THE SOH-ICE SYSTEM AND THE SHEAR STRENGTH OF FROZEN SOHS Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY ROY ROBERT GOUGHNOUR 1967 J'Hhams. This is to certify that the thesis entitled The Soil-Ice System and the Shear Strength of Frozen Soils presented by Roy Robert Goughnour has been accepted towards fulfillment of the requirements for __Pl-_D__ degree in __£°_§°__ an e, Mtdtflk Major professor Date August 18. 1967 0-169 . 1.. amhmc Inv‘ HMS & SONS' angumnm mo. m mu; OW!!! TOY [III "In! (mg a K1 WWI ABSTRACT THE SOIL-ICE SYSTEM AND THE SHEAR STRENGTH OF FROZEN SOILS by Roy Robert Goughnour This investigation was intended to provide informa- tion useful in describing or predicting the mechanical be- havior of frozen soils. It was first necessary to acquire an understanding of the physical behavior of polycrystalline ice in compression for constant deformation rates and for time dependent deformation. Observation of the effects on deformational behavior caused by the addition of soil par- ticles to the ice matrix led to an analysis which considered the overall soil-ice behavior in terms of their relative volume concentrations. Information was also obtained on the dependence of creep rates on absorbed energy, tempera- ture, stress, and ice density. Ice specimens were prepared from precooled, deaired, deionized, and distilled water in combination with snow or powdered ice. Examination of thin sections under a micro- scope showed angular grains approximately 1 to 2 millimeters in dimension. Sand-ice Specimens were formed by pouring precooled water into a mixture of one-sized fine sand and snow. A very uniform dispersion of sand particles was Roy Robert Goughnour obtained for small volume concentrations of sand. Two different sand sizes were included in the study. Frozen samples 2.26 inches high by 1.13 inches in diameter were tested in uniaxial compression with both constant axial strain-rate and constant axial stress creep tests. Temperatures were controlled to within i 0.05 de- grees Centigrade and a temperature range of minus 3 to mi- nus 12 degrees Centigrade was covered. Sample volume change measurements taken during deformation are included for certain tests. Elastic modulii were evaluated using additional samples for various levels of strain. Experimental data show that creep rates of poly- crystalline ice depend on stress, temperature, strain, and absorbed energy. An equation has been deve10ped for pre- dicting creep rates which includes a strain hardening term and a softening term. The hardening term influences creep behavior only at very low strains whereas the softening term predominates for larger strains. Both terms are some function of stress and temperature with the hardening term depending also on strain and the softening term depending also on absorbed energy. Excellent correlation between experimental data and predicted creep rates for a range of stresses and temperatures lend support to the equation. Shear strengths for constant strain-rate tests can be pre- dicted after rearranging the equation into a form more suitable for computations. Roy Robert Goughnour The addition of sand particles to the ice matrix alters the ice behavior in several ways. At low volume concentrations of sand, increase in shear strength is a simple linear relation to the relative proportions of sand and ice. On reaching a critical volume concentration of sand particles, a sharp increase in shear strength is noted. At this point friction between sand particles and dilatancy begin to contribute to the shear strength. Using results of constant axial strain-rate tests on the sand-ice samples, the effects of the several mechanisms on deformation rates are evaluated in terms of a stress factor. A combination of these stress factors and the creep equation for poly- crystalline ice gives a reasonable prediction of sand-ice behavior for slow creep rates. The deformation process is restricted to the ice matrix with no.breakage of sand par- ticles observed. At higher sand volume concentrations the deformation rates within the ice matrix will be greater than that experienced by the overall frozen sample. This places additional restrictions on the use of the creep equation for polycrystalline ice. Computations similar to those for the sand-ice material were carried out for data on clay-ice material available from an earlier study. Deformation mechanisms similar to those present in the sand-ice system are sug- gested. Correlation between the experimental data on the clay-ice material and predicted curves showed excellent agreement. THE SOIL-ICE SYSTEM AND THE SHEAR STRENGTH OF FROZEN SOILS By Roy Robert Goughnour A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Civil Engineering 1967 (.4536? 3-W'L% ACKNOWLEDGMENTS The writer is indebted to his major professor, Dr. 0. B. Andersland, AssoCiate Professor of Civil Engineering, for his aid and encouragement throughout the writer's doc- toral studies, and for his many helpful suggestions during the preparation of this thesis. Thanks are also due the other members of the writer's doctoral committee: Dr. R. K. Wen, Professor of Civil Engineering, Dr. G. E. Mase, Pro- fessor of Applied Mechanics, and Dr. J. 8. Frame, Professor of Mathematics. The writer is grateful to 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, and also to the Department of Health, Education and Welfare and the Ford Foundation for the financial assistance that made the writer's doctoral studies possible. ii TABLE OF CONTENTS‘ ACKNOWLEDGMENTS. . . . . . . . . . . . . . LIST OF FIGURES O O O O O O O O O O O O O 0 LIST OF TABLES O O O O O O O O O O O O O O NOTATIO Chapter I. II. III. IV. VI. NS. 0 O O O O O O I O O O O O O O 0 INTRODUCTION. . . . . . . . . . . . LITERATURE REVIEW . . . . . . . . . Experimental Evaluation of Creep. Rate Process Theory . . . . . . . Structure of Ice. . . . . . . . . Mechanical Properties of Ice. . . Structure of Frozen Soils . . . . Mechanical Properties of Frozen Soils MATERIALS STUDIED AND SAMPLE PREPARATION. Ice Samples . . . . . . . . . . . sand-Ice samples 0 o o o o o o o o EQUIPMENT AND TEST PROCEDURES . . . Equipment . . . . . . . . . . . . Constant Axial Strain-Rate Tests. Constant Axial Stress Creep Tests EXPERIMENTAL RESULTS. . . . . . . . Elastic Response. . . . . . . . . Constant Axial Strain-Rate Tests. Constant Axial Stress Creep Tests DISCUSSION AND PRESENTATION OF THEORY Polycrystalline Ice . . . . . . . Sand-Ice System . . . . . . . . . Clay-Ice System . . . . . . . . . iii Page ii ix 12 15 18 20 23 23 25 27 27 33 35 37 37 38 41 59 59 69 79 Chapter VII. SUMMARY AND CONCLUSIONS Polycrystalline Ice . Sand-Ice System . Clay-Ice System . VIII. BIBLIOGRAPHY . APPENDIX--Data iv RECOMMENDATIONS FOR FURTHER RESEARCH. Page 109 109 110 112 113 114 117 LIST OF FIGURES Figure Page 2-1 Typical Creep Curves for Polycrystalline Ice . . . . . . . . . . . 6 2-2 Schematic Representation of Energy Barriers . . . . . . . . . . . . . 9 2-3 Structure of Ice Lattice (After Pounder, 1961) . . . . . . . . . . 14 4-1 Schematic Diagram of Triaxial Cell Showing Sample Placement. . . . . . . . . 28 4-2 Triaxial Cell in Coolant Bath, Test Machine, Sanborn Recorder, and Refrigeration Unit. . . . . . . . . . 31 4-3 Deformed Ice Sample Compared with Undeformed Sample . . . . . . . . . . . . 31 5-1 Young's Modulus versus Plastic Axial Strain for Ice and Coarse sand-Ice samples. 0 o o o o o o o o o o o 44 5-2 Young's Modulus versus Plastic Axial Strain for Fine Sand-Ice Samples. . . . . . . . . . . . . 45 5-3 Young's Modulus versus Percent Sand by Volume for Samples with about 3 to 4 Percent Plastic Strain . . . 46 5-4 Typical Stress-Strain Curves for Constant Strain-Rate Tests. . . . . . . . 47 5-5 Effect of Volume Concentration of Sand on Peak Strength. (a) -12.03°C and -3085°Co (b) -7055°Co o o o o o o o o 48 5-6 Ice and Sand-Ice Samples. (a) Volume Change versus Axial Strain. (b) Stress-Strain Curves. . . . . . . . . 50 Figure 5-7 5-8 6-6 Constant Strain-Rate Tests on Ice and Sand-Ice Samples. (a) Influence of Confining Pressure at Low Strain- Rates. (b) Influence of Confining Pressure and Sand at High Strain-Rates. . Typical Creep Curves for Sand-Ice Samples Compared with Ice Samples . . . . Results of Creep Tests on Ice. (a) Strain-Rate versus Strain. (b) Creep Curves for Ice. . . . . . . . . Effect of Absorbed Energy on Creep Rates of Polycrystalline Ice. (a) Loading Paths. (b) Creep Curves for Two Loading Paths. . . . . . . Sample Volume Change versus Axial Strain for Sand-Ice Samples . . . . . . . Effect of Friction Reducer Thickness on Apparent Results . . . . . Behavior of Hardening and Softening Terms for Ice . . . . . . . . Comparison of Creep Data on Ice with Curves Predicted by Equation (6-3). . . . Experimental Constant Strain-Rate Data on Ice Compared to Predicted Curves. (a) Test 39. (b) Test 26. . . . . Comparison Experimental Creep Data on Ice with Curves Predicted by Equation (6-5). (a) Test 30. (b) Test 29. (0) Test 31. (d) Test 36. (e) Test 37 . . . . . . . . . . . . . . Comparison Glen's (1955) Experimental Creep Data on Ice with Predicted Curves. (a) 01-03 = 52 psi, T = -0.02°C. (b) 01-03 = 87 psi, T = -0.02°C. (c) 01-03 = 87 psi, T = -12.8°C and -6.7°C. . vi Page 51 52 53 54 55 83 84 85 86 87 89 Figure 6-7 6-10 6-12 6-14 6-17 6-18 Comparison Experimental Creep Data on Ice with Predicted Curves for Step Loading . . . . . . Sand-Ice Sample 5. (a) Computations for Stress Factors. (b) Stress Factor versus Axial Plastic Strain. Sand-Ice Sample 11. (a) Computations for Stress Factors. (b) Stress Factor versus Axial Plastic Strain. Sand-Ice Sample 42. (a) Computations of Stress Factors. (b) Stress Factor versus Axial Plastic Strain. Sand-Ice Sample 17. (a) Computations for Stress Factors. (b) Stress Factor versus Axial Plastic Strain. Mobilization of Third Mechanism and Volume Change. (a) Sample 42. (b) Sample 11. (c) Sample 17. . . . Consolidated-Undrained Test on Saturated Sand (After Bishop and Henkel, 1962). (a) Stress-Strain Curve. (b) Pore Water Pressure versus Strain . . . . . . . . . . . Stress Factors versus Volume Concentration of Sand. (a) T = -12003°Co (b) T = -3085°C o I o o 0 Possible Relationship of Stress to Friction Angle of Frozen Sand Material. Sand-Ice Sample 33. (a) Ice Loading Schedule. (b) Comparison Experimental Data with Predicted Curves. . . . . Sand-Ice Sample 55. (a) Ice Loading Schedule. (b) Comparison Experimental Data with Predicted Curves. . . . . Sault Ste. Marie Clay Sample C2-Sl7. (a) Computations of Stress Factors. (b) Stress Factors versus Axial Strain (Data after Dillon, in preparation) vii Page 91 92 93 94 95 96 99 100 102 103 104 105 Figure Page 6-19 Sault Ste. Marie Clay Sample Cl-SZ. (a) Ice Loading Schedule. (b) Com- parison Creep Data with Predicted Curves (Data after Dillon, in preparation) . . . 106 6-20 Flow Volume versus Percent Sand by Volume. . . . . . . . . . . . . . 107 6-21 Observed Activation Energy versus Percent Sand by Volume. . . . . . . . . . 108 viii LIST OF TABLES Table Page 5-1. Summary of experimental results . . . . . . 56 A-l. Constant strain-rate test data. . . . . . . 118 A-2. Constant axial stress creep test data . . . 132 A-3. Elastic modulus test data . . . . . . . . . 138 ix AF AH AS TI AV 'Boltzmann's constant = 1.3805 X 10- NOTATIONS angstrom units = 10_8 cm effective area represented by one flow unit free energy of activation heat of activation Planck's constant = 6.624 X 10.27 erg. sec. the specific rate of the process 16 erg/°C net relative distance moved by one flow unit in one transition percent sand by volume in sample critical volume concentration of sand a stress concentration factor universal gas constant = 1.987 cal/mole/°C a structure term entr0py of activation temperature in °C or absolute temperature temperature in degrees Centigrade without regard for sign plus 0.80 time sample volume change a parameter which is a function of the number of flow units in the direction of deformation and the average component of displacement in the same di- rection due to a single surmounting of the barrier shear strain shear strain-rate ice density true axial strain true axial strain-rate 01 - 03 = axial stress difference first principal stress confining pressure and third principal xi Stress CHAPTER I INTRODUCTION Frozen soils, like most other materials, lose their ability to sustain stress at near melting point tem- peratures because they creep. Considerable research has been devoted to the subject of creep since the early 19503. Most of this research has been directed toward crystalline materials, particularly metals, and considerable progress has been made in understanding their creep behavior. The increasing need for a theory to describe the time dependent deformation of frozen soils and the failure of conventional concepts to do this has forced investiga- tors to examine the microsc0pic aspects of creep. It is now generally accepted that creep is a thermally activated process, and the rate process theory (Glasstone, Laidler, and Eyring, 1941) has been applied to describe the steady- state creep of a large number of materials including ice (Butkovich and Landauer, 1960; Dillon and Andersland, 1966a) and unfrozen soils (Murayama and Shibata, 1958; Mitchell, 1964). The difference between saturated frozen and un- frozen soils lies in the fact that the former contains an ice matrix in which the soil particles are imbedded. Any temperature change greatly alters the physical state and mechanical properties of this ice matrix. On examin- ing problems of mechanics of frozen soils it is not enough to consider only homogeneous solid bodies or only the me- chanics of unfrozen soils, since neither approach will account for the adhesion of solid mineral particles to ice. Both ice and frozen soils undergo drastic struc- tural changes with deformation. Recrystallization, chang- ing grain size, and fracturing of some grains in the ice during deformation is believed to permit gradual reorien- tation of soil particles. An external load applied to frozen soils produces stress concentration at points of contact resulting in plastic flow and melted ice. This increased pore water migrates to zones of'lower stress where it refreezes. Simultaneously, structural bonds and ice cementation in the weaker places yield, and mineral particles slip. This is accompanied by reorientation of both ice grains and mineral particles (Vyalov, 1963). Akili (1966) and Dillon (in preparation) have in- vestigated the applicability of the rate process theory to the steady-state creep rate of frozen soils and have thrown light on the effects of stress and temperature on their creep behavior. These studies have shown that al- though the rate process theory appears to describe the steady-state creep rate of frozen soils quite well, this creep rate is quite sensitive to stress history and structure of the material. The purpose of this study was an attempt to define the nature of this stress history and structure dependence. Uniaxial compression tests were performed on poly- crystalline ice samples to investigate the suggestion (Dil- lon, in preparation) that the creep behavior of polycrys- talline ice may be dependent in part on absorbed energy. Experimental data from this study indicate that the creep rate of polycrystalline ice may depend on both strain and absorbed energy as well as stress and temperature. It was assumed that strain and absorbed energy affect creep rate primarily through their influence on structure during de- formation, and using this concept along with stress and temperature dependence similar to that predicted by the rate process theory a creep equation for polycrystalline ice was develOped. Data from constant axial stress creep tests were used to evaluate the parameters in this equa- tion which appears to account for the creep behavior of polycrystalline ice through primary, secondary, and ter- tiary regions for the range of stresses and temperatures studied. The approach adopted to study soil structure ef- fects on the creep of frozen soils was to observe the ef- fect on the creep behavior of polycrystalline ice tested in uniaxial compression by the addition of increasing amounts of solid mineral particles frozen in the ice in dispersed positions. Sand sized particles were used to minimize the variable of unfrozen water. In this way three mechanisms were identified which tend to strengthen sand-ice samples versus samples of pure ice. The first mechanism is dependent on the volume concentration of solid particles in the sample and the second two are the result of solid to solid contact and depend also on the frictional characteristics of the solid material. A method is presented to evaluate the effect of these mechanisms and thus to predict the results of con- stant axial strain-rate and axial creep tests for sand- ice material. Computations are included which indicate that these same mechanisms may Operate also in frozen clay soils. CHAPTER II LITERATURE REVIEW The failure of the fundamental concepts of the theories of elasticity and plasticity to explain the fail- ure of materials by time-dependent deformation or creep has lead investigators to look to the microstructure of materials in order to develOp a theory that will predict this phenomenon. Chapter II will review some of these theories as they relate to frozen soils and ice. Experimental Evaluation of Creep Creep is the time-dependent deformation of mate- rials which occurs under constant stress and temperature. Although the particular microsc0pic mechanisms responsible for creep in various materials may be quite different, the observable macroscopic creep is quite similar. Typical creep curves for polycrystalline ice are shown in Figure 2-1. In the general case a creep curve consists of four stages: Stage 1, termed the instantaneous strain, represents the strain which occurs on loading; stage 2, termed primary or transient creep, represents the initial region of decreasing creep rate; stage 3, termed secondary or steady-state creep, represents the region of relatively constant creep rate; and stage 4, termed Axial strain (in/in) Primary 0'05 . Secondary Tertiary 0.04 - .' . ' Sample 36 . ' T = -7.60°C 0.02 - . . Sample 37 0.01 - .’ °1‘°3 = 9: psl' °3 = 0 ' Damped creep T = ‘7°5§_§y__—- 0 . l l I l l 0 100 200 300 400 500 Time (minutes) Figure 2-1. Typical Creep Curves for Polycrystalline Ice. tertiary creep, represents the final region of increasing creep rate, leading eventually to failure of the specimen. Depending on the stress or temperature, one or more of these stages may be missing; for example,stage 3 is almost nonexistent for small stresses at low temperatures or for large stresses at warmer temperatures. Different materials show similar creep curves un- der prOper adjustment of stress and temperature; creep curves for metals, crystalline nonmetals and noncrystal- line materials are all similar. Considering the differ- ences in atomic structure of these materials, it must be evident that the details of the creep curve itself cannot identify the micro-mechanisms responsible for creep. How- ever, the similarity of the creep curves for these materials does indicate that a similar sequence of rate determining mechanisms is followed in all cases. It is now generally accepted that creep is a ther- mally activated process, where creep takes place as the result of the flow of activated units over a free energy barrier to move from one equilibrium position to another. Rate Process Theory The rate process theory (Glasstone, Laidler, and Eyring, 1941) has been used as a basis to derive a general equation for creep by an analytic approach. All viscous or plastic flow of incompressible material is the result of shear strain. In applying the theory of rate processes to creep it is assumed that flow takes place by the move- ment of flow units (atoms, molecules or aggregates of mole- cules) into vacancies in the material, thus moving from one equilibrium position to another. In making this transition from one equilibrium position to the next the flow unit must surmount an energy barrier of size AF. The energy necessary to surmount AF can be supplied either thermally or as the result of an externally applied force. An expression for the specific reaction rate of such a molecular process derived in accordance with the theory of absolute reaction rates is _ kT Kr — h eXp( AF/R'I‘) where Kr is the specific rate of the process, k is Boltz- 16 mann's constant (1.3805X10— ergs/°C), T is the absolute ’27 ergs sec.), temperature, h is Planck's constant (6.624X10 AF is the free activation energy, and R is the universal gas constant (1.987 cal/mole °C). In the absence of applied forces to the material no consequences of the periodic thermal activation are ob- served since barriers will be crossed with equal frequency in all directions. If, however, a directed shear force is applied to the material, then the barrier heights become distorted. Figure 2-2 depicts the energy barrier schemati- cally. The solid line represents the energy barrier in the absence of applied shear force. The dashed line shows the distortion of the barrier when shear force is applied. If A is the effective area represented by one flow unit and Q is the net relative distance moved by the flow unit in one transition, then the work done by the applied shear stress for one transition is rqAfl, where q is a stress concentration factor. Now the energy required to initiate a forward tran- sition is AF-IqAI, and the energy necessary to initiate a backward transition is AF+TqA£. Let Krf be the specific. rate of the forward transitions and Krb be the specific rate of the backward transitions, then the net specific forward transition rate is Shear stress T Energy / \ 7 thE/Z \‘ IqAQ/ZJQ | / _’ "—9 Without shearing force ----- With shearing force ¥ f Direction of strain Figure 2-2. Schematic Representation of Energy Barriers. _ _53 _AF IqAQ _kT (.933... TgASU Kerrb’hexP(fi+ RT) TexP RT RT) 111: _ A_§‘_ . ISAQ) 2h exp( RT) Slnh( RT If a parameter X is defined which is a function of the number of flow units in the direction of deformation and the average component of displacement in the same di- rection due to a single surmounting of the barrier, then the total displacement per unit time will be X(Krf-Krb) and corresponds to the shearing strain rate, y j = 2X13?- exp (— é—Fl) sinh (ii—T139) 10 Since k equals R/N, where N is Avogadro's number 23 (6.02 X 10 ), it merely requires a change of units to obtain AF can be eXpressed as AF = AH-TAS, where AH is the heat of activation for the system and AS is the entrOpy of activation for the system from which is obtained j = 2X15}?- exp(A§S-’) exp (—%) sinh(T—%Z,;—Q) (2-1) This is the general creep equation derived by utiliza- tion of the rate process theory. The derivation of equa- tion (2-1) was carried out for one mechanism. This is clearly not necessarily the case and many mechanisms may Operate simultaneously, each with their own values of X, AS, AH, q, A, and Q (Kauzmann, 1941). Thus the total shearing strain rate is the result of the total action of all possible mechanisms. Also, it should be noted that these values for any mechanism can change during deformation. In applying equation (2-1) to crystalline mate- rials such as ice it is assumed that the plastic defor- mation of the crystals takes place by the movement of dislocatiéns. The deformation of clays under an applied stress is assumed to be the result of the breaking and reforming of interparticle bonds which arise at the contact points 11 between particles as the result of microsc0pic force fields. The interparticle bond is assumed to present an energy barrier to relative motion between particles, and surmounting this barrier is assumed to be a thermally activated process (Christensen, 1964). In equation (2-1) the parameters X, AH, and qA£ may depend on stress r, temperature T, and structure 3. To obtain the detailed creep equation one must evaluate the nature of the dependence of these parameters. This is especially difficult, since 3 is determined by the history of stress, temperature, and strain-rate as well as their instantaneous values. Consequently, one must separate the effect of test variables on the structure from their effect on the deformation mechanism. Two types of mechanical tests are employed to evaluate the deformation equation (Conrad, 1961): 1. Conventional tests, i.e., the standard creep test where the conditions are held constant. Relationships are then developed between strain-rate, stress, and tem- perature for a given strain or for a given position on the creep curve. In these tests the effects of stress or temperature include structure changes. 2. Differential tests. In this type of teSt changes in stress, temperature or strain rate are made during the test. It is assumed that if the changes are small and rapid enough the structure will remain constant and the 12 effect measured will be related to the deformation mecha- nism. One then hOpes to derive the detailed deformation equation by solving the differential equation obtained by such tests. Observations indicate that strain rate depends on stress in generally one of four ways (Conrad, 1961): (1) linear (jar); (2), power law (turn); (3) exponential (jaexp B); and (4), hyperbolic sine law (jasinh B). The specific form of this dependence varies for different materials and can depend on stress and on temperature. More will be said in this regard with respect to ice and frozen soils. The effect of elevated temperature on strain-rate is, like increased stress, to increase the strain-rate. Observations seem to confirm the temperature dependence of strain-rate predicted by the rate process theory for most materials. Although a number of deformation mechanisms may be operating simultaneously, usually one is rate control- ling (Conrad, 1961). Thus by computing activation ener- gies (AF) and flow volumes (th) one can infer certain things about the dominant flow process under certain con- ditions for a given material. Structure of Ice The oxygen atoms in an ice crystal are formed in a tetrahedral pattern, with each oxygen atom being 13 surrounded by four approximately equally spaced oxygen atoms at the vertices of the tetrahedron. Each pair of oxygen atoms is linked by a hydrogen bond (Pounder, 1965). If the tetrahedron were perfect,that is if all bonds were of equal length and all the 0'00” and 0”00" angles (Fig- ure 2-3) were equal, these interior angles of the tetra- hedron would be 109° 28'5 There are slight deviations from this figure but this is a good first approximation. Figure 2-3 shows a sketch of a small section of ice lattice with interatomic distances. Solid lines represent hydrogen bonds and the outline of the tetra- hedron surrounding the oxygen atom marked 0 is shown by dashed lines. The three atoms marked 0"form an equi- lateral triangle in a plane which is called the basal plane of the lattice. The 0'0 bond gives the direction known as the c-axis, which is perpendicular to the basal plane. Consider now the four bonds of the atom 0'. One of them is the bond 0'0 and the other three must go to three equally spaced 0'” atoms as shown. These three atoms must also lie in a plane perpendicular to 0'0. Thus the tetrahedron about 0' is inverted, with its base parallel to that of the tetrahedron about 0. Figure 2-3 shows the complete bonding system for the 0 and 0' atoms, but of course each of the six 0" and 0'” atoms must have three additional bonds. In this way ‘the: lattice is extended in all three directions. This orderly arrangement of atoms is disrupted at grain bound- aries. 14 0 "I Io 0.923 A o A 2.760 Figure 2-3. Structure of Ice Lattice (After Pounder, 1961). Masses of polycrystalline ice are aggregates of single crystalline grains. In quickly frozen masses these grains may range from only a fraction of a millimeter to several centimeters in size. The boundaries between neigh- boring crystals in polycrystalline ice are usually irregu- lar and often depend on the mode of freezing. The exact nature of the ice contained in frozen soils is not known and may or may not be polycrystalline —‘ in nature. However, since the contagtmstresses from the .‘ m. ““ ' ...~—‘M~—.—— m...” ' " ~ ‘ ~ M ""‘ soil grains are iEPQ§edwon the ice grains in randgm di- ‘ -~ A--—-m._.m.“_...__ . rections, flow in the i Q“ .1. - M......_.... .‘ ce must take place in random di- \.-...-.—_‘. __ ‘ A - ._. rections and the ice probably behaves in a manner similar \"WNWMM- . - . "W“W'W'm'“““wmwwwHtuim... ' .11...“ W . ‘ to polycrystalline ice (Dillon and Andersland, 1966a). 15 Therefore information on the behavior Of polycrystalline ice was needed before any attempt could be made towards predicting the mechanical behavior of soil-ice combinations. Mechanical Properties of Ice Single crystals of ice deform plastically,by glide on the basal plane, and there is considerable evidence that this is the only effective slip direction (Glen and Perutz, 1954; Steinemann, 1954; Kamb, 1961). Thus in polycrystalline ice, where the orientation of the indi- vidual grains is random, continuity Of the material de- mands that other mechanisms Operate to permit the grains to conform to an arbitrary change of shape. Glen (1955) suggests grain boundary migration and recrystallization as mechanisms to allow the ice grains to conform to the imposed deformation. When a material is undergoing creep, its grains can be rigidly slipping past each other, with consequent boundary changes, or else ac- cumulating strain inside the grains. In the latter case, the probability of recrystallization, i.e., Of both nu- cleation of new grains and their subsequent growth, will rise as the internal stress rises, and new recrystallized material will be continually appearing, which can be con-- sidered as free from internal strain at the instant Of its formation. After a long time a steady-state will be reached in which the hardening caused by the rise in in- ternal strain is balanced by the softening caused by re- brystallization. 16 Gold (1963) in Observing surface features of ice during deformation has identified seven deformation mecha- nisms. 1. These are: Slip bands. This is the result of slip on the crystalline basal plane which takes place in discrete bands. Grain boundary migration. Grain boundary migration was one Of the first signs Of change in grain boundaries, and prac- tically every boundary Observed showed evidence of migration. Kink bands. Kink band formation is a mechanism by which bending moment in a direction transverse tO the slip direction can be relieved in crystals with only one or two slip directions. Distortion of grain boundaries. Crack formation (accommodation cracking). The rate of formation of these cracks was de- pendent on creep rate. The lower the creep rate, the fewer are the accommodation cracks that form and the longer is the time for the first to develop. Cavities. Cavities were observed in the region of grain boundaries, grain boundary triple points, and the intersection of slip planes and sub- boundaries. Recrystallization. In single crystals of ice the macrosc0pic behavior can be associated with microscopic details since the only geometric constraints are those within the crystal. In the case of polycrystalline material however, new con- straints to dislocation motion are introduced by grain boundaries, and if integrity Of the grains is to be pre- served, each must deform in a manner compatible with its 17 immediate neighbors. Since the constraints Of the grains differ according to orientation Of the grains, the Ob- served deformation in polycrystalline ice is the result of a complex relationship between a large number of grains, with each grain attempting to deform in its own way but being forced to compromise by its neighbors. Because of this the observed macrOSCOpic behavior of polycrystalline ice can only qualitatively be associated with the behavior Of single crystals. As indicated previously, by theoretical considera- tions, temperature has a strong influence on the creep .,,\\\_ffl_fl~__,fl____,,_. ‘,_1 ,~,,_ rate Of 01 cr stalline ice. There is considerable evi- dence to show that this influence is the result of ther- mal activation in accordance with the rate process theory (Dillon and Andersland, 1966a; Butkovich and Landauer, 1960; Glen, 1955). A hyperbolic sine stress dependence Of the steady- state creep rate for ice as predicted by the rate process theory has been proposed (Dillon and Andersland, 1966a; Butkovich and Landauer, 1960), as well as power law de- pendence (Glen, 1955; Steinemann, 1954; Nye, 1953). Dillon and Andersland (1966a) report activated flow volumes on the order of 107 cubic angstroms for polycrystalline ice indicating that boundaries of ice grains are probably involved in the creep of polycrystal- line ice. 18 The dependence Of the creep rate on the amount Of energy absorbed by a material has been suggested (Rabotov, 1963). Dillon (in preparation) has found that the creep rate of polycrystalline ice appears to be dependent on energy absorbed. Structure Of Frozen Soils Frozen soils can be considered as a four phase substance containing solid mineral particles, an ice ma- trix, water, and air. The physico-chemical properties Of the soil particles significantly influence the struc- ture and mechanical prOperties Of the frozen soil mass. It is believed that the major part of the resistance to shear develOped by granular materials is due to friction between solid particles, while true clays possess in ad- dition to this the prOperty Of cohesion. The cohesion parameter is dependent in part on such variables as clay mineral and soil composition, prestress history, soil structure, nature Of pore water, and degree Of saturation. In fine grained soils containing particles with a high specific surface area an appreciable portion of the water may remain unfrozen even at temperatures well below the freezing temperature of ordinary water. This unfrozen water surrounds the solid clay mineral particles, and is a function of specific surface area, colloidal activity of the clay minerals, and temperature (Dillon and Anders- land, 1966b). 19 During freezing bulk soil volume increases, pri- marily because Of the movement of water to the freezing boundary and the growth of ice crystals which attract moisture from adjacent locations in the soil. The dis- tribution Of moisture in the soil after freezing is a function of the direction of freezing, permeability of the soil, and time. It is known that the increase in volume of a satu- rated sand On freezing is only a small percentage of the total bulk volume, even when there is an external source Of water available (Tsytovich, 1963). On freezing, the change in volume of the water in the pores may amount to several percent Of the sample volume. It follows then that when freezing saturated sand excess pore water will be forced out from the freezing boundary. The amount of increase in volume Of soils on freezing is a function Of permeability. Thus in fine grained soils of silt-size one would expect a considerable increase in volume on freezing with development of ice lenses. Little water movement occurs in clay soils having low permeabilities. Note also the implication that in soils of low permeability excess pore water created by expansion on freezing may be dissipated through the material and some structural rear- rangement of the particles may result. The strength Of all saturated soils increases on freezing because Of adhesion between the ice and soil particles. The strength of saturated sands can be several 20 times greater than that Of frozen saturated clays for the same temperature. This can be explained in that a con- siderable amount of the water in clay soils remains un- frozen. If the soil is only partially saturated, its frozen strength increases with increased water content up to a limit close to the full saturation point. This will vary with soil type. For higher water contents the frozen soil strength falls Off and approaches that Of pure ice (Tsyto- vich, 1963). Mechanical Properties Of Frozen Soil The current trend is to consider the deformational characteristics of frozen soils as a function of its inter- particle bonds, such as electromolecular, aqueocolloidal, and ice-particle adhesion. The most important in frozen soils is the ice-particle adhesion, which is the strongest and most easily changed. Change in temperature produces a change in strength Of frozen soils due to the quality Of the ice and changes in ice-particle adhesion. Properties of pore ice are af- fected by temperature and pressure. _An external load pro- duces stress concentration at contact points resulting in w plastic flow and pressure melting of the ice (Barnes and “ Tabor, 1966). The liquid water in these high stress zones migrates to areas Of lower stress where it recrystallizes with orientation Of the basal plane parallel to the 21 slide direction. This results in a reduction of the shearing resistance. Denser packing Of the mineral par- ticles occurs simultaneously since the locations which become vacant as a result Of the displacement of the mois- ture are filled with solid particles under the influence Of pressure. This gives rise to molecular cohesion be- tween particles (Vyalov, 1963). Thus two mutually Opposed phenomena occur in frozen soils under the influence Of pressure: on the one hand there is weakening due to the gradual reorientation Of the ice crystals and destruction Of natural soil structure, and on the other hand there is strengthening due to the increased molecular cohesion caused by closer packing of the mineral particles. If the load is such that it leads to deformation, but does not exceed a certain threshold value, softening will be compensated by hardening and a steady-state de- formation rate will result. However, if this threshold load value is exceeded, then softening exceeds hardening and undamped flow takes place. This threshold value Of load defines the long term strength Of the frozen soil (Vyalov, 1963). Results Of studies by Akili (1966) and Dillon (in preparation) indicate that the time-dependent deformation Of frozen clays may be considered as a thermally activated process in accord with the rate process theory, with tem- perature dependence Of the strain-rate appearing in the 22 form exp(-AF/RT). Andersland and Akili (1967) show that an approximate straight line relationship exists between the logarithm of true axial creep rate and axial stress at high stress, suggesting that an expression for strain- rate include stress dependence in the form sinh(Bo). The B term is some function Of temperature and frozen soil structure. In undamped creep of frozen soils interparticle forces may be small as compared with the adhesion between soil particles and the ice matrix. This study recognizes that the softening and hardening phenomena may result from a number Of mechanisms all contributing simultaneously to the frozen soil behavior. In an attempt to predict the mechanical behavior of the frozen soil all softening mecha- nisms are grouped in one term and all hardening mechanisms are grouped in another. It has been convenient to include the absorbed energy, strain, and temperature in the equa- tion. Limitations in time have restricted the study to only certain combinations of ice and sand. The close agreement between experimental data and predicted defor- mations illustrated in Chapter VI lend support to the methods used. CHAPTER III MATERIALS STUDIED AND SAMPLE PREPARATION Materials studied and the methods used in preparing samples are described in Chapter III. General information pertaining to both ice and sand-ice samples includes sam- ple size; use Of only distilled, deaerated and deionized water; freezing temperatures; and aging history. All samples were cast in one aluminum mold which was 1.13 inches in diameter and 2.26 inches long. This diameter gave an initial sample cross sectional area of one square inch. After each use the mold was taken apart, cleaned, reassembled and a thin coat Of silicone grease applied to prevent adhesion of the next sample to the mold. Differences in samples due to aging were mini- mized by using the same aging history for all samples. The samples were left in the mold in a cold box, main- tained at a temperature of -18:2°C, for about 24 hours. They were then prepared for testing and mounted in the triaxial cell where they were left for another 18 hours before testing. Ice Samples The ice samples were prepared by first cooling the aluminum mold in the cold box. Dry natural snow was 23 24 then placed loosely in the mold and the prepared water, previously cooled to 0°C, was poured over the snow. Vir- tually none of the snow melted when combined with the pre- cooled water. The resulting polycrystalline ice sample was cloudy in appearance and measured densities ranged from 0.900 to 0.913 grams per cubic centimeter, except sample 1, which was found to contain a rather large void. There was some radial pattern visible when the samples were broken apart, but in general very homogeneous samples were formed.. Ex- amination Of thin sections Of this ice under a micrOSCOpe revealed irregular grains of about one millimeter in di- ameter. A few columnar grains were observed. During part Of this study natural snow was not available and ice samples 26 through 32, and 36 and 37, were made from specially prepared ice, powdered in a Waring food blender. The food blender was first chilled in the cold box. This powdered ice was then mixed with more Of the distilled and precooled water, forming a slurry which was put into the cold mold and allowed to freeze. There was no visible difference between samples prepared by these two methods and correlation tests showed very little, if any, difference in deformational charac- teristics. The density of the ice in the samples prepared with powdered ice ranged from 0.904 to 0.912 grams per cubic centimeter. 25 Sand-Ice Samples Two types of sand were used. The coarser material, used in samples up through 44, was standard Ottawa sand. The grains were well rounded and only that portion pass- ing a number 20 sieve and retained on a number 30 sieve was used. The specific gravity Of the sand was 2.65. A new supply Of Ottawa sand, used in samples num- bered 45 and higher, may have contained more angular shaped particles. Although there was nO visible difference in these materials, the first supply of sand which had been previously used in a density test apparatus showed less resistance to deformation. The sand used in samples up through 44 will be referred to as the first coarse sand or Cl material. The second batch of Ottawa sand will be referred to as the second coarse sand or C2 material. A few tests were performed on a fine sand material to show the effect of grain size. For these tests a dune sand from Silver Lake, Michigan was used. This raw mate- rial contained large amounts of fine material and only that portion which passed the number 70 sieve and was re- tained on the number 100 sieve was used for sample prep- aration. These sand grains were also well rounded and the specific gravity of the solids was 2.65. This material will be called the fine sand or F material. In order tO prepare sand-ice samples'with the sand particles in dispersed positions, the sand was 26 chilled tO below freezing and then mixed carefully with dry natural snow. This mixture was then placed into the cold aluminum mold and water, precooled to 0°C, poured over the mixture. Very little snow melted as a result of pouring ice water over the snow and sand mixture. The resulting sample contained uniformly dispersed sand par- ticles. The sand-ice samples containing the maximum vol- ume concentration Of sand were prepared by placing dry sand in the mold, pouring precooled water over the sand, and freezing. Each sample was weighed before testing. After testing the ice was melted, the water removed by drying, and the remaining sand weighed. With this information and the known volume Of the mold, the volume concentra- tion Of the sand and the density of the ice matrix was computed. The ice density in the sand-ice samples ranged from 0.848 tO 0.917 grams per cubic centimeter. The lower ice densities were the result of a few air bubbles being entrapped in the sand-ice samples. Volume expansion resulting from the change of water to ice forced some water out the top Of the mold. Some‘Of the fine sand grains were carried up with this water thus limiting the maximum volume concentration of sand obtainable for samples made with the fine sand mate- rial. CHAPTER IV EQUIPMENT AND TEST PROCEDURES The equipment used and the test procedures for the constant axial strain-rate tests and the constant stress creep tests are described in Chapter IV. Each sample was kept in the mold in the cold box for approximately 18 hours before the sample top was trimmed flush with the top Of the mold. The sample was then removed from the mold and weighed. Friction reducers and lucite disks were placed at each end of the sample and two rubber membranes were placed over the sample and disks. The friction reducers are described later in this chapter. Figure 4-1 shows schematically the triaxial cell and sample placement. Equipment The entire triaxial cell (Figure 4-1) was immersed in a coolant, ethylene glycol and water mixture, maintained at a constant temperature by circulating through a micro- regulator controlled cold box. Temperatures were recorded using a thermistor (Yellow Springs Incorporated #901) held adjacent to the sample by a stiff wire. The thermistor was calibrated with the aid of a OOpper-constant thermo- couple and a reference ice water bath. The temperatures recorded during the tests varied by no more than :0.05°C. 27 28 Linear differential transformer Leads to recorder Burette Air release valve Z::>Olant Therm— istor ction Coolant Rubber bands Lucite Valve for Force triaxial ducer cell // Figure 4-1. Schematic Diagram Of Triaxial Cell Showing Sample Placement. 29 The sample rested directly on a force transducer and de- flections were measured with a linear differential trans- former. The outputs of the thermistor, force transducer, and differential transformer were fed into a Sanborn 4- channel recorder which provided a continuous temperature, axial load, and axial deformation record. At maximum sen- sitivity one centimeter needle deflection on the recorder represented 0.05°C temperature change. Maximum sensitivity provided a needle deflection Of one centimeter per 0.002 inches sample displacement for the differential transformer. The force transducer had a rated capacity of 1000 pounds with overload tO 1500 pounds and at maximum sensitivity the needle deflection was one centimeter for 5 pounds load. The base line on the chart record made by the recorder could be shifted as a test progressed making it possible to use maximum sensitivity throughout the test if desired. Sample volume changes during a test were measured by means of a burette and flexible tube connected to the triaxial cell air release valve. The burette and tube were kept submerged in the coolant in order to minimize expansion of the fluid due to any temperature change. The burette was always read with the meniscus level with the surface of the coolant surrounding the triaxial cell, thus eliminating corrections needed for any change in head. 30 The burette was calibrated directly to 0.01 cubic centi- meters. For tests run with confining pressure the triaxial cell was connected to a constant pressure source. To min- imize leakage from the triaxial cell the Openings used for temperature and volume measurements were closed. Also, when volume measurements were made the thermistor Opening was closed and when temperature measurements were made no attempt was made to measure volume change. When temper- ature was not recorded by the thermistor a laboratory type thermometer with scale divisions to 0.1°C was used to meas- ure the temperature of the coolant bath. The temperature could be estimated to 0.0l°C. It was Observed that the temperature inside the triaxial cell adjacent to the sam- ple did not vary by more than 0.05°C from that measured with the thermometer in the coolant bath. Temperature fluctuations in the triaxial cell were reduced as com- pared tO changes in the larger coolant bath because Of the delayed response time. Figure 4-2 shows the test machine, coolant bath containing the triaxial cell, refrig- eration unit, and Sanborn recorder. The elastic deflection of the loading system was evaluated by substituting a steel plug corresponding to the sample size, applying a load, and Observing defor- mations with the differential transformer. This elastic deflection was close tO 0.0008 inches per 100 pounds of load and is corrected for in the data presented. 31 Figure 4-2. Triaxial cell in coolant bath, test machine, Sanborn recorder, and refrigerator unit. Figure 4-3. Deformed ice Sample (left) Compared with an Undeformed Sample (right). 32 The first friction reducers were made by coating both sides Of a piece of aluminum foil with a mixture Of silicone grease and powdered graphite. A thin polyeth— ylene film was then applied to both sides Of the aluminum foil and the excess grease mixture was squeezed out with a hydraulic press. This sheet was then cut into disks of the apprOpriate size. It was Observed that the volume Of grease and graphite which remained was sufficient to introduce un- predictable errors in deformation measurements. Grease expelled from the friction reducers during a test caused apparant sample deformation on the test record. This error was measured by means Of the same steel plug used to measure elastic error and it was observed that the original friction reducers deformed up to 0.012 inches. A modified friction reducer used only silicone grease spread on both sides of the aluminum foil placed in as thin a layer as could be applied by hand. The polyethylene films were then applied to each side Of the aluminum foil and any entrapped air was worked out by hand. The sheet was then cut into disks Of the prOper size and these disks were used beginning with sample 27. The modified friction reducers reduced the deformation error to approximately 0.003 inches and appeared to work as efficiently as the original ones. Figure 4-3 shows a sample before testing compared with one after 33 testing illustrating the uniform deformation and lack of "barreling." There was also a seating error introduced by the sample coming into more perfect contact with the lucite disks. The combination Of the errors from the friction reducers and from the sample conforming tO the lucite disks will be called seating error. Tests with the steel plug revealed that there was some viscoelastic behavior in the system presumably resulting from deformation Of the lucite disks. For this reason no attempt was made to evaluate the time dependent recovery Of the materials tested. It is recommended that in future studies the lucite disks be replaced by disks Of some material not subject to this type of deformation. Constant Axial Strain-Rate Tests The same triaxial cell and testing machine were used for all tests. For constant axial strain-rate tests the load was applied directly to the loading ram by a variable speed mechanical loading system. Two deformation rates (0.0003 and 0.0006 inches per minute) were used. These rates were chosen because Of ease in checking with the calibration of the Sanborn recorder. Note that the use Of a constant deformation rate produces a slightly increasing true axial strain-rate due to sample shortening as a test proceeds. This difference has been neglected unless otherwise noted. 34 The deformation rates were easily maintained except when the load was changing rapidly. Results showed that the maximum variation was less than 10 percent when ob- served over a 10 minute period, for all but the first few tests . At the end of each test the immediate elastic re- covery was measured. The remainder of the sample defor- mation was considered to be plastic and non-recoverable. No attempt was made to measure viscoelastic recovery since this was masked by the viscoelastic recovery of the lucite disks. No method was devised to separate the recovery of the disks from that Of the sample. The total Observed deflection consisted Of two parts, that contributed by the system and that contributed by the sample. The equipment deflection will be called system error and is composed of seating error and system elastic error as described earlier. The deflections con- tributed by sample deformation include elastic and plastic strains. The variation in the density Of the ice (0.900 to 0.913 grams per cubic centimeter for ice samples and 0.848 to 0.917 grams per cubic centimeter for sand-ice samples) caused some variation in the test results. These differ- ences in ice density were assumed to be due to small air inclusions in the ice. For most samples there were no voids present that were large enough to be visible. If no 35 inherent weakening Of the ice results from these air in- clusions, the effective area Of the ice may be considered to be diminished by an amount prOportional to the air con- tained. Test results were improved by correcting the com- puted stress on the samples by a factor proportional to the variation Of the sample ice density to a standard density of 0.900 grams per cubic centimeter. Although most Of the samples deformed very uniformly there were a few that indicated membrane leakage or eccen- tric loading. Flaring at one end of the sample was assumed to be caused by slight leakage Of the coolant between the membrane and the lucite disk. Bending was caused by either a bad sample or by the sample slipping laterally on its supports and hence an eccentric load application. Note is made in the data when these defects occured. Constant Axial Stress Creep Tests For the constant axial stress creep tests a load frame, supporting a dead weight Of lead bricks, was lowered onto the loading ram by the mechanical loading system. The load was lowered at a fairly fast rate and it took about 4 seconds for the entire weight to transfer to the sample. Dynamic effects would be small and were assumed to be neg- ligible. Lead shot was added tO the dead load as the sample deformed to compensate for increased cross sectional area Of the sample. Constant sample volume was assumed for this correction. General information on system error, corrections 36 for variations in density of the ice, membrane leakage, and possible eccentric loading are the same as for the constant axial strain-rate tests. CHAPTER V EXPERIMENTAL RESULTS Experimental results along with a brief discussion of implications of these results are given in Chapter V. This material is presented in three parts: elastic re- sponse, results of constant axial strain-rate tests, and results Of constant axial stress creep tests. Elastic Response The modulus of elasticity was computed from the sample elastic recovery and the load on the sample at the end of each regular test and a few samples were tested for the express purpose of finding the modulus Of elasticity. This computed value Of modulus Of elasticity was found tO be dependent on the amount Of deformation undergone by the sample, and was found to decrease with an increase Of plas- tic strain. The results Of these measurements and compu- tations are presented in Figuresfil and 5-2. The valueqof the modulus Of elasticity for coarse sand-ice samples was found to be about the same as for ice samples under equivalent conditions. Some increase in the value Of the elastic modulus was noted with an increase in temperature as shown on Figure 5-1. Fine sand-ice samples exhibited some decrease in the value Of modulus Of elasticity with increasing plastic 37 38 strain (Figure 5-2) but not nearly as much as that Of coarse sand-ice and ice samples, shown by Figure 5-1. Figure 5-3 shows modulus of elasticity plotted versus percent sand by volume for samples at -l2°C, and with plastic strains Of 3 to 4 percent. There is considerable Spread in the points due tO the scale, and also due to the fact that a range of plastic strains are covered, but it does appear that the elastic modulus is somewhat less for samples with about 10 to 40 percent sand. Discussion Of sample elastic behavior will be presented in Chapter VI. Data from Figures 5-1 and 5-2 were used for compu- tations requiring estimates Of sample elastic deformation. Constant Axial Strain-Rate Tests Constant axial strain-rate tests were used to determine the effect Of the volume concentration of the sand contained in the sample on sample strength. Typical stress-strain curves for samples at -12.03°C and deformed at 0.0003 inches per minute are shown in Figure 5-4. Note the similar appearance Of curves 3,8, and 13, whereas sam- ples 5 and 11 show a larger increase in strength with the strain for peak strength considerably larger. This shift in position Of peak strength for samples 5 and 11 shows additional strengthening at large stresses for samples with large volume concentrations of sand, and will be dis- cussed in the following chapter. 39 When peak strength is plotted versus percent vol- ume concentration of sand for samples deformed at the same rate and at the same temperature, a bilinear relationship is indicated, as shown by Figure 5-5. The method Of com- puting the points so indicated in Figure 5-5 will be covered in Chapter VI. There appears to be a critical volume concentration Of sand (about 42 percent by volume) where the sand grains just begin to make contact or where the sample behavior becomes dependent on the nearness of ad- jacent sand particles. Harr (1962) lists a porosity of 0.476 for uniform spheres in a cubical array (loosest possible packing). This corresponds to a volume concen- tration of solids of 0.524. The critical volume concen- tration Of sand would be expected to be a little lower than this since any irregular protrusions Of the sand grains must avoid contact with their neighbors during de- formation. Sample volume change during deformation was meas- ured for several samples and typical curves are presented in Figure 5-6. For pure ice there was an initial small volume increase followed by a decrease continuing to a little below the original. If the sample contained sand below the critical volume concentration there was an ini- tial volume decrease. Sand-ice samples with greater than 42 percent volume Concentration Of sand showed a more rapid initial volume 40 decrease followed by a volume increase which progressed at an increasing rate to the limit of the measuring equip- ment. The large volume increase for samples containing an amount of sand greater than the critical volume concen- tration is associated with solid to solid contact and is similar to the volume increase Of dense unfrozen sand (Bishop and Henkel, 1962). The effect Of confining pressure on ice samples indicates that the initial volume increase may be asso- ciated with failure. One would expect confining pressure to increase strength if failure were associated with vol- ume increase, and indeed for samples deformed at a rate above a certain limiting value, where failure mechanisms were presumably dominating, there was an increase in strength with confining pressure. The effect of con- fining pressure On samples deformed at a rate below this limiting value was very small or even weakened the sample slightly. Figure 5-7 illustrates this result. Note that for samples deformed at 0.0006 inches per minute either the addition of a small amount Of sand or the application of confining pressure considerably increased the strength. Note also that nearly the same peak stress was obtained for the computed curve for ice and the curve for ice with confining pressure. Andersland and Dillon (1966a) report a transition from one mode Of creep behavior to another in ice for 41 5 octahedral creep rates in the range of 9 X 10_ to 6 X 10- per minute. The transition octahedral rate here would be 4 and 3.8 X 10-4 per minute. between 1.9 X 10- The maximum volume decrease for any sample was about 0.06 cubic centimeters. This is about 0.16 percent. If it is assumed that this volume decrease is all accom- modated by entrapped air and that the ice density is con- trolled entirely by entrapped air then the density Of the ice for a sample with 60 percent sand by volume would need to be at least 0.914 grams per cubic centimeter Of less. Computations show that in all cases there was sufficient entrapped air to accommodate volume decreases and no fur— ther correlation could be found between the amount of en- trapped air and the amount Of volume decrease. Constant Axial Stress Creep Tests The creep behavior of the materials tested here conformed in general to "classical creep behavior" with several typical curves given in Figures 2-1 and 5-8. Note the large initial deflection of the sand-ice sample number 35 and the decelerating rate at large strain imply- ing strengthening, also shown by the constant deformation rate tests (Figure 5-4). Figure 5-9b shows creep curves for ice at several stresses and temperatures.‘ Figure 5-9a diSplays a plot of instantaneous plastic strain-rates versus plastic strains. All strains represented in Figure 5-9 have been 4 42 adjusted for system deflections and sample elastic strain. The numbers on the curves in Figure 5-9a give the time in minutes to reach the strain indicated. Figure 5-10 illustrates the results Of three tests to determine the effect Of load history on creep rates and to investigate a relationship between creep and constant strain-rate tests. Dillon (in preparation) has shown a similar relationship. Sample 4 was deformed at 0.0003 inches per minute (about 1.33 X 10-4 inches per inch per minute) giving a peak steady-state stress of about 321 psi at 2.5 percent axial strain. A constant axial stress Of about the same magnitude (325 psi) was applied to sample 7 which was permitted to deform at its own rate. A steady- state strain-rate Of 1.77 X 10-4 per minute was reached at about 2.5 percent strain. Note that this strain-rate is higher than that applied to sample 4. A step loading forced sample 6 to absorb the same amount of energy prior to reaching 2.5 percent strain as was absorbed by sample 4. At 2.5 percent strain the load was increased to approxi- mately 318 psi. The steady-state creep rate resulting from this loading was 1.37 X 10”4 per minute which is close to the strain-rate applied to sample 4. This re- sult suggests that if the energy absorbed by two samples is the same when a given strain is reached, the samples will behave identically from then on. 43 At the time this series Of tests was performed the importance Of the effects Of the friction reducers and sample elastic behavior was not realized, hence no corrections to energy absorbed were applied for these tests. In order to estimate what effect these factors would have on computed energy absorbed, consider as an estimate that the friction reducer for sample 6 deformed 0.012 inches (the data indicates that this is close). Then by subtracting system errors and sample elastic de- flection the true plastic strain when the loading was increased was 1.80 percent. The energy absorbed at this strain was then 4.12 inch pounds per cubic inch. Now refer ahead to Figure 6-4b showing plastic strains only for sample 26 which was deformed nearly identically with sample 4. The actual energy absorbed by sample 26 at 1.80 percent strain was 4.18 inch pounds per cubic inch, as shown by graphical computations. Figure 5-11 shows volume changes for samples Of two creep tests compared with two constant strain rate tests. Table 5-1 gives a summary Of all tests performed and the basic data for all tests is given in the appendix. 107C 44 )— _ V Ice -12.0°C @ Ice -4°C \\ A Ice -7°C - \\ B = 60% by volume coarse B \\ sand, -12°C _ \\ + = 60% by volume coarse \\ sand, -3.85°C 106-— 3: - '3. t m L s H - 5 O o - 2‘. U) m - a 5 0 >4 105— 104 1 l l |! Lil I I 1 1.1: III I I Figure 5-1. 10‘2 10'1 Plastic axial strain (in/in) Young's Modulus versus Plastic Axial Strain for Ice and Coarse Sand-Ice Samples. Young's Modulus (psi) 45 107_ C P 0 54.6% by volume fine sand, -70500C 106- O 57.9% by volume fine sand, - -7.6°C - O O 0 O O O O O 1057 )— 10441111.] 1 1111111! 1 11 10-2 10-1 Plastic axial strain (in/in) Figure 5-2. Young's Modulus versus Plastic Axial Strain for Fine Sand-Ice Samples. Young's Modulus (psi x 104) 46 Numbers indicate sample NO. T = -12°C r 20.0— 0113 18.0- 16.0- 14.0— (323 L. 011 020 12.0- 021 112. 10.0 8.0— 98 O9 1 I l l 1 J 1 0 10 20 30 40 50 60 70 Percent sand by volume Figure 5-3. Young's Modulus versus Percent Sand by Volume for Samples with about 3 to 4 percent Plastic Strain. 47 .mumme mo.o oomo.mau cae\vuoa x mm.H OOH mw Ocmm wm.¢m mw vcmm wo.¢m HH# 0 C C O Ucmm wN.Hm mw O mummlcflmupm pcmwmcou How mm>usu UGmm wm.¢¢ AOH\OHV cflmuum HOflxm maw Q :1 mo.o s ‘4 C «V Camuumlmmmuum HOOHmme HMDOB No.o .vlm Ousmflm J ooa com com oow com com can com com oooa OOHH coma (rsd) ssexas Terxv Peak axial stress (psi) 1200 1000 800 600 200 (a) -12.03°C and -3.85°C Computed point 48 2.66X10-4/min -12.o3°c (7). II II é=1.33x1d“&min = -12.03°c é=2.66X10-4/min T= -3.85°C Figure 5-5. 9 Indicates 100 psi confining pressure I I l 41 l l ' 20 3o 40 50 60 70 Percent sand by volume Effect Of Volume Concentration Of Sand on Peak Strength. 1200 1000 800 600 Peak Axial stress (psi) 200 I Computed point 49 _ (b) -7.55°C <2 Cl material _ O (a C2 material _ E = 2.66 x 10-4/min T = -7.55°C I I l I I L I O 10 20 30 40 50 60 70 Figure 5-5. Percent sand by volume (Continued). Volume change (cc) Axial stress (psi) +0.12 +0.10 +0.08 +0.06 +0.04 +0.02 -0.02 ‘0.04 -0.06 50 F (a) #13 _ 9 #11 lOOOF (b) " ‘ ’ ' #11 54.6% Coarse sand (C1) 800— , by volume ' #17 55.6% Fine 600- #13 44.9% C1 sand 400— #16 9.3% Coarse sand (C1) by volume " ' ' ' ' ' ' , #26 Ic 200— .‘ ' T = -12.o3°c _ . t = 1.33 X 10 /min 0 1 1 1 1 1 1 1 1 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Total axial strain (in/in) Figure 5-6. Ice and Sand—Ice samples. (a) Volume change versus Axial Strain. (b) Stress-Strain Curves. 51 (a) #25 = 10 ' ' - 300— 03 0 psi 73 . 0‘) if 200- . m #3 0 03 = 0 64 100.. 6 = 1.33 X 10 /min 0 ' I I I 1 0 0.01 0.02 0.03 0.04 Total axial strain (in/in) 500- (b) #21 o o o o o o (3 o o o o o #23 400— O A A A ‘5 A A A A A A A A o A a a a u a O 0 a a D I! U a F. n #19 '3 300 a {1‘ El = Ice, 03 = 0 (n a O == 11.7% Sand C-1, 03 = 0 o A = Ice, 03 = 100 psi. I 200 54 Computed curve for ice (03 = 0) E = 2.66 X 10 /min 0 I l I I 0 0.01 0.02 0.03 0.04 Total axial strain (in/in) Figure 5-7. Constant Strain-Rate Tests on Ice and Sand-Ice Sample: (a) Influence Of Confining Pressure at low Strain-Rate (b) Influence Of Confining Pressure and Sand at high Strain-Rate. Axial Strain (in/in) 0.12 0.06 0.02 52 #35 57.9% by volume fine sand ol-o3 = 735 psi 03 = 0 T = -7.63°C #36 Ice cl - 03 = 249 p51 03 = 0 T = T7.60°C 1 o 160 200 300 Time (min.) Figure 5-8. Typical Creep Curves for Sand-Ice Samples Compared with Ice Samples. Axial strain-rate (X104/min) Axial strain (in/in) 0 I I I I I I I 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Axial strain (in/in) O O O 0.05... o #31 01'O3=248 psi 0 #30 01-03 = 317 psi 0 ° T = -4.45°C o T = -12.05°C 00 O O O 0.041- ,, o O O 0 ° 0 (b) O O 0003'- O O O O O o o 9 o o o 9 0.02% O o O o 0 c a #29 01-O3= 248 psi 0 °,, ° 0 T = -12.05°c o o 9 O l/fl, Note: Data adjusted for system error 0 and elastic strain. 03 = 0 0 l l l . l O 100 200 300 400 Time (min.) Figure 5-9. versus Strain. Results Of Creep Tests on Ice. (b) Creep Curves for Ice. (a) Strain-Rate IpSl) Axial stress Total axial strain (in/in) 54 (a) Loading for #7 4:; 3001... " . Area indicates Loadin for 6 ‘\ I / / / / y/ /7 /g;/ /#/y77— m energy absorbed 200-4 >‘ by #4 at 2.5% / ' < strain. . < / #4 z: = 1 33 x 10'4/min ’ / ° ‘) ’ Area indicates 100-; < .11 energy absorbed by #6 at 2.5% / < strain. / . / 0 /CA \/ x!)(1NJOXINJ/y’)(/§/\/’x:g§./\/a( 1 1 0 0.01 0.02 0.03 0.1 Total axial strain (in/in) 0.05 0.04 0.03 0.02 0.01 0 I I 1 I 1 0 100 200 300 400 500 Time (min.) Figure 5-10. Effect Of Absorbed Energy on Creep Rates of Poly- crystalline Ice. (a) Loading Paths. (b) Creep Curves for Two Loading Paths. .mmamfimm OOHIOcmm How cannum HOde mOmHO> Omcmnu OEOH0> mamewm Acfi\afiv O cfimnum Hmwx< .HHIm musmflm mo.o 60.0 mo.o ~o.o Ho.o o T _ _ _ 0 0 O I O loomO.¢1 u a Ammoah u o .ummu QOOHOV vmw n O Aoomo.mau u a Eamon u o .ummu mmmuuv mg u G o loomo.maaue.casxzwooo.v ome n O a Ao.mo.~7u9.fie\:mooo; a: n O O O D e 6 6 \ - \ \ oo.o1 O0.OI No.o1 No.o+ vo.o+ mo.o+ mo.o+ ('O'D) AV 'abueqo amnIOA 56 muasmmu Hmucmfiflummxm mo humfifidm moa O~.H smmo.o coma auexnn mooo.o Omm.o Ho mo.ma- om OOH OH.H Omso.o mmm :He\eu mooo.o mom.o mo.~H- an scum H “mmumoo muecmm mmma cus\cfl mooo.o som.o mo.mau ma owe :He\:u mooo.o msm.o O mo.~H- ea mos mm.m «mmo.o mmm unexcfl mooo.o emm.o Ho mo.~a- OH I Oaam>ca mums .Omxmma unashamz . mo.~au ma 1 Oflam>afl when .Omxmma mcmunsmz . mo.~au 6H moa x em.a Gmmo.o mom cas\ca mooo.o mmm.o Ho m.66 mo.~au ma . 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HmmO OOHOOHO OH OHO HOOO OO0 66\O . . mxHOEOm MOO OHOHOO um hHOMum MOOHOO HOH MOOOQV A HO> any .woov M2 .608 m.mcsow .mmam xOOm Oumn .MOQ OOH OOOO w SOB OH Emm .HOOOOOUOOUO .H..m OHQOB 58 .AOOOOO OOHBHOBOO mmOHO: OHONO OHOmmOHm OOHOHHOOO Hmm OOH mOuOOHUOH«« .muHHOEOHDmMOE OHDflMHOQEOu. .HOH UOmD HOflmHEHOSBOs ONO :He\cH OOOO.O OOO.O No H.OO OO.NH: NO NOO OHs\cH OOOO.O OHO.O No O.NN OO.NH- OO OOH x OO.H OOOO.O HOO OOO OOO.O O O.OO OO.N . OO OOH x OO.N HOOO.O HOO OOO ONO.O O O.OO OO.O . OO OHOH OHE\OH OOOO.O OH0.0 NO O.OO OO.HH- OO O OOHOOos OOH x OO.O OOHO.O m. use» OOHe OH x NH.H ONOO.O IOOHOO OH Ommo WOH x OO.N HNOO.O OHO.O No O.OO OO.HH- NO OOH x NO.H HNNO.O HOO OHE\OH OOOO.O ONO.O O O.N OO.HH- HO OOH x NH.H NOOO.O OOH x OO.H OOOO.O OOH x OO.H ONOO.O OOH x OO.H NNOO.O OOH x OO.H OONO.O OOH x OO.N OHNO.O OOHOOoe OOH x OO.H OOHO.O O.Ocsos OOHe OOH x OO.H OHHO.O -HOHOO on OOOO OOH x NO.H HNOO.O NOO.O O O.OO OO.O . OO OOH x NO.H OOHO.O OOO cHs\cH OOOO.O OOO.O No O.OH OO.O 1 OO OOH x OO.O HHOO.O OOO cHe\cH OOO0.0 HHO.O No O.N O0.0 . OO OOH x OO.O OOOO.O NOO cHe\OH OOOO.O NOO.O No O.OO OOOO . NO OOH x NO.N ONNO.O OHO cHe\cH OOOO.O NOO.O No O.OO OO.O . OO OOH x NO.N NNNO.O OOO :Hs\cH OOOO.O OOO.O No O.OO OO.N . OO HOO OHE\OH OOO0.0 OOO.O Ho O.HO OO.O . OO HHOOO OOHOOHO AOH\OHO HHOOO OmoH AOO\OO . . OHHOEOO IOH OHOHOO um OHOHOO OOOHOO HO .OOOQ A Hmwmmmv .mmmw O mmmm .OOE O.OOOOH .mOHm HOOO OHOH .HOO OOH O H .HOOscHucooO .HIO mHnme CHAPTER VI DISCUSSION AND PRESENTATION OF THEORY Discussion and the develOpment Of theory to ex- plain the observed behavior Of ice and soil-ice mixtures are presented in Chapter VI. The presentation will in- chxkapolycrystalline ice, sand-ice system, and clay-ice system. Polycpystalline Ice Since it is known that the structure Of ice changes as deformation proceeds (Gold, 1963; Glen, 1955) it is rea- sonable to expect that the elastic modulus Of ice will also change. It appears that recrystallization Of the ice dur- ing deformation permits gradual reorientation Of the grains to a direction which accommodates deformation by the ap- plied stress. There is little evidence tO indicate that different orientations Of ice crystal axes affect the value of Young's modulus (Jellinek and Brill, 1956; Yamaji and Kuroiwa, 1956). Accommodation cracking (Gold, 1963) is the fracturing of ice grains so oriented as to act as hard sites and would tend to lower the elastic resistance of ice. This probably contributes to the change in the elas- tic modulus of ice as deformation proceeds. 59 60 Gold (1958) investigated the elastic behavior Of polycrystalline ice with respect to temperature and found an approximately linear increase in Young's modulus with colder temperatures. The measurement Of Young's modulus was made on ice that had undergone very little or no plas- tic deformation. In this study measurements Of Young's modulus are made on samples that have undergone plastic strains Of 0.0021 inches per inch and greater. The Oppo— site relationship Of Young's modulus tO temperature, Ob- served during this study, may indicate that accommodation cracking is more extensive at any given value Of larger plastic strains for colder temperatures. The initial volume increase for ice samples may be associated with some failure mechanism such as grain bound- ary sliding with consequent partial disruption Of inter- granular continuity. If this is so,confining pressure would tend to hold the grains in more intimate contact thus decreasing grain boundary sliding and increasing strength. Confining pressure did increase strength for ice samples deformed at axial strain-rates Of about 2.7 X 10.4 per minute (Figure 5-7). If the load is below a certain value (or strain-rate is less than some critical value) it may be that intergranular cohesion is sufficient to prevent grain separation. The addition Of a small amount Of sand may act as a "key" to impede grain boundary sliding. Dillon (in preparation) has Observed visible slip planes in deformed ice with orientation Of about 45 degrees to the applied stress. 61 The addition Of sand may also serve as "keys" on these planes. In order to develOp an equation which will predict the plastic behavior Of ice it is necessary to work with data that represents plastic deformation only. This means that both elastic sample deflections as well as the effect Of system errors must be subtracted from the Observed data. The elastic part Of the system error has been evaluated quite accurately but seating errors were inconsistent. Figure 6-1 indicates the possible magnitude Of the effect Of friction reducers. The seating error with the modified friction reducers was usually between 0.001 and 0.004 inches and any data correction was a trial and error pro- cedure. Sample elastic deflections have been estimated using data presented on Figure 5-1. Elastic moduli at other temperatures were Obtained by interpolation. The results of the series Of tests to determine the effect of loading history on ice (Figure 5-10) provide an insight into the behavior Of the hardening and softening mechanisms.inice. These results suggest that the effects Of hardening and softening are dependent only on strain and absorbed energy. Thus axial strain-rate may be ex- pressed by the functional relationship 6 = f(O,T,e,dee) where E is the axial strain-rate, o is 01 - 03 or the axial stress difference, T is the absolute temperature, a is the axial strain, and fade is the absorbed energy. 62 Several mechanisms which tend to cause hardening may Operate in the ice during deformation. It is assumed that the gross effect Of these mechanisms can be represented by one strain dependent term. It is also assumed that the gross effect of all softening mechanisms can be represented by another term which is dependent on absorbed energy. If we consider tests with temperature and stress constant, then an equation which appears to fit strain- rate versus strain curves shown in Figure 5-9a is é = Klexp(-nle) + K2exp(n2fode) (6-1) where K1, K2, n1, and n2 are parameters which are constant for a given temperature and stress. By trial and error it was found that the influence of the hardening term dies out rather quickly with in- creasing axial strain. This provides a method to evaluate. the parameters of this equation from the data Of a single constant axial stress creep test. If two rather high values OfEi and 62 are chosen tOgether with corresponding values él and 62, then since the effect 252the hardening term is negligible and since [ ads and j ode can be evalu- ated we have 0 ° 0 El 1 - K2exp(n2jg ode) _ r- _ — exp [h (06 - 06 fl . 6:2 K ex (n [fez ode) 2 l 2 2 P 2 O 63 With all values known n2 can be evaluated. Then K2 can be found from the relation 61 = Kzexp(nzcel) Now selecting two low values Of e and £2 with l the corresponding values of El and 62 we Obtain 61 - Kzexp(nzoel) Klexp(-nlel) €2:~H;gxan2062Y - Elexp(-nlez) Since all values on the left side are known, nl and K1 can be evaluated as before. These values can be improved by repeating the procedure while including the small ef- fect Of the hardening term. This procedure was followed for the data shown in Figure 5-9, and it was Observed that a better fit was obtained when the first term of equation (6-1) was divided 60's. Since tests 29 and 30 were performed with tem- by perature constant and tests 29 and 31 were performed with axial stress constant, the parameters that vary with stress and those that vary with temperature were easily observed. This information gave the following equation . C e = K [ZETE exp(-nle) + exp(nzfodefl (6-2) where C is a constant equal tO 1.03, K is dependent on.o and T, n1 is dependent on T, and n2 is dependent on T. Consider first the stress dependence of K. Con- siderable success has been Obtained by considering strain- 64 rate to be proportional to a power Of stress (Weertman and Breen, 1956; Glen, 1955; Butkovich and Landauer, 1959). The value Of the exponent equal to 3.25 indicated by the experimental data agrees rather well with values reported by Glen (1955) and Butkovich and Landauer (1959). The rate process theory predicts a temperature de- pendence for stain-rate of the form 6 = Const exp(dIH/RT) where AH is the heat of activation, T is the absolute tem- perature, and R is the universal gas constant. For temperatures near the melting point this rela- tionship is not valid because steady—state conditions are not satisifed and predicted strain-rates are too small. For temperatures below about -3°C the function 1 E = Const |T°C|n gives a very close approximation to the exponential rate process form, but now an infinite strain-rate is predicted at 0°C. Since ice at 0°C does have some strength and if the quantity T', equal to the temperature in degrees Cen- tigrade without regard to sign plus a constant is intro- duced, this constant can be evaluated to give consistent results for near melting point temperatures. Using data presented by Glen (1955) for polycrystalline ice at -0.02°C, a value for this constant of 0.80 was found. Assuming the 65 same form Of temperature dependence for all parameters equation (6-2) becomes 4 - 3.25 1.23x1o ( o ) [1.03 ( -696e ) (0.215f0d8] 6 = ———— exp ———————— + exp ) (6-3) (T.)1.75 109 80.5 (T.)o.49 (T.)o.3o4 Figure 6-2 shows the behavior Of the hardening and softening terms and how their combination approximates the actual data from sample 30. Figure 6-3 shows a comparison of experimental data with predicted curves for samples 29, 30, and 31. The influence Of temperature, stress, strain, and absorbed energy appears to be accounted for. A severe check on the performance Of this equation with respect tO stress is to determine how well it predicts the results of a constant strain-rate test where an entire Spectrum Of stress values are covered. In order to do this,equation (6-3) is used in the following form 0 3.25 é 1.23x1o’ [1.03 exp( -696e )+ exp(0.215fode)] (T.)1.75 2675 TTTIETI§ (T.)o.3o4 A small increment of strain is considered. The energy ab- sorbed by the sample is then computed based on a trial value for stress and a linear stress increase for the strain increment. The stress is now computed from equa- tion (6-4) and compared with the trial stress. If these two values Of stress are different a new corrected trial 66 value of stress is assumed and the process repeated until the trial and computed stress values agree with the desired precision. In applying this equation to a constant strain-rate test it must be remembered that the observed strain-rate is not necessarily the same as the sample plastic strain-rate. Figures 6-4a and 6-4b diSplay stress-strain diagrams for samples 39 and 26 reSpectively. The seating error for these samples was estimated by extending the straight line portion of the stress-strain curve as shown in Figure 6-1. The strains represented in Figures 6-4a and 6-4b have been adjusted for system errors and sample elastic deformation. The second vertical scale is the time in minutes to reach the strain indicated and the instantaneous plas- tic strain-rate can be computed from the second curve in these figures. Stresses were computed bY the method pre- viously outlined using the instantaneous strain-rates indicated by the time-deformation curve, and are shown by a solid line. Equation (6-3) appears to represent the behavior of the polycrystalline ice in the temperature and stress range studied. Integration Of this equation is difficult and the prediction Of creep test results involves numerical techniques. Since strain and time are not independent quantities in this equation it may be possible to write an equation for the creep of ice which is entirely time dependent. Again selecting an equation which appears to 67 fit the data for a single creep test, the following equation was tried K . _ 1 _ 0.5 e — E075 exp( nlt ) + K2exp(n2t) where t is the time and other symbols are as previously defined. It appears that this equation may predict the same form of curves as equation (6-3). This equation can be easily integrated. The effect Of the hardening term again diminishes very rapidly and the same technique can be used to match this equation to data for any given constant axial stress creep test. This was done with gOOd agreement between experimental data and the predicted creep curves except that in this equation all four parameters varied with both temperature and stress. The nature Of the dependence Of these parameters on temperature and stress was assumed to be the same as in equation (6-3). Using T' defined as before gives the following equation E = 6.50 ( o )1'85 exp[} 0.104 ( 0 )1°36 t0.5]+ (T,)0.68t0.5 100 (T,)0.328 100 2.92 6.68 0.436 ( o ) exp 0.00339 ( g ) t] (6_5) (T.) .13 100 ‘ETYET§5 100 Figures 6-5 and 6-6 illustrate predicted creep curves using this equation compared with actual data for several temperatures and stresses. The largest discrepancy occurs for data presented by Glen at -6.7°C, shown in 68 Figure 6-6c. Note that the predicted curve is approximately parallel to the actual data, hence some seating error may be included in Glen's data. Note that Glen's data is given in terms Of total strain whereas the predicted curves are for plastic strain only, so that the predicted and experi- mental curves should differ by some amount. Since the first exponent Of equation (6-5) ap- proximates some strain dependent quantity and the sec- ond exponent approximates some energy dependent quan- tityn tIHBSE exponents must be treated as integrals. If there is any change in stress for the test considered the quantities in the exponents must be allowed to accumulate. Figure 6-7 illustratesthe results Of such a situation. The results indicated in Figures 6-5a and 6-7 in- dicate that equation (6-5) may predict tertiary creep pre- maturely for stresses above approximately 300 psi. Aside from this either equation (6-3) or (6-5) seems to predict the creep behavior Of ice fairly well for the range Of tem- peratures and stresses investigated. The physical meaning Of the parameters is more difficult tO visualize in the time dependent form of equation (6-5). The more physically meaningful equation would be a strain dependent equation in the form -26000 RT -n e n fads E = K e 03°25 [169% e l + e 2 ] 69 where nl and n2 include the temperature dependence Of the ice structure. Other symbols are as previously defined. This equation can be correlated with equation (2-1) which was derived in accordance with the rate process theory. TO do this a and 6 are replaced by y and T, and 03'25 is replaced by sinh(rqA2/RT), where y may be taken as the octahedral shear strain and I is the octahedral shear k stress. Thus the structure dependent term 2X TEOf equa- tion (2-1) will correspond tO K 1.03 ‘nlY nzf'dY] ——-——O.5e +8 Y Note that any abrupt change Of stress has an immediate effect on the strain-rate only through the hyperbolic sine term. More will be presented later in this chapter about heats Of activation and flow volumes. Sand-Ice System Examination Of the stress-strain curves for samples 3 and 8 in Figure 5-4 point out the symmetric appearance Of these curves for samples that contain less than about 42 percent sand by volume. For all samples containing an amount Of sand below this critical volume concentration, it appears that the results Of a constant deformation rate test can be predicted by multiplying the stress predicted for ice, under the same conditions, by some constant stress factor. Examination Of Figure 5-5 indicates that this 70 factor should be directly proportional tO the volume con- centration Of solid material contained. However, if the same reasoning is applied to sam- ples containing sand in quantities above the critical volume concentration it can be seen from Figure 5-4, samples 13, 11, and 5, that the stress factor is now a function Of strain. Figure 6-8 through 6-11 illustrate a method for establishing this dependence. In these diagrams the sand-ice sample stress-strain curve for a constant axial strain-rate test is plotted using plastic strain and estimating the seating error by extending the initial linear portion Of the stress-strain curve down- ward to establish the zero strain position as before. Again a second vertical scale is used which is calibrated in time in minutes and the time-strain curve is plotted. A curve for ice is then computed using the temperature indicated and the strain-rates computed from the time-strain curve. The stress factors along the bottom Of the diagram are the factors that the stress for the computed ice at any strain must be multiplied by to obtain the stress for the sand-ice sample at the same strain and strain-rate. These stress factors are plotted versus strain in the top diagrams. The apparent inconsistency of the stress factors for low strains is believed to be due to the difficulty Of evaluating seating error accurately, particularly for the earlier tests using thick friction reducers. Aside from 71 this first inconsistency it can be seen that the value Of the stress factors start at some initial value and remain constant to some strain, then increase almost linearly with strain to some new value and then again appear tO remain constant. Figure 6-12 shows the relationship Of volume change to the change in stress factor. In each of these diagrams a stress-strain curve for a sand-ice sample constant strain- rate test is shown. The computed pure ice curve is also shown. The computed ice curve is then multiplied by the .initial stress factor and this curve plotted. The place where the sand-ice curve and the computed ice times stress factor diverge shows the mobilization Of some strengthening mechanism. Note that this strengthening mechanism is first mobilized in each case at about the same strain that the volume change reverses its initial decrease and that the mechanism appears fully mobilized at some point where the volume is well above its initial value and increasing very rapidly. Behavior similar to this is seen in consolidated- undrained tests on saturated unfrozen sand. Figure 6-13, from Bishop and Henkel (1962), illustrates such a case. Figure 6-13 shows a stress-strain diagram and pore water pressure diagram for unfrozen sand with a volume concentra- tion of 57 percent. An increase in strength similar to the frozen samples is Shown which begins at about one 72 percent strain. This is about the strain at which strength increase begins for the frozen samples Of C1 material. The increase in strength for unfrozen material begins at about the same strain that the pore water pressure reverses its initial increase. This change in pore water pressure is analogous to the volume change in frozen sand-ice samples. The additional strengthening in the unfrozen mate- rials is caused by the dilatancy of the sand material which in turn causes the pore water pressure tO decrease and the effective stresses on the solid material to increase, mo- bilizing more of the frictional resistance Of the sand. Presumably a similar process takes place in sand-ice sam- ples with the ice matrix imposing the equivalent Of a con- fining pressure to the mass of sand particles. Figure 6-14 shows stress factors for both initial and final states. Note that in Figure 6-14a the initial stress factor line for the fine sand-ice samples is merely an extension Of the line for less than the critical volume concentration. It was observed that some Of the fine sand was carried along with water forced out Of the top Of the mold during freezing. This did not happen with the coarse sand. The implication is that the coarse sand grains re- mained in closer contact after freezing whereas the fine sand grains were forced apart by the freezing water. This may be the reason why the initial stress factor for fine sand is merely an extension Of the stress factor below the 73 critical volume concentration whereas it is not for the coarse sand. Thus it appears that three mechanisms serve tO strengthen samples made with sand and ice versus those Of pure ice. The first mechanism is associated with volume concentration Of sand in the sample and is probably caused by virtually all Of the plastic deformation being accommo- dated by the ice. This means that the effective rate of deformation for the ice may be considerably greater than the Observed gross sample deformation rate. There may also be some keying effect by the sand grains which tend to im- pede some Of the deformation mechanisms of pure ice. It appears that this mechanism is dependent only on the volume concentration of sand particles, and is mobilized at all strains. The second mechanism is associated with solid to solid contact and is the result Of friction at these con- tacts. This mechanism is less apparent in some materials and is a function Of the frictional characteristics of the material and the degree of diSpersion Of the solid particles. Assuming saturated soil conditions the degree Of dispersion in frozen sand-ice samples is dependent on: (1) original void ratio , (2) permeability of the solid soil skeleton, (3) effective stress on the solid soil skeleton during freezing, and (4) the rapidity of freezing. 74 The third mechanism is associated with volume in- crease Of the sample and has a counterpart in unfrozen mate- rials. The sample volume increase caused by the deformation Of the sand is impeded by the ice matrix. Thus the ice ma- trix effectively exerts a confining pressure on the sand particles which increases as the volume increase takes place. This confining pressure continues to increase un- til either no more volume increase is experienced or the limiting cohesion Of the ice is overcome. NO fracturing of the sand grains was Observed in the melted specimens. The effect Of this ice exerted pressure is to increase the effective stress on the sand skeleton, thus increasing the resistance of the soil skeleton to deformation similar tO unfrozen material. Since the sample volume is still in- creasing at an accelerating rate when this mechanism is fully mobilized it is assumed that the limit Of the pres- sure that the ice is capable Of exerting is reached and that this is the limiting factor for the third mechanism. Confining pressures applied to a sand-ice sample may be carried by the ice matrix until dilatancy begins, as with unfrozen materials. The behavior indicated above would lead one to be- lieve that it may be possible tO define an effective fric- tion angle for frozen sand which.would Operate in a way similar to unfrozen material. A relationship such as sug- gested in Figure 6-15 may apply. The friction angle 75 indicated here may be larger than that for unfrozen con- ditions since the grains in unfrozen material are free to rotate within the confines Of their adjacent neighbors, while the grains in frozen material are held in a semi- rigid matrix Of ice. This relationship assumes that the effect Of con- fining pressure On the ice is negligible. Results of this study and observations by others (Rigsby, 1958) indicate that this may be the case. One should be able to evaluate this friction angle for the tests on sand-ice samples with and without confining pressure. Attempts to do this were quite disappointing. Inspection Of Figure 5-5a shows that the effect Of 100 psi confining pressure produces no more strength increase than might be expected from experimental error. This would in- dicate that either the friction angle is quite low or that the pressure exerted by the ice is quite high. One would expect that the friction angle would be higher for frozen materials than for unfrozen materials since the restriction of rotation of the grains by the ice matrix would cause a greater interlocking effect. Thus it seems reasonable that the ice cohesion and in turn the confining pressure on the sand is relatively high. It may require equipment capable Of exerting greater confining pressures to evaluate these quantities. 76 One method Of defining the dependence Of the stress factor on temperature is to assume a dependence proportional to some power Of T', as was found for the ice equations. Then the stress factor would have the form 0 = [Kl(l+N) + K2 (N—NCII CI for the final value, and o = [Kl(1+N) + MK2 (N-NC)] CI for the initial value, wherecxis the axial stress on sand- ice sample, 0 is the stress on ice under equivalent con- I ditions, N is the percent sand in sample by volume, NC is the critical volume concentration (about .42), K1 is a temperature dependent parameter, K2 is a temperature dependent parameter, and M is the percent initial mobiliza- tion Of friction mechanism (also temperature dependent). Evaluation Of these parameters under these assumptions equals .66(T')'155 .421 Yields K for all sand material, K2 1 equals 4.32(T') 6 for C-l material, M equals .158(T')'49 .421 for C-l material, K equals 4.02(T') for fine sand, and 2 M equals 0 for fine sand. Examination Of data presented in Figures 5-11 and 6-8 through 6-12 indicates that the strain at which mobili- zation Of the last mechanism begins and the strain at which it is completely mobilized may be both temperature and strain—rate dependent. These strains may be very difficult to define even under identical test conditions due tO the variable nature Of the factors affecting the dispersion Of 77 the sand particles and probably all that can be said here is that for reasonably slow rates (below about 3 X 10.4 per minute) the beginning mobilization for C1 material is about 0.01 strain with full mobilization at about 0.03 strain. The onset of mobilization Of this mechanism is about 0.02 strain for fine sand with full mobilization at about 0.06, for the samereasonably slow strain-rates. With this knowledge Of the structure and behavior Of sand-ice materials it may now be possible to explain their elastic behavior. Accommodation cracking is believed to be the primary reason for the decrease in Young's modu- lus with increasing plastic strain for ice. Faster strain- rates cause accommodation cracking to begin at lower strains and the cracks continue forming at a much faster rate (Gold, 1963). Now since the addition Of solid material causes the effective deformation rate Of the ice to be much faster than the gross deformation rate Of the sample, it is rea- sonable that accommodation cracking would be much faster, and Young's modulus would decrease much more quickly. In coarse sand-ice samples containing sand above the critical volume concentration, the sand grains are in intimate con- tact at all times. The effect of this continuous skeleton of solid material would be to raise the elastic resistance Of the sample. The sand grains in fine sand-ice samples do not make contact until about 2 percent strain is reached, thus leaving the ice alone to control the value of Young's modulus. Note that by 2 percent strain the value Of Young's 78 modulus is nearly the same for fine sand and coarse sand samples. Figure 5-3 shows the apparent effect Of increas- ing amounts of sand on Young's modulus. With the above information it is now possible to approximate the results Of a constant deformation rate test of sand-ice samples of these materials by computing the results Of the constant deformation rate test on ice and multiplying the results by the stress factor indicated. The question now becomes-—is it possible, by using this procedure in reverse, to predict the results Of a creep test on these materials? In order to do this with the present information the tests must be limited to those for which the strain-rates are "low." There are two rea- sons for this. First, the strain that occurs before mo- bilization Of the last mechanism has not been defined for faster rates and second, the stresses that are necessary to produce the faster rates are beyond the range Of the equations presented for ice. Figures 6-16 and 6-17 present the results Of such computations for two creep tests. The upper diagram in each Of these figures is the result Of dividing the axial load on the sand-ice sample by the indicated stress factor, and represents the loading schedule that must be applied to an ice sample in order to Obtain deflections equivalent to those Of the sand-ice sample under consideration. The computations for ice can be carried out in either of two ways. 79 First, the strain dependent equation form can be used along with some numerical integration technique and using the loading schedule given. The other method, and the one used here, is to approximate the loading schedule by a step func- tion and use the time dependent form Of equation for ice, remembering Of course that in the equation for strain rate the quantities in both exponents must accumulate, and that the constant Of integration must be re-evaluated at each step. The lower solid line in the bottom diagrams repre- sents the predicted plastic strain Of the samples. The top solid line is the predicted strain with the elastic de- flections added. The dots are actual data points from which have been subtracted all system deflections. Clay-Ice System In order tO determine if the methods presented here might also apply to frozen clay soils computations were performed in an attempt tO predict the results Of tests on clay-ice samples performed by Dillon (in preparation). Figures 6-18 and 6-19 present the results of these compu- tations. The clay used in these samples was a red glacially deposited clay from near Sault Ste. Marie, Michigan. It is the same as that used by Akili (1966) and a complete description is given there. 80 The degree Of saturation of this material was about 96 percent, and the unfrozen water content was about 12 percent for the temperature Of the tests considered (about -15°C). Based on this information an ice density Of 0.776 grams per cubic centimeter was used, and the same linear (Drrection with respect to ice density was used for the com- puted stresses, although this linear relationship may not extend tO this large variation. Figure 6-18 shows a stress-strain plot Of sample C2-Sl7. Young's modulus for the clay-ice material was as- sumed tO be about the same as that for the fine sand-ice materials used in this study and an estimated value Of 105 psi was used for computations. A second vertical scale for time is again used and the time-strain curve plotted. The stress-strain curve for ice is computed along with stress factors as before. With frozen clay materials it appears that the stress factor has some initial value with an approximately linear build up with strain, although the data is not carried far enough to determine the final value. Figure 6-19 illustrates the results of computations to predict the behavior of this frozen clay material in creep. The computations were carried on as before. The solid line in the bottom diagram displays the predicted plastic strain and the top solid line represents the total of the elastic and plastic strains. The agreement between 81 the predicted behavior and the actual experimental data is very good, and quite probably with more definitive data for clay materials these methods would also apply to frozen clay soils. Flow volumes (qAQ) and heats Of activation (AH) were computed using the rate process equation (2-1) for compari— son purposes. In order to do this,equation (2-1) was writ- ten as §/T = K exp(-AH/RT) exp(Br) (2-2) where K equals 2X§ exp (AS/R), and B equals qAQ/kT. This assumes that for large Br, the sinh is approximately equal to one-half the exponential. The octahedral shear strain- rate and the octahedral shear stress were used for these computations. For some of the constant axial deformation rate tests the deformation rate was changed when the load on the sample had reached a steady-state value. If it is assumed that all parameters are the same before and after the change Of deformation rate then = exp(Brl-Btz) And B can be computed, and from it the flow volume, qAQ. Figure 6-20 is a plot Of flow volumes versus percent sand by volume. 82 In order to find AH, the lOgarithm Of equation (2-2) is written logH/T) = lOg(K) + By - AH/RT Now using constant axial deformation rate tests run at dif- ferent temperatures and assuming that K and qu remain relatively constant for the temperature range, we have qAQIl/le - AH/RTl - lOg(Yl/Tl) qAYrZ/kT2 - AH/RT2 - log(y2/T2) The only unknown in this equation is AH. AH was computed using the series Of constant axial deformation rate tests performed at -12.03 and -3.85°C, and using values Of qAfi from Figure 6-20. The results Of these computations are presented in Figure 6—21. 83 .muHsmOm HOOHOmm< co mmOOxOHBB HOOOOOm OOHOOHHO Ho OOOHHm Oo.o .HIO OHSOHO AOH\OHV OHOHOO HOHxO HOOOH HOHHO OOHOOOO m0.0 N0.0 H0.0 I _ _ _ . O O H 1. H \ IOOH .o 0 o JOON OHOOOOOH OOHOOHHH HOHOHOH OOHOD o UomooNHl H B OHS x . u w \OIOH mm H 2 O o 0 O o 1oom o o o o o o o o o O mll¢1llw O o o OHOOOOOH OOHOOHHH OOHHHOOE OOHOD O.OO.HH- n O cHe\O-OH x OO.H O ONO (rsd) ssexqs Terxv .OOH OOH OEHOB OOHOOuHom GOO OOHOOOHOm mo HOH>O£Om .NIO OHOmHm AOH\OHV OHOuum HOHxO OHOOOHO m0.0 O0.0 m0.0 No.0 H0.0 O H _ _ _ O my Au 0 O — o my 5 o o o o o o o o o 1 o . m . O EHO OHOO O O O O-OH x OAOOOHOOO. V H . HO O o o o o 1 o 4 mum .vm .OEHOH OOHOOUHOO OOO OOHOOOHOQ mo 85m 8 1 EH; O .EHO OOHOO H O-OH x O OOON- OO.H H . O mm o UomooNHl H B O u mo .Hmm hHm u mOIHO .OO Hmmu scum mums Au V m N ,_1 O O O O O I l O O O O O Z01' X g) eqex-urexas Ierxe orasetd Ln 0 I O rm Jed O0.0 (u no.o .AmIOv OOHuOOvm he OOOOHOOHO mO>HOO nqu OOH co mama OOOHU mo OOmHHOmEOO .MIO OusmHm A:H\GHV OHOHOO HOHxO OHumOHm OO.O OO.O OO.O NO.O HO.O O _ O.OO.NH- u a H _ _ _ O Oum6.HmOOON u OO-HOOOO 0 -HO.O O.OO.NH- u a O In . I O H O- O HOOOHO I 6- O OOO -NO.O [OO.O O.OO.O- u a [OO.O OuO6.HmOOON n OO-HO HMO [OO.O -OO.O HO-OO.OO On OOHOHOOOO ; OuOO HOOOO< O O O0.0 (urm 19d act X e) eqex—urexqs terxe oraseta 86 150‘ 300 (a) Test 39 Time (min) A ' [’0’ 'H ,LY ‘3. ' ’ 100.. V200- O’O/‘O’ m G _ 1 ’ - g Slope — €_{T,AD”'Cr 4.; "O” G 0 Test 39 data 50' 7; 10°” . o. 9’ -— Predicted by Eq. (6-4) 3' ’0/0' T =-3.85°C ,£T’ 0h 0 "I 1 1 I 0 0.01 0.02 0.03 Plastic axial strain (in/in) (b) Test 26 600% 300 f: m 3* .5 400- m 200 5 O H 2 4:. .H ’20" a 200_:100_ .19’ 0 0 Test 26 data 'H fiy’ -——- Predicted by Eq.(6-4) é .19” T = -12.03°c AT"? 0- 0 0’ I 1 L 1 1 1 1 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Plastic axial strain (in/in) Figure 6-4. EXperimental Constant Strain-Rate Data on Ice Compared to Predicted Curves. Axial strain (in/in) Axial strain (in/in) 0.05- (a) Test 30 9 87 o o o 0.04b System erro ° .0 o elastic 0003— plastic 0.02- O ° O Data, suple 30 0 Predicted by Eq.(6-5) 0 0-01- 0 01-03 = 317 psi; T = -12.03°c 0 0 I l 1 0 100 200 300 Time (min) (b) Test 29 0.04- System error elastic 0.03‘ - plastic 0.02— 0.01% . G <3 Data, sample 29 Predicted by Eq.(6-5) 01-02 = 248 psi; T = -12.05°C 0 l I l I l J 1 1 0 100 200 300 400 500 600 700 800 Figure 6-5. Time (min) Comparison Experimental Creep Data on Ice with Curves Predicted by Eq. (6-5). Axial strain (in/in) Axial strain (in/in) (C) Test 31 88 0° 0005'- a System error .° ’ Elastic 0.04” Plastic 0.03- 0.02- 9 9 Data, sample 31 0,01 Predicted by Eq.(6-5) 01-03 = 248 p31, 03 = 0 T = -4.45°C 07 I 1 J 0 50 100 150 Time (min) '0 J— (d) Test 36 ' o 0.0 System error 0 04 7' Elastic 0.03— Plastic 0.02— 0.01 O 0 Data, sample 36 Predicted by Eq.(6-5) 01-03 = 249 p51, 03 = 0 T = ‘706OOC 0 I 1 100 200 300 Time (min) Figure 6-5. (Continued). Axial strain (in/in) Axial strain (in/in) 89 System error (e) Test 37 tic Plastic C) O Data, sample 37 Predicted by Eq.(6-5) 01-03 = 99 p31, 03 = 0 T = -7.55°C _ 1 1 1 11 0 1000 2000 3000 4000 Time (min) Figure 6-5 (Continued). O O (a) 01 - 03 = 52 psi 0 O F T = "O.OZOC G O O 7 0 Plastic O O _ O C) ' O C) Data (After Glen, 1955) ' ' ._____ Predicted by Eq.(6-5) 9 01-03 = 52 p31, 03 = 0 T = -0.02°C 1 y 1 1 0 1000 2000 3000 Time (min) Figure 6-6. Comparison Glen's (1955) Experimental Creep Data on Ice with Predicted Curve. Time (min) Figure 6-6 (Continued). ' o b — = ' ( ) 01 03 87 p81 90 T = -0.02°C O 0.08 '- ‘E O 1 Pl sti E 0.06- O a C c '3 r) O m 0.04— .-I O m -r-'| é C) 6 Data (After Glen, 1955) 0.02- o . -———— Predicted by Eq.(6-5) o -o = 87 psi, 03 = 0 T = -0.02°C 0 l 1 1 _1 0 200 400 600 800 Time (min) (C) 01- 02 = 87 psi ,’ ' / T = -12.8°C and -6.7°C 0 3; $3; / / ° / 0004— 0 // // A // E 0 / ’ .5 o 03- / / V ' (9 / g ,,” Translated . .3 // - e= 0.03 01-03 = 87 p81. H o/ _ u /' 03 — 0 m 0.027. / - O a // T - -6.7 c .2 / 0 o o ° 2 0 0 01-03=87psi,o3=0 o.oL~ 9 ° T = -12.8°C C) 0 Data (After Glen, 1955) -——— Predicted by Eq.(6-5) 0 l l 1 4 0 2000 4000 6000 8000 .mcflvmoq mwum How mm>usu omuoflomum sue? moH no muma mmmuo Hmucmfiflummxm QOmHHmmEOU .wlo mnsmflm O" 91 m . 35 «a? com oow com com OOH o \fi _ a _ . _o Amuse .vm an cmuoflomum o mump Hmucmfiflummxm 0 0 Hmm mmm u molao .mmuscfle mmm um w mHmEMm no mmmnum mmcmno UOMO.NHI H E o.Hmm mmmumolao 2 G Uomo.NHl H m G o n mo .Hmm mmm u 01H .mHflUflUOH GOHfiUHHM xoflsu 0» map cofluomammo Emummm m>flmmmoxm mpozt oflummam oflummam » B O a; Houuw Ewumhm H0.0 N0.0 mo.o vo.o mo.o mo.o (UT/UT) urexqs terxv Time (min) 4.0-— 92 (b) 300’- H O o .‘J 8 m 2.0— 9 U) m m u 33 100'- 0 l 1 n 0 0.01 0.02 0.03 Plastic axial strain (in/in) (a) o O O o o o o O a 1000— 9 ° #5 59.4% Sand c-1 a 0 C) o 400- 800— o o 7.: a U) o. 300:u 500- U) 0 U) m 33 E:p m 200;, 400- ° .3 computed ice 2‘ .. e T = -12.03°C 100— 200- Stress factors 0 r~ o o m a: v m H tn m> o m ..- “a“. °=z “3 “and. “l '4: “I“? 't ". I‘ O— O/ of N N 01 w to to on m m 0.01 0.02 0.03 Plastic axial strain (in/in) Figure 6-8. Sand-Ice Sample 5. (a) Computations for Stress Factors. (b) Stress Factor versus Axial Plastic Strain. Time (min) 93 (b) 3.0V 9 ._._ o 3 O o o o o 9 ° 9 ‘8 (9 J3 2.0— 9 m m m H 33 1.0— 0 1 g 0 0.01 0.02 Plastic axial strain (in/in) (a) . 80°" . #11 54.6% Sand c-1 3001 '3 600- .9: m 1 3 Slope gives T— 200- 33400- . , E:p m A; At Computed ice 3 -H 2 100- 200- T = -12.03°C N N N m N V‘ \D O \O 0‘ O N M \O \0 £0 \0 ‘0 l‘ l‘ l‘ l‘ I" 0 g 0 cu o: o; N cu N 0; fl N N & 0 0.01 0.02 Plastic axial strain (in/in) Figure 6-9. Sand-Ice Sample 11. (a) Computations of Stress Factors. (b) Stress Factor versus Axial Plastic Strain. Time (min) Stress factor 200 150 [.1 O O 50 0‘ O O l 1 Axial stress (psi) 8 O N O O 94 (b) I 0.01 0.02 0.03 Plastic axial strain (in/in) (a) - #42 61.0% Sand C—1 810 e ' s 1; At p give é P A8 Computed ice T = -3.85°C (D m on LG I\ 00 ON H O O l\ H r—i 8 CD Ch O H N m ‘3‘ 0 l\ 00 CD CD ON A A 4 cu N N N mu N N N m 04 p; 0.01 0.02 0.03 Plastic axial strain (in/in) Figure 6-10. Sand-Ice Sample 42. (a) Computations of Stress Factors. (b) Stress Factor versus Plastic Axial Strain. 600 400 Time (min) N O O 1 Axial stress (psi) Stress factor 800 600 A O O N O O (b) 95 Figure 6-11. 1 n 1 1 l 4 1 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Plastic axial strain (in/in) r (a) #17 55.6% Fine sand . . 1 Slope gives ?— L At ep As Computed ice ” T = -12.o3°c . L l L I L 1 1 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Plastic axial strain (in/in) Sand-Ice Sample 17. (a) Computations of Stress Factors. (b) Stress Factor versus Plastic Axial Strain. Volume change (c.c.) Axial stress (psi) +0.18 +0.16 +0.14 +0.12 +0.10 +0.08 +0.06 +0.04 +0.02 -0.02 800 600 400 200 (a) Sample 42 Wice x 1.88 ”f“‘ Computed ice I I L 0 0.01 0.02 0.03 Plastic axial strain (in/in) Figure 6-12. Mobilization of Third Mechanism and Volume Change. Volume change (c.c.) 97 +0010 '- (b) Sample 11 +0.08r- +0.06- +0.04 '- +0.02 — -0.02*-0 G -0004? ' Q -0.06- - 9 0 fl/"‘~—#11 ”’T:_—“ Computed ice x 2.60 800 600 400 //*--Computed ice 200 Axial stress (psi) T = -12.03°C o 0.61 0.02 0.03 Plastic axial strain (in/in) Figure 6-12. (Continued). +0.14 +0.12 +0.10 ,.+0.08 C C + O 0 0‘ +0.04 4. O O N Volume change -0.02 -0.04 —0006 -0.08 800 600 400 200 Axial stress (psi) . l 0 0.01 Figure 6-12. (c) Sample 17 I I 0.02 0.03 98 0.04 I 0.05 #17 #17 Computed ice x 1.49 fi Computed.ice T = -12.03°C I I l 0.06 0.07 0.08 Plastic axial strain (in/in) (Continued). Change in pore pressure 01 - 03 (psi) (psi) 200 ' (a) 160 ' 120 ' 80 - 99 +40 1- (b) —80 ‘ ' 0 0.05 Figure 6-13. Axial strain (in/in) N = 0.57 I 1 1 l 1 1 0.10 0.15 0.20 0.25 Axial strain (in/in) Consolidated-Undrained Test on Saturated Sand (After Bishop and Henkel, 1962). (a) Stress-Strain Curve. (b) Pore Water Pressure versus Strain. Stress factor 100 4.0'— (a) T = _12 03°C Final for C]. Final for fine sand 300'. Initial for C1 material 2.0~ fine sand 1.0 Both Cl and fine sand material T = —12.03°C 0 1 L 1 I 1 1 1 0 10 20 30 40 50 60 70 Figure 6-14. Percent sand by volume Stress Factors versus Volume Concentration of Sand. Stress factor 101 (b) T = -3.85°C 300- Final 2.0- Initial 1.0 T = -3.85°C C1 Material 0 I I I I I I I 0 10 20 30 40 50 60 70 Figure 6-14. Percent sand by volume (Continued). Axial stress on sand-ice sample (cl-o3) G H 102 01—03 = [K(1+N) CI +2(Nc-N)(PI+03)tan¢] 01-03 = deviator stress on sand- _ ice sam le. O1.03 - K(1+N)0I CI = stress iceptakes under equiv- alent conditions (deviator stress). K = a constant. N = % sand by volume. NC = critical volume concentra- tion 0.42. PI = pressure exerted by ice mazix. 03 = confining pressure. 3 = friction angle for material. 0 N 0 Percent sand by volume (N) Figure 6-15. Possible Relationship of Stress to Friction Angle of Frozen Sand Material. Axial strain (in/in) Axial stress on ice (psi) 103 275p (a) 250— = 233 6 Approximate with step 225— O4: 217 function 05= 201 200- ['06: 193 175 l 1. 1 0 0.01 0.02 0.03 Plastic axial strain (in/in) 0.03— (b) Elastic @ O O O 0 Plastic 0 o 02 _ G O O - o 6 Data test 33 _ 01-03 = 705 psi, 03 = 0 0-01 . T = -12.06°C 59.4% sand by volume (Cl) ‘———— Predicted by Eq. (6-5) using loading schedule. (Data corrected for system error) 0 L I I I 1 0 100 200 300 400 500 Time (min) Figure 6-16. Sand-Ice Sample 33. (a) Ice Loading Schedule. (b) Comparison Experimental Creep Data with Predicted Curves. Axial stress on ice (psi) Axial strain (in/in) 300 250 200 150 100 0.04 ' 104 (a) r01 = 265 _ 02 = 249 03 = 215 \ 04 = 181 _ 05 = 148 ”‘06 = 131 1 1 1 1 1 1 1 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Plastic axial strain (in/in) F Elastic (b) O Plastic O _ G) <9 (9 Data sample 55 01-03 = 390 p31, 03 = 0 . T = -7.55°C L 56.9% sand by volume (F) ——— Predicted by Eq. (6-5) ' using loading schedule. a (Data corrected for system error) 1 1 1 1 1 1 1 0 200 400 600 800 1000 1200 1400 Time (min) Figure 6-17. Sand-Ice Sample (b) Comparison Predicted Curve 55. (a) Ice Loading Schedule. Experimental Creep Data with Time (min) 600 400 200 Stress factor I I l Axial stress (psi) 800 O‘ O 0 1h 0 O 105 F (b) 1 1 1 1 1 1 0 0.02 0.04 0.06 0.08 0.10 0.12 Plastic axial strain (in/in) Clay—ice —9._L.o_ __ I’ o o — (a) 0 0 - ’:%; o 53,096 o 0 Stresses corrected 0 to ice density = 0.900 g/cc. Co = _ 0 Ice I I I l I J 0 0.02 0.04 0.06 0.08 0.10 0.12 Plastic axial strain (in/in) Figure 6-18. Sault Ste. Marie Clay Sample C2-Sl7. (a) Computations of Stress Factors. (b) Stress Factors versus Plastic Axial Strain. (Dataafter Dillon, in preparation.) Axial stress on ice (psi) Axial strain (in/in) 400 300 200 100 0.12 0.10 0.08 '0.06 106 1 I 1 1 1 1 0 0.02 0.04 0.06 0.08 0.10 0 12 Plastic axial strain (in/in) Elastic ' (b) ’,, Plastic _ O Data, sample C2-S2 ol-o3 = 705 p31, 03 = 0 _ (Corrected to ice density = 0.900 g/cc) T = 15.4°C ' -——— Predicted by Eq. (6-5) using loading schedule. 1 1 1 1 1 1 0 200 400 600 800 1000 1200 Time (min) Figure 6-19. Sault Ste. Marie Clay Sample C2-82. (a) Ice Loading Schedule. (b) Com- parison of Creep Data with Predicted (Data after Dillon, in Curve. preparation.) 107 d; U -H D :3 0 v o H 32’ 23 F1 0 > 3 0.4— 0 H m T = -12.03°C 0.2“ 0 l 1 1 1 1 1 1 0 10 20 30 40 50 60 70 Figure 6-20. Percent sand by volume Flow Volume versus Percent Sand by Volume. 50 40 30 20 10 Observed activation energy (K cal/mole°C) 0 10 Figure 6-21. 108 I l I I J I 20 30 40 50 60 70 Percent sand by volume Observed Activation Energy versus Percent Sand by Volume. CHAPTER VII SUMMARY AND CONCLUSIONS The conclusions are summarized under three headings: polycrystalline ice, sand-ice system, and clay-ice system. Items covered under each heading are intended to reflect the findings of this investigation and are limited to the materials used, methods of sample preparation followed, test procedures, and analysis and develOpment of the data presented. Polycrystalline Ice The experimental program has included both constant axial strain-rate and constant axial stress creep tests on polycrystalline ice. The ice samples were frozen from either a mixture of snow and ice water or a mixture of powdered ice and cold water. No observable differences re- sulted from the two methods. The data revealed that the value of Young's modulus for polycrystalline ice decreases as deformation proceeds, and accommodation cracking is believed to be primarily re- sponsible for this. Experimental results suggest that the creep rate of polycrystalline ice subjected to constant axial stress and temperature may also depend on strain and absorbed energy. 109 110 Using this concept and the results of constant axial stress creep tests an equation has been develOped which includes a strain hardening term and a softening term. The hardening term is some function of stress, temperature and strain whereas the softening term is a function of stress, tem- perature, and absorbed energy. The combined effect of these two terms appears to describe the creep behavior of poly- crystalline ice through primary, secondary, and tertiary creep regions for the range of temperatures and stresses studied. The range of temperatures extends from slightly below 0 degrees Centigrade to at least minus 12 degrees Centigrade, and the axial stress range includes 50 psi and up to about 300 psi. Correlations are made to show the similarity of this equation to the general creep equation derived in accordance with the rate process theory. These methods of analysis may also apply to the creep behavior of other materials. It appears that different mechanisms dominate the creep behavior of polycrystalline ice at strain-rates above a certain limiting value. This result was also confirmed by Dillon and Andersland (1966a). It is suggested that the inability of intergranular cohesion to maintain continuity of the ice grains at the high stresses caused by the higher strain-rates may be in part responsible for this behavior. Sand-Ice System The interaction of sand and ice during deformation was studied by observing the effect on the creep behavior 111 of polycrystalline ice by the addition of increasing amounts of sand frozen in the ice in dispersed positions. The sam- ples for this portion of the study were prepared by mixing natural snow with chilled sand and combining this mixture with ice water before freezing. Three mechanisms which tend to strengthen sand-ice samples as compared with polycrystalline ice samples have been identified. The first mechanism appears to depend only on the relative volumes of sand and ice in the sample. This strengthening may result from the fact that all sample plastic deformation must be accommodated by the ice matrix, thus causing the deformation rate within the ice to be greater than the overall sample deformation rate. There may also be some keying effect by the sand grains. No fracturing of sand grains was observed. The second mechanism is the result of friction at solid to solid contacts and Operates only at sand volume concentrations above a certain critical value. This ef- fect is less apparent in some materials. The first two mechanisms are mobilized at all strains. The third mechanism is related to the dilatancy of the dense sand material which occurs with deformation. This dilatancy must act against the ice matrix thus causing a negative ice pressure having the same effect as an increased confining pressure applied to the sand-ice material. Dila- tancy has a counterpart in undrained triaxial tests on 112 unfrozen saturated sand in that negative pore pressures can develOp. This mechanism appears to be dependent on strain and can be correlated with sample volume change. The data indicates that this third mechanism may also depend on strainJrate. The results of constant strain-rate tests on sand- ice materials were used to evaluate the effect of these mechanisms on creep rates by means of a stress factor. The use of a combination of these stress factors along with the creep equation for polycrystalline ice provides a method of approximating the creep behavior of sand-ice samples. This method correlates well with the experimental data for the range of temperatures and stresses studied when restricted to low creep rates. ClayeIceggystem Computations carried out using test data (Dillon, in preparation) for clay-ice material suggest mechanisms similar to those observed for sand-ice material. It may be possible to account for the effect of unfrozen water in frozen clay materials by a correction to the density of the ice matrix. Correlation of computed creep de- formations with the available experimental data was very good. CHAPTER VIII RECOMMENDATIONS FOR FURTHER RESEARCH Further research is needed in several areas related to the shear strength of soil-ice systems. Several specific problems are briefly described below: i 1. Extend the study of sand-ice materials giving greater consideration to the influence of particle shape and size distribution. The use of greater confining pres- sures may permit the evaluation of friction angles for frozen material. 2. Investigate the possibility of extending the methods described here to clay-ice systems, possibly by using a correction to the density of the ice to account for the effect of unfrozen water. This correction may not be linear. 3. Since it appears possible to include the effect of all hardening mechanisms in one term and the effect of all softening mechanisms in another term for polycrystalline ice, it may be possible to do the same for soil—ice mate- rial. Then an equation may be develOped for soil-ice creep behavior which is similar to that for polycrystalline ice with the parameters also dependent on soil properties. 4. Investigate the behavior of nonhomOgeneous frozen soils. It may be possible to approximate the behavior of these materials by using average strength parameters. 113 BIBLIOGRAPHY Akili, W. "Stress Effect on Creep Rates of a Frozen Clay Soil from Standpoint of Rate Process Theory," Ph.D. Thesis, Michigan State Univ., E. Lansing, Mich., 1966. Andersland, O. B., and Akili, W. "Stress Effect on Creep Rates of a Frozen Clay Soilfl Geotechnique, Vol. XVII, No. 1, March, 1967, pp. 27-39. Barnes, P., and Tabor, D. "Plastic Flow and Pressure Melt- ing in the Deformation of Ice I," Nature, Vol. 210, May 28, 1966, pp. 878-882. BishOp, A. W., and Henkel, D. J. The Measurement of Soil Properties in the Triaxial Test, Edward Arnold LTD, London, 1962. Butkovich, T. R., and Landauer, J. K. "The Flow Law for Ice," Research Report 56, U.S. Army Snow, Ice and Permafrost Research Establishment, Aug., 1959. Butkovich, T. R., and Landauer, J. K. "Creep of Ice at Low Stresses," Research Rpt. 72, U.S. Army Snow, Ice and Permafrost Research Establishment, Aug., 1960. Christensen, R. W. "Analysis of Clay Deformation by Rate Process Theory," Ph.D. Thesis, Michigan State Univ., E. Lansing, Mich., 1964. 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 Co., Inc., N. Y., 1961, p. 149. Dillon, H. B. "Temperature Effect on Creep Rates of a Fro- zen Clay Soilfl Ph.D. Thesis, Michigan State Univ., E. Lansing, Mich. (in preparation). Dillon, H. B., and Andersland, O. B. "Deformation Rates of Polycrystalline Ice," Internat. Conf. on Physics of Snow and Ice, The Inst. of Low Temp. Sci., Hokkaido Univ., Sapporo, Japan, Aug., 1966a. Dillon, H. B., and Andersland, O. B. "Predicting Unfrozen Water Contents in Frozen Soils," Canadian Geotech— nical Jo, V010 III, NO. 2' 1966b, pp. 53—600 114 115 Glasstone, S., Laidler, K. J., and Eyring, H. The Theory of Rate Processes, McGraw-Hill Book Co., Inc. N.Y., 1941. Glen, J. W. "The Creep of Polycrystalline Ice," Proc. Royal Soc. of London, Ser. A, 228, 1955, pp. 519- 538. Glen, J. W., and Perutz, M. F. "The Growth and Deformation of Ice Crystals," J. of Glaciology, Vol. 2, No. 16, 1954, pp. 397-403. Gold, L. W. "Some Observations on the Dependence of Strain on Stress for Ice," Canadian J. of Physics, Vol. 36, No. 10, 1958, pp. 1265-1275. Gold, L. W. "Deformation Mechanisms in Ice," Chapter 2, Ice and Snow, Properties, Processes and Applications, Ed. by W. D. Kingery, MIT Press, Cambridge, Mass., 1963. Harr, M. E. Groundwater and Seepage, McGraw-Hill Book Co., Inc., N.Y., 1962. Jellinek, H. H. G., and Brill, R. "Viscoelastic PrOperties of Ice," J. of Applied Physics, Vol. 27, No. 10, Kamb, W. B. "The Glide Direction in Ice," J. of Glaciology, V01. 3' NO. 30’ 1961’ pp. 1097-1106. Kauzmann, W. "Flow of Solid Metals from the Standpoint of the Chemical Rate Theory," Trans. Am. Inst. of Mining and Metalurgical Engin., Vol. 143, 1941, pp. 57-83. Mitchell, J. K. "Shearing Resistance of Soils as a Rate Process," J. of Soil Mechanics and Foundation Div., ASCE, Vol. 90, Sm 1, 1964. Murayama, S., and Shibata, T. On the Rheological Charac- teristics of Clay, Disaster Prevention Research Inst. Bu11., No. 26, Kyoto, Japan, Oct., 1958. Nye, J. F. "The Flow of Ice from Measurements in Glacier Tunnels, Laboratory Experiments, and the Jung- fraufirn Borehold Experiment," Proc. Royal Soc. of London, Ser. A, 219, 1953, pp. 477-489. Pounder, E. R. The Physics of Ice, Pergamon Press, Oxford, 1965. 116 Rabotov, Y. N. "On the Equations of State for Creep," Progress in Applied Mechanics, The Prager Anniver- sary Vol, The Macmillan Co.,NQY.: 1963- Rigsby, G. P. "Effect of Hydrostatic Pressure on Shear Deformation of Single Ice Crystals," J. of Glaci- ology, Vol 3, Oct., 1958, pp. 273-278 (Also Re- search Report 32, U.S. Army Snow, Ice, and Perma- frost Research Establishment). Steinemann, S. "Results of Preliminary Experiments on the Plasticity of Ice Crystals," J. of Glaciology, Vol. 2, 1954, pp. 404-412. Tsytovich, N. A. "Instability of Mechanical Properties of Frozen and Thawing Soils," Internat. Conf. on Perma- frost, National Academy of Science--National Re- search Council Publ. No. 1287, Washington, D.C., 11-15, Nov., 1963, pp. 325-330. Vyalov, S. S. "Rheology of Frozen Soils," Internat. Conf. on Permafrost, National Academy of Science--National Research Council Pub. No. 1287, Washington, D.C., ll~15, Nov., 1963, pp. 332-337. Weertman, J., and Breen, J. E. "Creep of Single Tin Crys- tals," J. of Applied Physics, Vol. 27, No. 10, Oct., 1950. Yamaji, K., and Kuroiwa, D. "Visoelasticity of Ice in the Temperature Range 0° to ~100°C," Defence Research Board Tr. T63J, Canada, Aug., 1958, pp. 171-183. APPENDIX--Data Table A—1. Constant strain-rate test data* Test 1. Ice Test 2. 60.2% sand by volume T = -12.03°C Cl material Yi = 0.880 gm/cc T = -12.03°C . _ -4 . e - 1.33 X 10 /min Yi = 0.898 gm/cc . _ -4 . 52 — 0.886 X 10 /m1n £1 = 1.33 X 10 4/min Defl. Load Time AV éz = 0.886 X 10-4/min (in.) (lbs) (min) (cc) Strain-rate = él Defl. Load Time AV 0.005 46 13 (in.) (lbs) (min) (cc) 0.010 175 39 0.015 185 55 0.020 215 82 0.025 240 99 0.030 245 115 0.035 252 132 0.040 255 146 0.045 256 162 0.050 256 175 0.055 254 189 0.060 250 202 0.065 247 217 0.067 244 223 Strain—rate = éz Strain-rate = él 0.005 15 7 0.010 75 26 0.015 288 44 0.020 539 60 0.025 700 77 0.030 789 96 0.035 859 113 0.040 914 129 0.045 950 144 0.050 972 161 0.055 982 181 0.060 998 201 0.065 1027 219 0.070 225 231 0.070 1060 238 0.075 198 259 0.075 1091 256 0.080 1110 273 0.085 1120 291 0.090 1130 309 Strain-rate = éz 0.095 1049 335 0.100 1045 361 0.105 1046 381 *Data listed includes the total observed deformation: system errors consist of elastic error (0.0008 in/lOO lbs load) and unpredictable seating error (see Chapter IV). Note: T = test temperature, Yi = ice density, 8 = axial strain-rate, AV = sample volume change, 03 = confining pressure (0 unless otherwise noted). 118 119 Table A-1. (Continued). Test 3. Ice Defl. Load Time Av (in.) (lbs) (min) (cc) T = —12.03°C Strain-rate = él _ 0.005 32 14 Y1 ‘ 0'903 9m/CC 0.010 98 38 . _ -4 . 0.015 185 56 61 — 1.33 X 10 /min 0.020 244 71 . -4 . 0.025 277 87 62 0.886 x 10 /min 0.030 303 103 0.035 307 118 Defl. Load Time A! 0.040 318 135 (in.) (lbs) (min) (cc) 0.045 323 150 . _ . 0.050 325 166 Straln'rate ‘ 61 0.055 327 182 0.005 12 11 0.060 328 199 0.010 60 30 0.065 332 215 0.015 132 48 0.067 332 224 0.020 201 64 Strain-rate = 62 °°°25 27° 80 0.070 290 233 °°°3° 287 97 0 075 290 256 0.035 304 114 - 0.040 318 131 0.045 329 147 0.050 333 163 Tg§E_§. 61.2% sand by volume 0.055 338 180 . 0.060 342 196 C1 material 0.065 344 213 _ 0.070 346 230 T ‘ ‘12'°3°C 0.075 346 247 _ 0.080 347 264 Y1 ‘ 0'890 9m/CC 0.085 344 280 . _ -4 . 0.090 342 297 5 ' 1'33 x 10 /mln Straln‘rate = 82 Defl. Load Time AV 0.095 303 321 (in.) (lbs) (min) (cc) . 0 29 346 8 185 292 371 °°°°5 35 4 ' 0.010 104 21 0.015 238 37 0.020 402 54 0.025 565 69 0.030 688 85 Test 4. Ice T = -12.03°c 0.035 744 101 0.040 798 118 yi = 0.902 gm/cc 0.045 842 135 . _ -4 . 0.050 885 151 E1 ‘ 1'33 x 10 /m1“ 0.055 944 167 6 = 0.886 x 10-4/min 0.060 982 183 120 Table A-1. (Continued). Test 5. (Continued). Test 9. 42.0% sand by volume 0.065 1005 200 C1 material 0.070 1047 216 ' 0.075 1075 232 T = 0.12.03°C 0.080 1098 249 0.085 1134 265 y. = 0.891 gm/cc 0.090 1135 281 1 _4 0.095 1136 298 él = 1.33 X 10 /min 0.100 1138 314 _4 0.105 1140 331 62 = 0.886 X 10 /min 0.110 1130 347 0.115 1135 363 Defl. Load Time AV 0.120 1125 379 (in.) (lbs) (min) (cc) 0.125 1112 396 . . Strain-rate = 81 0.005 50 12 Test 8. 24.5% sand by volume 0.010 140 28 0.015 290 44 Cl material 0.020 390 61 0.025 415 77 T = -12.03°C 0.030 438 94 0.035 453 111 yi = 0.883 gm/cc 0.040 462 127 _4 0.045 472 144 E = 1.33 X 10 /min 0.050 477 160 0.055 477 176 Defl. Load Time AV 0.060 477 192 (in.) (lbs) (min) (cc) 0.065 475 208 1. w 2.22.2.3: = 0.010 58 28 2 0.015 136 46 0.070 435 227 0.020 241 63 0.075 410 256 0.025 318 78 0.080 405 275 0.030 357 93 0.0660 Load removed 0.035 381 109 0.040 395 125 0.045 408 140 Test 10. 55.2% sand by volume 0.050 418 155 0.055 418 172 C1 material 0.060 419 189 0.065 420 205 T = -12.03°C 0.070 422 221 0.075 423 237 y.= 0.884 gm/cc 0.080 420 252 l _4 0.085 415 268 6 = 1.33 X 10 /min 0.090 407 284 0.095 397 300 0.0956 397 0.0858 Load removed 121 Table A-1. (Continued). Test 10. (Continued). 0.065 890 203 -0.034 0.070 910 219 Defl. Load Time AV 0.075 919 234 -0.021 (in.) (lbs) (min) (cc) 0.080 925 250 -0.005 0.085 930 266 +0.012 °°°°5 24 11 0.090 934 283 +0.014 0'010 75 29 Strain-rate = a 0.015 175 46 2 0.020 325 62 0.095 850 309 +0.050 0.100 848 332 0.0788 Load removed 0.025 538 78 0.030 673 93 0.035 727 109 0.040 776 124 0.045 812 140 Test 12. 0.050 829 156 0.055 852 182 0.060 870 198 0.065 893 214 Power failure--data invalid 0.070 905 229 Test 13. 44.9% sand by volume 0.075 912 245 _—__—_— 0.080 915 261 C1 material 0.085 917 277 0.090 915 295 T = -12.03°C yi = 0.885 gm/cc Test 11. 54.6% sand by volume _4 £1 = 1.33 X 10 /min C1 material _4 62 = 0.886 X 10 /min T = -12.03°C Defl. Load Time AV Yi = 0.908 gm/cc (in.) (lbs) (min) (cc) él = 1.33 X 10_4/min Strain rate E1 _4 0.005 38 15 -0.001 62 = 0.886 X 10 /min 0.010 96 32 -0.005 0.015 247 59 -0.018 Defl. Load Time ‘ AV 0.020 402 65 -0.025 (in.) (lbs) (min) (cc) 0.025 470 81 -0.027 . 0.030 500 97 -0.026 Strain-rate = é1 0.035 517 114 -0.017 0.005 18 11 -0.007 0.040 537 131 +0.002 0,010 54 27 -0.020 0.045 545 147 +0.008 0,015 122 43 -0.029 0.050 559 164 +0.019 0,020 225 59 -0.040 0.055 563 180 +0.033 0.025 385 74 -0.056 0.060 567 197 +0.047 0,030 542 91 -0.061 0.065 570 213 ‘ +0.055 0,035 659 106 -0.072 0.070 572 230 +0.065 0.040 732 123 -0.060 0.073 575 0,045 767 139 -0.063 Strain-rate = 62 0'050 798 155 ‘0'057 0.075 542 248 +0.074 0,055 837 171 -0.047 0.060 867 186 -0.040 0.080 515 274 +0.103 0.085 504 298 +0.125 0.0887 504 0.0790 Load removed 122 Table A-1. (Continued). Test 14. Defl. Load Time AV (in.) (lbs) (min) (cc) Membrane leaked--data invalid 0.005 20 7 +0.004 0.010 80 24 —0.002 Test 15. 0.015 175 41 -0.007 0.020 290 57 -0.012 Membrane leaked-~data invalid 0.025 356 73 -0.015 0.030 385 89 -0.018 0.035 402 105 -0.031 Test 16. 9.3% sand by volume 0.040 418 122 -0.034 0.045 437 139 -0.046 C1 material 0.050 457 155 -0.055 0.055 476 172 -0.052 T = -12.03°C 0.060 493 188 -0.061 0.065 508 205 -0.064 yi = 0.897 gm/cc 0.070 522 221 —0.057 _4 0.075 537 239 -0.060 E1 = 1.33 X 10 /min 0.080 548 256 -0.066 _4 0.085 562 274 -0.064 £2 = 0.886 X 10 ~/min 0.090 575 291 -0.070 0.095 593 309 -0.056 Defl. Load Time AV 0.100 610 326 -0.053 (in.) (lbs) (min) (cc) 0.105 621 342 -0.050 . _ . 0.110 631 361 -0.049 Straln'rate ‘ E1 0.115 648 378 -0.042 0.005 30 +0.014 0.120 657 395 -0.035 0.010 175 25 +0.003 0.125 670 411 -0.030 0.015 285 42 +0.002 0.130 682 429 —0.020 0.020 325 57 -0.004 0.135 690 446 -0.003 0.025 342 72 -0.011 0.140 698 462 +0.002 0.030 357 88 —0.012 0.145 703 480 +0.009 0.035 365 104 —0.015 0.150 723 498 +0.019 0.040 365 120 10.015 0.155 723 515 +0.022 0.045 366 137 -0.021 0.160 726 532 +0.035 Strain-rate = éz 0.165 733 550 +0.051 0.050 328 164 _0.021 0.170 740 567 +0.057 0.055 327 189 _0.024 0.175 750 584 +0.075 0.180 760 601 +0.09l 8'3233 :27d m d 0.185 766 618 +0.104 ' °a re °Ve 0.190 771 635 +0.118 0.195 775 652 +0.132 Test 17. 55.6% sand by volume 0'200 779 669 +0'146 F material Test 18. 66.2% sand by volume _ _ o T 12°03 C Mixed, 3(Cl matl.): 1(F matl.) Y1 = 0'849 9m/CC T = -12.03°c ‘ 6 = 1.33 x 10‘4/min y. = 0.904 gm/Cc 1 1.33 x 10‘4/min é é _. Defl. (in.) 0.005 0.010 0.015 0.020 0.025 0.030 0.035 Load (lbs) 36 120 210 259 294 316 338 2.66 x 10‘4/min Time (min) 9.5 18 26 34.5 43.5 52 60 Table A-1. (Continued). Test 18. (Continued). Defl. Load Time A V (in.) (lbs) (min) (cc) 0.005 35 8 -0.013 0.010 80 27 -0-013 0.015 255 47 0.000 0.020 558 64 -0.004 0.025 713 77 -0.010 0.030 775 93 -0.012 0.035 880 110 -0.011 0.040 900 125 +0.003 0.045 956 142 +0.005 0.050 1003 158 +0.010 0.055 1050 175 ,+0.019 0.060 1093 191 +0.027 0.065 1128 207 +0.038 0.070 1160 224 +0.045 0.075 1200 241 +0.059 0.080 1235 257 +0.071 0.085 1262 273 +0.096 0.090 1281 290 +0.106 0.095 1290 306 +0.127 0.100 1304 322 +0.148 0.105 1307 339 +0.172 0.110 1295 356 +0.202 0.115 1287 373 +0.230 0.120 1278 390 +0.262 0.125 1261 406 +0.317 Test 19. Ice T = -12.03°C yi = 0.903 gm/cc' AV (CC) -0.001 -0.007 +0.010 +0.026 +0.032 +0.037 +0.037 0.040 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 344 352 354 365 370 372 373 373 371 368 364 360 352 349 68.5 77 86.5 95 103.5 111.5 120 128 136.5 145 153 161 170 178.5 0.0960 Load removed Test 20. Cl material T = —12.03°C yi = 0.886 gm/cc E = 2.66 x 10-4/min Defl. Load Time (in.) (lbs) (min) 0.005 37 5 0.010 135 14.5 0.015 275 23 0.020 510 31 0.025 683 39 0.030 678 47 0.035 842 55.5 0.040 906 64 0.045 959 72.5 0.050 1013 81 0.055 1065 89 0.060 1105 97 0.065 1125 105 0.070 1180 113 0.075 1205 121 0.080 1220 129 0.085 1230 137 0.090 1238 145.5 0.095 1240 154 0.100 1235 162 0.105 1221 170.5 0.0750 Load removed 63.0% sand +0.035 +0.025 +0.029 +0.023 +0.023 +0.026 +0.025 +0.019 +0.022 +0.021 +0.015 +0.014 +0.016 +0.012 by volume Av (cc) -0.004 -0.012 -0.020 —0.031 -0.031 -0.032 -0.024 -0.023 -0.017 -0.012 -0.009 -0.002 +0.011 +0.027 +0.049 +0.068 +0.091 +0.115 +0.149 +0.175 +0.214 124 Table A-1. (Continued). Test 21. 11.7% sand by volume C1 material T = _12003°C yi = 0.907 gm/cc E = 2.66 x 10-4/min Defl. Load Time AV (in.) (lbs) (min) (cc) 0.005 35 4 -0.001 0.010 180 13 +0.018 0.015 302 21 +0.042 0.020 370 29 +0.046 0.025 415 38 +0.049 0.030 437 46.5 +0.053 0.035 450 55 +0.054 0.040 457 63 +0.048 0.045 465 71.5 +0.055 0.050 472 80 +0.054 0.055 472 88 +0.053 0.060 474 96 +0.053 0.065 475 104.5 +0.051 0.070 472 113 +0.062 0.075 470 121 +0.058 0.080 468 129 +0.052 0.085 465 136.5 +0.052 0.0853 465 0.0753 Load removed Test 22. 37.5% sand by volume Cl material T = -12.03°C yi= 0.917 gm/cc é ==2.66 x 10-4/min o3= 100 psi Defl. Load Time AV (in.) (lbs) (min) (cc) 0.005 150 12.5 0.010 350 21 (‘70 II 03 = 100 psi Defl. Load (in.) (lbs) 0.005 80 0.010 220 0.015 310 0.020 342 0.025 365 0.030 382 0.035 390 0.040 400 0.045 407 0.050 411 0.055 416 0.060 418 0.065 418 0.070 417 0.075 413 0.080 412 0.085 411 0.090 407 0.095 402 0.100 396 0.0910 Load removed 0.015 485 29.5 0.020 528 39.5 0.025 568 48.5 0.030 597 57.5 0.035 613 66 0.040 625 74 0.045 633 82.5 0.050 634 90.5 0.055 631 99 0.060 627 107 0.065 622 115.5 0.070 618 124 Test 23. Ice T = -12.03°C y = 0.907 gm/cc .2.66 x 10-4/min Time (min) 9 17 26 34 42.5 51 60 68.5 76.5 84.5 93 101 109 117 125.5 134 142 150.5 159 167 AV (CC) Table A-1. Test 24. 59.6% sand by volume C1 material T = -12.03°C Yi = 0.900 gm/cc 6 = 2.66 x 10'4/min 03 = 100 psi Defl. Load Time (in.) (lbs) (min) 0.005 100 9 0.010 270 17 0.015 468 24 0.020 675 31.5 0.025 825 39 0.030 884 47 0.035 944 55.5 0.040 1006 64 0.045 1050 72.5 0.050 1089 81 0.055 1129 89.5 0.060 1147 97 0.065 1188 105 0.070 1200 113 0.075 1222 121.5 0.080 1239 129.5 0.085 1249 137.5 0.090 1251 146 0.095 1269 154 0.100 1267 162.5 0.105 1262 171 0.110 1261 179.5 0.115 1265 188 0.120 1262 196 0.125 1252 205 Test 25. Ice T = -12.03°C Y = 0.904 gm/cc 1.33 x 10'4/min 100 psi (Continued). AV' (cc) Defl. (in.) 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080 Load (lbs) 65 160 223 257 276 295 302 310 315 318 322 327 325 325 323 318 26. Ice Test T = Yi= E; = Defl. (in.) 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080 0.085 0.090 -12.03°C Time (min) 12 29 44 6O 76 92 108 124 140 156 172 188 203 219 235 253 0.912 gm/cc 1.33 x 10'4/min Load (lbs) 30 85 150 207 249 282 306 320 329 335 340 344 345 345 337 335 333 327 Time (min) 27 43 58 74 91 108 124 140 161 177 193 210 226 242 260 276 293 AV (CC) AV (cc) +0.001 +0.001 +0.002 +0.011 +0.018 +0.018 +0.027 +0.028 +0.026 +0.027 +0.020 +0.018 +0.016 +0.015 +0.011 +0.012 +0.011 +0.009 126 Table A-1. (Continued). Test 26. (Continued). Test 38. 0.095 327 315 Extreme f1aring--data invalid 0.100 323 332 +0.006 0.105 318 349 +0.011 0.110 313 366 +0.006 Test 39. Ice 0.115 313 382 +0.004 0.120 308 398 +0.004 T = -3.85°C 0.125 304 415 -0.002 0.130 302 436 -0.003 y. = 0.913 gm/cc 0.135 295 449 -0.005 1 _4 0.140 294 466 -0.006 E = 2.66 X 10 /min 0.145 291 487 -0.004 0.150 287 498 +0.003 Defl. Load Time AV 0.155 284 516 -0.004 (in.) (lbs) (min) (cc) 0.160 283 533 -0.010 0.165 282 550 -0.006 0.005 90 8.5 0.000 0.170 280 566 -0.006 0.010 180 16 -0.002 0.175 279 582 -0.016 0.015 207 23.5 +0.003 0.180 276 600 -0.010 0.020 227 32.5 +0.006 0.1802 276 0.025 246 41 0.1708 Load removed 0.030 262 48.5 +0.013 0.035 265 56 +0.007 0.040 268 63.5 +0.011 Test 27. Ice 0.045 270 71 +0.005 0.050 270 78 +0.009 T = -11.95°C 0.055 266 85 +0.018 0.060 260 91.5 +0.012 yi = 0.904 gm/cc 0.065 250 98.5 +0.006 _4 0.070 240 106 +0.015 E = 1.33 X 10 /min 0.075 230 113.5 +0.009 0.080 222 121.5 +0.012 Defl. Load Time Av 0.085 218 129 (in.) (lbs) (min) (cc) 0.090 212 137 +0.009 0.095 210 145.5 0.005 140 16 0.000 0.100 207 154 0.010 225 31 -0.008 0.0962 Load removed 0.015 267 47 -0.006 0.020 290 63 -0.005 0.025 313 79 -0.009 Test 40. 28.3% sand by volume 0.030 322 95 -0.007 0.035 328 111 -0.008 C1 material 0.040 333 127 -0.007 0.045 338 143 -0.005 T = -3.85°C 0.050 337 159 -0.010 0.055 338 174 «0.015 y. = 0.895 gm/cc 0.060 337 190 -0.018 1 _4 0.065 336 206 -0.019 é = 2.66 X 10 /min 0.0590 Load removed 127 Table A-1. (Continued). Test 40. (Continued). yi = 0.905 gm/cc Defl. Load Time AV 4 = 2.66 x 10‘4/min (in.) (lbs) (min) (cc) Defl. Load Time 0.005 135 11 —0.006 (in.) (lbs) (min) 0.010 250 19 -0.012 0.015 275 28 -0.008 0.005 85 10 0.020 280 36 +0.004 0.010 181 19 0.025 282 44 0.000 0.015 305 28 0.030 292 52 +0.003 0.020 380 34.5 0.035 296 60 +0.007 0.025 423 42 0.040 288 68 0.030 465 51 0.045 285 76 +0.015 0.035 510 58.5 0.050 280 84 +0.019 0.040 560 66 0.045 595 73 0.050 610 81 Test 41. 14.4% sand by volume 0.055 630 89 0.060 645 97 C1 material 0.065 656 105 0.070 665 113 T = -3.85°C 0.075 673 121 0.080 675 129 Y1 = 0.904 gm/cc 0.085 675 137.5 _4 0.090 671 146 E = 2.66 X 10 /min 0.095 667 154 0.100 666 162.5 Defl. Load Time AV 0.105 662 171 (in.) (lbs) (min) (cc) 0.0912 Load removed 0.005 100 9 -0.006 0.010 190 17 -0.012 Test 43. 43.5% sand 0.015 225 25 —0.008 0.020 245 33 -0.004 C1 material 0.025 255 41 -0.006 0.030 260 49 “0.002 T = -3.85°C 0.035 263 57 +0.002 0.040 265 65 +0.011 y. = 0.906 gm/cc 0.045 263 73 +0.005 1 _4 0.050 260 81 +0.009 E = 1.33 X 10 /min 0.055 252 89 +0.013 0.0489 Load removed Defl. Load Time (in.) (lbs) (min) Test 42. 61.0% sand by volume 0.005 70 9 0.010 155 17 C1 material 0.015 255 25 0.020 282 33 T = -3.86°C 0.025 290 41 0.030 300 49 AV (CC) +0.064 -0.014 -0.017 -0.004 —0.001 +0.013 +0.01? +0.036 +0.079 +0.097 +0.11? +0.149 +0.175 +0.233 +0.286 +0.310 +0.388 by volume AV (cc) +0.004 -0.002 +0.002 +0.006 +0.019 +0.033 128 Table A—1. (Continued). Test 43. (Continued). Defl. Load Time AV (in.) (lbs) (min) (cc) 0.035 310 57 +0.047 0.040 317 65 +0.061 0.005 75 8 -0.016 0.045 320 73 +0.065 0.010 257 16.5 -0.032 0.050 318 81 +0.099 0.015 358 24 -0.038 0.055 314 89 0.020 397 32 -0.034 0.0470 Load removed 0.025 418 40 -0.040 0.030 433 48 -0.037 0.035 437 56 -0.043 Test 44. 41.8% sand by volume 0.040 441 64 -0.029 0.045 444 72 -0.025 C1 material 0.050 450 80 -0.021 0.055 445 87.5 -0.017 T = -7.55°C 0.060 435 95.5 -0.013 0.0518 Load removed yi = 0.889 gm/cc e = 2.66 X 10—4/min Test 46. 44.6% sand by volume Defl. Load Time AV C2 material (in.) (lbs) (min) (cc) T = -7.60°C 0.005 200 8 +0.004 0.010 358 16 +0.018 y. = 0.887 gm/cc 0.015 415 24 +0.022 1 _4 0.020 440 32 +0.026 E = 2.66 x 10 /min 0.025 454 40.5 +0.040 0.030 467 49 +0.033 Defl. Load Time AV 0.035 475 57 +0.047 (in.) (lbs) (min) (cc) 0.040 473 65 0.045 473 73 +0.065 0.005 150 8 -0.016 0.050 473 81 +0.069 0.010 300 17 -0.022 0.055 472 90 +0.083 0.015 368 26 -0.018 0.060 470 99 0.020 407 34 0.065 465 107 0.025 437 42 -0.015 0.030 465 50.5 —0.007 0.035 481 58.5 -0.003 Test 45. 39.6% sand by volume 0.040 496 67 +0.001 0.045 506 75 C2 material 0.050 519 83 0.055 523 91 T = -7.55°C 0.060 520 99 +0.027 0.065 515 107 yi = 0.905 gm/cc 0.070 506 115 0.0620 Load removed 2.66 x 10‘4/min m. (I 129 Table A-1. (Continued). Test 47. 58.9% sand by volume Defl. Load Time AV (in.) (lbs) (min) (cc) C2 material 0.005 85 7 +0.034 T = -7.55°C 0.010 172 15 +0.028 0.015 230 24 +0.022 yi = 0.907 gm/cc 0.020 268 32 +0.016 _4 0.025 285 40 +0.015 E = 2.66 x 10 /min 0.030 297 48 +0.013 0.035 308 56 +0.017 Defl. Load Time AV 0.040 318 63 +0.016 (in.) (lbs) (min) (cc) 0.045 317 71 +0.015 0.050 312 79 +0.010 0.005 50 7 0.055 308 88 0.010 144 16 0.060 305 96 0.015 332 25 0.065 302 105 +0.011 0.020 475 32 0.070 295 113 +0.015 0.025 588 39 0.075 288 121 0.030 642 47 0.080 282 130 0.035 682 55 0.085 274 139 0.040 723 64 0.090 270 147 0.045 763 72 0.095 266 155 0.050 795 80 0.100 260 163.5 0.055 824 88.5 0.105 254 172 0.060 855 97 0.110 249 181 +0.016 0.065 878 105 0.115 246 190 +0.015 0.070 900 113 0.120 243 198 +0.014 0.075 917 121 0.1120 Load removed 0.080 925 129 0.085 935 137.5 0.090 950 146.5 Test 49. 14.9% sand by volume 0.095 949 155 0.100 958 164 C2 material 0.105 960 173 0.0770 Load removed T = 07.55°C yi = 0.904 gm/cc Test 48. 2.7% sand by volume _4 2.66 X 10 /min é C2 material Defl. Load Time AV T = -7.55°C (in.) (lbs) (min) (cc) yi = 0.911 gm/cc 0.005 85 6 +0.014 _4 0.010 200 14 +0.018 6 = 2.66 X 10 /min 0.015 285 22 +0.012 0.020 330 31 +0.016 130 Table A-1. (Continued). Test 49. (Continued). Defl. Load Time AV (in.) (lbs) (min) (cc) 0.025 352 39 +0.010 0.030 366 46 +0.013 0.005 80 13 -0.006 0.035 371 53 +0.010 0.010 315 31 -0.013 0.040 373 61 +0.011 0.015 603 46 -0.010 0.045 373 69 +0.015 0.020 742 62 -0.002 0.050 368 77 0.025 815 78 +0.004 0.0430 Load removed 0.030 850 94 +0.015 0.035 895 111 +0.017 0.040 930 127 +0.028 Test 51. 7.8% sand by volume 0.045 953 143 +0.035 0.050 984 161 +0.039 F material 0.055 1007 178 +0.046 0.060 1028 195 +0.06? T = -11.80°C 0.065 1047 212 +0.073 0.070 1053 228 +0.075 vi = 0.873 gm/cc 0.075 1062 245 +0.089 é = 1.33 x 10 4/min Test 56. 22.8% sand by volume Defl. Load Time AV (in.) (lbs) (min) (cc) C2 material 0.005 123 15 —0.006 T = -12.05°C 0.010 245 32 -0.008 0.015 312 48 —0.019 y. = 0.914 gm/cc 0.020 353 63 -0.016 1 _4 0.025 360 79 E = 1.33 X 10 /min 0.030 363 94 -0.017 0.035 369 111 -0.013 Defl. Load Time AV 0.040 375 127 -0.004 (in.) (lbs) (min) (cc) 0.045 378 143 -0.015 0.050 378 159 -0.011 0.005 195 11 -0.006 0.055 378 175 —0.017 0.010 400 19 0.0576 376 184 0.015 500 28 -0.013 0.0494 Load removed 0.020 550 36 -0.021 0.025 560 44.5 0.000 0.030 548 54 +0.004 Test 53. 55.3% sand by volume 0.035 566 62 0.040 577 71.5 +0.011 C2 material 0.045 578 78 +0.041 0.050 565 86 +0.039 T = -11.80°C y = 0.913 gm/cc 1.33 x 10’4/min M. II Table A-1. Test 57. C2 material T *1 6 Defl. (in.) 0.005 0.010 0.015 0.020 0.025 0.030 0.035 Test C2-Sl7. -12.05°C (Continued). 35.1% sand by volume 0.903 gm/cc 1.33 x 10-4/min Load (lbs) 300 575 610 618 632 630 633 AV (CC) Time (min) 11 19 26 35 42 50 58 131 Defl. (in.) 0.0008 0.0013 0.0018 0.0021 0.0065 0.0106 0.0207 0.0620 0.1160 0.1544 0.2034 0.2723 0.2923 0.3136 (Data after Dillon, in preparation) Sault Ste. Marie Clay T y. Degree saturation = 96% Unfrozen water content = 12% -15.8°C 0.776 gm/cc l 6 1.29 x 10‘4/min Sample size 3.01 in. long 1.394 in. diameter Load (lbs) 16 34 73 109 196 296 511 841 1008 1082 1140 1204 1222 1215 Time (min) 10 20 30 45 60 90 180 270 330 405 510 540 570 Table A-2. Constant axial stress creep test data* Test 6. Ice Test 7. Ice T = -12.03°C T = -12.03°C Y1 = 0.907 gm/cc Yi = 0.907 gm/cc 01 - 03 = 229 and 318 psi 01 - 03 = 325 psi Defl. Load Time AV Defl. Load Time AV (in.) (lbs) (min) (cc) (in.) (lbs) (min) (cc) 0 - 0 = 231 psi 0.005 0 1 3 0 010 0 0'005 216 O 0.015 310 0.5 0.010 216 0 0.020 320 2 0.015 231 0.5 0 025 338 6 0.020 234 6.5 ’ 0.030 332 13.5 0.035 333 23.5 0.040 332 35 0.045 333 48 0.050 333 61.5 0.055 336 75 0.060 336 84 0.065 340 102 0.070 340 115 0.025 234 25 0.030 234 68 0.035 234 120 0.040 234 167 0.045 234 221 0.050 234 273 0.055 234 337 0.0564 234 354 o - 0 = 330 psi 1 3 0.075 340.5 128 0.0564 329 354 0.080 340.5 141 0.060 329 357 0.085 342 153 0.065 330 371 0.090 344 165 0.070 330 385 0.095 344 176 0.075 331 400 0.100 344 187 0.080 331 415 0.105 345 197 0.085 331 430 0.110 345 207 0.090 332 445 0.115 345 217 0.095 332 460 0.120 345 226 0.100 332 473 0.125 336 234 0.105 333 487 0.1254 336 0.110 334 500 0.1140 Load removed 0.115 334 513 0.120 334 525 0.125 334 538 0.1140 Load removed *Data listed includes the total observed deformation: system errors consist of elastic error (0.0008 in/100 lbs load) and unpredictable seating error (see Chapter IV). Note: T = test temperature,Yi = ice density, 01 - 02 = axial stress difference, 0 = confining pressure (0 unless otherwise noted), AV = sample volume change. 132 Table A—2. (Continued). Test 29. Ice T = -12.05°C Yi = 0.908 gm/cc 01 - 03 = 248 psi Defl. Load Time A\I (in.) (lbs) (min) (cc) 0.005 0 0.010 256 3 -0.002 0.015 257 19 +0.002 0.020 253 45.5 +0.012 0.025 253 80 +0.010 0.030 253 119.5 +0.013 0.035 253 161.5 +0.017 0.040 255 205.5 +0.031 0.045 257 248.5 +0.035 0.050 257 290 +0.029 0.055 258 335 +0.023 0.060 256 378 +0.027 0.065 256 420 +0.019 0.070 257 461 +0.015 0.075 258 501 +0.008 0.080 260 539.5 +0.002 0.085 260 576 +0.006 0.090 263 611 0.000 0.095 263 647 -0.006 0.0880 Load removed Test 30. Ice T = -12005°C Yi = 0.909 gm/cc 01 - 03 = 317 psi Defl. Load Time AV (in.) (lbs) (min) (cc) 0.005 0 0.010 321 0 0.015 321 4.5 -0.018 0.020 323 13 -0.014 0.025 325 24.5 -0.020 133 .030 .035 .040 .045 .050 .055 .060 .065 .070 .075 .080 .085 .090 .095 .100 .105 .110 .115 .120 .125 .130 .135 .140 .145 .150 .155 .160 .165 .170 .175 .180 .185 .190 .195 .200 .186 OOOOOOOOOOOOOCOOOOOOOOOOOOOOOOOOOOOO Test . *3 ll .< II o I 325 37.5 325 53 327 69 327 86.5 328 103 328 119 330 135 331 151 332 166 332 181 333 194 334 207 334 219 335 230 336 241 337 251 337 260 337 268 337 277 340 284 342 291 344 298 344 304 345 310 345 316 346 321 346 326 347 331 347 336 348 340 348 344 349 348 350 351 350 354 351 357 2 Load removed 31 Ice -4.45°C 0.907 gm/cc 03 = 248 psi -0.016 -0.025 -0.033 -0.035 -0.039 -0.046 -0.045 -0.049 -0.050 -0.053 -0.058 -0.054 -0.066 -0.068 -0.068 -0.064 -0.072 -0.072 -0.080 -0.077 -0.073 -0.071 -0.071 -0.071 -0.067 -0.071 -0.071 -0.067 -0.064 -0.062 -0.066 -0.062 -0.058 -0.049 Table A-2. Test 31. Defl. Load (in.) (lbs) 0.005 0.010 253 0.015 253 0.020 253 0.025 254 0.030 254 0.035 254 0.040 255 0.045 256 0.050 256 0.055 257 0.060 258 0.065 258 0.070 259 0.075 259 0.080 259 0.085 261 0.090 261 0.095 262 0.100 262 0.105 263 0.110 263 0.115 264 0.120 264 0.125 265 0.1180 Test 33. Load removed C1 material Time (min) 83 90.5 97 103.5 109.5 114.5 120 124.5 129.5 134 138.5 142 145 149 59.4% sand T = -12.06°C yi = 0.906 gm/cc Cl " c3 = 705 p51 Defl Load Time (in.) (lbs) (min) 0.005 0 0.010 0 0.015 0 0.020 721 11 (Continued). (Continued). AV (CC) -0.008 —0.004 —0.010 -0.009 -0.003 +0.001 -0.005 +0.009 -0.002 -0.003 -0.009 -0.005 -0.011 +0.034 +0.038 +0.034 +0.028 +0.030 +0.030 by volume AV (cc) -0.044 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060 0.065 0.0685 0.0540 Test 34. 721 721 722 725 727 728 729 732 735 735 Load C1 material 30 55 87 126 171 222 282 342 415 removed T = —4.65°C yi = 0.900 gm/cc 01 - 03 = 710 psi Defl. Load Time (in.)- (lbs) (min) 0.005 0 0.010 0 0.015 0 0.020 1.5 0.025 715 3 0.030 4.5 0.035 6.5 0.040 720 8.5 0.045 725 10.5 0.050 726 12.5 0.055 727 15 0.060 733 17 0.065 734 19.5 0.070 736 21.5 0.075 738 23.5 0.080 739 25.5 0.085 740 27.5 0.090 740 29.5 0.095 748 31.5 0.100 749 33 0.105 750 34.5 0.110 751 36 0.115 752 37 0.120 753 38.5 -0.041 -0.041 -0.032 -0.028 -0.014 0.000 +0.013 +0.046 59.8% sand by volume AV (CC) +0.061 +0.129 +0.326 135 Table A-2. (Continued). Test 34. (Continued). 0.145 761 70 ‘ "" 0.150 762 76 0.125 755 39.5 0.155 764 83 0.130 755 0.160 766 90 0.1304 755 0.165 768 97.5 0.1113 Load removed 0.170 770 105 0.175 771 113, 0.180 772 121.5 Test 35. 57.9% sand by volume 0.185 774 130 """”’ 0.190 778 138 F material 0.195 780 145.5 0.200 784 154.5 T = -7.61°C 0.205 787 163 0.210 789 172 yi = 0.868 gm/cc 0.215 790 180 0.220 791 189 01 — 63 = 735 psi 0.225 792 196 0.230 793 205 Defl. Load ‘Time AV 0'235 795 213 (in ) (lbs) (min) (cc) 0'240 797 221 ' 0.245 797 230 0.250 798 237 8'323 8 0.255 800 244.5 0°015 0 0.260 803 253 0°020 0 0.265 805 260 ' 0.270 808 268 0.025 0.5 0.275 810 275 0.030 717 1 0.280 812 283 0.035 719 2 0 2610 L d d 0.040 725 2.5 ' °a rem°Ve 0.045 727 3.5 0.050 730 4.5 0.055 731 6 EEEE—ié' Ice 0.060 732 7 _ 0.065 733 8.5 T ‘ ‘7'6°°C 0.070 735 10 _ 0.075 736 12 Yi ’ °°909 9m/CC 0.080 740 14.5 _ = 249 31 0.085 740 17 “1 03 p 0'090 743 19.5 Defl. Load Time A\/ 0.095 745 22.5 . . 0.100 747 25.5 (1n" (lbs) (m1n’ (CC) 0.105 749 29 0.005 0 °‘110 75° 33'5 0.010 250 2 -0.022 0.115 752 37 0.015 252 9 -0.018 0.120 752 42 0.020 254 20.5 -0.024 0.125 753 47 0.025 254 35 -0.020 0.130 754 52 0.030 256 54 -0.026 0.135 756 58 0.140 759 63.5 0.035 257 74 -0.023 0.040 258 95 -0.023 136 Table A-2. (Continued). Test 36. (Continued). Defl. Load Time AV (in.) (lbs) (min) (cc) 0.045 258 117 -0.025 0.050 258 138 -0.021 0.005 0 0.055 258 158 0.010 0 0.060 258 178 0.015 0.5 0.065 258 198 0.020 498 1.5 0.070 258 215 '0.025 0.025 501 4 —0.010 0.075 260 232 0.030 501 6.5 -0.012 0.080 260 252 0.035 501 9.5 0.085 260 264 0.040 502 14 -0.004 0.090 262 277 -0.030 0.045 504 19 +0.005 0.095 263 291 0.050 505 28 0.100 263 303 0.055 507 35 +0.018 0.0925 Load removed 0.060 508 45 +0.027 0.065 509 59 +0.031 0.070 510 71 +0.050 Test 37. Ice 0.075 511 94 0.080 512 116 +0.082 T = -7.55°C 0.085 513 144 0.115 517 290 yi = 0.907 gm/cc 0.1420 520 600 0.1840 525 1200 01 - 03 = 99 psi 0.1740 Load removed Defl. Load Time AV (in.) (lbs) (min) (cc) Test 55. 56.9% sand by volume 0.004 0 F material 0.0074 101 5 0.0080 101 10 T = -7.55°C 0.0087 101 20 0.0098 101 42 y. = 0.889 gm/cc 0.0167 103 420 1 0.0255 103 1290 01 03 = 380 psi 0.0305 104 1740 , 0.0330 105 2040 Defl. Load Time AV 0.0410 105 2800 (in.) (lbs) (min) (cc) 0.0383 Load removed 0.005 0 0.010 0 Test 54. 58.6% sand by volume 0.015 378 3.5 0.020 379 9 F material 0.025 380 16 0.030 380 25 T = -7.50°C 0.035 381 36.5 0.040 383 50.5 yi = 0.878 gm/cc 0.045 384 77 0.050 385 87 01 - 03 = 504 psi 0.055 386 109.5 137 Table A—2. (Continued). Test 55. (Continued). 0.060 387 136 0.065 388 166 0.0880 390 365 0.1042 393 537 0.1407 394 1480 0.1320 Load removed Test C2—SZ. (Data after Dillon, in preparation) Sault Ste. Marie Clay Degree saturation = 96% Unfrozen water content = 12% -150 4°C 6 ll 0.776 gm/cc .< II o - 03 = 705 psi Sample size = 3.05 in. long 1.39 in. diameter Defl. Load Time (in.) (lbs) (min) 0.0709 932 25 0.0827 936 30 0.0904 938 35 0.0974 940 40 0.1035 944 45 0.1194 950 60 0.1437 961 90 0.1637 967 120 0.1816 972 150 0.1987 978 180 0.2127 980 210 0.2274 983 240 0.3857 1020 750 0.3963 1020 780 Table A-3. Elastic modulus test data* Test 32. Ice T = -12.03°C Yi = 0.909 gm/cc Defl. Load Time E Plastic strain (in.) (lbs) (min) (psi) (in/in) 0.0206 317 70 '6 0.0176 0 70 1.51 x 10 0.0078 0.0414 354 135 5 0.0366 0 135 3.83 X 10 0.0162 0.0616 375 195 5 0.0548 0 195 2.08 X 10 0.0243 Test 50. 54.6% sand by volume F material T = -7.50°C yi= 0.872 gm/cc Defl. Load Time E Plastic strain (in.) (lbs) (min) (psi) (in/in) 0.0250 405 24 5* 0.0161 0 24 1.62 X 10 0.0071 0.0350 475 32 5 0.0257 0 32 1.96 X 10 0.0114 0.0450 525 44 5 0.0343 0 44 1.74 X 10 0.0153 *Data listed includes the total observed deflection: system errors consist of elastic error (0.0008 in/100 lbs load) and unpredictable seating error (see Chapter IV). Note: T = test temperature, Y1 = ice density, E = Young's modulus. 138 139 Table A-3. (Continued). Test 50. (Continued). 0.0602 606 51 5 0.0482 0 51 2.00 X 10 0.0216 0.0702 615 58 5 0.0580 0 58 1.48 X 10 0.0259 0.0851 669 65 5 0.0717 0 65 1.84 X 10 0.0322 0.1102 750 75 5 0.0944 0 75 1.64 X 10 0.0428 0.1352 768 85 5 0.1191 0 85 1.63 X 10 0.0533 0.1704 853 98 5 0.1520 0 98 1.12 X 10 0.0697 Test 52. 59.3% sand by volume C2 material T = —11.40°C yi = 0.910 gm/cc Defl. Load Time E Plastic strain (in.) (lbs) (min) (psi) (in/in) 0.0100 597 16 6 0.0047 0 16 2.54 X 10 0.0021 0.0258 877 45 6 0.0171 0 45 1.12 X 10 0.0076 0.0450 1063 79 5 0.0326 0 79 5.90 X 10 0.0145