S'fRESS EFFECT ON CREEP RATES OF A FROZEN CLAY SOIL FROM THE STANDPOINT OF RATE PROCESS THEORY Thad: for! 4:130 Degree 95 _Dh. D. MICHIGAN STATE UNWERSITY Waddah Akin 1966 THESIS 4“ -1 n LIBRARY MichiganSon U . . This is to certify that the thesis entitled STRESS EFFECT ON CREEP RATES OF A FROZEN CLAY SOIL FROM THE STANDPOINT OF RATE PROCESS THEORY presented by Waddah Akili has been accepted towards fulfillment of the requirements for Ph. D. degree in C1V11 Engineering Cr. ‘93 . \Wsh~& Major professor Date Ext” 230 .\ \0\L3<; 0-169 .. .‘R 9:. . . ABSTRACT STRESS EFFECT. ON CREEP RATES OF A FROZEN CLAY SOIL FROM THE STANDPOINT OF RATE PROCESS THEORY By Waddah Akili The effect of stress on the creep rate of a frozen clay soil has been approached in the light of the rate process theory. Experimental creep data were obtained from duplicate frozen Specimens of remolded clay crept over a range of stresses and temperatures. Stress re- duction techniques were employed to determine the stress effect on the creep rate under constant structure conditions. The rate equation of the form 6“: K sinh B6 , where é is the axial strain rate and 6 is the axial stress, was replaced by o = %- eBd for the relatively high stresses investigated. Experi- mental results show how the parameters B and K vary with the stress at the several temperatures investigated. For high stresses and a given temperature, B remains reasonably constant. For lower stresses (below the critical stress), B increases with decreasing '2 9A2 ) is attributed 1' d t . Th 't' ' B ‘ app 1e 8 ress e varia ion in (equals 3 ZkT to the change in flow volume (qAQ). The computed flow volume indicates that creep behavior is controlled at the particle and/or ice -AF/RT) contact points. The variation of the parameter K (equals to S e Waddah Akili appears to be related primarily to changes in the magnitude of the free energy of activation ( AF). An observed A F equal to about 100 k cal/mole was obtained for higher stresses (above the critical stress) at temperatures below -90C. Larger values of AF obtained at lower stresses and warmer temperatures may be fictitious. The structure term S involves stress and temperature history plus the instantaneous values of applied stress and strain. The division of creep into the damped and undamped regions by the critical stress was substantiated by test data. The estimated critical stress corresponds to a creep rate of about 164 in/in/minute. The varying stress-constant time method was applied on regular creep curves obtained concurrently with stress reduction data. The results of this method supported earlier observations regarding the separation of creep by the critical stress into the damped and undamped regions. A method is shown whereby present data may be extrapolated over a wider range of stresses and temperatures. STRESS EFFECT ON CREEP RATES OF A FROZEN CLAY SOIL FROM THE STANDPOINT OF RATE PROCESS THEORY BY Waddah Akili A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Civil Engineering 1966 ii ACKNOWLEDGEMENTS The writer wishes to express his deep appreciation to his thesis advisor, Dr. 0. B. Andersland, Associate Professor of Civil Engineering, for his help and guidance. Thanks are also due the other members of the writer's doctoral committee: Dr. L. E. Malvern, Professor of Applied Mechanics, Dr. C. P. Wells, Professor and Chairman of the Department of Mathematics, and Dr. T. H. Wu, Professor of Civil Engineering, who is presently at Ohio State University. The writer is indebted to his colleague, H. B. Dillon, for his assistance in the laboratory. Thanks go to the National Science Foundation and the Division of Engineering Research at Michigan State University for the financial assistance that made this study possible. CHAPTER TABLE OF CONTENTS I . INTRODUCTION II . REVIEW AND THEORY General Description Structure of Frozen Soils Deformation Aspects of Frozen Soils Development of the Rate Process Equation Application of the Rate Process Theory to Creep of Frozen Soils I I I . EXPERIMENTAL TECHNIQUES Stress Reduction Method Successive Stress Reductions Method Varying Stress-Constant Strain Method Varying Stress-Constant Time Method Comparison of Various Techniques I V . EXPERIMENTAL PROGRAM Soil Studied Sample Preparation Test Setup Sample Loading and Unloading V . EXPERIMENTAL RESULTS Single Stress Reduction Successive Stress Reductions Regular Creep The Effect of Stress History on the B and K Parameters V I . DIS CUSSION General The B Parameter The K Parameter V I I . SUMMARY AND CONCLUSION BIBLIOGRAPHY APPENDIX iii PAGE OHxOO‘rPh “1 NH 25 25 Z6 Z6 28 28 32 32 35 36 38 43 43 46 48 48 64 64 70 75 84 87 90 5-2 LIST OF TAB LES Index Properties of Sault St. Marie Clay Molded Moisture Contents and Average Dry Density of Soil Cakes (Sault St. Marie Clay) Summary of Creep Data on the Sault St. Marie Clay Using Single Stress Reduction (Temperature - 12°C) Summary of Creep Data on the Sault St. Marie Clay Using Successive Stress Reductions at Several Temperatures Summary of Data on the Duration of Test Method for Determination of the Free Energy of Activation Under a Creep Stress of 675 psi (Frozen Sault St. Marie Clay) iv PA GE 31 36 61 62 79 4-2 LIS T OF FIGURES Typical Creep Curves for Frozen Soils Distribution of Soil Water After Freezing in a Closed System (After Jackson and Chalmers, 1957). Energy Change of a System During the Course of a Reaction Modified Energy Map Upon Application of a Shearing Stress Distance that Flow Units Move in Direction of Strain and Distances Between Flow Units Varying Stress-Constant Strain Method Varying Stress-Constant Time Method Grain Size Distribution Curve for Sault St. Marie Clay Unfrozen Water Content - Sault St. Marie Clay (After Dillon, in preparation) Temperature Measuring Equipment Triaxial Cell and Test Specimens Schematic Diagram of the Constant Temperature Stress Reduction Setup Typical Examples of the Effect of Single Stress Reduction on Creep Rate - Sault St. Marie Clay Effect of True Stress on Creep Rate Using Single Stress Reduction — Sault St. Marie Clay PAGE 13 14 15 27 28 33 34 39 39 41 50 51 FIGURE 5-3 5—4 5-6 5-7a 5-7b 5-7c 5-7d 5-7e Typical Example of the Effect of Successive Stress Reductions on Creep Rate - Sault St. Marie Clay Effect of True Stress on Creep Rate - Sault St. Marie Clay Initial Portion of Creep Curves Stresses and Constant Temperature - Sault St. Marie Clay Creep Curves at Several Stresses and Con- stant Temperature Stress-Strain History Influence Parameters - Sample A-3 (l) Stress-Strain History Influence Parameters - Sample A-3 (10) Stress-Strain History Influence Parameters - Sample A—3 (6) Stress-Strain History Influence Parameters — Sample A—3 (l4) Stress-Strain History Influence Parameters — Sample A—3 (15) at Several on B and K on B and K on B and K on B and K on B and K Schematic Diagram Showing the Change in Strength of a Frozen Clay 5011 with Time Stress-Strain Curves Derived from Creep Tests for Selected Times Creep Rate-Stress Relationship at Constant Times (t1 = 5 min.; t2 =10 min.; t3 =15 min.) Axial Stress Versus Temperature for Selected Creep Rates Variation of B Parameter with Temperature at Constant Creep Rates vi PAGE 52 53 54 55 56 57 58 59 60 66 68 68 69 73 FIGURE 6-6 6-8 6-9 Simplified Representation of Contact Region Between Two Particles and Adjacent Ice Grains The Creep Rate Temperature Relationship at Constant Stress Creep Behavior of Frozen Sault St. Marie Clay - Evaluation of the Free Energy of Activation ( AF) at 9 Per Cent Conventional Strain Variation of Observed Free Energy of Activation with Axial Stress vii PA GE 72 81 82 83 AF AH AS viii‘ NOTATION area of flow unit in the shear plane E gel; 3 t th t It ra e eory parame er equa o ZkT a constant free energy of activation per mole the heat of activation per mole , _ -27 Planck s constant — 6. 626 x 10 ergs sec -16 Boltzmann's constant = 1. 3805 x 10 ergs/OC/mole the Specific rate of the process -AF/RT rate theory parameter equal to S e distance through which the shear stress acts in carrying the unit of flow from the initial to the final state a "transmission coefficient, " assumed to be unity a stress concentration factor gas constant = 1. 987 cal per mole per degree C a structure term, sensitive to stress history, temperature history, and the instantaneous values of stress and strain the entropy of activation per mole absolute temperature time flow volume equal to qAfl the microscopic shear strain rate 7oct € 51’ €11= €111 6 6'1. 6'2. 6'3 L\.€ A A, A; A3 CI’ 611’ 6111 C = ( (71- C7111) 61' (2' 63 Acrylic/21363 C C T Toct ix octahedral shear strain rate axial strain principal strains axial strain rate decreasing valuesof axial strain rate change in strain rate due to change in deviator stress the distance the flow unit, or activated complex, moves in the direction of flow the distance between flow units normal to the direction of flow the effective cross-sectional area of the flow unit in the direction of applied stress principal stresses principal stress difference or deviator stress decreasing order of deviator stress decrements or increments in deviator stress the critical stress which divides creep of frozen soils into damped and undamped regions applied shear stress on the flow unit octahedral shear stress CHAPTER I INTRODUCTION The phenomenon of creep has been one of the major subjects of research for a variety of materials in the past decade. Scientists and engineers alike have explored the theoretical and experimental a3pects of creep in search of a satisfactory general theory, but unfortunately no such theory has been developed as yet (Kennedy, 1963). Perhaps one source of the failure to uncover an adequate theory arises from the fact that practically all theories disregard the fact that material structure changes during creep (Dorn, 1954). During the process of search for a theory, considerable progress has been made in understanding creep behavior. Many of these advances are primarily related to crystalline materials and particularly to metals. The early work on creep was dominated by the model concepts whichare manifested in the great variety of empirical formulations. In the light of modern knowledge of crystal physics and material science, more emphasis has been placed on the microscopic aspects of creep and its constituent processes, particular- ly those that may be rate-determining. One of the theories that reduce flow processes to the molecular level is the rate process theory (Glasstone, Laidler and Eyring, 1941). Its application to a large number of materials such as ceramics, metals, rubber, asphalt, concrete and unfrozen soil has met with considerable success. (Kauzmann, 1941; Herrin and Jones, 1963; Mitchell, 1963). The theory explains macroscopic deformation in terms of the microsc0pic processes, and relates the rate of shear of a material to the applied shear stress, temperature and some basic properties of the material. The phase composition of frozen soils (solid, liquid and gaseous matter) presents problems during the deformation process. Structural changes in frozen soils during creep involve quantitative and qualitative changes. The amount of unfrozen water, the amount of ice in the frozen mass, the geometrical orientation of particles, and the mechanical properties of the ice are undergoing continuous change during creep (Tsytovich, 1963). These changes in structure complicate the creep process and hinder direct experimental analysis of conventional creep curves. Therefore, Special experimental techniques must be employed to measure the effects of stress on creep rate under conditions of constant structures. In this study the effect of stress on the creep rate of frozen soils has been approached in the light of rate process theory. Variables such as molded dry density and molded water content were excluded as much as possible. Data have been obtained using the stress reduction method. Deformation-time curves obtained con- currently with the above data were used to compare results by varying stress—constant time method. Experimental results show how the parameters in the basic rate equation vary with stress at the several temperatures used. Changes in flow volume appear to be related primarily to changes in contact area in regions of high stress concentration. An observed free energy of activation equal to 100 k cal/mole appears to remain reasonably constant in the undamped creep region at high stresses and temperatures below -9°C. Additional information was obtained on long term strength and a method whereby limited creep data may be extrapolated over a wider range of stresses and temperatures. CHAPTER II RE VIEW AND THEORY Gene ral De 3 c ription Frozen soils, like other deformable solids, exhibit time- dependent deformation under stress. The essential features of creep curves of frozen soils correspond to classical creep and may be divided into several sections representing the various stages of strain-time relation as illustrated schematically in the upper curve of Figure 2-1. Stage 1, termed primary or transient creep, represents the initial region of decreasing creep rate; Stage 2, termed secondary or quasi—viscous flow, represents the region of relatively constant creep rate; and finally, Stage 3, termed tertiary or progressive creep, represents the region of increasing creep rate leading eventually to failure. Tertiary creep may or may not take place; instead deformation may proceed at an ever decreasing rate. This depends on the magnitude of the applied stress and the temperature of the frozen medium. Creep curves of frozen soils may be divided, in general, into two categories, depending on the value of the creep stress (Vialov, 1961). If the stress does not exceed a certain limiting value, then the deformation is damped (damped creep) meaning that rate of deformation decreases 'with time until it approaches zero. Thus, Stages 2 and 3 are missing in damped creep as illustrated in the lower curve of Figure 2-1. If the applied stress does exceed the limiting value, then the deformation is undamped (undamped creep), where the de- celerating rate of deformation proceeds until a certain minimum rate is reached (depending on the magnitude of the applied stress) after which progressive flow takes place. 62 Undamped Creep Tertiary szdL 5 61 imit Prima ry Constant Tempe rature uasi- viscous (secondary creep) 6 ' l ' Creep Strain Damped Creep Time Figure 2-1. Typical Creep Curves for Frozen Soils The division of the creep process into damped and undamped, the separation of the various stages of creep, and the duration of any one stage often depends on the precision of creep observations and the duration of such observations. The creep rate in the so-called steady state region may slowly decrease if observed for long periods of time or on the contrary it may increase. How close is the creep rate in the steady state region to being a constant and the duration of the steady state depend primarily upon the applied stress (Vialov, 1961). The larger the stress, the shorter is the stage of steady state, and the faster is the transition into the tertiary stage. Change in creep rate results from weakening and strengthening processes that operate simultaneously. If the process of strengthening is greater than that of weakening, the creep rate decreases (primary); if the two processes compensate one another, deformation proceeds at approximately a constant rate (steady state); and if the process of weakening is greater, then progressive flow (tertiary creep) begins leading to failure. Structure of Frozen Soils Frozen soil is an aggregated structure made up of soil grains, ice, unfrozen water and the gaseous phase (usually air). Properties of soil particles including size, shape and mineral composition have a significant effect on the frozen structure and its strength character- istics. The degree of packing of soil grains and their geometrical arrangement prior to freezing affect appreciably the void space in the soil mass and in turn the amount of frozen water. At low temperatures some unfrozen water remains at the clay mineral surface. The relative thickness of this water film and the orientation of its molecules _ depend on the mineral type (Grim, 1953). During the process of freezing, particle reorientation takes place due to negative pore pressure’that develops during the freezing process and also due to the slight volume changes caused by freezing of the free water in the soil mass (Broms and Yao, 1964). The freezing point of the free water in the soil decreases with decreasing ave rage grain size of the soil. Ice forms in the large interstices (voids) before it forms in the minute channels within the soil mass. The ice formed is composed of many individual crystals and may be polycrystalline in nature. The distribution of moisture in the soil after freezing depends . on the direction of freezing, soil permeability and time. Tests con- ducted in a closed system by Jackson and Chalmers (1957), yielded results illustrated in Figure 2-2. Initial water content\ [Final water content Direction of Height Freezing L Water Content '- Figure 2-2. Distribution of Soil Water After'Freezing in a Closed System (After Jackson and Chalmers, 1957). Strength of the frozen soil may be considered as a function of bonding strength at particle to ice contacts, and at particle to particle contacts. The frozen mass may be thought of as a network of many contacts,where their strength and the total number of such contacts are necessarily a function of soil type, total amount of water present, temperature, and degree of packing of soil grains. Particle to particle bond depends upon the molecular forces of attraction between mineral particles, which are separated by water films, the amount of such separation and the extent of the particle surfaces (Vialov, 1963; Lambe, 1960). The soil-ice bond, which is believed to be the most important, depends upon the amount of ice, the area of contact and the temperature of the frozen soil. It is the least stable part of the bonding strength since it changes with any variation in temperature. Reduction in temperature causes an increase in the amount of frozen water and in turn an increase in the soil-ice bonds. Such a change in temperature is accompanied also by a change in the mobility of hydrogen atoms in the ice crystalline lattice upon which the quality of ice depends (Tsytovich, 1963). Temperature reduction also causes a decrease in the thickness of liquid water films absorbed by the surface of ice crystals and significantly increases their strength, thus contributing to the overall strength of the frozen mass. Deformation Aspects of Frozen Soils Frozen soils may be considered as elasto-plasto-viscous bodies based on the deformation characteristics and the constituents of the frozen media (Vialov, 1961). The presence of frozen and un- frozen water in the frozen media presents problems of phase com- position during the deformation process. Unlike other materials, frozen soils undergo drastic structural changes (ratio of frozen to unfrozen water) under the influence of stress. The dynamic equilibrium of ice and unfrozen water in frozen soils demands quantitative changes of unfrozen water and pore ice with any change of temperature and stress (Tsytovich, 1963). In other words, ice and unfrozen water strive to preserve the condition of equilibrium correSponding to a given stress and temperature. The deformational resistance of frozen structure rests in the network of bonds formed at contact points. The strength of these bonds may vary widely as explained earlier, depending primarily on the temperature, amount of water present, and clay type. When external stresses are applied, some of these bonds will fail while others remain intact. This failure is due to plastic flow and melting of ice at areas of contact, weakening and leading to eventual break-up of bonds (Vialov, 1961). After breakage of bonds, ice crystals and mineral particles tend to reorient themselves with reSpect to the stress-axis. At the same time the unfrozen water, which increases 10 upon partial melting of the ice at the contacts, migrates from highly stressed zones to zones of lower stress where it refreezes. The movement of mineral particles and ice crystals away from the initial configuration results in new contacts and the formation of new bonds. New bonds will form also upon refreezing of the melted ice. Re- crystallization of ice is accompanied by a reduction in the size of ice crystals and reorientation of such crystals into a favorable direction with the stress-axis. These latter changes occur rather slowly. Thus, deformation of frozen soils under applied stress may be envisioned as the result of breaking and forming of bonds at contact points in the aggregated structure. It may be said that at the contact level interaction of solid units (particles, ice crystals) is involved. A useful analogy can be drawn from the phenomenon of sliding friction between solid surfaces, where shearing resistance develops- by the interlocking aspe rities of the two surfaces brought together under the action of a normal force (Bowden and Tabor, 1954). Even in the case of highly polished ice surfaces, actual contact occurs over a very small area and the local stresses at the contact are sufficient to produce yielding. Therefore, if the shearing force applied at the contact equals or exceeds the shearing strength of that contact, sliding will occur and the bonds in that contact will be broken. The ratio of shearing strength to shearing stress at a contact is not a constant, but depends upon the 11 speed of sliding (Burwell and Rabinowicz, 1953). The deformation phenomenon, as viewed here, of contacts and shear forces acting at the contacts could provide a plausible explana- tion to the macroscopic aspects of deformation. However, to make use of the theoretical treatment of the rate process theory, the deformation-process in frozen soils will be envisioned as movements of atoms and molecules rather than displacement at the contact level. Development of the Rate Process Equation According to the rate process theory (Glasstone, Laidler and Eyring, 1941), the rate of a reaction in a molecular process involves an exponential dependence on the temperature of the form: -E kT Rate = Ce / (2 -1) Where C = constant E = energy supplied k = Boltzmann's constant T = absolute temperature Rate process theory requires that molecules involved in the process must form an activated complex. The formation of an activated complex can be described as a process in which atoms in the molecules involved regroup themselves giving rise to a modified form of the initial state. This new configuration of atoms, although originated within the system of the initial substance and formed from the same 12 atoms, posesses different properties: (a) Its atoms are less densely packed and their motion is more disordered. (b) The strength of the interatomic bonds of the activated complex is lower than those in the initial state. (c) The activated complex has higher energy than the initial state (Osipov, 1964). The formation of activated complexes requires energy. When this energy has been provided (either mechanically or thermally) from outside the system, the particular reaction goes to completion. A complex is regarded as being situated at the top of a free energy barrier lying between the initial and the final states. The course of a reaction may be represented by an energy map as shown in Figure 2-3. The points A and B correSpond to initial and final equilibrium states, while point C represents the maximum energy level or the so-called energy barrier. Overcoming this barrier is a necessary condition for the activated complex to be formed. In passing from A to B, the energy increases, passing through its maximum C, and then decreases passing through the second minimum at point B. The elevation .AH of point C above the level AB is termed the energy of activation or the heat of activation. 13 C no .E 3 m (L H 0 C H >‘ — .— no u o :1 £11 Course of a Reactiorn— Figure 2-3. Energy Change of a System During the COurse of a Reaction It is generally recognized that all processes proceeding at a finite rate involve the formation of activated complexes (Osipov, 1964). Flow processes reduced to the same molecular level, involve a similar movement as explained by the reaction rate theory (Glas stone, Laidler, and Eyring, 1941). Eyring's reaction rate equation of molecular processes based on the classical Maxwell-Boltzmann law of the distribution of energy in a system is: h Where k' = the specific rate of the process m = a "transmission coefficient”, assumed to be unity k = Boltzmann's constant 2 1. 3805 x 10'16 ergs/oC/mole -2 h = Planck's constant = 6. 624 x 10 ergs sec 14 AF = free energy of activation R = the universal gas constant T = the absolute temperature In the development of the theory, it is assumed that flow takes place by movements of molecules or aggregates of molecules (flow units) into vacancies (holes) in the material, or by displacements of the vacancies themselves with the material (Herrin and Jones, 1963). Since the production of such vacancies by the movement of flow units requires that an energy barrier be overcome, the absolute rate relationship (Eq. 2-2) should be applicable to the evaluation of the rate of flow in a deformable material. Equation (2—2), however, was derived for equilibrium conditions. In the case of an applied stress, Equation (2—2) must be appropriately modified. The energy added to the system due to the application of the shearing force, distorts the energy barrier. This distortion is additive on the ascending side of the energy barrier and subtractive on the descending portion as shown in Figure 2-4. Shear Stress N it) ‘x ,’ T412243 Direction of Flow I 1 Ed 8 —-- 0H m m H 8 Without shearin 8 (,2 53 force g S" CU I u) 8 '5 ’ aH \ .—a ---- With shearing E M l i/ ~ 8 We . \ uH H LA}. I l in 2 [z] Figure 2-4. Modified Energy Map upon Application of a Shearing Stress 15 I—z-—I f H4 T / A, (9—43 0 o H}, 4 O O OO Figure 2-5. Distance that Flow Units Move in Direction of Strain and Distances Between Flow Units The molecules {flow units) of the system may be arranged as shown in Figure 2-5, Where T: the applied shear stress A: the distance the flow unit or activated complex moves in the direction of flow A1 ‘ the distance between flow units normal to the direction of flow the effective cross-sectional area of the flow unit in the direction of applied stress p N >4 L» H Since the force acting on a flow unit with cross-sectional area A2A3 is TA2A3, the amount of work done in moving the unit a distance AisTlAZAy This is the work required to displace a flow unit from its initial state to its final state; i. e. , the work the flow unit must do to overcome the potential barrier. However, for a symmetrical barrier, the state of higher energy is reached when the flow unit has moved a distance A, and thus the amount of work required to sur— mount the energy barrier is TA A: 3 . After moving over the 16 peak of the barrier, it proceeds to its final state. As a result of the applied stress on the flow unit, the energy Tillz A3 2 barrier is altered by and the specific flow rate in the forward direction is given by k' exp ( TAAZA3) ZkI‘ (2-3) (a) and in the backward direction _ TAA2A3) ' ZkT (2-3) (b) k'exp( The net number of times any flow unit passes over the potential barrie r is then kl ( TAZAIEI‘A3I — exp (— (A A2A3) (2'4) ZkT The net rate of flow in the forward direction resulting from the applied shearing stress (7") is the net specific rate of movement of the flow unit; i. e. , the number of times per unit time that a flow unit moves forward over the energy barrier multiplied by the distance A traversed per movement. Multiplying this value by —1X—1 where Al is the distance between flow units normal to the direction of flow gives, by definition, the rate of flow ( T ): - AA TAX). 7 A 1" “PITAZZ‘I’WPI' 216:3) ’ ZkT A1 which may be written as (2-5) = k' sinh TA AZAB A1 7 ZkT 7 21 (2-6) 17 Since the applied stress on the flow unit is a shear stress,7is then the rate of shearing strain. Substituting equation (2-2) into (2-6) gives the shear strain rate . F I 7’: 2— kT “fir- sinh A’EfiTA3 (2—7) AlTe where the transmission coefficientlm) has been taken equal to unity. The projected area of each flow unit in the shear plane is A = A2A3, and the effective volume of the flow unit is Vf 4A2 A3 = qu: where q is a stress concentration factor. Equation (2-7) can be written as: 7: 2 L:— k_:_ {AF/RT sinh 97% Z, (2-8) I It should be stated that Vf, which is a measure of the volume of the moving unit in the direction of force, should be a measure of the volume of vacancy (hole) created by the applied force. In order for flow units to move from one position of equilibrium to another, it is necessary that space be provided into which the units can move (Fredrickson and Eyring, 1948). Thus, the two volumes can be used interchangeably since they are of the same order of magnitude. From thermodynamics, the free energy of activation ( A F) may be written as a function of temperature: AF AH - TAS (2-9) the heat of activation Where AH AS = the entropy of activation 18 It is noted when T 2 00k, AF =AH. Hence, the heat of activa- tion may be interpreted as being the energy which must be put into the system exclusive of thermal energy inherent in the system in order to bring about a reaction. However, the TAS term of the equation effec- tively represents the amount of thermal energy stored in the system due to its temperature. The free energy of activation (AF) is the amount of energy which must be added to the system to initiate a reaction. Inserting equation (2-9) in equation (2-8) gives the following expression: ° A kT --AH/RT AS/R VfT A1 h ZkT Herrin and Jones (1963) have indicated that A andll are only approximations of the order of the size of a flow unit, and it may be 21 ~ assumed that T — 1, with the result that: l 0 V 7: Eg- eAS/R e-AH/RT _ fT (2_11) Slnh ZkT Equation (2-11) may be reduced to the form: 7": 70 sinh —% (2,—12) 0 Where kT AS/R -AH/RT_ 7 h e e 7 o v and .__f__ : _l_ ZkT To 0 At constant temperatures 7 and 1' were found to be con- 0 o Stants for certain materials. Herrin and Jones (1963) have shown 19 that 70 and To are temperatureodependent terms for an asphalt mate rial. Dorn and co-workers (1954) have shown that for poly- crystalline aluminum the To term is independent of temperature and stress and appears to be independent of the structure of the metal, while the 70 term is dependent on temperature, structure and stress. . Obviously, the 70 and To terms in equation (2-12) are material dependent terms. For a given material their variation with external variables of stress and temperature can be determined experimentally. This theory is quite general regarding the nature of the unit of flow and of the energy barrier restricting flow. The unit of flow can be an atom, a single molecule or a group of many molecules. The barrier could arise directly from the repulsions between units of flow or from some more complicated mechanism depending on the internal structure of the material (Kauzmann, 1941). The development of the rate equation as expressed in equation (2—10) is based on a single molecular mechanism. However, this need not be true since in a given material different mechanisms may be ope rating simultaneously, each having its own characteristic values of AH, AS, Vf, A , and A1 (Kauzmann, 1941). 0 V 7: ZAi kT e- AHi/RT eASi/R sinh fi T (2‘13) . Al- h ZkT Where the sum is over all possible mechanisms. Usually, only one of 20 the mechanisms (i. e. , only one of the terms in equation (2—13))will account for the greater part of the observed rate, but it is possible that a single term will not give a major part of the shear rate under all conditions of stress and temperature. For example, one mechanism may account for most of the creep under low stresses, while under large stresses a different mechanism may be dominating. Each mechanism contributes something to the total observed rate under all conditions. Allied to this generalization of the simultaneous operation of many different mechanisms is the question of the interpretation of strain-hardening in terms of the present theory. This phenomenon is the result of the dependence of the constants in equation (2—13) on time and strain. Thus, hardening could result from an increase in AH or from a decrease in AS and Vf (Kauzmann, 1941). Application of Rate Process Theory to Creep of Frozen Soils One of the major difficulties encountered in the application of the theory entails the measurement of the true value of the shearing stress T, which acts on the flow unit. The value of the shearing stress T may vary greatly from one flow unit to another depending on applied stress conditions and structural aSpects of the frozen mass. It is important to note that the frozen mass is a skeletal framework of soil particles and ice or aggregated particles and ice crystals, and 21 not a continuum, so that the shearing process is not a single glide of perfect lattice planes. Since the appropriate values of T and 7'cannot be determined, the following two assumptions are made: 1. The rate process theory, equation (2-10) applies to the mean values of the microscopic shear stress 1’, and the microscopic shear rate 7 . 2. These mean values of Tand fare proportional, reSpectively, to the macroscopic octahedral shear stress ( Toot) and octahedral shear rate of deformation ( 70ct)° For triaxial loading, the principal stress difference ( 61 _ GIII) and the major principal strain €I’ are conveniently measured. Under constant volume conditions with 0/11 :GIII and €11 V2— TWII‘ 6111”“ 6‘III’ IV the octahedral shear stress is given by (oct = the octahedral shear rate of deformation is 7:)“ = V 2‘ €17 C7: ( 61 - GUI) is called the deviator stress in the nomenclature of 5 oil me chanics . For uniaxial loading 16a 2 —‘§G’and 7oct = V2€ . (jand 6 denote the applied axial stress and the axial rate of deformation respectively. Equation (2-10) can now be rewritten in terms of the measur- able quantities 6 and 6‘ as follows: 22 ' -AH RT V V 6 =V2 A— 12?— eAS/R e / sinh _2_ _£_c,’ (2-14) *1 h 3 2kT For experimental purposes and at a constant temperature, equation (2-14) has been used as follows: (Dorn, 1954) E: Ksinh B6 (2'15) Where K 2%- T and B = V}- vf 3 ZkT A kT eAS/R e-AH/RT. 1. or a more detailed version with temperature effects of the form e' AF/RT sinh 136 (2-16) é: s where S is a structure term, sensitive to stress history, temperature history, the instantaneous values of stress and strain. To obtain a detailed creep equation for frozen soils, in light of the previously developed rate equation, one must evaluate the proper terms (S, AH, AF, B, etc. ) and determine their functional dependence on the external variables, namely, the applied stress and temperature. In order to study the effect of the external variables on the rate of deformation, one must separate their effect on the structure from their effect on the controlling mechanism. Thus, the influence of stress and temperature should be examined at conditions of con- stant structure. Conditions of constant structure do not prevail throughout the process of creep. It is precisely these changes in the 23 structure that cause changes in the creep rate under constant con- ditions of stress and temperature. Most structural changes during creep of frozen soils take place during primary creep, as indicated by the rapidly decelerating creep rate over primary stage. These changes take place in a relatively short time. After the secondary stage (undamped creep) is reached the change in creep rate is comparatively small, reflecting the smaller change in structure. The rate process theory applies only to steady state flow. This restricts its application on frozen soils to secondary creep in the undamped region or to regions in the damped creep where con- stant rate of creep can be assumed over short intervals. If equation (2-16) expresses steady state flow under constant stress, then S, AF and B should be constants, while in transient creep one or more of these terms are changing. Transient creep implies that molecular processes responsible for macroscopic deformations are not occurring at a constant rate. Therefore the application of the rate theory successfully in the transient region is very doubtful. In order to isolate the effect of stress on the creep rate, the stress reduction method was employed to provide necessary creep data relating deformation mechanisms to applied stress, independent of structure. In thistype of test changes in stress are made during the test. If changes are small and rapid enough, the structure should remain constant and the effect measured will be related to the deformation mechanism. The details of this technique and other experimental methods are discussed in the next chapter. 24 CHAPTER I I I EXPERIMENTAL TECHNIQUES To examine the influence of stress on the creep rate, several techniques may be employed providing a wide spectrum of data, In order to evaluate the possible advantages and disadvantages of each method, an outline of these techniques is presented here. Stress Reduction Method This method has been used extensively by Dorn (1954) in isolating the effect of stress alone on the creep rate of polycrystalline aluminum. The method is simple. A frozen soil Specimen is precrept at a given deviator stress 6: ( 0’1 — 6111) and temperature to a selected conventional strain (change in length of Specimen divided by the initial length), at which time the stress is reduced to some lower value of the deviator stress. The instantaneous true creep rate éz (with 6 , the true strain, namely, the natural logarithm of the instantaneous length to the initial specimen's length) following reduction of the deviator stress 6 byAO’1 will then be determined. Second, third, etc. , the method is applied to duplicate samples under identical conditions except that the deviator stress is reduced by larger values, A62, A63, yielding 26 yet lower instantaneous creep rates, 6“ 3 and 6‘4. Inasmuch as pre- creep conditions are identical in each series of tests, the instantaneous structures obtained immediately following an abrupt decrease in de- viator stress must necessarily closely coincide with those that prevailed just before the deviator stress was reduced. This will indicate that the change in instantaneous creep rate Aé is due to the change in deviator stress ACalone excluding any influence of a structure factor on the change in instantaneous creep rate. This method is illustrated in Figure 5-1. Successive Stress Reductions Method This method is basically the same as the stress reduction method except that each specimen is subjected to several reductions in deviator stress. At a predetermined conventional strain, the precreep stress is reduced to a lower value of the deviator stress followed by a second reduction, a third reduction, etc. The number of reduction steps, the amount of each reduction, and the time interval between successive reductions depend on the precreep stress and test temperature. This method is illustrated in Figure 5-3. Varying Stress-Constant Strain Method Duplicate Specimens are crept under different deviator stress values, ranging from Cl to lower values of 0’2, 63, etc. where 61>Cz§63364- 27 For a selected conventional strain, the corresponding instan- taneous creep rates are 61 > éz >63 >614. The instantaneous creep rate in this type of test reflects not only the effect of applied stress, but also the effect of stress history on the substructure of the frozen sample since each specimen is subjected to a different creep stress from the start. If the variation in applied deviator stress is relatively small, identical structures may be approximated at a selected strain for a particular series of tests. This is illustrated schematically in Figure 3-1. '8 3:: C3 H-H o as 23 . <31"; .4 4 .5 as .‘3 U) 0-: o a) H 0 Time 1 Figure 3-1. Varying Stress-Constant Strain Method 28 Vamlg Stress-Constant Time Method This method is similar to the previous one except that instan- taneous creep rates are determined at a selected time instead of a selected strain. This is illustrated schematically in Figure 3-2. The objection here is that comparing test Specimens on the basis of constant elapsed time since the start of the test also means a dif- ferent structure for each specimen. 0’1 61 6 c O .3 '62 C 3,,‘3 I 3 e. E3 8 I I... o ‘ C I 64 ‘ 4 l I I . I I . ‘ Selected ' Time—/l Time Figure 3—2. Varying Stress-Constant Time Method Congaarison of Various Techniques In attempting to isolate the effect of deviator stress on creep rate of frozen soil specimens under constant temperature, the structure factor Should remain constant throughout a series of tests in order to obtain meaningful results. This may not be secured if the constant 29 time or constant strain methods are used, since a different stress history may lead to variations in the substructure. It appears that the single stress reduction method would secure an identical structure and consequently givesreliable data. However, the major objection to this method is the fact that each point for the deviator stress-creep rate relationship is obtained from a new specimen and some sample variatiors are expected. The single and successive stress reduction methods have been used extensively in this study in order to minimize structural differences. The constant strain and constant time with varying stress methods were also attempted for comparison purposes. Upon applying the stress re- duction methods, it was found that several factors should be con- sidered for proper analysis of the data. 1. It might be suspected that creep recovery immediately following the reduction in stress would interfere with accurate evaluation of the instantaneous true creep rate. However, preliminary data indicated that such recovery was not measurable for Specimens crept at high stresses, provided single reduction of the stress or successive reductions do not exceed approximately one—third of the initial stres s . 2. If the stresses are reduced too much, long times will be required to get accurate creep rates. During such 30 intervals of time, the structure may change from the instantaheous one generated during precreep treatment. Consequently, the range of stresses available for in- vestigation are limited to those that give measurable instantaneous strain rate 3 . Change in volume during loading and subsequent creep could alter sample cross-sectional area... Preliminary measurements showed no measurable volume change for the frozen samples used in this study. Hence, equi— voluminal deformation has been assumed. The extreme sensitivity of frozen soils to temperature history is known to alter the frozen water content and in turn the strength of the frozen media. Therefore, samples used in each series of tests were subjected to identical temperature history in order to eliminate the influence of history variationson the structure. It is known that negative pore pressures may exist in the unfrozen water within the frozen mass. However, recent work by Williams (1963) reveals that such negative pore pressures can only be estimated for temperatures down 0 to about -1 C. The temperature range used in this study 31 . 0 . 15 well below -1 C. Therefore, negative pore pressures are omitted and the analysis has been based on total stresses. After a number of Specimens had been tested with the single stress reduction method, the successive stress reduction method was tried. Although identical structures may not prevail in principle during all reduction steps, test data indicates comparable results to the single re- duction tests. Data reveal that if reduction steps are applied for short intervals, no significant change in the stress-creep rate relationship is observed. The main advantage in using the successive stress reduction method is the fact that more data may be obtained per sample. CHAPTER I V EXPERIMENTAL PROGRAM Soil Studied The soil selected for this study is a red clay obtained from a glacial lake deposit approximately 15 miles south of Sault St. Marie, Michigan. It is pedologically classified as Ontonogan. This soil has been used extensively in previous investigations at Michigan State University (Christensen and Wu, 1964; Wu, Loh, and Malvern, 1963). The results of identification and minerological tests on the clay soil are summarized in Table 4-1. The grain size distribution curve (Figure 4-1) shows the relative percentage of sand, silt and clay fractions according to the Unified Soil classification system. Unfrozen water contents for the temperature range used in this study are Shown in Figure 4-2. TABLE 4-1. Index Properties of Sault St. Marie Clay Properties Per Cent or Number Liquid Limit 60% Plastic Limit 24% Plasticity Index 36% Specific Gravity 2. 73 Per cent less than 2/1 60%2 Specific surface area (7042/1) 290'360M /gm Mineral Content (704%) Illite 50% Vermiculite 25% Chlorite 15% Quartz, Feldspar and Montmorillonite 10% 3 3 >30 wins .3 35mm new 05:30 GOSH—£339 03m £3.10 4th ouswwh aofimowfimmmfiv 20m @0339 I» warm 532.52 m 0 HO M £5 ncmm 2035322 5 onmm 4.39:0 ooo. mooo. Hoo. moo. Ho. . mo. H. m. A — - J1 - q d 1- J — u u q A u c - a a d d d u u - q a d I - u q a .H 8050.333 ow 35% enmecmsm .m .D C) N O 1' q .taurg wag 19d ow 8 am A m3! 34 Acowumummoum cw .GOSRH nouw20 3.2m: .um fismm I 30300 you-m3 cononmcD .Ntv 0.3th Do mug-mu 00508 A- m- m..- x- m- A- N.- m- o.- 2- St- NW- 2.- S.- 3- £- 2- m7 2.- cm- wcmEh a?! 0 $5300? X _ commune-amen .anm memento-firm I“. iqfitem Aq mag rad ‘iuaiuog 1939M uazoxjun 35 Samp_le Preparation The red clay was allowed to air dry and was processed by crushing and sieving until all material passed the 1/4 inch sieve; it was then stored in a galvanized can. To minimize initial structural differences among test specimens, duplicate samples were prepared. This was achieved by molding a large cake of soil and cutting it into a number of duplicate samples. Preparation of the 11 inch diameter by 3-1/2 inch high cake involved mixing uniformly predetermined amounts of air dry soil and distilled water. The moistened soil was left to stand for two days in a covered container to ensure an even water—content distribution. The prepared soil was placed in a compaction ring and com- pacted statically following the procedure developed by Leonards (1955). After removal from the ring, the cake was sliced into 21 pieces, each approximately 2 inches square in cross-section and 4 inches in height. The pieces were then wrapped in aluminum foil, waxed and stored in a container under water for at least a week prior to trimming. Each piece was trimmed to approximately 1. 4 inches in diameter and 2. 8 inches in height using a motorized soil lathe. Sample measurements included height, diameter, and weight. The initial water content for each sample was checked. Lucite discs were placed on each end of the sample with specially prepared friction 36 reducers. A layer of silicone grease was spread around the lucite discs. The friction reducers consisted of a perforated sheet of aluminum foil coated with a viscous mixture of silicone lubricant and graphite powder covered with a thin polyethylene sheet on top and bottom. Rubber membranes were placed over the sample with tight fitting rubber bands placed around the lucite discs thereby preventing any leakage during testing or any loss of moisture prior to testing. The maximum measured variations in water content and in dry density of individual samples within a cake were less than 0. 5% and l lb/cu ft reSpectively. Cake design was based on a 100 lb/cu ft unit dry weight and 96% degree of saturation, which meant a water content of 25. 5%. The molded water content and the average dry density for the three cakes used in this study are listed in Table 4—2. TABLE 4-2. Molded Moisture Contents and Average Dry Density of Soil Cakes (Sault St. Marie Clay) Molded Ave rage Cake No. Moisture Content Dry Density A-l 25.68% 98. O4 lb/cu ft AZ 26. 02% 98. 08 lb/cu ft A-3 26. 33% 98. O9 lb/cu ft. Test Setup Trimmed soil samples were mounted in the triaxial cell and secured in place on the pedestal of the cell. Electric tape was wrapped 37 around the lucite disc and the upper part. of the pedestal, thereby preventing any lateral movement of the mounted soil sample with respect to the cell. Prior to securing the top cap over the base, the friction reducers were checked for ease of sliding between the lucite caps and the top and bottom of the sample. If any friction was observed, friction reduce rs were replaced with new ones. To freeze the soil sample, the cell was filled quickly with the coolant, a mixture of ethylene glycol and water. Then the cell was centered in the cold temperature tank where the coolant circulates at a set temperature maintained by a low-temperature bath. The sample was cooled at least three degrees centigrade below test temperature, then warmed up to the test temperature after 12 hours and held at the test temperature for an additional 12 hours to insure temperature equilibrium. Cycling of sample temperature from cooling to warming and back to cooling alters the unit weight and weakens the sample due to expansion of water on freezing. Several samples were subjected to this cycling in temperature at the initial stage of testing due to temporary failure of temperature control of the low-temperature bath. Those samples were considered as preliminary samples and their results are not reported here. The low-temperature bath was controlled by a mercury thermostat submerged in the bath. The temperature difference 38 between the tank and the bath did not exceed half a degree centigrade. Periodic adjustment of the thermostat setting was necessary during the summer months be cause of temperature fluctuation within the room. Temperature measurements were made using copper- constantan thermocouples placed adjacent to sample, in the triaxial cell, and in the tank and connected to a Leeds and Northrup potentio- meter, Model K-Z. A bath of distilled, deionized, melting ice was used as a reference temperature. A standard cell and Leeds and Northrup Galvanometer aided in temperature measurements. The potentiometer and galvanometer were powered by a standard 6-volt battery. The temperature measuring equipment is shown in Figure 4-3. Sample temperature did not fluctuate more than i 0. 05°C after equilibrium was reached. This control was achieved because of the delay in temperature response of the coolant in the triaxial cell. The . . . . . O variation of temperature in the tank was limited to i O. 5 C. Sample Loading and Unloading After the sample temperature had reached equilibrium, an axial load was applied with an electrically powered mechanical jack. The initial load corresponding to a selected stress was predetermined, placed on a loading platform and the base of the loading platform was lowered by the jack onto the top of the stainless steel ram in the triaxial cell. The triaxial cell, lucite discs, and several tested FIGURE 4— 3. Tempe rature Measuring Equipment 39 40 samples are shown in Figure 4~4. The loading setup is shown schematically in Figure 4-5. The rate used to lower the load was 1. 0 inch per minute. The same rate was used throughout this experimental study to minimize differences in loading history. Friction problems were encountered at the early stage of this study when an aluminum triaxial cell with stainless steel ram was used. The friction was caused by different coefficients of contraction of the metals. The results were corrected afterwards by determining the amount of friction at various tempera- tures and various stress levels and subtracting the estimated friction for each incorrect test from the initial applied stress. This friction problem affected only several samples in Cake A-l. Afterwards, an allnsteel triaxial cell was used, thus minimizing any friction between the ram and the bushing due to the cold temperature. The stainless steel ram was kept lubricated with light oil to eliminate any possible friction in the ram. Normally, the ram falls slowly under its own weight prior to the application of the load. Upon sample deformation the constant compressive stress was maintained by adding dead weights to compensate for the small increase in sample cross-sectional area. A Syntron Vibro-Flow Feeder per- mitted uniform addition of lead shot at readily selected rates corresponding to the strain rate of the sample. Part of the initial dead load consisted of preselected amounts of lead shot in buckets m 1.] s.- g .—.<—— H CL (Coolant 8.. E ‘ Out :1 E a. t if Constant Bath and f— ‘— .———. Base C olant o (Ethylene Glycol and wate r)' /_/ //////////////////////// / / A 41 Electrically powe red jack Loading / Frame U ,..Dial Gaga , " (.0001") Load Th mo- couple leads to potentiometer \ \Iank \ \—'I i" ’ xial \ €211 \Fi’ozen Sample VJ \— Loading Frame Lead Shot . _ o,‘o.:oa.o Buckets .1,.;;}‘--' .038 r 2‘." ' 0": Clamped 2, Hose \- Dead Load (Lead Bricks) Figure 4-5. Lead. Shot Container Schematic Diagram of the Constant Temperature Stress Reduction Setim I.” 42 with funnel shaped bottoms connected to a 1 inch diameter clamped hose. Stress reduction was accomplished simply by removing the hose clamps permitting lead shot to drain from the buckets in a matter of seconds, or by carefully lifting an accessible part of the deadload by hand. No confining pressure was applied in this study except for abouta 6 inch head of cooling liquid on all samples. Sample deformation was measured relative to the top cap of the cell, using a 0. 0001 inch per division dial gage. From the instant the creep load was applied, axial deformation was recorded at thirty seconds, one minute, one and one-half mini: es, two minutes, etc. The time interval between readings was varied according to the amount of deformation. Readings were taken in short time intervals prior to stress reduction and immediately afterwards, permitting accurate determination of the creep rate upon partial unloading. The length of the creep tests conducted in this study varied from about one hour to more than a week depending on the stress level, the stress history of the specimen, and the test objective. CHAPTER V EXPERIMENTAL RESULTS Single Stress Reduction Two typical examples of the single stress reduction technique are shown in Figure 5—1. Each specimen was precrept under constant stress to a conventional strain of 11 per cent at an axial stress equal to 675 psi. This stress was reduced to 625 psi and 600 psi, respec- tively, and the instantaneous true creep rates before and after stress reductions were determined as shown in Figure 5-1. Although diffi- culties were anticipated in determining the instantaneous creep rates after reducing the stress, all of the creep curves using stress re- duction exhibited good straight lines immediately following reduction ,of the stress. A summary of creep data obtained for -12°C using this technique is given in Table 5-1 with basic creep data given in Table I and II of the Appendix. Creep test results have been divided into several series, as shown in Table 5-1, depending on the creep stress and strain. These results are shown in Figure 5-2, where axial stress is plotted against logarithm of the instantaneous creep rate for each sample. The dependence of the true instantaneous creep rate on the true instantaneous stress for the structure developed in each series of tests is expressed by an equation of the form 44 é: k*eBG (5-1) 2. 303 where k*is a constant and is the slope of the line for each test. Equation (5-1) is equivalent to equation (2-15) for the high stress range to which this study was limited. Equation (2-15) may be written as follows: €=KsinhBCf=K = 2 (5-2) or (2-15) eBG_ e-BC.’ K BC; ‘2" e since e is negligible. Series (1), (Z) and (3) shown in Figure 5-2 were conducted at 11 per cent conventional strain in the secondary creep region, while series (4) and (5) were conducted at 9 per cent conventional strain which corresponds to the beginning of secondary creep. Series (6) and (7) were conducted in the primary region of creep at 6 per cent conventional strain. In order to answer some questions regarding the effect of structural changes on the parameters B and K, as expressed in equation (5-2), the following observations are made from Figure 5—2 and Table 5-1. 1. Series (1), (2), and (3), conducted at a conventional strain of 11 per cent and varying precreep stress, indicate that B is almost independent of the precreep stress in the range from 525 to 675 psi, while the K term decreases very slightly with smaller initial stresses. This does not mean 45 that B would remain constant for precreep stresses under 525 psi. This is discussed later in the chapter. Series (1), (5) and (6) conducted at a stress of 675 psi and varying precreep strains (6 per cent, 9 per cent, 11 per cent) show that the B term is the same for the 9 and 11 per cent strain and is less for the 6 per cent strain. This indicates that the 510pe of the stress versus logarithm of strain rate relationship decreases with increasing precreep strain until the precreep strain reaches secondary creep where the slope remains almost constant. Little change during secondary creep is indicative of little change in structure. The K term is found to be more structure- sensitive, decreasing with increasing precreep strains even during secondary creep. In order to ascertain whether low precreep stresses in- fluence B and K, three single reduction tests were conducted at varied precreep stresses and strains (Samples A—3 (1), A-3 (2), A-3 (10)). Data are tabulated in Table 5-1 and plotted in Figure 5-4. These three tests indicate that B and K have changed considerably from their values in the previous range of high precreep stresses. The changes are an increase in B and a decrease in K. Similar and more explicit data in the low stress range obtained using 46 the successive stress reduction method, confirmed that B increases while K decreases with decreasing precreep stress. Successive Stres s Reductions A typical example using several stress reductions on a frozen sample of Sault St. Marie Clay is shown in Figure 5-3. The sample was crept under an axial stress of 675 psi to a conventional strain of 9 per cent. Stress reductions of 40 psi, 37 psi, and 36 psi were made at 9 per cent, 11 per cent, and 13 per cent conventional strains, respectively. Although precreep conditions had changed slightly at each stress reduction, comparable results to the previous technique were obtained. This method gives more information per sample and minimizes sampling variations because the same sample is used for several stress reductions. Test results employing this method are summarized in Table 5-2, and basic creep data given in Table III of the Appendix. A plot of axial stress versus logarithm of the instantaneous creep rate for each sample is shown in Figure 5-4. Successive stress reductions tests were conducted at several temperatures ranging from -3°C to -18°c. Table 5—2 and Figure 5-4 show the variation in B and K with decreasing stresses at several temperatures. 47 The change in B with temperature change reflects possibly the influence of temperature on the structure. The B parameter increases with inc reas ing tempe rature s . The following observations are made regarding the results plotted in Figure 5-4: 10 Tests conducted at -12°C indicate that B is nearly a con- stant above a certain stress level (500 psi). Below this stress level B increases with lower stresses, while K decreases. This same behavior occurs at -15°C and -18°C as shown in Figure 5-4. Thus, the change in B and K suggests a logarithm of creep rate ver sus stress curve that begins as a straight line and changes with de- creasing applied stress to a flat curve, such that B equals 2. 303 times the reciprocal of the slope and K equals the intercept of the tangent at zero stress. The straight line portion seems to disappear at temperatures warmer than .900. Since the plot of stress versus logarithm of creep rate does not show clearly the change in the magnitude of the B term, the following equation has been used to compute B: B = 1n %/ A61 (5-3) 48 where 61 and 62 are the instantaneous creep rates determined before and after stress reduction and A01 is the amount of stress decrease. These values are listed in Table 5-1 and 5-2. 3. The dashed lines in Figure 5-4 correspond to the change in creep rate under constant stress. This is observed mainly in the low stress region (damped creep) and is apparently due to strain-hardening. Regular Creep These data were obtained concurrently with the data of stress reductions at constant temperature (~120C) and several stress levels. Figure 5-5 shows the time—strain relationship during the initial stage of creep, while Figure 5-6 shows the same curves over a period of 200 minutes. Time zero begins at no load. Full load is reached be- tween 1-1/2 to 2 minutes. 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W. M ( ( O .m n d )u )u U G 0 l0\ 3 I. Q N % % I 3 _ ( ( l‘ s . A 883300: .88 8.38:; CHAPTER V I DISCUSSION General The numerical creep results presented in the preceding chapter show general characteristics typical of a frozen clay soil. Interpretations that follow include sections on the B parameter and the K parameter. The unfrozen water content has a significant effect on the stress versus creep rate relationship. This is indicated by the changing shape of stress versus logarithm of creep rate curves at various temperatures as shown in Figure 5-4. The straight line portion of the curve exhibited at low temperatures (42°C, -15°C and -l8oC) and higher stresses disappears at higher temperatures beginning at -9OC. Curves tend to get flatter at warmer temperatures. The plausible explanation to this change in shape is the appreciable increase in unfrozen water content for temperatures warmer than -9°C as indicated in Figure 4-2. This increase in unfrozen water alters the frozen soil structure and in turn changes the bonding strength at the particle contacts. Below -90C, the amount of un- frbzen water changes little with change in temperature (see Figure 4-2); thus, it has a less significant effect on the frozen structure. At low stresses, strengthening (or strain—hardening) 65 mechanisms control the creep process, leading to constantly decreasing rates (damped creep) while at high stresses, weakening mechanisms dominate creep, leading to eventual increase in the creep rate and sub- sequent failure. Damped creep begins when applied stress falls below a limiting stress (critical stress). This is indicated by the definite deviation from the straight line portion in the logarithm of creep rate versus stress relationship shown in Figure 5-4, which corresponds approximately to a creep rate of 10-4 in/in/min. Although such a deviation is not evident for higher temperatures, the stress correspond- ing to 10-4in/in/min. has been assumed to be the critical stress. A plot of estimated critical stresses, for the temperature range investi- gated in this work, is shown in Figure 6-4. It appears that the critical stress is a measure of the limiting long-term strength that frozen soils exhibit under an applied stress. During undamped creep, the strength of the frozen sample is gradually exhausted until it becomes equal to or exceeded by the applied stress. At this point progressiwe flow begins leading to eventual sample failure. This is shown schematically in Figure 6-1 where (R) denotes the strength of the sample corresponding to a given time since the applica— tion of the creep stress. The critical stress (Ole) or its equivalent, the limiting long-term strength, divides creep of frozen soils into two regions, damped and undamped creep. For a given creep stress (71, time t1 is required before the resistance of the frozen sample is 66 completely exhausted permitting progressive flow to take place. For a creep stress 0’2 time t2 is required before the progressive stage begins, etc. If the applied stress falls below the critical stress, sample resistance is greater than applied stress at all times and progressive creep never occurs. a, R (D 3 c’ a) 1 Undamped 'U a) z: 62 0.. . 2% \ Damped 6c t1 t2 Time Figure 6-1. Schematic Diagram Showing the Change in Strength of a Frozen Clay Soil with Time ' Sample. resistance during the creep process is the net result of the strengthening and weakening mechanisms that proceed si- multaneously. The strength of the frozen structure is attributed to the bonds between contacts. Such contacts may be particle to particle, particle to ice, or ice to ice contact. Upon application of a stress, these bonds get weaker causing partial or total break-up of bonds. This may be accompanied by pressure melting and refreezing of ice grains within the soil pores. New bonds may form if creep proceeds at a slow rate. The shearing strength at the contact may vary widely 67 from contact to contact. Such variation would depend on the area of contact and the orientation of the contact surface with respect to the direction of applied stress. The significance of the critical stress and its effect on creep strain and creep rate is observed by comparing the various creep curves in Figure 5~5 and 5-6. At selected times the values of the true strains associated with curves (1) and (2) are much larger than those of (4) and (5). Stress-strain curves derived from these creep curves are plotted in Figure 6-2 using times (t = 5 min. , 10 min. , etc.) A definite break in the stress-strain curves is observed between the two stages of creep, damped and undamped. Tests (4) and (5) fall below the so-called critical stress for this temperature, while (1) and (2) are above the critical stress. Critical stress for the ~12°C tempera- ture is estimated to be in the neighborhood of 500 psi. A plot of the stress versus logarithm of creep rates at various time intervals, as shown in Figure 6-3, indicates a possible straight line relationship among creep rates (1), (2) and (3) and another line with lesser slope for (4) and (5). An appreciable change in the creep rate between the two straight lines is observed around 500 psi. The ultimate strength, shown in Figure 6-4, was determined at several temperatures from samples subjected to stresses high enough so that frozen samples did not support the load long enough for actual strain measurements. Failure took place shortly after load 68 t = 5 min. t =10 min. 700‘ t = 15 rain. t = 25 min. 8. 600i a; m o 3 U) '3‘, . ~52. 500- <1 Temperature = -12°C 4008 / T I ' l r T l l I I 1 I 1 Z 3 r1- 5 6 7 8 9 10 ll 12 True Strain, % Figure 6-2. Stress-Strain Curves Derived from Creep Tests for Selected Times - Sault St. Marie Clay 700- min t = 5 niin. 3. 6008 a? U) o i: U) Q g 500. 4; Temperature = -12°C 400w I l lllllllll 111113 10'4 5 x10.4 10"3 5 x10- Creep Rate, in/in/min. Figure 6-3. Creep Rate-Stress Relationship at Constant Times (t1 = 5 min. ; t2 = 10 min.; t3 = 15 min.) - Sault St. Marie Clay >30 033% .5 35.6w I 83mm @6030 veaumfimm new cupuwhomfiofi mfimuo> mmmbw H.334 .v- c undmfim 9 Do .vHSumuvamH. 6 2 .. S- «87 mm- «A- mT M..- 2. OT @- w- h: on w. v- m: .7 _ _ _ _ _ _ _ _ L _ _ _ _ _ _ . _ Dog I com I com I 00% 8.8th V 1533330 m. wosmficmm I 38 w my 1 o a s I coon: 0.08 u .EEEHCE one )x 4 .m. muoM .EEEHCE mnoaee I cow . u .EE\£\GM 0H2 0 S 3- 8». during): Iofi )\ 4 m “ 8 883 ‘ ‘u‘ (Lumcouum QHNESHD .Gflbfiuicfl Mun: x m x/\ a ‘ ”.mmmmmflm 8-. ‘ - 888 a r.“ w. .m whammh Ghana 6.qu . H _ 3 m: mummy 23.50.83 no woman 850nm? X ooofi 70 application (3—5 min. ) and during the formation of a localized failure surface making an acute angle ranging from 45 to 60 degrees with the base of the sample. Using data presented in Figure 5-4, applied stress versus temperature was plotted at creep rates ranging from 5 x 163 in/in/min. to 10'6 in/in/min. as shown in Figure 6-4. This permitted a straight- line plot except for slight curvature at higher temperatures for each creep rate. The curved portion starts around -90C, where appreciable changes in unfrozen water content begin to occur with increasing temperature. The $10pes of the straight portions of these curves de- crease with decreasing creep rates. Thus, Figure 6-4 presents a complete picture of data obtained by the stress reduction method per- mitting a reasonable estimation of creep rates as a function of tem- perature and axial stress. The B Parameter Data presented in Chapter V show that the B parameter is not constant over the entire range of stresses and temperatures investi- gated in this study. The parameter B appears reasonably constant for a given temperature at stresses that fall in the undamped region. Below the critical stress B increases with decreasing applied stress as shown by the changing slope in Figure 5-4. The computed variation in B at a constant temperature is listed in Tables 5-1 and 5-2. 71 The variation is of the order of 200 to 300%. The increase in the B parameter due to stress decrements could be attributed to the change in the mechanism of deformation, as the creep process shifts from a steady-state type mechamism to pos - sibly different mechanism (or mechanisms) in the damped region of creep. This is accounted for in the rate process theory which assumes a constant B at a constant temperature if the same mechanism of deformation remains operative. In the basic theory, the B term is a measure of the theoretical Vi 2i. flow volume qAI since B = The computed flow volume for 3 ZkT frozen Sault St. Marie clay investigated in this study is roughly of the o3 - order of magnitude of 105 to 106 A (1!? = 10 8 cm.) Flow volumes 0 between 103 to 104 A3 exist in steel and glass. Flow volume of 5 5 03 . asphalt ranges from 2 x 10 to 6 x 10 A (Herrin and Jones, 1963). For comparison, a soil particle of 0. 001 mm in diameter, a typical particle size in the Sault St. Marie clay, has a volume equal to 12 [p3 . . . . 0. 52 x 10 . This would tend to indicate that the flow volume in question does not involve entire soil particles but rather contact areas between individual soil particles orice grains and soil particles. The change in flow volume at a constant temperature and varied stress would then be explained in terms of the change in contact area. If flow units involve molecules distributed along the contacts throughout the frozen mass, then a change in contact area would change the number 72 of these molecules per contact. Changes in contact area due to stress . increase may be attributed to glide of soil particles at the contact or rotation of such particles with resPe ct to initial position or both. The B value also increases with increasing temperature. This is illustrated in Figure 6-5 where B is plotted against temperature for constant creep rates. Volume of flow units of most metals tend to in- crease slightly with temperature (Kauzmann, 1941). In the case of frozen soils, an increase in temperature results in increase of the unfrozen water accompanied with a change in the nature and area of contact. The increase in contact area with increasing temperature could be explained in terms of the interfacial energies at the contact. Figure 6-6 shows a simplified representation of a contact between two particles and adjacent ice grains. Soil Particle , Increase in - I “‘3 /Contact area I \ I .1 T _ 1C6 Unfrozen wate at tempe ratur T2 -. Unfrozen water at temperature Tl Soil Particle T2;Tl Figure 6-6. Simplified Representation of Contact Region Between Two Particles and Adjacent Ice Grains 73 330 322 .3 :38 mound 8866.80 “83.38.8300 no 6559869359 3333 kuogmudnm m .80 8833.23, 55.3.5 .83 x m r NM : A: v m . m. _ _ E33583): mica \( e .a35\¢3\c3 muofi x m)‘ m. .ECQGQGM v.8: 2 o .Gmgifiifivuofi x m 2 1T .CMEEHQGM mic.— ..( Q “a 4.1m 0.8:me 98.8w 3ND _|_n «V F .88 9388.8 H L ‘ sings; admal Do 74 At temperature T the re is a definite configuration of the 1’ water layer between soil particles and adjacent ice. At a temperature T2 3 T1, the interfacial energy decreases moving the ice water inter- face to the outer region, thus increasing the area of contact involved in resisting deformation between soil particles. It should be noted that the increase in unfrozen water with increase in temperature is accompanied with decrease in the strength of ice crystals (Tsytovich, 1963). This indicates that although contact area may increase due to increase in temperature, the bonding strength due to ice cementation decreases simultaneously. It appears that the flow volume is restricted to that portion of the structure lying between contacts where contacts between individual particles or ice to soil particles would be involved. Thus, the flow units in question are most likely the water molecules held least tightly to the mineral surface. In other words, the water molecules (in liquid phase) farthest from the mineral surface are the most mobile. The study of the effect of stress-strain history on the B parameter as shown in Figure 5~7a through 5-7e indicates strongly that B remains nearly the same at the same stress level irrespective of the stress—strain history. This behavior is in agreement with the general interpretation of B just presented. 75 The K Pa ramete r It has been shown in Chapter V that K of equation (5-2) is not a constant for the range of stresses and temperatures investigated in this study. K decreases with: (a) Decreasing stresses (b) Increasing strains, and, (c) Increasing temperatures as shown in Figure 5-2 and 5-4. Figure 5-7a through 5-7e show that K is a history dependent parameter, unlike the B term which appears to be history independent. The parameter K may be written in an explicit form to include the energy temperature term as follows: (6-1) where S is a structure term, sensitive to stress history, temperature history, and the instantaneous values of stress and strain. The free energy of activation AF was defined in Chapter II . A change in K may be attributed to a change in S, AF or both. According to the rate process theory (equation 2-14) the S term is equivalent to film W- and since the change in T is relatively small in this 1 0 0 study (270. 3 K - 2.55. 3 K), the S term would be essentially constant zzl for the temperature range investigated if T equals unity. This is 1 true only if the rate determining process or processes remain un- changed. This supports the idea that any change in the parameter K 76 is due primarily to a change in AF. According to equation (2-16) and for the relatively high stress range investigated, the creep rate temperature relationship maybe written as follows: ° 1 me = lnS+ BC- Afil(_T)-1n2 (6-2) If S, B, andC are constants, then a plot of logarithm 6‘ versus TIT— should be a straight line with slope 2%. Equation (6-2) is applied to part of the results presented in Figure 5-4 and 6—4. Figure 6-7 shows the logarithm of creep rate versus the reciprocal of temperature for a range of stresses (800 psi - 400 psi). In the high stress range, where data was derived from Figure 5-4, logarithm of creep rates versus -TL are reasonably parallel lines. In the lower range of stress, where data was derived from Figure 6-4, the slape of the lines increases with decreasing stress. According to equation (6-2) the slope of these lines is a measure of AF since R is the gas constant. The value of AF in the high stress range (800 psi - 600 psi) is approximately 100 k cal/mole. It should be pointed out that B is a function of temperature and stress, asflshown in Figures 5-4 and 6-5. HovVever, its variation is rather small in the region below -9°C at high stresses, such that B may be considered a constant. In addition to this, there is some question whether the S term would remain constant over the entire range, since the controlling me chamism (or mechanisms) of 77 deformation are known to change with decreasing stresses. In order to supplement the stress versus free energy of activation results obtained by the stress reduction technique, several regular creep tests were performed under presumably constant structure conditions. Identical frozen samples were crept under a stress of 675 psi to a conventional strain of 9. 0% for temperatures of -lZ°C, -150C and -l8°C. The temperature range investigated cor- responds to the range where changes in unfrozen water are small as indicated in Figure (4-2). The assumption of a constant B is not too far off for the applied stress and temperature range chosen as shown by Figure (5-2) and (5-4). Thus the use of identical samples crept under constant stress with identical stress history, compared at constant strain and almost identical unfrozen water content justifies the assumption of a constant S. It appears that all terms in equation (6-2) should be constants except T and é . Figure (6-8) shows the straight line relationship between lné and 7—11;- , where T is determined on the absolute scale. From the slope of the straight line AF can be evaluated, thus AF = slope x Z. 303 x R Where R = l. 987 cal per mole per degree centigrade The estimated AF is 112 k cal/mole. Another approach for evaluating the free energy of activation 78 involving duration of test is presented below (Duorn, 1954). This approach is based on the assumption that creep curves for the same stress and different temperatures, when plotted as a function of the logarithm of the time under test, are identical except for parallel displacement along the time axis. Consequently, the same total creep strains are obtained for identical values of ln t + Va) (83) where t is the duration of the test and Wis some function of the tem- perature T. But, since creep is a thermally activated process, the function Wu“) might be replaced by — AF/RT, where AF is the free energy of activation and R is the gas constant. Under such an assumption, the total creep strain, 6‘ , would be given by the functional relationship. e. AFlRT) , (j: constant (6-4) 6‘ = f (t In this event, the free energy of activation for creep of frozen soils could be determined from two creep tests conducted under the same stress at two different temperatures. If the time to reach the same strains at temperatures T1 and T2 are t1 and t2 reSpectively, e- AF/RTl e- AF/RTZ (6_5) t1 13.2 and AF can be evaluated. The data employed in the previous method of 1n 6 versus 711-.— are used here for comparison purposes. For example, when t = 11 min. at 42°C and t = 127 min. at -15°c 1 l _1_1_ = em” R_T1 '—T2) 1 7 11 1 1 AF —— = AF ——-__ - __ In 127 (RTl RTZ) R A In .08661 = — —R—F (4.445.:10‘5) AF : 1. 06243 x 2.23026 x 105 R 1.445 and AF = l.987x.55035x105 = 109. 4 k cal/mole. 79 ( '3 ) 6. 749 x104— Similarly, the other two values of AF are determined. Results of this method are shown in Table (6-1). TABLE 6-1. Summary of Data on the Duration of Test Method for Dete rmination of the Free Energy of Activation Under a Creep Stress of 675 psi (Frozen Sault St. Marie Clay) Sample Test Average Time to Reach No. Temperature 9% Conventional Strain F in k cal/mole A-2(6) (l) -12°C 11 min. from(l)&(2) 109.4 A-Z (7) A—3(13) (2) -15°c 127 min. from(2) at (3) 83. o A-3(15) (3) -18°C 845 min. from(3) & (1) 96. 0 Average = 96. 33 The values of AF obtained at 675 psi by the logarithmic plot of creep rate versus 1;- , along with the duration of test method, agree 80 well with results presented in Figure 6-7 for a comparable stress. Figure 6-9 shows the observed free energy of activation versus axial stress for the range investigated. Plots similar to Figure 6-9 have been shown for a variety of metals where the free energy of activation increases with decreasing applied stress (Osipov, 1964). With increasing stresses the observed values tend to reach a limiting AF, which is considered as a minimum AF for creep. It may be stated here that the so-called minimum A F for frozen Sault St. Marie clay is of the order of 100 k cal/mole. Results obtained by Dillon (in preparation) indicate an observed AF from 90-100 k cal/mole for the same stress and temperature range investigated in this study. The observed AF may be due to single mechanism or several mechanisms operating simultaneously. If the mechanisms are operating in series (i. e. , the operation of one depends on the opera- tion of the others), the slowest mechanism is controlling; if they are in parallel, the fastest will be controlling. The particular mechanism (or mecha-niSms) which is controlling will depend on stress and temperature. Accordingly, for mechanisms in parallel, the strain rate may be given as follows: (Conrad, 1961). 6‘: 51 e- AFl/RT e.AF2/RT + ---- +52 where the observed AF : AFl + AFZ + ---- Creep Rate at 9 Per Cent Conventional Strain, in/in/min. 10 10’3 H ‘3‘. as 10 IW‘II l 82 AF = 112 k cal/mole Axial Stress = 675 psi 0 ° "115 C -18°C J_ 3.333 3. 64 3.335 3. s6 3.'87 3.T88 3.189 3.'90 3.'91 ’ 1000 T . Figure 6-8. Creep Behavior of Frozen Sault St. Marie Clay - Evaluation of the Free Energy of Activation (AF) at 9 Per Cent Conventional Strain 83 >30 3.8.62 um 3.9mm monouh mmouum H.383. £33 230363.304 mo >mu mam oonh po>uom£0 00 £032.83, 3mm . m m 0.3m 333. com cow 00¢ com 00* com _ _ _ _ _ ._ $me woumfiommnuxmv >10 oudwfim Eouh 2Q 366.80 Magmomv wno 6.8:me Eouh 2 . Acofiofipom mmvuumv 3.10 madman.“ Eouhxix 6 .010 6.35th com - _ 2: I on: I com r oom anuI/[BD )1 ‘JV panasqo CHAPTER V I I SUMMARY AND CONCLUSION . Creep behavior of frozen Sault St. Marie clay has been in- vestigated over a range of stress and temperature. . Duplicate frozen samples at constant initial density and moisture content, minimized initial structural differences during creep. Stress reduction was applied in the steady-state region of creep and where changes in creep rate were relatively small. This technique permits the measurement of stress effect on creep rate under conditions of constant structure. The functional dependence of creep rate on applied stress has been approached from the point of view of the rate process theory. The rate process equation, in the abbreviated form of é = K sinh B6 , has been applied to the experimental data in a range of high stress where it is approximated by 6": a}: e36 . The parameters B and K were determined from the creep rate 6: (in/in/min. ), and the applied stress (7 (psi). Figures 5-2 and 5-4 show the applied axial stress versus logarithm of creep rate over the range of stress and temperature investigated. Experimental results show that B and K change with applied stress and temperature. The parameter B remains almost constant in the undamped creep region and increases with decreasing stresses 85 in the damped region. It increases with increasing temperatures, and seems to be independent of the stress history and depends only on the applied stress. Results indicate that K decreases with de— creasing stresses, increasing strains, and increasing temperatures. The parameter K is also history dependent. According to the theory, the change in B corresponds to the change in the flow volume. This can be interpreted in terms of the change in the area of contact corresponding to changes in applied ; stress and temperature. The K parameter contains in it the free energy of activation, and a structure factor. The decrease in K at presumably constant conditions of structure is attributed tothe increase in the energy of activation. An observed free energy of activation equal to 100 k cal/mole was determined for the undamped region in the relatively low temperature region (below --9°C). The separation of the two regions of creep (damped and undamped) by the critical stress was substantiated by creep data over a range of temperature (Figure 6-4). Critical stress cor- responds to a creep rate of about 10“4 in/in/minute. It appears that critical stress is the long term strength that develops during the deformation process (Vialov, 1961). It is the net result of the strengthening and weakening mechanisms that ope rate during creep. At stresses below critical, the bond strength at the contact level increases with deformation. At stresses above critical, the bond 86 strength decreases with deformation leading to eventual break up of the bond. The presentation of the data in the form shown in Figure 6-4 permits prediction of creep rates under known creep stress and temperature. The straight line relationship at constant creep rates (Figure 6-4) below -9OC, permits extrapolation of present data over a wider range of stress and temperature. The creep behavior of frozen Sault St. Marie clay seems to be explained by the theoretical considerations suggested by the rate process theory. The theory appears to be quite applicable in the steady state region of creep at low temperatures. BIBLIOGRAPHY Bowden, F. P. and Tabor, D. Friction and Lubrication of Solids, Clarendon Press, Oxford, 1954. Broms, B. B. , and Yao, L. Y. C. "Shearing Strength of a Soil After Freezing and Thawing, " Journal of Soil Mechanics and Foundation Division, ASCE, vol. 90, no. SM 4, July, 1964. Burwell, J. T. and Rabinowicz, E. ”The Nature of the Coefficient of Friction, " Journal of Applied Physics, vol. 24, no. 2, 1953, pp. 136—139. Christensen, R. W. and Wu, T. H. "Analysis of Clay Deformation as a Rate Process, " Journal of Soil Mechanics and Foundation Division, ASCE, vol. 90, no. SM 6, Nov., 1964. Conrad, H. "An Investigation of the Rate Controlling Mechanism for Plastic Flow of Copper Crystals at 90° and 1700K, " Acta Metallurgica, vol. 6, 1958. Conrad, H. "Experimental Evaluation of Creep and Stress Rupture, " Chapter 8, Mechanical Behavior of Materials at Elevated Temperatures, Ed. by J. E. Dorn, McGraw-Hill Book Company, Inc., New York, 1961, pp. 149. Dillon, H. B. "Temperature Effect on Creep Rates of a Frozen Clay Soil, " Unpublished Ph. D. Thesis, Michigan State University. (In preparation) Dorn, J. E. "The Spectrum of Activation Energies for Creep, " Creep and Recovery, The American Society of Metals, Cleveland, Ohio, 1957, pp. 255-283. Dorn, J. E. "Some Fundamental Experiments on High Temperature Creep, " Journal of Mechanics and Physics of Solids, vol. 3, 1954, pp. 85-116. Feltham, P. "The Plastic Flow of Iron and Plain Carbon Steels Above the A3-Point, " Proc. Physical Society of London, Section B, vol. 66, 1953. 88 Fredrickson, J. W. , and Eyring, H. "Statistical Rate Theory of Metals, " Bulletin of the University of Utah, Bulletin no. 40 of the Utah Engineering Experiment Station, 1948. Glasstone, S., Laidler, K. J. , and Eyring, H. The Theory of Rate Processes, McGraw-Hill Book Company, Inc. , New York, 1941. Glen, J. W. "The Creep of Polycrystalline Ice,” Proc. Royal Society of London, Ser. A, 228, 1955, pp. 519-538. Grim, R. E. , Clay Mineralogy, McGraw-Hill Book Company, Inc. , New York, 1953. Herrin, M. , and Jones, G. E. "The Behavior of Bituminous Materials from the Viewpoint of the Absolute Rate Theory, " Proc. Association of Asphalt Paving Technologist, vol. 32, 1963, pp. 82-101. 3 Jackson, K. A. , and Chalmers, B. "Study of Ice Formation in Soils, " (Arctic Construction and Frost Effects Laboratory, for office of the Chief of Engineers, Airfields Branch, Engineering Division, Military Construction, Technical Report No. 65, Nov, 1957.) U. 8. Army Corps of Engineers, Boston, 1957. Jellinek, H. H. G. , and Brill, R. ”Viscoelastic Properties of Ice, " Journal of Applied Physics, vol. 27, no. 10, 1959, pp. 1198-1209. Kauzmann, W. "Flow of Solid Metals from the Standpoint of the Chemical-Rate Theory, " Trans. American Institute of Mining and Metallurgical Engr. , vol. 143, pp. 57-83, 1941. Kennedy, A. J. Processes of Creep and Fatigue in Metals, John Wiley and Sons, Inc. , New York, 1963. Lambe, T. W. "A Mechanistic Picture of Shear Strength in Clay, " American Society of Civil Engineers Research Conference on Shear Strength of Cohesive Soils, 1960, pp. 555-580. Leonards, G. A. "Strength Characteristics of Compacted Clays, " Trans. ASCE, vol. 120, 1955. 89 Mitchell, J. K. ”Shearing Resistance of Soils as a Rate Process, " Journal of Soil Mechanics and Foundation Division, ASCE, vol. 90, SM 1, 1964. Mitchell, J. K. and Campanella, R. G. ”Creep Studies on Saturated Clays, " ASTM Symposium on Laboratory Shear Testing of Soils, Ottawa, Canada, 1963. Nadai, A. Theory of Flow and Fracture of Solids, vol. 2, McGraw-Hill Book Company, Inc. , New York, 1963. Osipov, K. A. Activation Processes in Solid Metals and Alloys, American Elsevier Publishing Company, Inc. , New York, 1964. Sherby, O. D., Frenkel, J., Nadeau, J., and Dorn, J. E. "Effect of Stress on the Creep Rates of Polycrystalline Aluminum Alloys Under Constant Structure, " Trans. , American Institute of Mining and Metallurgical Engineers, vol. 200, 1954, pp. 275-279. Tsytovich, N. A. "The Instability of the Mechanical Properties of Frozen Grounds, " International Conference on Perma- frost, Purdue University, Lafayette, Indiana, Nov., 1963. Vialov, S. S. "Rheology of Frozen Grounds, " International Conference on Permafrost, Purdue University, Lafayette, Indiana, Nov., 1963. Vialov, S. S. "Mechanism of Rheological Processes, ” Chapter 2, The Strength and Creep of Frozen Soils and Calculations for Ice-Soil Retaining Structures, Edited by S. S. Vialov, 1961, U. S. Army CRREL Translation 76. Williams, P. J. "Suction and its Effects in Unfrozen Water of Frozen Soils, " International Conference on Permafrost, Purdue University, Lafayette, Indiana, Nov., 1963. Wu, T. H., Loh, A. K., and Malvern, L. E. "Study of Failure Envelope in Soils, " Journal of Soil Mechanics and Foundation Division, ASCE, vol. 89, no. SM 1, Feb., 1963. APPENDIX 91 TABLE I. CREEP DATA FOR SOIL. CAKE No. A-l Molded Moisture Content = 25. 68% Molded Dry Density = 98. 04 1b/cu. ft. Time True Strain Time True Strain Time True Strain . (Min. ) ("70) (Min- ) (‘70) (Min. ) (‘70) SAMPLE No- A-1 (9) 80 11.70 30 7.80 Axial Stress = 625 psi 81 11. 72 35 8. 33 Final Moisture 82 ll. 74 40 8. 83 Content = 25. 78% 84 11. 79 45 9. 32 90 ll. 93 50 9. 78 1/2 .02 100 12.14 55 10.30 l-1/2 .08 115 12,43 60 10.78 2 .28 125 12.63 65 11.24 2-1/2 .75 135 12.85 H 67 11.45 3 1.30 165 13.36 . 69-1/4 11.65 4 2. 28‘ 5 2. 76 SAMPLE NO- A-1(16) Stress Decrease: 6 3, 08 Axial Stress = 625 psi 50 P5191: 6: 11, 65% '7 3, 38 Final Moisture 8 3. 61 Content = 25.96% 71 11. 69 9 3. 85 73 ll. 74 10 4.05 1/2 .10 75 11.80 12 4.52 l .39 77 11.86 14 4.91 1-1/2 .93 80 11.92 16 5.29 2 2.03 82 11.97 18 5.61 2-1/2 2.27 85 12.05 20 5. 92 3 2. 61 87 12. 09 22 6. 23 4 3. 09 90 12.18 24 6.53 5 3.43 95 12.31 26 6.82 6 3.73 100 12.43 28 7.11 7 3. 99 105 12. 54 30 7. 36 8 4. 24 110 12. 66 35 8.01 9 4.49 115 12.80 40 8.57 10 4.73 120 12.91 45 9. 05 ll 4. 96 50 9. 49 12 5. 16 SAMPLE NO. A-l (17) 55 9. 89 l3 5. 34 Axial Stress = 625 psi 60 10. 30 14 5. 54 Final Moisture 65 10. 73 16 5. 88 Content = 25.63% 77 ll. 65 18 6. 22 20 6. 49 1/2 . 06 Stress Decrease = 22 6. 79 1 - 31 50 psi at €=11.65‘70 24 7. 06 1-1/2 .80 26 7. 31 2 1. 48 79 11.69 28 7.56 2-1/2 2.32 TAB LE I (Continued) . Time True Strain (Min. ) (‘70) SAMPLE NO. A-1(l7) Contd. 3 2.65 4 3.19 5 3.60 6 3.96 7 4.29 8 4.58 9 4.84 10 5.10 11 5.32 12 5.55 14 5.92 16 6.30 18 6.66 20 6.99 22 7.32 24 7.62 26 7.92 28 8.21 30 8.49 35 9.15 40 9.73 45 10.30 50 10.82 55 11.35 58 11.62 58-1/2 11.65 Stress Decrease = 25 psi at E = 11. 65% 59 11.74 60 11.79 62 11.90 65 12.06 67 12.17 70 12.32 72 12.44 75 12.60 77 12.71 80 12.87 85 13.15 90 13.42 95 13.70 93 TABLE II . CREEP'DATA FOR SOIL CAKE NO. A-2 Molded Moisture Content = 26. 02% Molded Dry Density = 98. 08 1b/cu. ft. Time True Strain Time True Strain Time True Strain (Min. ) (%) (Min. ) (%) (Min. ) (%) SAMPLE NO. A-2(1) 79 11. 87 30 12. 17 Axial Stress = 625 psi 81 11. 88 32 12. 27 Final Moisture 83 11. 89 34 12. 36 Content = 25. 72% 35 11, 9o 36 12. 44 92 ll. 96 38 12. 51 1 ”2 2(3) 95 11.98 40 12.58 1_1/2 .80 100 12.05 42 12.65 2 1'55 105 12.09 44 12.71 2-1/2 2'“ 110 12.15 46 12.78 ° 120 12.26 48 12.85 3 2. 44 50 12. 94 4 2. 99 SAMPLE NO. A-Z (6) 52 13. 01 5 3. 43 Axial Stress = 675 psi 57 13 1., 6 3. 74 Final Moisture 60 13. 25 7 4. 01 Content = 25. 70% 8 4 25 62 13. 33 9 4'47 1/2 .39 65 13.43 10 4.81 l 1.28 68 13.50 ° 1-1/2 1.77 70 13.58 12 5. 22 14 5 69 2 2. 82 16 606 2-1/2 3.94 SAMPLE NO. A-2(7) ° 3 4. 66 Axial Stress = 675 psi 18 6. 43 . . 20 6 76 4 5, 59 Final M01sture ° 5 6. 30 Content = 25. 70% 22 7. 02 24 .7 31 6 6.86 ' 7 7.39 1/2 .36 28 7. 80 35 8 58 8 7.90 1 .84 40 '9'00 9 8.41 1-1/2 1.41 45 9.48 10 8.90 2 2.94 50 9.87 12 9.71 2-1/2 3.45 55 10°29 14 10.37 3 4. 58 60 10.67 16 10.89 4 5.45 65 11°05 18 11.44 5 6.09 ° 18-3/4 11.65 6 6.64 70 11.43 7 7 21 72 11, 58 Stress Decrease= 8 7° 79 73 11.64 75 psi at 6‘ = 11.65% ° 73-1/4 11 65 " 9 8°29 ' 20 11. 81 10 8. 74 Stress Decrease = 22 11. 84 11 9.13 75 psi at 6 = 11.65% 24 11.92 12 9. 49 - 75 11.84 26 12.00 14 10.16 77 11.86 28 12.08 16 10.80 94 TABLE II (Continued) Time True Strain Time True Strain Time True Strain (Min) (%) (Min. ) (%) (Min. ) (%) SAMPLE A-Z (7) Contd. 7 6. 68 9 7. 70 18 11.36 8 6.81 10 7.95 19 11.62 9 6.94 11 8.22 19+ 11.65 10 7.11 12 8.46 11 7. 25 13 8. 64 Stress Decrease = 12 7. 38 14 8. 85 50 psi at E = 11. 65% 13 7. 49 15 9. 04 14 7. 62 16 9, 21 21 11.84 15 7.73 17 9.40 22 11.91 17 7.96 18 9.62 23 11. 99 19 8- 20 19 9. 82 24 12. 07 21 8. 39 20 9. 98 26 12. 23 23 8. 60 22 10. 29 28 12. 37 25 8. 81 24 10. 60 30 12. 53 27 9. 00 26 10. 91 32 12.69 29 9.19 28 11.19 34 12.84 31 9. 38 30 11.47 36 13.00 35 9.73 35 12.14 38 13.16 43 10. 39 37 12. 40 40 13. 30 40 12. 77 45 13. 70 SAMPLE No. A-z (9) 42 13.03 47 13. 86 Axial Stress = 675 psi ‘ 45 13. 43 Final Moisture 47 13. 68 SAMPLE NO. A-2 (8) ' Content = 25. 82% 50 14. 06 Axial Stress = 675 psi Final Moisture 1/2 . 48 SAMPLE NO. A-2 (10) Content = 25. 46% 1 . 99 Axial Stress = 675 psi 1-1/2 1. 81 Final Moisture 1/2 . 50 2 2. 88 Content = 25. 76% l . 74 2-1/2 4. 00 1-1/2 1.86 3 4.76 1/2 .48 2 2.88 3-1/2 5.35 1 1.09 2-1/2 3.91 4 5.83 1-1/2 2.02 3 4.61 4-1/2 6.19 2 3.22 3-1/2 5.00 2-1/2 4.29 4 5. 52 Stress Decrease = 3 4. 95 4-1/2 5. 88 50 Psi at 6‘ = 6.19% 4 5.88 5+ 6.19 5 6. 54 Stress Decrease = 2-1/2 2: 88 g 3' $63, 75 Pm at E - 6' 19% 7 7.12 8 8. 34 6 6. 56 8 7. 40 9 8. 81 95 TAB LE 1 I (Continued) Time True Strain Time True Strain Time True Strain (Min. ) (%) (Min. ) (%) (Min. ) (%) SAMPLE A-2(10)Contd. 2-1/2 4. 05 1 . 63 10 9.28 3 4.79 1-1/2 1.91 10-l»/2 9.43 4 5.74 2 2.81 5 6. 42 2-1/2 3. 21 Stress Decrease = 6 7. 04 3 3. 50 75 psi at €= 9. 43% 7 7. 59 4 3. 99 7-1/2 7. 85 5 4. 41 12 9. 74 8 8.10 6 4. 75 13 9.80 8-1/2 8.32 7 5.05 14 9.88 9 8. 53 8 5. 31 15 9.98 9—1/2 8.74 9 5.54 16 10.05 10 8.96 10 - 5.76 17 10.12 10-1/2 9.17 12 6.16 18 10.19 11 9.36 14 6.49 20 10.32 11-1/4 9.43 16 6.85 22 10.46 18 7.17 24 10. 59 Stress Decrease = 20 7. 46 26 10. 70 50 psi at E = 9. 43% 22 7. 72 28 10. 85 24 .3, 00 30 10. 96 13.-U2 3: 2: 26 8. 23 32 11.08 14 9.93 28 8.45 .34 11.19 15 10. 05 30 8.68 36 11.33 16 10.17 32 8.89 38 11.47 17 10. 32 34 9.09 40 11.59 18 10.44 40 9.67 42 11.70 20 10 71 45 10.07 44 ll. 82 22 10. 96 50 10.41 46 11.95 24 11.18 55 10.78 48 12.07 26 11.43 60 11.11 50 12.18 28 11.63 65 11.40 59 12.66 30 11.89 67 11.50 62 12. 83 32 12' 09 68 11. 54 65 13. 00 34 12.33 69 11.59 36 12:54 70+ 11.65 SAMPLE NO. A-2(ll) 38 12 74 Axial Stress I 675 psi 40 12° 93 Stress Decrease = Final Moisture ' 75 psi at E: 11. 65% Content = 25.53% SAMPLE NO. A-Z (12) Axial Stress = 600 psi 71'1/2 ”-75 1/2 . 23 Final Moisture 77 11. 77 1 . 78 Content = 25.70% 80 11, 79 1-1/2 1.71 82 11.80 2 2.80 1/2 .32 85 11.82 96 TABLE II 1 (Continued) Time True Strain Time True Strain Time True Strain (Min) (%) (Min. ) (%) (Min. ) (%) SAMPLE A-2(12) Contd. 47 10. 85 7 5. 09 87 11.83 49 11.00 , 8 5.32 90 11.87 53 11.29 9 5.53 92 11.88 56 11.51 10 5.72 94 11,89 57 11.56 12 6.07 98 11.92 58 11.62 14 6. 38 102 11,95 58+ 11.65 16 6.69 110 12. 01 18 6. 96 120 12, 09 Stress Decrease = 20 7. 21 130 12.16 50 pSi at E: 11. 65% 22 7. 45 . 24 7. 67 SAMPLE No. A-2(13) 59-1/2 11.72 26 7. 88 Axial Stress = 600 psi 62 11. 74 28 8. 06 Final Moisture 63 11. 75 3O 8. 26 Content : 25, 55% 64 , 11. 77 35 8. 66 65 11. 78 40 9. 06 1/2 .43 67 11.81 45 9.39 1 1.08 69 11.86 50 9.70 1—1/2 1.92 73 11.95 55 10.00 2 2.85 77 12.04 60 10.27 2-1/2 3.37 80 12.09 65 10-52 3 3.76 85 12.18 70 10-74 4 4.36 90 12.25 :3 11:33 5 4.79 95 12. 33 80 11.22 6 5.17 100. 12.40 82 11.31 7 5.47 105 12.48 85 11.43 8 5.75 110 12.56 87 ‘ 11.51 9 6°03 89 11.60 10 6-24 90+ 11.65 12 6. 67 SAMPLE NO. A-2(l6) Stress Decrease : 14 7. 05 Ax1a1.Stress.- 675 psi 50 psi at = 11. 65% 16 7. 42 Final M01sture 18 7. 74 Content = 25. 68% 92 11. 66 .20 8,06 94 11.68 22 8.35 1/2 .53 96 11.69 ‘24 8.60 1 1.35 93 11-71 26 8.84 1-1/2 2.26 100 11.72 28 9.07 2 2.81 103 11.74 30 9.29 2-1/2 3.23 107 11.79 32 9.46 3 3.57 110 11.82 35 9.82 4 4.09 115 11.88 40 10.28 5 4.50 120 11.91 45 10.67 6 4. 79 130 11.99 97 TABLE 11 (Continued) Time True Strain Time True Strain Time True Strain (Min- ) (%) (Min. ) (%) (Min. ) (%) SAMPLE NO. A-2(17) SAMPLE NO. A-2(20) 71-3/4 9.44 Axial Stress = 600 psi Final Moisture Axial Stress = 600 psi Final Moisture Stress Decrease = - Content 2 25. 58% Content = 25. 54% 50 psi at E: 9. 44% 1/2 .32 1/2 .35 73 9.48 l 1.00 1 1.03 74 9.50 1-1/2 1.94 1-1/2 2.04 76 9.52 2 2.47 2 2.76 78 9.54 2—1/2 2.86 2-1/2 3.13 80 9.56 3 3.13 3 3.38 82 9.59 4 3.54 4 3.86 84 9.61 5 3.86 5 4.20 86 9.63 6 4.11 6 4.48 88 9.65 7 4.33 8 4.92 90 9.67 8 4.54 10 5.30 93 9.71 9 4.72 12 5.65 95 9.73 10 4,91 14 5.95 100 9.78 12 5,22 15 6.08 105 9.82 14 5,43 15-3/4 6.19 110 9.87 16 5.73 115 9.91 18 5, 98 Stress Decrease = 120 9. 95 19 6.12 25 psi at e: 6.19% 125 9. 99 20 6. 19 17 6. 29 SAMPLE No. A-2(21) Stress Decrease = 18 6. 40 Axial Stress - 600 psi 75 psi at 6‘: 6. 19% 19 6.50 Final Moisture 20 6. 56 Content I: 25. 40% 22 6.21 22 6.74 23 6.22 24 6.94 1/2 .35 24 6.24 26 7.10 1 1.03 25 6.26 28 7.23 1-1/2 1.92 27 6.29 30 7.36 2 2.42 29 6.34 35 7.67 2-1/2 2.73 32 6.39 40 7.97 3 2.97 35 6.45 45 8.20 4 3.40 38 6.52 50 8.44 5 3.70 40 6.55 55 8.65 6 3.96 45 6.66 60 8.95 7 4.20 50 6.74 65 9.16 8 4.41 55 6.83 69 9.31 9 4.58 60 6.94 70 9.34 10 4.75 65 7,02 71 9.40 12 5.07 98 TABLE I I (Continued) Time True Strain Time True Strain Time True Strain . (Min. ) (%) (Min. ) (%) (Min. ) (%) SAMPLE A-2(21)'Contd. 115 9. 76 120 9.83 14 5.33 125 9.88 16 5.59 130 9.94 18 5.86 19 5.96 20 6.08 21 6.19 Stress Decrease = 25 psi at E: 6.19% 22 6.34 23 6.42 25 6.55 27 6.70 29 6. 83 33 7.07 35 7.19 '40 7.45 45 7.72 50 7.95 55 8.16 60 8.37 65 8.56 70 8.75 75 8.92 80 9.08 85 9.22 88 9.31 90 9. 36 92 9. 43 Stress Decrease = 25 psi at E = 9. 43% 93 9.46 94 9.48 95 9.49 97 9.52 101 9.57 105 9.63 108 99.66 99 TABLE III . CREEP DATA FOR SOIL CAKE NO. A-3 Molded Moisture Content = 26. 33% Molded Dry Density = 98. 09 lb/cu. ft. Time True Strain Time True Strain Time True Strain (Min-1 (%) (Min- ) (%) (Minol (%) SAMPLE NO. A—3 (1) 425 3. 03 3 1. 39 Axial Stress = 400 psi 535 3. 23 4 1. 58 Final Moisture 560 3. 27 5 1. 72 Content = 25. 93% 1150 3. 88 6 1. 86 1355 4. 00 7 1. 97 1/2 . 32 1440 4. 03 8 2. 09 1 .86 1560 4.08 9 2.19 1-1/2 1.00 1850 4.20 10 2. 30 2 1.06 2635 4.41 12 2.49 2-1/2 1.11 2875 4.45 14 2.64 3 1.15 3200 4. 50 16 2. 72 4 1.19 3370 4. 52 18 2. 93 5 1.24 4125 4. 64 20 2.99 6 1. 26 22 3.18 7 1. 31 Stress Decrease = 24 3. Z9 8 1. 33 40 psi at e: 4. 64% 26 3. 42 9 1. 35 28 3. 51 10 1.39 4365 4.64 30 3.61 11 1.41 4830 4.65 35 3.85 13 1.45 6120 4.67 40 4. 05 15 1.47 7155 4.68 45 4.26 17 1. 50 7795 4. 69 50 4. 44 19 1. 52 8820 4. 70 55 4. 63 21 1. 55 65 4. 90 23 1. 57 Sample Unloaded 75 5. 17 25 1.59 at 6: 4.70% . 85 5.42 27 1. 61 Sample Recovered 120 6.12 30 1. 64 Under Zero Stress to 135 6. 39 40 1.71 €= 4.21% and was 150 6.62 50 l. 79 Subjected to a Second 165 6. 85 60 1. 85 Cycle of Loading 185 7.16 70 1. 90 Where Axial Stress = 205 7. 43 90 2. 00 600 psi 225 7. 71 120 2.14 265 8.16 150 2.26 1/2 .21 295 8.51 180 2. 37 1 . 58 305 8. 62 255 2.60 Isl/2 .96 325 8. 86 325 2.79 2 1.14 340 9.06 375 2.92 2-1/2 1.28 350 9.18 100 TAB LE III (Continued) Time True Strain Time True Strain Time True Strain (Min. ) (%) (Min. ) (%) (Min. ) (%) SAMPLE A-3.(1) Contd. 6 1. 63 1850 7. 96 7 l. 69 ‘1925 7. 97 360 9.29 8 1.75 2690 8. 08 370 9. 40 9 1,78 2830 8.10 371 9.43 10 1.83 2965 8.11 12 1. 90 3380 8.16 Stress Decrease = 14 1. 97 4100 8. 23 40 psi at 6‘: 9. 43% 16 2. 03 4510 8. 26 ( E: 13. 60% with 18 2. 09 4780 8. 28 Respect to Initial 20 2. 14 5690 8. 35 Loading Cycle 22 2. 20 24 2, 27 SAMPLE NO. A-3 (3) 373 9. 48 26 2. 31 Axial Stress =‘ 675 psi 375 9. 49 28 2, 36 Final Moisture 380 9. 50 30 2. 40 Content = 26. 04% 385 9. 52 40 2. 61 390 9. 54 50 2. 81 1/2 . 34 400 9. 57 70 3.16 1 1. 02 420 9.65 80 3.31 1-1/2 2.05 440 9.73 130 3.97 2 3.19 465 9.84 160 4.29 2-1/2 3.98 490 9.94 170 4.40 3 4. 50 510 10. 02 240 4. 95 4 5. 30 1270 12.41 270 5.15 5 5.95 1490 13.27 290 5. 27 6 6. 47 1520 13. 43 320 5. 44 7 7. 02 1550 13.60 430 5.90 8 7.54 1605 13.96 445 5.95 9 8. 02 1665 14.27 460 6. 01 10 8.47 490 6.15 11 8. 88 SAMPLE NO. A—3(2) 1210 7. 36 12 . 9.25 Axial Stress = 475 psi 1270 7.. 44 12-1/2 9. 43 Final Moisture 1350 7, 52 ' Content = -- 1435 7. 59 Stress Decrease = 1470 7. 63 40 psi at 6: 9.43% 1/2 . 37 1530 7. 67 l .92 1560 7.70 13 9.55 1-1/2 1.13 1590 7.73 14 9.67 2 1.26 1630 7.75 15 9. 80 2-1/2 1.35 1670 7.80 16 9.99 3 1. 41 17 10.16 4 1. 51 Stress Decrease = 18 10. 32 5 l. 58 39 psi at 6: 7. 80% 19 10. 53 101 TABLE III (Continued) Time True Strain Time True Strain Time True Strain (Min. ) (%) (Min. ) (%) (Min. ) (%) SAMPLE A-3(3) Contd. Stress Decrease = 15 4. 06 35 psi at 6 = 16. 25% 20 4.47 20 10. 69 25 4. 81 21 10.86 177 16.26 41 5.75 22 11.02 180 16.29 60 6.60 23 11.17 185 16.31 90 ‘ 7.61 24 11.32 200 16.42 105 7.99 25 11.47 290 17.10 125 8.40 26+ 11.65 325 17.38 135 8.59 350 17. 60 145 8. 78 Stress Decrease = 400 18. 03 155 8. 95 37 psi at 6 = 11.65% 175 9.21 Stress Decrease = 190 9. 37 27 11. 79 35 psi at 6: 18. 03% 196 9. 43 28 11. 83 29 11. 91 405 18. 03 Stress Decrease = 30 11. 97 430 18. 07 40 psi at 6: 9. 43% 35 12. 25 445 18.11 40 12. 53 625 18. 52 197 9. 44 45 12.82 1420 20. 06 315 9.61 50 13.16 1540 20. 53 375 9. 72 55 13.44 1570 20.83 505 9.88 57 13. 58 565 9. 96 62-1/2 13.93 SAMPLE NO. A-3(10) 1195 10.54 Axial Stress = 525 psi 1245 10. 58 Stress Decrease = Final Moisture 1340 10. 66 36 psi at 6 = 13. 93% Content = 25. 12% 1440 10. 74 64 13. 98 1/2 .18 Stress Decrease = 67 14. 04 1 . 76 40 psi at e = 10. 74% 70 14.08 1-1/2 1.29 77 14.21 2 1.90 1442 10.80 80 14.28 2-1/2 2.31 1740 10.83 86 14.40 3 2.51 1985 10.84 90 14.46 4 2.80 2625 10. 89 115 15.01 5 2.98 2985 10.94 135 15.42 6 3.14 3585 10.97 150 15.71 7 3.27 4095 11.00 160 15.91 8 3.39 4755 11.01 165 16.02 9 3.51 5520 11.07 170 16.15 10 3.61 5895 11.08 170—1/2 16.25 12 3.81 7155 11.14 102 TABLE III (Continued) Time True Strain Time True Strain Time True Strain ‘ (Min. ) (%) (Min. ) (%) (Min. ) (%) SAMPLE A-3(10)Contd. 8975 12. 09 5 3. 46 9005 12. 21 6 3. 67 Stress Decrease 1' 9050 12. 32 7 3. 85 40 psi at = 11.14% 9080 12. 41 8 4. 03 9110 12. 50 9 4.18 9795 11.14 9140 12. 58 10 4.31 10235 11.15 9860 14. 08 12 4. 54 10865 11.16 9890 14.12 14 4. 76 9920 14.16 16 4. 95 Left Underc’ = 405 9985 14. 25 18 5.14 psi for a Long Time. 9990 14. 26 20 5. 31 Stress Increase = 22 5.47 40 psi at = 11.17% Stress Increase = 24 5. 63 40 psi at = 14. 26% 26 5. 77 0 11.17 28 5. 92 1550 11.17 9995 14. 34 30 6. 07 2960 11. 22 10000 14. 33 40 6. 73 4130 11. 23 10015 14. 53 50 7. 38 4790 11.24 10030 14.63 60 7.95 5540 11. 26 10040 14. 71 84 9. 26, 6320 11.27 10075 14.99 87+ 9.43 6980 11. 28 10080 15. 02 7115 11.28 Stress Decrease = Stress Increase = 40 psi at = 9, 43% Stress Increase = 40 psi at = 15. 02% 40 psi at = 11. 28% 88 9. 50 10085 15. 21 91 9. 56 7160 11.34 10095 15.49 97 9.73 7190 11.35 10100 15.64 105 9.95 7310 11.40 10105 15.77 120 10. 37 7370 11.42 10110 15.90 135 10.85 7610 11.52 150 11.32 7715 11.54 SAMPLE NO. A-3(4) 155 11.47 8405 11. 83 Axial Stress = 800 psi 160 11, 63 8615 11.91 Final Moisture 161 11.65 8780 11. 96 Content = 25. 56% 8960 12. 02 Stress Decrease = 8965 12. 06 1/2 . 39 40 psi at = 11. 65% l . 92 Stress Increase = 2 2. 37 162 11. 68 40 P313“ z 12'°6% 2-1/2 2.68 165 11.71 8975 12. 09 71 5: 38 175) 11.82 103 TAB LE I I I (Continued) Time True Strain Time True Strain Time True Strain (Min. ) (%) (Min- ) (%) (Min- ) (%) SAMPLE A-3(4) Contd. 20 3. 26 1595 9. 07 22 3. 35 1820 9.18 180 11.92 24 3.41 1910 9.22 190 12. 05 26 3. 49 2780 9. 59 200 12. 21 28 3. 55 2920 9. 64 215 12.41 30 3.62 285 13. 54 35 3. 79 Stress Decrease = 300 13. 79 55 4. 31 40 psi at e = 9.64% 305 13.89 110 5.36 307 13. 93 140 5.87 3260 9.65 170 6. 28 3380 9.66 Stress Decrease = 190 6. 55 4340 9. 72 40 psi at E = 13. 93% 210 6. 82 5450 9. 76 230 7. 05 6320 9. 78 310 13.94 240 7.15 315 13. 96 250 7. 2.1 SAMPLE NO. A-3 (15) 330 14. 08 253 7. 26 Axial Stress = 675 psi 345 14. 20 Final Moisture 360 14. 32 Stress Decrease 2 Content = 25. 89% 375 14. 46 40 psi at 6 = 7.26% 1/2 .17 SAMPLE NO. A~3(5) 255 7.32 1 .67 Axial Stress = 700 psi 265 7. 33 1-1/2 1. 27 - Final Moisture 270 7. 34 2 l. 61 Content = 26. 08% 275 7. 35 2~1/2 1. 79 285 7. 40 3 l. 85 1/2 .35 370 7.67 4 1.98 1 . 88 420 7. 85 5 2. 07 1-1/2 1.51 510 8.13 12 2.47 2 1.76 530 8.19 20 2.76 2-1/2 1.91 550 8.24 30 3.02 3 2. 02 570 8.29 50 3.48 4 2.18 582 8.34 120 4.55 5 2. 33 180 5. 35 6 2. 44 Stress Decrease = 345 6. 96 7 2. 52 40 psi at € = 8. 34% 410 7. 45 8 2. 61 465 7. 80 9 2.69 583 8. 38 505 8.06 10 2.75 605 8.38 630 8.68 12 2. 88 1235 8.86 1265 10.55 14 2. 98 1310 8.89 1305 10.65 16 3. 09 1370 8. 94 18 3.17 1430 8.97 1385 10.81 104 TABLE I I I (Continued) Time True Strain Time True Strain Time True Strain (Min.) (%) (Min. ) (%) (Min.) (%) SAMPLE A-3(15)Contd. 10200 14. 00 Stress Decrease = 10245 14. 06 40 psi at 6‘ = 10. 54% Stress Decrease = 10315 14.47 40 psi at E‘ = 10. 81% 35 10. 59 SAMPLE No. A-3 (8) 37 10. 65 1385 10. 84 Axial Stress = 750 psi 40 10. 73 1535 10. 94 Final Moisture 42 10. 83 1635 10. 99 Content = 25. 74% 45 10. 94 1875 11.16 47 11. 00 2105 11.29 1/2 .37 48 , 11.05 1 1. 04 49 11. 08 Stress Decrease = 1-1/2 1.83 49-1/3 11.09 40 psi at 6 = 11. 29% 2 2. 88 2-1/2 3, 37 Stress Decrease = 2720 11.35 3 4.22 40 psi at € = 11.09% 4955 11. 59 5 5. 37 6185 11.71 6 5.78 50 11.09 7 6,15 51 11.10 Stress Increase = 8 6. 48 53 11.14 40 psi at 6‘ = 11.71% 9 6.79 60 11.23 10 7. 07 66 11. 32 6245 11.74 11 7.33 75 11.44 6285 11.77 12 7.57 80 11.51 7045 12.02 14 8.03 85 11. 57 7225 12.10 16 8.48 90 11.64 7345 12.14 17 8.71 90-1/2 11.65 7655 12. 21 18 8. 94 8445 12,41 19 9,13 Stress Decrease = 20 9, 33 40 psi at 6 = 11. 65% Stress Increase = 20—1/2 9.43 40 psi at 6 = 12.41% 95 11.66 Stress Decrease = 107 11.70 8635 12. 61 40 psi at 6‘ = 9. 43% 120 11. 79 8725 12. 73 135 11. 86 8820 12.85 21 9.48 150 11.95 9095 13. 09 22 9. 54 165 12. 01 9885 13. 58 23 9.63 180 12.07 10015 13.66 24 9,73 205 12.19 25 9.81 210 12.21 Stress Increase = 27 9, 97 213 12. 22 40 psi at 6‘ = 13. 66% 28 10. 05 ‘ 30 10,20 Stress Decrease = 10115 13.85 34 10. 54 40 psi at 6 = 12. 22% 105 TABLE III (Continued) Time True Strain Time True Strain Time True Strain (Min- 1 (%) (Min. ) (%) (Min. ) (%) SAMPLE A-3(8) Contd. 120 9. 29 6 7. 00 125 9. 40 7 7. 48 375 12.33 127 9.43 8 7.87 435 12. 41 9 8. 39 475 12. 45 Stress Decrease = 10 8. 78 565 12. 54 40 psi at € = 9. 43% 11 9.15 11-3/4 9. 43 SAMPLE NO. A-3(13) 128 9. 46 Axial Stress = 675 psi 140 9. 52 Stress Decrease = Final Moisture 170 9. 75 40 psi at 6 = 9. 43% - Content = 26.16% 210 ' 9.90 235 10.03 12-1/2 9.60 1/2 .34 245 10.06 14 9.73 l . 99 15 9. 83 1-1/2 1.79 Stress Decrease = 16 9.96 2 2.47 40 psi at 6‘ = 10. 06% 17 10. 05 3 3. 00 18 10.16 4 3. 34 247 10. 09 19 10. 27 5 3. 58 345 10.18 20 10. 36 6 3.79 370 10.20 21 10.45 8 4. 13 420 10. 26 22 10. 54 10 4. 44 440 10. 27 12 4.69 Stress Decrease = 15 5. 02 Stress Decrease = 40 psi at 6‘ = 10. 54% 20 5. 50 40 psi at € = 10. 27% 22 5. 67 24 10. 60 26 5. 98 525 10. 27 25 10. 62 30 6. 25 590 10. 28 26 10. 66 33 6.42 1265 10. 39 27 10.69 36 6. 59 28 10. 71 40 6. 80 SAMPLE NO. A-3 (12) 29 10. 75 44 7. 00 Axial Stress - 525 psi 30 10. 77 48 7. 17 Final Moisture 32 10. 83 50 7. 26 Content = 25. 73% 35 10. 94 58 7. 57 39 ll. 06 64 7. 79 . 32 40 11. 08 68 7.89 1 1.06 40-1/2 11.09 72 8.08 1-1/2 2.15 77 8. 23 2 3. 43 Stress Decrease = 85 8. 45 2 4.24 40 psi at e = 11. 09% 95 8. 69 3 4. 76 105 8.95 4 5.61 50 11.11 116 9.20 5 6.37 55 11.13 106 TABLE I I I (Continued) Time True Strain Time True Strain Time True Strain (Min. ) (%) (Min. ) (%) (Min. ) (%) SAMPLE A-3(12)Contd. 15 9. 72 2980 13. 90 16 9. 81 3940 13. 93 90 11.38 17 9.90 4080 13.96 140 11.59 18 10. 00 - 14.02 150 11.62 20 10.18 158 11, 65 22 10. 39 Stress Decrease = 25 10. 61 30 psi at 6' = 14. 02% Stress Decrease = 28 10. 81 40 psi at 6 = 11.65% 30 10.95 0 0 33 11.11 (14. 02) 260 11.66 35 11.20 3 .03 440 11.73 39 11.43 8 .04 520 11.77 42 11.59 20 .05 570 11.79 43 11.65 65 .11 1230 11. 97 148 .17 Stress Decrease = 170 .19 SAMPLE NO. A~3 (6) 30 psi at 5‘ = 11. 65% 855 . 78 Axial Stress = 400 psi 945 . 86 Final Moisture 44 11. 73 1070 . 98 Content = 25. 62% 46 11. 74 1081 1. 01 50 11.79 (15.02) 1/2 . 28 55 11. 82 l l. 08 60 11. 89 Stress Increase = 1-1/2 2.23 70 11.99 30 psi at 6' =1.01% 2 3. 25 95 12.23 (Corresponds to E 2 2-1/2 4. 02 130 12. 52 15. 02% with respect 3 4. 58 170 12. 85 to initial length. ) 4 5. 48 180 12. 92 5 6.21 190 12.98 1093 1.08 6 6. 72 1098 l. 13 7 7. 25 Stress Decrease = 1108 l. 26 8 7. 67 30 psi at 6 = 12. 98% 1128 1. 46 9 8. 07 1160 1. 80 10 8.40 200 12.99 1175 1.93 11 8.76 360 13.10 1210 2.25 12 9. 07 610 13.31 (16.25) 13 9' 35 1180 13' 78 Stress Increase - 13+ 9. 43 1245 13. 82 30 psi at 6, = 2. 25% Stress Decrease = Stress Decrease = (Corresponds to 16. 25% 30 psi at 6‘ = 9, 43% 30 psi at 6‘ = 13, 32% with respect to initial length.) 14 9.61 1510 13.85 1213 2.41 107 TABLE III (Continued) Time True Strain Time True Strain Time True Strain (Min. ) (%) (Min. ) (%) (Min. ) (%) SAMPLE A-3(6)Contd. 1215 2.52 25 8.01 1/2 .71 1218 2.70 27 8.20 1 1.93 1220 2.80 30 8.46 1-1/2 3.46 1223 2.93 32 8.63 2 4.97 1226 3.09 35 8.87 2-1/2 6.39 1228 3.18 37 8.97 3 7.33 1230 3.26 40 9.15 4 8.65 (17.28) 42 9.24 5 9.43 44 9. 35 6 10. 46 Stress Increase = 45+ 9. 43 6-1/2 10. 78 30 psi at E = 3. 26% 7 11. 05 Stress Decrease = 30 psi at 6 = 9.43% (Corresponds to = 17. 28% with reSpect to initial length. ) Stress Decrease = 20 psi at E = 11.05% 46 9. 50 1231 3.50 50 9. 52 7-1/2 11.10 1232 3.69 60 9.63 8 11.19 1233 3.88 75 9.77 9 11.41 1234 4. 04 90 9.90 10 11.68 1235 4.23 130 10.17 11 11.89 150 10. 28 12 12. 14 SAMPLE NO. A-3 (7) 170 10. 40 13 12. 34 Axial Stress = 350 psi 175 10. 43 14 12. 53 Final Moisture Content = 25. 37% Stress Decrease = Stress Decrease = 30 psi at 6 = 10.43% 20 psi at 6 = 12.53% 1/2 . 36 1 1.29 180 10.47 15 12.66 1-1/2 2.14 330 10.51 16 12.69 2 2. 68 395 10.55 17 12.73 3 3.41 540 10.61 18 12.78 4 3.92 1170 10.83 19 12.87 5 4. 36 1390 10. 89 20 12. 94 6 4.73 1580 10.91 21 13.01 7 5. 06 1940 10. 99 22 13. 07 8 5. 36 2670 11.10 23 13.12 9 5.61 2810 11.13 24 13.18 10 5.84 2920 11.14 25 13.23 12 6. 28 26 13. 30 15 6. 82 SAMPLE NO. A-3 (14) 27 13. 40 18 7. 25 Axial Stress = 260 psi 20 7. 46 Final Moisture Stress Decrease = 23 7. 83 Content = 25. 63% 20 psi at 6‘ = 13. 40% TAB LE I I I Time True Strain Time (Min. ) (%) (Min. ) SAMPLE A-3(l4)Contd. 2120 2126 28 13.42 35 13.51 40 13.57 50 13.69 70 13.90 140 14.43 190 14.66 Stress Decrease 108 (Continued) True Strain (‘70) 16.81 17.14 Stress Increase = 20 psi at E 2126 2128 2130 2132 2133 = 17.14% 17.21 17.64 18.01 18.38 18.56 20 psi at E = 14.66% 310 14.69 370 14.71 420 14.73 1200 14.91 1260 14.93 1360 14.94 1440 14.95 1565 14.98 1825 15.01 Stress Increas e = 20 psi at E = 15.01% 1940 15. 34 2055 15. 56 2085 15. 61 Stress Increase = 20 psi at 6' 15. 61% 2090 15. 72 2095 15. 82 2100 15.89 2105 15.97 2110 16. 06 Stress Increase = 20 psi at € =16. 06% 2115 16.49 " '5: 41273.4»:- fr ‘p. "1111111111111111111“