ABSTRACT TIME DEPENDENT STRENGTH BEHAVIOR OF TWO SOIL TYPES AT LOWERED TEMPERATURES by Ilham AlNouri This study is concerned with the time-dependent deformation behavior of two frozen soils, under a specified stress-history and a range of temperatures, and the feasi- bility of develoPing time-dependent strength parameters for frozen soils. Part of the behavior study was to observe the creep deformation in the steady state region, and to determine the effect of temperature, stress difference, mean normal stress, and soil type on the creep rate of frozen soil. Two soil types were used; Sault Ste. Marie clay and standard Ottawa sand. The cylindrical samples were one square inch in cross section and 2.26 inches high. The clay was premixed to the desired water content and compressed to the desired density, then trimmed to the Specified sample size, while the sand samples were cast in an aluminum mold. The samples were tested in a triaxial cell submerged in low-temperature bath, with the temperature controlled to within ip.05 degrees Centigrade. Two types of test were conducted on both soil types. The first type Ilham AlNouri was a differential creep test in which the axial stress difference was maintained constant and the confining pres- sure was increased in increments. The differential creep tests were conducted at several values of constant axial loading on duplicate samples, and at several test temper- atures. The creep deformations were recorded continuously during the test. The second type of test conducted was a constant axial strain-rate test performed on duplicate samples of frozen Sault Ste. Marie clay and frozen satura- ted sand at relatively fast strain-rates and at -12° C. The results of the differential creep tests on frozen Sault Ste. Marie clay and frozen saturated sand indicate that the creep rate of frozen soil at a constant test temperature increases exponentially with increase in axial stress difference, and decreases exponentially with the increase in mean stress. This indicates that the mean stress does affect the creep rate of frozen soil. Accord- ing to the results of the differential creep tests, two equations.describing the steady state creep deformation. were developed; the first determines the effect of stress on creep rate of frozen soil at constant temperature, and the second equation determines the effect of temperature on creep rate under constant stress difference. A third equation has been suggested, to estimate the creep rate of frozen soil under the effect of both temperature and stress. Ilham AlNouri To provide more information on the time-dependent strength behavior of frozen soil, differential creep test results were used to develop time-dependent strength param- eter; a cohesion C, and an angle of friction ¢. For a specific creep rate, we can determine the values of major and minor principal stress 01 and 03, for each test, and then use these values to sketch a modified Mohr plot which shows the values of C and ¢ that correspond to that speci- fic creep rate. The cohesion C decreases with a slower creep rate, implying the dependence of C on time, while the friction angle ¢ appears to remain constant with change in creep rate. The constant axial strain-rate tests were used to determine the strength parameters of frozen soils at a relatively high strain-rate, and to determine the effect. of confining pressure on the ultimate strength of the two soil types. The confining pressure has no significant effect on the ultimate strength of frozen clay, while the ultimate strength of frozen saturated sand does increase with increase in confining pressure, therefore implying the development of friction during deformation of frozen saturated sand. TIME DEPENDENT STRENGTH BEHAVIOR OF TWO SOIL TYPES AT LOWERED TEMPERATURES BY Ilham AlNouri A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Civil Engineering January 1969 ACKNOWLEDGMENTS The writer is deeply indebted to his major profes- sor, Dr. 0. B. Andersland, Professor of Civil Engineering, for his continuous encouragement and assistance, and greatly appreciates the time he devoted most generously to discussions and consultations. The writer also wishes to express his gratitude to Dr. L. E. Malvern, Professor of Applied Mechanics, for his many helpful comments and sug- gestions. Thanks are also due the other members of the writer's doctoral committee: Dr. C. E. Cutts, Chairman and Professor of Civil Engineering; Dr. R. K. Wen, Profes- sor of Civil Engineering, and Dr. D. W. Hall, Professor of Mathematics. The writer wishes to express his appreciation to Dr. R. R. Goughnour, Associate Professor of Civil En- gineering, for his assistance and consultations concerning the testing equipment. Thanks are also due the National Science Founda— tion and the Division of Engineering Research at Michigan State University for the financial assistance that made this study possible. ii TABLE OF CONTENTS Page ACKNOWLEDGMENTS I O O O O O O O O O O O O I O O O O O i i LIST OF FIGURES O O O O O O O O O O O O O O O O O O 0 iv LIST OF TABLES O O O O O O O O O O O O O O I O O I C Vi NOTAT IONS o o o o o o o o o o o o o o o o o o o o o 0 Vi i CHAPTER I 0 INTRODUCTION 0 O O O O O O O O O O O O O O O O 1 II C LITEMTURE REVIEW 0 O O O O O O O O O O O I O 5 1. Frozen Soil Structure . . . . . . . . . 5 2. Strength of Frozen Soils. . . . . . . . 6 3. Rheological PrOperties of Frozen Soils. 12 4. Rate Process Theory and Frozen Soil Behavior. . . . . . . . . . . . . . . 15 III. SOILS STUDIED AND SAMPLE PREPARATION. . . . . l9 1. Frozen Clay Samples . . . . . . . . . . 19 2 o sand-Ice samples 0 o o o o o o o o o o o 2 3 IV. EQUIPMENT AND TEST PROCEDURES . . . . . . . . 27 1 0 Equipment 0 O O O O O O O O I O O O O I 2 7 2. Differential Creep Tests. . . . . . . . 31 3. Constant Axial Strain-Rate Test . . . . 33 V. EXPERIMENTAL RESULTS. . . . . . . . . . . . . 34 1. Differential Creep Tests. . . . . . . . 34 2. Constant Strain-Rate Tests. . . . . . . 37 VI. DISCUSSION AND PRESENTATION OF THEORY . . . . 54 VII. SUMMARY OF CONCLUSIONS. . . . . . . . . . . . 78 BIBLIOGRAPHY O O O O O O I O O O O O O O O O O I O O 8 1 APPENDIX- DATA 0 o o o o o o o o o o o o o o o o o o o 8 3 iii Figure 2-1 LIST OF FIGURES Relation Between Shear Strength of Frozen Soil and Temperature. 0 o o o 0 0'. o o o o o o o 0 Peak Strength Versus Percent Sand by Volume. . Creep Curves for Frozen Soils. . . . . . . . . Representation of Energy Barrier Separating Equilibrium Positions. . . . . . ._. . . . . . A Schematic Diagram of the Sample Placement in the Triaxial Cell . . . . . . . . . . . . . Diagramatic Layout of the Testing Apparatus. . Differential Creep Test on Sault Ste. Marie Clay, D Equal to 714.7 Psi . . . . . . . . . . Differential Creep Test on Sault Ste. Marie Clay, D Equal to 677.9 Psi . . . . . . . . . . Strain ~ Time Relations During Increase and Decrease of Confining Pressure . . . . . . . . Differential Creep Test on Sand-Ice Sample, D Equal to 76403 PSi o o o o o o 0'. o o I o o 0 Differential Creep Test on Sand-Ice Sample, D Equal to 81509 PSi o o o o o o o 0‘. o o 040 0 Differential Creep Test on Sand- -Ice Sample, D1 Equal to 764.3 Psi and D2 Equal to 815. 9 Psi . Differential Creep Test on Sand-Ice Samples, (A) @ T = -lO°C, (b) @ T = -18.1°C . . . . . . Stress ~ Strain and Strain ~ Time Curves for Sault Ste. Marie Clay, 03 Equal to 30 Psi. . . Stress ~ Strain and Strain ~ Time Curves for Sault Ste. Marie Clay, 03 Equal to 60 Psi. . . iv Page. 10 ll 12 15 28 30 43 44 45 46 47 48 49 50 50 6-9 6-10 Stress ~ Strain and Strain ~ Time Curves for Sault Ste. Marie Clay, 03 Equal to 90 Psi. . . Mohr ~ Coulomb Plot and Modified Plot for Sault Ste. Marie Clay Samples. . . . . . . . . Stress ~ Strain Curves for Sand-Ice Samples, (A) 0 Equal to 30 Psi, (B) 03 Equal to 60 P81, iC) 03 Equal 1:0 90 PSio o o o I o .0 o o o Mohr ~ Coulomb Plot and Modified Plot for sand-Ice samples 0 o o o o o o o I o o o o o o Creep Rate Versus Stress for Sault Ste. Marie Clay 0 O O O I O O O O O O O I O O O O I O O O Creep Rate Versus Stress for Sand-Ice Samples. b Value Versus Stress Difference for Sault Ste. maria Clay. 0 O O I O O O O O I O O I O O b Value Versus Stress Difference for Sand-Ice samples I O O O O O O O O O O O O I O O O O I 0 Typical Creep Rate ~ Stress Curves for Sand- Ice Samples Compared with Sault Ste. Marie Clay Samples . . . . . . . . . . . . . . . . . Measured and Estimated Creep Rates for Sand- Ice Material . . . . . . . . . . . . . . . . . Dependence of Creep Rate on Stress and Temper- ature of Saturated Frozen Sand . . . . . . . . Temperature Dependence of b2 in Equation (6-10) 0 o o o o o o o o o o o o o o o o o o o Time-Dependent Strength Behavior of Frozen Sault Ste. Marie Clay. . . . . . . . . . . . . Time-Dependent Strength Behavior of Frozen Saturated Ottawa Sand. . . . . . . . . . . . . Page 51 51 52 53 70 71 72 72 73 74 75 75 76 77 Table 3-1 5-111 LIST OF TABLES Page Physical and Mineralogical Properties of the Sault Ste. Marie Clay. . . . . . . . . . . . . 20 Differential Creep Test Results on Sault Ste. Marie Clay 0 O I I O O O O O I O I O O O O O O 40 Differential Creep Test Results on Sand-Ice samples 0 O O O O O O O O O O O O O O O O C O O 41 Stress, Temperature, and Creep Rate Test Results on Sand-Ice Samples. . . . . . . . . . 42 vi NOTATIONS C = cohesion D = 01 - 03 = axial stress difference f = shear force acting on a flow unit AF = free energy of activation, cal. per mole Plank's constant = 6.624 x 10"7 erg-sec”l :3” ll Boltzmann's constant = 1.38 x 10"16 erg °K’1 W ll 6, m, n = creep parameters R = universal gas constant = 1.98 cal°K"l mole-1 T = temperature in degrees Centigrade or absolute temperature t = time Y = frequency of activation, sec"l x = parameter relating activation frequency to strain rate ¢ = angle of internal friction X = distance between equilibrium positions of flow units Yd = dry density w = water content, percent a = true axial strain E = %% = true axial strain-rate, or creep rate in the steady state creep region vii MI 0I major principal stress minor principal stress, or confining pressure 01 - om = deviatoric stress % (01 + 02 + C3) = hydrostatic stress or mean normal stress equivalent strain or intensity of shear strain equivalent stress or intensity of shear stress viii CHAPTER I INTRODUCTION Soils in general are considered as a three phase material; solid particles, water, and gas. With decrease in temperature below freezing, the water will partially or almost completely change to ice, with the unfrozen water content dependent on the temperature and certain soil prop- erties. Now the soil becomes a complex four phase system, in which the four components are interrelated. The phase change of water is accompanied by an increase in adhesion between the soil particles, liquid water, and ice together with drastic changes in the physical and mechanical prop- erties of the soil. Shear strength of frozen soil depends on several factors including soil type, homogeneity, water content including ice content, temperature, mode of freezing, nor— mal stress, and deformation rates. The most significant factor determining the strength properties of a frozen soil is the temperature below freezing. The ultimate compressive strength increases drastically with decrease in temperature. Frozen soils, in general, exhibit a high value of instantaneous resistance to deformation. However, tests show that if the load is applied for a long time, the resistance of frozen soils to external forces decreases considerably. The influence of time of load on the strength of frozen soils is evident by comparing them with unfrozen soils; the strength of frozen soils is lowered with time to a much greater degree. Thawed soils, for all practical purposes, display no loss of strength with time. Neverthe- less, frozen soils under the continuous action of a load have a strength several times greater than that of unfrozen soils of the same type. Frozen and unfrozen soils commonly fail by shear under the influence of concentrated loads. The shear strength of unfrozen soil can be described, using the Mohr- Coulomb failure theory, by two parameters: an angle of internal friction ¢ and cohesion C. However, tests show that the shear strength of frozen soils is time-dependent. Thus, the need arises to develop time-dependent strength parameters. One phase of this study is concerned with the study of such parameters for two soil types, a cohesive soil (Sault Ste. Marie clay) and a cohesionless soil (Ottawa sand). The second phase of this study is concerned with an effort to describe and determine the deformation behav- ior of these soils for a specified stress history and range of temperature. In general, frozen soil behavior is approx- imated by anmelasto-plasto-viscousbody, since all the de- formations inherent in such bodies may develop, depending upon the stress and its time factor.’ Since design problems are concerned with a long term behavior, one must consider the range of stresses that cause undamped creep. Thus,. design problems are concerned mainly with a plasto-viscous type behavior (steady state creep). The presence of ice and unfrozen water constitute the viscous element in the material and are responsible for the development of rheol- ogical processes. Existing creep theories do not take the influence of the mean stress on deformation behavior into considera- tion (Vialov, 1965a). Since the equivalent strain E, in frozen and unfrozen soils, is not only a function of the equivalent stress 3, but also of the mean stress cm, the effect of the mean stress on the creep rate of the frozen soil has been included in this study in an effort to pro- vide more information on the time-dependent.behavior of frozen soil. Differential triaxial creep tests were plan- ned and conducted on frozen saturated Sault Ste. Marie clay and frozen saturated Ottawa sand. For a given test, the axial loading was maintained constant and the confining pressure was increased in increments, implying that in.a triaxial type apparatus, the deviatoric stress is held. constant while the mean stress is increased or decreased by increments. The creep rate was observed at several stress levels, under different axial loadings. The effect of temperature on deformation rates was observed by conducting differential creep tests at several test temper- atures under similar stress conditions. To minimize the effect of soil properties such as density, water content, and soil type, the tests were conducted on duplicate sam- ples of both soil types. The experimental results indicate that creep rates and time-dependent strength parameters can be predicted with a reasonable degree of accuracy once cer- tain soil parameters have been evaluated. CHAPTER II LITERATURE REVIEW 1. Frozen Soil Structure "Frozen Soil" is a term applied to those soils in which below freezing temperatures exist and in which at least a part of the water contained in the soil pores is frozen. The ice matrix formed serves to cement the soil particles into a much more coherent mass (Tsytovich, 1960). Frozen soil is a complex four phase system consisting of four interrelated component materials: solid mineral par— ticles and ice, liquid water, and air or gas. The physico-mechanical processes present in freez- ing soils produce pr0perties and structure of frozen soils which are quite different from those of unfrozen soils. A partial or almost complete change of water into ice, which occurs in freezing soils, is accompanied by the appearance of new ice cementation bonds between the mineral particles of the soil, and by sharp changes in the physical and mechanical properties of the soil. During the further cooling of frozen soils, especially in zones of intensive phase changes of water in the frozen soils, there occurs continuously the redistribution of moisture and the movement of water toward the line of cooling and freezing, and the subsequent freezing of water drawn up to the frost line. Change in the temperature of frozen soil changes the phase composition of water in frozen soil, which in turn controls the degree of cementation of particles by ice. However, at any temperature below freezing there always remain a certain amount of unfrozen water (Tsyto- vich, 1960). Since the cementation bond in frozen soil is a function of the ice content, it is necessary to deter- mine the amount of unfrozen water at any temperature, which can be estimated with a reasonable accuracy, on the basis of certain measurable soil properties (Dillon and Anders- 1and, 1966).' 2. Strength of Frozen Soils Under the influence of concentrated loads both frozen and thawed soils commonly fail by shear. According to the Mohr-Coulomb failure theory, the shear strength S along any place is a function of normal stress 0 on that plane, or S = C + 0 tan ¢ (2-1) wherein C is the intercept on the shearing stress axis and ¢ is the angle of internal friction. The quantities C and ¢ are material properties which are dependent on soil temperature, soil type, soil density, and time of loading. For cohesionless soils the failure envelope normally passes through the origin (C = 0). When moist or saturated soil is exposed to freezing temperatures, the free water contained in the voids freezes, whereupon the ice interconnects the soil particles and the shear strength increases at zero normal stress (increase in C value). The cohesion in thawed soils is some function of the molecular attraction betWeen solid particles, which may be separated by water films, the amount of such particle separation, and the specific area of the soil particles. These forces increase with reduction in particle spacing (greater density). In frozen soils, the mineral particles and ice grains are generally separated by a thin film of unfrozen water, and the forces between soil particles and ice are greatly increased with reduction in temperature. Some Russian scientists consider this increased cohesion analogous to "cementation." Cohesion in frozen soils is not constant (Vialov, 1965b), but varies with change in ice content and time; it also depends on the structural changes in the ice contained in the soil. Polycrystalline ice will deform with time under very small stresses (Dil- lon and Andersland, 1967). This type of cohesion, in fro- zen soils, is the least stable part of cohesion, since it changes with any variation of the temperature field. For a given pressure and temperature, a state of thermodynamic equilibrium exists between the ice and un- frozen water in frozen soil (Vialov, 1965¢9. A load applied to the soil disturbs the equilibrium condition, and may cause partial melting of ice. Under the influence of an increasing stress gradient, the water film may be dis- placed from a region of greater stress to one of smaller stress, where it again freezes. Plastic flow of the ice occurs at the same time. The flow of ice and the moisture shift is usually accompanied by: breaking up of the structural bonds, displacement of solid particles, and reorientation of the ice crystals. As this process con- tinues, it leads to the growth of creep deformation and to the reduction of the strength of the soil as well. At the same time, the processes cause regrouping of the par- ticles, recrystallization of the ice, and re-establishment of bonds. The instantaneous resistance of frozen soils is generally large. However, under the continued effect of a constant load, frozen soils yield under pressures which are many times smaller. This peculiarity of frozen soils is governed mainly by the plastic prOperties of ice con- tained in the soil voids and the molecular bonds between ice and the mineral particles. Constant stress-rate tests conducted by Tsytovich (1960) on different types of frozen soils showed that ultimate strength is proportional to the decrease in tem- perature, and that the frozen sands were characterized by a much higher value of ultimate compressive strength as compared to that of frozen clay. However, the resistance of frozen soils to external forces decreased considerably when the loads were applied for a long time, due to the relaxation of the ice-cementation cohesion. Frozen.soils fail under much smaller loads when the loading is of long duration. The strength of any material is described by its shear strength. Shear strength of frozen soils is a func- tion of at least three variables: where T is the temperature of soil below freezing, P is normal pressure, and T is the time of action of the load. Tsytovich (1960) considered frozen soils as analogous to over-consolidated soils, therefore assuming a propor- tionality between shear strength and normal pressure in the form: = _ x T CT + P tan ¢T . (2 3, where CT is cohesion, ¢T is the angle of internal friction at temperature T. At a temperature of 0°C, the angle of internal friction ¢ is practically equal to the angle of internal friction of unfrozen soil, but the cohesion of 10 frozen soil is much higher (see Figure 2—1). As an approx- imation, this made it possible to neglect the internal friction in evaluating the shear strength of frozen soils. Tsytovich (1960) suggested a ball penetration test for effective determination of the cohesive force. 4 '- "'—'_\-' _'-'-— N ________ T _— -10 E IN 0 E \ U U" \ M O‘ M N 0 N (\ o In II II 0 U ._ _ _ __ _. = o r d.) T‘b = 40 T +20 0 1‘ 0 P, kg/cm2 Figure 2-1. Relation Between Shear Strength of Frozen Soil and Temperature. (After Tsytovich, 1960). 11 Constant strain-rate tests conducted on frozen sand-ice samples (Goughnour and Andersland, 1968), showed that the ultimate shear strength of sand-ice material in- creased with the increase in strain-rate and with the de- crease in temperature, and that the ultimate strength in- creased sharply with the increase in the volume concentra- tion of sand in the sand-ice samples. For a sand concen- tration above 42%, it appears that particles contact is established. The relation between Peak strength and strain- rate, temperature, and sand volume concentration is shown in Figure 2-2. 1000 — T = -12.03° _ e = 2.66x10m4min-l 800 T=12.03° '8 8=1.33x10-4min-1 “ 600 .5 4.) 01 C: 8 .p 400 U) .34 8 r T=-3.85° “ ° -4 . -1 200 L €=2.66x10 mln L. O l l I I l I 0 10 20 30 40 so 60 Figure 2-2. Peak Strength Versus Percent Sand By Volume. (After Goughnour, 1967). 12 3. Rheological Properties 0 Frozen “oiIs Creep is defined as the time-dependent deformation of materials which occurs under constant stress and temper— ature. Frozen soils exhibit such a.behavior, a deformation increase with time, under.a constant uniaxial stress (Via- lov, 1965a). Figure 2-3a shows typical creep curves, which represent the relationship between strain 6, and time t. Each curve corresponds to a given constant axial stress 0. The magnitude of stress determines the nature of the creep curve. If the stress does not exceed a certain limit, which is usually defined as a limiting long-term strength, then the deformation is damped (damped creep); if the stress does exceed the above mentioned limit, then undamped creep develops, leading eventually to failure. (a) O6 O5 O4 0) 03 .fi 02 a 06>05>---01 u /' - 01 m , Time t (b) D “" l s l -a m "H I “ I m l I l 3‘ 1 | Time t Figure 203a. Creep Curves for Frozen Soils. (After Via- lov, 1965a). 13 In general, creep curves for frozen soils corre- spond to classical creep curves, and could be divided into four stages (see Figure 2-3b). l. Instantaneous Strain: represents the strain which occurs upon application of the load. This deformation may be either elastic or elasto-plastic, depending upon the value of such load. Upon removal of the load, this deforma- tion will be completely recovered in the elastic case, and partially recovered in the elasto-plastic case. This de- formation is represented by sectioncrdxof the creep curve. 2. Primary or Transient Creep: represents the stage of deformation which grows at a decreasing rate. For a damped deformation process, the rate of deformation will continuously decrease until it approaches zero. For un- damped deformation, the creep rate will continue to de- crease until it reaches a minimum value (depending upon the value of stress). This stage is represented by A-B section of the creep curve. 3. Secondary or Steady-State Creep: represents the region of relatively constant creep rate. This stage is represented by B-C section of the creep curve. 4. Tertiary Creep: represents the final stage of the creep curve, in which the deformation grows at an increas— ing rate (progressive flow), and leading eventually to failure. This stage is represented by C-D section of the creep curve . 14 It is evident that the creep curve in itself does not identify the detailed mechanisms which operate during the deformation. However, this identity of creep curves indicates that they all undergo a similar sequence of rate- determining changes. During creep one can consider that two types of processes Operate (Conrad, 1961): One increases resistance to flow (strain harding), the other decreases the resistance (recovery). If hardening predominates, the creep rate continually decreases (primary creep); a balance between hardening and recovery yields a constant creep rate (steady-state creep). Tertiary creep occurs if recovery is faster than hardening. It is now generally accepted that creep is a thermally activated process. From a physical standpoint, this seems to be the most reasonable explanation for the increase in strain with time under the conditions of con- stant stress and temperature. It has been shown, for frozen soils, that a plot of the logarithm of creep rate versus the reciprocal of temperature yields a straight line, in accord with theories of thermally activated pro— cesses (Andersland and Akili, 1967). With this background, rate process theory must be considered in formulating any expression for prediction of frozen soil behavior. 15 4. Rate Process Theory and Frozen Soil Behavior The rate process theory (Glasstone, Laidler, and Eyring, 1941) can be applied to any process involving the time-dependent rearrangement of matter, so it could be used to describe and predict soil behavior such as creep or consolidation (Mitchell, Campanella, and Singh, 1968). The basis of the theory is that the atoms and molecules participating in a deformation process (termed flow units) are constrained from movement relative to each other by energy barriers separating adjacent equilibrium positions. This is shown schematically by curve A in Figure 2-4. Shear Force ‘ Curve A Energy Displacement -—————> Figure 2-4. Representation of Energy Barrier Separating Equilibrium Positions. 16 The displacement of flow units to new positions requires that they become activated through aquisition of suffi- cient activation energy, AF, to overcome the energy bar- rier. From statistical mechanics, it is known that the flow units are continuously vibrating with a frequency of kT/h, as a consequence of their thermal energy, where 16 1), k = Boltzman's constant (1.38 x 10- erg - °K- 2 h Planck's constant (6.624 X 10- erg - sec—1), and T = the absolute temperature, °K. The division of thermal energies among the-flow units is given by a Boltzmann distribution, and the specific frequency of activation, v, may be shown to be (2-4) v = Eh: e-AF/RT in which R = Universal Gas Constant = 1.98 cal° K.l mol-l. If a shear stress is applied to the material, the barrier heights become-distorted. This is shown by curve B in Figure 2—4. The distance, 1, represents the distance between successive equilibrium positions. If f represents the-force acting on a flow unit, then the barrier height is reduced by fA/Z in the direction of the force and raised by the same amount in the opposite direction. The elastic distortion of the material causes the minimums of .the energy curve to be displaced a distance, 6. Since the barrier height becomes (AF - fl/2) in the direction of the force, and (AF + fA/2) in the opposite 17 direction, the net frequency of activation in the direc- tion of the force becomes + <— _ kT —AF . f). _ \J " V — 2 F exp (F) 811111 (575') (2 5) If a parameter, X, is defined which is a function of the number of flow units and the average component of dis- placement in the direction of deformation, then the total displacement per unit time will be: e = X (3 - 3) (2'6) fA = ZXk -- exp (a; F>S Sil‘lh (m) (2-7) If creep in frozen soils is thermally activated, (T). as experimental data have indicated (Andersland and Akili, 1967), one can write for the creep rate s s s exp (%%E> (2-8) Rate process theory supports a general creep equation (Conrad, 1961) of the form -AF.(0,T,S) = E Ci (0,T,S) exp [———i§T—————£]sinh [Bi(T,S)O] (2-9) m. 'where Ci is the frequency factor and Bi is the stress factor. Ci’ AFi, and Bi may correspond to one of i num- ber of deformation mechanisms. The frequency factor and 18 activation energy may depend on stress 0, temperature T, and frozen soil structure 8. The stress factor may depend on temperature and structure. Although a number of de- formation mechanisms may be operating simultaneously, usually one is rate controlling so that an evaluation of equation (2-9) is possible by gross mechanical measure- ments (Conrad, 1961). For one deformation mechanism con— trolling, and stress conditions such that sinh B0 = 1/2 exp Bo, equation (2-9) may be written é =.C exp (%%E exp (BO) (2-10) If temperature is held constant, the-effect of stress on the creep rate could be developed, while at con- stant stress, the effect of temperature could be developed. CHAPTER III SOILS STUDIED AND SAMPLE PREPARATION Two soil types were used in this study. The first, a cohesive soil, was a red glacial clay obtained from the vicinity of Sault Ste. Marie, Michigan. This clay will be referred to as Sault Ste. Marie clay. The second soil used was a cohesionless material, a standard Ottawa Sand. The properties of the two soils and the procedures for sample preparation are described below: 1. Frozen Clay Sample The Sault Ste. Marie clay has been used in previous studies conducted at Michigan State University. It is pedologically classified as Ontonagon. A summary of the index properties of this clay, and the results of miner- alogical test on it, are listed in Table 3-1 below. To minimize the effect of differences in density, water content, and degree of saturation between test specimens, duplicate samples were prepared. This was achieved by mixing a precalculated weight of air dried Sault Ste. Marie clay (Passing 1/4 in. Sieve) with a 19 20 Table 3-1.--Physica1 and Mineralogical Properties of Sault Ste. Marie Clay Liquid Limit _ 60% Plastic Limit 24% Plasticity Index 36% Specific Gravity ‘ 2.78 Gradation (% finer by weight) 2 mm. 100% 0.06 mm. 90% 0.002 mm. 60% For Material Less Than Zn: 1. Specific Surface Area 290 mz/gram 2. Cation Exchange Capacity 28 meg/100 gram 3. Mineral Content: Illite 50% Vermiculite 20% Chlorite 15% Kaolinite 5% Quartz and Feldspar 10% calculated weight of distilled water and compressing the mixture to a specified volume having the desired density, water content, and degree of saturation. Distilled, deaerated, and deionized water was used in preparing the clay samples. 21 The calculations were based on the following design values: (1) a dry density of 100 pounds per cubic foot, and (2) a degree of saturation of 96%. After mixing the calculated weights of air dried clay and distilled water, the mixture was left for three days in an airtight container to insure uniform distribution of moisture in the clay. Afterwards, the mixture was placed in an 11 inch diameter split mold and.compacted statically to the predetermined height of 4 inches. The procedure of com- paction was previously developed by Leonards (1955). The compaction produced a cake 11 inches in diameter and 4 inches high, and resulted in a dry density of 102.5 pounds per cubic foot and a water content of 24.5%. The cake was then cut into prismatic samples 2 x 2 inches in cross sec- tion and 4 inches high. Each sample was immediately wrapped with a polyethelyene sheet, covered with aluminum foil, and coated with several coats of wax. Then, the samples were numbered and stored under water. Prior to testing, the wax was removed and a water content sample was taken, then the specimen was trimmed in a soil lathe to a cylindrical shape approximately 1.13 inches in diameter (one square inch in cross sectional area). The top and bottom of the sample were trimmed in an aluminum mold to give a height of approximately 2.26 inches. After recording the diameter, height, and weight of the sample, lucite discs were placed on each end of 22 the sample with friction reducer discs in between. The friction reducers were made by coating both sides of a sheet of aluminum foil with a very thin layer of silicone grease. A thin polyethylene film was then applied to both sides of the aluminum foil. The excess grease and any entrapped air were worked out by a straight edge. The sheet was then cut into discs of the proper diameter. The clay sample was then.mounted on t0p of the force trans- ducer in the triaxial cell. Two rubber membranes were placed over the sample, and several.rubber bands were tightly placed on both caps and the pedestal to prevent leakage and loss of moisture prior to and during testing. The top of the triaxial cell was placed in position and tightened. The cell was filled with the coolant, an equal portion mixture of ethylene glycol and water. Then the cell was carefully placed in a low-temperature bath, where the temperature was set about 3°C lower than the desired test temperature. The cell was left at that temperature for twenty-four hours so that the clay sample would freeze. At the end of the twenty-four hours, the temperature in the low-temperature bath was raised to the desired test tem- perature, and left for another twenty-four hours to insure temperature equilibrium prior to testing. Freezing at temperatures at least 3° below test temperature insured that ice contents of frozen samples correspond to the maxi- mum possible in each test sample (Leonards and Andersland, 23 1960). The time allowed for freezing the clay sample and the duration allowed for the cold bath to reach and main— tain a steady state test temperature were kept constant for all prepared samples, so that the effect of aging on the freezing process and the structure of the frozen clay would be minimized. The sample was then ready for testing. After testing, the sample was weighed and left to dry in the oven, then weighed again. This was done to determine the sample's water content, and served as a check as to whether any leakage had occurred during the test. From checking density and water content for all the clay samples used, before and after testing, it was found that the maximum variation in water content between samples did not exceed 0.5%. And the variation in density was less than one pound per cubic foot. 2. Sand-Ice Samples A standard Ottawa sand and distilled, deaerated, and deionized water were used to prepare all the sand-ice samples needed. The sand was sieved and only that portion which passed a number 20 sieve and retained on a number 30 sieve was used in preparing the samples. The specific gravity of the sand was 2.65. All samples were cast in an aluminum split mold 1.13 inches in diameter, which gave an initial sample cross sectional area of one square inch. The height of 24 the mold was 2.26 inches. A sand-ice sample was prepared by taking a predetermined weight of dry sand, so that it would give a 64% concentration, by volume, of sand parti- cles in the sample. This particular percentage was chosen for convenience and to insure an interparticle contact be- tween the sand particles (Goughnour and Andersland, 1968). The 64% sand volume concentration was used for all the sand-ice samples tested. A thin coat of silicone grease was applied to the interior of the mold to minimize adhe— sion between the frozen sample and the mold. The sand was poured into the mold, and the mold was tapped lightly on the side in order that the predetermined weight of sand would fill the volume of the mold, so that the top of the sand would be flush with the top of the mold. Precooled water was then poured into the mold to fill the pores be- tween the sand particles. Great care was taken in doing that, so the compacted sand would not be disturbed. Then the mold was placed in a freezer at a temperature of -20°C and left to freeze for twenty-four hours. After freezing, the tOp of the sample was trimmed flush with the tOp of the mold. Prior to mounting the sample, the triaxial cell and the two plexiglass caps were cooled for three hours in the freezer. The mold was dismantled and the sand-ice sample was placed inside the triaxial cell with a plexiglass cap at both ends of the sample. A friction reducer was placed between the cap and the sample at both 25 ends. Then two rubber membranes were placed on the sample and held at both ends with several rubber bands. After- wards, the tOp of the triaxial cell was placed tightly in position and the cell was filled with precooled etheylene glycol and water mixture. The entire process of preparing the sand-ice sample and mounting it in the triaxial cell was done inside the freezer, in order to maintain the sand- ice system at low temperature and to prevent it from thaw- ing. To change the sample temperature to the required test temperature, the triaxial cell was lowered into the low-temperature bath, which was previously set at the test temperature. The cell was left for twenty-four hours, so that the sample would reach the test temperature, and to insure temperature equilibrium. The time for freezing the sand-ice sample and the duration required for the sam- ple to reach and maintain a steady state test temperature were kept constant for all prepared samples to minimize the effect of aging on the freezing process and the struc- ture of the various sand-ice samples. At the end of each test, the sand-ice sample was weighed, melted and dried in the oven, and the weight of the dry sand was recorded. From these measurements, the density of the sand-ice sample, the dry density of the sand sample, and the density of the ice matrix were cal- culated. The prepared sand-ice samples were based on the following design values: 26 Cross sectional area 1 sq. inch. Height = 2.26 inch. Volume concentration of sand = 64% Dry density =. 107.5 Pcf. For all the sand-ice samples prepared, the total density of the frozen saturated sand was (128 i 0.5) Pcf. and the water content of the unfrozen samples was (19.4 i 0.2) %. The bulk density of the ice matrix, based on the weight of the melted ice and the total volume of voids, was found to be (0.91 1 0.005) gm/cm3 at -1290. The actual density of ice is a function of temperature (Pound- er, 1967): y = 0.9168 (1 - 1.53 x 10'4T) (3-1) where.y is the density of ice in gm/cm3 at temperature T, and T is in degrees Centigrade. Using equation (3-1), the density of ice at -12°C is 0.91848 gm/cm3. This density was used to estimate the volume of air voids in the frozen saturated soil. The air voids in the prepared sand-ice samples were found to be less than 1% of the ice matrix. CHAPTER IV EQUIPMENT AND TEST PROCEDURES 1. Equipment The same triaxial cell and cold bath were used for the differential creep tests and the constant axial strain-rate tests. The sample rested on a brass pedestal in a standard triaxial cell. The pedestal was mounted directly on a force transducer (DYNISCO Model TCFTS-lM), which has a rated capacity of 1000 pounds with overload to 1500 pounds. Figure 4-1 shows a schematic diagram of the sample placement in the triaxial cell. The triaxial cell was entirely submerged in a coolant, an equal part mixture of ethylene glycol and water. The coolant was maintained at a constant test temperature by circulating through a microregulator controlled cold box. Before any testing was carried on, the temperature control was calibrated by measuring the temperature at the vicinity of the sample inside the triaxial cell, and the temperature at a fixed location in the low-temperature bath. The temperature of the sample was measured by plac- ing a copper-constantan thermocouple adjacent to the sam- ple at mid-height, and another one in a bath of distilled, 27 28 Load Linear [1 Differential Transformer L — To Constant Press. Apparatus b Leads to . Recorder Rubber Coolant‘\ _,.Bands \ Coolant o O \ Friction Membrane Reducer. CE:_ 1 Valve for filling cell. WW ///// * " Figure 4-1. A Schematic Diagram of the Sample Placement in the Triaxial Cell. 29 deionized,melting ice used as a reference point. The temperature was obtained by measuring the E.M.F. with a potentiometer (Leeds and Northrop Model K-2) and using an E.M.F.-Temperature calibration chart. At the same time the temperature was measured at specific locations in the low-temperature bath by a thermometer with scale divisions of 0.1°C. These temperature measurements were carried on over a period of twenty-four hours. It was observed that the temperature varied by no more than 0.05°C. The bath temperature control was set at the desired test temperature and left for three days until the temperature at the bath reached a constant value of the desired test temperature. Prior to testing the sam- ple was left for twenty-four hours in the low-temperature bath to insure temperature equilibrium in the sample. The axial pressure was supplied through the load- ing ram at the tOp of the triaxial cell. The confining pressure was supplied through a valve at the base of the triaxial cell from a constant pressure unit. The pres- sure unit was a self-compensating mercury control appara- tus, which was capable of supplying a constant pressure to a triaxial cell for testing over long periods. The pressure was provided through the valve assembly by the difference in head between the surface of mercury in the upper moving pots and the lower fixed pots. The constant pressure apparatus is shown in Figure 4-2. .mdumummmfl mafiumma man no usoqu oaumfimumMHQ .mlv musmam pas: whommmum usmumcoo nan: mafia nopuoomm 30 Hnmo Hmnme mamfimm summ musumummfimu mEmum mGHDmOB 31 The axial deformation was measured simultaneously with two different measuring devices, a Linear Differen- tial Transformer (Sanborn Linearsyn Differential Trans- former Model No. 575 DT-500), and a dial gauge with 0.0001 inch divisions. The outputs of the linear differential transformer and the force transducer were fed into a 2-channel recorder (Sanborn Recorder Model 77023 with a Sanborn Carrier Pre- amplifier Model 8805A). For the linear differential trans- former the preamplifier was calibrated so that, at maximum sensitivity, a deflection of 0.00025 inches will cause the stylus to deflect one millimeter on the chart (one divi- sion). For the force transducer the preamplifier was cali- brated so that, at maximum sensitivity, a load of 5 pounds would cause the stylus to deflect one centimeter on the chart. Figure 4-2 shows a diagrammatic layout of the test- ing apparatus. 2. Differential Creep Tests The same triaxial cell and testing equipment were used to conduct all creep tests on the frozen Sault Ste. Marie clay samples and the sand-ice samples. A constant axial pressure was supplied by a load- ing frame supporting a dead weight of lead bricks. The loading frame was lowered onto the loading ram by a mechan- ical loading device at a relatively fast rate. It took 32 less than 5 seconds for the total load to transfer to the sample through the ram. And since the dynamic effects are very small, they were assumed to be negligible. To compensate for the increase in cross sectional area as the sample deformed, lead shots were added to the dead load. The axial stress measured at the bottom of the sample and the axial deflection measured at the top of the sample were both recorded continuously on the charts of the recorder, at the highest possible sensitivity of the recording system. By observing the axial deflection data it was possible to know when the creep process had passed the primary creep stage and entered the steady state creep stage. When that stage was reached, and with axial loading constant, an increment of confining pressure was applied on the sample for a period of thirty minutes. Then the confining pressure was increased by four more increments of the same value, each increment applied for the same duration. In some of the creep tests, the con- fining pressure was decreased at the end of the test by increments of the same value, and the axial creep deforma- tion was observed. The creep test was conducted with tem- perature held constant for at least twenty-four hours prior to testing, and all through the test period. 33 3. Constant Axial Strain-Rate Test The same equipment and procedure were used for all constant axial strain-rate tests on the frozen Sault Ste. Marie clay and the sand-ice samples. Since the ultimate strengths of the frozen soil samples were expected to ex- ceed the force transducer's loading capacity, a 5000 pound proving ring was used to measure the axial load. The load was applied directly to the loading ram by a variable speed mechanical loading system. A deformation rate of 0.00678 inch per minute was used. The deformation rate was main- tained during the test, and periodically adjusted to give an approximate constant strain rate of 3 X 10-3 inch per inch per minute. Results showed that the variation was less than 10% when observed over two minute periods. The constant axial strain-rate tests were conducted with three different constant confining pressures of 30 Psi, 60 Psi, and 90 Psi. The confining pressure was applied prior to the axial loading in each case. CHAPTER V EXPERIMENTAL RESULTS 1. Differential Creep Tests The creep tests were conducted to study the be- havior of frozen soils under the effect of constant axial loading, and different values of confining pressures. The confining presure was increased by increments of 30 Psi, and maintained for 30 minutes for all creep tests, except Test No. C-4, in which the confining pressure incre- ment was 20 Psi. By keeping the axial loading constant and increasing the confining pressure in the triaxial cell, the stress difference D = (01 — 03), and the de- viatoric stress CD = (01 - cm), were kept constant, and the mean stress 0m and the major principal stress 01 were increased by the same increment. Typical creep tests on frozen Sault Ste. Marie clay samples, at a temperature of -12°C, with different values of axial loading, are shown in Figures 5—1a and 5-1b. These curves show the increase in true strain with respect to time under different confining pressures and a constant axial loading. Note that in the first portion of the curve, for which the confining pressure is zero, 34 35 the shape of the curve conforms to the classical "Creep Curve ". At the beginning, the strain increases at a high rate, then the creep rate starts to decrease progressively, implying strengthening, until it reaches a constant rate, which signifies the end of the primary creep region and the beginning of the steady state creep region. When the confining pressure was increased, there was a sharp rise in the strain ~ time curve, then the sample deformed at another constant creep rate (see Figure 5-2). The magni— tude of the sudden rise in strain, when an additional con- fining pressure increment was applied to the sample, was approximately constant for all tests. Calculations show that this rise was caused by the expansion in the triaxial cell due to the increase in the confining pressure. For some of the creep tests, at the end of which the confining pressure was decreased by increments, a delayed response in deformation was observed upon the decrease in confining pressure, then the strain increased atla constant rate. This delayed response in strain with respect to time, at the beginning of the confining pressure decrement, could be due to a delayed response in the sample and the testing system. This behavior is shown in Figure 5-2. It is evident from the creep curves in Figures 5-la and lb, that the steady state creep rate Q decreased, under a constant axial loading, with the increase in con- fining pressure. The creep rate for each loading condition 36 was numerically evaluated from the true strain ~ time curve for every test. A summary of the differential creep tests on the Sault Ste. Marie clay, at a temperature of -12°C, with the stresses for each stage of the test and the corresponding steady state creep rates, are listed in Table 5-1. Experimental data are given in the Appendix. Typical curves of the differential creep tests conducted on sand-ice samples, with a 64% volume concentra- tion of sand and a test temperature of -12°C, are shown in Figures 5-3a and 5-3b for axial loads of 764.3 Psi and 815.9 Psi, respectively. The confining pressure incre- ments were similar to those used for the clay samples. The shapes of the true strain ~ time curves of the sand- ice samples are similar to those of the frozen clay sam- ples. The creep rate 6 decreased, under a constant axial load, with the increase in confining pressure. A summary of the differential creep tests on the sand-ice samples, at a test temperature of —12°C, including the stresses for each stage of the test and the corresponding steady state creep rates, are listed in Table 5-2. Experimental data are given in the Appendix. In creep Test No. S-4, conducted on a sand-ice sample at a temperature of -12°C, the axial creep rates were observed under an axial creep load of 764.3 Psi and confining pressure values of 0 and 30 Psi, next the axial creep load was increased to a value of 815.9 Psi, and the 37 creep rateswere observed for confining pressures of: 30 Psi and 60 Psi. The true strain ~ time curve for creep Test No. S-4 is shown in Figure 5-4. To determine the effect of temperature variations on the time-dependent behavior of frozen soils, differen- tial creep tests were conducted at test temperatures of -10°C, -12°C, -l4°C, and -18°C on duplicate sand-ice sam- ples under a constant axial loading equal to 764.3 Psi. Figures 5-5a and 5-5b show true strain-time curves for creep tests at temperatures of -10°C and -18°C, respectively. By comparing these two curves with the one in Figure 5-3a, conducted on a duplicate sample under the same stress conditions and a test temperature of -12°C, a similar type of deformation behavior is observed. The magnitude of deformation varies with respect to the change in test temperature. This will be discussed in the next chapter. A summary of the differential creep tests conducted on duplicate sand-ice samples at different test temperatures, under the same axial loading, including the stresses at‘ all stages of the test and the corresponding steady state creep rates, are listed in Table 5-3. Experimental data are given-in the Appendix. 2. Constant Strain-Rate Tests Constant axial strain-rate tests were used to determine the strength of the frozen soils at a relatively 38 fast strain-rate of 3 X 10"3 in./in./min., with constant confining pressures of 30 Psi, 60 Psi, and 90 Psi. All tests were conducted at a constant test temperature of -12°C. The stress-strain curves for constant axial strain- rate tests on identical Sault Ste. Marie clay samples are shown in Figures 5-6, 5-7, and 5-8. ‘These figures also include the strain-time relation for each test. The stress- strain curve shape did not show a distinctive peak value. The stress increased rapidly with increase in strain, reach- ing an Optimum value around 12% strain. The ultimate strength values were approximately the same for all tests conducted on duplicate Sault Ste. Marie clay samples sub- jected to different confining pressures. This indicates that confining pressure has little or no effect on the ultimate strength of the frozen clay samples at a high degree of saturation. This behavior is similar to that of consolidated undrained cohesive soils subjected to tri- axial compression (Bishop and Henkel, 1962). The Mohr diagram for the constant strain-rate tests on Sault Ste. Marie clay is shown in Figure 5-9, and indicates a cohesion value of 402 Psi and a zero friction angle, at a tempera- 3 in./ ture of -12°C and a constant strain-rate of 3 X 10- in./min. The stress-strain curves for constant axial strain- rate tests on sand-ice samples with a 64% sand volume 39 concentration, at a temperature of —12°C, and constant confining pressures of 30 Psi, 60 Psi, and 90 Psi are shown in Figures 5-10a, 5-10b, and 5410c. These figures also include the strain-time relation during the progress of each test. The stress-strain curves for the sand-ice samples showed a peak value at a strain level of approximately 1.8%. The confining pressure showed a considerable effect on the value of the ultimate strength of the tested samples. The strength increased with higher value of confining pres- sure, showing an internal friction factor in strength. This is in agreement with the work by Goughnour (1967). A Mohr diagram for the constant axial strain-rate tests conducted on identical sand-ice samples, at a temperature of -12°C, is shown in Figure 5-11. Close linear agreement between the three plotted p ~ q valueé:>indicates excellent duplication between samples. The diagram gives a cohesion value of 435 Psi, and angle of internal friction equal to 25°, for sand-ice samples at -12°C and a constant strain- 3 rate of 3 x 10- in./in./min. 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I . _ II.\ I \ _; _ 3 & Hsmyonm~.mum_ _ n. ,.m5mIOme~.muw r——.—d—o\——_ _ _ _ _ _ _ _ _ _ omo.o mmo.o omo.o mmo.o o¢o.o meo.o 33 enll '3 axe: /'uT °UT 48 .Hmm m.mHm on Hmswm 0cm «mm m.vmh o» Hmswm HQ .moHIUGmm co umma mmmuo Hafiucmummmwn Na .GHE .mEHB .HIm musmHm omH ova ONH 00H om om ow ON 0 I q q q d # — a u — - d d — u u a . _ _ I Hm I _ _ _ hIoHo.o . moolmo _ ammomumo Humomumo _ oumb.|l.I% wmmm.mflmfla _ Hmmm.mHmuQ Hmmm.¢mhfla _ HmQMIvohuQ I I _ _ I _ L _ _ _ .ImHo.o _ L _ _ _ . I IN Hmm m mHmI a_ _ _ I Ham n.4ohuHo_ _ I oomHIna _ , .Iémo.o wom.aHu3_ _ I U mom m.FOHu >. _ . I I vlm .oz mamfimm mOHIUcmm_ _ . - m HIGHEvIonH mlwI _ _ _ .Immo.o _ _ _ I _ I QHE x . n I _ HI . ¢IOH m4 H w I _ _ _ I . I _ I _HIzHaHIonm HIm - . _ . . MN 0 "W _ _ I l .EVIOH mo HF P _ mmo.o °uT/°u; '3 uteanIanm 49 .ooH.mHIna g Hmv .uooHIna a Hay .wOHIwcmm so umwa mmouu HMHuanmmmHo .mIm musmHm .GHE .mEHB “mm m.hoau _ bIm .oz mamfimm moHIwcmm _ — — — — J Hum m.vohun ooH.mHIna _ «H.mHn3 _ c» _ I I _ .IL/xmwm.wwmmw_ _ _ _ UOOHIHB 4 0:30 — \. H I 5 _ mIm .oz mamamm mOHIvcmm _ J v 0 I. omH ooH owa oOH om ow cm 0 H H H d H H H _‘ H 4 _ H _ H H H _ H H H _ _ _ _ _ ,I.. I AlwaomHumoIllelwémomHumoLImmomumollvTammooumollllmmomumolllibwwmoumolI ,Il. IyI — H g l I _ I _ I _ I _ l Ham m.Hohua H UOOHIHB mnm.mHu3 I mom m.noHuc> I moo.o QHo.o .mHo.o ONOIO .mNOIO omo.o '3 uyexus-anxm ’UT *UT/ D = 01-03, P81 50 80fi— : a , é -H 7°C? , Sault Ste. Marie Clay 5 _ " Sample No. CF—l .J ’ Y =103.l Pcf soc— d a, . w=24.6% _§ ' T=-12°C 9- 5oc_ " o3=30 Psi 50- . e=3xlO-3min.-l 4OCF" //// 40- 3oc— . , ,/ ‘ 3o- _ e=3xlO-Bin./in./min,~j’4 2'oc_. /,/’/ 20- 10c ,—’1 ” 10_ /,/’f " Actual Strain-Rate I ’z’ A 00 ' 0:02 0504 0.66 ‘ oibe oil) 1 0:12 ' ' True Strain e, in./in. Figure 5-6. Stress ~ Strain and Strain ~ Time Curves for Sault Ste. Marie Clay, 03 Equal to 30 Psi. 800i - 3 :3 . :2 -H 700- E , v Sault Ste. Marie Clay 4;. b _ Sample No. CF-2 600.. . Yd=102.6 Pcf 2 ' . -I-l - w=24.49% 9- =-12°c 500’ o3=60 Psi 50— ' é=3x10'3min.‘1 400- . _3 // 4o- e=3x10 in./in./ in. t’,/:’ " 300- ‘ K ” 30. 200- - 20- 100_ ., Actual Strain-Rate 10— . J ”L A l l 4 l 1 1 I l I |.00 0.02 0.04 0.06 0.08 0.10 0.12 True Strain e, in./in. Figure 5—7. Ste. Marie Clay, 03 Equal to 60 Psi. Stress ~ Strain and Strain ~ Time Curves for Sault 51 BOCL - 3 c - I5 700L '2 Sault Ste. Marie Clay ' Sample No. CF-3 '5‘ 600— yd=102.5 Pcf 0 w=24.23% .5 ' T=-12°C B 500. 03=90 Psi 50— L e:=3x10"3min.'1 40CL . ,.»" 40— e=3x10'3in./in./min. ‘,v’T 3ocL \\‘\¢\\>.,—"L’ ' 30H ZML /,/<’ “ 20. - ’./f’< Actual Strain-Rate 100. ‘ I ‘ 10—‘ g’l 1 L I I l L I I I I I I 0.00 0.02 0.04 0.06 0.08 0.10 0.12 True Strain e, in./in. Figure 5-8. Stress ~ Strain and Strain ~ Time Curves For Sault Ste. Marie Clay, 03 Equal to 30 Psi. 600- 500- .Sault Ste. Marie Clay ‘ T=~12°C 03¢:0 €=3x10'3in./in./min. 40C 300. 20d, 100- ,1 l l L 1 l I 4 1 i l I O 200 400 600 800 1000 1200 014-03 p = T , PSi Figure 5-9. Mohr-Coulomb Plot and Modified Plot for Sault Ste. Marie Clay Samples. 52 m .flmm om op Hanan o .amm om on amsvm Auzo cflmuum z mmmuum m b Amv \.GH\.QH .w cflmuumImsHB. .oaum museum ovo.bn mmo.o omo.o mWo.o omo.o mHo.o .OHOMO . moo.o oo.w I d — d — [1 — d u — u q 1 J — u 1 — q q 4 4 A - q q d — d d d J — q a. q d — db”... 1..." . \I§9\I..K\ n damn whammm nDIIIISJI. .\\K\ I film . pm U z ODD\ \9IO\|\\ .: ICON n V/u I...» II 4 .10..” .b\ d bP. \a .GHE\.G..H\.GH oaxmum Idov . me.\.m .MI . I 3“ || ‘5 I mma o m>nso -ooo m - Iom ammomumo.< m>usu..a .oom ammomumod misolb I .Tm ammomumo.o 0>HsUI.o m m>usu Ioooa m. x. 4 m>uso I . JOONH .2 - III, . . , ,, > .83 u . 4 Jooma .GflE\.GH\.GflMIoaxmum . UONHIHB HMflumumz GOHIUGmm coma D I 53' .mmHmEMm oOHstmm How uoam omwMflUoz can uoam nEoHsoqusoz .HHIm musmwm Hmm s IIINI " nu s0 mo+ao _ coma oowH oomH oooH cam _ owe _ oau _ saw a. = J cc 6 w o .. m. a. Jam a d I s T. Lw ..\.Ioov \ L l \ \\\ b \\ Ioom __ \\\\\ £23535 «(Sam I m .2 u 5ng Ioom a some- n a \\ m. HMHHGHMZ OOHIUGMm omN III. 9 Ioooa Z En—To CHAPTER VI DISCUSSION AND PRESENTATION OF THEORY The results of the differential creep tests con- ducted on frozen Sault Ste. Marie clay at a constant tem— perature of -12°C, summarized in Table 5-1, show a linear relationship between the logarithm of the steady state creep rate E and a stress term 2. The stress termm Z = D - cm is a function of both the deviatoric component and the hydrostatic component of stress, where D is the stress difference5:>and am is the hydrostatic or the mean normal stress.C> This linear relation between log s and Z is shown in Figure-G-l as a family of linear curves. Each corresponds to a different constant value of stress differ- ence D. The equation representing this linear relation may be expressed in the following formz® (Do-=01 3 = 3/2 (01 - om), since 02 = 03 in the triaxial test apparatus. ®o m '0' +0 -l/3 (a1 + 02 3) l/3 (01 + 20 3). C)log: designates the common logarithm for which the base is 10. 2n: designates the natural logarithm for which the base is e = 2.71828. 54 55 ‘log 6 = (m log e) Z + log b which implies that the creep rate é is an exponential func- tion of the stress term 2, at constant temperature, and which can be put in the following form: é = b exp (m 2) @ T const. (6-1) where m is the absolute value of slope of the straight line on the log-creep rate verses 2 plot, and b is the projected value of creep rate at zero 2 on the same plot. b has no physical meaning. The value of m was determined graphically from Figure 6-1 for frozen Sault Ste. Marie clay at a constant temperature of -12°C. A nearly linear relationship is found between log b and the stress difference D for the differential creep tests on the Sault Ste. Marie clay, which implies that the b value approximates an exponential function of the stress difference D for dif- ferential creep tests on frozen clay. This relation is shown in Figure 6-3, and could be presented in the follow- ing form: b = C exp (n D) @ T = const. (6-2) The parameters C and n are constants at a constant test temperature and could be evaluated graphically from Figure 6-3. By substituting the exponential function b (equation 6-2) for the b value in equation 6-1 we obtain 56 e = C ° exp (n D) ' exp (m 2) @ T = const. (6-la) since M II D - om, if we let N = n + m, then: s = C - exp (N D) - exp (-m cm) @ T = const. (6-3) For frozen Sault Ste. Marie clay at a temperature of -12°C, equation 6-3 becomes: é = (2.77 x 10-4) . e(0.00268)D . e-(o.01049) @ T = -12°C (6-4) é is measured in inch/inch/minute, D and cm in Psi. Know— ing the stress conditions and the parameters C, N, and m for a frozen clay, we can use equation (6-3) to estimate the steady state creep rate for that clay at a constant temperature, as long as the applied stresses are within the range which exhibits a linear relation between log E and 2. Equation (6-3) indicates that the creep rate of frozen clay, at a constant temperature and the stress- history used, increases exponentially with the increase in stress difference D, and decreases exponentially with the increase in mean stress cm. The results of the differential creep tests con- ducted on sand-ice samples, at a constant temperature of ~12°C, showed the existence of a linear relationship be- tween the logarithm of the steady state creep rate and the stress term 2, which indicates a similar behavior to that 57 of the creep of frozen clays. This linear relation between log E and Z is shown in Figure 6-2 as a family of curves, each corresponding to a different value of stress differ- ence D. Figure 6-2 indicates that the creep rate of sand— ice samples, at a constant temperature, is an exponential function of the stress term 2, and could be described by a mathematical expression similar to the one used to describe the creep behavior of frozen clay in equation (6-1), except that the b and m parameters assume differ- ent values. m can be evaluated from Figure 6-2. Then, for a sand-ice material of 64% sand by volume concentra- tion, at a constant temperature of —12°C, equation (6-1) becomes: (0.01206)E e e = bl @ -12°C (6-5) The log bl verses D plot, shown in Figure 6-4, exhibited a nearly linear relation, indicating that b1 is an exponen- tial function of D at a constant temperature, and could be represented in a form similar to equation 6-2. For a sand-ice material at -12°C,.the linear relation in Figure 6-4 between log b1 and D can be expressed as: b = (9.103 x10'6) e‘(°'°398)D l @ T = -12°C (6-6) By substituting equation (6-6) for bl in equation 6-5 we get: 58 . (9.1o3x10'6) - e'(°-°°393)D. e(0-01206H: m ll @ T = -12°C (6—7) since 2 = D - om, then: 8 = (9.103> mumm momuo .HIm musmwm .sfl8\.sw\.sa .u ovum momuo MIoH «Ioa mloaxm I. i _ i s _ 4 _ _ _ r 7 (I _ 3 loom 3.4%.... - mom m.~oauu> UoNHIua loom undo mans: .mpm pasmm loov ammo .mmmua (0 (Gem . ammmKhmuo la ammaéfiua I s “ammmémhuol AV 1 com In ’ o Isa 71 MIOH .memEmm onIpsmm How mmmnum mamnm> mumm mwwuo .NIw mhsmfim VIOH .GHE\.Gfl\.nw .w spam mmmnu mloaxm Hmmm.owmnole \\ Hmmm.vmhnalb mm.mau3 mom m.aoanw> oomanua mmamfimm moHIosmm Hmmm.meHQlB _ _ Him .OZ umwB Mlm .OZ ummB _ _ ,3 NIm .oz umwe .Ioov '111 TSd 72 900T Sault Ste. Marie Clay T=-12°C 800_' Yd=102'5 Pcf w;24.5% r 700-— bPoint A from Test No. Point B from Test No. C-2 600"Point C from Test No. C-l Point D from Test No. C-4 D= 0'1 - 03, PS]. )- 500 1 I I I I I I I I I I I 3x10'7 10-6 6x10-6 b value, in./in./min. Figure 6-3. b Value Versus Stress Difference for Sault Ste. Marie. 900 Sand-Ice Samples T=-12°C ' yd=107.5 Pcf w;l9.3% 800%— -H m n. p, _ o u 57700 n rPoint A from Test No. S-3 0 Point B from Test No. S-2 ”Point C from Test No. S-l 600—- 7 ' I I I. I I I 2x10'7 9x10’7 b value, in./in./min. Figure 6-4. kJValue Versus Stress Difference for Sand-Ice samples. oIona 73 .mmamfimm moao mHHmZ .mum pasmm suflz pmnmmfiou moamemm GUHIUcmm How mm>nso mmouum mmumm momuu Havamhe .mIo musmwm .GHE\.cw\.cH .m oumm momuu VIOH mloa _ _ _ _ . _ _ _ _ _ d _ _ iced UONHI " B HID .Oz ummB z swam onus: .mum uaomm = mooao.o u s I .0 _ UONHI " B D Tm .02 some looo m. osmm pmumHsumm cmuoum M I t. .\ oomao o u s \\\ \V \\\\ \\ loom I\\\ \\ \.v\. Avx. I Iooo .74 mIoH .HMfiHoumz ooHIUcmm How mmumm mwwno pmumaflumm tam UwHSmmmz .sHE\.cH\.GH ~m mumm mwwuu .oIm musmflm oIoH mIonN _ _ fiI _ _ q _ a _ _ _ _ _ _ _ _ C nmm mo.mHouNo o H .l on Hum m.vohu Q UONHIHB oom.oau3 AoIm sweet I . w m mom m aoau > Hmm on n o com . Ia wIm .oz mHmEMm oOHIpcmm . H N . Ham m wool ow jams m ooh" no 0 oouommmz mIo can no cofluoHOm .Ioom \ C \ AbIo .qvmv Anlw .cwmv A Hmm on fine can I oumo cam / Hmm m.vw>uaowmw woumfiflumm /4// Hmm m.ooanaooao omuoaflumm , . . ofimm o.maou~ao.Iooo . . I ouH O GOH .5. o oumo cam / , I “mm m.ooauaooao oonsmmmzw . \(I Aoum ummao flmm owumo was .loom flmm o.mamu~ooom omuommmz ABIo .aomo AoIm umoeo Aan .cvmo I flmm omumo cam Hmm omnmo was Hmm omnmo 6cm Hmm m.mHmnNQ®mm Umumfiwumm flmm m.mamnmo®mm pmHSmmwz wmm m.meuNn®ww Umumfiwumm .Iooo Isa '3 75 60 .- ’/” ’/’ 500— ' ".1 _ In D; $5 400— a II _ ¢_T=-18.1°C,Test No.S-7 N Is?” ._T=-l4°C,Test No. S-6 ’ Sand-Ice System =_ o _ 300_. YdI107‘5 Pcf V_.T 12 C,Test No. S 2 w=19 3% a_.T=-10°C,Test No. S-5 20 I I I L I I I I I I _ 2x10‘5 10'4 10-3 Creep Rate a, in./in./min. Figure 6-7. Dependence of Creep Rate on Stress and Temperature of Saturated Frozen Sand. 0.00395-— I Sand-Ice System ' yd=107.5 Pcf _ é, w=l9.3% 0.00390-— ,—|-| .- ‘Q’ "Point A from Test No. 0 0.00385-— , ‘1 _Point B from Test No. 'E. -Point C from Test No. ._. I -Point D from Test No. 0.00380-— 0.00375 I I .J I I I I I 10-7 10-6 b2 value, in./in./min. Figure 6-8. Temperature Dependence of b2 in Equation (6-10). .hMHo mans: .muw uHsmm swuoum mo H0H>mnmm numswuum uswpsmmmoImEHB .mlm wusmflm Hmm . IIMII u m mo+Ho com com com com oov com com OCH 9 76 q — u _ u — - I— d — — _ — — q _I q o oomaIme I.ooH om.o~Iz mom m.~oauo> I hoao mans: .mum pasmm I.OON b \ \\\\\\\‘| z I.oom I .:Ha\.ofl\.ofimIonoumI.o .oae\.qa\.onmIonouwI.> - .oHs\.qn\.oflmIonoIWIIo .sHE\.cH\.cHVIoaxHHwIIa I.oov 9 can u a can lle L Tsd .pcmm msmuuo concusumm swuoum mo H0H>mswm numcouum usmwcomwnloEHB .OHIw onsmwm Hmm . u m mo+ com com 005 com com com com com OOH _ fl . _ . _ 1 fl — _ _ H AI _ d _ \\\ oomHIua \\\xn $.31; \\\\II C \\ \ \H \ mom m.\I0HN > \ \\\\\ \. HMHkumz mOHIpcmm \\.\. \ \I \ \. \ \I\ \ \ \ \\\ \ \ \ \ \ \ \ \ \ \\\ \ \ \ \\ \ 7 \\ \\ \\ \ I 7 \ \ \\ .Sax.oH\.onIonouo Io .s48\.cH\.chI0onuwIIo I .5 561.3?onme lo .is\.cH\.oHTonHuw I» o 5.0. no EB I CGA U s\.cH\.cHoIon~no I a o o ooH .b .— So To Z _ 0 to a m. oom ooo com CHAPTER VII SUMMARY OF CONCLUSIONS 1. The results of the differential creep tests con- ducted in this study, on frozen Sault Ste. Marie clay and frozen saturated Ottawa sand, indicate that the mean stress does affect the creep rate of frozen soils. Therefore, the creep rate of frozen soil at a constant temperature must be considered as a function of the mean stress as well as the deviatoric stress. The creep rate increases expo- nentially with the increase in stress difference D, and decreases exponentially with the increase in mean stress cm. The steady state creep rate for frozen soils can be estimated, at a constant temperature, from the following equation: a = C - exp (ND) - exp (-m am) where C, N, and m are parameters which can be determined by a differential creep test. 2. The effect of temperature on the creep behavior of frozen soils, under a constant stress difference, is de- scribed by an exponential function of the reciprocal of test temperature. This is in agreement with previous work showing that the creep phenomenon of frozen soil is a 78 79 thermally activated process. The effect of temperature on the creep rate can be described by the following equation: a = C’ ° exp (-£/T) ° exp (m2) where 2 = D-om, and C’, 2, and m are parameters which can be evaluated from differential creep tests. 3. To combine the effect of both stress difference and test temperature on the steady state creep deformation of frozen soil, the experimental data suggest an equation of the following form: é = A ° exp (ND) ° exp {-I/T) ° exp (-m cm) where A, N, I, and m are parameters which can be evaluated experimentally. Tests were conducted so as to minimize changes in soil structure, which may influence some of the parameters. The equation above is in agreement with the general equation (Eqn. 6-14) describing creep deformation. 4. The time-dependent strength of frozen soil may be described by two parameters; a cohesion C and a friction angle 0, for a given creep rate. Results of differential creep tests, on frozen Sault Ste. Marie clay and frozen saturated sand, indicate that the friction angle 0 appears to remain constant with change in creep rate, at constant temperature,. While the cohesion C decreases with a slower creep rate, implying the dependence of C on time. Cohesion also depends on temperature. Values of C and 0 can be 80 estimated, for a given creep rate, by using the equation describing the creep deformation. 5. The angle of friction 0 for the sand-ice system can be considered independent of time and temperature; there- fore it appears to be a prOperty of the material. Cohesion is controlled by the properties of the ice matrix and any unfrozen water; thus it is time-dependent. 6. In a constant axial strain-rate compression test, at a relatively high strain-rate, the confining pressure has no significant effect on the ultimate strength of fro- zen clayq While the ultimate strength of frozen saturated sand does increase with the increase in confining pressure, therefore implying that friction does develop during defor- mation of saturated frozen sand. This would be in agree- ment with data reported by Goughnour (1967). BIBLIOGRAPHY BIBLIOGRAPHY Andersland, O. B., and_Akili, W. "Stress Effect on Creep Rates of a Frozen Clay Soil," Geotechnique, Vol. XVII, No. 1, March, 1967, pp. 27—39. Bishop, A. W., and Henkel, D. J. The Measurement of Soil Properties in the Triaxial Test, Edward Arnold LTD, London, 1962. Conrad, H. "Experimental Evaluation of Creep and Stress. Rupture," Chapter 8, Mechanical Behavior of Mate- rials at Elevated TemperatureI Ed. by J. E. Dorn, McGraw-Hill Book Co., Inc., N.-Y., 1961, p. 149. Dillon, H. B., and Andersland, O. B. "Predicting Unfrozen Water Contents in Frozen Soils," Canadian Geotech- nical J., Vol. III, No. 2., 1966, pp. 53-60. Dillon, H. B., and Andersland, O. B. "Deformation Rates of Polycrystalline Ice," Int. Conf. on Physics of Snow and Ice, The Inst. of Low Temp. Sci., Hokkaido Univ., Sapporo, Japan, August, 1967. Glasstone, S., Laidler, K. J., and Eyring, H. The Theory of Rate Processes, McGraw-Hill Book Co., Inc., N. Y., 1941. Goughnour, R. R. "The Soil-Ice System and the Shear Strength of Frozen Soils," Ph.D. Thesis, Michigan State Univ., E. Lansing, Mich., 1967. Goughnour, R. R., and Andersland, O. B. "Mechanical Prop- erties of Sand-Ice System," Journal of the Soil Mechanics and Foundations DiviSion, ASCE, VoI. 94 No.'SM4, July, 1968. Hill, R. "The Mathematical Theory of Plasticity." Univer- sity Press, Oxford, 1950. Lambe, T. W. "Stress Path Method," Journal of the Soil Mechanics and Foundations Division,ASCE, VoI. 93, No. SM6, November, 1967. 81 82 Leonards, G. A. "Strength Characteristics of Compacted Clays," Tans. ASCE, Vol. 120, 1955. Leonards, G. A., and Andersland, O. B. "The Clay-Water System and the Shearing Resistance of Clays," ASCE Research Conf. on the Shear Strength of Cohe- sive Soils, Boulder, Colorado, 1960. Mitchell, J. K., Campanella, R. G., and Singh, A. "Soil Creep as a Rate Process," Journal of the Soil Mechanics and Foundations Division, ASCE, VoI. 94, No. SMl,January, 1968. Pounder, E. R. The Physics of Ice. Pergamon Press, Oxford, 1967. Tsytovich, N. A. "Mechanical Properties of Frozen Soils." Chapter 4, Bases and Foundations on Frozen§oi1, HRB Special Report 58, (A TranslatIon from Russian), Washington, D. C., 1960. Vialov, S. S. Ed., "The Strength and Creep of Frozen Soils and Calculations for Ice-SoiI RetainingStructures," CRREL, Trans. 767'1965a. Vialov, S. S. Ed., "Investigation of the Cohesion of Frozen Soil," Chapter II, Rheological Properties and Bearing Capacity of Frozen SoiIs, CRREL, Trans. 74, September, 1965b. Vialov, S. S. "Plasticity and Creep of a Cohesive Medium," Proc. of the Sixth Int. Conf. on Soil Mech. and Foundation Eng., Montreal, September, 1965c. Air" Appendix-Data 83 Table A—1.--Differentia1 Creep Test Data Test C-l.—-Sau1t Ste. Marie Clay T = -12°C Time Deflection (min.) (in.) Yd = 102.2 Pcf @ 03 = 60 Psi w = 24% 66 0.12656 L0 = 2.79 in. 68 0.12697 70 0.12748 do = 1.114 in. 72 0.12786 74 0.12809 D = 677.95 Psi 76 0.12848 80 0.12925 Time Deflection 85 0.13026 (min.) (in.) 90 0.13133 94 0.13206 @ 03 = 0 @ 03 = 90 Psi 0 0.00000 2 0.07329 96 0.13324 4 0.08952 98 0.13352 6 0.09351 100 0.13388 8 0.09873 102 0.13418 10 0.10190 104 0.13434 12 0.10459 106 0.13470 14 0.10691 110 0.13518 16 0.10830 115 0.13589 20 0.11056 120 0.13659 25 0.11268 124 0.13719 30 0.11498 34 0.11667 @ 03 = 120 Psi @ 03 = 30 Psi 126 0.13842 128 0.13855 36 0.11781 130 0.13878 38 0.11827 132 0.13901 40 0.11893 134 0.13928 42 0.11943 136 0.13937 44 0.11995 140 0.13976 46 0.12055 145 0.14033 50 0.12157 150 0.14079 55 0.12289 154 0.14124 60 0.12426 64 0.12536 84 Table A-l.--Continued Test C-1.--Continued Time Deflection (min.) (in.) Time Deflection (min.) (in.) 20 0.12548 25 0.12858 @ 03 = 150 Psi 30 0.13138 32 0.13238 156 0.14234 34 0.13328 158 0.14243 160 0.14254 @ 03 = 30 Psi 162 0.14268 164 0.14284 36 0.13448 166 0.14293 38 0.13508 170 0.14325 40 0.13558 175 0.14352 42 0.13628 180 0.14391 45 0.13703 184 0.14428 50 0.13833 55 0.13958 60 0.14058 Test C-2.--Sau1t Ste. Marie Clay 64 0.14148 T = -12°C @ 03 = 60 Psi Yd = 101.7 Pcf 66 0.14243 68 0.14258 w = 24.30% 70 0.14298 72 0.14343 L0 = 2.268 in. 75 0.14412 80 0.14483 do = 1.126 in. 85 0.14583 90 0.14663 D = 714.67 Psi 94 0.14718 Time Deflection @ 03 = 90 Psi (min.) (in.) 96 0.14813 @ 03 = 0 98 - 0.14838 100 0.14862 0 0.00000 102 0.14893 1 0.08348 105 0.14948 2 0.09358 110 0.15013 4 0.10248 115 0.15073 6 0.10838 120 0.15148 8 0.11238 124 0.15173 10 0.11558 12 0.11818 15 0.12128 18 0.12398 I Urn-kn 85 Table A—1.--Continued Test C-2.--Continued Time Deflection (minm) (in.) Time Deflection (min.) (in.) 226 0.16130 228 0.16148 @ 03 = 120 Psi 230 0.16155 240 0.16236 126 0.15318 244 0.16256 128 0.15348 130 0.15358 @ 03 = 60 Psi 132 0.15398 135 0.15438 247 0.16260 140 0.15493 250 0.16268 145 0.15548 252 0.16270 150 0.15593 254 0.16288 155 0.15618 256 0.16330 258 0.16340 @ 0 = 150 Psi 260 0.16353 3 265 0.16388 157 0.15763 270 0.16433 160 0.15793 274 0.16453 162 0.15813 165 0.15838 @ 03 = 30 Psi 170 0.15866 175 0.15918 276 0.16459 180 0.15955 278 0.16460 184 0.15960 280 0.16483 282 0.16505 @ G = 120 Psi 285 0.16539 3 290 0.16578 186 0.15958 295 0.16618 188 0.15958 300 0.16659 190 0.15958 304 0.16689 192 0.15958 194 0.15963 @ 03 = 0 195 0.15973 197 0.15990 306 0.16703 200 0.16025 308 0.16713 205 0.16058 310 0.16733 210 0.16093 312 0.16749 214 0.16123 315 0.16780 320 0.16838 @ 0 = 90 Psi 325 0.16863 3 330 0.16914 216 0.16121 334 0.16948 218 0.16121 220 0.16123 222 0.16125 224 0.16125 86 Table A-1.--Continued Test C-3.--Sau1t Ste. Marie Clay Time Deflection (min.) (in.) T = —12°C @ 03 = 60 Psi Yd = 102.9 Pcf , 61 0.18270 w = 24.33% 62 0.18290 65 0.18340 L0 = 2.291 in. 67 0.18380 70 0.18430 do = 1.116 in. 72 0.18465 74 0.18500 D = 782.25 Psi 76 0.18530 84 0.18665 Time Deflection 88 0.18710 (min.) (in.) 89 0.18735 @ 03 = 0 @ 03 = 90 Psi 0 0.00000 91 0.18805 1 0.10930 92 0.18810 2 0.12180 94 0.18825 4 0.13480 96 0.18850 6 0.14200 98 0.18870 8 0.14770 100 0.18890 10 0.15225 102 0.18915 12 0.15551 104 I 0.18945 14 0.15877 106 0.18970 16 0.16120 108 0.18990 18 0.16351 110 0.19010 20 0.16548 114 0.19045 24 0.16883 118 0.19080 28 0.17085 119 0.19090 @ 03 = 30 Psi @ 03 = 120 Psi 31 0.17330 121 0.19210 32 0.17378 122 0.19215 34 0.17433 124 0.19230 36 0.17515 126 0.19255 38 0.17586 128 0.19270 40 0.17659 130 0.19280 42 0.17699 132 0.19300 44 0.17749 136 0.19330 46 0.17790 138 0.19350 48 0.17855 140 0.19365 50 0.17910 145 0.19400 54 0.18030 148 0.19406 58 0.18130 149 0.19412 59 0.18155 87 Table A—l.--Continued Test C-3.--Continued Time Deflection (min.) (in.) Time Deflection (min.) (In,) 230 0.19795 232 0.19800 @ 0 = 150 Psi 234 0.19805 3 239 0.19832 151 0.19556 152 0.19560 @ 03 = 60 Psi 154 0.19575 156 0.19530 241 0.19832 158 0.19590 242 0.19832 160 0.19600 244 0.19832 162 0.19630 246 0.19832 164 0.19635 248 0.19832 166 0.19648 250 0.19832 168 0.19655 252 0.19845 170 0.19670 254 0.19860 174 0.19590 256 0.19870 178 0.19695 258 0.19885 179 0.19595 260 0.19895 264 0.19924 0 o = 120 Psi 268 0.19955 3 269 0.19960 181 0.19695 182 0.19695 @ 03 = 30 Psi 184 0.19695 186 0.19695 271 0.19968 188 0.19698 272 0.19968 190 0.19698 274 0.19968 192 0.19700 276 0.19968 194 0.19704 278 0.19980 196.5 0.19710 280 0.19995 198 0.19720 282 0.20010 200 0.19735 284 0.20020 204 0.19765 286 0.20035 208 0.19780 288 0.20050 209 0.19782 290 0.20060 294 0.20095 @ 0 = 90 Psi 298 0.20110 3 299 0.20120 211 0.19772 212 0.19772 @ 03 = 0 214 0.19772 216 0.19772 301 0.20125 218 0.19772 302 0.20125 222 0.19772 304 0.20135 224 0.19774 306 0.20155 227 0.19780 308 0.20175 228 0.19782 310 0.20195 Table A—l.--Continued 88 Test C-3.--Continued Time Deflection (min.) (in.) Time Deflection (min.) (in.) 34 0.09065 36 0.09130 312 0.20205 38 0.09180 318 0.20270 40 0.09240 320 0.20280 326 0.20310 0 = 40 Psi 328 0.20345 330 0.20370 43 0.09370 332 0.20385 44 0.09415 334 0.20400 46 0.09445 48 0.09495 50 0.09535 Test C-4.--Sault Ste. Marie Clay 52 0.09569 “"“"° 55 0.09625 T = '12 C 58 0.09674 = 102.8 Pcf * Yd @ 03 = 60 Ps1 w = 24.13% 60 0.09780 L0 = 2.29 in. 62 0.09820 64 0.09840 do = 1.123 in. 66 0.09875 68 0.09895 D = 569 Psi 69 0.09914 Time Deflection @ 0 = 80 Psi (min.) (in.) 3 70 0.09937 @ 03 = 0 72 0.09957 75 0.10080 0 0-00000 76 0.10095 2 0-05055 78 0.10125 5 0-05955 80 0.10140 10 0.07695 82 0.10190 15 0.08105 86 0.10213 18 0.08335 20 0.08445 _ - 22 0.08555 @ O3 100 P81 24 0-03555 88 0.10340 , 90 0.10375 @ 03 = 20 P31 95 0.10435 100 0.10480 25 0-03800 102 0.10505 28 0.08875 30 0.08945 32 0.09005 89 Table A—1.--Continued Test S-1.--Sand-Ice Time Deflection (min.) (in.) T = - 12°C 64 0.04144 Yd = 107.5 Pcf 66 0.04170 68 0.04204 w = 19.42% 70 0.04230 75 0.04300 Ice density (Bulk) = 0.915 gm/cm3 30 0.04360 85 0.04430 L0 = 2.26 in. 89 0.04500 60 = 1.13 in. @ 03 = 90 Psi D = 660.6 Psi 91 0.04580 92 0.04610 Time Deflection 94 0.04620 (min.) (in.) 96 0.04640 98 0.04660 @ O = 0 100 0.04680 3 105 0.04735 0 0.00000 110 0.04785 1 0.02130 115 0.04835 2 0.02280 119 0.04930 4 0.02600 6 0.02710 @ 03 = 120 Psi 8 0.02810 14 0.02960 121 0.05025 18 0.03110 124 0.05130 20 0.03140 128 0.05160 25 0.03300 130 0.05190 29 0.03410 135 0.05235 140 0.05275 @ O = 30 Psi 145 0.05320 3 149 0.05410 31 0.03490 32 0.03510 @ 03 = 150 Psi 34 0.03550 36 0.03590 151 0.05495 38 0.03640 152 0.05500 40 0.03675 154 0.05520 45 0.03770 157 0.05540 50 0.03860 160 0.05555 56 0.03960 165 0.05600 59 0.04020 170 0.05645 175 0.05675 @ 03 = 60 Psi 180 0.05680 61 0.04100 62 0.04120 90 Table A-1.--Continued Test S-2.--Sand-Ice @ 03 T = — 12°C Yd = 107.5 Pcf w = 19.32% Ice density (bulk) = 0.910 gm/cm3 L0 = 2.26 in. do = 1.13 in. @ 03 D = 764.26 Psi Time Deflection (min.) (in.) @ 03 — 0 0 0.00000 1 0.01550 2 0.01650 4 0.01870 6 0.02060 8 0.02220 @ 03 10 0.02380 12 0.02520 14 0.02650 16 0.02770 18 0.02900 20 0.03010 26 0.03310 29 0.03440 @ 03 = 30 Psi 31 0.03550 32 0.03585 @ 03 34 0.03660 36 0.03745 38 0.03810 40 0.03880 45 0.04040 50 0.04190 55 0.04340 59 0.04450 = 60 Psi 61 62 64 66 68 70 75 80 85 89 = 90 Psi 91 92 94 96 98 100 105 110 115 119 = 120 Psi 121 122 124 126 128 130 135 140 145 149 = 150 Psi 151 152 154 156 161 165 ~170 175 179 0.04540 0.04550 0.04600 0.04640 0.04675 0.04730 0.04830 0.04925 0.05040 0.05115 0.05185 0.05200 0.05230 0.05255 0.05290 0.05320 0.05400 0.05460 0.05550 0.05630 0.05715 0.05725 0.05750 0.05765 0.05790 0.05816 0.05865 0.05915 0.05955 0.06010 0.06145 0.06150 0.06160 0.06180 0.06225 0.06246 0.06288 0.06332 0.06370 91 Table A-l.--Continued Test S-3.--Sand-Ice Time Deflection (min.) (in.) T = -12°C '64 0.07315 Yd = 107.5 Pcf 66 0.07370 68 0.07425 w = 19.26% 70 0.07480 3 75 0.07616 Ice Density (bulk) = 0.907 gm/cm 80 0.07750 85 0.07870 L0 = 2.26 in. 89 0.07955 do = 1.13 in. @ 03 = 90 Psi D = 815.93 Psi 91 0.08105 92 0.08120 Time Deflection 94 0.08175 (min.) (in.) 95 0-03215 98 0.08250 @ 0 = 0 100 0.08290 3 105 0.08385 0 0.00000 110 0.08470 1 0.03950 115 0.08555 2 0.04090 119 0.08620 4 0.04310 6 0.04480 @ 03 = 120 Psi 8 0.04640 10 0.04790 121 0.08780 12 0.04830 122 0.08785 14 0.05065 124 0.08820 16 0.05195 126 0.08846 20 0.05410 128 0.08870 25 0.05665 130 0.08910 29 0.05880 135 0.08975 140 0.09030 @ o = 30 Psi 145 0.09106 3 149 0.09150 31 0.06000 32 0.06050 @ 03 = 150 Psi 34 0.06140 36 0.06225 151 0.09315 38 0.06315 152 0.09320 40 0.06395 154 0.09325 45 0.06595 156 0.09355 50 0.06780 158 0.09380 55 0.06955 160 0.09410 59 0.07095 165 0.09450 170 0.09510 @ 03 = 60 Psi 175 0.09560 179 0.09600 61 0.07220 62 0.07240 92 Table A—1.--Continued Test S-4.--Sand-Ice Time Deflection T = -12°C @ D = 815.93 Psi 03 = 30 Psi Yd = 107.5 Pcf 66 0.05930 w = 19.36% 68 0.05995 3 70 0.06065 Ice density (bulk) = 0.912 gm/cm 72 0.06141 76 0.06277 L0 = 2.26 in. 80 0.06396 85 0.06566 do = 1.13 in. 90 0.06740 ‘ 94 0.06866 D = 764.26 Psi, then 815.93 Psi @ D = 815.93 Psi Time Deflection 03 = 60 Psi (min.) (in.) 96 0.06959 @ D = 764.26 Psi 98 0.07004 03=0 100 0.07052 105 0.07171 0 0.00000 110 0.07291 1 0.01940 115 0.07397 2 0.02160 120 0.07515 4 0.02480 125 0.07621 6 0.02740 8 0.02970 10 0.03180 Test S-5.--Sand—Ice 12 0.03350 15 0.03610 T = -10°C 20 0.03965 25 0.04270 Yd = 107.5 Pcf 30 0.04540 34 0.04740 w = 19.37% @ D = 764.26 Psi Ice density (bulk) = 0.913 gm/cm3 03 = 30 Psi L0 = 2.26 in. 36 0.04855 ‘ 38 0.04945 do = 1.13 in. 40 0.05025 ” 42 0.05100 D = 764.26 Psi 45 0.05215 50 0.05375 55 0.05530 60 0.05665 64 0.05760 93 Table A-l.--Continued Test S-5.--Continued Time Deflection (min.) (in.) Time Deflection (min.) (in.) @ 03 = 90 Psi @ O = 0 96 0.05935 3 98 0.05955 0 0.00000 100 0.05985 1 0.01120 102 0.06020 2 0.01280 105 0.06065 4 0.01550 110 0.06140 6 0.01790 115 0.06210 8 0.02010 120 0.06290 10 0.02220 124 0.06375 12 0.02445 15 0.02690 @ 03 = 120 Psi 21 0.03140 25 0.03390 126 0.06518 30 0.03670 128 0.06550 34 0.03855 130 0.06570 133 0.06600 @ O = 30 Psi 135 0.06625 3 140 0.06675 36 0.04040 145 0.06720 38 0.04110 150 0.06775 40 0.04190 154 0.06825 42 0.04255 45 0.04375 @ 03 = 150 Psi 50 0.04545 55 0.04700 156 0.06960 60 0.04850 158 0.06980 64 0.05015 160 0.06995 162 0.07010 @ O = 60 Psi 165 0.07035 3 170 0.07880 66 0.05160 175 0.07115 68 0.05195 180 0.07155 70 0.05250 185 0.07190 72 0.05285 75 0.05366 80 0.05470 85 0.05580 90 0.05675 94 0.05765 94 Table A—1.--Continued Test S-6.--Sand-Ice Time ‘ Deflection (min.) (in.) T = -14°C @ 03 = 60 Psi Yd = 107.5 Pcf 66 0.04080 w = 19.34% 68 0.04125 3 70 0.04160 Ice density (bulk) = 0.911 gm/cm 72 0.04210 75 0.04265 L0 = 2.26 in. 80 0.04360 85 0.04450 do = 1.13 in. 90 0.04535 94 0.04625 D = 764.26 Psi @ 03 = 90 Psi Time Deflection (min.) (in.) 96 0.04700 98 0.04730 @ 03 = 0 100 0.04760 102 0.04785 0 0.00000 105 0.04825 1 0.01350 110 0.04890 2 0.01460 115 0.04960 4 0.01660 120 0.05030 6 0.01830 124 0.05115 8 0.01960 10 0.02090 @ 03 = 120 Psi 12 0.02210 15 0.02360 126 0.05220 20 0.02610 128 0.05245 25 0.02810 130 0.05260 30 0.03000 135 0.05310 34 0.03150 140 0.05360 145 0.05410 @ 03 = 30 Psi 150 0.05465 154 0.05560 36 0.03250 38 0.03310 @ 03 = 150 Psi 40 0.03365 42 0.03420 156 0.05650 45 0.03505 158 0.05665 50 0.03655 160 0.05680 55 0.03760 165 0.05715 60 0.03885 170 0.05750 64 0.04000 175 0.05780 180 0.05825 185 0.05860 95 Table A—l.--Continued Test S-7.--Sand—Ice Time Deflection (min.) (in.) T = —18.1°C 70 0.03045 Yd = 107.5 Pcf 75 0.03124 . 80 0.03196 w = 19.40% 85 0.03262 3 90 0.03339 Ice density (bulk) = 0.914 gm/cm 94 0.03406 Lo = 2.26 in. @ 03 = 90 Psi do = 1.13 in. 96 0.03545 100 0.03565 D = 764.26 Psi 105 0.03620 110 0.03670 Time Deflection 115 0.03725 (min.) (in.) 120 0.03765 124 0.03815 @ 03 = 0 @ 03 = 120 Psi 0 0.00000 1 0.01290 126 0.03950 2 0.01295 128 0.03965 4 0.01315 130 0.03975 6 0.01408 135 0.04018 8 0.01479 140 0.04060 10 0.01535 145 0.04100 12 0.01585 150 0.04140 15 0.01665 154 0.04162 20 0.01815 25 0.01955 @ 03 = 150 Psi 30 0.02075 34 0.02170 156 0.04330 158 0.04335 @ 03 = 30 Psi 160 0.04342 162 0.04355 36 0.02320 165 0.04366 38 0.02330 170 0.04395 40 0.02365 175 0.04425 45 0.02460 180 0.04455 50 0.02555 185 0.04485 55 0.02635 60 0.02720 64 0.02807 @ 03 = 60 Psi 66 0.03002 68 0.03020 96 Table A-2.-5Constant Strain-Rate Test Data Test CF-1.--Sau1t Ste. Marie Clay Test CF-2.--Sau1t Ste. Marie T -12°C Clay Yd = 103.1 PCf. T = -12°C w = 24.61% yd = 102.6 Pcf LP = 2.26 in. w = 24.49% ®Ao = 0.98134 in.2 - "QC-3‘ 7 Lw = 2.26 in. o _3. . . e - 3 x 10 in./1n./m1n. A0 = 0.95390 in.2 03 - 30 P31 6 = 3 x 10-3 in./in./min. Time Deflection Load 03 = 50 Psi (min.) (in.) (lbs.) Time Deflection Load 2 8:32338 §§§j2 (min.) (in.) (lbs.) 6 8:85:38 572:5 1 0.00630 159.6 8 0.06650 601.8 2 0-01415 332.8 10 0.07775 629.2 g 3'82338 223.3 12 0.08870 651.9 8 0.06050 592.7 14 0.10115 683.9 - . 16 0.11560 711.2 1° °-07515 624.6 18 0.12880 729.5 12 0-03750 647.4 20 0.14170 756.8 14 0.10000 674.7 22 0.15490 775.1 16 0.11230 697.5 24 0.16675 788.7 18 0.12510 720.4 25 0.17350 802_4 20 0.13870 743.2 23 0.19020 820.6 22 0.15175 755.7 30 0.20245 834.3 24 0-16500 773.9 32 0.21480 848.0 25 °-17850 791.0 34 0.22660 861.7 23 0-19200 800.8 36 0.23890 875.4 30 0-20575 817.9 38 0.25080 884.5 32 0-21850 832.2 40 0 26270 893 6 34 0.23050 842.5 ' ° 36 0.24265 854.1 38 0.25490 862.9 40 0.26700 871.4 ®I‘he corrected sample area, A = 3.0. 1-8 97 Table A—2.--Continued Test CF-3.--Sault Ste. Marie Clay T = -12°C Test SF-1.--Sand-Ice Yd = 102.5 Pcf T = -12°C w = 24.23% Yd = 107.5 Pcf L = 2.26 in. w = 19.40% 2 Ao = 0.98134 in. Ice density (bulk) = 0.914 gm/cm3 s = 3 x 10"3 in./in./min. Lo = 2.26 in. 03 = 90 Psi Ao = 1 in.2 , _ -3 . . . Time Deflection Load 5 - 3 x.10 in./1n./m1n. (min.) (in.) (lbs.) 03 = 30 Psi 1 0.00530 118.5 2 0.01250 319.1 Time Deflection Load 4 0.03150 510.6 (min.) (in.) (lbs.) 6 0.04650 574.5 8 0.06035 610.9 0.5 0.00450 24.7 10 0.07415 647.4 1.0 0.00690 78.5 12 0.08800 674.8 1.5 0.00999 224.4 14 0.10150 702.1 2.0 0.01250 390.4 16 0.11565 724.9 2.5 0.01585 642.1 18 0.12950 747.7 3.0 0.01921 865.6 20 0.14350 765.9 3.5 0.02297 1071.3 22 0.15765 784.2 4.0 0.02624 1200.1 24 0.17175 802.4 4.5 0.03081 1320.2 26: 0.18575 820.6 5.0 0.03508 1393.3 28 0.19900 834.3 5.5 0.03867 1422.8 30 0.21195 848.0 6.0 0.04200 1428.6 32 0.22475 861.7 6.5 0.04539 1437.3 34 0.23805 875.4 7.0 0.04855 1444.0 36 0.25075 884.5 7.5 0.05131 1418.6 38 0.26350 898.2 8.0 0.05402 1414.9 40 0.29275 907.3 8.5 0.05630 1407.6 42 0.31925 916.4 9.0 0.05854 1404.2 9.5 0.06130 1398.5 10.0 0.06405 1398.7 10.5 0.06769 1399.9 11.0 0.07113 1396.4 11.5 0.07411 1395.2 12.0 0.07714 1400.2 12.5 0.08046 1397.9 13.0 0.08362 1397.7 98 Table A-2.--Continued Test SF-3.--Sand-Ice Test SF—3.--Sand~1ce T = -12°C T = -12°C Yd = 107.5 Pcf Yd = 107.5 Pcf w = 19.35% w = 19.42% Ice density (bulk) = 0.912 Ice density (bulk) = 0.915 gm/cm3 3 Lo = 2.26 in. gm/cm L0 = 2.26 in. A. = 1 in.2 A. = 1 in.2 8 = 3 X 10 3 in./in./min. 8 = 3 x 10 3 in./in./min. 03 = 60 Psi 03 = 90 Psi Time Deflection Load Time Deflection Load (min.) (in.) (lbs.) (min.) (in.) (lbs.) 0.5 0.00412 38.2 0.5 0.00624 42.6 1.0 0.00624 105.6 1.0 0.00742 79.4 1.5 0.00963 220.4 1.5 0.01060 210.6 2.0 0.01219 353.6 2-0 0.01334 330-5 2.5 0.01625 586.8 2.5 0.01558 466.2 3.0 0.01978 826.2 3.0 0.01831 619.1 3.5 0.02324 1017.1 3.5 0.02166 879.7 4.0 0.02525 1130.1 4.0 0.02532 1137.9 4.5 0.02972 1300.3 4.5 0.02900 1300.7 5.0 0.03542 1434.2 5.0 0.03311 1426.5 5.5 0.03838 1470.0 5.5 0.03831 1503.8 6.0 0.04091 1483.1 6.0 0.04360 1533.9 6.5 0.04419 1487.9 6.5 0.04624 1532.4 7.0 0.04688 1469.9 7.0 0.04814 1521.9 7.5 0.04988 1449.2 7.5 0.05131 1497.3 8.0 0.05246 1433.1 8.0 0.05368 1467.0 8.5 0.05707 1422.2 8.5 0.05797 1433.0 9.0 0.06066 1420.5 9.0 0.06143 1418.9 9.5 0.06471 1428.1 9.5 0.06466 1404.9 10.0 0.06848 1439.2 10.0 0.06769 1400.4 10.5 0.07183 1448.6 10.5 0.07140 1395.2 11.0 0.07479 1454.3 11.0 0.07499 1395.0 11.5 0.07877 1454.3 11.5 0.07881 1401.0 12.0 0.08200 1453.9 12.0 0.08270 1410.6 12.5 0.08744 1449.8 12.5 0.08733 1415.1 13.0 0.09226 1441.2 13.0 0.09163 1420.7 IIIIIIIIILIIIIIIIIII(III