adjusting the bearing screw or by sliding the opposite end of the anti-tilt ring along the spring clip and tightening. The sample with the anti-tilt device and LVDT connected is shown in Figure 3.5. After the LVDT was adjusted, the aluminum cylinder of the triaxial cell was set in the base plate and the thermistor wires were set in place around the top and bottom of the sample. The top plate of the cell was then set in place and tightened and a connect- ing rod was screwed into the top cap of the sample through the top plate. Coolant was circulated over the top plate and the cold bath was covered with styrofoam. The sample was allowed to sit in the cold bath for at least one hour prior to testing to bring the temperature of the sample into equilibrium with the cold bath. Temperatures within the cell were 3T Table 3.l SUMMARY OF SAMPLES MADE AND TESTED Average Testing Hater Soil water ‘temperature Sample content Density content (%) (0C) number (%) (g/cc) Hanover silt 2l.4 -1 HS-l4 2l.7 2.04 HS-lS 22.l 2.08 -4 HS-6 24.5 2.0l HS-7 24.5 2.04 HS-ll 24.2 2.05 -l0 HS-2l 20.9 2.06 HS-22 2l.8 2.05 35.5 -l HS-l3 * l.74 HS-l6 * l.67 HS-l7 * l.66 -4 HS-3 * 1.87 HS-4 * l.85 HS-5 * l.78 HS-8 * 1.77 HS-lD * l.72 HS-l2 * l.72 HS-l8 * l.7l -lD HS-l9 * l.67 HS-20 * l.68 Alaska silt 20.5 -l AS-3 22.l 2.07 AS-4 2l.9 2.06 -4 AS-lD 20.8 2.06 AS-ll 2l.5 2.06 -l0 AS-l3 l9.7 2.09 AS-l5 l9.8 2.09 29.2 -l AS-5 27.l .90 AS-6 3l.2 .86 AS-7 3l.7 l.74 38.9 -I AS-l * l.59 AS-2 * l.65 -4 AS-8 * l.69 AS-9 * l.69 -l0 AS-l2 * l.66 AS-l4 * l.66 Kaolinite 28.l -l K-7 28.l l.84 K-8 27.2 l.86 -4 K-S 28.8 l.83 K-6 28.0 1.82 32 Table 3.l (cont'd) a Average Testing 'Water 'Soil water temperature Sample Content Density content (%) (0C)- number (%) (g/cc) Kaolinite 28.l -lD K-l 3l.7 l.75 K-2 28.l l.82 K-3 28.4 1.82 7l.3 -l K-ll 78.9 l.50 K-l2 75.9 l.5l -4 K-lO 7l.9 1.50 K-l3 66.5 l.50 -l0 K-9 63.9 l.52 K-l4 70.9 l.49 * Average water content determined from weighted average technique using single sample rather than individual samples. 33 Figure 3.5 FROZEN SAMPLE WITH LVDT AND ANTI-TILT DEVICE CONNECTED 34 monitored by means of the thermistors before and during testing to assure that testing was done at the proper temperature. 3.5 Test Procedure After the sample was installed and the triaxial cell was assem- bled, the sample was subjected to cyclic loading using an electro- hydraulic closed-loop test system. The start-up procedure for the testing of each sample was as follows: (1) The power was turned on and the electrohydraulic system was allowed to warm up for 15 minutes. The set point knob on the control unit was then used to lower the actuator rod to approximately 1/2" above the connecting rod. An LDVT in the actuator was used to pro- vide the control at this point. (2) The system was turned off and the control was switched to the LVDT attached to the sample; the voltage output from the load cell and the LVDT were then adjusted to zero. The supply value to the actuator was closed and the actuator rod was connected to the rod attached to the sample. A confining pressure of 200 psi was then applied to the cell. (3) The power was turned on again and the supply valve to the actuator was opened. Movement of the actuator was now controlled by the LVDT attached to the sample. (4) Any load in the sample as measured by the voltage output from the load cell was adjusted close to zero in compression by adjusting the set point knob on the control unit. In general, the LVDT output was non—zero; a voltage offset was used to bring the net LVDT output on the recording devices close to zero. 35 (5) The desired strain amplitude and frequency for each test were selected by adjusting the span knob on the control unit and the frequency selector on the function generator, respectively. A sinusoidal strain wave of the selected amplitude and frequency was then applied to the sample by pressing the run button on the func- tion generator. Output was recorded in the form of load and defor- mation sine waves on a strip-chart recorder and in the form of hysteresis loops on a storage oscilloscope. 36 CHAPTER 4 DYNAMIC PROPERTIES OF FROZEN SILT UNDER CYCLIC TRIAXIAL LOADING CONDITIONS 4.1 General Cyclic triaxial tests were conducted on the frozen Hanover and Alaska silt samples described in Chapter 3. Samples of both silts were tested at two water contents to determine the influence of sam- ple density on the dynamic properties. To determine the influence of other parameters which might affect the dynamic properties of frozen silts, samples were tested at temperatures of -1, -4, and -10°C, confining pressures of 0, 50, and 200 psi, frequencies of 0.05, 0.3, 1.0, 5.0, and 10.0 cps, and over a range of axial strain amplitudes from .002 to.08%. 4.2 Testing Sequence The test history (i.e. the sequence in which the various test condition parameters - confining pressure, frequency, and strain amplitude - were applied) used on the frozen silt samples in the re- search program is shown in Figure 4.1. The test history was similar to one used in previous research by Chaichanavong (1976). Chaicha- navong found that with a test sequence similar to that used, the in- fluence of sample disturbance on the measured dynamic properties was negligible. The ranges of the various test condition parameters were as follows: (1) Temperature - three temperatures (-1, -4, and -10°C) were used in the testing program; each sample was tested at only one 37 m3 m3 m3 m3 m3 m3 m3 m3 m3 m3 o.o_u.+l 30 Cattle: cattle; Oétlau 0.2"..lm8 oéucl m8 oéuclau c.0729 l mau o.o_.u.+l mau .. 0.0—.fl% fl WQU can» lmau oft l R: oat .lau 0.9... l8 oat lac 9m... lac o.muo...al3u can; l 36 06".. l. 36 06"», l 36 >30 oz< .53 ESE mo...— >mo._.mH: 5m» .5 25.38 0.7”. Ill 3”. 9 Te ll 3... 97¢ lmau 0. Tel 36 o” 7.. l 30 97., l 25 97¢ l 38 o. 7., l 36 o.. Te l 30 91 l 88 Te 95 m.ouelmao modilwma oomuaublll_ 2... amuop x o.m u cwmgpm mexm mpmewxoc m.o....¢ lmau moduelwma o "33L Wong, lmnu moduwlwmq om ugul Wane Ill m3 mod"; ll .35 oomuaul m2 RNIOF x m._. u wagum mexw mum—5.x?» "Q0 I mantles moatlza o HQU .ll, mailman. modumlwma om m.ou.+ ll .30 mo.ou.._. Ill wmn oomuqu l, E? lwwwop x o.m u :_mcpm _mwxm mumewxog m.o.l¢ l «3 modil .23 o v.3 l. mane. l 36 moéuml .me om Roi l 3... 36am. l 78 oomuau l "Q0 ‘III mac. amlop x o.~ u cwmcpm Pawxm muoswxog mgaumgqum» penumcou mm? 38 temperature. (2) Strain amplitude - each sample was tested at four strain amplitudes ranging from approximately .002 to .08% axial strain. In general, the strain amplitude of .08% was applied only at 200 psi confining pressure; the strain amplitude at 0 and 50 psi was limited to approximately .02% axial strain. (3) Confining pressure - the samples were tested at three con- fining pressures (0, 50, and 200 psi). (4) Frequency - each sample was tested at five loading fre- quencies (.05, .3, 1.0, 5.0, and 10.0 cps). (5) Number of cycles - each sample was generally subjected to a maximum of 10 cycles per loading condition. (6) Water content - both silts were prepared at two water con- tents; average water contents were 21.4 and 35.5% for Hanover silt and 20.5 and 38.9% for Alaska silt. Two samples of Alaska silt tested at -1°C were prepared at an intermediate water content (29.2%). The dynamic Young's modulus for each loading condition was calculated from the amplitude of the load and deformation sine waves from the strip-chart recorder output. Research by Chaichanavong (1976) indicated that the dynamic Young's modulus does not vary significantly with the number of cycles of loading up to 20 cycles of loading. Therefore, a representative cycle of loading less than 20 was selected to determine the dynamic Young‘s modulus for each loading condition. The damping ratio for each loading condition was calculated from a hysteresis loop recorded on the storage oscilloscope. A 39 cycle of loading within the first ten cycles was chosen and re- corded; the trace on the oscilloscope was then observed for subse- quent cycles to assure that the loop recorded did not differ from loops at other cycles for the particular loading condition. The loops on the oscilloscope were then photographed, enlarged, and pro— jected onto sheets of paper and traced; areas of the traced loops were found with a planimeter and damping ratios were calculated. Typical hysteresis loops recorded in this manner are shown in Figure 4.2. Any deviations from symmetry in the loops generally indicated imminent sample failure, melting at the couplings,or off scale. 4.3 Dynamic Young's Modulus of Frozen Silt Values of dynamic Young's modulus were plotted versus the log of axial strain expressed as a percent for all loading conditions. Plots for both silts at all water contents are given in Appendix A. Each plot represents a silt at a particular water content, tempera- ture, and frequency. Data from at least two samples are included in each plot. It can be seen that, in general, data points from dupli- cate samples are in good agreement. There is somewhat more scatter in the data points for high water content samples; this is due per- haps to the lack of unifOrmity and the difficulty in reproducing the high water content samples. ‘It was apparent early in the testing program that confining pressure had a negligible influence on dynamic Young's modulus re- gardless of strain amplitude, frequency, temperature, or water con- tent. A typical plot of dynamic Young's modulus versus confining pressure for a single sample is shown in Figure 4.3. Since dynamic 40 Frequency (cps) 0.05 - 0.3 ' l.0 5.0 10.0 Load li;;) .- Deformation' Figure 4.2 TYPICAL HYSTERESIS LOOPS OBTAINED DURING CYCLIC TRIAXIAL TESTING 4l quhzou zucoz “assoc: m.cz=o> u~z<2>c ¢.v ~L=S.L an-o_ x o m Lo z_<¢pm 3<_x< z< h< as.” <2m<3< mom umammmma uz~z~mzou mammu> madzoo: m.oz=o> u~zo m.v «Lamvm Aucoucaa mo_v c_ocum _o*x< A_mav acammoca mc_cvecou con.. oo._- cm..- oo.~- om.~- oo.n- com om— cop om _ _ H q _ d _ . q q I! .0 [so I4 I. II .c I... I .m d. < a u.o_- mm mm . w I ‘ ‘ 3382.58. 1 .2 0 1 a. 1.2 .. .m .q .q . m. .L 3 1 .m: A Lép .1 m U 6| 1 5 ll .ON W l.°N p L m. l m . ) m3 9o. 4 .. SN mu ...v~ .5 «no o.m .1 ... l d .I. «no final .. ms... «.3 o; d m u mo 0 . J .mN mac . 4 .1 .mw 35.62... I m o ma.wn.ucmucou Luau: mnu mo.o AV .1 mocaumocq acvc_c=ou .1 . . —_a La» mupamug oooLo>< NM u.e-.oc=~ago¢5~p xucaaaacm ...~n .. .mm ...on 1 I. 1 .o« 1 co (15d SOl) snlnpow s.5uno. Jimeufia 42 Young's modulus was not influenced by confining pressure, data points for all confining pressures were plotted together in the graphs of dynamic Young's modulus versus axial strain amplitude. 4.3.1 Effect of Strain Amplitude To assess the influence of strain amplitude on dynamic Young's modulus, a "best fit" line was drawn through the data points shown on the plots given in Appendix A. The relationships between dynamic Young's modulus and strain amplitudes for both silts are summarized in Figures 4.4 to 4.12. Each graph represents one silt at a parti- cular water content, at three temperatures (-1, —4, and -10°C), and at least two frequencies. Values for dynamic Young's modulus range 5 from 1 x 105 to 35 x 105 psi for Hanover silt and l x 10 to 22 x 5 10 psi for Alaska silt. The dynamic Young's modulus for both silts decreases as the axial strain amplitude increases; the decrease is more pronounced at -4 and -10°C than at -l°C. The relationship between dynamic Young's modulus and strain amplitude appears to be independent of water con- tent and frequency. To assess the influence of frequency, temperature, and water cpntent on dynamic Young's modulus, values of dynamic Young's modulus were obtained from Figures 4.4 to 4.12 at axial strain amplitudes of 3.16 x 10'3% (log axial strain = -2.50) and 3.16 x 10'2% (log axial strain = -1.50). The modulus values were then plotted versus frequency, temperature, and water content. 4.3.2 Effect of Frequency The relationship between dynamic Young's modulus and frequency 43 hzmhzou mur<1 um.mn h< haum ¢u>oz maaaooz m.uz=o> u~za u.v «Lam—g. 2:088 3: $83 :22 com.. oo.p- on..- oo.~- cm.~- oo.n- _ 141 _ a q .4 8..-. .. «3 n .o «no mo.o .............. .3538... l L 1 3.5393 «5523 :~ .3.— 333. 3222 I # .~— .op .o~ .vN .~n .ov (isd S01) snlnpou s,6unog otmeuxu hzupzcu ¢wp<3 nv.—~ h< p4~m xu>oz magaoo: m.uz=o> u~za m.v osnovu 359.8 no: £95m 222 com.. co..- on... oo.~. om.~- oo.n- _ dl a d u q _I I l /./Ifl/IoI/Il l a..- 74/ /.w/M/, L // // //, 11 L /w/ ll / / /.I II / a //. / / .4 I .//I / I. / ./ / // UGO—l II . I [I l / / / / I z /. I z /’ ll / / l/ I. 9.39.3.3... /”,/ // ./. /. z/ p / . / // x L // l/ . v/ II /. l/I // /./ '/ II .1 3o o.2|.l.l /. /..//. S I 1 23 9... .l-l /. /.x.// L x. / // So a; ...... /. I/VI/ L 3:259; // 4”! I 3.532.. 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L w u I .z 0 S d 39 n6 1 m... I. 30 no.0 ............. I. .QN 3.5.52... 1 3.5393 2:523 .~n —_a so; “p.33ug oo~Lo>< .8 .9 (lsd Sal) snlnpau 3.6.110; anemia 47 for both silts is given in Figures 4.l3 to 4.22; each plot repre— sents the relationship for a silt at a single water content at all three temperatures (-l, -4, and -lO°C). Dynamic Young's modulus increases with increasing frequency. In general, the rate of in- crease is slightly greater at very low and very high frequencies than at intermediate frequencies. At a high strain amplitude, the relationship between dynamic Young's modulus and frequency appears to be independent of water content and temperature. At a low strain amplitude, the rate of increase of dynamic Young's modulus with fre- quency is somewhat greater at -4°C than at -l and -l0°C. In the case of Hanover silt, the value of dynamic Young's modulus at —4°C approaches.the value at -lO°C at high frequencies. 4.3.3 Effect of Temperature llme relationship between dynamic Young's modulus and tempera- ture for both silts is given in Figures 4.23 to 4.30. Each plot represents the relationship for a silt at a particular water con- tent, at: five frequencies (0.05, 0.3, l.O, 5.0, and l0.0 cps), and at one of two axial strain amplitudes (3.l6 x l0'3% or 3.16 x l0'2%). In all cases, dynamic Young's modulus increases significantly with decreasiru; temperature. The rate of increase is fairly constant at a high strain amplitude (3.l6 x l0'2%), with a slightly greater rate 0f increase: at higher temperatures (-l to -4°C) than at lower temperatures (-4 to -lOOC). At a lower strain amplitude (3.l6 x 10-3%) the Ifiate of increase is generally significantly greater at hl'Slher tenmuaratures (-l to -4°C) than at lower temperatures (-4 to _ o 10 C)- ‘Ther rate of increase of dynamic Young's modulus with de- 48 umoo— x a...” .6 :2th 45: z< 5 5; 5325. so... 3230mm... mam; maze? Page» 8x55 2.4 0.53... 73V 3538... . a6— o.m 0.. ad 36 a a . _ q i L Q\Ifll illnfllllll‘lllh- 4 L 000—: ‘ IL 00?. < 3.538.. 9552.8 1 Z. .5 333.. 3222 u.—. 4 3.3-accuse”. .52: 8323.5» I 1 unuc— x 36 .3 ,2:sz 45: .2 E .5; 5325.. «o... 3233:... mama; 3.5%! Page» 93223 2.6 «an: 73. 3538... 92 c..». a._ «.0 mod n _ . q u .0 H6 .. if .0 I.” .2 a 1.2 m L m. . 3 . up A 1 2 m .w 1 s. L .8 6.». W m I. .3 W Li S d l m... .3 1 cu . l.~n S 92- 4 UGO! q I. «9.33.... 0552.3 1. .3 2. c8 333.. 822$ u... 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G I. .QN l\ I. 00¢. a 00¢. q nosanuoga o=.=*;cou 1 «ogamuoga o:_c.»cou I __- Lou u»_:mog ooago>< o._- AV P_~ gofi uu—anog oo~Lo>< u... an ao.mn.ucoucou Loan: ognuogoaeo» ...~n no.an.ucoucou Lou-3 «can-Luann» l L .mn l 1 L I .O' l. :: 22 2' :5 (:84 sat) ’"lnPOH 8.6un0A 3tI'0‘h 05 N 53 .1: x 2." 3 =5: 3.2 .2 z :3 58,3. «2 2.33.3» was, 358... 922: 2523 2.... 23: a; 2.3.121: 2. a. a- n. o1 m1 T n- «1 7 _ .. . . . . . . . q a... 92 4 L. :5 H; d I «an O._. q .1. 3.532.. 9.25:8 «8 n6 4 L :- ..£ 333.. 8933 3... 36 d l affiniflcoo .82: 3:83;... a O '- 53 V N G N 1% .3 ($54 9m) sntnpou 5.6m” ammo unb— n 26 .3 33.5. .3: .2 S 5.» 55.5. «on 235.25.. 33% 352! ".932 2.3.3 2.. 0.53... GL 839398.— 21 a- a- T o- m. c. «.1 ~1 _1 - — u u d u - u d d 1. .o I .v 1 I. .0 I .~— L 1 .2 J 1 .ON 1. .vn L .3 0.2 4 1 I11 an 3 < 1 .8 Ru 0.. Q 1. 3.532.. 9.25:8 n3 . . 2. .3. 3.3! 32.3 n a Q 1 on «no . 3.5-33:8 1.3-3 3 c Q 1. 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(;sd Sal) snlnpou s,6unoA agmwuxn an-o. x o—.n mo z_<¢hm 4<.x< z< kc h4.m <2m<4< mom uzah<¢uuxuh m2m¢u> maqaoo: m.uz:0> u.:o a~.¢ us:o.u Au.. ogzuoLanoh o.- o- Q. ~- o. m- o. no N- .- d d I— T 4 u d u q — .L.a l :44 16 ..~. 4 1 L3 1 ..d~ :3 0.2 4 [6N an 0.... 4 «3 o; a L «nu . du n o 41 mugammoga m:.c..cou ..u no. mu—amug omogo>< «no mo.o AV .1 ua.wn.ucou:ou Loan: mucuscogu |a~n 1.3 dv (;sd S01) snlnpou s,6unoA 31muu£u 57 creasing temperature is generally more uniform over the entire range of temperatures (-1 to -10°C) at lower frequencies than at higher frequencies. 4.3.4 Effect of Water Content The relationship between dynamic Young's modulus and water content is given in Figures 4.31 to 4.36. Each graph represents a silt at a given temperature at two strain amplitudes (3.16 x 10'3 and 3.16 x 10'2%) and five frequencies (0.05, 0.3, 1.0, 5.0, and 10.0 cps). Each relationship shown is based on only two points with the exception of the relationship for Alaska silt at -1°C (Figure 4.34) which is based on three points. At a temperature of -1°C, dynamic Young's modulus increases by a moderate amount as the water content increases (from 21.4 to 35.5% for Hanover silt and from 20.5 to 38.9% for Alaska silt) for both strain amplitudes (3.16 x 10"3 and 3.16 x 10'2%); this relationship does not appear to be affected by frequency. In the case of Alaska silt, most of the increase in dynamic Young's modulus with water content occurs l°" the higher water content range (29.2 to 38.9%). At lower temperatures (-4 and -10°C) there appears to be little 0": no significant influence of water content on dynamic Young's mOdUl us at a higher strain amplitude (3.16 x 10'2%). At a lower strain amplitude (3.16 x 10'3%) the relationship between dynamic YOUNQ'S modulus and water content is not clear. In the case of Han‘WF—W‘ silt, dynamic Young's modulus decreases by a small amount as the water content increases at both -4 and -10°C; in the case of AlaSka silt, dynamic Young's modulus appears to increase by a small amount at -4°C and decrease by a small amount at -10°C as the water 58 gov- mo mun—(ammxuh < ~< h4.m ¢u>oz maaaoo: m.uz=0> u.z<2>c ~m.e «Lam.u acoucou goua: 0.. mm. an. mw. o~. m_. u d u q d d 1 .o L I 0v «l [a L "#2 x 2.... .1. u. 1 .o .l in - 4 e 1 .N. u 1 1.2 "72 e 2.” 1.41 1.8 Ifl‘ 4 1 .3. £55 3.2 1.8 3e 3: d 1 .Nn “3 9m 4 30 o; 4 1 «nu n.o 4V 1..wn .3 3.0 q 1 ”233.3 .5528 .o. S. .3. 3.38 as»: 3538.; 1 (15d S01) snlnpou s,6unoA 31meufiu gap. 3 355.3. < E :5 $825. «9. E58 55 was. 358: 328. 2.3.3 5.. 23...: acoucou Loam: oe. mm. on. m~. cu. m.. 4 q A q _ a 1.0 a~.o. x o..n 4 . .1 .o :72 . 2." 1 \ I.” 1. ¢.-gum \ PCGK< 1 oNp w 11 m m. 1..o— mu m .1 6 en L2 m 1 n «nu o.o. aV ”n we as d 1 x as l d 26 o; 4 .1..." «3 n6 4 1 3 «no mo.o AV 1+ mogammoea ac.c..:ou ._. so. mu.amog amoeo>< Aucoacosu 1L.~n l .8 .ov 59 97 .3 #2535.— < h< :3. 5.2.2 «on. hzmhzou «ER: mama; 34:8: mbzao» 2.223 3”; 0.53... acuucou Loan: 3. mm. on. 3. ow. 3. . q d _ _ _ 1m- u «#2 x 2.” ,‘I . . L Hi“ a7... x 2.... 1 . l c..eum 2:2 L L l 1 “3 ad. 4 m3 0.... Q IL mnu o.. 4‘ “3 ad 4 L nee mo.o AV .1 3.532.. 2.52.3 ..a so. nu.amog omago>< aucoaowg. .1 1L .N. .8 .8 (15d Sal) snlnpou s,6unog 3111mm 902. 3 2.23.2: < 2 :3. $825. «on. 2:28 5:; was. ”389. 9252 2.225 2.. 23: acoucou Luau: 8. mm. 8. a. 8. 2. q q q u d u .o l 1... I. .0 . J... 1 r in l u "To. x 2.... . ~— 1 I 1... . L 1.8 L "mg: e 2." . 1 cm L 523 .3: L .3 L .2 «8 0.2 d 1 «no o.m ‘ l .8 3.538.. 9:528 «3 . z. .8. :32: 8:... a _ fl .3 n a Q .8 3o 36 Q 3:38.: (:51! 501) snlnpou 8.6mm sputum 60 u.o_. mo ugae¢¢mexup < h. .4.“ (gm<4< ace ezuezou mu.< c.agum —o.x< a... 0.2 4 ”3 o.m 4 mac o.. ‘V «no n.o 4‘ 23 3.0 Q aucoaaoem .c. (15d S01) snlnpou s,6unoA 31meuxn ue.. mo u¢=F<¢uezuh < e< ks_m <2m< nucoacosu 1..NM 1 ... .ov (134 Sal) snlnpou 3,6uno; agmeufia (Sl content increases. ‘ The influence of temperature on the relationship between dynamic Young's modulus and water content may be a function of the unfrozen water content of the silt. At a low temperature (-10°C) where the influence of unfrozen water content is small, dynamic Young's modulus tends to decrease with increasing water content. At F' higher temperatures where the unfrozen water content is greater, dy- namic Young's modulus increases with increasing water content; this may be due to the relatively larger proportion of water in the form of ice in the higher water content samples than in the lower water content samples. 4_.4 Damping Ratio of Frozen Silt Values of damping ratio were plotted against the log of axial strain amplitude expressed as apercent for all loading conditions. Plots for both silts at all water contents are given in Appendix B. Each plot represents data points for a silt at a particular water content, temperature, and frequency. Data points for all three con- fining pressures (0, 50, and 200 psi) are included in each plot. EaCh plot represents at least two samples; in general, there is good aSIY‘eement between data points from duplicate samples. At very low $1iY‘ains, the scatter of the data points is due to the influence of baCkground "noise" during testing, which results in difficulty in accurately measuring damping from the single hySteresis loop recorded for each loading condition. The scatter of data at the high water contents ‘is due to the lack of uniformity and the difficulty in reproducing the high water content samples. 62 £31 Effect of Strain Amplitude To determine the influence of strain amplitude on damping ratio, a "best fit" line was drawn through the data points given in the p1 ots in Appendix B. The relationship between damping ratio and strain amplitude is summarized in Figures 4.37 to 4.58. Each graph represents a silt at a given loading frequency at each of three temperatures (-1, -4, and -10°C). In cases where damping ratio was influenced by confining pressure, a separate curve was drawn for each confining pressure. In general, damping ratio increases as strain amplitude in- creases. At a temperature of -1°C, the rate of increase is moderate at low frequencies and somewhat greater at higher frequencies for low water contents. For higher water contents, the rate of increase is moderate at all frequencies. At lower temperatures (-4 and -10°C) damp‘ing increases significantly with increasing strain amplitude at low frequencies. At high frequencies, damping ratio increases by a Smaller amount and in some cases decreases by a small amount with in- creasing strain amplitude. In some instances, the relationship be- comes U-shaped with a slight decrease in damping followed by an increase with increasing strain amplitude. To assess the influence of confining pressure, frequency, temperature, and water content on damping ratio, values of damping r‘c‘ltio were obtained from Figures 4.37 to 4.58 and Appendix B at “Xi“ Strain amplitudes of 3.16 x 10’3% (log axial strain = -2.50) and 3-16 x 10‘2% (log axial strain = -1.50). 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Nn. 0‘193 Bugdmea hzwhzou zuh<3 av.—~ oz< »uzu3¢u¢m mnu o.o_ h< »4_m mu>oz o_p<¢ wz_a:< I_~n l8. emu flusdma 66 hzmbzou «u»<: um.mn az< >uzu=cu¢. «no c.. k< hdum ¢u>oz o_h< NF. mm. mm. o;3uu Sugdmea hzupzou mwp<3 mm.mn oz< ruzu30uam u.p- _ 00¢! ogauagoq20» vouoc om.zgoguo mmoFcn mogammoga m:_:—ucou P.» Low mu—amog omago>< «nu m.o p< »4_m ¢u>oz o~p<¢ uznmzuzuacu¢m «no 0.0— »< h4_m ¢u>oz o_h<¢ ozmazoz o~h<¢ oz—mz< I.~n 3. cc. 05m: Busch-mo 68 hzmhzou «wh o_p<¢ a=_gz< Igov. one}; Bugdumo hzmhzou a-<3 um.o~ az< >uzu=omxm mau mo.o h< pqam <2m<4< mom =_<¢hm 4<~x< mam¢u> o-<¢ azumx< 031's 50[dfll0 69 2228 35 3:8 92 55583 a. 9m p< ~4~m c~h<¢ az_mx< |.ov. o;1ea 6u1dm90 hzuhzou xu»<3 um.o~ nz< >uzuzowxu "no o.— ~< hgmm ouh<¢ az—¢:< oom.- oo.p- cm.—- oo.~- om.~. oo.n. _ _ _ q _ _ IL.o I1 3. l 8. 1.~—. 3.. SN 12. .ma om _ma O on. ogaumuga ofccguL 3. 00—1 n '_ m - UoO—I N u.c- 9.38353 1 «n l a. coco: «23350 “mo—c: ”whammogq mcvzwycou emu 601mm 70 ham—zoo «uhcr n~.o~ h< h4_m o_»<¢ mz_m:uzu=cu¢u mag o.op p< h4_m <2m<4< mo; z.<¢~m 4<_x< mamxu> o~h<¢ u=_az< d u u.c- UGO—I 00—1 assu-goasop 1.~p. |.~n. 011's Susdwvo 71 FZuhzou u-<3 no.3m az< >uz~=0umm may mo.o h< ~4_m <2m<4< mo; z~ o_p<¢ uz_az< 01193 bugdwea pzupzou m~p<3 n~.m~ k< hqfim <2m<4< mob z_<¢hm 4<~x< mammu> o_h< u._-.ogauogogso~ ov 72 hzuhzou ¢u~uzu20u¢u «an o.. P< hgfim <2m<4< mom z_<¢»m 4 o_p<¢ uz_az< d q '- NF. op. ow. em. mm. Nn. on. ow. 01123 6u1dwea thHzou «uh<3 uo.on oz< >uz~=o~¢m Aucougoa oo—V =_ouum P~_x< oom.- co..- om.—- oo.~- mau m.o h< »4_m o~h<¢ oz_m:< _ _ 14 uc_c—$:ou l assuagua-o» 1. mp. mu. ov. 011Iu Bugdmua 73 1 E? ' hzwhzou «uh¢x “a.mn oz< >92u30m¢u “a. a, pzwhzOQ «uhuzu30u¢m P< pamm <1m<4< go“ z_ o_h<¢ uz_az< goo”- _ vo. ~_. . _ u°.- In... 0.0,- \\\\\\\\w m_. 00¢- m. .m ogauogaaEmh ow..w Hu 9.. 19 m- cw. mm. mm. awgaumogq o=_:_u=ou __o 50‘ uu_:mog oo~u~>< _ «p. o—. v~. ow. ~n. av. o;1ou 6u1dmoa 711 5.4.2 Effect of Confining Pressure The relationships between damping ratio and confining pressure aire summarized in Figures 4.59 to 4.63. Since it was apparent that (:onfining pressure did not influence damping ratio at low tempera- tures {-4 and -10°C), plots were prepared only for a temperature of —1°C. In general, at a temperature of -10C and at a low strain amplitude (3.16 x 10'3%) damping ratio decreases with increasing confining pressure at low frequencies and is not significantly affected by confining pressure at higher frequencies. At a high strain amplitude (3.16 x 10'2%) damping ratio decreases slightly with increasing confining pressure at low frequencies and is not affected by confining pressure at higher frequencies. Since the change in damping ratio with confining pressure is small to negligible at a high strain amplitude, only one curve has been shown for the damping ratio—confining pressure relationship at a high strain amplitude (Figure 4.61). In general, the rate of decrease of damping ratio is more pronounced at low confining pressures (0 to 50 psi) than at high Confining pressures (50 to 200 psi). It appears that confining pres- Sure has a more significant influence on damping ratio at low water Contents than at high water contents. M3 Effect of Freflengy The relationships between damping ratio and frequency are given in Figures 4.64 to 4.73. Each graph represents the relationship for a silt at a particular water content at three temperatures (-1, -4, and -10°C) and, where applicable, at three confining pressures (0, 50, and 200 psi). At a temperature of -1°C, the damping ratio de- 75 am.mn ma hzuszU au»<: < p< p4.m ¢u>oz o_»<¢ az_mzoz oup<¢ oz_mt o_»<¢ uz_azozuzuacumu mam¢m> o_p<¢ 02—mz< 00—: q . av._~uu:oacou Laue: ..Oc mgzuagmqsmh ogzou Gugdwea ao.mn mo hZuhzOU c~p o_h<¢ uz_axozuzu20umu mam¢u> o_h<¢ oz~¢zozuzm30umu m3m¢m> o_h<¢ uz_az< L xm.mmuucoucou Laue: Ismm. _mq cow ~n *mn cm 9.2. 4 on. 9.2. 4 .3 o L 0%.. 4 I use: uflfofio one- 4 on wmm_ca mocammoca m:_=_uc0u ocamuoca Uo—- AV F—o sou mupamac omacm>< uo_- AV o:_c_.cou ocauocaQEo» usoe. uv._~.u:uucou Logo: «Launcoqeo» ow. 0,193 buidwoq 79 a -o. x o_.n no z_<¢hm 4<_x< z< p< p4_m <2m<4< mo; >uzmaoH¢u mama“) o_h<¢ az_az< u.—- Aw am.o~uucoucou Logo: 333853 .4 ~—. op. o~. mm. mm. on. oe. ogzeu butdwea u~-op . o,.m co z_<¢hm 4<~x< z< p< »4_m mu>ozuzu:¢u¢u mam¢u> o_h<¢ ez_¢z< um.mnuu:oucou Laue: A q «an oo~ .ma on pan 0 1 ocaauuca 9:523 L 9.6... 4 9.7 4 u... AV «gauagoaswh vo. ~_. mp. ow. cw. mw. ~n. on. 011'; Bugdmeo 80 «To. x 2.... “5 55.5 ..S: a -3 x 0.6 ...o 55.5 z< E .53 5.2.2 «on. 5528”: max; 0:5. 332% ofio 0.53“. 2:2 z< .2 5:... 5.2.2 «9. 553mm... mama; 02.5. 9.253 an; 9:51 7.9: 3:03am: 7un 3:33: 92 o.m o._ «6 mod 06. o.m 0.. n6 mod 4 q . . _ . q _ _ . l1 .0 L .0 L vo. 1 3. 18. L 8. 12. L 2. l o 1 to a 9. m m. U low. 5 cm. w ...... 0 [ll I; .4 3a com. «N. 4 4 13. .Sa 9... ..3 o 18. 4 .pma o ObameLm gammy-Q afictcouL mm. 9.2.2.391 ~n. nouo: om_zcacuo 3.2:: 3.5395 9:523 :o ..8 333.. @9223 9.2.. 4 2.33528 L32. Lem. 3.3: uflEofio 9... Au 1 on 32:: «2:39... 9:523... :a ..8 333.. 32o: u..- G. 9....23233 . o v. 3.85533 g3”: Eageoqefl cw. 81 o;1ou bu;dwea unuo— x o—.n mo z~<¢hm 4<~x< z< H< p4_m <2m<4< «em >uzu20m¢m m2m¢u> o~h<¢ wz~¢z¢ mop- AV m. vm.mmuu:oucou Luau: acauocmaeop ILm Lon. ..oe. og1eu bugdweq "TS .. 2..” co 55.5 .32 E E :3 5.2: «8 65:8: .32.: 25 2:55 .3 23: annoy xucmacocm o.c_ o.m c._ n.o mo.o _ . . q q 1..o 1 v0. nLco. n.~—. 1 9.. ..ow. L z. .mq oo~ . .3 818 van a «cannon; . l nauo: om_xcoguo mc_c_;cou ~n mum—ca mmcammmca m:_c_ccou ~_o com mu—amoc om~Lo>< L . a~.a~.ucoucou Laue: on uc_-.ucauacoae~» 1.ov. 01193 Buidmoq 82 n -o_ n o—.n no z_<¢hm 4<_x< z< p< h4_m ¢u>oz o~h<¢ uz_¢z< we . —NuucouCOu Laue: m- o- n- N- —- . _ . _ d _mn cow _3 8 ..a o ocammogn mc_:_ucou “no mo.ouxucmaaucm 1 mp. up. om. «N. am. um. 04. 01193 6u1dweg n~-o— x o—.n ma z_<¢pm 4<~x< z< h< h4~m uzm=ou¢u m3w¢u> o_h<¢ oz_a:< u..- my «admzcscou .33: 8383...: L NM. .Lon. 9. 01193 6u1dmea 83 creases by a moderate amount in the frequency range 0.05 to 5.0 eps and decreases sharply from 5.0 to 10.0 cps. In general, at 10w water contents the influence of frequency on damping ratio is more significant at a low strain amplitude (3.16 x 10'3%) than at ii high strain amplitude (3.16 x 10'2%). At higher water contents, the rate of decrease of damping ratio with frequency is not signi- ficantly influenced by strain amplitude. At a temperature of -4°C, damping ratio decreases with in- creasing frequency at a low strain amplitude (3.16 x 10'3%) at a rate somewhat more uniform than at -1°C. At a higher strain ampli- tude (3.16 x 10'2%) the damping ratio-frequency relationship is similar to that at -1°C with a more pronounced decline in damping ratio at high frequencies than at low frequencies. At a low water content for both silts, there appears to be an initial increase in damping ratio at low frequencies followed by a sharp decrease at high frequencies. At a temperature of -10°C and at a low strain amplitude (3. 16 x 10“3%) damping ratio generally decreases by a small amount wi th increasing frequency at low frequencies (0.05 to 5.0 cps) and increases at higher frequencies (5.0 to 10.0 cps). At a high strain amp? itude (3.16 x 10'2%) the damping ratio-frequency relationship is 5""?1' 'lar to that at -1 and -4°C. The rate of decrease of damping mtic. is greater at high frequencies than at low frequencies. 4°4-\4Effect of Temperature The relationship between damping ratio and temperature is given in FiQures 4.74 to 4.90. Each graph represents the relationship for a Si 1 t at a particular water content, at one of two axial strain 84 z< p< Psnm mu>ozoz<= «om u¢=c<¢uazuc mama“) o_»<¢ uz_ax< mag o._ AV F_u Lou mu—ammc moaco>< ue..~uucoacou cane: xucwacocc 11mm. ne._-u=mucou Luau: 1Lwn. If»? «no Mdnxucwaaocu .18. low. a». onvu Bugdzueq £355 Auov unauocoQEmp op- o- m- R. q . u 4 nova: «n.3cazuo «nope: mucammoca oc_cwccou PP. Lac mu_=muc coaco>< we . —Nuu:0.~cou Luau: a -o. x o_.m no z_<¢»m 4<_x< z< h< kgmm mm>oz o_p<¢ oz~azoz o~h<¢ oz~az< no._~uucmu=ou cone: «no mo.o.»ucmacocu 1.ov. 0&193 6U1¢m90 86 am-o_ x o—.n co z~<¢pm 4<_x< un-o— x o—.n no z_<¢hw z< p< h4_m mu>oz o_»<¢ uz_mzoz o_»<¢ oz_¢x< um.mnuucuu=ou Logo: mau m.on»uco=aucc 11mm. vuuo: am_3coguo 1 «mm—:3 mucammmca mc_c_ccou __o coc m»_:moc omocm>< 1-em. mm.mm-ucuucou Luau: mau mo.onxuca:cmcu 1 11oc. I 87 01393 6u1dwoo a -o_ x o_.n mo zu¢¢hm 4<_x< z< H< h4~m ¢m>oz o_h<¢ oz_mz< mag mo.o n4 um.mm-ucoucou Luca: Aucoaaocc mo. Np. mp. ow. «N. mN. mm. on. ow. 01193 6u1dmeg un-op x up.m mo z_<¢pm 4<_x< z< F< #4_m ¢u>oz o_»<¢ cz~mz o_—<¢ uz_mz o~p<¢ u=_az< mau mo.o AV um.o~uucaucou Logo: Aucoaaucc 1.04. 01193 6u1dweq 89 >uzw30umc "no m.o oz< u~-o. x o_.n co z_<¢hm s<_x< z< ~< hs_m <1m< . . um.o~uucmucou scan: 1me. 1 on. 10v. 01193 Gugdmeq >uzw30m¢u mau mo.o az< un-o— x m—.m mo z_<¢»m 4<2x< z< h< »4_m o_w<¢ uz_az< wm.o~uucaucou capo: L2. 11o—. “ma oo~ 2mg om 2mg o 9539:. 1 acyc.ccou ow. ..mm. N n. 01193 6u1dmoa S9() uw-o. x o—.n mo z~<¢pm >uzuacu¢u mnu o.— oz< a 4<_x< z< h< h4~m <2m<4< mom m¢3h<¢mazuh m=m¢m> o_h<¢ oz~¢z o—»<¢ ozucz< um.o~uu:oucou Lona: -.om. 1 1.04. 1 ~_. mp. ow. NM. on. 01193 6u1dmoa 91 u~-o. u 3.... .3 2.5.5 45: .2 .5 5; 5.3.2 x9. HEP—(aunt: mama”; 0:5. ozEvZo ooé 95m: 8.. 9.32350... 0.- m- m- T o- m- e- .n. w- T _ _ . u _ . _ q . 1 l L L IL «no o.o_ AV L 3”. 9m 4 mag o.. 4V n. au .5 4 “unannoua oc.c..cou ... so. mu.amog omngo>< mag mo.o Aw 3.8.2380 :25 3:83: L IL to o N V N mm. mm. on. o... oneu Bugdmea “72 x 26 .3 55.5. 2:2 2.. E .55 5.2.2 «o... $35.35.. 322. 2:». ”.2223 mm... 9:6: 3.. 232352. 2. a- o. 7 o- m- T n- N- _- - q — . . . q - q u nL.o Iva. 18. L~.. .3 8N .3 cm 12. .3 o .3 o8 .3 on .3 o 13. 95393 a: e co . r. u... 3. 3”. od. 4 43. mag o.m A. 3.... o.. 6 . .Jn. nouoc om.zgozuo «cu m o AV www.ca mogammogn a:.:..cou ..o no. mu.:mog omego>< «no mo.o AV no.mmuu:oucou Luau: mucuaaogu nLon. ... 3. only); 611;de 92 amplitudes (3.16 x 10"3 or 3.16 x 10‘2%), and at one or more fre- quencies. In general, damping ratio decreases with decreasing temperature. The influence of temperature on damping ratio appears to be more significant at low water contents than at high water con- tents. At a low strain amplitude (3.16 x 10'3%) at low water con- tents, the rate of decrease of damping ratio is generally greater in the high temperature range (-1 to -4°C) than in the low temperature range (-4 to -10°C); at high water contents the rate of decrease appears to be more uniform over the entire range of temperatures (-1 to -10°C). At a very high frequency (10.0 cps) there is an initial decrease in damping ratio from -1°C to —40C followed by an increase from -4°C to -100C. At a high strain amplitude (3.16 x 10'2%) the rate of decrease in damping ratio with decreasing temperature is generally somewhat less than at a low strain amplitude (3.16 x 10'3%). In many cases, there appears to be either little change or a slight increase in damping ratio from -1 to -4°C followed by a gradual decrease from -4 to -10°C. 4.4.5 Effect of Water Content The relationship between damping ratio and water content is given in Figures 4.91 to 4.102. Each figure represents the relation- ship for a silt at a particular temperature, at two axial strain amplitudes (3.16 x 10"3 and 3.16 x 10‘2%), and at one or more fre- quencies. The relationships are based on only two data points with the exception of those for Alaska silt at a temperature of -1°C, which are based on three data points. At a temperature of -1°C, 93 a a n N uop. no uxah<¢umzup < h< h4.m ¢u>oz c~h<¢ uzumzoz o.»<¢ uz.azoz o.h<¢ oz.¢:< |_~m. L . ...3 0.2 4 on ”no o.m ‘1 3:33....— 4 o... ogleu bugdweg o.- no u¢3~<¢umtuh < h< p..m ¢u>oz o.»<¢ oz.3xoz o.h<¢ oz.32< a um-o_ x a... N :.ogum .o.x< 0.0. As o.m 4. o.. d n.o ,q 85 a xucoacocu -o. x o—.m l ~.. VD ,— O N V N wN. wm. ow. ogzeu fiugdwea 00.- mo u¢=.<¢uaxu. < .< .... ¢u>oz o.p<¢ uz.mz o.h<¢ uz_3x o_h< «no o.o— AH mag o.m 4‘ zucmzcogm op. C) N V N mm. mm. ov. 01123 Bugdmeg 9...- 3 323%: < »< h4~m <2m<4< «on kzupzou a~p c~h<¢ uz~ax ouh<¢ az_mz o~p<¢ uz_a:< mau o.o— AV 1 «99 o.m 4. ago o.— AV .1 .99 «.9 4w 2.9 3.9 d 1 mucaaoogu no. ~—. 9.. ow. cm. m~. ~n. cc. 01393 5U1dwvo 99 damping ratio decreases significantly with increasing water content. The relationship does not seem to be significantly affected by strain amplitude. It appears that at low frequencies most of the decrease in damping ratio occurs in the higher water content range while at high frequencies the rate of decrease is more uniform over the entire range of water contents. At lower temperatures (-4 and -lO°C) there appears to be no significant influence of water content on damping ratio at a low strain amplitude (3.l6 x 10‘3%). At a high strain amplitude (3.16 x l0'2%) damping ratio decreases with increasing water content; the relationship appears to be dependent on frequency, with a slight decrease occurring at low frequencies and a more significant decrease at high frequencies. 100 CHAPTER 5 DYNAMIC PROPERTIES OF FROZEN CLAY UNDER CYCLIC TRIAXIAL LOADING CONDITIONS 5.1 General Cyclic triaxial tests were conducted on the frozen kaolinite clay samples described in Chapter 3. The kaolinite samples were tested at two water contents to determine the influence of water content on the dynamic properties. To determine the influence of additional parameters which might affect the dynamic properties of frozen clay, samples were tested at temperatures of -1, -4, and -10°C, confining pressures of 0, 50, and 200 psi, frequencies of 0.05, 0.3, 1.0, 5.0, and 10.0 cps, and axial strain amplitudes from .002 to .08%. 5.2 Testing Sequence The testing history used on then frozen clay samples was the same as that used for the frozen silt samples and is shown in Figure 4.1. The ranges of the various test condition parameters (tempera- ture, axial strain amplitude, confining pressure, frequency, and num- ber of cycles of loading) were also the same as those for the frozen silt samples. The clay samples were tested at water contents of 28.1 and 71.3%. The testing apparatus, procedure, and data recording and reduction methods are as described in Chapter 4. 5.3 Dynamic Young's Modulus of Frozen Clay Values of dynamic Young's modulus were plotted versus the log of axial strain amplitude expressed as a percent for all loading conditions. The plots for clay at both water contents are given in TO] Appendix C. Each plot represents clay at a particular water content, temperature, and frequency. Data from at least two samples are in- cluded in each plot; in general, there is good agreement between data points from duplicate samples. It was apparent from the test results that confining pressure had a negligible influenceon dynamic Young's modulus of frozen clay. A typical relationship between dynamic Young's modulus and confining pressure is shown in Figure 5.1. Since dynamic Young's modulus was not significantly influenced by confining pressure, data points for all three confining pressures were plotted together. 5.3.1 Effect of Strain Amplitude To assess the influence of axial strain amplitude on dynamic Young's modulus of frozen clay, average "best fit" curves were drawn through the data points given in the plots in Appendix C. The rela- tionships obtained are summarized in Figures 5.2 to 5.4. Each curve represents the relationship between dynamic Young's modulus and axial strain amplitude for clay at a particular water content, temperature, and frequency. Values of dynamic Young's modulus for frozen clay range from 1 x 105 to 14.5 x 105 psi. Dynamic Young's modulus decreases with increasing axial strain amplitude. At a temperature of -1°C, the rate of decrease is fairly uniform over the range of strain amplitudes while at a temperature of -10°C the rate of decrease increases significantly at higher strain amplitudes. The relationship at -4°C is intermediate between those at -1 and -10°C. The relationship between dynamic Young's modulus and strain amplitude does not appear to be affected by frequency or water content. 102 hzuhzou x-<3 u—.m~ H< uh~zugo m343coz m.az:0> u_zo ~.m ogam.m Aucaugoa oo_v c.9cum ...x< cem.- . 00.»- om.—. Uo—I U0?- UoO—I ocauocuan» .93 99.1.12! 39 c.m l-l.l mau 0.. 111111 «nu n.o 1111111 «nu mo.o ::::.:: aucoacocu magnumoca o:.:..cou ... so. “9.299. amaco>< oo.~- cm.~- oo.mi .o. .m. .v. .m— .m— .ON a mic. x o.m mo z.<¢hm 4<_x< z< h< w»_z_4o m=4=oot m.uz:o> u_z<2>o ..ma. «cannot; oc.c..cou oo~ om— cc. cm a a 41 u .o .~ .v .m 3 w M. An NE 3 m. an .0. .m n _w «a N SI fl ‘ m «F a. .... m. m . mm .n— C; d m. ( a. 9.9. 4 ... a. o.“ 4 a9 9.. d a. 8... 4 .m. .o~ (15d s01) snlnpou s,6uno1 atuvuxa 103 hzmszU xuh< L L .o. .m. .e— .m— .m— .om 01) snlnpou $.6unoA otmeuKo 9 (15d hzuhzou «wh<. oo.n- .v— .o. .m— .o~ (15d S01) snlnpou s,6unoA atmeuxa 104 To assess the influence of frequency, temperature, and water content on dynamic Young's modulus, values of dynamic Young's modulus were obtained from the plots of dynamic Young's modulus versus axial strain amplitude and plotted versus frequency, temperature, and water content, respectively. The modulus values were chosen at axial strain 3 2 amplitudes of 3.16 x l0' and 3.l6 x lO' %. 5.3.2 Effect of Frequency The relationship between dynamic Young's modulus and frequency is shown in Figures 5.5 to 5.8. Each graph represents the relation- ship at a given strain amplitude and water content at all three temperatures (-l, -4, and -l0°C). In general, dynamic Young's modulus increases by a small amount as frequency increases. The rate of in- crease is fairly constant over the frequency range 0.05 to 5.0 cps, but increases somewhat in the frequency range 5.0 to l0.0 cps. The relationShip does not appear to be significantly influenced by temperature, strain amplitude, or water content. 5.3.3 Effect of Temperature The relationship between dynamic Young's modulus and tempera- ture is shown in Figures 5.9 to 5.12; each graph represents the relationship at a given strain amplitude and water content at all frequenCies (0.05, 0.3, l.0, 5.0, and l0.0 cps). Dynamic Young's modulus increases significantly with decreasing temperature. The rate of increase is generally more uniform over the entire tempera- ture range (-l to -lO°C) at a high strain amplitude (3.l6 x l0-2%) and a low water content (28.1%). At a low strain amplitude (3.l6 x lO-3%) the rate of increase is somewhat greater in the high tempera- 105 umio. x o..m no z.<¢.m 4<.x¢ z< .< m..z.90 magaoo: m.0z:0> 0.z0 o.m 9930.9 .999. 9999:9999 0.0. 0.m 0.. n.o m0.0 J J a O 4|l1c||1||||¢||||$1 1 L L 1. IL .L I. UJO—I ‘ cl 9.... < 1 999399999 99.9.9999 9... AV ..9 999 99.3999 9oa99>< 9999999959. 1 a..m~ . 9:999o0 99993 19 L .0. .N. .e. .0. .0. .0m (15d 90” snlnpoH slfiunoA atmeuxg unio. x o..n 90 z.uzunowmu mammm> m09000z m.0z:0> 0.z0 m.m 9930.9 .999. 99:999999 0.0. o.m 0.. m.0 m0.0 d d - a u L L I. L l L 1 IL L L .1 1L UoOPI ‘ I. 0001 d L 999999999 ac.c_9c99 0..- AV ..9 99. 99.3999 99999>< 9939999959. 1 u..m~ - 9:99:90 9999: L L .v. .o. .0. (1‘4 S01) snlnpou $.6unog atmwuxa 106 u~-0. x 0..n 90 z.<¢.m .<.x< z< .< m..z..00z000009 m0mmw> m09000z m.0z:0> 0.x<2>0 0.0 9930.9 .999. 39:93:99. 0.0. 0.m 0.. 0.0 00.0 d d - — . _ L L 1 L L 19 L 0.0.. ‘ 1 999399999 0:.:C:o9 0....- 4 l ..9 99. 99.3999 90999>< 0... Au 9939999959. 1 an... . 9:99:99 9999: 1. .0. .N. .c. .0. .0. (15d S01) snlnpow s,6unoA atmeuxg umio. x 0..n 90 z.<¢.m .<.x< z< .< u..z.90uzmaom¢9 m0m¢u> 0090001 m.0200> u.:< 0o.u AV 9939999959. 1 L .v. .0. .0. (15d S01) snlnpou s,fiun01 atmouia 107 nN-o. x o..n 90 z.<¢hm 9<.x< z< H< uh.z.90 m09000: m.0z:0> 0.:0 0..m 9930.9 .0.. 9939999959. 0.1 0. 0- 9- 01 mu 01 n- N- .a . — d _ _ d . . q — 1 l C u L L l -L 999 0.0. AV 1- 999 9.9 9. .1 999 9.. 99 999 9.0 .V .L 999399999 0:.:.9:99 999 90.0 AV 1. 9 9 399 909 93 ..9 9 9 9. 9 9 < 999939999 u..0~ - 9:99:99 9999: -. .v. .0. .00 (15d S01) snlnpou s,6unoA atmeuxg “0-0. x u..n 90 z.<¢hm 4<.x< z< p< uh.z..0 m04000: 0.0200» u.z0 0.m 9930.. .0.. 9939999959. 9.- 9- 9- .- 9- 9- 9- n- - .- . _ _ _ _ d — a 0 d [9° L ION L 1.0 I. [.0 1. I..@ 1 1.0. . 1.9. . L... 999 0.0. 4 L 999 0.9 4‘ 1 999 0.. d .9. 999 0.0 9V L 999399999 9:.:.9:99 999 90.0 AV ..9 99. 99.3999 90999>< 399939999 ...0. 9..9~ - 9:99:99 9999: 1 1.99 (1:4 501) snlnpou $.6un01 atmouxu l()£3 uV-o. x 0..m 9° z.<¢hm 9<.x< z< p< mp.z.do 909000: 9.0220» u.z0 ~..9 9939.9 .99. 99399999599 0.- 9- 9- . 9- 9- 9- 9- 9- N- .- _ T _ . . _ . 9 9 9 Q l 4 I1 . .9 1 IL L 98 9.9. 4 .1 999 . 0 9 4 L 999 9.. d 999 9.9 99 -. 999 . 999399999 959.9999 90 0 d 1. :9 999 99.3999 9999939 3:93.999... 99.: 9 9:99:99 9999: .1. L O F- N .— G .— .0. (gsd scl) snlnpou s,6unog agmeuxn 9.9-0. 9. 0.6 90 2.59.5 ._<.x< z< 2 3.2.-.05 90... 990599959 90999.. 909009. 9.9200» 9.25.90 ...9 9939.... .99. 9939999959» 0.. 9- 9- 7 9- 9- 9- n- - .- _ 9 9 _ 9 9 A 9 9 1 1+9 L L. It. 1 [so [.0 L 1.0. L loN— L 1.9. 999 0.0. < l 999 0.9 4 IL 999 0.. 4 .9. 999 9.0 4 1. 999399999 99.5959 999 90.0 d. ..9 999 99.3999 99999>< x99939999 [.0. 99._9 - 9:99:99 9999: L 4.99 (gsd Sal) snlnpou 5.51100; ”111-Ma 109 ture range (-1 to -4°C) than in the low temperature range (-4 to ~l0°C). The relationship does not appear to be influenced by fre- quency. 5.3.4 Effect of Water Content The relationship between dynamic Young's modulus and water content is shown in Figures 5.l3 and 5.l4. Each curve is based on two points and represents the relationship at a given strain ampli- tude, temperature, and frequency. At higher temperatures (-l and -4°C) dynamic Young's modulus increases by a small amount with in- creasing water content. The relationship is not influenced by frequency or strain amplitude. At a low temperature (-lO°C) dynamic Young's modulus appears to decrease slightly with increasing water content at a low strain amplitude (3.l6 x l0'3%) and is not signi- ficantly influenced by water content at a high strain amplitude (3.l6 x 10'2%). 5.4 Damping Ratio of Frozen Clay Values of damping ratio were plotted versus the log of axial strain expressed as a percent for all loading conditions. The plots for clay at both water contents are given in Appendix D. Each plot represents clay at a particular water content, temperature, and frequency. Data points for all three confining pressures (0, 50, and 200 psi) are included in each plot. Each plot represents at least two samples; the agreement between the data points of duplicate sam- ples is generally good. Some minor scatter of data points at low damping ratio values is probably due to limitations in the recording and reduction methods. In general, however, the data is considered 110 “NIO— x o~.n no z_<¢»m 4<_x< z< h< uh_z—Jc magzoo: m.uz=o> u_:o ¢—.m ogzmvm acoucou L0... a3 On. om. Om. .O'. on. ON. 4 d u q a - I1 1 00—... l UOVI l L UGO—I IL 1 ocauacoaeop I IL “go 0.0. Aw I «no o.m .c. L au 9. 4 «no n.o 4‘. I magnumaca oc_=¢ucou «no mo.o AV I __o Lou uu—amuc oon1o>< aucaaaogu I .N. .op .m— .mp (isd S01) snlnpou s,5unoA aimeufia nnIOF x o—.n no z_<¢hm 4<_x< z< p< wh~z_do madame: m.uz:¢> u~t<2>a mp.m 0530.“ acoucou Laue: cm. on. om. ov. on. ow. d _ . . a . l accumuogq o:.=.$cou FF. co» mapamog coago>< «nu «no «no «no «no assuacuace» o.o— ‘1 o.m 4‘ o._ 4‘ n.o 4‘ mo.o AV xucoaaocu L, 1, l 1* J, 1, 41_, l L l, 41* L i 4 .o— (gsd s01) snlnpou 5,6unog atmnulu lll quite reliable. 5.4.1 Effect of Strain Amplitude To assess the influence of axial strain amplitude on the damping ratio of frozen clay, average "best fit" curves were drawn through the data points given in the plots in Appendix D. The re— lationship between damping ratio and strain amplitude is summarized in Figures 5.l5 to 5.24. Each graph represents the relationship for clay at a particular water content and frequency at each of three temperatures (-l, -4, and -l0°C). In cases where confining pressure appeared to have an influence on damping ratio, separate curves are given for each confining pressure (0, 50, and 200 psi). Damping ratio generally increases with increasing strain ampli- tude. In most instances, the rate of increase is greater at higher strain amplitudes than at lower strain amplitudes. The influence of strain amplitude on damping ratio is greater at lower frequencies than at higher frequencies; at the highest frequency (l0.0 cps) there is an initial decrease in damping ratio at low strain amplitudes fol- lowed by an increase at higher strain amplitudes. The relationship between damping ratio and strain amplitude does not appear to be significantly influenced by water content or temperature. To assess the influence of confining pressure, frequency, temperature, and water content on damping ratio, values of damping ratio were obtained from the plots of damping ratio versus axial strain amplitude in Figures 5.l5 to 5.24 and Appendix D and plotted versus confining pressure, frequency, temperature, and water content, respectively. Damping ratio values were obtained at strain ampli- 3 2 tudes of 3.16 x l0' and 3.l6 x 10' %. 112 hzmhzou xmw<3 u—.m~ h< mp_z_40 o~h<¢ oz~mz< mqu m.o - Aucozcmgu l cm. 1 oc- otzeu Sugdmeq hzuhon amh onh<¢ uz_mx¢a m—.m «Lao.m Aucuucoa ao—V c_agum ~o_x< cam.- oo._- om..- oo.~- om.~- oo.m- . . q _ d _ .L.o ILvo. .3 8~ . .3 8 18 .3 a 833.... 9.25:8 L2. ILoF. U0?! 9.2- 18. Dept on: a one IGN- L NM. “.38 3.3..an $2.5 nogammoga oc_cv»=ou :. ..e 3.38 a5: "3 3.0 . 3:35 L8. IS. 051'; Bugdmea 113 hzmhzou amh o_h<¢ uz—az< mau o.m u Aucmacogm I, mo. wp. op. om. ow. mN. mm. ow. ogzeu buidmea hzmhzou cup<3 n—.m~ h< mh~z_go o_h<¢ oz~ax< «nu o.— - xucoaaogu vo. ~—. mp. vN. aw. NM. ov. 05193 buydmea H4 pruhzou mmh o~h<¢ oz~mz< «no mo.o . xucmaaucm on I.oe. 0&198 Bugdweg bzwhzou awP o~w<¢ oz_mx< mag o.op . sucoacocu I 00. ~—. op. ow. ow. mu. ~n. otzeu fiuIdwea 115 hzupzou m~p<2 n.ps h< mh_z_qo o~h<¢ uz~mz< mnu o._ . aucoacocu I «o. N—. mp. ow. em. ow. NM. ow oIzeu BuIdwea hzuhzou aup<3 un.—~ h< up_z_ao o~h<¢ oznmzda —~.m «Laovu «acoucoa 50—. c.agum _a_x< P—u so» mu_:moc caeso>< oom.- oo.p- cm._- oo.~- om.~- oo.n- Illa . . . . q 000—: l Uovu UOPI 1 assuagoaso» IL I I _I mocammoga ocwcvmcou «no m.o . xucoaaogu ~—. 9". ow. ov. oIzou Dugdmea 116 qupzou a~w o_h<¢ uz_¢z< mau o.o_ . zucoaaocu mo. N—. op. 0N. cN. mN. Nm. on. oe. ogaeu fiugdweo _Fo Lou mu—amoc omaLa>< hzuhzou m-<3 an.—N h< mh_z~go o_h<¢ oz_azuzu=om¢u m=m2u> o_h<¢ uz~gz 02.5. 922% «Nd 0.5m...— 39: 3532... cg: o6. 9. ad 36 q 4 A d - l .3 8N .3 on 1 .3 a 0.5395! oc.c.~cou 9.2- 4 I 232 3.3.2.3 325 3.5393 9:528”. u..- G :a .52 3.39.. 2.3.32 u... d 2.3 .. 2328 23.2 83939.8. 1 2. «N. Na. emu Bald-m 120 uNuo— x o—.n no 2~uzu=ou¢u wzmzu> o_»<¢ o2~az< . 007 q Rn.pu I ucuucou Luau: Ogauosmgoh. 1 Wm. I.ov. ogzeu Bugdwea anuo— x w_.n mo z~<¢hm 4<_x< z< h< N»_z_aouzuscumm m=m¢m> c_»<¢ oz_¢:¢a mN.m 0230'; .unuv xucoacogm o.op o.m o.. n.o mo.o . _ _ _ . .32 oo~ .32 on .32 o I. unannoga ac'c_2cou J l 232. 3.2550 32.5 9.2- § 30539:. 922.528 u..- 4 .2. no. mu—amog mango>< cop- Aw I; um._h - acuacau Luau: menu-Loaso» N—. 0.. ON. Nn. ogacu Sugdmea 121 of decrease is somewhat more uniform over the entire range of fre- quencies. The relationship at a high strain amplitude does not appear to be influenced significantly by water content. 5.4.4 Effect of Temperature The relationship between damping ratio and temperature is sum- marized in Figures 5.31 to 5.34. Each graph represents the relation- ship at a given water content and strain amplitude at all five fre- quencies (0.05, 0.3, 1.0, 5.0, and 10.0 cps). In general, damping ratio decreases slightly with decreasing temperature. In most in- stances, the decrease appears to be more pronounced at lower fre- quencies than at higher frequencies. At the highest frequency (10.0 cps) the relationship reverses as damping ratio increases by a small amount with decreasing temperature. At a low water content (28.1%) and low strain amplitude (3.16 x 10'3%) at 10.0 cps there is an initial decrease in damping ratio between -1 and -4°C followed by an increase between -4 and -10°C. In general, the rate of change in damping ratio is somewhat greater in the high temperature range (-1 to -4°C) than in the low temperature range (-4 to -10°C) at a high water content (71.3%). At a low water content, the rate of change is somewhat more uniform over the entire range of temperatures. The influence of strain amplitude on the relationship between damping ratio and temperature is not clear. 5.4.5 Effect of Water Content The relationship between damping ratio and water content is summarized in Figures 5.35 to 5.40. Each graph represents the re- lationship at a given temperature and strain amplitude at all five 122 uN-o— x o—.n no z_<¢hm 4<_x< z< h< mh~z_go c~h<¢ uz_¢z< «no mo.o AV u_.wN . acuucou Luau: sucoaaogm on otzeu Bugduea 0| 4 mo _ Auov «cauoguaswh ea — MI 4 an.o_ 2 o_.n mo 2_(¢»m 4<_x< z< h< uh~z~40 o~p<¢ oz_mz< RF.QN n uCOHCOU Loam: l .3 8N .3 S I .3 o 0.5395L uc—cv22ou IL .I L mac o.o— 4. ac o.” 4 I a. 9. 4 "no n.o ‘1 so 35 d I 2Ucoaaogm no. N p. o—. 0mm 5‘1in 123 a -o. x o_.n no z_<¢hm q<_x< z< h< wh_z_go o~h<¢ oz~¢z< «nu mc.o Aw I nn.p~ u acoucou Logo: aucoacmgm IL mo. Np. «N. mm. Nm. on. oe. oIzeu BUIdmea am-o_ x o..n mo z_<¢hm 4<_x< z< h< uh~z_4o o~h<¢ uz~mx< «nu no.0 Aw I um.Fu - acoucou Laue: xucosaugm on. «N. mw. ~n. ov. 0}}?! 50}dm90 124 uwuop x o—.n no z_<¢hm 4<~x< an-c_ x o_.n no z_<¢hm 4<_x< z< h< up~z~40<¥ mo; hzmpzou mmh<3 mamau> o_h o_»<¢ uz_mz o_»<¢ uz_nz< mnu mo.o AV uov- u unnuogunEm» xuconcogn co. mo. NF. op. 0N. cw. mw. «m. on. ogzea fiuIdwea unuop x c—.n no z_<¢hm 4<_x< z< h< m»_z_uo< «no m°.o Aw woe. . ounuouonsuh aucoaaogn ~—. op. v~. mm. Nn. on. ow. ogzcu 6uIdmoa 126 u ucoucou Laue: ~-o— x o—.n no z~<¢hm 4<_x< z< h< uh~z_uo o—w<¢ mz_nz< «nu . «o 0 «V on. ooop- . unauouunEu» zucuacugn on. 193 fiuIdeQ Ol unnop x o—.n no z~<¢hm 4<—x< z< ~< wp_z~uo o_h<¢ oz~n1< «nu no.0 «V on. goop- - uuaungunEup Aucuacogn ov. 0‘193 fiuIdmoa 127 frequencies (0.05, 0.3, 1.0, 5.0, and 10.0 cps). In general, it appears that water content has at most only a slight influence on damping ratio over the range of water contents tested. At a high temperature (-1°C) and a low strain amplitude (3.16 x 10'3%) damping ratio increases by a small amount with increasing water content. The change is most significant at lower frequencies and becomes negligible at higher frequencies. At a high strain amplitude (3.16 x 10'2%) damping ratio increases by a slight amount with increasing water con- tent at the lowest frequency (0.05 cps) and decreases by a slight amount at higher frequencies. At lower temperatures (-4 and -10°C) the relationship between damping ratio and water content and the in- fluence of frequency and strain amplitude on the relationship are not entirely clear; it appears that, in general, water content has a slight to negligible influence on damping ratio. 128 CHAPTER 6 COMPARISONS 0F DYNAMIC PROPERTIES OF FROZEN SILT AND CLAY 6.1 General This chapter presents a comparison of the dynamic properties of frozen Silt and clay obtained in this study with the results ob- tained in previous studies., To allow a direct comparison to be made, the dynamic properties obtained in all of the studies were converted to common units. Thus, dynamic elastic properties are presented in ' terms of compressional or longitudinal wave velocities and damping properties are presented in terms of damping ratios. Values of dynamic Young's modulus obtained in the present study were converted to longitudinal wave velocities using: VL (6.1) in which VL = longitudinal wave velocity, Ed = dynamic Young's modulus, and p = material density. Results of field investigations are presented in terms of compression- al wave velocities, which are related to longitudinal wave velocities - (1 - II) V - V P fiA + u)(1 - 2..) (6'2) P compressional wave velocity and as follows: in which < ll Poisson's ratio. 1: II 129 Values of damping ratio were calculated from loss factors determined in previous investigations using: D = sin-%} ' (6.3) in which C II damping ratio and O: 11 phase lag. 6.2 Comparison of Dynamic Properties of Frozen Silt 6.2.1 Longitudinal and Compression Wave Velocity The relationship between longitudinal or compressional wave ve- locity and temperature for frozen silt obtained in the present study and in previous studies is summarized in Figure 6.1. In general, there is fairly good agreement among the basic wave velocity-temperature re— lationships_obtained in the several studies. The variation in the magnitude of the wave velocities may be attributed to differences in testing technique and material characteristics and may be summarized as follows: (1) Frequency - the range of frequencies associated with the pre- sent study using cyclic triaxial equipment (0.05 to 10.0 Hz) is signi- ficantly less than the frequencies associated with the testing tech- niques used in the previous studies (resonant frequency, approximately 1 to 10 kHz; seismic, approximately 150 Hz; ultrasonic, approximately 50 to 1000 kHz). It was shown in the present study that dynamic Young's modulus of frozen silt increases with increasing frequency between 0.05 and l0.0 cps. The relationship between longitudinal wave velocity and frequency determined in the present study and by Stevens (1973) is shown in Figure 6.2. Since the wave velocity decreases at frequencies 130 Compression or Longitudinal Nave Velocity, Vp or VL (km/sec) 3.5 3.0 2.5 2.0 1.5 1,0 0.5 ‘ /‘ ' / ;,,,.— _ / /’//l’ 1 ’ 1 ’ T” ‘.::.T.:.::............::::::: 3 .......... ../ ............ I .... . ......................... —- / 4’ .0.]: ....................... / '.- I ................... 5/ -" 2 . ..... .0.. ........ _ 6 ..0 .-‘ ........ 7r' 8//// l - silt 2 - silt with ice lenses . . _ 9 ‘T Hunter (1974) 3" New Hampshire Silt j_ (seismiC' V ) ' 33'7% WC 10 . ’ P 4 - Manchester silt - I Blouin (1976) 26.0% we 1] (seismic; VP) 5 - Hanover silt 6 - Fairbanks silt - —-——---——-Nakano-and Froula (1973) 23-0% WC (ultrasonic; VL) 7 - gukog silt - 1.1 we """" Stevens (1973) 8 - Hanover silt - (resonant frequency; VL) 35.5% wc .............. Kaplar (1969) 9 - Hanover silt - - (resonant frequency; VL) 21-4% WC . 10 - Alaska silt - present study (cyclic 38 9% wc triaxial; VL; frequency = 1] _ Alaska silt _ 1.0 cps; ax1a1 strain = 20 5% we 3.16 x l0'3 %) ° L L l l l J I L I I -I -2 -3 -4 -5 -6 -7 -8 -9 -l0 Figure 6.1 Temperature (0C) HAVE VELOCITY VERSUS TEMPERATURE OF FROZEN SILT 131 >uzm=cmmn mammm> >hHuoum> m><3 4m.u guwgnoouIII, III u; w2.3.III......III...II..........III.....IIIII.. u: Nn— I xmpu uruwmmzm mu.:.~ou¥ uz Rm.mm u: Now u..« mx«m.< u..« .uumuzucmz-gu>ocmx "AnnmPV «cu>uum .uu.m u: Rm.mm III u..« Lu>ocmz ”>u=u« ucumugn :2... . . ...—... . . b.5CE. . _....p.. . 7...... . _.:.... P 7:... . . ...-...- 132 (oas/wx) KlgoolaA BAEM Lequn1I6u01 less than l0.0 cps, the longitudinal wave velocities obtained in the present study should be lower than those obtained in previous studies. (2) Strain amplitude - the strain amplitudes associated with the cyclic triaxial method (approximately 2 x 10"3 to 8 x 10'2%) are greater than the strain amplitudes associated with the other methods (resonant frequency, approximately 10'6 to 10'3%; ultrasonic and seismic methods, I 7 F approximately 10' to 10'4%). It was shown in the present study that the dynamic Young's modulus of frozen silt decreases with increasing strain amplitude over the entire range of strain amplitudes in the testing program. The relationship between longitudinal wave velocity and axial strain amplitude obtained in the present study and by Stevens (1973) is summarized in Figure 6.3. Since the longitudinal wave ve- locity is higher at very low strain amplitudes than at high strain am- plitudes, the longitudinal wave velocities obtained in the present study at an axial strain amplitude of 3.16 x 10'3% should be lower than the wave velocities obtained by other methods at lower strain amplitudes. (3) Material characteristics - in general, the wave-velocity- temperature relationships from the several studies shown in Figure 6.1 are associated with frozen silts over a relatively narrow range of water contents. It can be seen from the relationships obtained for Hanover and Alaska silt in the present study that water content did not influence the longitudinal wave velocities to a large extent; it is, therefore, not likely that the differences in wave velocities among the several laboratory studies are due to the relatively small differences in water contents. 0n the other hand, it appears that the wave veloc- ity can be influenced to a larger extent by the nature of the silt itself, such as the grain size characteristics. In the present study, 133 > >HHooum> m><3 uocmz MN I a V ..o.« m « u 0.. u n I\ u:u« u:m«u.n uz New I u..« .mu«u;ucmz ..m.m Amnmpv «cu>uum Loutm . :L-p. - F —:..P. . . 7.... . p _ —..-. . . . _pb.-. . p - 134 for example, the lower longitudinal wave velocity obtained in Alaska silt than in Hanover silt may be a function of the finer grain size and corresponding large clay content in the Alaska silt. Overall, the wave velocities obtained in the present study appear to be in good agreement with the wave velocities obtained in the previous studies. 6.2.2 Damping Ratio The relationship between damping ratio and temperature for fro- zen silt obtained in the present study and in a previous study by Stevens (l973) is summarized in Figure 6.4. The values of damping ratio obtained by Stevens (1973) are lower than the values obtained in the present study. This variation may be attributed to differ- ences in the testing technique in the two studies and may be explained as follows: (1) Frequency - the frequency associated with Stevens' (1973) resonant frequency procedure is much greater than that associated with the present study. It was shown in the present study that the damping ratio of frozen silt decreases with increasing frequency between 0.05 and 10.0 cps. The relationship between damping ratio and frequency obtained in both studies is summarized in Figure 6.5 Since the damping ratio is smaller at high frequencies than at low frequencies, the values of damping ratio Obtained in the present study should be higher than those obtained by Stevens (1973). (2) Strain amplitude - the strain amplitude associated with the present study are greater than the strain amplitudes associated with the resonant frequency method. It was shown in the present 135 Damping Ratio .30- .’25 _ .20- present study (cyclic triaxial) _3 - Axial strain = 3.16 x 10 %; f=l.0 cps Hanover silt 15 _. 21.4% wc ' 35.5% wc ‘ Alaska silt 20.5% we .10 — after Stevens (1973) _ (resonant frequency) .05 - Manchester silt 26% we torsional _____________________________ longitudinal --------------- 40. '- I I I L I I I I I L Temperature (0C) Figure 6.4 DAMPING RATIO VERSUS TEMPERATURE OF FROZEN SILT 136 >ozwzommn mammm> loocmz . A. Io.xu..m I c...u« ...xmv . I m zunum ucumunn I.@. o OQI u unsumnunsuh 7...... . —:.:. p _ —_:—.-_ n 7:...— . 7:... . . _.P..-. _ —.P:.pL . —.:.-—_ 137 study that.damping ratio of frozen silt increases with increasing axial strain amplitude between approximately 2 x 10'3 and 8 x 10'2%. The relationship between damping ratio and strain amplitude obtained in the present study and by Stevens (1973) is shown in Figure 6.6. Since the damping ratio is less at low strain amplitudes than at high strain amplitudes, the values of damping ratio obtained in the present study should be greater than those obtained by Stevens (1973). Overall, it is felt that the comparison between the damping ratios obtained in the present study and by Stevens (1973) is rea- sonable. 6.3 Comparison of Dynamic Properties of Frozen Clay 6.3.1 Longitudinal and Compyession Wave Velocity The relationship between longitudinal or compressional wave velocity and temperature for frozen clay obtained in the present study and in previous studies is summarized in Figure 6.7. In general, the longitudinal wave velocities obtained in the present study compare favorably with the wave velocities obtained in previous studies. The variation in wave velocity from different studies can be attributed to differences in testing technique and material charac- teristics and may be summarized as follows: (1) Frequency - as in the case of frozen silt, the frozen clay in the present study was tested at frequencies significantly lower than the frequencies associated with the testing techniques used in nmst of the previous studies. As shown in Figure 6.2, the longitudinal vmve velocity of frozen clay increases slightly with increasing fre- quency in both high and low frequency ranges. Therefore, the wave 138 >.omhocmx $8 0.. I t Iom. >u:u« ucummnn . o onI u unnunnunEmh 7...... . 7...... . 7...... . _....... p 139 Compression or Longitudinal Nave Velocity, VP or VL (km/sec) alluvial clay l 2 - Goodrich clay l0 - Fargo clay - 35% wc, 3 - Boston blue clay 98% LL 59% wc, 47% LL ll - Montmorillonite + 4 - Kaolinite - 7l.3% wc, 40% LL Ontanagon clay 3.5.— 5 - Kaolinite - 28.1% we 57% wc, 98% LL 6 - Goodrich clay ~ 26% wc, ...—’ 41% LL /‘/ 7 - Suffield clay — l7% wc, ,,r"' 45% LL ,/ 8 - Ontanagon clay ,a”’ 3.0.. 55% wc, 6l% LL ,«/’ ’/ I/ 1/ ............. 2.5 ... ’/ ........ u- .......... 2/ o ........... 1 ......... 2.0- .......... 3 ______ __6 W"‘= ----------- 7 .— .. ’35.. ’0’...’ —. ; ."’..,,.._.. , .___8 / ’-°"' . ,/. /./° ........... 10 l.5- -”' ‘,.-—”' ............... /./ ./o .............. .____.°"-—..—_ “‘11 4 /o /./.......,o"”./."’ 5 °’/” dz’“f::i::::7°”fl 9", .«<:§==$"" .4“, l.0- ai” ---—-- Nakano and Froula (l973) :7” (ultrasonic; VL) """ Stevens (l973) (resonant frequency; VL) . Barnes (1963) ............ Kaplar (1969) 0,5- (seismic; VP) (resonant frequency; VL) ————— Chaichanavong.(1976) present study (cyclic (CYCIlC tr1ax1al; VL; triaxial; V ; frequency = frequency f 7-0 CPS~ _3 1.0 cps; axkal strain = ax1al strain = 3.16xl0 %) 3.l6xl0'3%) L l .1, l 1 l l L_ l [L_L -l -2 -3 .4 -5 -6 -7 -8 -9 -10 Temperature (0C) Figure 6.7 WAVE VELOCITY VERSUS TEMPERATURE OF FROZEN CLAY 140 9 - Ontanagon clay - 36% wc velocities obtained in the present study should tend to be somewhat lower than wave velocities obtained in previous studies using high- frequency techniques. (2) Strain amplitude - the strain amplitudes associated with the present study are higher than the strain amplitudes associated \Nlth most of the previous studies. The relationship between longi- tudinal wave velocity and strain amplitude for frozen clay determined in the present study and by Stevens (1973) is summarized in Figure 6.3. It can be seen that the wave velocity decreases with increasing strain amplitude at high strain amplitudes, but is not significantly influenced by strain amplitude at lower strain amplitudes. Since the values of wave velocity in the present study were chosen at a suffi- ciently low strain amplitude (3.16 x 10’3%) for purposes of comparison, it appears unlikely that differences in strain amplitude can account to a large extent for the significant variation in wave velocity among the several studies shown in Figure 6.7. (3) Material characteristics - the wave velocity-temperature relationships shown in Figure 6.7 are associated with frozen clays with wide variation in plasticities and water contents. Results obtained by Chaichanavong (1976) and in the present study indicate that water content has a relatively small influence on longitudinal wave velocity. It appears that the wave velocity in frozen clay is influenced to a larger extent by the properties of the clay particles. Algeneral relationship between wave velocity and liquid limit using the data of Kaplar (1969), Chaichanavong (1976), and the present study is shown in Figure 6.8; while an exact relationship cannot be determined from the data given, it appears that the wave velocity 14] Ir. 1h". mm _ Longitudinal Nave Velocity (km/sec) 5 _ triaxial; frequency = l.0 c s; I I i r r f T I r Boston blue clay Temperature = -40 C after Kaplar (l969) (resonant frequency) 7 Kaolinite Ontanagon clay Fargo clay Montmorillonite after Chaichanavong (l976) + Ontanagon C13Y" and present study (cyclic strain amplitude = 3.l6xlO- %) - 1 g l L l L L L L 30 4O 50 60 7O 80 90 I00 110 Liquid Limit (% wc) Figure 6.8 LONGITUDINAL WAVE VELOCITY VERSUS LIQUID LIMIT OF FROZEN CLAY I42 is significantly greater in clays with lower liquid limits than in clays with higher liquid limits. This may be an indication of the influence of the unfrozen water content on the wave velocity in fro- zen clay, since the liquid limit is related to the specific surface area of the clay which is in turn related to the unfrozen water con- tent. Overall, the longitudinal wave velocities for frozen clay obtained in the present study appear to be very reasonable in com- parison with the wave velocities obtained in previous studies. 6.3.2 Damping Ratio The relationship between damping ratio and temperature for fro- zen clay obtained in the present study and in previous studies by Chaichanavong (1976) and Stevens (l973) is summarized in Figure 6.9. It can be seen that the damping ratio values obtained in the present study compare favorably with the values obtained by Chaichanavong (1976) but are significantly less than the values obtained by Stevens (l973); this variation may be attributed to differences in the testing techniques and material characteristics in the studies and may be ex- plained as follows: (l) Frequency - the frequency associated with Stevens' (l973) re- sonant frequency procedure is much greater than that associated with the present study and the study by Chaichanavong (l976). It was shown in the present study that the damping ratio of frozen clay at a strain amplitude of 3.l6 x lO'3% decreases with increasing frequency between 0.05 and 5.0 cps and increases with increasing inequency between 5.0 and 10.0 cps. The relationship between damping ratio and frequency obtained in the present study and by 143 Damping Ratio .30'- ------—Stevens (1973) (resonant frequency) ------Chaichanavong (l976) (cyclic triaxial; frequency = l.0 cps; _3 .25L. axial strain = 3.l6xlO present study (cyclic triaxial; frequency = l30 cps; axial strain = 3.l6xlO“ %) 76) .20.. l - Suffield clay l7% wc, 45% LL 2 - Goodrich clay 26% wc, 4l% LL 3 - Montmorillonite + Ontanagon clay 57% wc, 98% LL . _ 4 - Ontanagon clay .15 ‘55% we, 61% LL 5 - Ontanagon clay 36% we 6 - Kaolinite 7l.3% we, 40% LL 7 - Kaolinite .10__ 28.3% wc .05- l l i L l l l L L L -l -2 -3 -4 -5 -6 -7 -8 -9 -lO Temperature (0C) Figure 6.9 DAMPING RATIO VERSUS TEMPERATURE OF FROZEN CLAY I44 Stevens (1973) is summarized in Figure 6.5; it can be seen that the damping ratio of frozen clay associated with higher frequencies (103 to 104 Hz) is greater than the damping ratio associated with the upper limit of lower frequencies (5 to 10 Hz). Therefore, since it appears that the damping ratio of frozen clay will continue to in- crease to a certain extent at frequencies greater than 10 cps, the damping ratios obtained in the present study should be lower than those obtained by Stevens (1973). (2) Strain Amplitude - the strain amplitudes associated with the present study are higher than the strain amplitudes associated with Stevens' (1973) studies. It was shown in the present study that the damping ratio of frozen clay increases with increasing strain ampli- tude and that the rate of increase is less at low strain amplitudes than at high strain amplitudes. The relationship between damping ratio and strain amplitude obtained both in the present study and by Stevens (1973) is shown in Figure 6.6. It can be seen that the damping ratio of frozen clay is not significantly influenced by strain amplitude at very low strain amplitudes (10‘5 to 6 x 10'4%). Therefore, since the damping ratios in the present study and in the study by Chaichanavong (1976) were chosen at a sufficiently small strain amplitude (3.16 x 10'3%) for purposes of comparison, it is not likely that the variation in damping ratio among'the several studies is due to differences in strain amplitude. (3) Material characteristics - it was shown in the present study that the damping ratio of frozen clay is not significantly influenced by water content. While the influence of the type of clay on damping ratio is not clear from the data shown in Figure 6.9, it appears that 145 the influence of clay type is relatively small. Therefore, it is not likely that the variation in damping ratio among the several studies is due primarily to differences in material characteristics. Overall, the damping ratios of frozen clay obtained in the‘pre- sent study appear reasonable in comparison with the damping ratios obtained in previous studies. I46 CHAPTER 7 SUMMARY AND CONCLUSIONS Cyclic triaxial tests were conducted on samples of frozen Hanover silt, Alaska silt, and kaolinite. Values of dynamic Young's modulus and damping ratio were obtained for each soil as a function of strain amplitude, temperature, frequency, confining pressure, and water con- tent. The test results may be summarized as follows: (1) Values of dynamic Young's modulus obtained for the range of 2 test strain amplitudes (approximately 2 x 10-3 to 8 x lO' %), frequen- cies (0.05 to 10.0 cps), temperatures (-l to -lO°C), confining pres- sures (0 to 200 psi), and sample water contents (21.4 and 35.5% for Hanover silt and 20.5, 29.2, and 38.9% for Alaska silt) ranged from 5 5 l x lo to 35 x l05 psi for Hanover silt and l x 105 to 22 x 10 psi for Alaska silt. Values of damping ratio ranged from .02 to .36 for Hanover silt and .02 to .32 for Alaska silt. (2) The influence of the various parameters on the dynamic Young's modulus of frozen silt in the order of their importance is as follows: (a) Strain amplitude - the dynamic Young's modulus of both silts decreases as the axial strain amplitude increases, with a more pronounced effect at low temperatures (-4 and -l0°C) than at high temperatures (-l°C). The relationship between dynamic Young's modulus and strain amplitude appears to be independent of frequency and water content. (b) Temperature - the dynamic Young's modulus increases signifi- cantly with decreasing temperature. At a low strain amplitude .(3.l6 x lO-3%) the rate of increase is generally greater at I47 (C) higher temperatures (-l to -4°C) than at lower temperatures (-4 to -lO°C); at a high strain amplitude (3.l6 x 10-2%), the rate of increase is more uniform over the entire temperature range. The rate of increase of dynamic Young's modulus with decreasing temperature is generally more uniform over the en- tire range of temperatures (-l to - lOOC) at low frequencies FF- than at high frequencies. Frequency - dynamic Young's modulus increases with increasing frequency. The rate of increase is slightly greater at very low and very high frequencies than at intermediate frequencies. 1 A At a high strain amplitude (3.16 x 10'2%) the relationship be- tween dynamic Young's modulus and frequency appears to be inde- pendent of water content and temperature. At a low strain am- plitude (3.l6 x l0—3%) the rate of increase of dynamic Young's modulus with frequency is somewhat greater at -4°C than at -l and -l0°C. Water content - the dynamic Young's modulus increases by a moderate amount as the water content increases at a high tem- perature (-l°C); this relationship does not appear to be af- fected by frequency. At lower temperatures (-4 and -lO°C) there appears to be little or no significant influence of water con- tent on dynamic Young's modulus at a high strain amplitude (3.l6 x l0'2%). At a lower strain amplitude (3.l6 x l0'3%) the relationship between dynamic Young's modulus and water content is not clear. In the case of Hanover silt, dynamic Young's modulus decreases by a small amount as the water content in- creases at both -4 and -l0°C; in the case of Alaska silt, 148 (e) (3) dynamic Young's modulus appears to increase by a small amount at -4°C and decrease by a small amount at -lO°C as the water con- tent increases. Confining pressure - the dynamic Young's modulus does not appear to be influenced by confining pressure under any test conditions. The influence of the various parameters on the damping ratio of frozen silt in the order of their importance is as follows: (a) Strain amplitude - in general, the damping ratio increases as strain amplitude increases. At a high temperature (-l°C) the rate of increase is moderate at low frequencies and somewhat greater at higher frequencies for low water contents; for higher water contents the rate of increase is moderate at all frequen- cies. At lower temperatures (-4 and -l0°C) damping increases significantly with increasing strain amplitude at low frequencies. At high frequencies the damping ratio increases by a smaller amount and in some cases decreases by a small amount with in- creasing strain amplitude; in some instances the relationship becomes U-shaped, with a slight decrease in damping followed by an increase with increasing strain amplitude. Temperature - damping ratio generally decreases with decreasing temperature. The influence of temperature on damping ratio ap- pears to be more significant at low water contents than at high water contents. At a low strain amplitude (3.l6 x 10'3%) at low water contents the rate of decrease of damping ratio is generally greater in the high temperature range (-l to -4°C) than in the low temperature range (-4 to -lOOC); at high water contents the rate of decrease appears to be more uniform over the entire temperature 149 (C) range (-l to -l0°C). At a high strain amplitude (3.l6 x l0'2%) the rate of decrease in damping ratio with decreasing temper- ature is generally somewhat less than at a low strain ampli- tude (3.16 x lO'3%). In many cases, there appears to be either little change or a slight increase in damping ratio from -l to ‘ -4°C followed by a gradual decrease from -4 to -lO°C. F: Frequency - damping ratio generally decreases with increasing I frequency. At a high strain amplitude (3.l6 x l0-2%) at all temperatures and at a lower strain amplitude (3.l6 x lO'3%) at a high temperature (-l0C) the damping ratio generally decreases by a smaller amount in the frequency range 0.05 to 5.0 cps than in the frequency range 5.0 to l0.0 cps. At a low strain ampli- tude (3.l6 x l0'3%) at a temperature of -4°C, the damping ratio decreases with increasing frequency at a rate somewhat more uniform than at -l°C. At a low temperature (-l00C) at a low strain amplitude (3.16 x lO-3%) the damping ratio generally decreases by a small amount with increasing frequency at low frequencies (0.05 to 5.0 cps) and increases with increasing frequency at higher frequencies (5.0 to 10.0 cps). Water content - damping ratio decreases significantly with in- creasing water content at a high temperature (-l°C); the rela- tionship does not seem to be significantly affected by strain amplitude. It appears that at low frequencies most of the de- crease in damping ratio occurs in the high water content range while at high frequencies the rate of decrease is more uniform over the entire range of water contents. At lower temperatures (-4 and -lO°C) there appears to be no significant influence of I 150 (e) water content on damping ratio at a low strain amplitude (3.l6 x l0'3%). At a high strain amplitude (3.16 x l0-2%) the damping ratio decreases with increasing water content; the relationship appears to be dependent on frequency, with a slight decrease occurring at low frequencies and a more significant decrease at higher frequencies. Confining pressure - damping ratio is not influenced by con- fining pressure at low temperatures (-4 and -l0°C). At a high temperature (—l°C) and a low strain amplitude (3.16 x l0-3%) damping ratio decreases with increasing confining pressure at low frequencies and is not significantly affected by confining pressure at higher frequencies. At a high strain amplitude (3.l6 x l0'2%) damping ratio decreases slightly with increasing confining pressure at low frequencies and is unaffected by con- fining pressure at higher frequencies. In general, the rate of decrease of damping ratio is greater at low confining pres— sures (O to 50 psi) than at high confining pressures (50 to 200 psi). Confining pressure appears to have a more signifi- cant influence on damping ratio at low water contents than at high water contents. (4) Values of dynamic Young's modulus obtained for kaolinite for ranged from 1 x l0 the range of test strain amplitudes (approximately 2 x l0”3 to 8 x l0-2%), frequencies (0.05 to l0.0 cps), temperatures (-l to -l0°C), confining [wessures (0 to 200 psi), and sample water contents (28.l and 71.3%) 5 to l4.5 x l05 psi. Values of damping ratio ranged from .01 to .22. 15) l'.‘ (5) The influence of the various parameters on the dynamic Young's modulus of frozen clay in the order of their importance is as follows: (a) (C) Strain amplitude - the dynamic Young's modulus decreases with increasing axial strain amplitude. At a high temperature (-l°C) the rate of decrease is fairly uniform over the range of strain amplitudes while at a low temperature (-l00C) the rate of de- crease increases significantly with increasing strain amplitude. The relationship at -4°C is intermediate between those at -l and -lO°C. The relationship between dynamic Young's modulus and strain amplitude does not appear to be affected by fre- quency or water content. Temperature - dynamic Young's modulus increases significantly with decreasing temperature. The rate of increase is generally more uniform over the entire temperature range (-l to -l0°C) at a high strain amplitude (3.l6 x 10-2%) and a low water content. At a low strain amplitude (3.l6 x lO-3%) the rate of increase is somewhat greater in the high temperature range (-l to -4°C) than in the low temperature range (-4 to -l0°C). The relation- ship does not appear to be influenced by frequency. Frequency - in general, dynamic Young's modulus increases with increasing frequency. The rate of increase is somewhat greater in the frequency range 5.0 to 10.0 cps than in the frequency range 0.05 to 5.0 cps. The relationship does not appear to be influenced by temperature, strain amplitude, or water content. Water content - at higher temperatures (-l and -4°C) dynamic Young's modulus increases by a small amount with increasing 152 rF= wannicontent. The relationship is not influenced by frequen- cytn'strain amplitude. At a low temperature (-l0°C) dynamic Yowufs modulus appears to decrease slightly with increasing hatercnntent at a low strain amplitude (3.16 x 10-3%) and is notsfignificantly influenced by water content at a high strain amplitude (3.16 x 10’2%). (e) Confhfing pressure - dynamic Young's modulus does not appear to be influenced by confining pressure under any test conditions. (6) The influence of the various parameters on the damping ratio of frozen clay in the order of their importance is as follows: (a) Strain amplitude - damping ratio generally increases with in- creasing strain amplitude. In most instances the rate of in- crease is greater at higher strain amplitudes than at lower strain amplitudes. The influence of strain amplitude on damping ratio is greater at lower frequencies than at higher frequencies; at the highest frequency (10.0 cps) there is an initial decrease in damping ratio at low strain amplitudes fol- lowed by an increase at high strain amplitudes. The relation- ship between damping ratio and strain amplitude does not appear to be significantly influenced by water content or temperature. (b) Temperature - in general damping ratio decreases slightly with decreasing temperature. In most instances the decrease appears to tuarnore pronounced at lower frequencies than at higher fre— quencies. At the highest frequency (10.0 cps) the relationship deviates somewhat as damping ratio tends to increase by a small amount with decreasing temperature. In general, the rate of change in damping ratio is somewhat greater in the high 153 (d) temperature range (4 to -4°C) than in the low temperature range (-4 to 40°C) at a high water content (71.3%). At a low water content (28.l%) the rate of change is somewhat more uniform over the entire range of temperatures. The influence of strain amplitude on the relationship between damping ratio and temperature is not clear. F” Frequency - at a low strain amplitude (3.16 x 10-3%) damping ratio decreases by a small amount with increasing frequency to a minimum value at approximately 5.0 cps and then increases The relationship at a low & sharply between 5.0 and l0.0 cps. strain amplitude is not influenced significantly by water con- tent or temperature. At a high strain amplitude (3.16 x 10—2%) damping ratio decreases with increasing frequency over the en- tire range of frequencies. At higher temperatures (—1 and -4°C) the rate of decrease is fairly uniform from 0.05 to 5.0 cps and significantly greater from 5.0 to 10.0 cps. At a lower temper- ature (40°C) the rate of decrease is somewhat more uniform over the entire range of frequencies. The relationship at a high strain amplitude does not appear to be influenced signi- ficantly by water content. Water content - in general, it appears that water content has at most only a slight influence on damping ratio over the range of water contents considered. At. a high temperature (4°C) and a low strain amplitude (3.l6 x 10-3%) damping ratio increases by a small amount with increasing water content. The change is most significant at lower frequencies and becomes negligible at higher frequencies. At a high strain amplitude (3.l6 x l0'2%) ‘154 (e) damping ratio increases by a slight amount with increasing water content at the lowest frequency (0.05 cps) and decreases by a slight amount at higher frequencies. At lower temperatures (-4 and -lO°C) the relationship between damping ratio and water content and the influence of frequency and strain amplitude on the relationship are not entirely clear; it appears that, in ”5' general, water content has a slight to negligible influence on ’ damping ratio. Confining pressure - damping ratio is not influenced by confin- ing pressure at low temperatures (-4 and -l0°C). At a high tem- ; perature (-l0C) and a low strain amplitude (3.l6 x 10-3%) damp— ing ratio decreases with increasing confining pressure at the lowest frequency (0.05 cps). The rate of decrease is greater in the low confining pressure range (0 to 50 psi) than in the high confining pressure range (50 to 200 psi). At frequencies greater than 0.05 cps and at higher strain amplitudes (3.16 x 10'2%) confining pressure does not have a significant influence on damping ratio. The relationship is not influenced by water content. A comparison of the dynamic properties of frozen silt and clay obtained in the present study with those obtained in previous studies may be summarized as follows: (1) The values of longitudinal and compression wave velocities of frozen silt obtained in the present study are somewhat lower than those obtained in previous studies. This may be due to the much lower frequencies and higher strain amplitudes associated with the present study than with previous studies. Differences in the types of silts 155 used in the several studies may also contribute somewhat to the varia- tion in values of wave velocity. . (2) The values of damping ratio of frozen silt obtained in the present study are somewhat higher than those obtained in a previous study. This may be due to the much lower frequencies and higher strain amplitudes associated with the present study than with the previous study. (3) The values of longitudinal and compression wave velocities of frozen clay obtained in the present study generally compare favorably with those obtained in previous studies. The variation in wave veloc- ity from the different studies may be due to the much lower frequen- cies associated with the present study than with previous studies. In addition, it appears that differences in the types of clays tested have a significant influence on the wave velocities obtained in the several studies. (4) The values of damping ratio of frozen clay obtained in the present study compare favorably with those obtained in previous studies. The variation in damping ratio between the present study and the study by Stevens (1973) may be due to the much lower frequencies associated with the present study. 156 APPENDIX A CYCLIC TRIAXIAL TEST RESULTS - DYNAMIC YOUNG'S MODULUS OF FROZEN SILT mQHIHHLHwIIZEL mQNZIHHLHmIIEaI 2.55 xx .zummm moo zEEm xc .235 on: #6 8m; 8;- 8. T 8.? 8.? of? F5 8w... 8.7 8.7 8.? 8.? 8...”- q _ _ _ _ L _ o _ _ . _ _ _ S 0 LI. 11.1. L IL .7 Id ’ Id « L I .I. I 9 9 1w 3 L o 3 + o + 1 0 1 0 1 u n: 1 ...a. 9 .0 m. l .1 l 0 3 L 0 . 3 1 u N L m. 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L .0 7.. .6 0 ... +- o 240 APPENDIX D CYCLIC TRIAXIAL TEST RESULTS - DAMPING RATIO OF FROZEN CLAY L I!!- ..‘_.._-.-., « .. m...ZLH>¢-.0Lv.8-88: m0.L.LF>¢-.0Lz..88: 2:.me x0 820008. 00.. 2:8me .2. 820008. 00.. ..8 888. - 88. .- 88..- 88. 8- 88. 8- 88.8- L. 8 888.- 88. .- 88..- 88. 8- 88.8- ..8- . . . . . . . .0 . . . . . . 0 L .U L G U U .- N .. H .l m Id I. m d M no .... ud L z H. J m U I. I. I I L .- 0 r 0 w. L w. I. W l W d L W. 1 W8 . .88 888 4 . L m .88 88 a L n .88 8 4 0 . 88888888 82.2.8288 . l M I. 8 8.2.88 8. 0 . u 8..88..28.288 88.82 8.2.88 8. 88888888. 82.2.8288 ..8 .... 2.8-28.288 88.2.. .... 8-.. ..-. 88.8288 0 8-.. .3. 88.8.8.8 L .0. ..8 .8 o . 242 88.-..8.8-8...: ...-..8.8-8...8 2.0080 x0 pzummm 00. z.¢mpw xq 820mmm 00. _.o oom.u oo..u om..L oo.NL om.ul oomnl LIL»: oom.u co._L om..u OO.NI om.ul ocean q _ _ . d . _IL _ _ _ _ q - — r-0 [.0 30'3000'7 01168 dNUU 20'3000'7 l l L l l 083 0’3 003' 09! OZ! I L l l l 003 0'3 003 091 031' 01188 dHUU 028' 8.2.88 8. L 8.2.88 8. 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L m o 0 0 o ..- L 8,. l r ’ 0 0 7w 7v 1 8 I. a 0 0 8p. m. 8:882 88 L M 85888 88 L8 m 88.—7:88:88 88:88 88.88.288.88 88:88 888888888 888888888 888 .... 888888888 888888888 888 .... 1.88 .3. 8888828 L M 1-88 .88. 88.8858 L m .8 .- .- W 8 256 LIST OF REFERENCES l0. ll. l2. l3. LIST OF REFERENCES Baladi, 6., personal communication, class notes, Purdue University, T975. Barnes, D. F., "Geophysical Methods for Delineating Permafrost," Proceedings of the Permafrost International Conference, National Academy of Sciences, National Research Council Publication No. 1287, l963, PP. 349-355. Bell, R. A. I., "A Seismic Reconnaissance of the McMurdo Sound Region, Antarctica," Journal of Glaciology. Vol. 6, No. 44, 1966, PP. 209-22l.. Black, R. F., "Eolian deposits of Alaska," Arctic 4, l95l, pp. 89-lll. Black, R. F., "Gubic Formation of Quaternary Age in Northern Alaska," U.S. Geol. Surv. Prof. Paper 302-C, l964, pp. 59-91. Black, R. 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