m mm m l nu mm fl" MI :21: fig um um nu u; u 3 1293 320 y: 211% ABSTRACT MECHANICAL PROPERTIES OF SAND-ICE MATERIALS BY Bernard D. Alkire Experimental shear strength and creep data obtained for confining pressures up to 1000 psi are presented for sand-ice materials. To investigate factors that affect the strength of the material, constant axial strain rate tests were conducted on samples with various void ratios, strain rates, and ice contents. Uniaxial, confined and step-stress creep tests were conducted to determine the effect of confining pressure on sand-ice materials and to develop an expression that would be descriptive of the creep behavior for confining pressures up to 1000 psi. The granular part of the samples consisted of Ottawa sand sized between the number 20 (0.84mm) and 30 (0.59mm) U. S. Standard sieve sizes. The ice was pre- pared from deaired, deionized and distilled water with sample ice contents ranging from 33 to 100 percent of the sand void volume. Samples prepared in a split aluminum mold were 1.13 inches in diameter by 2.26 inches in height. All tests were conducted in a high pressure Bernard D. Alkire triaxial cell with temperature controlled by submersion in a low-temperature bath maintained very close to -12.0° C. The constant strain rate teSts showed that high confining pressure causes a distinctive stress—strain curve. This curve has an initial linear portion, up to approximately two percent strain, followed by a near linear increase in stress up to failure of the sample. Strains at failure increased with confining pressure and were six to seven percent for samples tested with 700 psi confining pressure. Results from the constant axial strain rate tests are presented in terms of the Mohr-Coulomb theory where the factors that affect the frictional and cohesive components of strength are identified. It is shown that the cohesive component of strength is due to the response of the ice matrix to test conditions. The cohesion is dependent on strain rate and ice content for constant temperature. The frictional component is shown to be dependent on the void ratio and the confining pressure. It is shown that the frictional behavior of the sand-ice material is very similar to the frictional characteris- tics of unfrozen sand tested at high confining pressure. Uniaxial creep tests conducted at various levels of constant axial stress were used to obtain the general creep behavior of the sand—ice materials. With these Bernard D. Alkire tests as a basis for comparison, the effects of confining pressure were determined from step-stress and confined triaxial creep tests. The results show that increases in the confining pressure reduce the strain rate. An expres- sion for calculating the strain rate as a function of deviator stress and confining pressure was developed. This expression indicates that creep decreases exponen- tially with increasing confining pressure. Confining pressure below 200 psi has the greatest effect on the strain rate, and two regions of definition are necessary to totally describe the effects of confining pressures up to 1000 psi. Results from the creep tests with reduced ice content samples are used to show the influence of rela- tive ice content by a term called the percent of maximum deviator stress. The term,regardless of ice content: is defined as the applied creep deviator stress divided by a peak deviator stress. The peak deviator stress is obtained from a constant axial strain rate test conducted at a confining pressure equal to the confining pressure used in the creep test. All creep tests performed at the same percent of maximum deviator stress produced the same strain rates. Using this fact the equation developed for high ice content samples may be used for the reduced ice content if the deviator stress is modified to include the effect of ice content. MECHANICAL PROPERTIES OF SAND-ICE MATERIALS BY .3 '5 Bernard D. Alkire A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Civil Engineering 1972 (333 ACKNOWLEDGMENTS The writer wishes to express his appreciation to his major professor, Dr. 0. B. Andersland, Professor of Civil Engineering, for his guidance, assistance and numerous helpful suggestions during the preparation of this thesis. Thanks also to the members of the writer's doctoral committee: Dr. R. R. Goughnour, Professor of Civil Engineering; Dr. W. A. Bradley, Professor of Metallergy, Mechanics, and Material Science; and to Dr. C. C. Ganser, Professor of Mathematics. The writer also owes his appreciation to: Mr. Leo Szafranski of the Division of Engineering Research Machine Shop for his help in modifying and setting up the experimental equipment; Dr. S. S. Kuo for his assistance in the laboratory; and to my wife, Pat, for her help and encouragement. Thanks are also due to the National Science Foundation and the Division of Engineering Research for their financial assistance which made this research possible. ii TABLE OF ACKNOWLEDGMENTS . . . . LIST OF TABLES LIST OF FIGURES . . . . NOTATIONS . INTRODUCTION . . LITERATURE REVIEW . MATERIALS AND SAMPLE PREPARATION Chapter I. II. 2.1 2.2 2.3 2.4 2.5 2.6 III. IV. EQUIPMENT AND TEST PROCEDURES CONTENTS Frozen Soil Structure Freezing Process . Cohesion . Mechanical Properties Shearing Resistance . 2.5.1 Sand (Unfrozen) Sand-Ice Materials 2.5.2 Creep Behavior 2.6.1 Theory 2.6.2 4.1 Triaxial Tests 4.2 Creep Tests 4.2.1 Uniaxial 4.2.2 Step-Stress iii Application of Process Theory of the Page ii vi 10 11 13 14 15 20 23 29 32 38 42 44 44 45 Chapter V. EXPERIMENTAL RESULTS . 5.1 Constant Axial Strain Rate Tests 5.1.1 Drained Tests High Ice Content Reduced Ice Content 5.1.2 5.1.3 Creep Tests . 5.2.1 High Ice 5 2.1.1 VI. DISCUSSION OF RESULTS 6.1 VII. 7.1 7.2 BIBLIOGRAPHY APPENDIX-DATA Behavior H cnoxncnoxmcnoxw ac 1 1 1 1 l e 2 2 Shearing Resistance Creep Behavior Content Uniaxial Confined Step-Stress Ice Content Uniaxial Confined Step-Stress SUMMARY AND CONCLUSIONS iv Failure Criteria High Ice Content Reduced Ice Content tors Controlling Shear Strength 1 Frictional Component 2 Void Ratio (Density) 3 Relative Ice Content 4 Confining Pressure . 5 P l 2 Page 47 47 47 48 52 54 54 55 56 56 57 58 58 59 89 89 9O 92 95 97 99 102 104 114 154 154 156 159 164 LIST OF TABLES Page Experimental results for constant axial strain rate tests, high ice content . . . . . 60 Experimental results for constant axial strain rate tests, reduced ice content . . . . 62 Experimental results for creep tests, high ice content . . . . . . . . . . . 63 Experimental results for creep tests, reduced ice content . . . . . . . . 65 Calculated versus measured strain rates using Equation 6-17, reduced ice content . . . 123 Constant axial strain rate data . . . . . 165 Creep test data . . . . . . . . . . 186 LIST OF FIGURES Page Typical constant axial stress creep curves . . 21 Layout showing test equipment . . . . . . 41 Stress-strain and volume change curves for unfrozen Ottawa sand. . . . . . . . . 67 Drained test results on unfrozen Ottawa sand . 68 Effect of confining pressure on the stress- strain behavior of sand-ice materials . . . 69 Effect of volume of sand on strength . . . 70 Effect of volume of sand on strength for a confining pressure of 700 psi . . . . . 71 Effect of strain rate on strength for uncon- fined tests 0 O I O I O O O O O O 72 Effect of strain rate on strength for confining pressure equal to 700 psi . . . 73 Effect of confining pressure on strength for reduced ice contents . . . . . . . . 74 Stress-strain curves for high and reduced ice contents . . . . . . . . . . . . 75 Stress-strain curves for various ice contents . 76 Stress-strain curve for polycrystalline ice samples . . . . . . . . . . . . . 77 Uniaxial stress creep curves for high ice contents . . . . . . . . . . . . 78 Corrected uniaxial stress creep curves for high ice contents . . . . . . . . . 79 Constant axial load creep with constant confining pressure . . . . . . . . . 80 vi Corrected constant axial load creep with constant confining pressure . . . . . Step-stress creep for high ice content . . Uniaxial and step-stress creep for high ice content 0 O O O O O O O O O O O Uniaxial stress creep for reduced ice content Effect of ice content on uniaxial stress creep O O O O O I O O O O I O Corrected constant axial load creep with constant confining pressure and reduced ice content . . . . . . . . . . Step-stress creep for reduced ice content, D = 400 and 640 psi . . . . . . . Step-stress creep for reduced ice content, D = 750 pSi O O O O O O I O O 0 Effect of confining pressure on volume change The effect of percent sand, temperature, and strain rate on peak strength . . . . . Effect of confining pressure and void ratio on peak strength . . . . . . . . . Effect of confining pressure and void ratio on the principal stress ratio . . . . Effect of ice content on strength . . . . Reduction in strength versus confining pressure 0 O O O O O O O O 0 Typical effect of confining pressure on sand-ice . . . . . . . . . . Principal stress ratio versus confining pressure 0 O O I C O O O O C 0 Influence of confining pressure on the principal stress ratio . . . . . . . vii Page 81 82 83 84 85 86 87 88 124 125 126 127 128 129 130 131 132 Axial strain at failure for sand-ice samples Kf failure line for sand—ice (typical values) Strain rate versus strain for uniaxial stress creep tests, high ice content . . . . Strain rate versus strain for constant confining pressure test, high ice content State of stress for uniaxial and confined creep tests . . . . . . . . . . creep behavior for a deviator 400 psi, high ice content . . Step-stress stress of creep behavior for a deviator 640 psi, high ice content . . Step-stress stress of Step-stress stress of creep behavior for a deviator 750 psi, high ice content . . creep behavior for a deviator 1070 psi, high ice content . . Step-stress stress of Strain rate versus stress factor 2 . . . Effect of confining pressure on strain rate Slope value m versus confining pressure . . Slope factor K versus percent of maximum deviator stress . . . . . . . . . Uniaxial creep test for reduced ice contents Effect of various levels of ice content on uniaxial creep test behavior . . . . . Effect of confining pressure on creep of low ice content samples . . . . . . . . Step-stress creep behavior for deviator stress of 400 psi, low ice content . . . . . Step-stress creep behavior for a deviator stress of 640 psi, low ice content . . . viii Page 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 Figure Page 6-28 Step-stress creep behavior for a deviator stress of 750 psi, low ice content . . . . 151 6-29 Strain rate versus stress factor 2 for low ice content samples . . . . . . . . . 152 6-30 Slope factor K versus percent of maximum deviator stress, low ice content . . . . 153 ix AF AF 7G w NOTATIONS Area of ice, high ice content Area of sand, high ice content — Area of ice, low ice content — Area of sand, low ice content Cohesion 01-03 = Axial stress difference = Deviator stress Dilatancy component Relative density Modulus of elasticity Void ratio Shear force acting on a flow unit Free energy of activation, calories per mole Activation energy required to overcome cohesion Particle gradation Planck's constant = 6.624 x 10—27erg—sec_l Mineral type Interparticle forces Ice content Slope factor Frictional constant 16 1 Boltzmann's constant = 1.38 x 10_ erg OK- Percent of maximum deviator stress C, A, N, G = creep parameters Exponent in creep equation Flow value = 1 + Sin ¢ 1 - Sin ¢ (01+o3)/2 Particle shape Force causing shear, high ice content Force causing shear, low ice content (cl-o3)/2 Universal gas constant = 1.98 calories OK-l mole-l Time Temperature Frequency of activation, sec-l Parameter, a function of the number of flow units True axial strain, in/in True axial strain rate, min--l Arbitrary strain rate in creep Distance between equilibrium positions of flow units Stress factor = D—om Uniaxial stress Proof stress in creep equation Mean normal stress Shear stress Shear stress, high ice content Shear stress, low ice content Angle of internal friction Major principle stress Minor principle stress = confining pressure xi CHAPTER I INTRODU TION The mechanical properties of sand-ice are studied to determine the strength and creep behavior of the material. Originally the strength of frozen soils was determined as for an undrained clay, with strength being stated in terms of cohesion (Vialov, 1965a). As more elaborate testing equipment became available, and strength was determined to be time dependent (Tystovich, 1960), creep testing was used to study the nature of this time dependency and its relationship to strength. Presently, many testing techniques are used to study the mechanical prOperties of frozen soils. Tension tests (Vialov, 1965b), shear tests (Vialov, 1965b), uniaxial compression tests (Goughnour and Andersland, 1968), confined compression (Andersland and AlNouri, 1970) and constant axial stress tests (Andersland and AlNouri, 1970; Sayles, 1968) have been conducted on frozen soils. These tests have resulted in various empirical formulations that describe the time dependent mechanical properties of frozen soils. One of the most common methods used to describe the strength of frozen soil is the Mohr-Coulomb failure theory. This theory has been used by Vialov (1965b); Tystovich (1960); and Andersland and AlNouri (1970) to describe the time dependent behavior of sand-ice materials. The basic problem in this approach to shear strength is determining the interrelationship of the cohesive and frictional components of strength for given test condi- tions. Assuming that the Mohr-Coulomb theory is valid for frozen soils, a portion of this study is concerned with identifying factors that affect the frictional and cohesive components of strength. The basic factors that influence strength of sand-ice materials include tempera- ture, strain rate, ice content and the percent of sand in the system. These factors have been discussed by other investigators of sand-ice materials (Vialov, 1965b; Kaplar, 1971; Goughnour and Andersland, 1968). However, the effect of these factors when the sand—ice is subjected to high confining pressures is not known. One of the main objectives of this study is to use the results of tests conducted at high confining pressures as a means of identifying frictional and cohesive components of strength. By using triaxial testing techniques and confining pres- sures up to 1000 psi, the effects of strain rate, ice content and void ratio on the strength of sand-ice are determined. In order to eliminate the effect of temperature on the results, all constant strain rate tests were conducted at a temperature of -12.0° C. From the results of the experimental portion, the Mohr-Coulomb theory is applied for the entire range of confining pressures and an effective angle of friction is determined.. It is shown that the angle of friction is independent of ice content and is related to the angle of friction for unfrozen sands tested at high confining pressures. The second part of this study describes the effect of confining pressure on the creep of sand-ice materials. Andersland and AlNouri (1970) have indicated that the steady state creep rate can be estimated using the rate process theory. For confining pressures up to 150 psi, the steady state creep was determined to be a function of deviator stress and the mean stress. In order to verify this result and to extend the range of mean stresses used, creep tests were conducted at confining pressures up to 1000 psi. From the results of these tests an expression for creep in terms of deviator stress and confining pres— sure is developed for the entire range of confining pres- sures. A problem in determining the time dependent behavior of sand-ice is the identification of the active component of creep. By using samples with reduced ice content, it can be shown that the ice matrix is the primary agent of creep. Further, it is noted that there is a relationship between the peak deviator stress as determined in a constant strain rate test, and the creep behavior of a sand-ice sample tested at a deviator stress less than the peak value. ConStant deviator stress testing was used to obtain the creep behavior of the sand-ice material. The effect of confining pressure was obtained using step- stress testing techniques where the deviator stress is held constant and the confining pressure is increased in steps as the tests progress. These tests covered a range of confining pressures from 0 to 1000 psi. Uniaxial creep tests were conducted to obtain the general creep char— acteristics of the material and to verify the effect of confining pressure on creep. Reduced ice content samples were also tested using uniaxial and step-stress techniques. CHAPTER II LITERATURE REVIEW 2.1 Frozen Soil Structure In order to understand the shear strength and creep characteristics of a sand-ice material, it is use- ful to describe the various components that make up the system. Frozen soils, in general, can be considered to be multi-phase systems made up of an assemblage of soil particles, unfrozen pore water, polycrystalline ice and entrapped air. The relative proportions of each of these components will have substantial effects on the mechanical behavior of the material. Some of the phases are interrelated, such as the amount of unfrozen pore water and the type of soil particles. Others are directly affected by ambient conditions and testing techniques. Overall, the picture obtained is a compli- cated system responsive to numerous changes in conditions. The discussion to follow will emphasize sand-ice materials, but other types of frozen soil will be included to give a better idea of the available theories used to determine the strength characteristics of sand-ice materials. Vialov (1965b), Scott (1969) and Tsytovich (1960) have shown that variations in mechanical properties of frozen soils can be related to the amount of unfrozen pore water in the soil-ice system. There are two phases of unfrozen water in frozen soil: water vapor having a variable composition, and water that is strongly attracted to the soil particles by intermolecular forces. Water vapor is a gaseous phase found in the void spaces. At temperatures below freezing its properties remain the same until frozen. Water vapor has been found in polar ice at temperatures as low as -40.00 C (Tsytovich, 1960). Water vapor transport may contribute substantially to the formation of ice lenses in soil systems where the freezing front is isolated from the source of the water. In this process, moisture is transported by vapor diffusion from the warmer source to the colder freezing front (Jumikis, 1966). For soils that were saturated before freezing this phenomenon does not occur. The other type of unfrozen water that may be present in a frozen soil can be explained using the ”diffuse double layer" concept. According to this theory the layer of water molecules closest to the soil particles are attracted to the surface molecules and have higher energy states and different characteristics than water which is located at some distance from the particle surface. The amount of water in the bound layer that will freeze is dependent upon the interaction of the forces of crystalliza- tion and the forces of attraction to the particle surface. The forces of attraction are dependent on the mineralogical composition of the particles and will be influenced by the specific surface of the particles while the forces of ice crystallization are dependent to a large degree on the temperature. For any given temperature, the larger the specific surface area of the mineral, the larger the amount of unfrozen water. Tsytovich (1960) showed that unfrozen water was present in clays even at temperatures below -30.00 C. Anderson (1967) verifies this fact and states, It seems beyond a doubt thatixlfrozen silicate mineral- water systems, the ice crystals are separated from the substrate surface by an unfrozen fluid-like interfacial zone of water. Some of the differences in behavior between frozen sands and clays can be explained when it is known that the sands with their round large sized particles have low specific area as compared to clay particles. Because sands have low specific surface, and unfrozen water contents are directly related to these surface areas, nearly all available water in sand is frozen at temperatures slightly below 0 0.0 c (Scott, 1969). 2.2 Freezing Process Since all frozen soils are at some time unfrozen, it is necessary to understand the mechanism of freezing. Basically, freezing is a thermodynamic process. By sufficiently lowering the temperature, molecules in a higher state of energy--the liquid state—-change to molecules in a lower state of energy--the solid state. It is possible (Scott, 1969) to visualize the liquid state as consisting of aggregates of liquid molecules, which for a given temperature will have an equilibrium size that is determined by the ambient conditions. From quantum mechanics it is known that other aggregates of molecules will exist that are both larger and smaller than the equilibrium size. The larger aggregates will grow to form 'nuclei' of solidification. The formation of ice crystals depends upon the existence of these nuclei in the water as distinct starting points for crystallization of ice (Jumikis, 1966). The actual temperature at which crystallization will take place is a function of the grain size. When a soil freezes, the soil structure may be considerably altered by the formation of ice lenses. In addition, the soil may be consolidated by the development of negative pore pressures developed below or adjacent to the ice/water interface. The degree of this alteration depends primarily on the mineralogical composition of the soil, grain size, freezing history and saturation. For large grained sand or gravel the soil structure is unaltered (Vialov, 1965b) as freezing occurs with void spaces being filled with randomly oriented crystals of ice. It was noted that the unfrozen water may have two different phases: water vapor and water attached to or adsorbed on the soil particles. For sand-ice materials these types of water are not present in any great amount. At temperatures slightly below 00 C all water freezes directly in the pore spaces forming a massive structure (Vialov, 1965b) with little sensitivity to freezing history (Scott, 1969; Sayles, 1968). Another factor in the freezing of a soil is the change in volume of water as freezing takes place. This factor may have considerable importance in the laboratory if samples of constant void ratio are to be prepared. The amount of soil volume increase (frost heave) is dependent upon the amount of water available and the grain size of the material. When water freezes there is an increase in volume of approximately nine percent. The change in volume may or may not affect the soil structure depending on the drainage conditions. Tsytovich (1960), states that under the conditions of free drainage, no changes in soil volume for sand will occur because the excess water resulting from freezing will be squeezed out. This will not be the case for fine grained soils since their low permeability will inhibit drainage of the excess 10 water resulting in expansion of the soil system as volume change occurs during freezing. 2.3 Cohesion (Unfrozen sand has no unconfined shear strength. When sand is saturated and frozen, there will be a substantial unconfined strength. The increase in strength due to the confinement of the ice matrix is called cohesion. In general, cohesion may result from three causes (Vialov, 1965b): (1) intermolecular cohesion due to forces of attraction between particles, (2) structural cohesion resulting from the process of formation and (3) cohesion due to confinement of the ice matrix (ice cementation). Depending on the type of soil, any or all of these com— ponents may be present. For sand-ice materials it is reasonable to assume that the first two components of cohesion are negligible and consider only the cohesion due to confinement of the ice matrix. Cohesion due to the ice matrix is very responsive to temperature change and is a function of time, moisture content, plastic strain, load, and strain energy. One theory used to explain cohesion is based on variations and move- ment of unfrozen water in the soil-ice structure (Scott, 1969; Vialov, 1965a; Tsytovich, 1960). This theory states that upon application of some stress, high pressures are caused near the points of contact of the grains, resulting 11 in the melting of the ice in these regions. The melted ice flows to zones of lower stress where it refreezes. On the macro-scale this may be considered a weakening process followed by a strengthening process. Goughnour (1967), used this basic idea to explain creep characteristics of ice and identified the weakening and strengthening mechanisms. Vialov (1965a), using rigid ball penetration test techniques, has obtained extensive data for the cohesion of frozen soils. His basic observations are: (l) sandy soils have small rheological response compared to clays; (2) cohesive properties increase up to some maximum as ice content increases; (3) temperature changes are one of the main causes of variations in the cohesive component in frozen soils; and (4) long term cohesion may be significantly less than the instantaneous cohesion (three to nine times). Vialov's tests are the most extensive long term investiga- tions available into the cohesive properties of soils. However, the resulting mathematical formulations may be in question due to the testing technique (Scott, 1969). 2.4 Mechanical Properties of Ice The properties of the pore ice may affect the mechanical behavior of frozen soil. It is know that the direction of the applied loads in relation to the direction of the ice crystal's axis has a definite effect on the i-. r “m, 12 mechanical behavior of the ice (Gold, 1963). However, it is generally assumed that when ice freezes in the pore spaces of a soil-ice material, a polycrystalline structure is formed and there exists no oriented planes of weakness (Goughnour, 1967). It is for this reason that the dis- cussion of the mechanical properties of ice, as they affect sand-ice systems, is limited to polycrystalline ice. In addition to the orientation of the crystals, the mechanical properties of ice are affected by a substantial number of variables. Among the most important of these are strain rate and temperature. Leonards and Andersland (1960) have shown that unconfined compressive strength increases approximately 15 psi per degree centigrade from 370 psi at -40 C. Their tests were conducted at a strain rate of 2 x 10_2min-l; and results showed considerable scatter due to the random nature of the freezing process. The strain rate also affects the strength of polycrystalline ice. Halbrook (1963) noted both an increase in Young's modulus and ultimate strength with an increase in rate of strain. However, Sanger (1971) in his review of available test results, indicates a decrease in strength of fresh water ice with an increase in strain rate. Concerning the creep of polycrystalline ice, Gold (1963) noted that slip takes place only along basal planes and the deformation mechanism must be described in ways 13 which ice grains respond to this constraint. (Gold (1963) has identified seven mechanisms which may take part in the response to applied loads. In the central part of the ice grains, slip bands and kink bands develop to conform to imposed deformations. However, for the grain boundary regions; boundary migration, crack formation, and distortion of the boundaries may take place as the grains respond to the applied loads. As a final response, recrystallization may take place, which is usually an indication of tertiary creep. The rate of loads application has a definite effect on which mechanisms predominate. For high loading rates, accommodation cracking and grain boundary migration are the controlling mechanisms. 2.5 Shearing Resistance The shear resistance of sand-ice materials is dependent (n1 a complex interaction of the ice matrix and the granular portion of the system. The Mohr-Coulomb theory is most frequently used to describe the shear strength of soils. It is a summation of the cohesive component and a frictional component. The cohesive component of frozen soils was discussed in section 2.3. The frictional component is best understood by examining the frictional characteristics of unfrozen sands. 14 2.5.1 Sand (Unfrozen) I In a sand-ice system it is apparent that for some conditions the frictional characteristics of the sand will contribute to the shear strength of the sand-ice material. The frictional properties of sands are well known and have been the subject of many articles. A good basic discussion of the many factors that affect the frictional behavior of single mineral sand was prepared by Koerner (1970). More important in relation to frozen sand is the frictional behavior of sand at high confining pressure. Several investigators have considered this problem (Hirschfeld and Poulous, 1963; Hall and Gordon, 1963; Vesic and Clough, 1968; Lee and Seed, 1967). The basic conclusions from their work that may be applied to sand-ice materials are: 1. Shearing resistance is made up of three components; sliding friction, dilatancy, and particle crushing and rearranging. 2. The dilatancy component of strength becomes small at high confining pressures. 3. The angle of friction decreases as confining pressure increases. 4. The strain at failure increases with increased confining pressure. 5. At high confining pressure sands exhibit a plastic stress-strain relationship. 15 2.5.2 Sand—Ice Materials Shear strength of soil has traditionally been determined by the Coulomb equation which divides the shear strength into a frictional and cohesive component. The equation, I = c + on tan o (2-1) may be used for soil-ice materials if the coefficients are adequately descriptive of the behavior of the frozen soil system. It is known that shear strength in frozen soils is time dependent (Vialov, 1965a) making it necessary to include the time factor in the defining equation. Considering the Coulomb equation term by term, the frictional cOmponent may be expressed as: H II 0 tan ¢ = O K n f n f and (2—2) Kf = f(o3,I,e,€,PS,g,H) where 03 = confining pressure I = interparticle attractive or repulsive forces e = void ratio é = strain rate PS = particle shape 9 = particle gradation H = mineral type 16 It is usually assumed that the interparticle forces are insignificant for sand, and for a given type of sand the particle shape, gradation and mineral type can be held constant. Then for a given soil: 1 = f(03,e,é) (2—3) f The strain rate dependency is small for granular soils and for tests of short duration may be considered constant (Whitman, 1957). Thus, the functional relationship is usually interpreted as being related to initial void ratio and the applied confining pressure. Then, Kf = f(o3,e) = tan ¢ where tan ¢ may be defined at failure or at intermediate points along the stress path (Schmertmann and Osterberg, 1960). The cohesive component in equation 2-1 representing a frozen soil is a function of three components (Vialov, 1965a). For sand-ice materials the interparticle and structural cohesion are negligible in magnitude and it is the confinement due to the ice matrix which controls cohesion. The component of shear strength contributed by the ice may be defined as: ci = f(e,T,e,j,t) (2-4) where e = strain strain rate M II E! II temperature 17 ice content u. ll time d- II The composite soil shear strength is: T = c. + c K (2-5) n Although the equation indicates a summation, it is possible that ci and Kf do not reach their maximum at the same time. In fact, experimental evidence for clays (Schmertmann and Osterberg, 1960) indicates they do not. Further, if the cohesive component due to the ice is time dependent, eventually reducing to zero, then the shear strength will be a purely frictional phenomenon. It is doubtful that this is ever completely true; however, the contribution to shear strength due to the ice may approach a constant as this component is fully mobilized. Other attempts have been made at defining the shear strength of frozen soils using the Mohr-Coulomb failure theory (Tsytovich, 1960; Vialov, 1965b). However, the fact that the strength of frozen soils is time dependent requires the modification of the usual form of equations to include the time factor. Tsytovich (1960) indicated that the shear strength of frozen soil is a function of at least three factors: I = f(T,o3,t> <2—6) 18 T = temperature of the soil below freezing c3 = confining pressure time of action of the load Thus, the shear strength for frozen soils can be determined by the equation I = cT + P tan ¢T (2-7) where both cT and ¢T are functions of temperature and time. For a given time and stress the angle of friction increases as the temperature increases until at 00 C the value is equal to the value for unfrozen soils. The above relation- ship does not necessarily hold for all types of soils. Vialov (1965b) showed that the frictional component tan ¢T’ is not time dependent for frozen sands, sandy loams and dense clays. Other tests from the same study showed that for sands, the angle of friction at failure was constant for times to failure of 1 to 24 hours. The difference in the time factor, as it affects the friction term for various types of soil makes it very difficult to eXpress the strength characteristics of clays and sands with one all inclusive equation. Andersland and AlNouri (1970) have also used the Coulomb expression to evaluate the time dependent strength characteristics of frozen sands. They obtained a constant value of C and tan ¢ when the factors affecting the cohesive component were held constant. Intflmfllistudy the 19 cohesion and angle of friction were determined from both constant strain rate and differential creep tests. Another approach to the determination of the shear strength of sand—ice is to relate thestrength of the sand-ice material to the strength of ice by a stress factor (Goughnour and Andersland, 1968). In this procedure the strength of a sand-ice material is obtained by multiplying the strength of ice at various strains by a stress factor. The stress factor is the ratio of sandfice strength to the strength of ice obtained from samples tested at similar conditions. For this type of presentation it was noted that for strains less than approximately two percent, the stress factor is constant. Above this amount the stress factor is no longer constant, but increases in a linear manner up to a maximum value. After the peak strength of the sand-ice is reached the stress factor is again constant. Using the results from stress factor versus strain graphs, Goughnour (1967), identified the three stages of strengthen- ing in a sand-ice system as follows: 1. The initial strengthening occurs at low values of strain where the characteristics of the ice predominate. In this stage the strength of sand-ice materials is a linear function of the strength of ice. 20 2. The second stage occurs where solid to solid contact becomes apparent. This effect may be mobilized throughout deformation when the volume of sand is greater than 42 percent. 3. The third stage, related to dilatancy of the sand occurs as the particles act against the confinement of the ice matrix. 2.6 Creep Behavior Since the strength of frozen soils has a strong time dependence, it is necessary to understand the rheologic behavior of the soil-ice system. One of the manifestations of the rheological characteristics of soil-ice is creep. It has been demonstrated by several investigators (Vialov, 1965b; Sayles, 1968; Goughnour and Andersland, 1968) that soil-ice systems when subject to constant stress will develop what is considered to be a "classic" creep curve. Figure 2-1 shows this curve as a strain-time relationship for damped and undamped creep. Damped creep is defined as creep in which the strain approaches a limit as time increases. It is characterized by an instantaneous elastic strain and a region of decreasing strain rate approaching a constant strain. The undamped creep does not approach a constant strain and is typically divided into four sections: (1) instantaneous elastic strain resulting 21 .mm>nso mmwuo mmomum Hmwxw ucmumcoo HMUHmmBII.HIN wusmwm u .msee mwwuu pmmEmo aw m>uso mum>oomm >um>ooom owummHm commaoa mumbooom oflumMHm muomcmucmumCH ousuomnm o .ll counmum it counmmm aumfiuuwa xumpcoowm mmmnu pmmEmpcD i““"““ ... cowmom humaflum ,urezas ornsetz SHO auequ'en SUI 3 ’urexns {erxv 22 from the application of the load, (2) primary creep with a decreasing rate of strain, (3) a secondary region of constant or minimum strain rate and (4) the tertiary region in which strain rates increase to failure. Vialov (1965b), identifies these regions in terms of deformation processes. The region of instantaneous deformation is termed elasto— plastic since not all of the deformation is recoverable. The primary region is the region of plastic deformation if irreversible deformation takes place. The secondary region is termed plastic-viscous since the constant deformation with time is comparable to the flow of a viscous fluid. Finally, the tertiary region is the region of progressive flow leading to a viscous failure. The division between damped and undamped creep is somewhat arbitrary since what at first glance is considered to be damped creep could be the secondary region of creep leading to failure if long term readings were obtained. It has been suggested (Scott, 1969) that the maximum load that can be applied and still produce damped creep is related to the unfrozen strength of the soil system. Any load which exceeds the ultimate strength of the soil structure alone will eventually lead to a creep failure. If the undamped sample had been unloaded during the test a recovery curve similar to the one shown in Figure 2-1 would have resulted. Recovery is broken into two sections: 23 the instantaneous elastic recovery and the delayed elastic recovery. Not all of the strain that accumulated up to the time of removal of the load will be recovered, and most of the deformation remains permanently (Scott, 1969). 2.6.1 Theory Various methods have been used to describe the behavior of a material as it deforms under a constant load. The most common methods include power law relation— ships, hyperbolic relationships and the hereditary creep theory as prOposed by Vialov (1965a). The hereditary creep theory is based on the assumption that the deformation at any time depends not only on the level of stress applied, but also on the history of prior deformations (Vialov, 1965b). The theory is straight forward mathematically and reduces to an equation for strain as a function of time as follows: €(t) = EECCL + [K(t—t0)o(tO)At] (2-8) 0 where the various components may be identified. The first 0(t) E I 0 which takes place after the application of the load 0(t) term on the right, is the instantaneous deformation at the present time t. E0 is the instantaneous modulus of elasticity. The second term is the result of previous loading and is the history dependent term. K(t-t0) is a relaxation term, where K is a coefficient and (t—to) is the 24 time of relaxation. 0(t0) is the previous load applied to the system at time t0 and At is the duration of the previous loads. Using this equation and the principle of superposition, all possible loading histories may be considered. In this equation the temperature dependency appears in the evaluation of the coefficient K and has a very strong influence on the developed strains. The hereditary creep theory has been used extensively by various Russian investigators to describe the rheological prOperties of both frozen and unfrozen soils (Vialov, 1965b). The most recent theory to be used extensively to explain the creep characteristics of frozen soil is the rate process theory. This theory, as proposed by Gladstone, Laidler, and Eyring (1941), has its basis in statistical and quantum mechanics, and its application has been discussed by a number of investigators (Abdel-Hady, 1964; Dillon and Andersland, 1967; Mitchell, 1964) for various types of materials. The rate process theory treats creep as a thermally activated process in Which flow units of atoms, molecules or groups of molecules move across an energy barrier from one equilibrium position to another. The movement across the energy barrier is determined on a statistical basis and requires a flow unit to obtain sufficient energy AF, 25 termed the free energy of activation to surmount the barrier. For equilibrium conditions the movement is entirely random and the flow units cross the energy barrier equally in all directions resulting in no net flow of the material. If a directed potential is applied to the system, such as an axial stress, then the energy barrier becomes distorted in the direction of the applied potential and more flow units have sufficient energy to move in the direction of the potential than in the direction opposing the potential. The result is a net flow in the direction of the applied potential. Expressed in mathematical terms; the division of thermal energy among flow units is given by the Boltzmann distribution (Mitchell, 1964) and the frequency of activation V may be expressed as: kT v = 3— exp [-AF/RT] (2-9) where k = Boltzmann's constant (1.38 x 10-16 erg OK-l) T = absolute temperature, degrees Kelvin h = Planck' constant (6.624 x 10-27 erg-sec-l) R = universal gas constant (1.98 caloK-l mole-l) AF = free energy of activation, Cal/mole With application of the directed potential the energy barrier becomes distorted by an amount qu where f is the 26 applied potential and A. is the distance between equilibrium positions. The result is that the energy barrier has a height of (AF + £%) in the direction opposing the potential and (AF - £9) in the direction of the potential. Sub- stituting these values into equation 2-9 and subtracting: results in an expression for the net increase in frequency of movement in the direction of the applied potential. If both sides of the expression are then multiplied by a parameter X, a function of the number of flow units, an eXpression for strain rate is obtained as: 2XkT h é = epr-AF/RT] sinh [fl/ZkT] (2-10) If the applied stress is large enough, the expression reduces to é = ——— eXp [-AF/RT] exp [fl/ZkT] (2-11) This is the form of the equation that is most frequently used in describing creep. Using equation 2-11, some insight into factors that affect the frictional component of a sand—ice material can be shown. Mitchell (1964) proposed that AF = AFO + P(¢+Da) (2-12) in which AFo is the activation energy required to overcome the cohesive component of strength and P is the interparticle 27 component of activation energy composed of a frictional part o and a dilatancy part Da' Then, substituting into equation 2-11 -AFO-P(¢+Da) kT ] exp [-34% (2—13) E = ——— exp [ If logarithms of both sides are taken, the result is int = in ——— - ———-- ——————— +-——— (2-14) The shear force f is equal to the applied stress difference (cl-03) divided by a structural factor 8, and solving for the stress difference: (01-03) = constant + constant + constant + P (¢+Da) (2-15) This equation separates the deviator stress into various components and can be used to study the factors that affect these components. For example, the frictional component is shown to be independent of both temperature and strain rate. In addition, the equation can be related to the Mohr-Coulomb equation if it is assumed that the test results were obtained at constant strain rate, temperature and structure. ‘This result is particularly interesting since constant strain rate tests can be used to define an effective angle of friction that is independent of the ice properties. 28 Ladanyi (1972) has discussed the creep character- istics of frozen soils using a power law relationship. In this discussion of creep behavior the steady state strain rate is determined to be some power of the applied uniaxial stress. n _ O ._ _ e — ECEEZTTT] T — Constant (2 16) In this equation, éc is a small normalizing strain rate, oC(T) is the uniaxial stress that causes éc’ and n is an experimentally determined power. Using the basic power law formulation in equation 2-16, it is possible to obtain a relationship between the strain rate equation and the constant strain rate test results predicted by the Mohr-Coulomb equation. Starting with the expression: T = C(t,T) + 0 tan ¢ (2-17) the equation can be rewritten in terms of the maximum stress difference as: (cl-o3)f = ofu(t,T) +_03(NC—l) (2—18) where (cl-o3)f = deviator stress at failure Ofu = unconfined compressive strength at time t and temperature T N = flow value = (1+sin ¢)/(1-sin ¢> 29 solving equation 2-16 in terms of the unconfined strength and substituting into equation 2-18 results in an expression for the deviator stress in terms of the confining pressure. -c l/n 01-03 = ocu0[§;] f(T)+o3(NC-l) (2-19) where Ocuo = unconfined compression strength for temperatures near 00 C. EC = constant strain rate of the test .c = normalizing strain rate f(T) = temperature term This equation shows the shear strength as being dependent upon a cohesive term and a frictional term. The frictional term is dependent only on the angle of friction of the material and the confining pressures. It is interesting to note that both the power law relationships and the rate process equations can be reduced to the form of the Mohr-Coulomb equation. In this form both contain a frictional component that is independent of strain rate and temperature. 2.6.2 Application of the Rate Process Theory The most extensive investigation into the creep behavior of sand-ice using ideas from the rate process theory was reported by Andersland and AlNouri (1970). In determining the effect of mean stress, the logarithm of 30. the secondary creep rate was plotted against a stress factor X which is a function of the deviator stress and the mean stress. The resulting curve was linear and could be expressed as: é = b exp (m2) (2-20) where b and m are experimentally determined parameters. The b term was found to be an exponential function of the deviator stress and the resulting equation took the form: é = C exp (ND) exp (-m cm) (2-21) where C and N are constants, D is equal to the deviator stress and cm is equal to the mean stress. This equation is in the form of the equations from rate process theory at large stresses and indicates an exponential increase in strain rate with increasing stress difference and an exponential decrease in strain rate with increasing mean stress. In the same investigation (Andersland and AlNouri, 1970) the effect of temperature on the creep of sand-ice was determined using differential creep testing techniques and was found to be in the form 5 = A exp (1%) (2-22) 31 where A is an experimentally determined parameter that includes the effects of the applied stress. This equation predicts creep to be an exponential function of the temper- ature. Ladanyi (1972) has noted that this is not descriptive of experimental work conducted over a wide range of temperatures, and suggests that there is evidence of a near '1 1.3 linear temperature dependence for sand-ice down to -20.00 C. ;a l'.A '_ CHAPTER III MATERIALS AND SAMPLE PREPARATION To eliminate the variables caused by particle composition and gradation, standard Ottawa sand, obtained from Soiltest Incorporated, was used in all sand-ice samples. The sand was composed of uniform sub-angular quartz particles with a specific gravity of 2.65. To insure uniform gradation only particles between the number 20 (0.84mm) and 30 (0.59mm) U. S. Standard sieve sizes wenaused. A sand volume of 64 percent was selected to obtain a dense soil structure. This volume of sand was well above the critical volume of 42 percent determined by Goughnour (1968) to be the point where intergranular friction is a major factor in the develOp- ment of strength in sand-ice materials. Actual values of the percent of sand varied between 61.6 and 64.3 as noted in the test data shown in the Appendix. A sand volume of 64 percent produces a sample with a void ratio of 0.562. The ice matrix was formed from deaired, deionized, distilled water. Using techniques outlined below, poly- crystalline ice with densities of 0.918 to 0.854 gm/cm3 32 33 were obtained. The density of ice at -12.0° C is 0.91848 gm/cm3 (Pounder, 1967). The difference between the actual and the test ice densities was due to small air bubbles trapped in the sample voids as the sample was saturated. If the voids had been completely saturated with ice, an ice content of 100 percent would have been Iii obtained. Actual ice content for the high ice content samples ranges from 92.5 to 99.0 percent. Some Special tests were made with ice contents of approximately 55 and 35 percent. These tests are noted in later sections. E Sample size and sample preparation were essentially the same as that used by Goughnour (1967) and ,AlNouri (1969). The sample size, 1.13 inches in diameter by 2.26 inches in height, was selected to yield a one square inch end area and a volume of 2.26 cubic inches. Knowing the specific gravity of the sand and the percent sand by volume the correct amount of oven dried sand could be predetermined. The samples were prepared by pouring the pre— determined amount of sand into a split aluminum mold that had been lightly greased with silicone vacuum grease to reduce adhesion between the mold and the sample. The mold was filled half full of sand and tamped 25 times with a rubber hammer. The remaining portion of the sand was poured into the mold and tamped just enough to bring the level of sand to the tOp of the mold. 34 Initial tests exhibited a tendency to flare at the top of the sample. It was believed that this was caused by local variations in density near the top of the sample. To eliminate this tendency, the mold was built up 0.3 inches and the top part of the Sample was trimmed off to the correct height of 2.26 inches. This method eliminated the problem with flaring and the samples exhibited a more uniform cross section after testing. After the sand had been poured into the mold, deaired, deionized, and precooled water was added to the sample until it appeared at the top of the mold. The mold was then tapped lightly to remove air bubbles that may have been trapped in the sample. This procedure was only partially successful since all samples contained less than 100 percent ice content. The sample was then placed in a cold box maintained at ~18.0° C, and allowed to freeze for approximately 24 hours. After this period of time essentially all water was frozen and additional freezing time would not affect the strength of the sample (Sayles, 1968). Prior to mounting the sample in the triaxial cell, one sample end was trimmed with a sharpened paint scrapper to permit uniform seating with the loading cap. The sample was then removed from the mold and transferred to another cold box for future mounting on the triaxial cell's pedestal. Here, the sample was 35 weighed both in air and immersed in fuel oil having a specific gravity of 0.832. The sample weight, volume, and ice content were obtained from these measurements. To reduce end effects, friction reducers made of a sandwich of two layers of polyethelene and a greased aluminum disk were placed on each end of the sample. Next the sample was placed on top of the pedestal and capped with a lucite cap. A protective membrane was placed over the sample and fastened with rubber bands. The sample was then transferred to another cold box where it was mounted on the triaxial cell base plate. Three additional light membranes and one heavy membrane were placed over the sample. The triaxial cell's cover was placed over the sample and bolted to the base plate. The loading ram was brought into contact with the sample and the entire cell assembly was transferred to a work bench and the confining pressure gauge was attached. Finally, the cell and appurtenances were transferred to the cold bath and the cell was filled with coolant. Before testing, the triaxial cell and sample were allowed to stabilize in the cold bath for 12 hours at -12.0° C. This compli- cated mounting procedure was necessary to insure that the sample was never exposed to an environment that had any contact with the ethylene glycol coolant used in the cold bath since this could cause disintegration of the ice. This procedure took about 20 minutes and resulted ‘— 0. flu a". .Is Va.-. _ a ~——————.b W wwfi. 36 in an unusual temperature history for the samples. How- ever, the samples were exposed to temperatures greater than -10.0° C for only a few seconds, and for sand—ice materials at temperatures less than -10.0° C, history has little effect on the strength of the materials (Scott, 1969). After the sample had been tested the triaxial cell was removed from the cold bath and disassembled. The sample was inspected for membrane leaks and for indi- cations of failure planes. The sample was weighed and the final volume obtained using the procedure described above. The entire sample was placed in a drying oven and the dry weight of sand and moisture content were obtained. The sample preparation for the reduced ice content samples was the same, except a known volume of water was added to the sand instead of completely saturating the sample. The amounts of water used were 10, 8, and 4.5 ml, which resulted in ice contents of approximately 75, 55 and 35 percent, respectively. In preparing reduced ice content samples there was some question as to the actual distribution of ice in the pore spaces. It is doubtful that the procedure described will result in a completely uniform distribu- tion of water, and the ice contents indicated are nominal, based on the moisture content of the entire sample. The actual ice content distribution was higher 37 than the nominal at the bottom of the sample and lower than the nominal at the top. Use of snow or fine ice particles mixed with the sand was not attempted because of anticipated compaction problems for the desired high sand density. The results from reduced ice content samples did give a fairly reasonable indication of general magnitudes of strength. CHAPTER IV EQUIPMENT AND TEST PROCEDURES Since triaxial tests covering a range of confining pressures from 0 psi to 1000 psi were conducted, the triaxial cell had to be constructed of a material that would withstand this range of pressures. The type of cell used was a special high pressure triaxial cell. The cell was a stainless steel Wykeham—Farrance triaxial cell constructed for a maximum working pressure of 1500 psi and tested to 2250 psi. The cell had a stainless steel hardened ram and adequate valves to provide for drainage and pressure control. Two base plates for the cell were specially designed and constructed at Michigan State University to provide for a 15,000 pound or a 5,000 pound capacity stud transducer. For the constant strain rate tests the base plate with the 15,000 pound capacity transducer was used. The creep and step— stress tests were performed using the base plate with the 5,000 pound capacity transducer. In order to conduct the triaxial tests at pres- sures up to 1000 psi a pressure transmitting system was used similar to that described by Warder (1969). This system used pressurized nitrogen gas as the activating 38 “1:22;. 1 39 source. The gas was transmitted from the nitrogen tanks through a regulating valve to a high pressure cell. In this cell the gas was brought into contact with the coolant liquid which transmitted the pressure to the triaxial cell. The high pressure cell also kept the coolant from backing up the line into the nitrogen tank during depressurizing. I} Gages were placed at various locations to monitor the ‘— pressure. A master gage attached to the triaxial cell was used to read the confining pressure in the triaxial : cell. This gage had a 5 psi increment with an accuracy .3 of 1/2 percent. The constant pressure regulator and the system described held the pressure constant during the tests with very little variation. The other part of the system consisted of the refrigerator unit and its appurtenances which controlled the test temperature of the coolant. A micro-regulated portable refrigerating unit was used to control the temp- erature of the coolant. The coolant was circulated from the refrigerating unit to a cold bath in which the tri- axial cell was immersed. This system provided very good temperature control. Goughnour (1967) using a similar system determined, by using a thermocouple attached inside the triaxial cell, that temperature varied by not more than 0.05° C from the temperature of the coolant liquid in the cold bath. Temperature at the cold bath was monitored using a thermometer with scale divisions 40 of 0.1° C from which the temperature could be estimated to : 0.01° C. The coolant used in the refrigerating unit was a mixture of about 1/2 ethylene glycol and 1/2 water. Figure 4-1 shows a schematic layout of the testing equip- ment. Various types of transducers were used to measure the axial force and displacements during a test. The transducer used to measure the loads during the constant axial strain rate tests was a Strainsert model Q-1096 stud transducer with a 15,000 pound capacity. Loads measured with this transducer were accurate to i 10 pounds. This unit had no provision for pressure equalization, and when the confining pressure was applied the transducer would indicate a negative load. The value for the negative load was set equal to zero and increases in load were measured from this value. For the constant strain rate tests (samples 77- 89) and the creep tests a Strainsert flat load cell type FLSU-ZSP with 5,000 psi capacity was used. This load cell had an accuracy of i 5 pounds. To measure the axial displacement, a Sanborn Linearsyn differential transformer was used. The trans- former was attached to the triaxial cell with the core element bearing On a collar plate fixed to the cell's loading ram. This allowed measurement of axial dis- placement within the cell and eliminated all other var - V I .ucofimflsvw umwu mcflsonm uSOMMQII.H|v wusmflm snap HHwo mafiumnwmflummm mRSmmwum :mfim _ . _ _ _ ucmaooo _ wauoowm “ _ _ 41 w. -Illl_r-u uwpcflazo cwmouuwz swam CHOU Hfimo Hmflxmnhe «Emnm cmoq ‘a’lr‘u‘ll'. 42 displacement measurements. The accuracy of measurements was : 0.0004 inches. The force transducer and the differential trans— former were connected to a Sanborn 150 4-channel recorder for permanent display of the results. Two different load frames were used for the test series. The constant strain rate tests (samples 77—89) and the creep tests were performed on a Soiltest load frame Model T-118—X with a Graham variable speed transmission. The transmission was of the screw type and allowed displacement rates to be changed while tests were in progress. All other constant strain rate tests were conducted on a Wykeham-Farrance variable speed load-~ ing frame. This frame had a 30 speed gear box with speed selections from 0.225 to 0.000024 inches per minute. The machine performed satisfactorily, but there was no provision for changing the rate of displacement once the machine had started. The results indicate that as the load was applied, the displacement rate dropped off from the selected rate and did not return to this rate until after the peak load had been reached. 4.1 Triaxial Tests Triaxial tests with constant strain rates were conducted on both confined and unconfined sand-ice samples. After the sample and triaxial cell had been 43 in the cold bath for about 12 hours, the test procedure outlined below was followed: 1. The temperature of the cold bath was observed and recorded. 2. The force transducer and the displacement transformer were connected to the Sanborn recorder which was allowed to warm up. After an adequate warm up period both trans- ducers were brought to a zero reading. 3. The load frame ram was lowered until it was just in contact with the triaxial cell's ram, with no load applied. 4. If the test was to be confined, the appro- priate level of pressure was applied to the triaxial cell. If the test was unconfined, this step was omitted. 5. The drive mechanism was set at the desired speed (usually 0.006 in/min) and the loading ram was activated. 6. The trace of the load and deflection readings were observed on the recorder output charts. As the trace approached the top of the graph, the stylus was turned back using the zero suppression capability of the recorder.' 7. After the peak load was observed on the recorder the driving mechanism was stOpped 44 and the confining pressure, if any, was removed. 8. The temperature of the cold bath was recorded and the triaxial cell was removed from the cold bath. Most of the constant strain rate triaxial tests were conducted on the Wykeham-Farrance load frame. How- ever, 15 tests were conducted using the Soiltest appara- tus. In these tests the procedure was as noted above with the exception of step six in which the trace of the displacement curve was observed and adjustments of the strain rate were made as the test progressed. 4.2 Creep Tests All creep tests were conducted on the Soiltest load frame. Loads were applied by a loading yoke sup- porting a dead weight of lead bricks. The yoke was lowered by the drive motor of the load frame. When loads were applied to the sample, the drive was lowered at the fastest rate possible. Loading time was approximately five seconds. 4.2.1 Uniaxial The procedure for conducting a uniaxial creep test was basically the same as the triaxial tests. The preliminary steps were the same as steps 1-4 listed in section 4.1. After the load was applied the trace of the 45 deflection curVe was observed and at predetermined intervals small increments of weight were added to the sample to compensate for the increase in cross sectional area and to maintain a constant stress. The increments of weight were noted and used to check the load readings obtained from the recorder. The tests were allowed to run for approximately six hours before the load was removed. The samples were allowed to recover for one hour, then the triaxial cell was removed from the cold bath and disassembled. 4.2.2 Step-Stress In step-stress testing the deviator stress was held constant and the confining pressure applied to a sample was changed by increments or steps. Except for the loading stage, the step-stress tests were conducted in the same manner as the uniaxial creep tests. During loading the selected level of stress was applied to the sample which was permitted to deform in the uniaxial state of stress for 60 minutes. At the end of this time an initial increment of confining pressure of 100 psi was applied to the sample. After the confining pressure was applied it was necessary to add weight to the dead load to retain the selected level of deviator stress. This was accomplished by observing the load trace on the recorder and adding weight until it returned to the 46 initial value. Additional increments of confining pres- sure were added at 120, 180, 240, 300 and 360 minutes. The total confining pressure after each of these incre- ments was 200, 400, 600, 800 and 1000 psi, respectively. When operating at elevated confining pressure, the mem- branes were easily ruptured causing several of the step-stress tests to be terminated. " CHAPTER V EXPERIMENTAL RE SULTS (5.1 Constant Axial Strain Rate Tests The mechanical properties of soils are usually measured using triaxial compression tests. More recently the effect of strain rate has been recognized as one of the many variables that affect the stress-strain rela- tionships. As a consequence, constant axial strain rate testing was used to eliminate this potential variable. This section presents the results from constant axial strain rate tests on unfrozen sands, sand-ice with high ice content and sand-ice with reduced ice content. 5.1.1 Drained Tests To provide a correlation between the frictional characteristics of frozen and unfrozen sands, the fric- tional behavior of the unfrozen sand was obtained for the same test conditions as the frozen sands. A series of drained triaxial tests were conducted on unfrozen 3min“1 and a Ottawa sand at a strain rate of 2.66 x 10— void ratio of 0.58. These tests were conducted‘in a standard perspex triaxial cell and were limited to 110 psi confining pressure. The frictional 47 48 characteristics for unfrozen sand at higher confining pressures were obtained from data presented by Lee and Seed (1967) and Vesic and Clough (1968). Typical results of drained triaxial tests on unfrozen sand are shown in Figures 5-1 and 5-2. An angle of internal friction equal to 37° was obtained from the Mohr diagram shown in Figure 5—2. This value is typical for Ottawa sand with a void ratio of 0.58. Figure 5—1 shows the stress—strain and volume changes characteristic of the Ottawa sand. The curves indicate: (1) Volume change is negative (increases) for all tests with little variation between the tests at different con- fining pressures. At higher confining pressures the amount of volumetric strain decreases but will remain negative for pressures through 1000 psi (Lee and Seed, 1967); (2) Strain at failure ranges from four to six percent for all tests and (3) The peak strength increases as confining pressure increases. These results are in agreement with expected behavior. 5.1.2 High Ice Content The effect of confining pressure on the strength of sand-ice materials tested at confining pressures from 3 . -l min are 0 to 1000 psi and a strain rate of 2.66 x 10- shown in Figure 5.3. This rate of strain is fairly fast and resulted in failure times of 10—30 minutes, depending 49 on the confining pressures. In this figure it is apparent that strains at failure and peak strength of the sand-ice samples increase with confining pressures. This is also typical of results for unfrozen sand at high confining pressures (Lee and Seed, 1967). However, the curves for sand-ice materials show two yield points depending on the amount of confining pressure. For confining pressures in excess of 100 psi the curves have an initial yield point followed by a fairly linear increase in strength up to a second yield point that progresses to failure. This behavior is typical of all the samples tested at higher confining pressures. There is no indication that confining pressure greatly alters the value of the Young's modulus for the initial portion of the curves and except for the sample 44, there was little variation in the value of the initial yield point. Figure 5—3 includes a plot of strain versus time for the various tests. The fact that this curve has a slight curvature indicates that the actual strain rate varies only slightly from the nominal strain rate of 3min—l. The variation is due to the test 2.66 x 10' apparatus and appears to be typical of all the tests conducted on the Wykeham-Farrance loading frame. Volume of sand, or void ratio is an important factor in determining the strength of sand—ice materials. To obtain the effect of confining pressure on this 50 variable, tests were conducted at various void ratios and confining pressures. Figure 5-4 and 5-5 show that void ratio affects strength through the entire range of confining pressures tested. The initial yield for these tests is approximately 1200 psi and appears to be independent of the volume of sand. This value is greater than the maximum shear strength of ice tested under similar conditions, indi- cating some reinforcing effect due to the sand. The spread of the curves above the initial yield is the result of variations in the development of the frictional component resulting from the different volumes of sand. These figures show that the ice matrix does not appear to affect the basic frictional mechanism of a sand. An additional factor which may affect the strength of a sand-ice sample is the strain rate. It is generally considered that increasing the strain rate will increase the strength of frozen soils (Kaplar, 1970). The results of uniaxial constant strain rate tests performed at three different strain rates are shown in Figure 5-6. These tests show an increase in peak strength as strain rate increases; however, the magnitude of the increase is only 250 psi for a ten-fold increase in the strain rate. What is more interesting is the trace of the curves. For the slowest strain rate there is a low initial yield followed by a non—linear increase of stress progressing to failure. 51 The faster strain rates have higher values for the initial yield point, and then progress much more rapidly to failure. Since the soil structure and volume of sand for the samples are constant, this indicates that the strain rate primarily affects the ice matrix. The difference in peak strength noted is approximately equal to the dif- "‘fl ference in the initial yield values. To investigate the effect strain rate has on con- fined samples, a series of tests were conducted at 700 psi confining pressure for various strain rates. The strain rates varied from 7.07 x 10n5min-l to 5.3 x 10-3min-l or a factor of 75 when compared to the lower rate. Figure 5—7 shows the results of this test series. As is typical for confined samples, there is an initial yield followed by a linear increase of stress leading ultimately to failure. The initial yield is shown to be dependent upon strain rate, although the peak stresses for the samples varies by only a small amount. If the samples with constant strain rates are corrected for variations in percent of sand to a constant 63 percent, the peak strengths are as follows: sample 50, 2750 psi; sample 38, 2745 psi; and sample 48, 2450 psi. The differences noted are of the same magnitude as noted for the unconfined tests and are only a small percent of the peak stress. Of particular interest in this test series are the results for sample 19 where three values of 52 strain-rate were used. For each increase in strain rate there is a corresponding linear increase in the stress followed by another yield point. As the strain rates increase, Young's modulus also increases. This implies that the ice matrix is responsive to the strain rate, and any change in test conditions will interrupt the existing equilibrium relationship and cause a new relationship to r form. ‘ I The results of the constant axial strain rate tests on high ice content samples are summarized in Table 5-1. 5.1.3 Reduced Ice Content To determine the effects of ice content and con- fining pressure, a series of tests were conducted on samples with ice contents of approximately 55 percent. The confining pressures were the same as used for the samples with high ice contents. The results for this test series are shown in Figure 5-8. The stress-strain behavior for samples with reduced ice contents was about the same as for the high ice contents, except that the peak strength was lower for all confining pressures. These curves also show that confining pressure does not increase the Young's modulus to any great extent, but the initial yield value does increase with increasing confining pressure. For the reduced ice content sample, 53 the initial yield that was so prominent for the high ice content samples was almost completely obscured until a confining pressure of 700 psi was applied. This suggests that the initial yield is related to the ice matrix and as the ice content is reduced, the behavior becomes more frictional in nature. A better indication of the effect of reduced ice content on the stress-strain characteristics is shown in Figure 5-9. In this figure the results of both high and low ice content tests for typical unconfined and confined conditions are shown. It can be seen that for reduced ice content: (1) the strains at failure are slightly less than for the high ice content and (2) the difference in peak strength between high and low ice content is greatest for the unconfined samples. To obtain a wider range of reduced ice contents, additional tests were conducted with an ice content of approximately 35 percent. Figure 5-10 shows that results of samples with four different ice contents and 100 psi confining pressure. These curves clearly show a small increase in Young's modulus as the ice content increases. One anomaly in the results of these tests is the strain at failure. As the ice content decreases, the strains at failure decrease. However, for the sample with zero ice content the strain at peak strength was larger than for any of the other tests. 54 The results obtained for all samples with reduced ice content emphasize the nonfrictional behavior of the initial portion of the stress-strain curve and the domie nance of the frictional components as soon as adequate yielding has taken place. The results for the reduced ice content tests are summarized in Table 5-2. Two samples of polycrystalline ice were prepared (as suggested by Goughnour (1967)), and tested at 0 and 685 psi confining pressure to verify the fact that ice is not appreciably affected by confining pressure. The results from these tests are shown in Figure 5-11 and indicate the effect of confining pressure is not very great. The small increases in strength may be due to confining pressures tending to prevent cracking of the ice as failure is approached. However, these tests may be inconclusive since only two samples were tested. 5.2 Creep Tests It is known that the strength of frozen materials are highly dependent upon the time of load application and their behavior can be studied using creep testing tech- niques. In the following section the results of creep tests on sand-ice materials will be presented. 5.2.1 High Ice Content The creep behavior of sand—ice materials and relationships that are descriptive of their behavior ‘w \W-.- 55 were studied using creep tests conducted in three differ- ent ways: uniaxial, confined and step-stress. Tempera— ture was held constant at -12.0° C for all tests and selected constant deviator stresses of 400, 640, 750 and 1070 psi were used to give a wide range of creep behavior. 5.2.1.1 Uniaxia1.-—The main objective of the uniaxial tests on the sand-ice was to obtain the general creep behavior of the material and the magnitude of strains that result for a test time of approximately six hours. Typical results for the selected levels of stress are shown in Figure 5-12. Each of the curves show an instantaneous strain immediately after the application of the load followed by a region of decreasing strain rate. In sample 90 the region of noticeable decreasing strain rate was up to 200 minutes. Beyond this time the curves approach linearity. The initial instantaneous deformation does not exhibit any clear trend because of slight variations in friction reducers and sample seating. To eliminate these variables, the strains for all the tests have been cor- rected by subtracting the strain at one minute. Figure 5-13 shows the corrected results for the four levels of axial stress. This curve gives a much clearer picture of the variations in strain between the stress levels. 56 5.2.1.2 Confined.--Before conducting step-stress creep tests where the confining pressure was varied at selected time intervals, it was necessary to observe the creep reSponse of sand-ice under continuous confining pressure. The results of two tests conducted at a con— stant deviator stress and constant confining pressure are plotted in Figure 5-14. Shown for comparison are the results of a uniaxial test at the same stress level. If the test results are corrected as described in section 5.2.1.1, and replotted as in Figure 5-15, the effect of confining pressure is more apparent. As the confining pressures increase, the strains and strain rates decrease for any selected time. It is noted that the effect of confining pressure is greatest at low values since the original 200 psi increase in confining pressure had more than twice the effect of the 390 psi increment between the 210 psi and 600 psi level. 5.2.1.3 Step-Stress.-—The effect of confining pressure on creep rate is shown by step-stress creep tests conducted at 400, 640 and 750 psi levels of constant deviator stress. Test results are shown in Figure 5-16 for confining pressures added at one hour intervals in the sequence 100, 200, 400, 600, 800 and 1000 psi. As each increment of confining pressure was applied, a rapid increase in strain took place due primarily to expansion 57 of the triaxial cell. Following this increase in strain due to cell expansion there was a region of fairly rapid increase in strain with time which quickly decreased, resulting in a strain rate less than the minimum for the preceding increment. One additional test conducted to observe the step—stress characteristics at a constant deviator stress of 1070 psi is shown in Figure 5-17. A uniaxial creep test at the same level of stress has been shown for comparison. The increase in strain due to cell expansion followed by the region of decreasing strain with time, demonstrates that there was no basic difference between the step—stress test shown here and those discussed above. The region of decreasing strain and dampening effect of the confining pressure are more noticeable here than for the samples tested at lower levels of deviator stress. Table 5.3 contains a summary of the experimental results for the creep tests on high ice content samples. 5.2.2 Reduced Ice Content The creep behavior of frozen sand at reduced ice contents was studied by using constant deviator stresses of 400, 640 and 750 psi. These constant stresses were the same as for the high ice content samples. Sand volume and temperature (-12.0° C) were held as constant as possible. It was expected that reduced ice contents 58 would increase the frictional characteristics of creep and lead to a better identification of the processes involved in sand-ice materials. 5.2.2.1 Uniaxial.--The results of uniaxial creep tests on reduced ice samples are shown in Figure 5-18. The curves illustrate the changes in creep behavior as axial stress increases. The curves all have the char- acteristic chape of "classical" creep curves, and one has progressed into the tertiary region and is in the process of failing. When compared to the high ice content samples with equal axial stresses, shown in Figure 5-12, the reduced ice content greatly accelerates the strain rates for any given axial stress. The change in creep behavior for reduced ice content is shown by samples with three ice contents and a constant axial stress of 750 psi in Figure 5-19. As the ice content decreases, the strains at a constant time increase substantially, indicating a close rela- tionship between the ice matrix and the creep behavior. 5.2.2.2 Confined.--The results of a uniaxial creep test and a constant deviator stress creep test with continuous confining pressure on reduced ice content samples are plotted in Figure 5-20. When compared to the uniaxial test, the effect of the confining pressure is to dampen the response of the sample to the applied 59 stress. The same effect was noted for the high ice con— tent samples, but the magnitude of the change of strain rates was not nearly as great. 5.2.2.3 Step-Stress.--Step-stress tests for the reduced ice content samples illustrated in Figure 5—21 include two levels of constant deviator stress. The sample tested at 640 psi developed a leak after the third increment of confining pressure was applied and the test was terminated after 180 minutes. The effect of confining pressure and development of the strain versus time curves are similar to the high ice content samples presented in section 5.2.1.3. Uniaxial tests showed that a reduced ice content sample tested at an axial stress of 750 psi would progress to failure within one hour. Therefore, the time increments for applying confining pressure in the step-stress tests were decreased. The results of a step-stress test at a constant deviator stress of 750 psi is shown in Figure 5-22. For this test the confining pressure decreased strain rates significantly. Even at 90 minutes, the test did not progress into the tertiary region and strain rates were still decreasing. 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LI L1 L1 L1 L1 L 11. 11. 11. 141 1a. 11. 1a oooa oom oom ooa ooa ooa 0 am@ .muswmoum msasamcoo ut/ut ’urexqs Iatxw anx; 88 .amm oma n o .usmucoo ooa pmonmom Mow mwmuo mmmaumnowpmul.mm1m muomam .caz .mfiae om om on om om ov a a a . _ _ mao. omo. mmo. omo. woo u ucoucou ooa 1 mmo. UoO.NHIfl B amo oma u o aaaw 1 ovo. .1 L1 .ks 1P. 1P, 1P. .L .4 41 1a 41 11 11. 1a oom oom oov oom ooa o amm .mHSmmmHm mcacamsoo ut/ur futexis Iatxv anx; CHAPTER VI DISCUSSION OF RESULTS 6.1 Factors Controlling Shear Strength Assuming that shear strength of a sand-ice material is composed of cohesive and frictional components which may be identified and isolated, the effect of various factors on these components can be shown. Vialov (1965b) has shown that the cohesive component of sand-ice is due primarily to confinement by the ice matrix and factors that alter the ice matrix will change the shear strength pro- portionately. The major cause for variations in the cohesion of the ice matrix is temperature (Vialov, 1965b), with strain rate and ice content having effects that are less well understood. By holding temperature constant, while changing the strain rate or ice content, the effect of these factors was observed. The frictional component of strength for dense sand-ice materials tested to failure is independent of time, strain rate and ice content, and dependent on the void ratio and confining pressure. The effects of these factors were obtained by testing samples at constant strain rates and various void ratios over a large range of con- ‘fining pressure. 89 90 In the following sections each of the factors which affect the frictional and Cohesive component of strength will be discussed. The effect of confining pressure on the various factors will be discussed as it occurs. 6.1.1. Frictional Component The frictional component of strength for sand-ice materials is dependent on the frictional characteristic of the sand material. Koerner (1970) has identified particle size, shape and gradation as factors which may affect the frictional behavior of single mineral soils. By using only Ottawa sand between the number 20 (0.84mm) and 30 (0.59mm) U. S. Standard sieve size, these factors were minimized. Once these factors have been eliminated, the frictional Characteristics of the single mineral sand is dependent on sliding friction, dilatancy, and particle crushing and rearranging. Because of the high volume of sand in the sand-ice samples tested herein, particle to particle contact is likely to occur and sliding friction will develop with deformation. This will be true even if it .is assumed that each grain of sand is surrounded by a layer of ice, since the contact pressures that develop will be high enough to cause pressure melting and migration of moisture at contact points. Particle crushing is known (Lee and Seed, 1967) to be small for Ottawa sand tested up to 1000 psi confining pressure and will not contribute 91 significantly to the frictional component of strength. Thus, the only unaccounted-for component of frictional strength is dilatancy. As the confining pressure increases, the volume changes associated with dilatancy are resisted by the confining pressure resulting in a lower component of strength due to dilatancy, and a lower angle of friction. For sand-ice materials both the applied confining pressure and the confinement due to the ice matrix retard volume changes , 1 resulting in a low component of strength due to dilatancy. As a result, the angle of friction for sand-ice materials will be lower than those obtained from unfrozen sands at similar confining pressures. To verify these observations, volume measurements were taken both before and after testing selected samples. Since the equipment did not allow the measurment of volume changes during the test, total volumetric strain per test was divided by the unit strain at the end of the test to obtain an average change per unit of strain. The results of this procedure, shown in Figure 6-1, permit several observations to be made: (1) volume changes are small and are all negative (increase) for the sand densities tested; (2) volumetric strain per unit strain decrease as confining pressure increases; and (3) volume changes are less for sand—ice materials than for unfrozen sand at equal confining pressures. These observations verify the original assumption that dilatancy must contribute to the strength of sand—ice materials. However, the fact that the values of volumetric strains are small implies that the contribution to strength will be small. The resulting angle of friction obtained for sand-ice materials should be comparable to those obtained for dense sands at high confining pressures where dilatancy has also been reduced. 6.l.2 Void Ratio (Density) One of the variables that affects the peak strength is the variation of void ratio between sand-ice samples. This factor has been reported by other investigators (Kapler, 1971; Goughnour, 1967; and Yong, 1963) for sand- ice materials and is an indication that the material retains some of the frictional characteristics of unfrozen sand. A decrease in void ratio for unfrozen sand tends to increase the maximum deviator stress at failure (Koerner, 1970; Lee and Seed, 1967). This is due to dilatancy and particle rearranging and crushing. For sand-ice materials the actual magnitude of the strength increase appears to be dependent upon the confining pressure in addition to the void ratio. Using uniaxial compression tests, Goughnour and Andersland (1968) showed a bilinear relationship between the volume of sand and peak strength. A similar presentation is shown in Figure 6-2. The majority of the data for this graph was obtained from Goughnour (1967) with additional points added from the tests conducted in this study. The 93 test procedures and sample preparation were the same for all tests. This figure also shows an increase in peak strength due to changes in temperature and strain rate. It is interesting to note that above a sand volume of approximately 42 percent the change in slope of the curves at the different temperatures appears related to the ability of the ice matrix to exert various effective stresses in the sample. If the ability of the ice matrix m to apply confining pressure is the requirement for increas— ing the slope of the curves, it would be expected that other factors which increase the cohesive component of strength may also increase the slope of the line. There is an indication in Figure 6-2 that this is the case. The tests conducted at a strain rate of 2.66 x lO-D3min-l have a slightly greater slope than the tests conducted at 2.66 x 10‘4min'l . There is a limitation for which this will occur, since there is a confining pressure at which dilatancy will be prevented and the friction angle will become constant. The results of increased confining pressure and volume of sand on the peak deviator stress are shown in Figure 6~3. Increased confining pressures serve to increase the maximum deviator stress per unit increase in sand volume. Above 350 psi the increase in maximum deviator stress per unit increase in sand volume appears to be constant, nearly parallel curves. These results reinforce 94 the previous discussion concerning a limiting value of confining pressure that can cause an increase in the slope of the strength versus percent of sand curves. Lee and Seed (1967) showed that as the confining pressure on unfrozen sand samples increased, the difference in failure stresses between a loose and a dense sample increases up to a maximum value and then remains essentially constant. The same behavior is shown in Figure 6-3 for the sand-ice material. Thus, for sand~ice at low confining pressures, dilatancy contributes to the variations in strength between samples with different void ratios. At high confining pressures the dilatancy component of strength is reduced, producing a fairly constant difference in deviator stress between dense and loose sand-ice samples. This explanation implies that the response of the ice matrix can be con— sidered analogous to higher effective stresses, and variations in sand volume do not increase or decrease that response. Since the effect of void ratio is influenced by the confining pressure applied to the sample, it is necessary to account for all pressures. For a sand-ice system, there is not only the externally applied confining pressure but an internal increase in effective stresses provided by the ice matrix. If the internal and external pressures are added, it is apparent that the frictional component of strength in sand-ice systems can be compared to unfrozen 95 sands only if the unfrozen materials are tested at higher confining pressures. Another indication of the interrelationship of confining pressure and percent of sand by volume can be obtained by plotting the peak stresses in terms of the principal stress ratio. In Figure 6-4 the principal stress ratio versus the percent of sand by volume is shown for various confining pressures. This graph shows that the lower the confining pressure, the more sensitive the principal stress ratio is to changes in sand volume. In fact, at high confining pressure the principal stress ratio is quite insensitive to changes in the sand volume and approaches a constant level. This type of behavior is also typical of unfrozen sands at high confining pressure (Lee and Seed, 1967). 6.1.3 Relative Ice Content In order to magnify the frictional characteristics of a sand—ice material, tests on samples with reduced ice content were conducted. To relate strength to a function of ice content, the term "percent of ice" is uSed. The percent of ice is defined as the volume of ice divided by the volume of voids multiplied by 100. The calculation of the volume of ice is determined by dividing the weight of water in a sample by the density of ice at -12.00 C (0.91848 gm/cm3). 96 Kaplar (1971), Vialov (1965b), and Yong (1963) have shown that strength of sand-ice materials decrease approximately linearly with a decrease in the percent of ice in the sample. These results were obtained for ”unconfined tests with no indication of the effects of confining pressure. The results of confined compression tests on samples with different ice contents are shown in Figure 6-5. Values for the high percent of ice were obtained from Figure 6-3 using the same volumes of sand as contained in the reduced ice samples. This figure indicates a linear and constant decrease in deviator stress with reduced ice content for all confining pressures. Since each line of equal confining pressure has a different volume of sand, the reduction in strength due to changes in the ice content is independent of both confining pressure and volume of sand. From this result it can be concluded that the reduction in strength is due entirely to a loss of cohesion and samples at reduced ice content will have the same frictional characteristics as samples at high ice contents. To compare the significance of the percent of ice for various confining pressures a plot of reduction in strength versus confining pressure is shown in Figure 6-6. The reduction in strength is calculated as follows: 97 where DH DL = Maximum deviator stress for low percent ice. Maximum deviator stress for high perCent ice. This figure indicates that the reduction of strength decreases as the confining pressure increases. This is another indication that strength at high confining pressure is less dependent on the ice matrix and becomes primarily frictional in nature. 6.1.4 Confining Pressure Previous investigations into the strength behavior of frozen soils have been primarily conducted on samples that were unconfined or at low confining pressures. Yong (1963), Goughnour (1967), and AlNouri (1969) have conducted tests on sand-ice materials at confining pressures up to 150 psi. In order to extend the data of these investigators confining presSures up to 1090 psi were used to determine the effect on the strength of sand-ice materials. This range of pressures has been used on unfrozen sand by Lee and Seed (1967). The data from this study was used to interpret the results for frozen sand. Typical stress-strain behavior for unconfined and confined tests is shown in Figure 6-7. These tests indiCate that for low confining pressures the curves progress through. an initial period of high stress increase per unit strain 98 followed by partial yielding leading ultimately to failure. The sample with the higher confining pressure behaves in a similar fashion up through the initial yield point. However, after this point additional strengthening due to dilatancy and sliding friction takes place and there is a long, fairly linear increase in stress, progressing eventually to failure. Similar results have been observed in unfrozen materials with a cohesive matrix (Schmertmann and Osterberg, 1960) where the initial yield point is identified as matrix yield. An indication of the relative magnitudes of the proportions of shear strength due to cohesion and friction is given, by a graph of principal stress ratio versus confining pressure in Figure 6-8. When compared to unfrozen Ottawa sand values obtained from Lee and Seed (1967) it is apparent that forlow values of confining pressure, the shear strength of frozen sand is primarily nonfrictional and dependent on the strength of the ice matrix. As the confining pressure increases, the principal stress ratio for sand-ice decreases and approaches the value for unfrozen sand. However, even at high confining pressure, there is a small component of strength due to the ice matrix. This plot also gives an indication of the shape of the failure envelope since decreasing values of the principal stress ratio with increasing confining pressure correspond to a progressive flatting of Mohr's envelope. 99 If the same results are plotted on logarithmic scales as shown in Figure 6-9, a bilinear relationship occurs with the area of transition in the region between 100-200 psi confining pressure. Later sections show that creep test reSults give a similar change in behavior for these pressure ranges. Another effect of confining pressure on the stress- strain characteristics of a sand-ice sample is an increase in axial strain at failure. Axial strain at failure is plotted against the confining pressure in Figure 6-10. The data shows that as confining pressure increases the strain at failure also increases. This behavior is similar to sands as reported by Vesic and Clough (1968), and Lee and Seed (1967). However, when compared to unfrozen sands, the strains at failure are substantially less for sand-ice materials. For reduced ice content samples, there is also an increase in strain at failure with increasing confining pressure, but the strain at failure has decreased compared to the results for high ice content samples. 6.1.5 Failure Criteria Using the Mohr-Coulomb theory to describe the time dependent strength of sand-ice materials, the results of the constant strain rate tests are summarized by the p-q diagram shown in Figure 6-11. Data for unfrozen sand (Lee 100 and Seed, 1967) are also plotted as an aid in comparing the results and identifying the components of strength. If the ordinate to the unfrozen Kf failure line is considered to be caused by sliding friction, dilatancy, and particle crushing; the remaining distance to the sand-ice failure line must be attributed to the ice matrix. What is of interest is the consistency of this value regardless of the value of the normal stress. Over the entire range of con- fining pressure this component varies from only 330-260 psi. This implies that confining pressure has no significant effect on the component of strength due to the ice matrix. If the results of the constant axial strain rate tests on polycrystalline ice are used, the values of calculated q are nearly the same as the value of the cohesive component shown in the p-q diagram for the sand-ice material. Since the value of the cohesive component is nearly constant, it may be concluded that the ice matrix applies a pseudo- confining pressure analogous to a higher effective stress that is also nearly constant. The magnitude of this pressure may be obtained by evaluating the horizontal stress increment obtained by projecting a line from a point on the sand-ice Kf failure line to a point on the unfrozen sand Kf failure line. For high ice content samples this value is approximately 600 psi. 101 When the angle of inclination of the Kf failure line in the p-q diagram is measured, it decreases slightly with increasing values of normal stress but is approximately 26 degrees. This gives an angle of 29.2 degrees on the fail- ure plane. This value is low when compared to the fric- tion angle for unfrozen sands, which are typically 37-45 degrees depending on the initial void ratio. However, the friction angle for unfrozen sands at high confining pressures is less than the value at low confining pressures. Lee and Seed (1967) obtained a value of approximately 30 degrees for high confining pressure tests on Ottawa sand with an initial void ratio of 0.49. For unfrozen sands the reduction in the angle of friction is due to a decrease in the dilatancy component of strength as confining pressure increases. The same effect is produced in sand-ice materials by the combination of the applied confining pressure and the pseudo-confining pressure caused by the ice matrix. If sand-ice samples with a different initial void ratio were plotted, the result would be a downward displacement of the failure envelope as the void ratio increased. This does not mean that the cohesive component will decrease, since the failureplane for unfrozen sand will also be displaced. The result shown previously on the effect of void ratio indicated that at high confining pressures, the change in strength per increase in void ratio is constant and not dependent on the ice matrix. 102 Also shown on the p-q diagram (Figure 6-11) are the results of the constant strain rate tests on reduced ice content samples. The observations for these samples are similar to those for the high ice content discussed above. Again it is apparent that at failure a full frictional component is mobilized and the reduction in strength is due entirely to a reduction in the cohesive component. The net result is that sand-ice materials tested to failure has strength characteristics that can be divided into a cohesive component due to the ice matrix and a component due to friction. It has been shown that the frictional component can be related to the behavior of unfrozen sands at high confining pressure. The cohesive component is the part of strength which will be most responsive to variable test conditions and controls the time dependent characteristics of the shear strength. In addition, the cohesive component of strength is dependent on the percent of ice in the sample and for given conditions of temperature and strain rate is nearly constant at failure. 6.2 Creep Behavior In order to describe the creep behavior of sand- ice materials for various stress levels, it is necessary to determine the effect of confining pressure on creep. 103 This section presents the results of uniaxial, confined and step-stress creep tests on high and reduced ice content samples for confining pressures up to 1000 psi. Throughout this section constant deviator stress will be shown as a function of the peak deviator stress obtained from the constant axial strain rate tests. The 1 term M will be used to describe this relationship, where M is equal to the ratio of constant deviator stress for the creep test divided by the peak deviator stress from the constant strain rate test conducted at a similar con- fining pressure. For example if the creep test conditions are: constant deviator stress, (01-03) = 1070 psi confining pressure, 03 = 350 psi volume of sand, = 63.6% ice content, = 100% Then from Figure 6-3 the maximum deviator stress would be equal to 2360 psi and _ 1070 psi _ Values of M for all creep tests have been calculated and are shown in Table 5-3 and 5-4. 104 6.2.1 High Ice Content To show the effect of applied stress on the creep behavior of sand-ice materials at high ice contents, the results of uniaxial creep tests conducted at 400, 640, 750 and 1070 psi are plotted as a logarithm of strain rate versus strain in Figure 6-12. The near linear relationship for each stress level indicates that for the time of load application for these tests, the creep strains are small and the strain rates are decreasing at a constant logarithmic rate. These tests have not reached the steady state region. of a typical creep curve since this would require a horizontal segment of the strain rate versus time curves. The low values of strain also imply that this should be a region of little volume change. The actual values of volume change that were measured at the end of each test are noted on the figures. Through 750 psi the volume decreased as would be expected for low values of strain. Goughnour (1968) made volumetric measurements during uniaxial creep tests and constant strain rates tests, and demonstrated that an increase in volume will be associated with the matrix yield which is required prior to the mobilization of the dilatancy component of friction. Thus, for the stress levels applied in this series the creep behavior is primarily dependent on the ice matrix and the component of friction associated with solid to solid contacts. Any attempt to 105 determine an effective angle of friction within this region as proposed by AlNouri (1969) should result in low values since the loads applied are not great enough to mobilize the full frictional value of the sand particles, and the component due to interlocking of the particles. The effectof confining pressure on a constant deviator stress creep test is to increase the slope of the line of strain rate versus strain as indicated in r“?! - A Figure 6-13. This supports the observation by Andersland and AlNouri (1970) that strain rate decreases with increased mean stress. This may be explained by noting that an increase in confining pressure increases the level of normal stress applied to the sample. Part of this increase is carried directly by particle to particle contact and part is carried by particle to ice contact. When the p-q values for typical sand-ice tests are calculated, the results may be plotted as shown in Figure 6-14. It can be seen that for the unconfined Samples, a large portion of the total applied stress must be carried by the ice matrix (F). As confining pressure is applied to the system the stress circle moves to the right and the shear strength required of the ice will be less (G), and the strain rate will decrease, since creep is primarily a function of the shear stress applied to the ice matrix. This mechanistic 106 picture of creep assumes that the frictional component of strength due to sliding friction is mobilized during the application of the axial stress. For a dense material prepared in thenanner described herein, it appears reasonable that this be the case, since the packing is such that grain to grain contact is assured. In order for a sample to proceed to failure, it would be necessary for the Mohr's circle for the test condition to become tangent to the failure plane for the frozen soil. This may occur, since the cohesive component of strength decreases with time causing a downward displacement of the failure envelope. A comparable reduction in strength occurs in overconsolidated clays at large strains. For sand-ice materials time serves the same purpose as the large strains required for the clays. Step-stress tests have been used (AlNouri, 1969) as a method of determining the steady state creep rate at different levels of confining pressure. When using this method of testing, the axial load is held constant and the major and minor principal stresses are changed by an amount equal to the change in confining preSsure. Since the principal stresses are changed by equal amounts, the deviator stress is held constant. With step-stress testing it is assumed that the sample structure remains 107 the same prior to and immediately after changing the con- fining pressure and any changes in the creep rate are due only to the change in confining pressure. The results for step-stress creep tests plotted as logarithm of strain rate versus strain for three levels of constant deviator stress are shown in Figures 6-15 to 6-17. In these tests each new increment of confining pressure causes an increase in the slope of the curves. As noted in Figure 6-12, a decrease in axial stress produced a similar increase in slope. For the step-stress tests the deviator stress was constant and the confining pressures were altered. Therefore, increasing the confining pressure has the same effect as decreasing the applied stress for a uniaxial test. As each increment of confining pressure was applied, the strain rate increased. Then follows a period of decreasing strain rate until the next increment of pressure was applied. The initial increase in strain rate was dependent upon the deviator stress and the strain of the sample. At low stresses the samples show the greatest change in strain rates due to confining pressure. This is an indication of the greater structural dependency of the system at lower stresses. At low deviator stress levels the strain that took place during an increment of confining pressure was small and the structure remains nearly Constant. When 108 the next increment of confining pressure was applied, the deviator stress and structure were nearly the same as for the previous increment and the initial response of the material was the same. The step—stress creep tests involved increments of confining pressures applied at one hour intervals. To give an idea ofthe time effect on the strain rate, a sample with a constant deviator stress of 1070 psi was tested with zero confining pressure for three hours and then a confining pressure of 350 psi was applied for three hours. The logarithm of strain rate versus strain in Figure 6-18 demonstrates that time does not alter the basic characteristics of the curve and a decrease in strain rate takes place in a manner similar to the tests with confining pressures applied at one hour intervals. A The results of the step-stress creep tests are ‘ summarized in Figure 6-19. Andersland and AlNouri (1970) demonstrated that when the logarithm of secondary creep rate was plotted against a stress factor, X, a straight line relationship appeared for confining pressures up to 150 psi and time increments of one-half hour. The data summarized in Figure 6-19 indicate that the relationship predicted by Andersland and AlNouri (1970) are correct for low confining pressures. However, for confining pressure in excess of 200 psi the strain rates predicted gs: L(I i a? :1". ,1. 1 I. 1 .5 I. 3) j‘h J: 109 by their equation are substantially less than those indicated by the experimental results. In addition to the increase in strain rate at higher confining pressure, it appears that the equation used by Andersland and AlNouri (1970) is dependent upon the time interval at which the strain rates are obtained. The equation can be changed to reflect this by making the intercept term a function of time as shown below: é = b(t) exp (m2) (6-1) stress factor = D—Gm where E m = absolute value of the slope of the line b = time dependent intercept on the Z axis Figure 6-19 also indicates that strain rate is most responsive to changes in confining pressure for the range of 0-200 psi. Above 200 psi confining pressure, the strain rate continues to decrease with increased confining pressure; however, the change per increment is much smaller and approaches a constant at the higher levels of confining pressure. This implies that confining pressure changes the creep characteristics by a mechanism that is mobilized at low confining pressure. From these results it appears that in order to adequately predict strain rates using a stress factor as described by Andersland and AlNouri (1970), a bilinear relationship that is a function of time and confining pressure will be required. 110 When the results of the step-stress creep tests are summarized as shown in Figure 6-20, the interrelationship between stress difference and confining pressure is more clearly shown. To eliminate time dependency in this presentation, time intervals equal to one hour were selected. Changes in slope for lines of equal confining pressures indicate a definite dependency of strain rate upon the confining pressure. For a given deviator stress the strain rates decrease as the confining pressure increases. The) exact functional relationship can be derived empirically since a linear relationship on a semi-log plot has the basic form: é = b(t) exp (mD) (6-2) Taking logarithms of both sides results in the expression log é = log b(t) + (m log e) D (6-3) where (m log e) is the absolute value of the slope of the lines of equal confining pressure and b is the intercept on the ordinate. To determine the relationship between the slope, m, and the value of confining pressure, m is plotted against confining pressures as shown in Figure 6—21. The results of this graph exhibit a bilinear relationship , of slope versus confining pressure. From this figure the equation for the slope m as a function of confining pressure is: m. l where mi 111 = Ci + Gi 03 (5-4) value of slope for the line of equal confining pressure. 1, for confining pressure equal to or less than 200 psi. 2, for confining pressure greater than 200 psi. intercept of the ith segment of the m versus confining pressure graph. slope of the ith segment of the m versus confining pressure graph. Combining this expression with the equation 6-3 results in the £011 log Equation 6— owing expressions: E = log b(t) + [(ci+Gio3) log e D] (6-5) e = b(t) exp [(Ci+GiO3)D] ' (6-6) é = b(t) exp (CiD) exp (GiOBD) (6-7) 7 is of the same form as that describing the rate process theory. For the range of confining pressures studied (up describe th equation 6- to 1000 psi) an equation can be derived to e strain rate of a sand-ice sample. Using 7, the coefficient Ci and Gi must be determined for the appropriate ranges of confining pressure. From Figure 6-21 , when confining pressure is equal to or less than 200 psi 112 ml = C1 + G103 (6-8) _ -3 . -l . where Cl — 2.97 x 10 min /pSi Gl =-6.04 x 10"6 min-l/psi likewise for confining pressures greater than 200 psi m2 = C2 + G203 (6‘9) —3 . -l . where C2 = 1.98 x 10 min /pSi !r G2 =-1.03 x 10-6 min—l/psi The resulting equation for the entire range of confining pressures is: s = b(+) exp(CiD) exp(Gio3D) (6-l0) when . -6 . -l 03 i 200 pSi b(60) = 4.7 x 10 min C1 = 2.97 x 10.3 min-l/psi G1 = -6.04 x 10‘6 min-l/psi _ -6 . -l .03 > 200 b(60) - 4.7 x 10 min C2 = 1.98 x 10-3 min-l/psi G2 = -l.03 x 10.6 min-l/psi 113 The bilinear relationship noted for this equation may be explained for a sample at low confining pressures. When the sample is loaded instantaneously, numerous micro- cracks form at the sand-ice interface because some of the sand grains apply stresses to the ice in excess of the instantaneous ice crystal strength. Increased confining “A pressure prevents the cracks from forming, resulting in a more homogeneous material with greater strength and 1- lower creep rates. Equation 6-10 shows that strain rates are most responsive to confining pressures below 200 psi. The term b(t) in the equation has no physical significance but is an indication of the minimum strain rate that will be encountered in the range for which the equation is applicable. The previous discussion has indicated that given the results of step-stress creep tests, a family of curves may be constructed that will allow the calculation of strain rates for various combinations of confining pressures and deviator stress. This method has the disadvantage of being time dependent. It would be much more helpful if the creep characteristics of the sand-ice material could be obtained independent of time. It was observed that the strain rate decreases in an exponential fashion either after the initial application of the deviator stress (uniaxial tests, Figure 6-12) or 114 after the application of increments of confining pressure (Figures 6-15, 6-16, and 6-17). If the slopes of these lines are calculated and are plotted versus the percent of maximum deviator stress M as shown in Figure 6-22, a band of points is obtained. Using the results of this graph it is possible to approximate the decrease in strain rate for any test condition as long as the initial elastic strains and the percent of maximum deviator stress are known. The curvature of the graph as M approaches zero is an indi- cation that the response of the sand-ice materials to low levels of applied stress is different and the approximation would not be valid in this region. On the other end of the scale it is expected that the curve would be nonlinear as M approached 100 percent. From the data shown here, a range of 20-75 percent of the maximum deviator stress can be used for the approximation. For samples that progress to failure, the strain rate versus strain graph exhibits an initial linear portion followed by an upward curvature as the sample approaches the beginning of the tertiary region of creep. The results shown in Figure 6-22 can be used only to describe the linear portion of the curve. 6.2.2 Reduced Ice Content Since creep is related to the strength of a material, it would be expected that for a given constant axial stress 115 and void ratio, reduced ice content samples would have greater creep response than high ice content samples. In Figure 6-23, the results of uniaxial creep tests at 400, 640 and 750 psi are shown. It is apparent that these samples, as with the high ice content samples, exhibit typical strain rate versus strain characteristics. For the low level of axial stress (400 psi), the sample exhibits linear characteristic for the entire duration of the test. At higher levels of axial stress (750 psi) the sample has not only an initial linear portion, but also a segment of increasing strain rate. This is the type of behavior that would be expected of a sample that progresses to failure. The intermediate level of axial stress (640 psi) exhibits the initial linear portion and a small region of decreasing strain rate. These curves indicate that reducing the ice content does not alter the basic character- istics of the creep and any differences between high and low ice content samples are in magnitude only. If the applied deviator stress is related to the maximum shear strength of sand-ice samples for reduced ice content (as was done for the high ice content samples in the previous section) it is possible to define the term M, percent of maximum deviator stress, for the reduced ice content samples. In order to generalize the use of this term, it is necessary to show the relationship between the percent of maximum deviator stress for high and 116 reduced ice contents. It can be shown intuitively, that for any given percent of maximum deviator stress, the shear stress carried by the ice is constant and the response of the system will be essentially constant. Considering any failure plane with a shear force resulting from the applied force, then: PH PL TH = ngixgg- and TL - ALI+ALS (6-ll) where TH = shear stress resulting from applied load on high ice content samples TL = shear stress resulting from applied load on low ice content samples PH = force causing shear for high ice content samples PL = force causing shear for low ice content samples area of ice, high ice content 5.” A = area of ice, low ice content area of sand, high ice content sample a” ll ALS = area of sand, low ice content sample For a constant percent of maximum deviator stress MH=ML where MH - percent of maximum deviator stress high ice content sample ML = percentcf maximum deviator stress low ice content sample. 117 Assuming that the shear forces are proportional to the applied loads: PH = PH max X MH and PL = PL max X ML with PH max = maximum shear force resulting from the maximum deviator stress high ice content PL = maximum shear force resulting from the max maximum deviator stress low ice content For any given sample, let j equal the ice content expressed as a decimal fraction. Then the area of ice is proportional to the ice content in the sample, and AHI = "-'l— (6‘12) Since P max is proportional to the maximum applied loads, and the maximum applied loads are proportional to the ice content of the sample, as shown in Figure 6-5 _ PL max * PH max - 3 Using the Adhesion Theory of Friction (Lambe and Whitman, 1969), which states that an increase in normal loads must mean a proportional increase in area of contact between two bodies, the area of sand contact is: 11113:? 118 Substituting these relationships into equation 6-11 and solving: TH = iL mixMH) (6-13) ALI ALs and TL = .21.: mixmL) (6-14) ALI ALS ' but, MH r? and, therefore The above proof obviously is not rigorous because of the assumptions regarding the distribution of forces and the increase in area due to the applied loads. How- ever, the proof is useful for supporting the initial assumption that given a percent of maximum deviator stress, the resulting creep characteristics should be the same. Using this fact, the results from the tests on the reduced ice content samples are presented in a fashion similar to the high ice content samples. 119 A plot of strain rate versus strain for the various ice contents is shown in Figure 6-24. This figure demon- strates the invariance of creep behavior with respect to ice content. As an additional indication of the effect of various percents of ice, an intermediate percentage of ice of 70 percent has been included. At the applied axial stress of 750 psi the three different ice contents produce curves similar to those obtained by increasing the axial stress and holding the percent ice constant as was shown in Figure 6-23. As with the high ice content, there was a test in which the sample was subjected to high confining pressure for the entire test period. The results of test plotted as strain rate versus strain in Figure 6-25 shows that the effect of confining pressure is immediately apparent. The confined sample has a steadily decreasing strain rate through the entire test and has undergone much less strain ' than the unconfined sample. The substantial increase in slope of the curves as the percent of maximum deviator stress was reduced from 71 percent to 34 percent is apparent. The results of the step-stress_creep tests on reduced ice content samples shown in Figures 6-26 to 6-28 include three levels of deviator stress used for the high ice content samples. The increase in slope of the curves with decrease in percent of maximum deviator stress is common to all the step-stress creep tests conducted, and 120 indicates a definite response to increased confining pressures. Figure 6-28 is particularly interesting in this respect. Forthe uniaxial test, the sample proceeded into the tertiary range within 45 minutes after application of the axial stress of 750 psi. As the increments of confining pressure were applied, the creep rate decreased and at the end of the test there was no sign of failure, even though the time of the test was 90 minutes. Since the increments of confining pressure were applied at various time intervals, it may be misleading if strain rates obtained from Figure 6-28 are compared to strain rates from the other tests with lower percents of maximum shear stress. Figure 6-29 is a plot of the stress factor 2 versus strain rate for the reduced ice samples. AS With high ice content samples, there is a definite bilinear behavior. Reduced ice content samples are also more responsive to confining pressure in the 0-200 psi range. In order to describe the creep behavior of reduced ice Samples, it is possible to modify equation 6-7 such that the peak deviator stress is a function of the ice content. Therefore, an expression relating the deviator stress for the high and low ice contents can be written: DL = DH f(j) (6-15) 121 Deviator stress high ice content DH DL = Deviator stress low ice content assuming that the function is linear, as shown in Figure 6-5, then: U _ L _ _ ,. DH 3—- 03 — constant (6 16) Substituting this expression into equation 6-7, results in an equation for creep in terms of the applied deviator stress for reduced ice content and the percent of ice. D D e = b(t) exp(Ci 3;)exp (Gig3 TE) (6-l7) If the parameters b(t), Ci' and Gi are obtained from equation 6—10, it is possible to obtain strain rates for a time interval of one hour. The calculated and experimental results are tabulated in Table 6-1. The data show a good correlation between measured and calculated values and support equation 6-17 for calculating strain rates for reduced ice samples. Presentation of the creep test results as a function of percent of maximum deviator stress and the slope factor K in Figure 6-30 confirms the trend of increasing K with increasing values of M as was shown for high ice content samples. 122 From the discussion of results for the reduced ice content samples it can be stated that the creep character- istics of these samples are essentially the same as for the high ice content samples. If the two test series are related by the factor M, percent of maximum deviator stress, the formulations obtained for high ice content may be used. It is noted that considerable scatter occurs for some of the tests on the reduced ice samples. This scatter was due to difficulty in making duplicate low ice content samples. Even though the same amounts of sand and water were added to each sample, it is probable that the distri- bution of water in the pore spaces for the unsaturated condition may be different between any two samples, resulting in slightly different ice contents on the plane of maximum shear. It was originally assumed that a reduction in the percent of ice in a sample would accelerate the creep response so that it would be possible to study a wider range of loading conditions in a shorter amount of time. This has not proven to be the case. Rather, it has been demonstrated that for a given percent of maximum deviator stress the creep characteristics are essentially the same for both the high and low ice content samples. This fact may be useful in conducting experiments on frozen sand-ice materials where limited loading capabilities are available or for the analysis of partially saturated sand-ice systems. 123 TABLE 6-l.-—Calculated versus measured strain rates using Equation 6-l7, reduced ice content. Calc. Strain Measured Confining Rate Strain Saggle % Ice DL Pressure Eq 6-17 Rate % psi psi min-l min-1 -5 -5 93 60.8 400 0 3.3x10 . 4.2x10 97 58.8 640 0 1.10x10"5 1.1x10’5 120 64.6 640 600 1.7x10'5 3.6x10'5 94 59.4 400 0 3.5x10:g 4.5x10:§ 100 2.2x10_5 2.5x10_5 200 1.5x10_5 1.8x10_5 400 1.3x10_5 1.5x10_5 600 1.2x10 _5 1.3x10_5 800 1.06x10_S 1.2x10_5 1000 .89x10 .9x10 98 60.0 640 0 ll.0x10:§ 9x10:§ 100 5.7x10_5 5.4x10_5 200 3.1x10 2.7x10 Time of Measured Strain Rate = 60 min Temp. = 12.0° C 124 .mucmno mEsHo> co whammmum mcflcflmcoo mo uommmmll.alo ousmflm flmm .musmmmum mcHGflmcoo oom 02. oom oom oov oom ooa . ooa m 1 fl _ _ 1 . . - o.o . O . [1%, @ om m. o a o w m u 0 .A 1 ov. 8 III CHE OH x m®.N u w w // T . m: . n . a / UOO NHI I .H. m / l / A / / o m. A3 / om m o / T. :62 :83 6:6 mad // e W pcmm m3muuo cmuoumcs II II M m / D P / / l M.” l 8. e m 8 E / 0 m c... / T..- 1 84 w T: u 125 1600 — T = -12.0°c _ _ é = 2.66 x 10 min _ / 1200 ~ - -12.03°c _ -1 é = 1.33 x 10 min (Goughnour, 1967) = _ o 800 1 12°03 C —4 -1 ’ e = 2.66 x 10 min (Goughnour, 1967) Peak Strength, psi 400 _ T - -3.85°C _ -l é = 2.66 x 10 min (Goughnour, 1967) O l 1 J l l I 10 20 30 40 50 60 70 Percent Sand by Volume 7.0 2.50 2.33 1.50 1.00 0.667 0.429 Void Ratio Figure 6-2.--The effect of percent sand, temperature, and strain rate on peak strength. Peak Deviator Stress, psi 126 P 03 = 1000 ps1 = 700 psi 2800 - ‘ . / c3 — 640 p51 2 600 f- / T = _12.0°C - é = 0.266 x 10 min 2400 "' / 2200 __ c3 = 350 psi 2000 - // 1800 b / L43 = 100 psi Q/ / 3 /"/‘D / / O A. _ . o3 — 0 p51 1400 __ 1.. ’ A 1200 ' ‘ ‘ ' ‘ ‘ 60 61 62 63 64 65 Percent Sand by Volume 0.667 0.612 0.562 Void Ratio Figure 6—3.--Effect of confining pressure and void ratio on strength 127 15 _ T = -12.0°c _ -1 é = 2.66 x 10 min 0’) o \. H 0 3+ 10 - m m 3 1:,1—03 = 350 p51 0 u 4J m " —' r-i )— I, m o. 8 / 5 ,/”’ ___,_.03 = 700 psi H D4 Z 5 b M ’’’’’ * ..—--—O—-—'“"0"—” LO3=1000 psi O l l 1 1 62 63 64 Percent Sand by Volume 0.667 0.587 0.562 Void Ratio Figure 6-4.--Effect of confining pressure and void ratio on the principal stress ratio Peak Deviator Stress, psi 128 = -12.0°C T 6 =h2.66 x 10"3 min"1 , 2800 .- 2400 ._ 2000 '- 1600 +- 1200 b 800 400 r- 0 1 l I l I O 20 40 6O 80 100 Percent of Ice, % Figure 6-5.--Effect of ice content on strength. 129 oom oom HI oom cfiE m .mucmmmum mcflcflmcoo msmnm> cumcwuum ca cofluostmmll.olm wusmflm flmm .ousmmmum mcflcflmsou oom oom 00¢ oom oom OOH _ . . _ . 1. o u sow IOH N ©®.N UoO.NHl I OOH 001 x 90 - H0 unbuexns u: uornonpeu 130 .mowlpcmm so mnnmmoum mcficfimcoo mo uommmm HMUfim>BI|.hto ousmflm cfl\cfl .cflmuum Hmwxa onus 00. mo. v0. MO. ND. HO. . _ _ q q . . ; \JT \ pamww xflnumz. : 1 o O H MD 1 see m OH x eo.m u m met 1 H UOOONHI " rH. 4 A: a 0 came» 1 o xfluumz ems 005 u me o v¢¢ oom OOOH ooma OOON 00mm T. 15d ’89 - Principal Stress Ratio 36 32 28 24 20 16 12 131 T = -12.0°C e: 2.66 x 10-3 min- B (AlNouri, 1969) ” C) % Ice 3 100 [X % Ice E'55 I 1. 0 Ah 9 (Cohesive Component Due to Ice) _ O A Unfrozen Ottawa Sand I . 9 (Lee and Seed, 1967) _ __ __ A. o f _________ -1 r*—————(Frictional Component Due to Sand) *1 1 1 1 1 4 6 8 10 12 . . . 2 Confining Pressure, p51 x 10 Figure 6-8.--Principal stress ratio versus confining pressure. l Principal Stress Ratio 60 40_ 20 10 132 % Ice ; 100% — T = -12.0°C 1 \\- 6 = 2.66 x 10- min- \\ \\ \\ :;>. (Alnouri, 1969) %Ice=55 \ p- Unfrozen Ottawa Sand _~ _(Lee and Seed, 1967) 1 1 1 1 1 1 1 1 1 1 1 1 1 111 40 60 80 100 200 400 600 800 Confining Pressure, psi Figure 6-9.--Influence of confining pressure on the principal stress ratio. 133 .mmHmEMm oofllpcmm flmm .mHSmmmum mcflcflmcou OOOH oom oom 00h oom oom oov oom oom OCH 0 J. _ d 1 . q _ _ . e o w Aw AU 8 N u 4 4 same 4 : acoucou ooH 30A a v u LQ 1 a g 6 «V 11 o 4 Aeooac 4V 1 . pcoucoo on Ewe: a m 1 AV .1 m 1 0H How musaflmm um cflmuum Hafixfiul.oalo musmflm ’ezntreg 12 urexas Ierxv % 134 .Amosamb HMUflmxuv mofllcCMm How mafia mHDHHmm MM11.HH10 wusmam «OH x ewe .mxfime + ace 1 e .6 AN ma ma NH m o m - q . \\ . . \\ H1ces m-oa x co m u w xexumz 66H on \\ ooo.NH1 n B ucocomfioo HMCOHuome map ucmEmcflmcoo .\\\\ \\ \\ _ \ _ \ \ \\ \\ wmm u mod w .Il pawn Ho> mmm .\\\\\. a m \. . 0:: M \ \ \ . \\ _ \ Aneme .pmmm ppm mmec .\\\\ o newcomsoo 6>emmeoo Ucmm m3muuo CONOHMCD V\ 4 \\ o \ \ \\ \\ \\ \ \\\x 0 l \\ wOOH I OOH w 4 6686 Hop wmp mane ex M \0 30': x Isd"z/;(€o — To) = 5 I1 m NH Axial Strain Rate,min 135 #101 D = 640 psi _ M = 42.5% A Vol =-0.012 cc ‘#102 _4 D = 1070 psi 1 x 10 ‘ M = 70.5% _ A Vol = +0.144 cc ’ T = -12.0°C Time = i300 min )- -5 l x 10 . ~#108 ' D = 750 psi ‘ M = 49.0% ' A Vol = -0.054 cc b D = 400 psi M = 26% . A Vol = —0.078cc 3 x 10'.6 l L l I O .01 .02 .03 .04 True Axial Strain, in/in Figure 6-12.--Strain rate versus strain for uniaxial stress creep tests, high ice content. Axial Strain Rate, min _ .#118 03 = 600 psi M = 30% Avo1 = -0.220 cc 0 1 x 10-4 *- - n h- - #108 03 = 0 psi * #115 o 49% = ' 1 =-0.054 cc 03 210 p51 a 0 _ M = 38% A Vol = -0.012cc n o a 00 b n a T = -12.0°C D = 750 psi 1 x 10"5 t r L. 5 x 10-6 1 1 l l 0 .01 02 True Axial Strain, in/in Figure 6—13.--Strain rate versus strain for constant confining pressure test, high ice content. .mummu mmwuo pmcflmcoo tam Hafixmfics How mmmupm Mo mumumll.valo musmam “mmm .N\Am.o + H3 1.. Q Tmo .1— 137 o onupcmm cmnonm pmcflwcou u m “H ooHlpcmw cmnoum pmcwmcooco u d mumme moouu mmouum mo mumum ccmm cmuoumco \\ \\ i mmon>cm ondaflmm \\ 1 \ b \\ = \ ) \ o \. T. \x _ \ D 8" U cemxum Hmexa ucmumcoo 1 pcmm cmnoum .m omoam>cm mHsHflmm t. 138 Sample 109 T = -12.0°C M = 26% -4 03 = 0 1.x10 - r t 17.5% = 400 psi — M = 15.5% 03 = 600 p51 a - ' g M = 14% , 0 = 800 psi ‘ 3 °’ I 4..) m - a: I M = 13% G 0 = 1000 si .5 I / 3 P a; I / / '3 10"5 I I I .H — / é - / _ Cell Expansion __ (Typlcal) O G! P 91 3 x 10‘6 1 1 1 1 1 -005 .01 .015 True Axial Strain, in/in Figure 6-15.--Step-stress creep behavior for a deviator stress of 400 psi, high ice content. 139 Axial Strain Rate, min ' Sample 100 T = -12.0°c 1 x 10'4_ #— - M = 41.5% J— 03 = 0 p51 M = 366 1— 03 = 100 p8]. M = 22.5% -31. 5% 03 = 600 psi _ 0‘ \ 2=00 psi C) __ M= 25. 5% O 03 = 400 931 M = 20.5% Cell Expansion 93 = 800 P31 " / I / / / , / / / 1 x 10'5 - 0 O /' P 4 x 10"6 1 1 1 1 1 .0075 .010 .0125 .015 .0175 True Axial Strain, in/in Figure 6-16.-—Step-stress creep behavior for a deviator stress of 640 psi, high ice content. 140 L Sample 121 T = -12.0°c 1x 10"4 5 F‘ 37.5% I: = 400 psi '2 M a 32.0% a? 03 = 600 4.) g " M = 29.0% .5 / C3 = 800 g / m / m I "-4 Q I G 0 x 10"5 __ 1— o 0 P 4 x 10"6L 1 L 1 J 1 .01 .015 .020 True Axial Strain, in/in Figure 6-l7.--Step-stress creep behavior for a deviator stress of 750 psi, high ice content. 141 3 x 10-4 .. Sample 91 M = 69.5% o O O. T — ~12.0 C 1— 10’4 .. M = 45.5% H .— 03 = 350 p51 ‘2 1.. G" a} .. 4.) m 04 c --1 (U 1:— u 4..) U) H m S 10'5 —. L- 4 x 10‘6 1 1 1 1 1 .01 .02 .03 True Axial Strain, in/in Figure 6-18.--Step-stress creep behavior for a deviator stress of 1070 psi, high ice content. 142 .w MOHOMM mmmnum mcmum> mums :flmnumll.mauo wusmflm :flE .oumm :flmuum Hcflx¢ H x OH x N mIOH.x m mtoa H mt _ _ _ 1 _ q _ _ . _ _ _ 0081 mg l CON... _u H: H H mafia”. I. UoO.NHl H B I. 0 IL Gm 0mm 1 o I oom Hmat ewe cos n a moat l usmucoo 00H smem moms mmou 1mm 0 um um I. oov 3 101323 858133 m I D _ G = rsd Axial Strain Rate, min 8 x 10'5 1 x 10' 3 x 10' 143 Time = 1 hr after load // application /’ ’0 l as“? / 6'5 8 / D 65 ‘/ ° “/ 0 O 4 // 19 2 4 67> O /’ e / 6 0 /’ zll / O 9’5 4.500 / e o 0 l/ I ‘_60 / O 0 0 O 900 ¢ 0 // O 0 '5 ‘X000 / ° 0 ° ° 0 o // o o O o o o Constant 03 Lines T = -12.0°C 1 1 1 1 1 1 11, 1 l 200 400 600 800 1000 Deviator Stress, psi Figure 6-20.--Effect of confining pressure on strain rate. Slope m, min 3.0 2.5 2.0 ' .50" O 200 Figure 6-21.--810pe 2.975 x 10— 144 3 - 6.04 x 10‘ 0 m2 = 1.98 x 10"3 - 1.03 x 10’ l l I L 400 600 800 1000 Confining Pressure, psi value m versus confining pressure. 6 O -4 145 High Ice Content 150 _ )— U Uniaxial g 100 - . x C) Confined a V Step-Stress Q A = 400 psi .5 v = 640 psi >4 1- A = 750 psi ‘ = 1070 psi H 0 4J 8 1. o \ & One Cycle 2 50 Semi-Log m = E .- C V K 2 1 0 1 1 1 1 2O 4O 6O 80 100 M,% Figure 6-22.--Slope factor K versus percent of maximum deviator stress. 146 )1— -#107 M = 90% - % ice = 59.6 0 = 750 psi 1 x 10’3 - p— h.- h- T = ~12.0°C r-i |C 1— -g #97 3 % ice = 58.8 g 10-4 __ o = 640 p51 a _ "-1 1— m H h 13 U) h- H .3 5 #93 _ g r M = 48% % ice = 60.8 0 " c = 400 psi 1 x 10'5 - 5 xlO-6 ‘ ' 1 1 1 1 1 1 1 1 0 .01 .02 .03 .04 .05 True Axial Strain, in/in Figure 6-23.--Uniaxial creep test for reduced ice contents. 147 r- T = '12.0°C o = 750 psi 1x10- ITTTTI 1 #114 M = 68.5% % ice = 70.5 1x10" ! ll '1 1 Axial Strain Rate, min 1 1x10— - IT 7 x 10- True Axial Strain, in/in Figure 6—24.--Effect of various levels of ice content on uniaxial creep test behavior. Axial Strain Rate, min 148 1 x 10' IUTT I l x 10- III1 l T 1 x 10- 'T Ch I 7 x 10' o .01 .02 ‘ .03 .04 True Axial Strain, in/in Figure 6-25.--Effect of confining pressure on creep of low ice content samples. 149 low ice content. 4 x 10.4 _ Sample 94 T = -12.0°C 1 x 10'4 1- p— c ".1 _ E 6‘ E _ c "-1 m H 1— 4..) U) r-I m «4 £15. 1 x 10"5 - )- r- 6 x 10-6 1 1 1 1 1 1 1 1 1 1 -005 01 02 03 True Axial Strain, in/in Figure 6-26.--Step-stress creep behavior for deviator stress of 400 psi, 150 4 x 10'4 *- 1x10" _ M=60% . 03 = 100 psi M = 51.5% 5 Sample 112 G) 03 ' 200 P31 T = -12.0°C Axial Strain Rate, min 1 x 10- - True Axial Strain, in/in Figure 6-27.--Step-stress creep behavior for a deviator stress of 640 psi, low ice content. 151 1x10’3- — M = 70% _ 03 = 100 psi 03 = 200 p51 T: Sample 117 = _ o '2 T 12.0 C M = 51% J _ o 03 = 400 p51 “ / g / .E 9 0 M = 45% m 1x164 _ 03 = 600 p31 3 - 00-0 M = 40% x - U = 800 psi c 3 - I ° I / - o o 2 10—5 1 1 1 1 1 v x .02 .03 .04 True Axial Strain, in/in Figure 6—28.——Step-stress creep behavior for a deviator stress of 750 psi, low ice content. 152 .mmHmEMm ucmucoo wow 30H you w Houomm mmouum msmuw> mum“ cwmuumll.mmlo ousmwm a? cums seesaw H652 H o x x «IOHNH m1 H H oloa e d _ 41 _ _ fl _ _ _ q _ a d — _ _ _ _ q — 00v: 0 S 1 oom: n a S s 1 m o q o I 1 o 3 = G 1 . D m, 1 00m .d 3 To 0 o.ma .. a L. Hmnm 0mm. H C o I I . meow mmmn 1mm haat U um um L cow and ova u o maax ~11- 153 E] r 150 _ n: Curve for High Ice Content '1 P ‘1" 2 100 - x 1: D Uniaxial < O Confined -5 13 Step-Stress g“ £1 = 400 psi ‘7 = 640 psi 8 .LJ 0 m m m 04 .9 50 - m 0 l h 0 20 40 60 80 100 Figure 6-30.--Slope factor K versus percent of maximum deviator stress, low ice content. CHAPTER VII SUMMARY AND CONCLUSIONS 7.1 Shearing Resistance The shearing resistance of sand-ice materials has been studied in terms of the Mohr-Coulomb failure theory in which the shear strength is a summation of a cohesive term and a frictional term. For a constant temperature, it was shown that the cohesive term is dependent on the ice content and strain rate and is independent of the granular component for the percent sand by volume tested. The frictional component was shown to be dependent upon void ratio and independent of the strain rate and ice content. It was observed that the behavior of a sand— ice material is dependent on the magnitude of confining pressure applied to the system. For the unconfined test the ice matrix was the primary contributor to the strength of the material and when the ice matrix yielded, the sample progressed to failure. For confining pressures greater than 200 psi the sand-ice samples showed bilinear stress- strain characteristics. The initial portion of the stress-strain curve was attributed to the ice matrix ending at a matrix yield point. The second portion was due to the development of the frictional component of 154 155 ‘strength, which was dependent on the void ratio and the amount of confining pressure. It was shown that dilatancy contributes to the frictional strength of the sand-ice samples. When maximum deviator stresses are used to plot Mohr's circles, the failure envelope exhibits a slight curvature as the normal stress increases. Comparisons c: with unfrozen sand show that the cohesive and frictional components exist over the entire range of applied stresses. ~- The results indicate a system in which the cohesive com- ponent depends on the ice matrix and the frictional com- ponent has characteristics similar to those for unfrozen sands tested at high confining pressures. The major con- clusions regarding the shear resistance of sand-ice materials are as follows: 1. Dilatancy occurs in sand-ice samples tested to failure and decreases slightly with increasing confin- ing pressure. The dilatancy of sand-ice is less than for unfrozen sands tested at equal condition. 2. A decrease in void ratio (higher density) increases the peak strength for the range of void ratios tested. At higher confining pressures the effect is reduced and the ratio of principal stresses increases only slightly with smaller void ratios. 3. Smaller ice contents reduce the peak strength with a linear dependence on the ice content. This rela- tionship is independent of confining preSsure. 156 4. High confining pressures produce strength characteristics which are predominantly frictional in nature. 5. Failure strains increase as confining pres— sure increases and decrease slightly with reduced ice content. V 6. The failure envelope for sand-ice materials exhibits a slight curvature as normal stress increases, but for engineering design it can be approximated by a straight line. The effective angle cf internal friction approximates that for unfrozen sand at high confining pressure. This relationship is independent of the ice content. 7. The cohesive component of strength at failure decreased only slightly with increased confining pressure and remains essentially constant for a constant temper- ature and strain rate. 732 Creep Behavior The creep behavior of sand-ice materials was shown to follow "classical" behavior exhibited by other materials such as clays, metals and plastics. By con- ducting uniaxial creep tests at various levels of constant axial stress, the general creep characteristics of the sand-ice materials were obtained. Using these tests as a basis for comparison, the effects of confining pressure 157 were obtained using step-stress and confined testing techniques. The experimental results show that increases in confining pressure reduce strain rates. Confining pressures below 200 psi have the greater effect whereas above 200 psi creep rates decreases less rapidly with in. increased confining pressure. Step-stress testing proved useful in predicting the effects of confining pressure so that creep rate could be calculated as a function of *' the confining pressure and deviator stress. The expres- sion obtained was defined for regions both above and below 200 psi. Reduced ice contents have no basic effect on the shape of the creep curves. It was shown that the same equations used for high ice content samples can also be used for the reduced ice content samples when the deviator stress was modified. Finally, it was observed that all creep tests could be related by a term called the percent of maximum deviator stress, M. Tests conducted at equal percents of maximum deviator stress produced similar results and the decrease in strain rate for a particular value of M were the same for both high and reduced ice contents. Conclusions concerning the creep of sand-ice materials include: 1. For a constant deviator stress, strain rate is decreased exponentially by increasing confining 158 pressure. The high and low stress regions appear to be bounded by the common 200 psi stress level. 2. The effect of confining pressure on creep rate is greatest for pressures less than 200 psi. 3. Reduced ice content has no basic effect on the creep characteristics of sand—ice material but at i equal deviator stresses, higher strain rates occur for the reduced ice samples. n. 4. The applied deviator stress for high and reduced ice content samples can be related to the maximum deviator stress obtained from constant strain rate tests by a term M, percent of maximum deviator stress. Samples tested with the same percent of maximum deviator stress exhibit the same creep behavior and the resulting strain rates are equal. 5. The strain rate versus strain curve for sand- ice materials can be approximated using a constant slope factor K, which describes the decrease in strain rate per increment of strain for any given percent of maximum deviator_stress. BIBLIOGRAPHY 159 BIBLIOGRAPHY Abdel-Hady, M. A. "Rheological Properties of Bituminous Stabilized Soils." Unpublished Ph.D. disserta- tion, University of Illinois, 1964. AlNouri, I. "Time Dependent Strength Behavior of Two Soil Types at Lowered Temperatures." Unpublished Ph.D. dissertation, Michigan State University, 1969. Andersland, O. B., and Akili, W. "Stress Effects on Creep Rates of a Frozen Clay Soil." Geotechnique, XVII, No. 1 (March, 1967), 27-39. Andersland, O. B., and AlNouri, I. "Time Dependent Strength Behavior of Frozen Soils." Journal of the Soil Mechanics and Foundations DiViSion, ASCE, XCVI, No. SM4 (July, 1970), 1249-1268. Anderson, Duwayne M. "Ice Nucleation and the Substrate- Ice Interface." Nature, CCXVI (November, 1967). Dillon, H. B., and Andersland, O. B. "Deformation Rates of Polycrystalline Ice."' Proceedings of Inter— national Conference on Physics of Snow and Ice. The Institute of Low Temperature Science, Hokkaido University, Sapporo, Japan, August, 1967. Glasstone, S.; Laidler, H. J.; and Eyring, H. The Theory of Rate Processes. New York: McGraw-Hill Book CO., Inc., 1941. Glen, J. W. "The Creep of Polycrystalline Ice."' Pro- ceedings of Royal Society of London, Series A, 228, 1955, pp. 519-538. Gold, T. W. "Deformation Mechanisms in Ice." Chapter 2, Ice and Snow Properties, Processes and Applica- tions. .Edited by W. D. Kingery. Cambridge, Mass.: MIT Press, 1963. 160 161 Goughnour, R. R. "The Soil—Ice System and the Shear Strength of Frozen Soils." Unpublished Ph.D. dissertation, Michigan State University, 1967. Goughnour, R. R., and Andersland, O. B. "Mechanical Properties of a Sand-Ice System." Journal of the. Soil Mechanics and Foundations Division, ASCE, XCIV, No. SM4 (July, 1968), 923-950. Halbrook, T. R. "Mechanical Properties of Ice." Unpub- lished M.S. thesis, Michigan State University, 1964. Hall, E. B., and Gordon, B. B. "Triaxial Testing with Large Scale High Pressure Equipment.” Laboratory Shear Testing of Soils, Special Technical Publi- cation, No. 361, American Society for Testing and Materials, 1963, pp. 315-328. Hirschfeld, R. C., and Poulous, S. J. "High Pressure Triaxial Tests on a Compacted Sand and an Undis— turbed Silt." Laboratory Shear Testing of Soils, Special Technical Publication, No. 361, American Society for Testing and Materials, 1963, pp. 329-341. Jumikis, A. R. "Natural Freezing." Thermal Soil Mechanics. New Brunswick, N.J.: Rutgers Uni— versity Press, 1966. Kaplar, C. W. "Some Strength Properties of Frozen Soils ‘ and Effect of Loading Rate." Special Report 159, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, June, 1971. Koerner, R. M. "Effects of Particle Characteristics on Soil Strength." Journal of Soil Mechanics and Foundations Division, XCVI, No. SM4 (July, 1970), 1221-1234. Ladanyi, B. "An Engineering Theory of Creep of Frozen Soil." Canadian Geotechnical Journal, LXIII (September, 1972), 63-80. Lambe, T. W., and Whitman, R. V. "Shear Resistance Between Soil Particles." Soil Mechanics. New York: Wiley, 1969. 162 Lee, K. L., and Seed, H. B. "Drained Strength Charac- teristics of Sands." Journal of the Soil Mechanics and Foundations Division, ASCE, XCIII No. SM6 (November, 1967), 117-141. Leonards, G. A., and Andersland, O. B. "The Clay-Water System and the Shearing Resistance of Clays." Research Conference on Shear Strength of Cohes1ve Soils, ASCE, June, 1960, pp. 793—818. Mitchell, J. K. "Shearing Resistance of Soils as a Rate Process." Journal of Soil Mechanics and Founda- tions Division, ASCE, XC, No. SMl (January, 1964), 29-61. MitChell' J' K'7 Campanella, R- G.; and Singh, A. "Soil.“ Creep as a Rate Process." Journal of Soil Mechanics and Foundations Division, ASCE, XC, No. SMl (January, 1964), 29-61. Pounder, E. R. The Physics of Ice. Oxford: Pergamon Press, 19675 Sayles, F. J. "Creep of Frozen Soils." Technical Report 190, 1968, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire. Schmertmann,J. H., and Osterberg, J. 0. "An Experimental Study of the Development of Cohesion and Friction with Axial Strain in Saturated Cohesive Soils." Proc. Research Conference on Shear Strength of Cohesive Soils, ASCE (June, 1960), 643-694. Scott, F. S. "The Freezing Process and Mechanics of Frozen Ground." Cold Regions Science and Engineering Monograph ll-Dl, October, 1969, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire. Trollope, D. J., and Zafar, S. M. "A Study of Saturated Sand, and Sand: Clay Mixtures in Triaxial Com- pression." Proc. Second Australia-New Zealand Conference of Soil Mechanics and Foundation Engineering, I (1956), 7-13. Tsytovich, N. A. "Instability of Mechanical Properties of Frozen and Thawing Soil." Proc. of the Permafrost International Conference, National Academy of Sciences—National Council Publication No. 1287, 1963, pp. 325-331. 163 Tsytovich. N. A. "Mechanical Properties of Frozen Soils." Highway Research Board Special Report 58 (a trans- lation from Russian), Washington, D.C., 1960. Vesic, A. S., and Clough, G. W. "Behavior of Granular Materials Under High Stresses." Journal of Soil Mechanics and Foundations Division, ASCE, XCIV, No. SM3.(June, 1968), 661-688. Vialov, S. 8., ed. "Rheological Properties and Bearing Capacity of Frozen Soils." Translation 74, 1965a, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire. . 'The Strength and Creep of Frozen SOils and Calculations for Ice-Soil Retaining Structures." Translation 76, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, 1965b. Warder, David J. "Behavior and Analysis of a Model Soil-Ice Barrier." Unpublished Ph.D. disserta— tion, Michigan State University, 1969. Whitman, R. V. "The Behavior of Soils Under Transient Loading." Proc. Fourth International Conference of Soil Mechanics and Foundations Engineering, Vol. 1, London, 1957, pp. 207-210. Yong, R. N. "Soil Freezing Considerations in Frozen Soils Strength." Proc. of the Permafrost Inter- national Conference, National Academy of Sciences- National Research Council Publication No. 1287, 1963, pp. 315-319. APPENDICES 164 TABLE A-l CONSTANT AXIAL STRAIN RATE TEST DATA 165 TABLE A-1.--Constant Axial Strain Rate Test Data. SAMPLE NUMBER 1 SAMPLE NUMBER 4 TEMPERATURE STRAIN RATE PERCENT SAND = 61.6 PERCENT ICE 99.8 TOTAL VOLUME CHANGE = NA ”12.00 C 3 _'I - TEMPERATURE = -12.0° C 3 _] 2.66 x 10 min STRAIN RATE = 2.66 x 10' min 'PERCENT SAND = 63.5 PERCENT ICE = 97.4 TOTAL VOLUME CHANGE = NA CONFINING PRESSURE = 0 psi CONFINING PRESSURE = 0 psi TIME DEFL. LOAD TIME DEFL. LOAD (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) 1.0 0.001 95.0 0.0 0.0000 0.0 2.0 0.003 160.0 0.5 0.0004 20.0 3.0 0.007 250.0 1.0 0.0017 65.0 4.0 0.009 360.0 1.5 0.0039 105.0 5.0 0.012 510.0 2.0 0.0063 135.0 6.0 0.016 725.0 2.5 0.0086 175.0 7.0 0.019 945.0 3.0 0.0116 220.0 8.0 0.024 1125.0 4.0 0.0144 330.0 9.0 0.030 1285.0 5.0 0.0170 475.0 10.0 0.035 1345.0 6.0 000210 670-0 11.0 0.041 1395.0 7.0 0.0251 875.0 12.0 0.047 1395.0 8.0 0.0290 1100.0 13.0 0.052 1395.0 9.0 0.0343 1265.0 14.0 0.058 1360.0 10.0 0.0394 1360.0 15.0 0.064 1150.0 11.0 0.0452 1400.0 SAMPLE NUMBER 2 12.0 0.0508 1400.0 13.0 0.0564 1400.0 TEMPERATURE = -12.0° C _3 _1 14-0 0-0627 1380-0 STRAIN RATE = 2.66 x 10 min 15-0 0-0636 1345-0 PERCENT SAND = 52.] 16.0 0.0752 1290.0 PERCENT ICE = 92.8 17.0 0.0814 1230.0 TOTAL VOLUME CHANGE = NA 18.0 0.0870 1160.0 CONFINING PRESSURE = 0 psi 19.0 0.0888 1088.0 TIME DEFL. LOAD 20.0 0.0905 1010.0 (MIN.) (INS.) (LBS.) 21.0 0.0922 925.0 22.0 0.0938 860.0 23.0 0.0956 810.0 0.0 0.0 0.0 24.0 0.0976 770.0 1.0 0.0004 60.0 24.5 0.0987 750.0 2.0 0.0018 175.0 3.0 0.0048 330.0 4.0 0.0078 540.0 5.0 0.0110 815.0 6.0 0.0147 1055.0 7.0 0.0190 1245.0 8.0 0.0241 1350.0 9.0 0.0291 1415.0 10.0 0.0346 1455.0 11.0 0.0399 1480.0 12.0 0.0458 1495.0 13.0 0.0508 1495.0 15.0 0.0445 0.0 166 L4 01 \1 TABLE A 1.--Continueif_ SAMPLE NUMBER 7 ‘12.0° C _3 _] 2.66 x 10 min SAMPLE NUMBER 5 TEMPERATURE TEMPERATURE -12.0° C 3 _1 STRAIN RATE 2.66 x 10 min STRAIN RATE PERCENT SAND = 62.5 PERCENT SAND = 62.9 PERCENT ICE = 94.5 PERCENT ICE = 94.5 TOTAL VOLUME CHANGE = NA TOTAL VOLUME CHANGE = NA CONFINING PRESSURE = 0 psi CONFINING PRESSURE = 0 psi TIME DEFL. LOAD TIME DEFL. LOAD (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) 0.0 0.0000 0.0 0.0 0.0000 0.0 1.0 0.0010 10.0 1.0 0.0026 65.0 2.0 0.0043 125.0 2.0 0.0054 170.0 3.0 0.0078 240.0 3.0 0.0084 -330.0 4.0 0.0108 425.0 4.0 0.0117 555.0 5.0 0.0146 640.0 5.0 0.0154 800.0 6.0 0.0196 830.0 6.0 0.0186 1005.0 7.0 0.0238 1030.0 7.0 0.0231 1205.0 8.0 0.0289 1170.0 8.0 0.0283 1310.0 9.0 0.0344 1255.0 9.0 0.0341 1345.0 10.0 0.0408 1325.0 10.0 0.0401 1360.0 11.0 0.0455 1360.0 11.0 0.0461 1360.0 12.0 0.0509 1400.0 12.0 0.0522 1360.0 13.0 0.0569 1435.0 13.0 0.0586 1350.0 14.0 0.0617 1465.0 14.0 0.0647 1340.0 15.0 0.0677 1495.0 15.0 0.0708 1325.0 16.0 0.0740 1515.0 16.0 0.0769 1310.0 17.0 0.0800 1540.0 17.0 0.0829 1280.0 18.0 0.0861 1550.0 18.0 0.0887 1245.0 19.0 0.0905 1545.0 19.0 0.0948 1215.0 20.0 0.0965 1540.0 20.0 0.1010 1190.0 21.0 0.1028 1535.0 21.0 0.1072 1170.0 22.0 0.1084 1530.0 22.0 0.1133 1150.0 23.0 0.1148 1520.0 23.0 0.1193 1130.0 24.0 0.1202 1505.0 24.0 0.1255 1110.0 25.0 0.1267 1480.0 25.0 0.1318 1100.0 26.0 0.1327 1445.0 26.0 0.1384 1085.0 27.0 0.1402 1405.0 27.0 0.1449 1080.0 28.0 0.1459 1355.0 28.0 0.1512 1065.0 29.0 0.1515 1300.0 30.0 0.1581 1240.0 31.0 10.1642 1180.0 32.0 0.1707 1115.0 33.0 0.1763 1045.0 34.0 0.1830 990.0 35.0 0.1886 930.0 168 TABLE A-1.--Continued. SAMPLE NUMBER 10 TEMPERATURE -12.0° STRAIN RATE 2.66 x PERCENT SAND = 63.0 PERCENT ICE 95.0 TOTAL VOLUME CHANGE = NA CONFINING PRESSURE = 355 psi SAMPLE NUMBER 8 TEMPERATURE -12.0° C_3 _] STRAIN RATE 1.33 x 10 min PERCENT SAND = 62.9 PERCENT ICE 96.0 TOTAL VOLUME CHANGE = NA CONFINING PRESSURE = 0 psi C 10"3 min TIME DEFL. LOAD TIME DEFL. LOAD (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) 0.0 0.0 0.0 0.0 0.0000 0.0 1.0 0.0006 0.0 1.0 0.0037 165.0 2.0 0.0020 45.0 2.0 0.0080 345.0 3.0 0.0034 90.0 3.0 0.0126 540.0 4.0 0.0050 145.0 4.0 0.0172 765.0 5.0 0.0067 210.0 5.0 0.0222 960.0 6.0 0.0085 270.0 6.0 0.0276 1115.0 7.0 0.0104 355.0 7.0 0.0331 1225.0 8.0 0.0125 460.0 8.0 0.0388 1310.0 9.0 0.0146 580.0 9.0 0.0447 1385.0 10.0 0.0168 690.0 10.0 0.0505 1455.0 11.0 0.0192 780.0 11.0 0.0564 1515.0 12.0 0.0217 870.0 12.0 0.0621 1575.0 14.0 0.0270 1020.0 13.0 0.0680 1635.0 16.0 0.0336 1130.0 14.0 0.0738 1695.0 18.0 0.0394 1205.0 15.0 0.0796 1760.0 20.0 0.0454 1265.0 16.0 0.0856 1630.0 22.0 0.0514 1320.0 17.0 0.0914 1890.0 24.0 0.0574 1360.0 18.0 0.0974 1945.0 26.0 0.0633 1390.0 19.0 0.1032 1985.0 28.0 0.0694 1420.0 20.0 0.1091 2005.0 30.0 0.0755 1445.0 21.0 0.1152 2015.0 32.0 0.0816 1470.0 22.0 0.1214 2010.0 34.0 0.0878 1495.0 23.0 0.1277 1985.0 36.0 0.0937 1515.0 24.0 0.1338 1950.0 38.0 0.0998 1535.0 25.0 0.1399 1905.0 40.0 0.1061 1550.0 26.0 0.1462 1885.0 42.0 0.1126 1555.0 27.0 0.1523 1885.0 44.0 0.1188 1555.0 28.0 0.1585 1885.0 46.0 0.1250 1555.0 29.0 0.1645 1885.0 48.0 0.1312 1545.0 30.0 0.1706 1880.0 50.0 0.1375 1535.0 52.0 0.1436 1515.0 54.0 0.1498 1500.0 56.0 0.1560 1475.0 58.0 0.1623 1455.0 60.0 0.1688 1435.0 -1 ll"! 169 TABLE A-1.--Continued. -.--.___ SAMPLE NUMBER 13 TEMPERATURE -12.0° C _3 _] STRAIN RATE 2.66 x 10 min SAMPLE NUMBER 11 TEMPERATURE -12.0° C _3 _] STRAIN RATE 2.66 x 10 min PERCENT SAND = 62.9 PERCENT SAND = 62.8 PERCENT ICE 95.0 PERCENT ICE 97.5 TOTAL VOLUME CHANGE = NA TOTAL VOLUME CHANGE = NA CONFINING PRESSURE = 105 psi CONFINING PRESSURE = 350 psi TIME DEFL. LOAD TIME DEFL. LOAD (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) 0.0 0.0000 0.0 0.0 0.0 0.0 1.0 0.0040 75.0 1.0 0.0049 0.0 2.0 0.0082 155.0 2.0 0.0106 20.0 3.0 0.0125 240.0 3.0 0.0154 110.0 4.0 0.0169 345.0 4.0 0.0202 220.0 5.0 0.0213 480.0 5.0 0.0248 370.0 6.0 0.0255 660.0 6.0 0.0293 560.0 7.0 0.0305 850.0 7.0 0.0342 755.0 8.0 0.0358 1020.0 8.0 0.0393 930.0 9.0 0.0411 1170.0 9.0 0.0447 1070.0 10.0 0.0469 1270.0 0.0 0.0503 1180.0 11.0 0.0526 1340.0 0.0559 1260.0 2.0 0.0584 1405.0 0.0618 1320.0 13.0 0.0644 1455.0 0.0676 1365.0 14,0 0.0701 1500.0 0.0736 1420.0 15.0 0.0761 1540.0 0.0795 1465.0 16.0 0.0819 1580.0 0.0855 1510.0 17.0 0.0876 1615.0 0.0905 1550.0 18.0 0.0936 1640.0 0.0975 1585.0 19.0 0.0993 1670.0 0.1036 1615.0 20.0 0.1051 1695.0 0.1097 1630.0 21.0 0.1112 1720.0 0.1157 1630.0 22.0 0.1170 1735.0 0.1219 1615.0 23.0 0.1232 1745.0 0.1281 1590.0 24.0 0.1292 1755.0 0.1344 1575.0 25.0 0.1355 1755.0 0.1404 1570.0 26.0 0.1420 1745.0 0.1467 1565.0 27.0 0.1481 1735.0 0.1529 1560.0 28.0 0.1545 1700.0 0.1591 1550.0 29.0 0.1609 1675.0 0.1654 1550.0 30.0 0.1672 1635.0 0.1714 1540.0 0.1777 1530.0 0.1838 1520.0 0.1518 0.0 170 TABLE A-1.--Continued. SAMPLE NUMBER 18 TEMPERATURE -12.0° C 1 SAMPLE NUMBER 14 TEMPERATURE -12.0° C _3 _] 2 _ STRAIN RATE 2.66 x 10 min STRAIN RATE 2.66 x 10' min PERCENT SAND = 62.3 PERCENT SAND = 62.5 PERCENT ICE 97.5 PERCENT ICE 97.0 TOTAL VOLUME CHANGE = NA TOTAL VOLUME CHANGE = +0.193 cc CONFINING PRESSURE = 700 psi CONFINING PRESSURE = 700 psi TIME DEFL. LOAD TIME DEFL. LOAD (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) 0.0 0.0 0.0 0.0 0.0000 0.0 1.0 0.0051 100.0 0.1 0.0048 165.0 2.0 0.0104 205.0 0.2 0.0091 400.0 3.0 0.0154 355.0 0.3 0.0135 710.0 4.0 0.0202 545.0 0.4 0.0180 1090.0 5.0 0.0253 735.0 0.5 0.0223 1475.0 6.0 0.0302 955.0 0.6 0.0272 1810.0 7.0 0.0352 1150.0 0.7 0.0324 2055.0 8.0 0.0406 1325.0 0.7 0.0370 2135.0 9.0 0.0457 1440.0 0.8 0.0380 2130.0 10.0 0.0513 1525.0 0.9 0.0453 1815.0 11.0 0.0571 1605.0 12.0 0.0628 1675.0 13.0 0.0686 1740.0 14.0 0.0743 1800.0 15.0 0.0802 1870.0 16.0 0.0858 1940.0 17.0 0.0920 2010.0 18.0 0.0977 2080.0 19.0 0.1034 2160.0 20.0 0.1098 2230.0 21.0 0.1149 2295.0 22.0 0.1208 2360.0 23.0 0.1265 2425.0 24.0 0.1324 2480.0 25.0 0.1380 2530.0 26.0 0.1438 2575.0 27.0 0.1496 2615.0 28.0 0.1554 2650.0 29.0 0.1614 2685.0 30.0 0.1672' 2695.0 31.0 0.1735 2710.0 32.0 0.1793 2725.0 33.0 0.1854 2730.0~ 34.0 0.1914 2730.0 35.0 0.1974 2730.0 36.0 0.2035 2730.0 36.5 0.2065 2730.0 .1... 171 TABLE A-1.-—Coptinued. SAMPLE NUMBER —19 -‘ SAMPLE NUMBER 20 - ICE '-12.0° C _5 _] TEMPERATURE -12.0° C _3 _1 7.07 x 10_4min_1 STRAIN RATE 2.66 x 10 min 3.54 x10_3min_1 PERCENT SAND = O ‘ TEMPERATURE STRAIN RATE 1.76 x 10 min PERCENT ICE = 98.0 PERCENT SAND = 62.4 TOTAL VOLUME CHANGE = -0.403 cc PERCENT ICE = 97.5 CONFINING PRESSURE = 700 psi TOTAL VOLUME CHANGE = +0.362 cc TIME DEFL. LOAD CONFINING PRESSURE = 700 psi (MIN 1 (INS.) (LBS-1 TIME DEFL. LOAD (MIN.) (INS.) (LBS.) 0.0 0.0000 0.0 0.5 0.0025 60.0 0.0 0.0000 0.0 1.0 0.0049 135.0 25.0 0.0028 75.0 2.0 0.0098 275.0 50.0 0.0061 180.0 3.0 0.0149 415.0 75.0 0.0092 300.0 4.0 0.0206. 500.0 100.0 0.0124 425.0 5.0 0.0264 570.0 125.0 0.0159 520.0 6.0 0.0319 635.0 150.0 0.0196v 585.0 7.0 0.0378 685.0 175.0 0.0233 645.0 8.0 0.0436 715.0 200.0 0.0271 695.0 9.0: 0.0496 740.0 225.0 0.0308 740.0 10.0 0.0557 755.0 234.0 0.0321 745.0 12.0 0.0679 760.0 235.0' 0.0325 785.0 14.0 0.0802 750.0 240.0 0.0357 1000.0 16.0 0.0927 735.0 245.0 0.0392 1125.0 18.0 0.1047 715.0 250.0 0.0429 1215.0 20-0 0-1172 700.0 255.0 0.0466 1275.0 22.0 0.1296 690.0 260.0 0.0505 1325.0 24.0 0.1418 670.0 265.0 0.0544 1370.0 26.0 0.1510 665.0 275.0 0.0621 1445.0 28.0 0.1663 655.0 285.0 0.0700 1535.0 30.0 0.1784 650.0 295.0 0.0777 1625.0 32.0 0.1907 640.0 305.0 0.0856 1730.0 34.0 0.2027 635.0 315.0 0.0931 1835.0 36.0 0.2151 630.0 325.0 0.1009 1930.0 37.0 0.2210 630.0 335.0 0.1085 2000.0 345.0 0.1164 2105.0 355.0 0.1242 2190.0, 365.0 0.1319 2265.0 368.5 0.1347 2300.0 369.5 0.1363 2470.0' 370.0 0.1392 2675.0 371.0 0.1427 2800.0 272.0 0.1462 2885.0 373.0 0.1500 2940.0 374.0 0.1539 2970.0 375.0 0.1579 2980.0 376.0 0.1618 2975.0 377.0 0.1660 2965.0 377.5 0.1680 2945.0 TABLE A-1.--Continued. 172 SAMPLE NUMBER TEMPERATURE STRAIN RATE PERCENT SAND = PERCENT ICE TIME (MIN.) OOCDNO‘mkUNh-‘o 0.00.0.0... OOOOOOOOOOO p—o b—‘H Nb—o 0 00 13.0 14.0 15.0 16.0 17.0 .18.0 19.0 20.0 21.0 22.0 23.0 24.0 25.0 26.0 27.0 28.0 29.0 30.0 31.0 32.0 33.0 34.0 34.41 21 = -12.0° C _3 _] = 2.66 x 10 min 63.0 = 97.0 TOTAL VOLUME CHANGE = +0.662 CC CONFINING PRESSURE = 350 psi DEFL. LOAD (INS.) (LBS.) 0.0 0.0 0.0047 130.0 0.0095 320.0 0.0140 555.0 0.0187 835.0 0.0237 1105.0 0.0292 1305.0 0.0351 1430.0 0.0411 1510.0 0.0477 156000 0.0540 1580.0 0.0604 1610.0 0.0688 1635.0 0.0730 1670.0 0.0794 1700.0 0.0856 1730.0 0.0921 1770.0 0.0985 1810.0 0.1048 1840.0 0.1111 1860.0 0.1175 1875.0 0.1238 1895.0 0.1305 1915.0 0.1367 1935.0 0.1431 1955.0 001495 197000 0.1559 1980.0 0.1622 1985.0 0.1685 1980.0 0.1748 1975.0 0.1814 1945.0 0.1880 1915.0 0.1944 1890.0 0.2011 1890.0 0.2074 1890.0 0.2101 1875.0 0.1633 10.0 35.0 SAMPLE NUMBER 22 TEMPERATURE = -12.0° C _3 STRAIN RATE = 2.66 x 10 min PERCENT SAND = 62.8 PERCENT ICE = 96.0 TOTAL VOLUME CHANGE = NA CONFINING PRESSURE = 350 psi TIME DEFL. LOAD (MIN.) (INS.) (LBS.) 0.0 0.0 0.0 1.0 0.0041 130.0 2.0 0.0082 285.0 3.0 0.0125 500.0 4.0 0.0167 755.0 5.0 0.0212 1025.0 6.0 0.0265 1250.0 7.0 0.0318 1395.0 8.0 0.0375 1490.0 9.0 0.0435 1550.0 10.0 0.0493 1575.0 11.0 0.0555 1590.0 12.0 0.0615 1610.0 13.0 0.0676 1630.0 14.0 0.0738 1650.0 15.0 0.0796 1680.0 16.0 0.0857 1720.0 17.0 0.0918 1765.0 18.0 0.0979 1805.0 19.0 0.1040 1830.0 20.0 0.1100 1855.0 21.0 0.1161 1880.0 22.0 0.1222 1890.0 23.0 0.1285 1890.0 24.0 0.1349 1880.0 24.41 0.1374 1870.0 25.0 0.0952 0.0 -1 TABLE A-1.--Continued. 1731 SAMPLE NUMBER 24 TEMPERATURE -IZ.0° C _3 _] STRAIN RATE 2.66 x 10 min PERCENT SAND = 63.0 EST. PERCENT ICE = 96.0 EST. TOTAL VOLUME CHANGE = NA CONFINING PRESSURE = 350 psi TIME DEFL. LOAD (MIN.) (INS.) (LBS.) 1.0 0.0045 205.0 2.0 0.0087 410.0 3.0 0.0129 665.0 5.0 0.0223 1280.0 7.0 0.0334 .1470.0 10.0 0.0509 1635.0 13.0 0.0691 1730.0 16.0 0.0869 1885.0 19.0 0.1045 2075.0 22.0 0.1224 2225.0 25.0 0.1404 2285.0 27.0 0.1631 2275.0 SAMPLE NUMBER 26 .TEMPERATURE -12.0° C _3 _] STRAIN RATE 2.66 x 10 min PERCENT SAND = 62.0 PERCENT ICE 97.5 mbwmwoomqom¢umwo‘ TOTAL VOLUME CHANGE =+.656 cc CONFINING PRESSURE = 0 psi TIME DEFL. LOAD (MIN.) (INS.) (LBS.) 0.0 0.0 0.0 1.0 0.0029 105.0 2.0 0.0059 230.0 3.0 0.0093 355.0 4.0 0.0129 525.0 5.0 0.0168 730.0 6.0 0.0210 945.0 7.0 0.0257 1140.0 8.0 0.0305 1280.0 9.0 0.0360 1370.0 10.0 0.0417 1425.0 11.0 0.0476 1460.0 12.0 0.0536 1470.0 13.0 0.0596 1480.0 15.0 0.0719 '1480.0 17.0 0.0843 1470.0 19.0 0.0968 1470.0 21.0 001094 145000 23.0 0.1221 1410.0 23.62 0.1257 1395.0 24.0 0.1075 0.0 'TEMPERATURE STRAIN RATE ‘_SAMPLE NUMBER 27 -12.0° C _ 2.66 x 10 PERCENT SAND = 62.5 PERCENT ICE 96.5 3min"1 TOTAL VOLUME CHANGE =+0.403 cc CONFINING PRESSURE = 350 psi TIME (MIN.) OOOOOOOOOOOOOOCO 16.0 17.0 18.0 19.0 20.0 21.0 22.0 22.41 23.0 DEFL. (INS.) 0.0 0.0039 0.0081 0.0124 0.0166 0.0216 0.0269 0.0325 0.0382 0.0439 0.0499 0.0557 0.0617 0.0675 0.0734 0.0792 0.0850 0.0909 0.0967 0.1028 0.1089 0.1151 0.1214 0.1240 0.1124 LOAD (LBS.) 0.0 175.0 390.0 645.0 930.0 1165.0 1320.0 1430.0 1505.0 1540.0 1600.0 1650.0 1705.0 1760.0 1810.0 1870.0 1930.0 1990.0 2040.0 2070.0 2080.0- 2045.0 1985.0 1955.0 0.0 F- 174 TABLE A-1.--Continued. _.— _ -__. ._. SAMPLE NUMBER 28 SAMPLE NUMBER 34 TEMPERATURE TEMPERATURE -12.0° C 3 _] 2.66 x 10' ‘12.0° C _3 _'I STRAIN RATE 2.66 x 10 min STRAIN RATE min PERCENT SAND = 62.7 PERCENT SAND = 62.9 PERCENT ICE = 96.5 PERCENT ICE = NA TOTAL VOLUME CHANGE = +0.484 cc TOTAL VOLUME CHANGE = +0.282 cc CONFINING PRESSURE = 700 psi CONFINING PRESSURE = 0 psi TIME DEFL. LOAD TIME DEFL. LOAD (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) 1' 2.0 0.0095 415.0 1.0 0.0033 190.0 -. 3.0 0.0142 760.0 2.0 0.0064 370.0 A 4.0 0.0191 925.0 4.0 0.0144 905.0 “ 5.0 0.0241 1120.0 6.0 0.0243 1310.0 6.0 0.0303 1315.0 8.0 0.0355 1490.0 8.0 0.0414 1560.0 12.0 0.0593 1610.0 10.0 0.0529 1740.0 16.0 0.0817 1670.0 14.0 0.0759 2040.0 18.0 0.0958 1720.0 18.0 0-0992 2365-0 SAMPLE NUMBER 35 22.0 0.1224 2680.0 26-0 0-1458 2869-0 TEMPERATURE = -12.0° c _3 _] 29.0 0.1638 2885.0 STRAIN RATE = 2.66 x 10 min PERCENT SAND = 63.0 EST. ‘ * PERCENT ICE = NA SAMPLE NUMBER 33 TOTAL VOLUME CHANGE = NA CONFINING PRESSURE = 700 psi TEMPERATURE = -12.0° C _3 _] TIME DEFL. LOAD STRAIN RATE = 2.66 x 10 min PERCENT SAND = 62.4 (MIN') (INS') (LBS') PERCENT ICE = NA ' TOTAL VOLUME CHANGE = NA 1'3 3:333; $3213 TIME DEFL- LOAD 4'0 0.0182 1155.0 (MINo) (IN5°) (LBS') 6:0 0.0286 1530.0 . 8.0 0.0398 1725.0 1.0. 0-0025 95-0 10.0 0.0514 1820.0 29° 0-0060 300-0 14.0 0.0748 2020.0 4.0 0-0139 535-0 18.0 0.0980 2320.0 69° 0-0222 1905-0 22.0 0.1210 2605.0 8-0 °-°33° 1325-0 26.0 0.1444 2775.0 10.0 0.0445 1350.0 29.0 0.1620 2830.0 12.0 0-0667 1415-0 30.7 0.1726 2840.0 14.0 0.0689 1465.0 16.0 0.0809 1530.0 18.0 0.0932 1585.0 21.0 0.1118 1630.0 23.0 0.1246 1610.0 TABLE_A-1.--Continued. 175 SAMPLE NUMBER 36 SAMPLE NUMBER 38 continued. TEMPERATURE = -12.0° C _ _] (JiflE) (gfigLs (tggo) STRAIN RATE = 2.66 x 10 »_~——thu ' 4. 4 ' PERCENT SAND = 63.5 EST. 20-0 0-1052 2675-0 PERCENT ICE = 96.0 EST. 22~0 0-1165 3790-0 TOTAL VOLUME CHANGE = NA 24.0 0-1280 2875-0 CONFINING PRESSURE = 700 psi 26-0 0-1397 2960-0 TIME DEFL. LOAD 28.0 0.1517 2940.0 (MIN.) (INS.) (LBS.) 29.0 0.1577 2935.0 29.25 0.1591 2935.0 1.0 0.0047 320.0 30-0 °~1136 0'0 3:3 3:333: 333:3 39 2:3 813:3: {523:8 TEMPERATURE = -12.0° c _3 . _1 8.0 0.0398 1600.0 STRAIN RATE = 2.66 x 10 m1n 10.0 0.0514 1880.0 PERCENT SAND ‘ 53°2 14.0 0.0751 2085.0 PERCENT ICE = 97-0 18.0 0.0980 2400.0 TOTAL VOLUME CHANGE = +0.69§ CC 22.0 0.1208 2685.0 CONFINING PRESSURE = 360 p51 26.0 0.1438 2870.0 TIME DEFL- LOAD 30.0 0.1875 2970.0 (MIN°) (INS-1 (LBS-1 32.0 0.1794 2990.0 -3--- 0.0 0.0000 0.0 SAMPLE NUMBER 38 1.0 0.0042 140.0 2.0 0.0084 320.0 TEMPERATURE = -12.0° C _3 _] 3.0 0.0123 525.0 STRAIN RATE = 2.66 x 10 min 4.0 0.0166 775.0 PERCENT SAND = 63.0 5,0 0,0213 995,0 PERCENT ICE = 97.0 6.0 0.0262 1175.0 , TOTAL VOLUME CHANGE = +0.559 cc 7.0 0.0313 1310.0 CONFINING PRESSURE = 700 psi 8.0 0.0366 1420.0 TIME DEFL. .LOAD 9.0 0.0419 1520.0 (MIN.) (INS.) (LBS.) 10.0 0.0475 1615.0 , 12.0 0.0582 1775.0 0.0 30.0000 0.0 14.0 0.0693 1950.0 1.0 0.0044 190.0 16.0 0.0804 2095.0 2.0 0.0088 470.0 18.0 0.0917 2215.0 3.0 0.0132 740.0 20.0 0.1029 2315.0 4.0 0.0179 1010.0 22.0 0.1144 2370.0 5.0 0.0225 1230.0 24.0 0.1259 2375.0 6.0 0.0277 1400.0 25.0 0.1318 2350.0 7.0 -0.0330 1530.0 26.0 0.1378 2295.0 8.0 0.0383 1645.0 27.0 0.1017 0.0 9.0 0.0439 1750.0 10.0 0.0492 1840.0 12.0 0.0604 2010.0 14.0 0.0716 2200.0 16.0 0.0827 ,2375,0 18.0 0.0938 2535.0 176 TABLE A-1.--Continued. —_— ‘ -— SAMPLE NUMBER. 40 SAMPLE NUMBER 42 TEMPERATURE = -12.0° C _3 _1 TEMPERATURE = -12.0° C _3 _] STRAIN RATE = 2.66 x 10 min STRAIN RATE = 2.66 x 10 min PERCENT SAND = 63.0 PERCENT SAND = 62.8 PERCENT ICE = NA PERCENT ICE = 96.0 TOTAL VOLUME CHANGE = NA TOTAL VOLUME CHANGE = +0.240 cc CONFINING PRESSURE = 100 psi CONFINING PRESSURE = 0 psi TIME DEFL. LOAD TIME DEFL. LOAD (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) 1.0 0.0044 100.0 1.0 0.0033 140.0 2.0 0.0084 180.0 2.0 0.0062 275.0 4.0 ' 0.0165 435.0 3.0 0.0098 440.0 6.0 0.0248 910.0 4.0 0.0139 665.0 8.0 0.0348 1295.0 5.0 0.0185 900.0 10.0 0.0457 1495.0 6.0 0.0229 1100.0 12.0 0.0573 1630.0 8.0 0.0338 1345.0 14.0 0.0686 1730.0 10.0 0.0453 1440.0 16.0 0.0808 1790.0 12.0 0.0568 1480.0 17.0 0.0868 1790.0 13.0 0.0627 1485.0 18.0 0.0932 1770.0 14.0 0.0687 1482.0 SAMPLE NUMBER 43 SAMPLE NUMBER 41 TEMPERATURE = —12.0° C _3 _] TEMPERATURE = -12.0° C _3 STRAIN RATE = 2.66 x 10 min STRAIN RATE = 2.66 x 10 PERCENT SAND = 63.6 PERCENT SAND = 62.9 PERCENT ICE = 96.5 PERCENT ICE = 96.0 TOTAL VOLUME CHANGE = +0.426 cc TOTAL VOLUME CHANGE = +0.246 cc CONFINING PRESSURE = 0 psi CONFINING PRESSURE = 100 psi TIME DEFL. LOAD TIME DEFL. LOAD (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) . 0.0 0.0000 0.0 0.0 0.0000 0.0 1.0 0.0028 100.0 1.0 0.0035 80.0 2.0 0.0057 205.0 2.0 0.0070 135.0 4.0 0.0141 565.0 6.0 0.0248 965-0 8.0 0.0319 1385.0 8.0 0.0347 1285-0 10.0 0.0430 1545.0 10.0 0.0456 1505.0 12.0 0.0545 1635.0 12.0 0.0572 1645.0 13.0 0.0604 31660.0 14.0 0.0688 1735-0 14.0 0.0661 1660.0 16.0 0.0807 1770-0 15.0 0.0721 1650.0 16.5 0.0838 1755.0 15.25 0.0737 1640.0 17.0 0.0601 0.0 16.0 0.0548 A 0.0 177 TABLE A-I.--Conti ued. SAMPLE NUMBER 44 SAMPLE NUMBER 47 TEMPERATURE = -12.0° c _3 _] TEMPERATURE = -12.0° c STRAIN RATE = 2.66 x 10 min STRAIN RATE = 5,33 x 10'3min'] PERCENT SAND = 63.5 PERCENT SAND = 53.5 PERCENT ICE = 96.0 PERCENT ICE = 96.5 TOTAL VOLUME CHANGE = +0.450 cc TOTAL VOLUME CHANGE = +1.00 cc CONFINING PRESSURE = 700 psi CONFINING PRESSURE = 700 psi TIME DEFL. LOAD TIME DEFL. LOAD ‘ (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) 0.0 0.0000 0.0 0.0 0.0000 0.0 1.0 0.0043 250.0 1.0 0.0084 595.0 2.0 0.0084 530.0 2.0 0.0172 1305.0 4.0 0.0171 1170.0 3.0 0.0270 1865.0 6.0 0.0265 1740.0 4.0 0.0378 2145.0 8.0 0.0372 2070.0 5.0 0.0489 2305.0 10.0 0.0482 2220.0 6.0 0.0601 2455.0 12.0 0.0595 2355.0 7.0 0.0714 2585.0 14.0 0.0729 2535.0 8.0 0.0832 2675.0 16.0 0.0842 2660.0 9.0 0.0952 2770.0 18.0 0.0954 2800.0 10.0 0.1071 2885.0 20.0 0.1067 2935.0 11.0 0.1187 2980.0 22.0 0.1181 3040.0 12.0 0.1305 3035.0 22.5 0.1210 3050.0 13.0 0.1420 3050.0 22.75 0.1226 3045.0 14.0 0.1539 3060.0 24.0 0.0771 200.0 15.0 0.1658 3050.0 SAMPLE NUMBER _ ICE 16.0 0.1224 370.0 TEMPERATURE = -12.0° C _3 _] STRAIN RATE = 2.66 x 10 min PERCENT SAND = PERCENT ICE = 98.0 TOTAL VOLUME CHANGE = +0.294 cc CONFINING PRESSURE = 0 psi TIME DEFL. LOAD (MIN.) (INS.) (LBS.) 0.0 0.0 0.0 1.0 0.0032 120.0 2.0 0.0062 245.0 4.0 0.0148 460.0 6.0 0.0254 590.0 8.0 0.0368 660.0 10.0 0.0485 685.0 12.0 0.0602 685.0 15.0 0.0786 660.0 18.0 0.0967 630.0 21.0 0.1146 615.0 24.0 0.1325 580.0 27.0 0.1503 565.0 30.0 0.1682 560.0 31.75. 0.1746 550.0 178 TABLE A-T.--C0ntinaed. m ‘3 r -...._._'. J". ‘- SAMPLE NUMBER 48 SAMPLE NUMBER 50 TEMPERATURE = ~12.0° C _3 _] STRAIN RATE = 5.33 x 10 min PERCENT SAND = 53.2 PERCENT ICE 5 95.0 TOTAL VOLUME CHANGE = +0.745 cc CONFINING PRESSURE = 690 psi TEMPERATURE = -12.0° C _3 STRAIN RATE = 2.66 x 10 min PERCENT SAND = 63.7 PERCENT ICE = 96.0 TOTAL VOLUME CHANGE = +0.493 cc CONFINING PRESSURE = 700 psi «1 TIME DEFL. LOAD TIME DEFL. LOAD (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) 0.0 0.0000 0.0 0.0 0.0000 0.0 10.0 0.0046 210.0 1.0 0.0084 545.0 20.0 0.0092 445.0 2.0 0.0171 1250.0 30.0 0.0140 675.0 3.0 0.0265 1850.0 40.0 0.0190 885.0 4.0 0.0373 2135.0 50.0 0.0236 1065.0 5.0 0.0987 2290-0 60.0 0.0291 1215.0 6.0 0.0601 2435.0 70.0 0.0346 1355.0 7.0 0.0716 2585.0 80.0 0.0400 1475.0 8.0 0.0833 2720.0 100.0 0.0513 1715.0 9.0 0-0951 2840-0 120.0 0.0627 1935.0 10.0 0-1062 2950-0 140.0 0.0739 2145.0 11.0 0.1177 3040-0 160.0 0.0853 2330.0 12.0 0.1290 3100.0 180.0 0.0967 2535.0 13.0 0.1409 3120.0 200.0 0.1082 2695.0 13.5 0.1470 3130.0 220.0 0.1199 2840.0 14.0 0.1016 360.0 323:8 821232 33333919911114 51 7 . . 4 . 275.3 3.15:; 3323.3 TEMPERATURE = —12.0° C _ _] ' = 2 66 x 10 276.0 0.1072 360.0 STRAIN RATE - PERCENT SAND = 63.5 EST. PERCENT ICE = 96.0 EST. TOTAL VOLUME CHANGE = NA CONFINING PRESSURE = 660 psi TIME DEFL. LOAD (MIN.) (INS.) (LBS.) 1.0 0.0044 270.0 2.0 0.0087 535.0 3.0 0.0131 815.0 4.0 0.0177 1110.0 5.0 0.0226 1340.0 6.0 0.0277 1520.0 8.0 0.0355 1780.0 10.0 0.0500 1980.0 12.0 0.0613 2160.0 14.0 0.0726 2335.0 16.0 0.0840 2495.0 18.0 0.0955 2590.0 19.0 0.1014 2595.0 TABLE A-I.--Continued. SAMPLE TEMPERATURE STRAIN RATE NUMBER 52 .12.00 C -3 2.66 x 10 min PERCENT SAND_= 63.2 PERCENT ICE TOTAL VOLUME CHANGE = CONFINING PRESSURE = TIME (MIN.) OVOQNIO‘UTPUNHO 0.0.0.00... OOOCOCOOOOO HHHv—r-o OJ>N- .0. 0 o<>c>o DEFL. (INS. 0.0046 0.0084 0.0126 0.0171 0.0219 0.0269 0.0321 0.0375 0.0429 0.0484 0.0538 0.0594 0.0705 0.0816 0.0922 0.1036 0.1148 0.1264 0.1378 0.1426 0.1020 ) 96.5 LOAD (LBS.) 0.0 190.0 425.0 700.0 985.0 1215.0 1395.0 1535.0 1650.0 1750.0 1650.0 1940.0 2030.0 2215.0 2385.0 2540.0 2655.0 2745.0 2800.0 2830.0 2830.0 260.0 +0.60] 640 psi -1 CC 179 SAMPLE NUMBER TEMPERATURE = STRAIN RATE = PERCENT SAND = PERCENT ICE CONFINING PRESSURE TIME (MIN.) pinyin bUNHOOGNOm¢UNHOO p... COOOOOOOOOOOOOOOU‘O Hru 0“." 17.0 18.0 19.0 ~12.0° C 4.42 x 10‘3min 62.7 = 57.0 TOTAL VOLUME CHANGE = NA = 0 psi DEFL. LOAD (INS.) (LBS.) 0.0000 0.0 0.0033 67.0 0.0071 121.0 0.0142 264.0 0.0204 436.0 0.0271 616.0 0.0342 767.0 0.0419 873.0 0.0510 909.0 0.0610 865.0 0.0717 755.0 0.0833 631.0 0.0953 475.0 0.1083 298.0 0.1204 220.0 0.1308 188.0 0.1411 164.0 0.1510 155.0 .0.1611 142.0 0.1713 132.0 0.1817 126.0 0.1920 121.0 20.0 -1 P TABLE A-1.--Continued. 180 SAMPLE NUMBER 73 SAMPLE NUMBER 76 TEMPERATURE = -12.0° C _3 _] TEMPERATURE = -12.0° C _3 _] STRAIN RATE = 2.66 x 10 min STRAIN RATE = 2.66 x 10 min PERCENT SAND = 62.] PERCENT SAND = 63.4 PERCENT ICE = 53.6 PERCENT ICE = 58.2 TOTAL VOLUME CHANGE = NA TOTAL VOLUME CHANGE = NA CONFINING PRESSURE = 350 psi CONFINING PRESSURE = 700 psi TIME DEFL. LOAD TIME DEFL. LOAD (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) 000 000000 000 0.0 0.0000 000 2.0 0.0073 325-0 2.0 0.0097 500.0 3.0 0.0113 478.0 5.0 0.0270 '1161.0 4.0 0.0152 620.0 7.0 0.0389 1438.0 5.0 0.0197 733.0 10.0 0.0565 1797.0 8.0 0.0338 1109.0 12.0 0.0676 1992.0 10.0 0.0440 1302.0 15.0 0.0845 2252.0 12.0 0.0546 1463.0 17.0 0.0964 2372.0 14.0 0.0956 1559.0 20.0 0.1164 2459.0 16.0 0.0770 1678.0 22.0 0.1266 2405.0 18.0 0.0892 1709.0 25.0 0.1428 2377.0 20.0 0.1040 1683.0 30.0 0.1696 2313.0 25.0 0.1352 1572.0 33.0 0.1859 2260.0 30.0 0.1691 1465.0 35.0 0.1963 2230.0 35.0 0.2038 1303.0 40.0 0.2232 2136.0 40.0 0.2373 1163.0 45.0 0.2499 2055.0 45.0 0.2697 1077.0 q SAMPLE NUMBER 74 SAMPLE NUMBER 77 TEMPERATURE = -12.0° C _3 _1 TEMPERATURE = -12.0° C _3 _1 STRAIN RATE = 2.66 x 10 min STRAIN RATE = 2.66 x 10 min PERCENT SAND = 62.5 PERCENT SAND = 62.3 PERCENT ICE = 55.8 PERCENT ICE = 95.0 TOTAL VOLUME CHANGE = NA TOTAL VOLUME CHANGE = +0.890 cc CONFINING PRESSURE = 1000 p51 CONFINING PRESSURE = 1000 psi TIME DEFL. LOAD TIME DEFL. LOAD (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) 0,0 0.0 0.0 0.0 0.0000 0.0 1.0 0.0059 214.0 2.0 0.0082 464.0 2.0 0.0104 487.0 5.0 0.0229 1451.0 4.0 0.0208 975.0 7.0 0.0356 1940.0 6.0 0.0318 1307.0 10.0 0.0568 2160.0 8.0 0.0428 1607.0 12.0 0.0693 2314.0 10.0 0.0542 1880.0 15.0 .0.0877 2548.0 12.0 0.0658 2135.0 17.0 0.0998 2689.0 14.0 0.0774 2365.0 20.0 0.1182 2873.0 16.0 0.0895 2551.0 22.0 0.1291 2961.0 18.0 0.1013 2653.0 24.7 0.1471 3040.0 20.0 _ 0.1131 2715.0 26.0 0.1551 3012.0 22.0 0.1251 2144.0 28.0 0.1652 2945.0 24.0 0.1377 2737.0 30.0 0.1745 2938.0 26.0 0.1496 2684.0 28.0 0.1609 2660.0 181 TABLE A-T.--Continued. 78 SAMPLE NUMBER SAMPLE NUMBER 80 TEMPERATURE -12.0° C 3 _] TEMPERATURE -12.0° C 3 _] STRAIN RATE 2.66 x 10' min STRAIN RATE 2.66 x 10' min PERCENT SAND = 62.9 PERCENT SAND = 63.4 PERCENT ICE = 55.0 PERCENT ICE = 95.5 TOTAL VOLUME CHANGE = NA TOTAL VOLUME CHANGE = +1.184 cc CONFINING PRESSURE = 100 psi CONFINING PRESSURE = 200 psi TIME DEFL. LOAD TIME DEFL. LOAD (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) 0.0 0.0000 0.0 0.0 0.0000 0.0 1.0 0.0092 125-0 1.0 0.0036 208.0 2.0 0.0086 259.0 2.0 0.0074 495.0 4.0 0.0190 572.0 3.0 0.0111 820.0 6.0 0.0313 809.0 4.0 0.0159 1172.0 8.0 0.0431 964.0 5.0 0.0198 1467.0 10.0 0.0558 1055.0 6.0 0.0248 1665.0 10.3 0.0581 1060.0 7.0 0.0311 1732.0 12.0 0.0689 1045.0 8.0 0.0375 1793.0 15.0 0.0875 988.0 9.0 0.0445 1852.0 20.0 0.1199 848.0 10.0 0.0508 1810.0 25.0 0.1537 702.0 11.0 0.0579 1725.0 30.0 0.1883 576.0 12.0 0.0639 1664.0 35.0 0.2214 999.0 SAMPLE NUMBER 81 39.0 0.2474 485.0 TEMPERATURE = -12.0° C -3 -1 SAMPLE NUMBER 79 0 STRAIN RATE = 2.55 x 10 min TEMPERATURE = -12.0° C _3 _] PERCENT SAND: 92265 STRAIN RATE = 2.66 x 10 min PERCENT ICE ' - PERCENT SAND = 63.7 TOTAL VOLUME CHANGE - +1.178 cc PERCENT ICE = 59 4 CONFINING PRESSURE = 1000 p51 ' 4 = TIME DEFL. LOAD TOTAL VOLUME CHANGE NA (M N ) (INS , (LBS ) CONFINING PRESSURE = 0 psi 1 ' ° ° TIME DEFL. LOAD (MIN.) (INS.) (L85.) §:g 3:3};3 133313 4.0 0.0228 1413.0 9'3 3'8323 lag'g 5.0 0.0293 1694.0 ' 2‘0 0'0109 369'0 6.0 0.0363 1888.0 3'0 0:0179 558'0 7.0 0.0436 2035.0 4'0 0 0254 096’0 8.0 0.0511 2144.0 5'0 0’0324 801.0 9.0 0.0588 2247.0 6'0 0‘0405 537’0 10.0 0.0662 2362.0 7:0 020485 655:0 12.0 0.0807 2552.0 8.0 0.0559 852.0 14.0 0.0950 2758.0 10 0 0 071# 786 0 16.0 0.1093 2907.0 .' ' ‘ 18.0 0.1236 3022.0 15.0 3'2902 592'0 20.0 0.1382 3083.0 2070 o'lgf§ ggg°g 22.0 0.1527 3121.0 25°0 0'1559 201.0 24.0 0.1676 3013.0 ,' ° ° 26.0 0.1824 3086.0 30.0 0.2135 3000.0 .182 TABLE A-1.--C0ntinued. SAMPLE NUMBER 84 “12.00 C -3 _II 2.66 x 10 min SAMPLE NUMBER 82 TEMPERATURE = '12.0° C 3 _] STRAIN RATE = TEMPERATURE = 2.66 x 10' min STRAIN RATE PERCENT SAND = 62.8 PERCENT SAND = 63.7 PERCENT ICE = 97.0 PERCENT ICE = 95.5 TOTAL VOLUME CHANGE = NA TOTAL VOLUME CHANCE = NA . CONFINING PRESSURE = 200 psi CONFINING PRESSURE = 100 p51 TIME DEFL. LOAD TIME DEFL. LOAD (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) 0.0 2.264 0.0 1.0030.S 0.0031 80.0 1.0 0.0059 131.0 1.0 0.0068 168.0 2.0 0.0111 281.0 2.0 0.0123 450.0 3.0 0.0149 510.0 3.0 0.0174 794.0 4.0 0.0186 791.0 4.0 0.0226 1184.0 5.0 0.0222 1087.0 5.0 0.0284 1546.0 6.0 0.0264 1371.0 6.1 0.0362 1680.0 7.0 0.0313 1637.0 7.0 0.0424 1657.0 8.0 0.0371 1805.0 10.0 0.0607 1555.0 9.0 0.0437 1894.0 15.0 0.0882 1532.0 10.0 0.0505 1943.0 20.0 0.1258 1500.0 11.0 0.0576 1984.0 25.0 0.1555 1409.0 13.0 0.0705 2025.0 16.0 0.0877 1973.0 20.0 0.1112 1906.0 25.0 0.1387 1786.0 SAMPLE NUMBER 87 28.0 0.1544 1728.0 SAMPLE NUMBER 83 TEMPERATURE = -12.0° C _3 _] STRAIN RATE = 2.66 x 10 min TEMPERATURE = -12.0° C 1 PERCENT SAND = 63-2 STRAIN RATE = 2,55 x 10'3m1n‘ PERCENT ICE = 32.9 PERCENT SAND = 63.5 TOTAL VOLUME CHANGE = NA PERCENT ICE = 95,0 CONFINING PRESSURE = 100 psi TOTAL VOLUME CHANCE = NA TIME DEFL. LOAD CONFINING PRESSURE = 0 psi (MIN.) (INS.) (LBS.) TIME DEFL. LOAD (MIN.) (INS.) (LBS.) 1.0 0.0055 168.0 2.0 0.0110 322.0 1.0 0.0037 173.0 2.5 0.0138 400.0 2.0 _0.0078 378.0 3.0 0.0168 471.0 3.0 0.0111 613.0 4.0 0.0234 600.0 4.0 0.0195 570.0 5.0 0.0303 705.0 5.0 0.0184 1139.0 6.0 0.0377 782.0 6.0 0.0230 1358.0 7.0 0.0455 824.0 7.0 0.0288 1502.0 7.5 0.0495 838.0 8.0 0.0348 1564.0 8.0 0.0533 828.0 9.0 0.0416 1597.0 10.0 0.0677 799.0 11.0 0.0546 1537.0 15.0 0.0983 695.0 13.0 0.0671 1496.0 20.0 0.1286 575.0 15.0 0.0801 1438.0 20.0 0.1127 1215.0 25.0 0.1499 840.0 30.0 0.1892 322.0 35.0 0.2251 170.0 F. 183 TABLE A-1.-—Continued. SAMPLE NUMBER S-T UNFROZEN SAND SAMPLE NUMBER 88 TEMPERATURE = -12.0° C TEMPERATURE = 20° C _3 _] STRAIN RATE = 2.66 X 10-3 STRAIN RATE = 2.66 X 10 min PERCENT SAND = 64.3 PERCENT SAND = 64.0 PERCENT ICE = 98.0 PERCENT ICE = 0 TOTAL VOLUME CHANGE = NA CONFINING PRESSURE = 100 psi CONFINING PRESSURE = 110 psi TIME DEFL. LOAD TIME DEFL. LOAD AV (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) (CC) 0.5 0.0020 105,0 1.0 _ 0.0059 64.0 +0.10 1.0 0.0042 300.0 3.0 0.0179 182.0 +0.15 2.0 0.0093 474.0 5.0 0.0298 244.0 +0.05 3.0 0.0143 793.0 10.0 0.0625 310.0 +0.20 4.0 0.0199 1188.0 15.0 0.0935 335.0 +0.40 4.7 0.0239 1451.0 20.0 0.1254 346.0 +0.60 5.0 0.0253 1553.0 25.0 0.1574 341.0 +0.95 5.7 0.0315 1640.0 30.0 0.1896 332.0 +1.15 6.0 0.0330' 1620.0 35.0 0.2216 313.0 +1.30 7.0 0.0406 1574.0 40.0 0.2540 297.0 +1.40 9.0 0.0523 1495.0 45.0 0.2870 277.0 +1.50 11.0 0.0636 1432.0 50.0 0.3195 ~255.o +1.50 65.0 0.4151 243.0 +1.50 SAMPLE NUMBER 89 SAMPLE NUMBER ’S-2 UNFROZEN SANL TEMPERATURE = -12.0° C _3 _1TEMPERATURE = 20° C 3 1 STRAIN RATE = 2.66 x 10 min STRAIN RATE = 2.66 x 10' min- PERCENT SAND = 63.0 PERCENT SAND = 54.0 PERCENT ICE = 99.0 PERCENT ICE = 0 TOTAL VOLUME CHANGE = NA CONFINING PRESSURE = 100 psi CONFINING PRESSURE = 48 psi TIME DEFL. LOAD TIME DEFL. LOAD AV (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) (CC) 0.5 0.0027 107.0 0.0 0.0000 0.0 0.0 1.0 0.0060 222.0 1.0 0.0060 » 5200 “0.05 1.5 0.0083 355.0 3.0 0.0184 104.0 -0.10 ,2,0 0.0111 506.0 5.0 0.0307 122.0 -0.05 3.0 0.0167 857.0 10.0 0.0626 144.0 +0.25 4.0 0.0223 1227.0 15.0 0.0951 152.0 +0.55 4.5 0.0273 1412.0 20.0 0.1267 156.0 +0.85 ‘5.0 0.0313 1500.0 25.0 0.1593 148.0 +1.05 5.5 0.0358 1534.0 30.0 0.1913 136.0 +1.30 6.0 0.0406 1532.0 35.0 0.2237 126.0 +1.40 8.0 0.0560 1330.0 40-0 0-2542 118-0 LEAK 10.0 0.0659 1203.0 45-0 0-2881 115.0 48.0 0.3073 114.0 184 TABLE A-1.--Continued. SAMPLE NUMBER S-3 UNFROZEN SANDSAMPLE NUMBER S-4 UNFROZEN SAND TEMPERATURE = 20° C _3 _] TEMPERATURE = 20° C _3 _] STRAIN RATE = 2.66 x 10 min STRAIN RATE = 2.66 x 10 min PERCENT SAND = 64.0 PERCENT SAND = 64.0 PERCENT ICE = o PERCENT ICE = 0 CONFINING PRESSURE = 21.5 psi CONFINING PRESSURE = 14.3 psi TIME DEFL. LOAD AV TIME DEFL. LOAD AV (MIN.) (INS.) (LR5.1 (CC) (MIN.) (INS.) (LBS.) (CC) 1.0 0.0400 6.0 -0.01 0.0 0.0000 0.0 +0.0 2.0 0.0040 24.0 -0.03 0.5 0.0050 3.0 -0.03 3.0 0.0090 42.0 -0.07 1.0 0.0080 5.0 -o.o4 4.0 0.0180 56.0 -0.09 2.0 0.0110 10.0 -0.09 5.0 0.0260 67.0 -0.07 3.0 0.0190 23.0 -0.20 6.0 0.0360 75.0 +0.0 4.0 0.0280 32.0 -0.27 7.0 0.0460 89.0 +0.09 5.0 0.0380 39.0 -0.32 8.0 000570 10000 +0.17 600 0.0490 4400 “0.32 9.0 0.0670 111.0 +0.38 7.0 0.0590 48.0 -0.32 10.0 0.0800 115.0 +0.43 8.0 0.0700 52.0 -o.25 11.0 0.0930 116.0 +0.72 9-0 0-0810 55.0 -0.14 12.0 0.1050 116.0 +0.89 10.0 0.0930 56.0 +0.03 13.0 0.1160 117.0 +1.10 11.0 0.1040 58.0 +0.09 16.0 0.1280 128.0 +1.28 12-0 0-1160 60-0 +0.20 17.0 0.1400 120.0 +1.49 13.0 0.1280 62.0 +0.29 18.0 0.1520 120.0 +1.70 14.0 0.1410 63.0 +0.42 19.0 0.1640 121.0 +1.88 15-0 0-1520 64-0 +0.55 20.0 0.1820 117.0 +2.14 16.0 0.1640 65.0 +0.67 21.0 0.2020 116.0 +2.40 17.0 0.1760 65.0 +0.85 22.0 0.2130 116.0 +2.57 18.0 0-1880 65-0 +1.00 23.0 0.2290 116.0 +2.74 19-0 0-2000 65-0 +1.16 24.0 0.2510 116.0 20.0 0.2110 66.0 +1.26 25.0 0.2630 115.0 21.0 0.2250 66.0 +1.46 26.0 0.2770 115.0 22.0 0.2350 66.0 +1.61 27.0 0.3010 112.0 23.0 0.2500 96-0 +1.71 28.0 0.3170 112.0 24.0 0.2620 66.0 +1.85 29.0 0.3350 112.0 25.0 0.2740 66.0 +1.99 30.0 0.3410 112.0 26.0 0.2860 66.0 +2.09 31.0 0.3420 100.0 27.0 0.2980 65.0 +2.21 r 185 TABLE A-1.--Continued. SAMPLE NUMBER S-5 UNFROZEN SAND - SAMPLE NUMBER S-6 UNFROZEN SAND TEMPERATURE = 20° C . _3 _] STRAIN RATE = 2.66 x 10 min TEMPERATURE = 20° C _3 _1 PERCENT SAND = 64.0 STRAIN RATE = 2.66 x 10 min PERCENT ICE = 0 PERCENT SAND = 64 PERCENT ICE = 0 CONFINING PRESSURE = 28.6 psi TIME DEFL. LOAD AV CONFINING PRESSURE = 50 psi (MIN.) ((INS.) (LBS.) (CC) TIME DEFL. LOAD AV (MIN.) (INS.) (LBS.) (CC) 0.0 0.0000 0.0 0.0 1.0 0.0020 27.0 -0.03 0.0 0.0000 0.0 0.0 2.0 0.0020 37.0 -0.03 1.0 .0055 60.0 0.0 3.0 0.0120 54.0 -0.05 3.0 0.0173 120.0 -0.01 4.0 0.0200 67.0 -0.08 5.0 0.0297 139.0 -0-20 5.0 0.0300 89.0 -0.08 10.0 0.0608 157.0 -0.10 6.0 0.0400 109.0 -0.02 15.0 0.0942 162.0 +0.10 7.0 0.0510 123.0 +0.02 20.0 0.1242 192.0 +0.30 8.0 0.0640 131.0 +0.14 25.0 001542 15700 +0.40 9.0 0.0770 136.0 +0.30 30.0 0.1818 152.0 10.0 0.0900 140.0 +0.45 35.0 0.2004 151.0 11.0 0.1020 144.0 +0.60 12.0 0.1120 147.0 +0.76 13.0 0.1260 149.0 +0.91 14.0 0.1380 152.0 +1.21 15.0 0.1510 155.0 +1.41 16.0 0.1620 158.0 +1.61 17.0 0.1760 160.0 +1.82 18.0 0.1890 162.0 +2.03 19.0 0.2020 163.0 +2.27 20.0 0.2130 164.0 +2.45 21.0 0.2270~ 164.0 +2.70 22.0 0.2400 165.0 +2.88 23.0 0.2520- 165.0 +3.06 24.0 0.2650 166.0 +3.24 25.0 0.2770 166.0 +3.32 26.0 0.2920 164.0 +3.50 27.0 0.3050 162.0 +3.68 28.0 0.3180 156.0 +3.86 TABLE A-2 CREEP TEST DATA 186 TABLE A-2.--Creep Test Data. SAMPLE NUMBER UNIAXIAL TEMPERATURE = -12.0° C CONSTANT AXIAL STRESS = PERCENT SAND = 63.3 _PERCENT ICE = 94-7 TOTAL VOLUME CHANGE = +0.228 cc TIME (MIN.) 1.0 10.0 30.0 60.0 90.0 120.0 150.0 180.0 210.0 240.0 270.0 300.0 310.0 322.0 322.0 330.0 DEFL. (INS.) 0.0176 0.0265 0.0361 0.0444 0.0501 0.0544 0.0580 0.0613 0.0639 0.0663 0.0686 0.0706 0.0712 0.0720 0.0644 0.0620 LOAD (LBS.) 1074.0 1074.0 1072.0 1066.0 1065.0 1065.0 1065.0 1064.0 1065.0 1065.0 1067.0 1065.0 1065.0 0.0 0.0 1070 psi SAMPLE NUMBER 91' STEP-STRESS TEMPERATURE = -12.0° C CONSTANT AXIAL STRESS = PERCENT SAND = PERCENT ICE = 95.1 TOTAL VOLUME CHANGE = +0.108 CC TIME (MIN.) 1.0 10.0 20.0 30.0 60.0 90.0 120.0 150.0 180.0 187.0 191.0 200.0 210.0 240.0 270.0 300.0 330.0 360.0 380.0 187 DEFL. (INS.) 0.0181 0.0262 0.0311 0.0348 0.0427 0.0482 0.0527 0.0563 0.0594 0.0600 0.0663 0.0672 0.0681 0.0700 0.0714 0.0724 0.0737 0.0749 0.0757 63.6 LOAD (LBS.) 1077.0 1086.0 1087.0. 1090.0 1095.0 1097.0 1104.0 1105.0 1104.0 1108.0 1116.0 1109.0 1119.0 1123.0 1124.0 1124.0 1123.0 1121.0 1121.0 1070 psi (3‘31) 0 350 350 h TABLE A-2.--Cont1n6ed. SAMPLE NUMBER 93 UNIAXIAL TEMPERATURE = -12.0° C . CONSTANT AXIAL STRESS = 400 p51 PERCENT SAND = 63.8 PERCENT ICE-= 60-8 TOTAL VOLUME CHAN6E = NA TIME DEFL. L0A0 (MIN.) (INS.) (LBS.) 1.0 0.0150 400.0 10.0 0.0201 403.0 30.0 0.0242 405.0 60.0 0.0275 405.0 90.0 0.0300 406.0 120.0 0.0316 409.0 150.0 0.0330 409.0 180.0 0.0340 408.0 210.0 0.0349 406.0 240.0 0.0357 408.0 270.0 0.0364 407.0 300.0 0.0371 406.0 330.0 0.0378 406.0 350.0 0.0382 407.0 351.0 0.0358 0.0 355.0 0.0352 0.0 SAMPLE NUMBER TEMPERATURE = -12.0° C CONSTANT AXIAL STRESS = 400 psi PERCENT SAND = 63.8 PERCENT ICE = 59.4 TOTAL VOLUME CHANGE = NA TIME (MIN.) DEFL. (INS.) LOAD (LBS.) 0.0152 0.0190 0.0210 0.0236 0.0254 0.0269 0.0280 0.0290 0.0293 0.0327 422.0 402.0 402.0 402.0 “0100 “0200 402.0 402.0 404.0 405.0 94 STEP-STRESS (PSI) O SAMPLE NUMBER 94 Continued TIME (MIN.) 70.0 80.0 90.0 100.0 110.0 120.0 122.0 124.0 130.0 140.0 150.0 160.0 170.0 178.0 181.0 190.0 200.0 210.0 220.0 230.0. 240.0 242.0 245.0 250.0 260.0 270.0 280.0 290.0 300.0 303.0 307.0 310.0 320.0 330.0 340.0 350.0 360.0 361.0 365.0 370.0 380.0 390.0 400.0 409.0 DEFL. (INS.) 0.0338 0.0347 0.0355 0.0363 0.0369 0.0375 0.0376 0.0391 0.0398 0.0406 0.0412 0.0419 0.0423 0.0426 0.0453 0.0462 0.0472 0.0476 0.0479 0.0482 0.0483 0.0504 0.0508 0.0514 0.0519 0.0522 0.0525 0.0528 0.0530 0.0558 0.0560 0.0565 0.0569 0.0572 0.0575 0.0577 0.0577 0.0606 0.0610 0.0614 0.0618 0.0620 0.0622 LOAD 407.0 406.0 406.0 406.0 40000 407.0 407.0 410.0 41100 413.0 41300 406.0 417.0 417.0 415.0 414.0 411.0 412.0 402.0 402.0 412.0 412.0 390.0 392.0 393.0 411.0 411.0 411.0 41100 411.0 411.0 410.0 41100 412.0 412.0 412.0 41200 412.0 415.0 41500 416.0 415.0 416.0 416.0 03 '(LBS.)E(PSI) 100 200 200 400 400 600 600 800 800 1000 1000 189 TABLE A-2.--Continued. SAMPLE NUMBER 96 UNIAXIAL ‘sAMPLE NUMBER 98 STEP-STRESS TEMPERATURE = -12.0° c . CONSTANT AXIAL STRESS = 640 p51 TEMPERATURE = -12.0° C CONSTANT AXIAL STRESS = 400 psi PERCENT SAND = 63.8 PERCENT SAND = 63.6 PERCENT ICE = 95.2 PERCENT ICE = 60.0 EST. TOTAL VOLUME CHANGE = -0.078 cc TOTAL VOLUME CHANGE = NA (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) (p51) 1.0 0.0066 405.0 1.0 0.0172 616.0 0 10.0 0.0085 405.0 10.0 0.0307 650.0 30.0 0.0098 402.0 30.0 0.0403 651.0 90.0 0.0120 403.0 56.0 0.0470 653.0 0 120.0 0.0125 403.0 58.0 0.0513 660.0 100 150.0 0.0131 402.0 60.0 0.0518 660.0 180.0 0.0135 405.0 70.0 0.0535 659.0 210.0 0.0140 404.0 80.0 0.0548 660.0 240.0 0.0145 403.0 90.0 0.0560 660.0 270.0 0.0148 403.0 110.0 0.0579 660.0 300.0 0.0152 403.0 115.0 0.0585 660.0 100 320.0 0.0154 402.0 118.0 0.0600 662.0 200 320.0 0.0140 115.0 120.0 0.0602 658.0 330.0 _10.0135 115.0 130.0 0.0610 663.0 SAMPLE NUMBER 97 UNIAXIAL 140.0 0-0616 665-0 ' 150.0 0.0622 ' 670.0 TEMPERATURE = -12.0° C 160.0 0.0629 670.0 200 CONSTANT AXIAL STRESS = 640 psi 163.0 0-0652 962-0 400 PERCENT SAND = 63.3 170.0 0.0663 960.0 PERCENT ICE = 53.3 180.0 0.0679 662.0 TOTAL VOLUME CHANGE = NA 210.0 0.0726 964-0 230.0 0.0757 664.0 TIME DEFL. LOAD 239.0 0.0774 663.0 400 (MIN.) (INS.) (LBS.) 243.0 0.0804 660.0 600 250.0 0.0809 664.0 1.0 0.0194 639.0 260.0 0.0816 663.0 10.0 0.0329 648.0 270.0 0.0835 665o0 30.0 0.0429 651.0 280.0 0.0914 665.0 60.0 0.0514 656.0 ——-—-— LEAK AT 180 MIN. 90.0 0.0571 655.0 120.0 0.0619 659.0 150.0 0.0659 661.0 180.0' 0.0697 663.0 150.0 0.0659 661.0 180.0 0.0697 663.0 210.0 0.0734 662.0 240.0 0.0766 663.0 270.0 0.0798 662.0 300.0 0.0829 662.0 330.0 0.0861 662.0 360.0 0.0891 662.0 365.0 0.0895 662.0 365.0 0.0865 120.0 380.0 0.0851 120.0 TABLETA-2.--Continued. “ «.kan ‘u. 190 “‘-""e’l". . x SAMPLE NUMBER UNIAXIAL TEMPERATURE = -12.0° C CONSTANT AAIAL STRESS = PERCENT SAND = 63.9 PERCENT ICE = 95.1 TOTAL VOLUME CHANGE = -0.078 cc TIME . DEFL. LOAO (MIN.) (INS.) (LBS.) 1.0 0.0042 627.0 10.0 0.0062 642.0 30.0 0.0083 641.0 60.0 0.0107 645.0 90.0 0.0122 645.0 120.0 0.0136 644.0 150.0 0.0147 643.0 180.0 0.0156 643.0 210.0 0.0165 645.0 240.0 0.0174 645.0 244.0 0.0175 645.0 244.7 0.0150 135.0 250.0 0.0142 135.0 256.0 0.0133 133.0 SAMPLE NUMBER 100 TEMPERATURE = -12-0° C 640 psi STEP-STRESS CONSTANT AxIAL STRESS = 640 P51 PERCENT SANO = 63.8 PERCENT ICE = 95.5 TOTAL VOLUME CHANGE = -0.078 Cc TIME (MIN.) 1.0 10.0 20.0 30.0 40.0 50.0 58.0 60.0 70.0 80.0 90.0 100.0 110.0 119.0 121.0 DEFL. (INS.) 0.0114 0.0146 0.0160 0.0171 0.0181 0.0187 0.0194 0.0228 0.0236 0.0242 0.0249 0.0253 0.0259 0.0264 0.0275 LOAD (LBS.) 668.0 64400 650.0 648.0 650.0 645.0 645.0 64400 650.0 649.0 650.0 650.0 649.0 649.0 654.0 03 (PSI) 0 100 200 SAMPLE NUMBER 100.Continued. TIME (MIN.) 130.0 140.0 150.0 160.0 170.0 177.0 181.0 190.0 200.0 210.0 220.0 225.0 230.0 240.0 243.0 245.0 250.0 260.0 270.0 280.0 290.0 300.0 302.0 305.0 310.0 320.0 330.0 340.0 350.0 358.0 361.0 365.0 370.0 380.0 390.0 400.0 405.0 DEFL. (INS.) 0.0281 0.0285 0.0289 0.0293 0.0296 0.0299 0.0320 0.0325 0.0328 0.0330 0.0333 0.0335 0.0336 0.0339 0.0363 0.0364 0.0367 0.0370 0.0373 0.0374 0.0377 0.0379 0.0380 0.0405 0.0408 0.0410 0.0413 0.0416 0.0417 0.0420 0.0445 0.0446 0.0448 0.0450 0.0452 0.0454 0.0455 LOAD (LBS.) 656.0 651.0 650.0 650.0 654.0 651.0 655.0 648.0 653.0 650.0 653.0 653.0 653.0 653.0 655.0 651.0 651.0 651.0 651.0 651.0 653.0 653.0 653.0 652.0 653.0 653.0 655.0 655.0 655.0 655.0 655.0 655.0 655.0 655.0 655:0 655.0 655.0 °3 (PSI). 200 400 400 600 600 800 800 1000 1000 ‘ _ , 191 TABLE A-2.--Cont1nued. SAMPLE NUMBER 101 UNIAXIAL SAMPLE NUMBER 102 Continued.m— TEMPERATURE = -12.0° C . TIME DEFL. LOAD CONSTANT AxIAL STRESS = 640 PSI (MIN.) (INS.) (L85.) PERCENT SAND = 62.9 290.7 0.0573 130.0 PERCENT ICE = 95.7 291.0 0.0548 130.0 TOTAL VOLUME CHANGE = -0.012 cc 300.0 0.0530 130.0 - -310 0.0526 130.0 TIME DEFL. LOAD 320.0 0.0523 130.0 (MIN.) (INS.) (LBS.) . SAMPLE NUMBER 104 STEP-STRESS 1.0 0.0108 650.0 10.0 0.0142 642.0 TEMPERATURE = -12.0° C 30.0 0.0169 644-0 CONSTANT AAIAL STRESS = 750 psi 60.0 0.0195 043.0 PERCENT SANO = 64.0 » 90.0 0.0214 646.0 PERCENT ICE = 60.0 EST. 120.0 0.0231 648.0 TOTAL VOLUME CHANGE = NA 150.0 0.0246 650.0 $03.3 g-ggzg gig-g TIME DEFL. LOAO 03 O 9 . 0 NS.) ( BS.) 240.0 0.0275 649.0 (MIN ) (I L (PSI) 270.0 0.0283 647-0 1.0 0.0265 745.0 0 300.0 0.0291 650.0 2.0 0.0324 763.0 330.0 0.0298 650.0 3.0 0.0351 753.0 350.0 0.0302 650.0 4.0 0.0398 766.0 351.0 0.0302 650.0 5.0 0.0413 766.0 352.0 0.0269 105.0 5.7 0.0427 766.0 0 360.0 0.02:9 105-0 8.0 0.0498 772.0 100 ' . o S 9 7 7o SAMPLE NUMBER 102 UNIAXIAL i?.8 3.85:7 7:8,8 TEMPERATURE _ 12 0° C 12.0 0.0535 778.0 ‘ ’- ° , . 0.054 778.0 CONSTANT AXIAL DTRESS = 1070 ps1 {3.3 0.054; 778.0 100 PERCENT SAND = 53°3 ' 15.0 0.0575 786.0 200 PERCENT ICE 3 95-8 16 0 0.0582 786.0 TOTAL VOLUME CHANGE = +0.]44 CC 17:0 0.0588 786.0 - 9. 0. 59 78 . _ 21.0 0.0610 786.0 200 1.0 0-0183 1065-0 23.0 0.0644 776.0 400 30.0 0.0348 1084.0 25:0 0.0656 776-0 60.0 0.0421 1090.0 26.0 0.0661 776.0 120-0 °-°§°9 1°97-0 28.0 0.0686 775.0 400 150.0 0.0541 1100.0 . 180.0 0.0568 1098.0 LEAK 210.0 0.0591 1097.0 240.0 0.0609. 1099.0 270.0 0.0626 1103.0 290.0 1103.0 0.0637 u Hm: TABLE A-2.-—Continued. SAMPLE NUMBER UNIAXIAL TEMPERATURE = -]2.0° C CONSTANT AXIAL STRESS ‘ 63.5 PERCENT SAND = PERCENT ICE = 59.6 TOTAL VOLUME CHANGE = NA TIME (MIN.) OLH¢WJOOH 00.0.0 <5cro<3c>o 15.0 20.0 25.0 30.0 35.0 40.0 43.0 44.0 45.0 46.0 46.7 47.0 48.0 50.0 54.0 DEFL. (INS.) 0.0269 0.0328 0.0377 0.0409 0.0437 0.0539 0.0614 0.0677 0.0733 0.0788 0.0843 0.0902 0.0945 0.0961 0.0978 0.0996 0.0932 0.0920 0.0916 0.0911 0.0908 LOAD (LBS.) 760.0 757.0 762.0 765.0 765.0 768.0 772.0 773.0 776.0 778.0 780.0 783.0 790.0 788.0 788.0 788.0 80.0 80.0 80.0 80.0 80.0 SAMPLE NUMBER TEMPERATURE = -12.0° C 750.0 p51CONSTANT AxIAL STRESS = PERCENT SAND = 63 7 PERCENT ICE = 95.2 108 UNIAXIAL 750 psi TOTAL VOLUME CHANGE = -0.054 CC TIME (MIN.) 1.0 10.0 30.0 60.0 90.0 20.0 50.0 80.0 10.0 40.0 i70.0 290.0 394.0 296.0 100.0 110.0 120.0 DEFL. (INS.) 0.0211 0.0264 0.0308 0.0348 0.0376 0.0399 0.0418 0.0434 0.0449 0.0461 0.0470 0.0478 0.0479 0.0453 0.0446 0.0441 0.0438 LOAO (LBS.) 752.0 760.0 760.0 763.0 764.0 765.0 765.0 765.0 768.0 767.0 767.0 767.0 767.0 122.0 115.0 115.0 115.0 TABLE A-2.--Continued. , STEP-STRESSSAMPLE NUMBER 109 Continued. SAMPLE NUMBER TEMPERATURE = ~12° C TIME DEFL. LOAD °3 CONSTANT AXIAL STRESS = 400 psi (MIN.) (INS.) (LBS.) (PSI) PERCENT SAND = 63.1 330.0 0.0339 411.0 PERCENT ICE = 95.5 340.0 0.0340 405.0 TOTAL VOLUME CHANGE = -0.072 cc 350.0 0.0341 410.0 359.0 0.0343 410.0 800 TIME DEFL. LOAO (5 362.0 0.0365 410.0 1000 (MIN.) (INS.) (LBS.) (p51)370.0 0.0368 410.0’ 380.0 0.0371 405.0 1.0 0.0125 400.0 0 390.0 0.0373 410.0 10.0 0.0147 404.0 400.0 0.0376 405.0 20.0 0.0155 400.0 410.0 0.0377 405.0 30.0 0.0161 405.0 413.0 0.0378 411.0 1000 40.0 0.0165 405.0 50.0 0.0169 406.0 SAMPLE NUMBER UNIAXIAL 59.0 0.0171 404.0 0 61.0 0.0204 '407.0 100 TEMPERATURE = -12.0° C 70.0 0.0207 404.0 CONSTANT AXIAL STRESS = 750 psi 80.0 0.0210 405.0 PERCENT SANO = 63.4 90.0 0.0214 406.0 PERCENT ICE = 70.5 100.0 0.0227 405.0 TOTAL VOLUME CHANGE = NA 110.0 0.0219 405.0 120.0 0.0221 405.0 100 TIME DEFL. LOAD 122.0 0.0231 409.0 200 (MIN.) (INS.) (LBS.) 130.0 0.0234 409.0 140.0 0.0238 405.0 1.0 0.0158 750.0 150.0 0.0240 406.0 10.0 0.0250 756.0 160.0 0.0242 405.0 30.0 0.0330 764.0 170.0 0.0243 405.0 60.0 '0.0391 767.0 180.0 0.0245 409.0 90.0 0.0431 767.0 182.0 0.0246 409.0 200 120.0 0.0459 767.0 185.0 0.0266 408.0 400 150.0 0.0433 763.0 190.0 0.0268 *410.0 180.0 0.0502 767.0 200.0 0.0270 405.0 210.0 0.0519 770.0 210.0 0.0273 911-0 240.0 0.0534 770.0 220.0 0.0274 405.0 270.0 0.0547 770.0 230.0 0.0276 405.0 300.0 0.0559 770.0 240.0 0.0277 410.0 330.0 0.0571 770.0 241.0 0.0277 410.0 400 360.0 0.0584 772.0 243.0 0.0298 410.0 600 390.0 0.0594 772.0 250.0 0.0302 408.0 420.0 0.0602 772.0 260.0 0.0304 405.0 450.0 0.0611 772.0 270.0 0.0305 410.0 480.0 0.0621 773.0 280.0 0.0307 405.0 510.0 0.0629 773.0 300.0 0.0311 410.0 530.7 0.0582 108.0 304.0 0.0312 410.0 600 533.0 0.0566 108.0 307.0 0.0333 407.0 800 310.0 0.0334 407.0 320.0 0.0337 405.0 193 TABLE A-2.--C0ntinued. 194 SAMPLE NUMBER TEMPERATURE = -12.0° C 112 STEP-STRESS CONSTANT AXIAL STRESS = 640 ps PERCENT SANO = 64.0 PERCENT ICE = 60.0 EST. TOTAL VOLUME CHANGE = NA TIME DEFL. LOAD 6 (MIN.) (INS.) (LBS.) (p51 1.0 0.0180 648.0 0 5.0 0.0255 650.0 10.0 0.0303 654.0 20.0 0.0357 655.0 30.0 0.0395 653.0 40.0 0.0423 655.0 50.0 0.0446 655.0 60.0 0.0464 652.0 0 62.0 0.0502 656.0 100 70.0 0.0515 654.0 80.0 0.0527 657.0 90.0 0.0538 657.0 100.0 0.0547 657.0 110.0 0.0556 660.0 120.0 0.0565 660.0 100 123.0 0.0581 663.0 200 130.0 0.0587 663.0 140.0 0.0593 660.0 150.0 0.0598 662.0 160.0 0.0603 665.0 170.0 0.0607 665.0 180.0 0.0611 661.0 200 183.0 0.0637 660.0 400 190.0 0.0643 662.0 200.0 0.0647 662.0 205.0 0.0650 663.0 LEAK SAMPLE NUMBER TEMPERATURE = CONSTANT PERCENT -12.0° C AXIAL STRESS = SAND = 63.] PERCENT ICE = 60.0 EST. TOTAL VOLUME CHANGE = NA TIME (MIN.) 1.0 10.0 30.0 60.0 62.0 64.0 70.0 90.0 120.0 122.0 124.0 130.0 150.0 180.0 182.0 DEFL. (INS.) 0.0124 0.0192 0.0243 0.0283 0.0286 0.0320 0.0330 0.0348 0.0365 0.0366 0.0382 0.0391 0.0424 0.0476 0.0478 LEAK LOAD (LBS.) 407.0 405.0 406.0 406.0 406.0 405.0 407.0 407.0 410.0 410.0 414.0 412.0 411.0 410.0 410.0 1 'l 3" STEP- STRESS 400 psi 93 (PSI) 100 100 200 TABLE A-2.--Continued. 114 UNIAXIAL SAMPLE NUMBER .SAMPLE NUMBER“ 117 STEP-STRESS 767.0 TEMPERATURE = -12.0° C . TEMPERATURE = -12-0° C . CONSTANT AXIAL STRESS = 750 P51 CONSTANT AXIAL STRESS = 750 PSI PERCENT SAND = 64.2 PERCENT SAND = PERCENT_ICE = 68-5 PERCENT ICE = 60-5 TOTAL VOLUME CHANGE = NA TOTAL VOLUME CHANGE = NA TIME DEFL. LOAD TIME DEFL. LOAD 03 (MIN.) (INS.) (LBS.) (MIN.) (INS.) (LBS.) (PSI) 1.0 0.0239 751.0 1.0 0.0344 750.0 0 10.0 0.0393 762.0 2.0 0.0399 765.0 30.0 0.0501 765.0 3.0 0.0438 765.0 60.0 0.0583 770.0 4.0 0.0475 770.0 90.0 0.0636 771.0 5.0 0.0502 770.0 120.0 .0.0677 774.0 6.0 0.0524 770.0 150.0 0.0709 775.0 7.0 0.0544 770.0- 180.0 0.0740 775.0 8.0 0.0562 770.0 210.0 0.0766 775.0 9.0 0.0578 770.0 220.0 0.0775 780.0 10.0 0.0592 770.0 0 230.0 0.0784 780.0 12.0 0.0644 775.0. 100 240.0 ‘0.0793 780.0 13.0 0.0655 775.0 240.5 0.0756 100.0 14.0 0.0663 776.0 241.0 0.0741 100.0 15.0 0.0672 776.0 245.0 0.0729 100.0 16.0 0.0679 777.0 100 250.0 0.0723 100.0 18.0 0.0704 776.0 200 SAMPLE NUMBER 115 CONFINED 20.0 0.0717 730.0 21.0 0.0724 780.0 TEMPERATURE = -12.0° C 22.0 0.0729 780.0 CONSTANT AXIAL STRESS = 23.0 0.0732 782.0 PERCENT SAND = 63.2 24.0 0.0736 780.0 PERCENT ICE = 95.9 25.0 0.0740 780.0 ' TOTAL VOLUME CHANGE = -0.0'|2 cc 26.0 0.0744 730.0 CONFINING PRESSURE = 210 psi 27.0 0.0747 780.0 200' TIME DEFL. LOAD 29.0 0.0770, 780.0 400 (MIN.) (INS.) (LBS.) 30.0 0.0774 780.0 31.0 0.0778 780.0 1.0 0.0163 750.0 32.0 0.0780 780.0 10.0 0.0209 758.0 33.0 0.0783 ‘780.0 30.0 0.0249 762.0 34.0 0.0786 780.0 60.0 0.0283 762.0 35.0 0.0789 780.0 90.0 0.0306 762.0 36.0 0.0791 780.0 120.0 0.0324 762.0 37.0 0.0793 780.0 150.0, 0.0340 762.0 38.0 0.0796 780.0 180.0 0.0353 767.0 39.0 0.0797 780.0 210.0 0.0364 767.0 40.0 0.0799 780.0 240.0' 0.0374 767.0 41.0 0.0801 780.0 400 270.0 0.0383. 767.0 43.0 0.0825 780.0 600 300.0. 0.0391 45.0 0.0829 - 780.0 ‘ I TABLE A-2.--Continued. l??“-?=' “ TIME (MIN.) 47.0 49.0 51.0 53.0 55.0 57.0 59.0 61.0 64.0 67.0 70.0 75.0 80.0 85.0 90.0 95.0 100.0 104.0 105.0 115.0 120.0 130.0 135.0 137.0 142.0 145.0 150.0 155.0 160.0 165.0 170.0 180.0 190.0 195.0 200.0 210.0 220.0 240.0 250.0. 253.0 254.0 255.0 260.0 265.0 270.0 274.0 196 ~u~ 4...... SAMPLE NUMBER 117+Cont1nued. DEFL. (INS.) 0.0833 0.0836 0.0838 0.0841 0.0844 0.0849 0.0851 0.0853 0.0877 0.0883 0.0888 0.0893 0.0898 0.0901 0.0905 0.0907 0.0909 0.0896 0.0896 0.0896 0.0899 0.0901 0.0902 0.0904 0.0883 0.0885 0.0886 0.0887 0.0889 0.0889 0.0862 0.0864 0.0866 0.0867 0.0842 0.0856 0.0868 0.0878 0.0897 0.0900 0.0819 0.0806 0.0794 0.0790 0.0789 0.0787 LOAD (LBS.) (PSI) 780.0 780.0 785.0 785.0 785.0 785.0 785.0 785.0 780.0 783.0 784.0 785.0 785.0 785.0 785.0 785.0 785.0 775.0 775.0 775.0 775.0 775.0 775.0 775.0 .775.0 775.0 775.0 775.0 775.0 775.0 775.0 775.0 775.0 775.0 775.0 775.0 775.0 775.0 775.0 p775°° 75.0 75.0 75.0 75.0 75.0 75.0 “SAMPLE NUMBER °3 TEMPERATURE = -12.0° C 62.7 118 CONFINED CONSTANT AXIAL STRESS = 750 psi PERCENT SAND = PERCENT ICE = 94.7 TOTAL VOLUME CHANGE = -0.216 cc CONFINING PRESSURE = 600 psi TIME DEFL. LOAD (MIN.) (INS.) (LBS.) 600 2.0 0.0192 750.0 800 10.0 0.0227 760.0 30.0 0.0266 762.0 60.0 0.0298 762.0 90.0 0.0324 767.0 120.0 0.0342 767.0 150.0 0.0357 767.0 180.0 0.0371 767.0 210.0 0.0381 765.0 300240.0 ’0.0390 765.0 500270.0 0.0398 764.0 276.0 0.0327 0.0 280.0 0.0322 0.0 290.0 0.0317 0.0 300.0 0.0315 0.0 310.0 0.0313 A 0.0_h 500 SAMPLE NUMBER 119 CONFINED 400 TEMPERATURE = -12.0° C CONSTANT AXIAL STRESS = PERCENT SAND = 53.5 PERCENT ICE = 60.5 650 psi 400 TOTAL VOLUME CHANGE = NA.‘ = 205 psi 200 CONFINING PRESSURE TIME (MIN.) 200 0 1.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 0 120.0 150.0 DEFL. (INS.) 0.0225 0.0309 0.0346 0.0373 0.0397 0.0423 0.0450 0.0474 0.0506 0.0534 0.0564 0.0597 0.0632 0.0757 LEAK LOAD (LBS.) 650.0 650.0 650.0 656.0 656.0 656.0 656.0 656.0 656.0 656.0 656.0 656.0 656.0 656.0 197 TABLE A-2.--Continued. SAMPLE NUMBER 120 CONFINED SAMPLE NUMBER 121-Continued. TEMPERATURE = -12.0° 0 TIME' DEFL. ,LOAD 63 CONSTANT AXIAL STRESS = 640 psi(MIN.) (INS.) (LBS.) (PSI) PERCENT SAND = 63.9 120.0 0.0367 762.0 | PERCENT ICE = 64.6 122.0 0.0368 762.0 100 TOTAL VOLUME CHANGE = NA 124.0 0.0379 760.0 200 CONFINING PRESSURE = 600 psi 130.0 0.0333, 760.0 TIME DEFL. LOAD 140.0 0.0389 761.0 (MIN.) (INS.) (LBS.) 150.0 0.0394 763.0 . 160.0 0.0399 765.0 2.0 0.0394 655.0 170.0 0.0403 765.0 5.0 0.0438 656.0 180.0 0.0407 765.0 10.0 0.0473 656.0 181.0 0.0408 765.0 200 20.0 0.0510 660.0 133.0 0.0427 755.0 400 30.0 0.0531 662.0 190.0 0.0433 767.0 60.0 0.0566 662.0 200.0 0.0437 767.0 90.0 0.0585 660.0 210.0 0.0441 767.0 120.0 0.0597 660.0 220.0 0.0445 767.0 150.0 0.0606 660.0 230.0 0.0449 767.0 180.0 0.0614 660.0 240.0 0.0451 767.0 210.0 0-0619 660-0 243.0 0.0452- 767.0 400 240.0 0.0624 665.0 245.0 0.0482 767.0 600 260.0 0.0628 665.0 250.0 0.0485 767.0 260.0 0.0488 767.0 SAMPLE NUMBER STEP-STRESS 270.0 0.0490 ‘ 767.0 ~ 280.0 0.0493 767.0 TEMPERATURE = -12.0° C 290.0 0.0497 767.0 CONSTANT AXIAL STRESS = 750 psi 300.0 0.0500 767.0 PERCENT SAND = 62.3 304.0 0.0501 767.0 600 PERCENT ICE = 95.5 306.0 0.0515 770.0 800 TOTAL VOLUME CHANGE = -0.048 cc 310.0 0.0517 770.0 320.0 0.0521 770.0 TIME DEFL. LOAD 03 330.0 0.0524 770.0 (MIN.) (INS.) (LBS.) (PSI) 340.0 0.0526 770.0 ' 350.0 0.0529 770.0 1.0 0.0170 755.0 0 360.0 0.0530 770.0 10.0 0.0216 760.0 365.0 0.0532 770.0 300 20.0 0.0237 760.0 ~ 30.0 0.0252 757.0 40.0 0.0266 757.0 50.0 0.0278 760.0 60.0 0.0288 757.0 61.0 0.0288 757.0 0 63.0 0.0325 760.0 100 70.0 .0.0332 759.0 80.0 0.0341 763.0 90.0 0.0347 761.0 100.0 0.0354 761.0 110.0 0.0361 757.0 N STQTE UNIV. L MICHIGR IBRRRIES WIWIWIIW IWHWHIIN ”WWI 31 9 6 205 2 31002 3