SOIL DEFORMAT-ION RATES AND ACTIVATKON ENERGTES f j Thesis for the Degree of 'Ph. D. ‘ MICHIGAN STATE UNWERSITY ARTHUR GORDON DOUGLAS 1969 I hul- LIB .1? .4 R Y ’ Miclng, State University AAA \ TIA I IIIIIIIIA I This is to certify that the thesis entitled SOIL DEFORMATION RATES AND ACTIVATION ENERGIES. presented by Arthur Gordon Douglas has been accepted towards fulfillment of the requirements for Ph.D. Civil Engineering degree in O. . A3 . WWII! AWL Major professor Date February 2], I969, 0.169 To)“ ABSTRACT SOIL DEFORMATION RATES AND ACTIVATION ENERGIES By Arthur Gordon Douglas The free energy of activation of flow for Sault Ste. Marie clay has been determined by the application of the absolute reaction rate theory. The viscous flow of dilute soil-water mixtures and the steady state creep of con- solidated samples were considered. The viscosity of the soil-water mixtures increased slowly as the concentration of solids was increased until there were sufficient solids to form a continuous structure. At this point the mixture became thixotropic. The rate at which the viscosity increased was dependent upon the nature of the adsorbed ions. The highly hydrated lithium ion caused a more rapid increase than the less hydrated potassium ion. This is considered to be due to the in- creased effective size of the particles. The free energy of activation of the dilute suspensions was found to be independent of the concentration and equal to that of pure water. It is concluded that the flow mechanism is that of free water in a porous medium and that the isolated clay particles make no contribution to the free energy. Arthur Gordon Douglas Creep tests on consolidated samples were conducted at constant temperature with several increments of axial stress. These tests indicate that the free energy of activation for this soil is approximately 28 K. calories/ mole and is independent of the nature of the adsorption complex. Also, the volume of the flow unit was calculated to be 1.7 cubic angstroms. These results suggest that the bonding mechanism is not related to the adsorbed water layer and is in the form of ionic bonds at points of direct mineral to mineral contact. SOIL DEFORMATION RATES AND ACTIVATION ENERGIES By 'Arthur Gordon Douglas A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Civil Engineering 1969 ACKNOWLEDGMENTS The writer wishes to express his deep appreciation to his major professor, Dr. 0. B. Andersland, Professor of Civil Engineering, for his aid and encouragement throughout the writer's doctoral studies and for his help and guidance in the preparation of this thesis. Thanks are also due the other members of the writer's doctoral committee: Dr. M. M. Mortland, Professor of Soil Science; Dr. R. K. Wen, Professor of Civil Engineering; and Dr. L. E. Malvern, Professor of Applied Mechanics. Thanks go to the National Science Foundation and the Division of Engineering Research at Michigan State Univer- sity for the financial assistance that made these studies possible. 11 TABLE OF CONTENTS ACKNOWLEDGMENTS LIST OF TABLES . . . . . . . . . .‘ . LIST OF FIGURES . . . . . . . . . . . CHAPTER I. INTRODUCTION. . . . . . . . . . II. REVIEW AND THEORY . Flow Processes . . . .' Physicochemical properties .of clays. Molecular energies. . . . . . . Rate Process Theory . l . . . . Creep as a Rate Process . . III. MATERIALS AND METHODS . . . . . Viscosity Tests. . . . . . . . Creep Tests . . . . . . . . . IV. EXPERIMENTAL RESULTS . . . . . . . Viscosity tests. . . . . . . . Creep Tests . . . . a . . . V. ANALYSIS AND INTERPRETATION. . . . . Theory. . . . . . . The Flow of Free Water . . . . The Creep of Polycrystalline Ice . The Relative Movement of Soil Grains. Soil Suspensions . . . . . . . Unfrozen Soil . . . . . . . . Frozen Soil . . . . . .' . . . VI. SUMMARY AND CONCLUSIONS . . . . . . BIBLIOGRAPHY . . . . . . . .' . . . .* APPENDICES iii Page ii iv LIST OF TABLES Table Page A-l Values of Activation Energy and Flow Volume from Creep Tests . . . . . . 39 5-1 Degree of Hydrogen Bonding of Water . . . 51 A-l Viscosity of Soil—Water Mixtures . . . . 72 A-II Creep Test Data for Soil-Water Samples (Lithium Saturated Clay). . . . . . 73 A-III Creep Test Data for Soil-Water Samples (Sodium Saturated Clay) . . . . . . 74 A-IV Creep Test Data for Soil-Water Samples (Potassium Saturated Clay) . . . . . 7S A-V Creep Test Data for Soil—Carbon Tetrachloride Samples (Lithium Saturated Clay). . . . . . 76 A-VI Creep Test Data for Soil-Carbon Tetrachloride Samples (Sodium Saturated Clay) . . . . . . 77 A—VII Creep Test Data for Soil-Carbon Tetrachloride Samples (Potassium Saturated Clay) . . . . . 78 iv Figure 2-1 4-3 A-U A-s A-6 14—7 14—8 LIST OF FIGURES Rheological prOperties indicated by viscosity tests. . . . . . . Typical creep curve . . . . . . . Structure of minerals. . .- . . . .* . Attraction and repulsion between surfaces Modes of vibration for water and associated energy levels. . . . . Representation of energy barriers. Observed activation energy versus percent sand by volume . . . . . . . . Grain size distribution curve for Sault Ste. Marie Clay. . . . . . . .' Brookfield viscometer . . . Viscosity of soil-water mixtures at 250 C Variation of viscosity with concentration at different temperatures for potassium saturated clay . . . . . . . . . Variation of viscosity with temperature for lithium saturated clay . .~ . Variation of viscosity with temperature for sodium saturated clay . . . Variation of viscosity with temperature for potassium saturated clay . . . Variation of flow volume with concentration or 8011 O O O I Q 0 I O O O Creep curve for potassium saturated clay . Variation of strain rate with strain. . Structure of ice . . . Page 22 23 2A 25 26 27 28 32 33 A0 A1 A2 43 AA “5 “7 63 >0 NOTATIONS angstrom units = 10"8 cm. .shape factor dielectric constant allowable energy levels of a particle quantum of energy experimental activation energy free energy of activation degeneracy enthalpy of activation Planck's constant = 6.62“ x 10"27 erg. sec. equilibrium constant Boltzmann's constant = 1.3805 x 10-16 molecule erg/degree rate constant applied force mass of a particle dipole moments number of molecules in all energy levels of A number of particles at energy level E1 electric potential attractive potential partition function universal gas constant 1.987 cal/degree mole vi AS N >" ‘6 F)- 03.404 3 T” entropy of activation absolute temperature ° Kelvin. time potential energy flow volume valency shear strain rate of shear strain horizontal displacement natural axial strain rate wave function distance between equilibrium positions. coefficient of viscosity concentration of soil major principal stress minor principal stress octahedral stress octahedral shear stress frequency of vibration vii CHAPTER I INTRODUCTION The mechanisms of viscosity, plasticity, and diffu- sion are now accepted as examples of the theory of absolute reaction rates as formulated by Glasstone, Laidler and Eyring (19Al). In recent years, this theory has been applied to the study of time-dependent deformation of both liquids and solids. Attempts have also been made to apply the theory to the creep of both frozen and unfrozen soil. This research is still in its preliminary stages, but the results obtained indicate that the creep of soils can be treated as a thermally activated process. The theory of absolute reaction rates concerns the movement of particles of atomic size from one equilibrium positionix>another by surmounting an energy barrier. The magnitude of this barrier is the "free energy of activa- tion" and is the factor which controls the rate of any process in which matter rearranges itself. It is probable that some particles will pass through a barrier instead of surmounting it and this action is known as tunneling. The proportion of the total number of particles involved in tunneling is small and this mechanism is not considered in the development of the equations presented. The rate equations are derived from quantum mechanics and are based upon the distribution of thermal energies between atomic particles. Despite many superficial simi- larities, they are not applicable to a mass of soil particles. For while there is an energy barrier re- straining a grain from moving from one equilibrium position to the next, such movement requires the direct application of a mechanical force. This is a mechanically activated process, and must be distinguished from a thermally activated process. It will be shown that when the flow of a soil mass is considered, the energy which is used in overcoming the mechanical resistance must be deducted in order to determine the free energy of activation due to surface forces. In saturated clays this mechanical energy is negligible but in sands it is the dominant term. In an equilibrium situation, particles which have sufficient energy cross the energy barrier with equal frequency in both directions. A flow process will be induced if the shape of the barrier is distorted by the application of a directed potential so that the height from one side is less than from the other side causing a greater net flow in one direction than in the reverse direction. Since the rate of flow is controlled by the height of the barrier and the thermal energy of the particles, the free energy of activation may be found by observing the change in the flow rate at constant stress with a change in temperature. This is a convenient method for use with viscosity tests on fluids but with solid materials undergoing creep it has the disadvantage that continuous structural changes are taking place and the temperature change can not be induced instantaneously. For this reason the method which was deveIOped here was to apply a small increment of stress to a sample under- going steady state creep and observe the change in the creep rate. The free energy of activation could then be calculated from two simultaneous equations. The application of the rate theory to liquids and metals has led to a greater understanding of flow mech- anisms. In general, there are two factors involved. The particle must make a hole for itself as it moves forward and it must break the bonds with which it is attached to its neighbors. The energies which have been measured for a great many materials are less than those required to form a hole of molecular size and so it is concluded that holes already exist in all materials and that the particle only has to enlarge an existing hole. It has been found that for many materials, the ratio of the energy required to enlarge a hole to the energy required to form a hole is about 0.25 (Glasstone, Laidler and Eyring, 1941). For non- associated liquids, the enlargement of the holes accounts for most of the free energy of activation but for associ— ated liquids such as water, a relatively large proportion is used in breaking the hydrogen bonds. The experimental results indicate that both changes in the adsorbed ion and dehydration followed by saturation with carbon tetrachloride had no effect on the value of the free energy of activation. This indicates that ionic bonding between particles is a major factor in the rate controlling mechanism. Further support for this view is provided by the fact that the magnitude of the calculated value of the free energy of activation is in the range of strengths of ionic bonds. CHAPTER II REVIEW AND THEORY Flow Processes In very dilute concentrations, soil—water mixtures exhibit typical Newtonian flow characteristics as illus- trated in Figure 2-la and the coefficient of viscosity n may be represented by the Einstein equation [Baver, 1956] n = no (1 + ac) (2-1) where no is the coefficient of viscosity of the fluid, o is the concentration of the particles and "a" is a shape factor. As the concentration of solids is increased and interaction occurs between the particles, the flow becomes thixotropic as illustrated in Figure 2-lb, and becomes both rate and time dependent. The variation of the yield stress with water content as determined by this method for sodium and hydrogen saturated kaolinite is shown in Figure 2-10 [Scott, 1963]. Compacted soils also exhibit time-dependent deforma- tion under constant stress and temperature. The basic features of typical creep curves are illustrated in Figure 2-2. In the general case, a creep curve consists of four stages: Stage I, termed the "instantaneous strain," represents the strain which occurs on loading; Stage II, termed the "primary" or "transient" creep, represents the initial region of decreasing creep rate; Stage III, termed "secondary" or "steady-state" creep, represents the region of relatively constant creep rate; Stage IV, termed the "tertiary" creep, represents the final stage leading to failure. One or more of these stages may not occur at certain stress levels in a particular specimen. At low stress levels, Stages III and IV do not occur and the creep is said to be damped. If the stress exceeds the limiting value, Stages III and IV do occur and the creep is said to be undamped. Variations in the creep rate are considered to be the result of the simultaneous operation of weakening and strengthening processes. When the strengthening process predominates, the rate decreases (primary creep); when the strengthening and weakening processes are equal, the rate is constant (secondary creep); and if the weakening process predominates the rate increases and leads to failure (tertiary creep). Physicochemical Properties of Clays The strengthening and weakening processes involved in the flow of clays depend upon the inter-particle forces which exist as a consequence of the mineralogical structure of the clay. The structure of the four minerals mentioned — in this project is illustrated in Figure 2—3 [Grim, 1953]. At the edges of the sheets, the continuity of the structure is broken and a net negative charge is produced although local concentrations of positive charges may occur. Negative charges may also be produced on the surfaces by isomorphous substitution of lower valence ions for the silicon and aluminum in the tetrahedral and octahedral sheets. The net negative charge tends to attract the positive hydrogen ions in the water and develops a degree of orienta- tion in the molecules close to the surface. The degree of orientation and the thickness of this adsorbed layer are uncertain. Low and Anderson [1958] in two reviews of experiments with bentonite found no evidence of orientation at a distance of 8AA but at 12A the water had a density of 0.97 g./c.c. compared to 0.99987 for water at 0°C. and 0.917 for ice at 0°C. It is therefore suggested that the first layer of water molecules is rigidly held, and possibly hydrogen bonded to the surface, and that the degree of orientation decays rapidly away from the surface. If any metallic cations are present in solution, they are also attracted towards the negatively charged surface and come to an equilibrium position where the attrac- tion to the surface is balanced by their mutual repulsion and form a mobile cloud near the surface. The negatively charged plate and the positively charged cation cloud form a system known as the "diffuse double layer." The electric potential P at a distance x from the surface may be expressed by a simplified form of the Guoy—Chapman equa- tion as: 2 2 A 8 P = z"— <-ssZ—A> <2-2> where k is Boltzmann's constant, T is the absolute tempera- ture, Z is the valency, e is the electrostatic unit of charge and D is the dielectric constant. Verwey and Overbeek [19A8] attributed the attractive forces between clay particles to van der Waal's forces and derived the following equation for the attractive potential Q between two dipoles: 2 2 9— mlm2 (2-3) 3 Dka6 Q: where C is a constant and ml, m are the two dipole 2 moments. Thus the attractive potential varies inversely as the sixth power of the distance while the repulsive potential varies inversely as an exponential function of the distance. The result of the combination of these two potentials is illustrated in Figure 2-4. 9 Molecular Energigs ‘ The clay and water molecules are in a constant state of thermal agitation with an intensity which depends upon the environmental temperature. Each molecule, however, is held to its neighbours by bonds which are strong in the case of the clay crystal and weak.in the case of water. Periodically, a molecule may attain sufficient energy to break its bonds and move to another equilibrium ~position. If a stress is applied to the system, the energy barriers will be altered and movement will tend to occur in a preferred direction. The nature and magnitude of the molecular energies is therefore a prime factor in the consideration of the mechanism of flow. The View that the energy of particles was "quantized" and that only certain discrete energy levels.were allowed was suggested by Max Planck [1900] when he prOposed the following relation: AB = hv (2—H) where AB is the quantum of energy emitted when an oscillating particle moves to the next lower energy level, h is a constant known as Planck's constant and has the value 6.624 x10"27 erg. sec. and v is the frequency of the radiation emitted. Niels Bohr's description of the atom [1913] was based upon this equation but_although this description gave many acceptable results, it failed 10 as a complete description because it did not recognize the simultaneous corpuscular and wave nature of matter. This was conSidered by Erwin Schroedinger [1926] who suggested that the behavior of particles of atomic dimensions may be calculated from a wave equation, which for a particle restrained to the x axis is: 2 2 E‘I’ = .. h2 «d—Jg- + U(XNJ (2-5) 8n.m. dx where E represents the allowable energy levels of the particle, w is a wave function, a function of x such that $2 is the probability of the particle being at various distances along the x axis, m is the mass of the particle and U(x) is the potential energy. In the region 0 < x < a, the potential is constant and may be taken as datum, so that in that region, equation (2-5) becomes: 2 2 EW 3 - ~2§—' d (2-6) 8H m dx Functions which solve this equation are: A. .. A sin 9-335- where n = 1, 2, 3, (2-7) and A is a constant. Hence, ll nzh2 2 . 8ma E a n = l, 2, 3 "'. (2-8) The solutions in three dimensions are obtained by taking equations (2-7) and (2-8) in each of the co- ordinate directions. Then, T = (Ax) (wy) (AZ) (2-9) and E = Et + Ey + Ez These equations are difficult to understand in terms of ordinary sized particles but the following observations may be made. (i) There are certain positions where the probability of finding the particle is zero. (ii) Only certain discrete energy levels are possible. (iii) A particle may not have zero energy (iv) The more closely a particle is confined, the greater the spacing of the allowed energy levels. Also, if only one electron in each atom or molecule may be in an excited state, the energy of an Avagadro's number of these atoms or molecules is 21.6n2 kilo calories/mole. Hence the allowed energy levels for electrons in atoms or l2 molecules are very widely spaced compared with ordinary thermal energies. The distribution of particles through the various allowed energy levels was given by Boltzmann as: n1/no = exp. (—AEi/kT) (-10) where n1 is the number of particles at energy level E 1’ no is the number of particles at energy level EO and k is g- Boltzmann's constant equal to 1.380 x 10'16 erg./degree molecule. The appearance of the term kT in this expression is of particular significance. It indicates that if a molecule possesses energy in excess of the lowest allowable level, this excess, which is known as "thermal energy," is dependent upon the temperature of the system. The allowed energies in a cubic container are given by: 2 h --—75 (2-11) 8ma E =(n2 + n2 + n2) x y z The total number of combinations of values of nx, ny and nZ corresponding to the same energy state is called the "degeneracy" denoted by "g" so that n 52.: g exp. (-AEi/kT) . (2-12) 0 V l3 Molecules may possess thermal energy due to motion in the form of vibration, rotation or translation. The average translational energy of an Avagadro's number of molecules is 1/2 RT per degree of freedom where R is the universal gas constant. Each molecule is free to rotate about each of the co-ordinate axes and hence has three rotational degrees of freedom. A linear molecule, however, has no rotational energy about its axis. The average rotational energy is 1/2 RT per degree of freedom and hence for linear molecules becomes RT and for non-linear molecules becomes 3/2 RT. Each atom in a molecule has three degrees of freedom and hence the total number of degrees of freedom for a molecule of n atoms is 3n. For a non-linear molecule there are three degrees of transla- tion and three degrees of rotation so that the number of degrees of vibrational freedom is 3n-6.. Of particular interest here is the H20 molecule which is non-linear with an internal angle of 105°. With three atoms it is seen to have three degrees of vibrational freedom as shown in Figure 2-5. The thermal energy of a non-linear molecule is then given by E - E0 = 5/2 RT + Evib. (2-13) 14 Rate Process Theory For many simple chemical reactions of the type nA + B the rate at which the reaction occurs is given by k'(A)n and the reaction is designated as first, second or third order depending upon whether n is l, 2 or 3. k' is called the rate constant. Only second order reactions will be considered. The equilibrium constant K for the reaction A213 is given by K s —— (2-114) where NA and NB represent the number of molecules in all of the energy levels of A and B respectively. So that from equation (2-10) E exp. (-iEB/kT) K = exp. (-AEo/kT) E exp. (-iEA/ET) (2-15) which may be written as QB x .. exp. (-AEO/kT) '62— (2-16) A where QA'and QB are known as "partition functions." 15 According to the transition state theory as developed by Glasstone, Laidler and Eyring [l9Al], when two species A and B react, a transition activated state is formed so that A + B + (AB)* + products and the rate of the reaction depends upon the concentration of the activated species and the rate at which it breaks up. The equilibrium constant for the activated state according to equation (2-16) is: Q(AB)* . f K* - QX—RE— exp. (-AEO/RT) (2—17) hence Q s k' §£A%%—- exp. (-AEZ/RT) (2-18) A which may be written as k' = A exp. (-Ea/RT) (2-19) and is known as the Arrhenius equation. Ea is called the "activation energy." An alternative form of equations (2-18) and (2-19) may be obtained by considering that the average vibrational energy of the bonds in the activated complex is given by l6 kT and the vibrational mode that breaks the complex is given by Plancks equation (2-H). Hence hv kT or kT/h (2-20) C II the rate of reaction is equal to m fi? (A)(B) hence k' = K' 1&1 (2-21) The "free energy of activation" is given by: (AE°)* = -RT ln K* or K* = exp. (-(AF°)*/RT) (2-22) and since (AF°)* = (AH°)* - T(As°)* where (AH°)* is the "enthalpy of activation" and (AS°)* is the "entropy of activation" 17 K* = exp ((As°fi/R) exp. (-(AH°)*/RT) (2-23) and kT o * o x k' = T? exp. ((AS ) /R) exp. (-(AH ) /RT) (2-2“) so that in equation (2—19) the constant A becomes A = §§ exp. ((AS°)*/R) (2-25) Creep as a Rate Process The concept of the free energy of activation forming an energy barrier which restricts relative movement of flow units is illustrated in Figure 2-6., The equilibrium condition is shown by curve A and the application of a directed potential, such as a shear force, distorts the curve to position B. The horizontal displacement 6 represents the elastic strain and the difference in level of adjacent minima becomes TAA where T is the shear stress, A is the area of the flow unit and A is the distance between equilibrium positions of the unit. Thus the level of each minimum is altered by tAA/2. From equations (2-21) and (2-22) k' = %? exp. (-AF°/RT) (2-26) and when the barrier height in the direction of the force becomes (AF — TAA/2) and in the direction Opposite 18 the force (AF + TAA/2). The net rate of activation in the direction of the force is given by + T kT k' - k' = 2 TT-exp. (-AF/RT) sinh (TAA/2kT) (2-27) The net rate of flow in the forward direction resulting from the applied shear stress is the net specific rate of movement of the flow unit multiplied by the dis- tance A traversed per movement. Dividing this value by A the distance between flow units normal to the direc- 1! tion of flow gives the rate of shear strain. kT TT-exp. (-AF/RT) sinh (IAA/2kT) (2-28) < 0 ll 1 As a reasonable approximation, A 8 Al [Herrin and Jones, 1963], hence equation (2-28) becomes, p = 2%T_ exp. (-AF/RT) sinh (va/2kT) (2-29) where Vf is the volume of the flow unit. If the energy supplied by the action of the shear force is small compared to the thermal energy, sinh (IVf/ZkT) = TVf/2kT hence equation (2-29) becomes l9 Vf y = T ‘H’ exp. (~AF/RT) (2-29a) that is, the shear rate is proportional to the shear stress which constitutes Newtonian flow. Thus the coefficient of viscosity is given by n = 3L exp. (AF/RT) (2-30) f For the flow of soils and solids however, the energy supplied by the action of the shear stress will be greater than the thermal energy and sinh ( TVf/ZKT) = l/2 exp. (TVf/2kT) hence equation (2-29) becomes y = E? exp. (-AF/RT) exp. (IVf/2kT) (2-31) It is this form which is most useful in the study of the creep process. Mitchell, Campanella and Singh [1968] modified equation (2—31) to a = X exp. (-EX/RT) I (2-32) where e is the axial strain rate and 20 Ex = AF - TVf/2 (2-33) where Ex is called the "experimental activation energy." Then from equation (2-32) 3 2n (é/T) _ a (1/T) ‘ ’Ex/R (2'3“) By observing the steady state creep rate at several temperatures it was possible to plot £n(é/T) against (l/T) for several soils and establish that the relationship was linear as predicted by the theory. Values for Ex were obtained by means of equation (2-34) and for San Francisco Bay mud consolidated at 1 kg./sq. cm. and at a deviator stress of 0.A5 kg./sq. cm. a value of 31.u k. calories/mole was obtained. Also, from equation (2—33) a linear rela- tionship should exist between Ex and T. Tests on remoulded illite verified this relationship and by extrapolation to T = 0 AF was found to be ”3.5 k. calories/mole. The behavior of polycrystalline ice was investigated by Dillon and Andersland [1967] who found an enthalpy of activation of 11.” k. calories/mole and the following values of AF. Temp. °C Toot (psi) AF (k. cal./mole) -10 120 28.“ -10 100 22.8 _ A 90 2A.? 21 Goughnour and Andersland [1968] extended this investigation to sand—ice systems and found that AF varied with sand concentration as shown in Figure (2-7). Earlier work by Andersland and Akili [1967] on frozen Sault Ste. Marie clay, which is predominantly illite, found AF to be of the order of 9A k. calories/mole. 22 A ‘I‘ dv -' dv dz dz I J / (a) - T (b) V Newtonian fluid ' Thixotropic fluid lOO‘F SOT 10%)- N E 5x 0 \. E) x 11 it . l-I’ "' 30 n e 5) 005‘" m“ (D g 0.1“ Na-Kaolinite .p "’ 0.05» 'c H m H 10 50 100 500 1000 Water content - 1 (0) Variation of yield stress with water content Fig. 2-1. Rheological properties indicated by viscosity tests. 23 .m>n30 moose Hmoaoze .mlm .me mafia eoseessoeee HeHeHeH gecko unmafinm oomno hnmncoomm amono mnmfipnma uteaqg C>=.Hydroxyl Octahedral unit (9 = Oxygen O Tetrahedral unit Kaolinite I I— ‘I I Chlorite Fig. 2-3. 24 0= Aluminum, Magnesium, etc. Symbol Octahedral Sheet 0 = Silicon Tetrahedral sheet ' ' - +—-—Potassium >—< IIIIIII ------ *-'Water )7 A Vermiculite Structure of minerals. 25 Net force IA "'“'Exponential repulsive force—electrolyte from (1) dilute to (3) strong. (1) (D \ g \ ._-__-Attractive force 0 \ m \ a) \ p. H (D H 3 Q. Q) m DisIance O) C) n o c... O.) > -.—I 4-3 O m L. 4.) i.) <: A Fig. 2-A. Attraction and repulsion between surfaces (after Scott, 1963). 26 3,652 cm- 3,756 cm- 1 I 1,595 cm- Fig. 2-5. Modes of vibration for water and associated energy levels. 27 .mnmfinnmn mmnocm no coapmucomonmmm .mnm .mflm AI pcmEoomHQmHQ E __. \ m 2550 \v, < o>nzo wnfipom monom_l\L// weapon monom oz M / mono.“ smonm / \ e——————-iuamaoetdstp sense 01 DSJIHDSJ ASJaug ca1./mole 00) Observed activation energy (K. U1 ' O .0- 30* 20+ 28 10 A» 0 i T i i I I 41 O 10 20 30 A0 ‘50 60 70 Percent sand by volume Fig. 2-7. 'Observed activation energy versus percent sand by volume (after Goughnour, 1967). CHAPTER III MATERIALS AND METHODS The-soil used in this investigation was a glacial lake clay from Sault Ste. Marie, Michigan. It is peda— logicly classified as Ontonogan and the basic properties are listed below.- The grain size distribution curve is shown in Figure 3-1. Index Properties Properties Per Cent or Number Liquid Limit 60% Plastic Limit 2A% Plasticity Index 36% Specific Gravity 2.70 Less than 2p 60% Specific surface Area 290 sq. M./g/ Cation Exchange Capacity 28 meg/100 g. Mineral Content of Fraction Less than 2p Illite 50% Vermiculite 20% Chlorite 15% Kaolinite 5% Quartz and Feldspar 10% 29 m 30 A quantity of the soil was treated with 1N hydro- chloric acid to dissolve the carbonates and then washed with distilled water until the filtrate was free of chlorides as indicated by the silver nitrate test. It was then divided into three separate samples which were soaked in lithium, sodium or potassium chloride and again washed with distilled water and air dried. In order to obtain further information on the role of the adsorption complex in the creep mechanism, a portion of each of the three samples was heated at 165°C. for seven days and then saturated with carbon tetra— chloride. This procedure dehydrated the clay and caused the double layer to collapse. The non-polar carbon tetra— chloride does not form an oriented adsorbed layer and the clay loses many of its common characteristics. For example, it becomes almost non-plastic. Viscosity Tests Viscosity measurements were made on the fluid soil- water mixtures with a "Brookfield" viscometer which operates on the principle of a rotating disc as illustrated in Figure 3-2. The calibration of the instrument was checked by using glycerin-water mixtures. The exact proportions of these mixtures were checked with a specific gravity hydrometer. The soil—water mixtures were dispersed in a standard soil dispersion unit and allowed to stand for one hour Tinnitus... J. 4 a . .\ 31 before testing. This permitted the coarser particles to settle out and eliminated the problem of rapidly changing density during the period of measurement. When the measure- ment was made, 25 ml. of the mixture was withdrawn from the vicinity of the disc and oven dried to determine the concentration of solids in grams per litre. All of the viscosity tests were performed in a thermostatically controlled water bath and the temperature of each mixture was checked before testing. Creep Tests Remoulded samples of each of the three soils were consolidated in triaxial compression cells at pressures of 1.75, 3.5 and 7.0 kg./sq. cm. then subjected to creep at constant volume by the application of axial loads. The initial axial stress for each of the consolidation pres- sures was 0.83, 1.25, and 1.66 kg./sq. cm. respectively. When secondary creep was established, an additional increment of axial stress equal to 0.10“, 0.208 or O.Al6 kg/sq. cm. was added. These axial stresses were applied by means of dead weights and the figures quoted are in terms of total stress. When secondary creep was again established, a further increment of the same magnitude was applied. The room temperature for those tests was controlled to 25°C 1 1°C. Hooo. + 32 mooo. .zwao mfinmz.mum pasmm pom m>n30 soapsnfinpmfin oufiw manna .Hnm .wfim ensuesefiflez es seem asses Hoo. moo. Ho. mo. r-l Ln - _ _ _ _ _ _ . . _ _ _ _ _ _ _ _ _ _ _ _ _ .-_-_-~-““_--_-_-—_--_--_--—-—b ——_—_ oom 00H 0: wo>mam unaccepm .m.D 1 [ON TO: vow QQSIGM Kq JGUIJ queoaed .OOH 33 Gears Motor Speed Selector :::::\ Clutch —\ N \\ x W $31.1 ——'=T\ Calibrated Pointe Spring Disc ——\\\\: 7 Sample Fig. 3-2. Brookfield viscometer CHAPTER IV EXPERIMENTAL RESULTS Viscosity Tests Viscosity measurements were made over a range of soil concentrations for each of,the lithium,sodium and potassium saturated soil samples at temperatures of 25, 35 and 45°C. As the concentration of soil solids was increased, the viscous flow changed from Newtonian to thixotropic. The limit for Newtonian flow of the lithium and sodium satur- ated samples was of the order of 100 g./litre, but for the potassium saturated sample it extended to about 500 g./ litre. The variation in the coefficient of viscosity with concentration of soil solids for each of the three soils at 25°C is shown in Figure A-1 and for the potassium saturated soil at each temperature in Figure A-2. Values of the free energy of activation AF were calculated by the use of equation (2—30) in the form AF ( in TI 3 An —- + —- ) (AI-l) eu- from which it is seen that there is a linear relationship between in n and (1/T). From Figures (A-3), (4-H) and (4-5) this is found to be approximately true for each soil 3A ,. '.. "1",.- I, 35 and the slope of the lines is parallel to the line for pure water. The approximation is due to straight lines being drawn through the points recognizing that AF for water is also a function of temperature. This variation is not significant over the temperature range considered Thus there is no evidence that AF varies with concentration .'—f .-.'_ of soil solids over the range of Newtonian flow. There 1 _, -.L. and the value of AF may be taken as 3.8 k. calories/mole. E "I I is a change in the size of the flow units with concentra- I tion and this is shown in Figure (4-6). Creep Tests The results of a typical triaxial creep test are illustrated in Figure (A-7) which shows the variation of natural strain with time and the effect of the additional increments of axial stress. All of the samples gave curves of similar form. At low stress levels there is a simple linear relationship between the strain and the logarithm of the time but as the stress level is increased there is a pronounced deviation from such a relationship. This point has been discussed by Singh and Mitchell [1968]. A linear relationship was observed between the logarithm of the strain rate and the strain which was found to be useful in the evaluation of the activation energies. From equation (2-31), in A = in kT/h - AF/RT + T Vf/2kT (u-2) 36 and if y is changed by the application of an additional increment of stress, in (Yl/Y2) = (Tl - T2) Vf/2kT (U—3) Since V is not constant, possibly due to continuous structural changes as the creep proceeds, it is necessary to determine "1 and Q, at the same instant. This was accomplished by calculating N1 and A2 at each side of the discontinuity caused by application of the additional stress increment. The application of additional stress causes rapid initial strain due to elastic compression of the system and a certain amount of additional primary creep. It is therefore necessary to make use of the linear rela- tionship which exists between the logarithm of the strain rate and the strain to extrapolate back to the initial value as illustrated in Figure (A—8). The usual assump- tion that the intensity of plastic action is governed by the octahedral shear stress is also made here and octahedral shear stresses are employed in all relevant equations. Vf/2kT was calculated by means of equation (4-3) from the data in Figure (4-8) and then AF was calculated from equation (4-2) as illustrated in the example below. The results are listed in Table (4-1). 37 Example Potassium saturated sample, 03 = 3.5 kg./sq. cm. initial axial stress = 1.25 kg./sq. cm.,first increment of axial stress of 0.208 kg./sq. cm.,temperature 298°K., Boltzmann's constant k = 1.380 x 10-16 erg/degree molecule, Planck's constant h = 6.62M x 10'27 erg—sec and the gas constant R = 1.987 calories/degree mole. From equation (4-3) Vf/2kT = in (Tl/"2)MT1 - 12) From Figure (A-8) Vl = 125 x 10"6 and T2 = 8.u x 10"6 hence in (Al/)2) = 2.698 Now T1 and T2 are octahedral shear stresses and since T =£(o_o) oct 3 1 3 Tl — 12= /2/3 (axial stress increment) = 0.098 kg./sq. cm. therefore Vf/2kT = 2.698/0.098 38 27.50 sq. cm./kg. 27.00 x 10"6 sq. cm./dyne. so that 16 27.00 x 10-6 x 2 x 1.38 x 10- x 298 < II 2.25 x 10'18 c.c. From equation (4-2) AF = RT in (kT/h) + TRT (Vf/2kT) - RT in k In Figure (A-8) the strain rate is shown in terms of axial strain for convenience, but for this calculation it must be in terms of octahedral shear strain which means that the axial strain rate figure must be multiplied by /2. Also h should be multiplied by 60 to convert to erg. minutes. Now considering the end of the first period of creep when the axial stress was 1.25 kg./sq. cm. AF 15,130 + /§/3 x 1.25 x 981 x 103 x 1.987 x 298 (27 x 10-6) - 1.987 x 298 (-ll.33) 31.u k. calories/mole. rail: 1." 1". WEI ‘- '4' ._‘ 39 0.5m 0.0 0He.0 . 4. m.5m 0.H 0H:.0 00.H mm.H 00.5 e H.0m m.H m0m.0 H.wm m.H 00m.0 mm.H. 05.H 0m.m H00 0.Hm 0.m 30H.0 H.5e 0.0 30H.0 m0.0 m0.H m5.H assessoos 0.0m ._5.0 0H:.0 m.mm 0.0 0H:.0 00.H mm.H 00.5 e 0.mm e.H 00m.0 5.mm H.H 00m.0 mm.a :5.H 0m.m H00 m.0m 0.H :0H.0 0.3m m.H 30H.0 mm.0 00.H m5.H Esseom 0.mm 5.0 0H:.0 m.em 0.0 0He.0 00.H m0.a 00.5 a 0.0m H.H m0m.0 0.0m N.H 00m.0 mm.H e5.H 0m.m H00 m.0m 5.H 30H.0 H.3m H.H 30H.0 m0.0 m0.H e5.H Seances e.mm 0.m 0H20 m.0m 0.H 0H:.0 00.H 50.H 00.5 H.mm m.m 00m.0 s.Hm m.m 00m.0 mm.H m5.H 0m.m - 0.3m m.e 30H.0 0.Hm 0.m 30H.0 m0.0 mm.H m5.H Esammsooa 0.5m N.H 0H:.0 0.mm 5.0 0H:.0 00.H 00.H 00.5 0.0m 0.0 000.0 s.wm 5.H m0m.0 mm.H m5.H 0m.m 0.0m 0.m 30H.0 0.0m 0.m :0H.0 mm.0 mm.H m5.H Esseom 0.mm m.H 0H:.0 0.5m m.H 0H:.0 00.H 00.H 00.5 m.mm :.H 00m.0 m.mm 5.H 00m.0 mm.H 05.H 0m.m 0.mm m.a :0H.0 3.0m H.m :0H.0 mm.0 mm.a m5.H ssscosq oHoe\.Hsc .x 0Hx ma oHoe\.Hso .x 0H x ma m4 0 m o .Eo\.mx w m o .E0\.wx .Eo\.wx .o.o\.w m.EO\.mx . > m ma > m m mmonpm zpfimcmo madmmosm pcmEommne Hefix< sea .Homcoo Hsom pcoEonocH mmome Hme< pcoomm pcmEonocH mmonum Hmfix< owned HmeHcH .mumme doono Eonm mezao> 30am new zwnmcm cofipm>apo< no modam>ll.a.: mqm oanH\w coaomnpcoocoo - lwI AMI .HI: .wE astodtquao - AqrsoostA .mmao popmnsumm Esammmuoo now moLSumanEop pcmnoMMHU pm coapmnpcmocoo Spa: anamoomfl> go Coapmfinm> .ml: .wfim onufia\m coapmnusmocoo oooa owa 0H LU P :4 ._qTJI1__ a fl — _I ‘ .J .J l c Al 1 l I O H - AirsoostA estodrqueo -s....—-.-:— a. a.-.».. .I >-_,. 5......»..« — > Viscosity - centipoise 2. 0) .0031 Fig. A2 A Experimental values C)Tabulated values 1 L 1 r .0032 .0033 Inverse of temperature OK-l A-3. Variation of viscosity with temperature for lithium saturated clay. .003A Viscosity - centipoise 20 O. A3 A Experimental values 6) Tabulated values 100 g./litre '\¢\ 5 i A A .0031 .0032 .0033 .003A Inverse of temperature OK-l Fig. A-A. Variation of viscosity with temperature for sodium saturated clay. 0 U1 1 Viscosity — centipoisep H 2) AA A Experimental values G) Tabulated values 200 g./1itre A (Pure Water) 086 / / / // // /43 / / : t A .0031 .0032 .0033 .003A Inverse of temperature OK"l Fig. A-5. Variation of viscosity with temperature for potassium saturated clay. A5 LI T- c) 3 __ ? 0 j ox I“. N 1 I c S x 2 1‘ K a — A I :> (D 5 Na "3 > 1 fl- Li 3 o H [In 0 i P40 i i 0 50 100 150 200 Soil concentration g./litre Fig. A-6. Variation of flow volume with concentration of soil. -A Natural strain x 10 A6 SO‘T 03 = 3.5 kg./sq. cm. 1.666 kg/sq.cm. 30 ‘ cm. 20 i 10 1 cl = 1.25 kg/sq. cm. 0 50 100 150 200 Time - minutes Fig. A-7. Creep curve for potassium saturated clay. Strain rate min.-1 A7 I 03 = 3.5 kg./sq. cm. A- .OOOli' )— .'.'. - G) G) G I. 9 t 0 ~ (9 .OOOIiL L A . i .' .L t 4, O .001 .002 .003 .00A .005 Natural strain Fig. A-8. Variation of strain rate with strain for potassium saturated clay. CHAPTER V ANALYSIS AND INTERPRETATION Theory If the values of AF are to be regarded as other than merely parameters in the Arrhenius equation, and they are to be given a physical interpretation with respect to the 1 nature of the rate controlling bonds, further considera— tion must be given to the assumptions which are implicit in the derivation of the rate equation. Up to this point it has.been assumed that the flow process involves the movement of a particle by a single step from an equilibrium position A to the next equili- brium position B. It may be necessary for the particle to move through a series of intermediate steps before reaching position B and then the strain rate is given by: i= M (5-1) ‘where tn is the delay time associated with each obstacle. Equation (5-1) may be written-as ’ M (5-2) exp. (AFl/RT) + ' ‘ ' + An exp (AFz/RT) A8 A9 where An are constants with other symbols as previously defined. It is seen from these equations that if one step is.much slower than any of the others, then it may be regarded as the rate-controlling step and that it is associated with the highest energy barrier. In this case the other steps may be neglected. If two or more steps are of the same order of magnitude the calculated value of AF will have no meaning unless it can be resolved into its component parts. There may also be more than one available path by which the particles may proceed so that several different mechanisms are Operating in parallel. In this_case the strain rate is given by v= 371+V2+-~yn (5-3) 01” -< ll Al exp. (—AFl/RT) + A2 exp (—AF2/RT) + . . . (S—A) The rate—controlling step will now be the fastest one, but again, if two or more steps are of the same order of magnitude as the fastest step, the calculated value of AF will have no physical meaning., Some of the possible mechanisms which could be Operating simultaneously in the ice and soil water systems to be considered are: 50 (i) the flow of free water (ii) the creep of polycrystalline ice (iii) the relative movement of soil grains, which may involve the action of adsorbed water. These three systems will now be considered before attempt- ing to analyze the various combinations of them. The Flow of Free Water In this context, "free water" refers to water which is not under the action of surface forces from the clay particles. However, there is a mutual association between the individual water molecules in the form of hydrogen bonding. This is best described by reference to the structure of ice shown in Figure (5-1) in which the hydro- gen bonding is complete and each hydrogen atom shares its' electron with two oxygen atoms to make a regular hexagonal crystal arrangement. In the liquid phase, some of these bonds are destroyed and individual molecules may exist. It is thought that the closer packing of these free molecules contributes to the fact that the density of water is greater than that of ice. As the temperature is increased the thermal energy of the molecules increases and progressively more of the hydrogen bonds are broken as indicated in Table (5-1). In order for a molecule to move into a new position, a hole must be available for it. The free energy of activation of viscous flow therefore generally consists of 51 TABLE 5-1.—-Degree of Hydrogen Bonding of Water. Temperature State 3 Degree of Bonding 0° 0 Ice . 100% 0° C Water 85% A00 0 Water 50% 100° C Steam 10% two parts, (a) the energy required to form the hole and (b) the energy required for the molecule to move into the hole. Now it may be shown that the energy required to form a hole in a liquid of molecular size is equal to the energy required to evaporate a molecule without leaving a hole. Since the necessary holes already exist in a liquid, the energy required to form the hole will only be that which is necessary to increase an existing hole to molecular size. This is a relatively constant fraction of the energy of vaporization. In non-associated liquids, a plot of viscosity against 1/T will give a linear relationship, but in the case of water the plot is slightly curved. This curvature is due to the fact that the free energy of activation of flow consists not only Of the energy required to form a hole, but also the energy required to break the hydrogen bonds with which it is tied to its neighbors. As the temperature is increased, the number of bonds decreases. The free energy of activation for viscous flow of water is 52 about A k. calories/mole and the strength of a hydrogen bond is about 6 k. calories/mole [Glasstone, 1959]. Significant changes in AF with pressure only occur with pressures of the order of thousands of atmospheres and hence are not directly relevant here. The principle which is involved will be relevant in later discussion. If the external pressure on the system is increased, the formation of a hole will involve doing work against this pressure. Hence AF will be increased by an amount pAV. The Creep of Polycrystalline Ice Values quoted in the literature for the activation energy of polycrystalline ice range from 10.7 k. calories/ mole [Mellor and Smith, 1967] to approximately 25 k. calories/mole [Dillon and Andersland, 1967] with small variations in this latter value according to the tempera- ture and pressure. There is some confusion in terminology which accounts for most of the apparent differences. Many of the authors, including Mellor and Smith, have determined the enthalpy of activation (AH) and referred to it as the free energy of activation. According to Dillon and Andersland [1967], the value of AH is 11.A k. calories/mole which is the order of the commonly quoted values. The number of bonds which must be broken to permit slip along the basal plane of ice is much less than the number which must be broken for slip to occur normal to 53 this plane. Consequently all reported observations of the creep of a single ice crystal indicate that the creep mechanism is associated with movement along the basal plane. In the polycrystalline state where the crystals are randomly oriented this movement is restricted at the grain boundries, and the additional mechanisms which come into operation include cavity formation, accommodation cracking, rotation and migration of the grain boundaries [Gold, 1963]. The Relative Movement of Soil Grains If the creep of soil is a thermally activated process, then some form of molecular bonding must exist between the grains. This may be in the form of hydrogen bonding through the adsorbed water layer or it may be in the form of ionic bonding as the result of direct mineral to mineral contact. The probability that any such mechan- ism exists will be discussed later in this chapter on the basis of the experimental values obtained for the free energy of activation. There is one other factor contribut- ing to the experimental value of AF which must be con- sidered, and that is the energy involved in the creep of a frictionless unbonded soil. The stress required to induce flow in a closely packed hexagonal arrangement of spherical balls was con— sidered by Thurston and Deresiewicz [1959]. Any one ball in such an arrangement rests on three balls in the layer 5A telow, makes contact with six others in the plane of its centre, and is acted upon by three contact forces normal to its surface from the three balls in the layer above. The force acting on the sphere in the direction normal to the hexagonal layer is the resultant of each of these 2 three normal stresses which have a magnitude of /2 R 03 where O is the hydrostatic pressure acting on the system 3 and R is the radius of the balls. Each of these forces has a direction cosine with the vertical of /2//3. The resultant force normal to the layer is therefore 2/3 R2 03. If a force L is now applied at angles a and B to the z and y axes, where z is normal to the plane of the hexagon, so that L has both shear and normal components, it can then be shown that the ratio of the shearing to the normal forces is given by: L 6°” 1:. -.- 0.35 (5-5) 2 2/3 R2 03 + L cos d if the coefficient of friction of the material is zero. The existence of a normal force on the plane of sliding will therefore mean that some of the applied shear stress will be utilized in moving the soil grains even if there is no form of bonding between them. The stress required to overcome this resistance on the octahedral plane will be 0.35 x 1/3 (01 + 02 + 03) and therefore equations (2-29), (2-29a) and (2-31) should be modified to read 55 y: ail-$1" exp. (-AF/RT) sinh ((T-O.350 ) oct. Vf/2kT) (5-6) t = (T _ 0'35°oct.) v1.3,h exp. (-AF/RT) (5-7) and . kT y'= Tr-eXp. (-AF/RT) exp. ((r-O.3500ct.)Vf/2kT) (5~8) The factor 0.35 may vary with the shape of the grains and the density of packing. Aleouri [1969] has shown experi- mentally that creep rates for frozen saturatet sanfl decrease with increase in Go while holding the devia- ct. toric stress constant. Soil Suspensions The viscosity of the soil suspensions increased with increasing concentration of solids in the order Li, Na, K but no variation in the free energy of activation of flow was observed. In dilute suSpensions where it is assumed that the grains are widely Spaced, the flow mechanism is that of pure water with boundary conditions defined by the container and the soil grains. The effect of the adsorbed water layer on the grains is not funda- mentally different from that of the boundary layer on the walls of the container. 56 The measurement of a coefficient of viscosity of a suspension has a real significance for such problems as the pumping of such a material, but for a fundamental investigation of the nature of the prOperties of the water and soil it may be preferable to regard such a measurement, as the determination of the viscosity of water in a viscometer of complex boundary conditions and the Einstein equation (2-1) might be better written as no n/(l + a¢) (5-9) and the results used to deduce facts about the nature of the boundary conditions. For example, the order of vis- cosities at a given concentration for each of the three samples tested would indicate that the effective volume of the lithium saturated clay was greater than that of the sodium saturated which was greater than that of the potassium saturated and due to the different degrees of hydration of their ions. When the concentration is increased to the point that the particles come within range of their mutual force fields a multiple flow situation is established. The free water still follows its normal flow mechanism within the new boundary conditions but there is now the added flow mechanism of the interacting grains. The two systems can not be regarded as operating independently, for the rate of movement of the grains is controlled not only by the 57 activation barriers of the inter-particle bonds but also by the viscous drag of the water. When a bond is broken, the movement to the new equilibrium position is restrained by the effect of the water thus establishing the time delay associated with thixotropic materials of this type. Hence an activation energy determined from the bulk behavior would represent some combinations of the various energies involved. It may therefore be concluded that the calculated values of the activation energy for each of the samples is valid since the method of calculation involves a ratio of viscosities and the measured viscosity differs from that of water by a constant factor which will cancel out. The calculation of the flow volume involves the direct use of the measured viscosity and will therefore deviate from the true value in inverse proportion to this factor. Unfrozen Soil The modified strain rate equation (5-6) implies the existence of a yield stress, below which creep will not occur. This phenomenon is known to occur in sands but does not exist in saturated clays. Even a small stress will produce creep at the correspondingly slow rate. The experimental values of AF listed in Table (fl-l) may therefore be accepted without modification. It is significant that there is no apparent dif- ference between the values of AF for any of the three soils 58 even when dehydrated and mixed with carbon tetrachloride. This would appear to eliminate any possibility that the source of the bonding is associated with the adsorption complex. In addition, the mean value of approximately 28 k. calories/mole is within the range of ionic and covalent bonding and is five times the strength of a hydrogen bond. It might be thought that value of 28 is suggestive of the 25 k. calories/mole that Dillon and Andersland [1967] found for polycrystalline ice and it could be postulated that the bonding was associated with the first one or two molecular layers of adsorbed water where the structure is ice—like. The lack of variation in the values obtained from the carbon tetrachloride samples precludes such a possibility. The only bonding mechanism which can be consistent with the data is that of a portion of the edge of a clay plate which is deficient in oxygen (or hydroxyl) atoms and has a local positive charge, associates with a portion of another plate which has lost a metallic atom and has a local negative charge. A junction would then be formed between the two plates, but due to the lack of orientation would not be of full strength and would be readily broken. The values of VI. also show no significant variation between the samples which lends support to the suggestion that the type of bond is similar in each case. While V f is called the "flow volume," this is only true if the 59 stress on the flowing unit is equal to the applied stress. In the case of a particulate media where the spacing of the units is large in comparison to their size, a correc- tion must be made in order to determine the actual volume of the flowing unit. If Vf is multiplied by the number. of contacts per sq. cm., the length A will be obtained and in the derivation it was assumed that all of the dimensions of the unit are of the same order of magnitude so that an approximation to the actual flow volume is given by A3. The average volume of a particle of this clay has been estimated by Christensen and Wu.[l96u] to be 2 x 10'15 c.c. and from Figure (3-1) it is seen that 60% of the soil is less than 2 p. Also from Table (M-l) the mean dry density of the samples is 1.75 g./c.c. The volume of clay per c.c. of soil is therefore 0.39 c.c. and the number of clay particles is approximately 2 x 101“. Rosenquist [1959] has estimated that each particle forms six con- tacts, so that if this estimate is accepted, the number of contacts per c.c. will be three'times the number of particles (since each contact is formed between two par- ticles). The number of contacts per sq. cm. is then (3 x no. of particles)2/3 which is 7 x 109. Hence the length A is 1.2 K and the actual flow volume is 1.7 33. This estimate of A is approximately half of that which would be expected from the crystal structure of the 6O minerals. This discrepancy is probably related to the assumption that the shape of the flow unit was cubic, for while the dimensions of the unit would be of the same order of magnitude, they are unlikely to be equal. It, is therefore considered to be a good estimate and does establish that the flow units involved are of molecular size. It is also observed that for each sample the value of Vf decreases with increasing density. This is to be expected as the contacts between the grains are improved. Frozen Soil The behavior of frozen soil is in many ways similar to that of soil suspensions. Goughnour [1967] has reported that at low concentrations there is a linear relationship between the creep rate and the volume of solids and an equation similar to the Einstein equation (2-1) could be proposed. A small increase in activation energy is reported over this range possibly due to the interlocking effect of the grains on the dislocations. When the concentration is increased to the point where there is contact between the grains there is a rapid increase in activation energy as illustrated in Figure (2-7). Andersland and Akili [1967] found a value of approximately 100 k. calories/mole for frozen clay. It is assumed that the confinement of the particles by the ice makes the modified rate equation (5—8) relevant in 61 this case. The value of the hydrostatic pressure exerted by the ice in resisting the movement of the grains is not readily determined, but a check calculation will be made to establish the order of magnitude which would be required. From equation (5-8) kT )Vf/ZkT)-RT2n—— - RT in y AF = RT ((T-O.350 h oct. (5-10) Selecting one of the reported test results which yields a value of 112 k. calories/mole at a creep rate of 2.5 x 10-” and a temperature of -15°C was selected. The value of 112 k. calories/mole represents an excess of approximately 55 over the combined energies of the ice and clay and if this is to be explained entirely in terms of the confining pres- sure, the effect of the term 0.350OCt must be to reduce the energy by 55 k. calories/mole. Thus 0.350oct RVV/2k = 55,000 01" Q I 6 oct - 22 x 10 dynes/sq. cm. 319 1b./sq. in. which is of the order of magnitude which would be expected. 62 While this approach is considered logical for sands, its application to clays may have to be further modified until more is known about molecular exchange activity at the depressed temperatures. Although it is now believed that a supercooled liquid phase does exist around the particles, the site activity would be greatly reduced and the true free energy of activation may probably be only that of the ice. 63 Structure of oxygen atoms in ice lattice Hydrogen atoms lie in the bonds. I l l \\\o’//}p\\‘o’//X\\\CV//J(\\‘o’/’ x x x qu \\o’// ‘\\‘o’/’ ‘\\‘o’/’ ‘\\ o’// /X\ 0/ x\ O/ "\O / X\ I l l Projection of ice lattice on basal plane; circles and crosses indicate oxygen atoms on different planes. Fig. 5-1. Structure of ice (after Founder, 1965). if -- Ami-x" I l ' I _. CHAPTER VI SUMMARY AND CONCLUSIONS The free energy of activation of Sault Ste. Marie Clay was determined for both viscous flow and secondary creep situations. The clay was treated to remove the carbonates then divided into three batches which were saturated with lithium, sodium, or potassium ions. Portion of each monionic batch was heated to 1650 C for seven days and then mixed with carbon tetrachloride to remove the adsorbed water layer. The viscosity of the three soil-water mixtures increased slowly with increasing concentration of solids until there were sufficient solids present to form a continuous structure. Once a structure had developed,the mixtures became thixotropic and the viscosity increased rapidly. .Analysis of the viscosity tests was confined to the region of low concentration. It was found that the lithium saturated soil recorded the highest viscosity and the potassium saturated the lowest at any given concen- tration. This is related to the different degrees of hydration of the three ions. The greater degree of hydration of the lithium ions increased the effective size of the particles and decreased the partial volume of the free water resulting in a higher viscosity reading. 6A The free energy of activation was determined by repeating the viscosity tests at three different temper- atures, 25, 35, and 450 C. It was found that in the region where the particles do not form a continuous structure, there was no change in the free energy from that of water. Hence the flow mechanism involved is that of free water moving in an increasingly restricted space and that the isolated particles made no contribution to the free energy of activation. Remoulded samples of each soil, including those saturated with carbon tetrachloride were consolidated in triaxial cells at pressures of 1.75, 3.5, and 7.0 Kg/sg. cm. They were then lightly loaded and when secondary creep was established, additional load increments were applied. This procedure provided sufficient data for the calculation of the free energy of activation and the volume of the flow unit. The free energy of activation was found to be approximately 28 K. calories/mole and there was no indication of any variation with either the nature of the adsorption complex or the degree of consolidation. The bonding mechanism is therefore not related to the adsorpted water layer but is direct mineral to mineral contact with the formation of ionic bonds at the points of contact. Increased consolidation apparently increases the number of contacts but does not affect the contacts already formed. ‘ 66 The flow volumes derived directly from the experi- mental data were corrected for the fact that in a particulate medium there is a finite number of contacts and the stress on each contact is therefore greater than the stress calculated on the gross area of the specimen. It was then found that the flow volume was approximately 1.7 cubic angstroms which indicates that the bond is of atomic dimensions. There was a small decrease in the size of the flow unit with increasing density due to the increase in the number of contacts and improvement of the contact Junctions. Application of the rate process theory to sands in both the frozen and unfrozen states was considered and it was concluded that a correction would be needed to allow for the mechanical energy involved in moving the grains against the external forces. The form of this cor- rection was derived. BIBLIOGRAPHY 67 BIBLIOGRAPHY Akili, W. "Stress Effect on Creep Rates of a Frozen Clay Soil from Standpoint of Rate Process Theory." Unpublished Ph.D. dissertation, Michigan State University, 1966u Al-Nouri, 1.. "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 Effect on Creep Rates of 3 Frozen Clay Soil." Geotechnique, Vol. XVII, No. 1 (March, 1967), pp. 27—39. Baver, L. D. Soil Physics. New York: John Wiley and Sons, 1956— Christensen, R. W. and Wu, T. H. "Analysis of Clay Deformation as a Rate Process." Proc. H1A7. Journal of Soil Mech. and Found. Eng. Div., Amer. Soc. of Civil Engineers (November, 196H7, pp. 125- 157. Dillon, H. B. and Andersland, O. B. "Deformation Rates of Polycrystalline Ice." Internat. Conf. on Physics of Snow and Ice, The Inst. of Low Temp. 801., Hokkaido Univ., Sapporo, Japan, August, 1967. Dorn, J. E. "The Spectrum of Activation Energies for Creep." Creep and Recovery, The American Society of Metals, Cleveland, Ohio (1957), pp. 255-283. Dorn, J. E. "Creep and Fracture of Metals at High Tempera- tures." Proc. of Symposium of National Physical Lab. London: Her Magesty's Stationery Office, 1959. Glasstone, S. Textbook of Physical Chemistry. New York: D. Van Nostrand Co., Inc., 1959. Glasstone, S., Laidler, K. J. and Eyring, H. The Theory of Rate Processes. New York: McGraw-Hill Book Co., Inc., 1991. Gold, L. W. "Deformation Mechanisms in Ice." Ice and Snow, PropertiepJ Processes and Applications. Edited by W. D. Kingery. Cambridge, Mass.: MIT Press, 1963. 68 69 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 Mech. and Found. Div., Amer. Soc. of Civil Engineers, Paper 6030, SM”, July, 1968. Grim, R. E. Clay Minerology. New York: McGraw-Hill Book Co., Inc., 1953. Herrin, M. and Jones, G. E. "The Behaviour of Bituminous Materials from the Viewpoint of the Absolute Rate Theory." Proc. Association of Asphalt Paving Technologists,5Vol. 32 (1963), pp. 82-101. Kauzmann, W. "Flow of Solid Metals from the Standpoint of the Chemical Rate Theory." Trans. Amer. Institute ‘4'. -J’ Ann-*uvm r of Mining and Metallurgical Engr., Vol. 193 (l9ul), pp. 57-830 . Kruyt, H. R. Colloid Science. Vol. I. New York: Elsevier Puinshing Co., 1952. Lambe, T. W. "A Mechanistic Picture of Shear Strength in Clay." Amer. Soc. of Civil Engineers Research Con- ference on Shear Strength of'Cohesive Soils (1960), pp. 555-580. Low, P. F. and Anderson, D. M. "The Partial Specific Volume of Water in Bentonite Systems." Proc. Soil Science Soc. Amer., Vol. 22 (1958), pp. 22-23. Low, P. F. and Anderson, D. M. "The Density of Water Adsorbed by Lithium, Sodium and Potassium Bentonite," Vol. 22, 1958. Marshall, C. E. The Physical Chemistry and Minerology of Soils. New York: John Wiley and Sons, Inc., 1963. Mellor, M. and Smith, J. M. "Creep of Snow and Ice." Internat. Conf. on Physics of Snow and Ice. The Inst. of Low Temp. Sci., Hokkaido Univ., Sapparo, Japan, August, 1967. Mitchell, J. K., Campanella, R. G., and Singh, A. "Soil Creep as a Rate Process." Journal of the Soil Mech. and Found. Div., Amer. Soc. of Civil Engineers, January, 1968. 70 Murayama, S. and Shibata, T. "Rheological Properties of Clays." Proc. 5th Internat. Conf. on Soil Mech. and Found. Eng., Paris, 1961:5pp. 269-273. Nadai, A. Theory of Flow and Fracture of Solids. Vol. 2. New York: McGraw-Hill Book Co., Inc., 1963. Pounder, E. R. The Physics of Ice. Oxford: Pergamon Press, 1965. Rosenquist, I. Th. "Physical-Chemical Properties of Soils: Soil-Water Systems." Journal of the Soil Mech. and Found. Div., Amer. Soc. of Civil Engineers, Vol.885iti9597f Scott, R. F. Principles of Soil Mechanics. Reading: Addison-Wesley Publishing Co., Inc., 1963. Singh, A. and Mitchell, J. K. "General Stress-Strain- Time Function for Soils." Journal of the Soil Mech. and Found. Div., Amer. Soc. of Civil Engineers, Paper 5728, SMl, January, 1968. Thurston, C. W. and Deresiewicz, H. "Analysis of a Com- pression Test of a Model of a Granular Medium." Trans. Amer. Soc. of Mech. Engineers, Vol. 81 (1959). van Olphen, H. An Introduction to Clay Colloid Chemistry. New York: Interscience Publishers, 1965. Verwey, E. J. W. and Overbeek, J. Th. G. Theory of Stability of Lyophobic Colloids. Amsterdam: Elsevier Publishing Co., 1948. APPENDICES 71 «mu-w— 72 APPENDIX TABLE I.--Viscosity of Soil-Water Mixtures. Temperature = 25°C Temperature = 35°C Temperature = 45°C Concentration Viscosity Concentration Viscosity Concentration Viscosity g./1itre Centipoise g./1itre Centipoise g./1itre Centipoise Lithium Saturated Clay 5.32 1.20 8.12 0.95 7.57 0.80 12.26 1.23 14.37 1.02 16.02 0.85 2 .40 1.28 31.62 1.10 37.31 0.92 63.94 1.65 72.51 1.41 73.62 1.25 137.53 3.1 128.20 2.30 141.24 2.33 309.33 35.0* 273.80 10.35 252.19 8.00 Sodium Saturated Clay 7.02 1.15 6.85 0.92 8.25 0.77 17.10 1.18 15.12 1.00 18.47 0.84 49.81 1.37 37.33 1.13 52.39 0.97 125.22 2.11 94.66 1.35 111.64 1.33 285.76 7.50 181.29 2.52 231.75 3.05 410.37 40.00* 342.81 10.03 372.69 11.00 Potassium Saturated Clay 6.07 1.07 9.73 0.93 11.04 0.70 14.12 1.10 23.15 1.00 21.62 0.78 57.30 1.18 77.81 1.11 52.43 0.935 118.25 1.77 116.21 1.42 110.69 1.05 421.82 4.21 381.48 3.79 273.25 1.52 605.10 12.80* 640.34 8.92 580.50 3.81 708.62 44.50* 758.00 36.50* 810.00 47.50* * At this concentration the viscosity reading was time-dependent. The tabulated figure was read after one minute. 73 APPENDIX TABLE II.--Creep Test Data for Soil—Water Samples. c3 = 1.75 kg./sq. cm. 03 = 3.5 kg./sq. cm. 03 = 7.0 kg./sq. cm. Lithium Saturated Clay Time natural natural natural natural natural natural mins. strain strain strain strain strain strain xlo'u rateu x10-u rateu xlo—u rateu x10" /min x10- /min x10- /min Axial Stress Axial Stress Axial Stress = 0.83 kg./sq. cm. = 1.25 kg./sq. cm. = 1.66 kg./sq. cm. 0.25 2.2 8.8 2.3 9.2 3.5 16.0 0.50 3.7 6.0 3.8 6.0 5.9 9.6 1 5.2 3.0 5.3 3.0 8.3 4.8 2 9.4 3.2 8.0 2.7 10.7 2.4 4 14.3 2.5 11.1 1.5 13.5 1.4 6 18.9 2.3 13.0 1.0 15.9 0.80 8 21.9 1.5 14.6 0.80 17.5 0.60 10 25.0 1.4 16.1 0.70 18.6 0.50 15 30.3 1.1 20.7 0.90 21.0 0.40 30 41.2 0.72 24.6 0.26 26.6 0.30 45 49.3 0.54 28.9 0.30 30.6 0.20 60 54.5 0.34 2.7 0.25 33.7 0.10 Stress Increment Stress Increment Stress Increment = 0.104 kg./sq. em. = 0.208 kg./sq. cm. = 0.416 kg./sq. cm. 60.25 57.2 10.8 35.3 10.4 39.7 24.0 60.50 57.9 2.8 36.1 0.8 41.3 1.6 61 58.7 1.6 36.5 0.8 41.3 1.6 62 59.9 1.2 37.6 1.1 42.5 1.2 64 61.8 0.95 39.2 0.80 44.5 1.0 66 63.3 0.75 40.4 0.60 46.1 0.80 68 64.8 0.75 41.5 0.50 47.3 0.70 70 66.4 0.80 2.3 0.40 48.5 0.60 75 70.2 0.75 45.0 0.18 50.9 0.50 90 77.8 0.50 50.1 0.34 56.9 0.40 105 84.6 0.45 54.6 0.30 60.9 0.30 120 89.6 0. 3 58.1 0.23 65.3 0.25 120.25 92.7 12.4 61.2 12.4 70.9 22.4 120.50 93.1 1.6 62.0 3.2 72.0 4.4 121 93.8 1.4 62.8 1.6 73.2 2.4 122 95.3' 1.5 63.6 0.8 75.3 2.1 124 96.8 0.75 65.1 0.75 77.7 1.2 126 98.8 1.0 66.7 0.8 80.4 1.3 128 100.3 0.75 68.2 0.75 82.4 1.0 130 101.8 0.75 69.4 0.60 84.0 0.80 135 104.9 0.60 72.0 0.50 8.5 0.80 150 113.3 0.55 78.7 0.45 97.3 0.58 165 120.2 0.46 84.0 0.35 105.0 0.50 180 126.7 0.43 88.3 0.29 109.7 0.31 74 APPENDIX TABLE III.-—Creep Test Data for Soil-Water Samples. Sodium Saturated Clay r‘f $.4' “TIP.-— 03 = 1.75 kg./sq. cm. 03 = 3.5 kg./sq. cm. 03 = 7.0 kg./sq. cm. Time Natural natural natural natural natural natural mins. strain strain strain strain strain strain x 10' rate“ 10‘“ rate“ x 10-4 rateu x10‘ /min X x10- /min x10" /min Axial Stress Axial Stress Axial Stress = 0.83 kg./sq. cm. = 1.25 kg./sq. cm. = 1.66 kg./sq. cm. 0.25 17.0 38 0 4.4 17.6 3.7 14.8 0.50 28.4 4‘ t 7.7 14.2 6.2 10.0 1 39.4 22 0 11.4 7.4 8.3 4.2 2 53.1 13 7 15.9 4.5 10.4 2.1 4 70.3 3 ' 21.7 2.9 12.9 1.25 6 81.2 5 L 25.8 2.0 15.4 1.20 8 89.7 1.3 28.6 1.4 17.1 0.80 10 96.9 3.6 31.1 1.25 18.4 0.65 15 109.9 2.6 35.: 0.90 21.7 0.30 30 134.1 1.6 46.3 0.70 28.7 0.46 45 149.1 1 0 5 .7 0.50 33.9 0.35 60 159.4 0 7 59 4 u 3“ 38.5 0.30 Stress Increment Stress Increment Stress Increment = 0.104 kg./sq. cm. = 0.208 kg./sq. cm. = 0.416 kg./sq. cm. 60.25 165.2 23.2 64.8 21.6 44.4 23.6 60.50 166.3 4.4 65.6 3.2 45.2 3.2 61 168.3 4.0 6?.2 3.2 46.5 2.6 62 170.9 2.6 69.3 2.1 48.2 1.7 64 176.3 ‘.7 72.1 1.4 50.7 1.2 66 181.0 “.3 75.0 1.45 53.2 1.2 68 184.8 1.9 77.5 1.25 55.8 1.3 7 188.3 1.8 79.6 1.00 5 .0 0.60 75 196.8 1.7 83.6 0 8 60.3 0.60 90 215.8 1.3 95.2 0.80 68.4 0.55 105 228.9 0.87 102.7 0.50 75.1 0.45 120 238.9 0.67 108.9 0.40 80.2 0.35 120.25 244.0 20.4 114.7 23.2 86.5 25.2 120.50 -- —— 115.9 4.8 87.7 4.8 12 246.7 3.6 117.6 3.4 89.9 4.4 122 249.9 3.2 119.6 2.0 92.4 1.2 24 254.8 2.5 23.8 2.1 97.0 2.3 126 259.1 2.2 127.1 1.6 100.4 1.7 128 263.0 2.0 130.0 1.5 103.4 1.5 130 266.7 1.8 132.9 1.5 106.0 1.3 135 275.1 1.7 138.6 1.15 111.9 1.2 150 295.7 0.4 152.8 0.94 124.1 0.80 165 310 5 1.0 163.2 0.76 133.8 0.65 180 321.9 0.76 172.7 0.57 141.0 0.50 1 Y . i 5 1‘1 natural r -4 natural strain x 10 r” 01v v 1 q/min ." K4 _. cm. e {1 natural strain Lurat x10 51 I 75 1.25 kg./sq. ssium natural Pota 111 '7 x10 e cm. natural {‘31: P958 .‘ O 9 L.) L' --4. PC ‘;'p r v. :ril -3. r 11., A X rain tural -ABLE na st FT‘ A x 7 4‘8 \ l / mins . APPHHI floOnUQJ7 . KOOAUOL 0.5 O 0 2 he 0 r) 1... Ox. 0,. C). 53 7.. t m 0 ; .?.. ,7... l .1 DJ 5.-.. O at.“ 2.70 .20 9. I 7! 510 0 r0 .0 I). 53 I I I I I I I I I I I I n C I I I I I I I I I I I I I I I I I I I I I I I I Ox.a§.,?J.xdllOOnH/0.0 e I... 7-10111:3n;.LlllOnU.07139n(u 314301100 4.9 n. m . .13 01.1 1 e O. n. S C /. r” . Iflb ,r. S Sfu 81 P0. 0 €1.11 r.) F) r.) 0.0 .0 0; v! ...0 7: t . 0.. l U. 30 to O 9 Q. A... .49).. .0 NH O...» A)... O l n» C) Wing 90 Q). 010 I I I I I I I I I I I I "k.“ 0 I I I I I I I I I I I I I I I I I I I I I I I I O :5 11 .:....Q,.. O D. .{J 33.3 ...._ l 13.20 .H rm .1 x0 ,C 1.... 2 .3 a.) 3 {o l .11.. 00 r) «J .4 a: .2 0J2; 31 11.-..2 12 we 30.14.31rq-u,r;. = .h.;h..b fl, 7;nmt.r.:u OJ..onu 11 as 52.15414n4 :gzpexnofl/.w/ 0114, 11.111171111111111 l)..nd-..,,.On,..t)..FO Ome.)UUUUL)AU OF-nUr.\.,OW¢O.DO ,0 0031.017110 «314 1... .....,L.Ii . Man/.0 .L .7th (9.-...2.‘ 1..li\ih.oQ~HH,uu£/-u. «(Jinn dam/all I I I I I I I I I I I I *y m I I I I I I I I I I I I I I I I I I I I I I I I lh.iUl.UaandnundiUO UC 03.1.0,UmddlunuaUndrUthflAILIIOrdnUOOOAUOO l on m . .8 O. P S n1. // n . Tl CC 3 no :3 e .2 Q/HH C ...o No .r. 3). l ,1; C) 8+ 0 n. x. y o 7- C112... .U .U 1 TI «.10 ”Lug/0 .1). O DU 0; "(NH .J; 3 3 flu r) I I O I I I I I I I I I ‘IV I I I I I I I I I I I I I I I I I I I I I I I I I 2 4.. .4 a.) 7 Cw no. .0 11,1... .3 C «L O 3 .1. .1 .1 .2 3,1... 4 r , 7. O 1 )1 .314 he £216.. «(2.. OJ 2 .6370 .1 .- . 1 .1 .1 a... 1.2 .. a 1.. 2 .3... a 1,. a ,1... 7) a). D). 3.. .3 3-11,-.. :15 3) 73.1... L. )0. = 0 .I- .. ... 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O 3/0 ,0 n( 00 O 3 _ .b 9 7 _ _ 1 l x 31.14 14 K.,?C 7! n! 71...! 7: "(up D... 3,. 4,. .5 O5 mU O O mu .0. «U l .1. l l 0... = l l l l l l l l l l l r) J r), 5 O .1. r.) 1... {3 9L 5 I I I I I I 0nd10.L“/OOAH.0F3;UCJAJ OO.10L.M...OQOOR,OCJ.OO lDLurOQuOrD..OCJO l 11 «3-4 .0 {O .6... flu 6 .10 r0 EU 7 7 O/ O 3L. 0... 2 2 2 9.. 2 O... 33 3 EJ/O GO 11111111111111.1111 76 APPENDIX TABLE V.--Creep Test Data for Soil—Carbon Tetrachloride Samples. Lithium Saturated Clay 03 = 1.75 kg./sq. cm. 03 = 3.5 kg./sq. cm. 03 = 7.0 kg./sq. cm. Time natural natural natural natural natural natural mins. strain strain strain strain strain strain x lO—“ rateu x 10‘“ rateu x 10-“ rate“ xlO- /min x10 /min xlO— /min. Axial Stress Axial Stress Axial Stress = 0.83 kg./sq. cm. = 1.25 Kg./sq. cm. = 1.66 kg./sq. cm. 0.25 3.0 l‘.0 l.l “.“ 1.5 6.0 0.50 5.3 9.2 2 3 “.8 2.7 “.8 l 8.0 5.“ “.2 3.8 “.3 3.2 2 ll.“ 3.“ 6.1 1.9 5.9 1.6 5 17.9 2.2 10.8 1.56 9.8 1.3 10 2f.2 l.“6 15.“ 0.90 13.8 0.80 15 30.2 1.00 18.9 0.70 17.0 0.6“ 20 3“.3 0.“0 22.0 0.60 19.7 0.5“ 30 “0.9 0.66 26.7 0.“7 2“.5 0.“8 “o “5.5 0.210 30.9 0.42 28.1 0.36 50 “9.“ 0.39 3“.0 0 31 31.2 0.31 60 52.8 0.3“ 36.7 0.2 3“.0 0.28 Stress Increment Stress Increment Stress Increment = 0.103 kg./sq. cm. = 0.208 kg./sq. cm. = 0.“l6 kg./sq. cm. 60.25 53.9 “.“ 39.1 9.6 37.9 15.6 60.50 5“.3 1.6 39.5 1.6 38.3 1.6 61 5“.7 0.60 39.9 0.80 38.7 1.6 62 55.0 0.30 “0.6 0.7' 39.9 1.2 65 56.6 0.50 “3.0 0.80 “1.9 0.67 70 58.9 0.“6 “6.1 0.90 “5.1 0.6“ 75 61.2 0.316} “8.3 0.5“ “7.9 0.56 80 -- -- 51.2 0.“8 50.3 0.“8 90 66.3 0.3“ ’ 55.0 0.38 53.8 0.38 100 69.3 0.30 58.5 0.35 57.“ 0.36 110 72.0 0 27 61.6 0.31 60.6 0. 2 120 7“.7 0.27 6“ “ 0.28 62.6 0.20 120.25 76.2 6.0 66 7 9.2 65.“ 11.2 120.50 76.2 0 67.1 1.6 65.8 1.6 121 76.6 0.80 67.5 0.80 67.8 1.2 122 77.0 0.“0 68.3 0.80 67.8 1.2 125 78.6 0.53 70.6 0.7“ 70.2 0.80 130 80.5 0.“2 73.7 0.60 73.7 0.70 135 82.8 0 “6 77.2 0.70 76.5 0.56 l“0 8“.7 0.“0 79 2 0.“0 78.9 0.“8 150 88.2 0.35 83.8 0.“6 83.7 0.“8 160 91.3 0.31 87.7 0.“l 87.3 0.36 170 9“.0 0.27 91.3 0.36 90.5 0.32 180 96.2 0.22 9“.“ 0.31 93.3 0.28 77 APPENDIX TABLE VI.--Creep Test Data for Soil-Carbon Tetrachloride Samples Sodium Saturated Clay 03 = 1.75 kg./sq. cm. 03 = 3.5 kg./sq. cm. 03 = 7.0 kg./sq. cm. Time natural natural natural natural natural natural mins. strain strain strain strain strain strain x 10-“ rate“ x 10’“ rateu x 10-“ rateu x10” /min x10- /min xlo‘ /min Axial Stress Axial Stress Axial Stress = 0.83 kg./sq. cm. = 1.25 kg./sq. cm. = 1.66 kg./sq. cm. 0.25 3.0 12.0 1.5 6.0 3.1 12.“ 0.50 “.9 7.6 2.7 “.8 5.1 8.0 1 6.9 “.0 3.8 2.2 6.7 3.2 2 10.9 3.8 5.“ 1.6 9.1 2.“ 5 17.2 2.2 8.1 0.90 13.5 1.5 10 2“.2 1.“ 10.8 0.5“ 18.6 1.0 15 2 .6 1.08 13.2 0.“8 22.2 0.72 20 33.3 0.7“ 15.1 0.38 25.“ 0.6“ 30 39.9 0.66 18.2 0.31 30.9 0.55 “0 ““.6 0.“7 21.0 0.2 35.3 0.““ 50 “8.“ 0. 8 23.7 0.27 39.3 0.“0 60 51.1 0.27 26.0 0.2 “2.9 0.36 Stress Increment Stress Increment Stress Increment = 0.10“ kg./sq. cm. = 0.208 kg./sq. cm. = 0.“16 kg./sq. cm. 60.25 53.5 9.2 28.“ 9.6 “8.1 20.8 60.50 53.9 1.6 28.8 1.6 “8.9 3.2 61 5“.2 0.60 29.2 0.80 50.1 2.“ 62 5“ 5 0.30 30.0 0.80 51.3 1.2 65 56 1 0.53 31.8 0.6 5“.0 0.90 70 58.0 0.38 3“.5 0.5“ 58.0 0.80 75 -- -- 36.5 0.“0 -- -- 80 61.9 0.39 38.5 0.“0 6“.0 0.55 90 6“.6 0.27 “2.0 0.15 68.9 0.“9 100 67 0 0.2“ ““.7 0.19 72.“ 0.39 110 69 3 0.23 “7.1 0.2“ 76.“ 0.33 120 70 9 0.16 “9.“ 0.23 79.2 0.35 120.25 72.3 5.6 52.6 12.8 83.7 18.0 120 50 72 5 0.80 53.0 1.6 8“.“ 2.8 121 72.7 0.“0 53.6 1.2 85.2 1.6 122 73.1 0.“0 5“.“ 0.80 86.“ 1.2 125 7“.3 0.“0 56.“ 0.67 89.6 1.1 130 76.2 0.3“ 59.9 0.70 93.7 0.82 135 77.“ 0.2“ 2.7 0.56 96.8 0.62 1“0 78.9 0.30 6“,? 0.“0 99.6 0.56 150 81.3 0 2“ 08.6 0.39 105.3 0.53 160 83.1 0.18 72.0 0.3“ 108.8 0.39 170 85.1 0.20 7“.8 0.28 -- -- 180 87.0 0.19 78.0 0.32 115.6 0.68 '78 APPENDIX TABLE V11.--Creep Test Data for Soil-Carbon Tetrachloride Samples. Potassium Saturated Clay 03 = 1.75 kg./sq. cm. 03 = 3.5 kg./sq. cm. 03 = 7.0 kg./sq. cm. Time natural natural natural natural natural natural mins. strain strain strain strain strain strain x 10‘” rate” x 10‘“ rate“ x 10’“ rate“ x10— /min x10- /min x10- /min Axial Stress Axial Stress Axial Stress = 0.83 kg./sq. cm. = 1.2) kg./sq. cm. = 1.66 kg./sq. cm. 0.25 0.7 2.8 0.70 2.8 1.1 “.“ 0.50 1.“ 2.8 1.5 6.0 1.9 3.2 1 2.9 3.0 2.6 2.2 3.8 3.7 2 9.6 6.7 “.5 1.90 5.7 1.9 5 21.“ 3.9 8.6 1.37 9.9 1.“ 10 25.9 0.90 11.6 0.60 13.“ 0.70 15 27.7 0.30 13.5 0.38 16.5 0.62 20 28.5 0.16 15.0 0.30 18.0 0.30 30 29.6 0.11 17.3 0.23 20.7 0.27 “0 30.6 0.10 19.2 0.16 23.0 0.23 50 "2.8 0.22 2 .3 0.1“ 2“.6 0.16 60 33.9 0.1“ 2 .“ 0.11 25.7 0.11 Stress Increment Stress Increment Stress Increment = .10“ kg./sq. cm. = 0.208 kg./sq. cm. = 0.“l6 kg./sq. cm. 60.25 -— -- 23.0 6.1“ 27.6 3.8 60.50 35.8 7.6 23.3 1.2 23.0 1.6 61 35.8 0.0 25.3 o.“o 28.“ 0.80 62 36.2 0.“0 23.9 0.“0 29.2 0.80 65 36.2 0.0 25.2 0.“0 32.2 1.0 70 37.3 0.2" —- -- 32.2 0.0 5 37.7 0.03 27.1 0.2“ 33.7 0.3 80 33.0 0.06 23.5 0.28 35.3 0 30 90 38.8 0.08 30.“ 0.19 37.6 0.23 100 39.2 0 0“ 31.9 0.15 39.1 0.15 110 39.3 -- 33.5 0.16 “0.7 0.20 120 39.5 0.03 3“.6 0.11 “1.8 0.11 190.25 “0.6 '4.“ 35.7 “.‘4 “3.“ 6.“ 120 50 “0.8 0.80 36.1 1.0 “3.8 1.6 121 “0.9 0.20 36.3 0.“0 ““.2 0 8 122 “1.8 0.90 36.9 0.60 ““.5 0.30 125 “2.1 0.10 38.0 0.37 “6.1 0.50 130 “2.5 0.08 39.9 0.27 “8.0 0.38 135 “2.9 0.00 -- -- “9.6 0.32 1“0 “3.3 0.08 “1.8 0.2“ 50.7 0.22 150 “3.6 0.03 “3.3 0.15 2.7 0 2' 160 ““.0 0.0“ “5.2 0.19 5“.5 0.18 170 ““ “ 0.0“ “6 0 0.08 55.7 0.12 180 ““.6 0.02 “7 5 0.15 5 .8 0.11 "1111111111““7111111113