.~..\\" - ‘ KAN “w,“ r \ ’\ ! \' ~ ~51} ‘ffi'k’fi‘. ' \‘;K“;髧l‘v ”l'ifr"l‘ ,r. ., /: ' /. fi- 44 ,9 ,2: «4 I m! 4,1; .1»; W4 ‘ ‘ MATERIAL PROPERTIES FOR SAND-13E '_ STRUCTURAL SYSTEMS ' . Dissertation ‘for,the Degree of Ph.v.D.e - MICHIGAN STATE UNIVERSITY . : ' RICHARD ALAN .B'RAGG ' - ' 1980' ' ’ AAAAALAAAAAAAA/1A I 17201 [I w: 25¢ per day per item RETURNING LIBRARY MATERIALS: —————.—_____________ Place in book return to remoI charge from circulation recon ABSTRACT MATERIAL PROPERTIES FOR SAND—ICE STRUCTURAL SYSTEMS BY Richard Alan Bragg Controlled ground freezing has been profitably used as a construc— tion aid to provide temporary support for excavations, tunnels, mine shafts, buildings experiencing severe settlement distortions, and to provide an impermeable barrier to seepage into excavations. Mbre widespread application of frozen soil as a structurally effective material has been limited by difficulty in predicting the mechanical behavior of the soil-ice material and the influence of temperature on rthis behavior. Experimental data has been obtained in an effort to define the material prOperties of frozen sand required for design of frozen soil structures subject to flexure. The effects of strain rate, temperature, and sample size on the compreSSive and tensile properties of frozen silica sand have been determined from uniaxial compression and split cylinder tests. Data are presented which describes the temperature and strain rate effects on the elastic modulus, strength, failure strain, and failure mode. Observations are presented relating the influence Of machine stiffness and test system errors on the observed frozen soil behavior. Test methods used are reviewed with respect to possible Standardization of test procedures for frozen soils. To eliminate the influence of mineral composition, ice content, and SOil density on the observed mechanical properties, all tests were 67 // (2-2) F(o, T) + t G(o, T) where 6(1) is the pseudoinstantaneous strain, dependent on stress (0) and temperature (T), and E(C) is the time dependent creep strain as a function of stress and temperature. The pseudoinstantaneous strain (6(1)) may be separated into an elastic strain, C(16), and a plastic strain, €(lp): E(1) =€(1e) + E(1p) (2_3) The elastic portion can be expressed as: e(1e) = o (2_4) E(T) where E(T) is a fictitious Young's modulus, smaller than the modulus corresponding to the instantaneOus elastic modulus. The plastic portion may be written as a pure power expression of the form presented by Ladanyi (1972): . k(T) (1p) _ o e - ek-E—(ET (2 5) k where 0k is a temperature dependent deformation modulus, the exponent k > 1 is usually little dependent on temperature, and Ek is an arbitrary small strain introduced for convenience in calculation and —————v 11 plotting data. For a given constant temperature, the numerical values of 0k and k are determined from a log-log plot of E(ip) vs stress (0) since Equation 2—5 linearizes on a log—log plot. (Figure 2—3) Similarly, the time dependent creep strain may be written as a ‘ simple power expression (Hult, 1966; Odqvist, 1966; Landanyi, 1972; and e(°) = t C(o, T) . _O' n(T) = tSC [Ere—(f):' (2‘6) Andersland, et a1, 1978) of the form: ' where 0C(T) and n(T) are defined as temperature dependent creep para— meters (n much less dependent than 0C). The quantity SC is an arbitrary I standard strain rate introduced for normalization. The quantity oC(T) 1 is the uniaxial stress necessary to cause the secondary creep rate of e; and was described by Hult (1966) as the creep proof stress. The magnitude of OC(T) is dependent on the value of éc (éc = lO-Smin-l or V 1.67 x 1077sec-1 is normally chosen for frozen soils; Landanyi, 1972). For a constant temperature, the numerical values of OC and n are obtained from a log—log plot of experimental stress vs strain rate data as shown in Figure 2-4. The constitutive equation of the frozen soil may now be written in terms of a step load as: 5(1) (C) e = + e o o k 0 n 7IT_ + 6k [ o ] + 8c [ o J t (277) k c In frozen soils, according to Vyalov (1959), the immediate strains considered in the first two terms of this equation may be less than 10 percent of the total creep strain for time intervals greater than 24 hours. Thus, for time intervals greater than 1 day the last term may be 12 considered sufficient to estimate the creep strain at constant stress and temperature. The creep strength of a frozen soil may be defined using Equation 2-7 (Ladanyi, 1972; Andersland, et. al, 1978). Creep strength is defined as the stress level, at which, after a finite time interval, instability or rupture of the material occurs. In constant stress compression creep testing, the beginning of the tertiary creep period (increasing strain rate) is generally accepted as the first sign of instability for ductile materials such as frozen soils. In tension creep testing, the creep strength is usually taken as the stress at which rupture actually occurs. According to Ladanyi, experimental data (Sayles and Epanchin, 1966; Vyalov, 1962) shows that axial strain at the beginning of instability (tertiary creep) is approximately constant for compression creep testing at a given temperature. Ladanyi (1972) adopted the constant permanent strain at the onset of tertiary creep as the creep—failure criterion. If the service life of the structure is known, the steady state creep rate may be estimated as: (i) A“) = 41—5 28 (2-8) where sf is the strain at creep failure and tf is the service life of the structure. Substitution of Equation (2—7) into (2—8) gives: é(c) _ of _ ef _ ek(of/ok)k _ (of/E) ‘ t (2-9) c f For time intervals greater than approximately 24 hours the immediate deformation may be neglected and for a constant temperature and a large time interval or service life Equation (2—9) becomes: 13 sf l/n or o = o [ ] = creep strength (2—10) f c t e f c When the service life of a structure coincides roughly with the duration of primary creep, the constitutive equation, based on the linearized creep curves, will over estimate the strain with time. The constitutive equation must then describe the decrease in strain rate with time in order to more accurately estimate the creep strain. Figure 2-5 shows characteristic creep curves for most materials (including frozen soils) during the primary creep phase. Immediately after application of a constant uniaxial stress the strain 80 develops, followed by a gradual development of the creep strain, E(c). The immediate strain, to, contains both a plastic and an elastic deformation. For small stresses,the plastic deformation is small and if neglected (Hult, 1966; Andersland, et. al, 1978),the immediate deformation may be approximated by: where E0(T) is the temperature, (T), dependent instantaneous Young's modulus. . c . . . The creep strain, e( ), is a functlon of stress, time, and temperature: E(C) = f (o, t, T) , (2-12) Hult (1966) presents a strain hardening creep law corresponding to the constant stress condition: c a ( ) 0 tb e = K , b < 1 (2-13) 111' 1111.11. , 14 The constants K, a, and b are material and temperature dependent. Differentiation with respect to time and elimination of t results in a creep law of the form presented by Hult (1966) and Andersland, et a1 (1978): b “n a“) = —S 3— t-b (2—14) with b, n, and 0c temperature and material dependent creep parameters determined from a set of creep curves obtained at a constant temperature. The constant éc is an arbitrarily selected strain rate. Note that the constants n and ac are the same for both steady state and primary creep (Andersland, et al, 1978). 2.1.2 Vyalov's Hereditary Creep Law Vyalov (1962) proposed that the Volterra—Boltzman nonlinear hereditary creep theory was suitable for describing the time-dependent ' 1 deformations in frozen soil. The theory assumes that the strain at 1 any time depends not only on the applied stress and temperature,but 1 also on the prior strain history. Vyalov (1962) introduced parameters, 1 derived from experimentation, into the equations to characterize the ‘ behavior of actual soils. The total strain may be expressed as a function ofthe instantaneous strain, primary creep, and secondary creep,as was presented by Equation 2—1. The initial strain 80 can be completely recoverable or can include a residual nonrecoverable strain depending on the stress level. The strain 6: includes both recoverable and residual strains and a: and a; are completely residual strains (5: is not normally taken into consideration). As the deformation at any time (ti) consists of an elastic strain, whe [ES 0111 15 linearly related to the stress level, and a plastic strain, which is nonlinear, the relationship between stress and strain may be written as (Vyalov, 1962): o + [or/m (2-15) e. = -—— 1 E. 1 Ai where Ei and Ai are moduli of linear and nonlinear deformation, respectively. To simplify calculations, one common law can be used for the entire stress range: c1 = f(o) or o = f(€i) (2—16) As strain increases with time, every ti is characterized by its own stress-strain curve or isocurve (figure 2-6). The curve at t = 0 corresponds to the initial deformation, while the curve at t = infinity represents the strain with unlimited time duration of the stress (0). The intermediate curves represent the strain at some time ti. Vyalov (1963) indicates that experimental data shows that all the curves are similar and may be described by a power law of the form: '1/m m e = fi or o = A(t)£~: (2-17) in which A(T) is the modulus of total deformation. The value of A(t) is dependent on temperature and test duration (changes with time). The strengthening factor m.: l is independent of both time and temperature. In compliance with the theory of nonlinear hereditary creep, the small initial strain (to) can be neglected and the expression rewritten as (Vyalov, 1963): 0 tA 1““ . (2—13) w(e+l)k The parameters w, A, k, and m are constants representative of the frozen soil and 6° = 273 — T(°K). These constants must be evaluated H; W “Eafiiifif;f 16 experimentally from a set of creep curves. The long—term strength of the frozen soil for uniaxial stress conditions may also be obtained from an expression proposed by Vyalov (1959): (I O of = ___.0___ = __0_ (2-19) ‘ i: 1n[(tf + t )/to] ln(tf/t0) in which 00 and t0 The time to failure is given by tf and of is the long-term strength. The parameter t* = t exp(o o ), where o. is the instantaneous stren th 0 0/1 1 g’ may be neglected (Vyalov, 1963). .are parameters dependant on soil type and temperature. Equation (2—19) results in of = 0 when tf = infinity, which is not consistent with the idea of continuous strength at some finite stress. However, Vyalov (1963) indicated that in engineering practice, after some long period of time the strength reduction is so insignificant and so slow that it can be neglected in engineering calculations. 2.2 Constant Strain Rate Tests The constant strain rate compression test is commonly used to test a number of materials including unfrozen soils and would seem to be readily adaptable to frozen soils. The test is conducted by deforming cylindrical samples along the longitudinal axis at a constant rate. This test method results in a constant engineering strain rate (é = (d/dt)(AL/LO)) or a true strain rate (é = (d/dt)[ln(L/LO)]) which increases linearly with time. Andersland, et al (1978) suggest that the stress—strain curves obtained from constant uniaxial strain rate tests may be used to determine both a time dependent deformation modulus (or initial tangent modulus) and the time dependent strength of frozen soils The peak ——fi 17 strength is plotted against either time to failure strain or the applied axial strain rate on a log—log plot. The latter plot is believed to be i equivalent to the relationship between secondary creep rates and the . corresponding stress levels in constant axial stress creep tests (Figure 2-4). However, the primary advantages of the constant strain } rate test, with respect to the constant stress creep test, are the reduction in dynamic effects due to the sudden initial stress condition required in the uniaxial creep tests and the relatively short test duration. 2.2.1 Compressive Strength Experimental data obtained by a number of investigators (Sayles and Epanchin, 1966; Perkins and Ruedrich, 1972; Sayles, 1974; Baker, > 1978; and Parameswaran, 1980) would seem to support the use of the con- stant uniaxial strain rate. test to obtain the time dependent strength in compression. The linear relationship between the peak compressive stress and applied axial strain rate may be expressed as: o = oc(é)m (MO) or é = (o/oc)n (2—21) where m is the slope of a straight—line throughthe data on a log-log plot, n = l/m, and 0c is a temperature dependent proof stress evaluated at a strain rate of l sec—l. Equation 2-21 is of the same form as the steady state creep law given by Ladanyi (1972). This observation Suggests that constant uniaxial strain rate tests may be used to deter— mine the creep parameters needed to predict the secondary creep deforma- tion of frozen soils subject to constant uniaxial stresses (when using the linearized approximation to the creep curves shown in Figure 2~2). The relationship between constant stress creep tests and constant str pol 18 strain rate compression tests can be visualized from the data for polycrystalline ice, obtained by Goughnour (1967) and presented in Figure 2-7. According to Andersland, et a1 (1978), a horizontal section across the plot in Figure 2—7a corresponds to a particular constant strain rate test. The corresponding stress-strain curve for a given strain rate may be deduced by reading the stresses as a function of strain at all intersection points with the curves. These stress—strain curves are quite different from the isocurves described by vyalov (1963), 'which correspond to the total strains attained at a given time. The isocurves are obtained from vertical sections through the creep curves in Figure 2-7b. 2.2.2 Tensile Strength At present very little data is available from constant strain (or deformation) rate tensile tests conducted on frozen soils. Ladanyi (1972) summarizes data from other investigators which indicates that the compressionztensile strength ratio for Ottawa sand varies from greater than 5 to less than 8. Vyalov (1962) presented limited data suggesting that the momentary strength of sandy loam was approximately 1.7 times the corresponding tensile strength and the continuous strength in compression was about 2.8 times the continuous tensile strength at -4.5°C. Offensend (1966) conducted direct tensile tests at constant deformation rates on frozen Manchester fine sand using briquette-shaped samples. The tensile strength was observed to be temperature dependent, but independent of the deformation rate for rates between 0.1 and 10 inches per minute. Haynes, Karalius, and Kalifut (1975) conducted constant strain rate tensile tests on dumbbell shaped samples of frozen silt at a temperature of —9.5°C. The tensile strength was observed to be rel was The EVE St] qua fn 19 relatively independent of strain rate, while the compressive strength was very sensitive to strain rate. The compressive strength increased by 4 10 times over a range of strain rates ( 2.9 x 10_ to 2.9 sec-l). The tensile strength was observed to only double over this range. How— - . —2 — _ ever, for strain rates below approx1mately 10 sec 1 the ten511e strength was approximatley equal to the compressive strength. Conse- quently, there is some evidence to indicate that the strength of frozen soils may differ in tension and compression at high strain rates and be approximately the same at lower strain rates. This would also imply that test rates could influence the creep parameters (0c and n) determined in the laboratory. 2.2.3 Factors Affecting Uniaxial Strength Several factors influence the compressive behavior of frozen sand. Goughnour (1967) investigated the effect of sand density on the compressive strength of saturated frozen Ottawa sand. Figure 2-8 shows the relationship between sand volume fraction and peak axial stress at the same temperature and strain rate. A bilinear relationship appeared to be appropriate. For low volume fractions of sand, the shear strength increased linearly with increasing sand content. At a critical volume fraction of approximately 42 percent, a rapid increase in the compressive strength was observed. Interparticle friction and dilatancy are believed to Significantly influence the shear strength for sand volume fractions above this critical value (Goughnour and Andersland, 1968). As the sand volume fraction increases the dry density of the sand increases proportionally. The net result is an increase in the number 0f interparticle contacts and the amount of particle interlocking. Data presented by Alkire and Andersland (1973) indicates that the 'F————_v 20 shear strength of frozen sand decreased with decreasing ice saturation (ratio of ice volume to sand pore volume). The reduction in peak stress was proportional to the volume of ice in the sand voids and was primarily the result of a decrease in cohesion in the ice matrix and 'adhesion between the ice and the sand particles. Ladanyi and Arteau (1978) investigated experimentally the effect of speciman shape on the creep response of frozen sand. Uniaxial constant stress and constant strain rate compression tests were conducted on cylindrical samples with Slenderness ratios (Height/Diameter) varying from 0.5 to 2.0. When the strength of the frozen sand was expressed in terms of strain rate (by the power law creep equation), it was concluded that, for smooth loading platens, the apparent strength of the frozen sand increased with increasing Slenderness ratio for any given strain rate. The value of the creep parameter n (Equation 2-6) also increased with increasing Slenderness ratio as shown in Figure 2—9. Baker (1978a) considered the effects of end conditions on the uniaxial compressive strength of frozen sand. Four different loading platen configurations were used to determine the uniaxial compressive strength of Ottawa sand at temperatures from -5°C to -6°C and at a strain rate of 0.7 x 10_3min_l. A compliant platen was designed to reduce friction between the sample and platen, to distribute the load uniformly, and to minimize stress gradients produced by eccentric loading. Experimental results indicated that at large Slenderness ratios (greater than 2.0) aluminum end caps, aluminum disk platens, and aluminum disk platens with rubber inserts gave about the same average compressive strength. The compressive strength determined using the compliant platens was about 25 percent higher than with the other [0U CUE] sle (IOU the em 0t! 21 platens at Slenderness ratios greater than 2.0. He attributed this higher strength to reductions in stress concentrations resulting from rough specimen ends in contact with the platens. In addition, the compressive strength was found to be relatively independent of the Slenderness ratio for the compliant platens (for ratios between 0.75 and 2.6). This would suggest that smaller Slenderness ratios could be used to determine the compressive strength while eliminating the possibility of buckling or tilting. In a later publication, Baker (1978b) considered the influence of end conditions on the creep parameters and compressive strength of Ottawa sand. Cylindrical specimens with a Slenderness ratio of 2.0 were tested at constant axial strain rates between 2 x 10"7 and 2 x 10—3 Sec-l at a temperature of -5.5°C. Neither the unconfined compressive strength nor the axial strain at failure was observed to depend signifi- cantly on platen type. However, the value of the exponent m (Equation 2—20) obtained from log-log plots of strain rate versus compressive strength was observed to vary from 0.09 for aluminum disk platens to —0.06 for Maraset compliant platens. Similar studies considering the influence of testing conditions on the tensile behavior of frozen sand have not yet been conducted. However, Offensend (1966) encountered problems in direct tensile tests on frozen Manchester fine sand using briquette shaped samples (ASTM specified shape and gripping clamp). Rather than failing at the neck of the briquette, the samples broke at the points where the clamps gripped the samples. Apparently, stress concentrations at contact points caused the specimens to fail in a complex interaction of shear and tension. Pads of various materials were inserted between the clamps am 'T—r———‘v 22 i and the samples in an attempt to reduce the stress concentrations. These efforts were unsuccessful and it was necessary to reduce the cross—sectional area of the briquettes in order to insure that they would break in the middle section. Additional research is needed I to develop and evaluate test methods for determination of the tensile strength and behavior of frozen sand. 2.3 Temperature Effects On Creep Rate And Strength Experimental data summarized by Sayles (1966), Figure 2—10, indicates a substantial increase inuniaxial compressive strength with decreasing temperature for frozen soils. Other researchers (Andersland and AlNOuri, 1970; Parameswaran, 1978; Perkins and Reudrich, 1973; and ' Sayles and Epanchin, 1966) have also presented data which shows an increase in compressive strength with decreasing temperature at constant , strain rate or an increase in strain rate with decreasing temperature at a constant compressive stress. Several investigators have proposed relationships to describe 1 the effects of temperature on strength and creep rate. Andersland and AlNouri (1970) suggested that the temperature dependence of the creep rate was related to the thermal activation energy by an expression of the form: 5:“) = Aexp(—L/T) (2—22) where L = U/R with units of temperature, U is the apparent activation energy, T is the absolute temperature, and R is the universal gas constant. Landanyi (1972) combined this relationship with Equation 2-6 and eliminated the constant A to obtain: I—"'{ 23 O = 0 —L9___ = f 6 c6 c0 exp 273n(273-e) Geo ( ) (2—23) °r é(°) = é ——~° n (2-24) c o f(e) CO where see is the temperature dependent proof stress in Equation 2—6, Geo is the proof stress for uniaxial compression tests extrapolated to 0°C, 6 is the absolute value of the temperature in °C, and n is assumed relatively independent of temperature. Equation 2-24 indicates that the compression strength should increase exponentially with decreasing temperature. The data presented in Figure 2-10 only partially supports this prediction. It appears that an exponential relationship between strength and temperature is limited primarily to clays. For coarser grained materials (silts and sands) the relationship between strength and temperature is more nearly. parabolic or linear. According to Ladanyi (1972) there would appear to be some justification in selecting the power law relationship proposed by Vyalov (1962), which can be written in the following normalized form (Assur, 1963): 0CG oc0(l + e/ec)w = 0C0 £(e) (2-25) where 6C is an arbitrary temperature (1°C usually) and e is the absolute value of the temperature in degrees Celsius. The value of the exponent m can be obtained by plotting oce versus (1 + else) on a log-log scale, where w is the slope of a straight-line drawn through . 0 the data points and o is the intercept on the Gee ax1s at 0 C- c A log Oce _________. (2-26) A log(l + e/ec) ' 0) For sm Equati where coast aH Tie in 1 24 For small temperature intervals,cu is approximately equal to one and Equation (2—26) reduces to a linear expression of the form: ace = oCo(l + e/eo) = OCO f(6) (2-27) where 0C0 and 60 are determined from a plot of ace versus 6. The constant 60 is the intercept on the axis and 0C0 is the proof stress at 0 = 0. The uniaxial compressive creep strength at a given temperature T is obtained by substituting 0c (Equations 2—23, 25 or 27) for ac in Equation 2—10. . 1/n ef f(6) (2—28) where éf = ef/tf (Ladanyi, 1972). The validity of the expressions presented above have not yet been clearly demonstrated for the tenSile behavior of frozen sand. Experi- mental data obtained by Offensend (1966) from direct tensile tests indicates that the tensile strength of Manchester fine sand increases with decreasing temperature. However, temperature—strength relation- ships were not developed and no comparison was made of the compressive strength—temperature variation. 2.4 Tensile Tests For Sand-Ice Material Analysis of sand—ice structures subject to bending requires an understanding of the tensile behavior of the frozen sand. Various test methods have been developed and used to determine the tensile Strength of brittle and composite materials. These tests can be classified as (1) direct tenSile tests, (2) bending tests, or (3) indirect tensile tests. 25 The direct tensile test is simple in theory. It consists of applying an axial tensile force directly to a sample of the material and measuring the stress—strain behavior. A variety of speciman configurations and gripping devices exist. While the direct tensile test seems simple, several difficulties have been encountered in practical applications of the method. The major problems have concerned the influence of bending stress due to misalignment of the applied load and stress concentrations near the gripping devices. Any eccentricity of the applied load results in bending stresses which introduce errors in the assumed uniform tensile stress distribution over the cross-sectional area. This problem is particularly serious in brittle materials, which can not relieve bending stresses by plastic flow. Since it is believed that the behavior of frozen sand in tension will be governed by the ice matrix, the frozen sand may exhibit brittle fractures (at least at the higher loading rates). The second major problem in direct tension testing is that of gripping the specimen. Use of the common briquette, which is the accepted tension test for mortar, is complicated by stress concentrations. Mitchell (1961) indicates that the maximum stress at the central cross- section is about 1.75 times the average stress, and photoelastic studies indicated large stress concentrations at the loading grips. The tests conducted on frozen sand by Offensend (1966) using standard mortar briquettes often failed in shear adjacent to the gripping device. The Sample shape was modified to reduce the minimum cross—sectional area, but stress concentrations undoubtedly still existed. A second method of determining the tensile strength is to find the mOdulus of rupture by testing beams in flexure. The modulus of rupture 26 is calculated by the standard flexure formula using the dimensions Of: the beam and the applied bending moment at the point where the beam fails. This analysis assumes that the neutral axis is at the centroid of the cross-sectional area and that the stress is linearly proportional to the distance from the neutral axis. These assumptions are valid only if the stress-strain behavior of the material is linear and the material behavior is the same in both tension and compression. Grieb and Werner (1962) estimated that the modulus of rupture for concrete may be equal to or greater than two times the tensile strength. A conversion factor from the rupture modulus to tensile strength does not appear to be successful. Mitchell (1961) indicates that the conversion factor for concrete seems to be a variable that decreases as the tensile strength increases and most studies have attempted to determine a constant conver- sion factor. If frozen soil may be assumed analogous to concrete, this test method does not appear too promising. In addition, develop- ment of a conversion factor would seem to require some prior knowledge of the true strength in tension. The indirect tensile or split cylinder test was developed simultan— eously by Carniero and Bacelleros (1953) in Brazil and Akazawa (1953) in Japan. The test consists of compressing a disc or cylinder along diametrically opposite generators (Figure 2—11). This loading condition creates a nearly uniform tensile stress perpendicular to and along the loaded axis of the cylinder. Failure occurs by splitting of the speciman along this axis. It has been demonstrated that the split cylinder test gives reason- able values for the tensile strength of a variety of materials. Mitchell (1961) concluded that the split cylinder test appears to be superior in 27 most aspects to other tension tests on Portland cement concrete and that the indirect tensile strength compared favorably with data obtained by others using direct tensile tests on cylindrical shaped specimens. Mellor and Hawkes (1971) evaluated the split cylinder test with respect to the determination of the tensile strength of several materials (including rocks). Their conclusion was that the split cylinder test appeared to provide a good measure of the tensile strength for brittle materials when it was carefully performed, with special attention paid to control of contact stresses and accurate load readout. Hudson and Kennedy (1968) reviewed existing information and conducted a testing program with the conclusion that the split cylinder test appeared to be the best test currently available for evaluating the tensile characteristics of stabilized subbase materials (asphaltic concrete and cement treated gravel) for pavement design. The viscous behavior of asphalt is not unlike that of ice, suggesting the potential suitability of the split cylinder test for the determination of the tensile strength of frozen sand. 2.4.1 Theory Of The Split—Cylinder Test Timoshenko (1934) and Frocht (1948) developed relationships for the stress distributions in circular elements subjected to concentrated forces applied at the boundaries based on the theory of elasticity and photo— elastic studies, respectively. A complete stress solution for the case of a circular element subjected to distributed loads applied over finite arcs for both plane strain and plane stress conditions was given by Hondros (1959). The stresses on the vertical and horizontal axes are given by the following equations (see Figure 2—12): 28 (l) Stresses Along the Horizontal Axis (0X) a. Tangential stress (parallel to the loaded axis) ‘ r2 2 - —5- sin 26 1 — £3 _ —2P R -l R _ 09X — REE. 2 2 4 + tan . 2 tan 0 (2-29) l+—E§COSZO+‘r—Z 1+3? R R R b. Radial stress (perpendicular to the loaded axis) 2 2 - 57 sin 20 1 — r—z _ +2P R _ —1 R tan a rX flat 2 2 r4 tan 2 (2_30) l +-£§ cos 20 + _4 l +-£§ R R R c. Shear stress Tex 0 (2—31) (2) Stresses Along the Vertical Axis (OY) a. Tangent stress (perpendicular to the loaded axis) 2 r2 1-5—2— sin20 1+—2 _ +2P R _ -1 R BY - flat 2 2 r4 tan r2 tan 0 (2—32) 1 - —£§ cos 20 + -Z- l — —E R R 29 b. Radial stress (parallel to the loaded axis) 2 2 l --£§ sin 20 1 + £5 —2P R -l R orY — rat 2 — tan 2 tan 0 (2—34) 2r r r l-TCOSZO-F—Z l-‘—2 R R R c. Shear stress Tre 0 (2-35) where tensile stresses are taken as positive, P is the applied load, and a, t, R, r and o are defined in Figure 2—12. The stress distributions along these principal axes for a loading strip width less than D/lO are shown in Figure 2-13 (where D is the diameter of the sample). According to the Griffith criterion for fracture in brittle materials, the exact center of the disc is the only point at which the conditions for tensile failure at a value equal to the uniaxial strength are'met (Mellor and Hawkes, 1971). The principal stresses at the center of the speciman are given by: __P_M_ 2i _ 06 _ rRt [ o 1] nRt (2 36) _ :2_ sin 20 + 1 ~ -P -_ Ur _ th [ o J _ nRt (2 37) If the arc of contact is less than or equal to 15°, the error introduced by use of the approximate formula for GB (the tensile strength) is less than 2 percent (Mellor and Hawkes, 1971). Hadley, Hudson, and Kennedy (1971) presented techniques for estimating the modulus of elasticity, Poisson's ratio, and the tensile Strain assuming that the material tested behaved as a homogeneous, m 30 istropic, and elastic (obeying Hooke's Law) material.This method 9| requires that the total horizontal and vertical deformation be 'a monitored during testing. The relationships for Young's modulus and ru- . Poisson's ratio are obtained from application of Hooke's Law and -—— __._...___ integration of the unit stresses over the vertical and horizontal diametrical axes giving: “—3. H Q H M + W l H H Q H N -r ‘ v = (2—38) ” r r F DR[ 09X + I O Y -r —r . and In > ) r r o o . _ P_ rX _ ex _ E — XT P v P (2 39) —r —r where v is Poisson's ratio, E is Young's modulus, P/XT is the slope of the least squares line of best fit between the load (P) and the total horizontal deformation (XT), andlnkis the absolute value of the slope of the least squares line of best fit between the total vertical deformation (YT) and the corresponding total horizontal deformation up to the failure load. Integration of the theoretical relationships presented above was performed by Anagnos and Kennedy (1972) for 4—inch and 6-inch diameter samples. The simplified relationships for calculating Poisson's ratio, the modulus of elasticity, and the total tensile strength at failure are presented in Table 2—1. The loading strip width ———_—fi 31 for both size samples was assumed to be 0.5 inches. 2.4.2 Factors Influencing the SpliteCylinder Test Several factors appear to influence the indirect tensile strength determined from the split—cylinder test. Characteristics and properties of the loading strip may have a definite effect on the type of failure . and test results. It is also possible that the desirable characteris— tics of the loading strip may vary with the type of material being tested. In addition, theoretical evidence indicates that the compres- sionztension strength ratio of the material may influence the value of the indirect tensile strength. In conducting a split—cylinder test, it is beneficial to apply a distributed load to the sample since it reduces the magnitude of the maximum compressive and shear stresses and causes the stress acting perpendicular to the loaded diameter to change from tension to compres— sion just below the strip, thus minimizing the effect of surface 1 irregularities in the specimen. Mitchell (1961) investigated experi— mentally the influence of the composition and width of the loading strip. Concrete cylinders were tested using cardboard strips of varying sizes. The size of the loading plate was found to influence the type of rupture abserved. Large strips usually resulted in double—cleft failures with large pieces, which in some cases did not split completely to a central fracture (Figure 2—l4a). Small strips caused shattering of material immediately adjacent to the applied load as shown in Figure 14c. Intermediate size plates produced fractures ranging from ideal (Figure 2-14b) to extreme. However, the failure mode did not seem to produce any significant effect on the computed tensile strength provided the specimen ultimately failed in tension. Tests conducted 32 on concrete cylinders (with strain gages mounted on their faces) using cardboard and masonite strips, indicated differences in the load—strain behavior of the cylinders. With the cardboard strips, the strain increased constantly up to failure. Using the masonite strips, the strain increased constantly and, for the same load, were similar to those with the cardboard strips. At the failure strain of the first cylinder, there was a strain reversal in the speciman tested with masonite and the speciman failed from the bottom. The author concluded that the masonite strips did not provide good bearing over the entire width of the strip and that cardboard strips were preferred. Other investigators have also looked at the influence of the loading strips. Wright (1955) conducted tests on Portland cement concrete using wood, steel, and rubber strips. He found that the strength results did not differ significantly for wood and rubber strips, but that the steel strips resulted in lower and somewhat less uniform results. Hudson and Kennedy (1968) investigated the influence of platen width ' and composition on the compressive strength of asphaltic concrete. Tests were conducted on 4—inch diameter samples using neoprene and steel loading strips 0.5 and 1.0 inches wide. It was recommended that steel strips be used for future work with asphalt concrete because of its practical advantage in determining vertical deformation of the sample even though experimental results indicated the scatter in the tenSile strength data to be slightly less for the neoprene. They also recom- mended that the l.O-inch wide strip (a 30 degree loading are) be selected on the basis of reduced data dispersion. Mellor and Hawkes (1971) reviewed existing experimental and theoretical evidence and concluded that an acceptable upper bound of 15 degrees for the loading 33 are was appropriate for testing brittle materials. Both Wright (1955) and Mitchell (1961) state that a nonlinear stress-strain relationship tends to relieve stress concentrations. This would tend to increase the load required to cause failure in the specimen and to give higher strength values. Chen and Chang (1978) examined the validity of using the elasticity solution for computing the tensile strength of concrete as compared with solutions obtained from the theory of plasticity. Three types of analysis were considered for the plane strain condition: (1) Limit analysis assuming the material to be perfectly plastic, (2) slip—line field based on perfect plasticity, and (3) finite element analysis of work-hardening theory of plasticity. The relevant formulas for computing the tensile strength based on the various plasticity analyses were found to be similar to that of the elasticity solution.» It was concluded that the elasticity solution gave a fairly good estimate of the tensile strength for materials such as rocks and concrete. Since these materials exhibit more elastic (or linear) stress—strain curves at high loading rates, it seems reasonable to select loading rates which are sufficiently high to suppress non— linearity for best agreement with elastic theory. For materials with low compression:tension strength ratios, there is some concern regarding where fracture initiates in the cylinder. Fairhurst (1964) examined theoretically the dependence of the computed tensile strength using the Hondros solution as a function of the compres— sion:tension strength ratio. Based on an empirical generalization of the Griffith criterion, he concluded that for low values of the ratio and for narrow contact strips there was a tendency for off-center fracture initiation. This was accompanied by a systematic underestimation of the 34 tensile strength. The dependence of the indicated tensile strength on the strip angle was determined to decrease with increasing values of the compression:tension strength ratio. However, for a constant value of the ratio, the critically stressed region was increased with increasing loading arcs. 2.5 Flexural Behavior The deformation response of frozen sand to static loading is characterized by immediate and time dependent deformations. The immediate deformation consists of both an elastic and a plastic component which are stress dependent for a given temperature. Time dependent creep deformations are predominantly a plastic deformation resulting from ice flow and particle reorientation as a function of stress and temperature. The response of a frozen sand structure to stress induced by bending would then consist of both immediate and time dependent strains. Analysis of the beam behavior would require that the stress distribution both immediately after load application and during the creep process be known. Design for flexure must consider both rupture and allowable deflection over the service life of the structure. 2.5.1 Elastic Materials At any cross—section of a beam subject to external loading there exist internal forces which may be resolved into components normal and tangential to the cross-section. Those components which are normal to the secrion include bending Stresses. Their function is to resist the bending moment at the section. The tangential components are known as shear stresses, and they resist the transverse or shear forces applied ————fl7 i 35 to the beam. According to Popov (1968), the strength of materials approach to relating applied bending moments to the cross—sectional properties of.a member, the internal stresses, and deformations, requires three fundamental steps: a plausible deformation assumption is required to reduce the statically indeterminate problem to a determinate one, the deformations causing strains must be related to stresses through appropriate stress—strain relationships, and equilibrium must be satisfied. The fundamental assumption in flexure theory is that plane sections through a beam taken normal to the axis of the beam remain plane after the beam is subjected to bending. This c0ndition implies that in a beam subjected to bending, fiber strains (8) vary linearly as their respec— tive distances from the neutral axis of the beam. Based on these assumptions the bending stress at any point depends on the strain at that point in a manner determined by the stress-strain curve for the material. For a homogeneous material whose stress-strain curve in tension and compression is similar to that shown in Figure 2—153, the strain is proportional to the distance from the neutral axis (Figure 2-15b) if the maximum strain in the outer fibers is less than the limit of proportionality (ep). If the strain at the outer fibers exceeds ep this is no longer true. Where the strain is greater than a P the magnitude of the stress is no longer proportional and depends on the stress-strain curve above the limit of proportionality (Figure 2‘15C). Thus, for a given strain, the stress at a point is the same as that given by the stress-strain diagram. When the stresses in the outer fibers are smaller than the 36 proportional limit op, the beam behaves elastically. In this case, the neutral axis passes through the center of gravity of the cross- section. The intensity or magnitude of the bending stress normal to the section increases directly with the distance from the neutral axis according to the elastic flexure formula: 0 = “Iii—Z (2—40) where M is the applied bending moment, 2 is the distance from the neutral axis, and I is the moment of inertia of the cross—section about the neutral axis. This expression satisfies the condition of equili— brium (Popov, 1968) and indicates that the maximum stress occurs in the external fibers (where z = zmax)' The distribution of shear stresses over the beam cross-secion depends on the shape of the cross—section and of the stress—strain curve. For bending stresses below the limit of proportionality, the fundamental strength of materials equation defines the shear stress (V) at any point in the beam cross—section as: _ V_Q _ V - lb (2 41) where V is the total shear force at the section, I is the moment of inertia about the neutral axiS, b is the width of the beam at the given point, and Q is the static moment about the neutral axis of that portion of the cross—section lying between a line through the point of interest parallel to the neutral axis and the nearest outer fiber of the beam. The shear stress is largest at the neutral axis and equal to zero at the outer fibers. Shear stresses on horizontal and vertical Planes through any point are equal as required to satisfy equilibrium. Due to the combined action of shear stresses and bending stresses, -—-'- r 5 37 at any point in the beam there are inclined stresses of tension and compression. The largest of these stresses form an angle of 90 degrees with each other. The intensity of the inclined stresses (principal stresses) at any point is given by: O V/bz 2 t = “E i T + V (2-42) where o and v are as previously defined. The inclination of the stress makes an angle a with the horizontal, where tan 2a = 2v/o (Popov, 1968). If an element of the beam is chosen at the neutral axis (where o = 0) the tensile and compressive stresses are inclined at 45 degrees to the horizontal and are of the same magnitude as the shear stress. Based on the fundamental hypothesis that plane sections remain plane during deformation, one may express the fundamental relationship between the curvature (K) of the beam and the linear strain distribution across the beam section as (Popov, 1968): I I N|m (2-43) where K is the curvature, p is the radius of curvature of the neutral axis, and z is the distance from the neutral axis to the point of interest. According to Popov (1968) the derivation of this expression requires no use of material prOperties, and therefore, the expression can be used for inelastic problems as well as for elastic. In the case of elastic Problems, the strain may be related to the bending moment as follows: _ 9. = E = E _ e — E IE p (2 44) so that 1 _ §L_ _ p — IE (2 45) 38 This equation relates the bending moment M at a section of an elastic beam, having a moment of inertia I about the neutral axis, to the curvature l/p. For small deflections the curvature is approximately equal to the second derivative of the deflection with respect to the x coordinate of the beam (the x—axis coincides with the longitudinal axis of the beam) 2 % z 51—1 (2—46) dx2 where y is the transverse deflection of the beam (in the z—direction) at point x. Equating expressions (2—45) and (2-46) yields the governing differential equation for the deflection of an elastic beam: 2 M L2. = if (2-47) dx This treatment of beam deflections neglects shear deformations. If shear stresses exist, according to the theory of elasticity shearing strains must also exist. These shear strains warp the initially plane sections of the beam, which contradicts the basic assumption. However, for slender beams, it can be shown that these shear distortions are negligible (Popov, 1968) and that the bending theory is adequate provided the length of a beam is at least two to three times greater than the total depth of the member. It has also been assumed that the deflections are small in compar— ison to the length of the beam. Popov (1968) indicates that for deflec— tions on the order of one—twentieth of the length, the error with respect to the exact solution for deflections is approximately one percent. If the deflection is increased to one—tenth the length the error is increased to approximately 4 percent. 39 2.5.2 Time Dependent Plastic Materials The time dependent plastic deformation of beams may be considered on the basis of linearized creep curves shown in Figure 2—2. Hult (1966) indicates that for materials whose creep curves may be approxi- mated in this manner a state of stationary creep will always be approached. The term stationary creep here describes a creep process in which the spacial distribution of stresses remain constant. Hult (1966) and Odqvist (1966) consider the stationary creep stress distribution in a beam subject to pure bending using the elastic analogue. For a structure where a constant state of stress prevails 1 during the creep process the creep strain may be written as: a“) = ¢(0.T)‘P(t) <2-48) where T(t) is a monotonically increasing function of time. If, as (C) 3 time progresses, the creep strain, 8 tends to dominate the immediate strain, 80’ Equation (2—48) provides a estimate of the total strain. If the Bernoulli assumption of plane sections is made, the ratio of strains between any two arbitrary points on the section must be a constant. This same ratio also prevails in a beam if the material is elastic according to: e = (I>(o,T)C (2—49) where C is a constant. Therefore, the stress and strain distributions subject to stationary creep can be formed by analyzing a corresponding problem of nonlinear elasticity. The elastic analogy simply implies that the elastic strain is made to correspond to a plastic creep strain rate. In this fashion the time element is eliminated from the analysis. The elastic analogy is then expressed as (Hult, 1966; Odqvist, 1966): 40 sgn o = e (2‘50) where the signum function (sgn o) is -l.0 for o < 0, 0 for o = 0, and +1.0 for o > 0 (o is taken as positive in tension). Equation (2-50) corresponds to the secondary creep law (Equation 2—6) when éc = 1.0. A similar expression can be written for the strain—hardening creep law given by Equation (2—14) by equating E(C) to e. For the case of a beam in pure bending, as shown in Figure 2—16, Hult (1966) gives the stress distribution as: EL- 2 l/n sgn z (2—51) I n where H/2 Izll - 1/n H II |z|l + 1'“ dA b(z)dz (2—52) —H/2 The positive sense of the bending moment M is taken as shown in Figure 2-16 and the quantity In is characteristic of the cross—section and reduces to the ordinary moment of inertia for n = 1. Since the above expression for the stress is based on the assumption that the stress— strain—time relationship is the same for both tension and compression, the neutral axis of the beam must pass through the centroid of the cross— section. Consequently, the stress distribution is symmetric about the neutral axis. The maximum stress occurs in the Outer fibers and is a function of the geometry of the cross—section and the creep parameter n. As the value of n decreases the magnitude of the maximum stress increases. Hult (1966) and Odqvist (1966) present the governing differential equation for the time dependent deflection of the beam in pure bending as: 41 2. n d M -—% = — o I sgn M (2-53) dx c n where y is the rate of deflection of the beam in the z direction and (ocIn)n corresponds to the bending stiffness E1 in linearly elastic bending. The total deflection of the beam at any time t may be obtained by solution of the nonlinear differential equation for y with respect to the boundary conditions and integrating with respect to time. The creep equations (2—51 and 2—53) for the bending stresses and deflections of the beam are based on the Bernoulli assumption of plane strain. Consequently, they are most applicable when beam deflections are small. As in the case of elastic deformations, the error should not be large for deflections, on the order of 1/10 the beam length. Klein and Jesseberger (1978) presented a method of transforming the power law given by Equation 2-6 from the uniaxial case to multi—axial states of stress based on the Prandtl-Reuss equation and the Von Mises flow rule. A finite element computer program was developed to consider an incremental treatment of creep in frozen ground assuming that the stress—strain behavior was the same in tension and compression. The computer program was used to compute the stress distribution and deflection rate of the simply supported frozen soil beam shown in Figure 2-l7a. Both the rate of deflection and the stress distribution were in close agreement with the analytical solutions presented by Hult (1966) and Odqvist (1966). Figure 2—17b shows the stress distribution at a cross-section as computed from Equation (2-51) and with the finite element computer program. For a beam loaded as 42 shown in Figure 2-l7a and composed of Karlsruher sand at —33°C, the finite element program predicted a deflection rate at the midpoint of the beam of 3.56 x lO-6m/hr and the analytical solution gave a deflection rate of 4.11 x 10_6m/hr. Thus, the analytical solution and the finite element analysis were shown to be in good agreement. 43 Table 2—1: Equations For Calculation Of Tensile Properties (Anagnos and Kennedy, 1972) Diameter of Specimen Tensile Property 4-Inch 6—Inch Tensile Strength S psi PFail PFail T’ 0.156 —h 0.105 h.— Poisson's ratio v 0.0673DR - 0.8954 0.04524DR — 0.68040 -0.2494DR - 0.0156 —0.16650DR - 0.00694 Mum“? 9f . SH [0.9976v + 0.2692] SH [0.99900 + 0.2712] Elast1c1ty E, ps1 17' E— Total Tensile Strain 0.1185v + 0.03896 X 0.0529v + 0.0175 At Failure ET TF 0.2494v + 0.06730 TF 0.1665v + 0.0452 . PFail = total load at failure (maximum load Pmax or load at first break p01nt), in pounds h = height of specimen, in inches XTF = total horizontal deformation at failure (deformation at the maximum load or at first break point), in inches DR = deformation rate ET_(the slope of line of best fit between XT vertical deformation YT and the corresponding horizontal deformation XT up to failure load PFail) SH = horizontal tangent modulus é— (the slope of the line of best T fit between load P and total horizontal deformation XT for loads up to failure load PFail) ‘WIXLU QL “Np fur-“inns“ 13h Tertiary Creep (stress > long—term strength) Secondary Creep Dominant (ice-rich soils) (a) a“ w m I: m Primary Creep Dominant ,z”’—f (ice-poor Soils or Low Stress) 0 Time, t (a) (4.) “ Primary Creep c‘ (c .H (a ) m l B W Secondary Creep (C) 5(1) (62 ) g Tertiary Creep O (aw) 3 -‘ H II -m w. 4..) ‘0 Di .5 l I (U s L/ m 0 r1— H F1" Time, t (C) Figure 2‘1: Constant Stress Creep Test; (a) Creep Curve Variations, (b) Classical Creep Curve, (c) Strain Rate versus Time (Andersland, et al, 1978). QEHRNUW ”SUI ' 45 Temperature Constant (i) 64 (.0 c? 5(1) ‘H 3 a .y) .9 Figure 2-2: Linearized Creep Curves with 01 (Hult, 1966). < Figure 46 ’(a 05‘60 0 ¢ 0 Q 8 k(T) = Cot B o 3‘ (D U) o H U (I) 8° A ok(T)- I Lo 8 ék . (1) Log Pseudoinstantaneous Strain, s Figure 2-3: Log-Log Plot of Pseudoinstantaneous Strain versus Stress for Determination of ok and k. O l mmuuu m med” Figur 47 Log Stress, o L ‘ . 0g 6c Log Strain Rate, a Figure 2-4: Log—Log Plot of Stress versus Strain Rate for Determination of n and Ge. AEHMHUM 'iglJre 04 Strain, e 0 Time, t Figure 2—5: Primary Creep Curves (Hult, 1966). UOQ$LV figure 2 Strain, e 0 t t t Time, t Stress, o Strain, e (b) Figure 2‘6: Curves Showing Relationship Between Stress and Deformation; (a) Creep Curves, (b) Isocurves (After Vyalov, 1963). Fig. 9 True axial strain rate x 104 min—1 True axial strain, mm/mm Figure 2—7: 1.0- Sample 31 Sample 30 __ __ .. Sample 29 1 ‘ I l 1 1 1 0.01 0.02 0.03 0.04 0;05 0.06 0.07 Axial strain, mm/mm (a) ,, Sample 31 01 - 03 a 248 ps1 T = —4.45°C 0 Sample 30 o.oq_ ol 4 03 = 317 psi T = —12.05°C 0.03 a 0.02_ Sample 29 ‘ 0 01 01 — 03 = 248 psi T = —12.05°C 1 l ' ' 100 200 300 400 Time, min (b) Creep Tests on Polycrystalline Ice; (a) Strain Rate versus Strain, (b) Creep Curves (Goughnour, 1967). \ TU f I L L. fix m M m V~ m um I.“ W 1H Fig“ 51 1200 L . _ e = 2.66 x 10 4min ° T = -12.03°C ‘ o O 1000 _ . _ -4 , E - 1.33 x 10 min . ‘ T = -12.o3°c ° 1 800 _ A w m n- 15 Computed l 3 500 _ p01nt 8 3 0 U m — O H 3 400x x . K m r' X 0 fé 0 . o I _4 ‘3‘ I D e = 2.66 x 10 min 200 T = -3.85°C GD Indicates 100 psi confining pressure 0 , n 1_ l 1 I 1 0 10 20 30 4O 50 60 Percent sand by volume Figure 2-8: Effect of Volume Concentration of Sand on Peak Strength (Goughnour, 1967). .Amaaa . .smouu< pom HkEMpmqv .ooml H H pom .mm.o u o no .mooumam CuooEm oomsuom mommwuoaou mosumm mmmnuopooam uooHoMMHQ Sofia mooEHomom pom wo>uoo oumm :Hmuum mouH momsm> mmosum "aim moowam HIEHE .w .oumo :Hmuum mosH 52 8 ~6 u a c .4 u c>53 c c>;}: @@@@ Ban ‘9 ‘ssains 1 c c H 18d ‘0 ‘ssaiis I. OOOH ; OOOOH OOH .III I'll’llln. . t} Havanfimwflnounb Figx 9000 L 8000 - 7000 - 6000 - 5000 .. 4000 _ 3000 .. 2000 _ Unconfined Compressive Strength, 1’31 1000 - Figure 2—10: 60- Sandy silt 50— 40 " Ottawa sand / Unconfined compressive strength, MN/m2 ilnllllnllllllt 0 —50 —100 —'150 Temperature, °C Temperature Dependence of Unconfined Compressive Strength (After Sayles, 1966). 54 Loading Strip Specimen Indirect Tensile Test. Figu 55 +Y P Stainless Steel Loading Strip Specimen 20 00x 0 1 ——-—. 0 X rx r R 00y 0 ry [a P = Applied Load a = Width of Loading Strip 2n = Angle at Origin t = Height of Specimen Subtended by Width R = Radius of Specimen P 0f Loading Strip Figure 2-12: Loading Conditions for the Indirect Tensile Test (After Hondros, 1959). Fig“ 56 -1.0 _ _\ o ry Tens ion <_h——‘> Comp res s ion 0 . l I (D N + l l l l l l I l l I l 1.0 .8 .6 .4 .2 0 —.2 —.4 -.6 —.8 -l.0 Tension 4—f—v Compression Figure 2-13: Stress Distribution Along the Principal Axes for Loading Strip Width, a, Less Than D/lO (Hudson and Kennedy, 1978) . .Aaems .Hawsuuazv eepum wceemon was: Ace a mfluum maflpmoq HmowH Aav .mwpum wofipmog oz Amv “mowoz oHSHHmm Hmuaaha "calm shaman on Amv on . ‘I‘ 57 Figure 2 58 Stress, o P I : Strain, e l | ___ —o i p (a) Z I Emax 8p Z 0 < {\J w max t; ‘0 ‘7 M ——.- —‘> X x ,. :3 > (b) Z I e > a 1 Z 0 > max p max ‘3 e 5 o P P M< fl _._ x x E < ‘2 a 3 (C) Figure 2—15: Elastic and Inelastic Stress Distributions in a Homogeneous Beam; (a) Stress—Strain Curve, (b) Elastic Stresses, (c) Plastic Stresses. 59 Ta. 3368 mIN mlm .Emom aflsumaahmwm m we wcfiwdom whom AEUV WHUNAV IHNIFU-ulz E(lehu 60 Z P = 4m<9oo lbs) 0'10‘“ = b 0.5m L Z 1.64' J: / II L. 3 1.0m o' A 'f 3.28' l (a) Finite element Analytical I l I -400 E 3 6.0 (n H d 3.0_ a m H ‘5 o o 2 5 .fi -3.OF o 8 m -6.0 :3 F H D Figure 2—17: —300 —200 —100 0 100 200 300 400 Normal Stress (ox), PSI at x = 0.475m (b) Frozen Soil Beam; (a) Diagram of Simply Supported Beam; (b) Stress Distribution (After Klein and Jessberger, 1978). A DiViSiI select sub-an sand g dense tion is a] 'by (k dila: froz vari ratj ind tom eac mo] CHAPTER III MATERIAL AND SAMPLE PREPARATION A commercially available silica sand produced by the Wedron Division of the Pebble Beach Corporation of Wedron, Illinois was selected for this investigation. The 40-40 Wedron sand consisted of sub-angular quartz particles with a specific gravity of 2.65. The sand gradation was uniform with all material passing the number 30 U.S. standard sieve and retained on the number 140 sieve. The coefficient of uniformity was approximately 1.50. A sand volume fraction of 64 percent was selected to give a dense soil mass. This volume fraction was selected for ease of compac— tion and is comparable.to values normally encountered in the field. It is also well above the critical volume fraction of 42 percent determined 'by Goughnour (1968) to be the point where interparticle friction and dilatancy contribute significantly to the compressive strength of frozen sand. The actual sand volume fractions for all samples tested varied from 63.1 to 64.9 percent. These values correspond to void ratios varying from 58.5 to 54.1 percent, respectively. All samples were prepared in split aluminum molds. Extensions, 0.375 inches high, were attached to the open end of each mold to aid in COmpaction. The molds were disassembled and cleaned prior to compacting each sample. A thin coat of silicone grease was applied to the inner mold surfaces to reduce adhesion at the sample-mold interface and to aid in Sample removal after freezing. The correct amount of oven dried sand, to provide a volume fraction 0f 64 percent, was predetermined using mold volumes (with extensions 61 attached degree 0 deminere into the degree I from 96 -12°C (] mold $11 the mol Th allowed assumed were fj sharper Platem EllelOSI 3.1 U U and at Sample height sample °f st] con“ and a Sampl at ‘6 62 attached) and the specific gravity of the sand. To insure a high degree of saturation, the molds were partially filled with distilled demineralized water and the sand was slowly poured through a funnel into the molds, allowing air bubbles to escape to the surface. The degree of ice saturation for samples prepared in this manner ranged from 96.1 to 99.9 percent based on an ice density of 0.9185 gm/cm3 at ~12°C (Pounder, 1967). Sample compaction was achieved by tapping the mold sides and bottom sufficiently to level the sand with the top of the mold. The mold and samples were then placed in a cold box at -12°C and allowed to freeze for at least 12 hours. After this period it was assumed that essentually all of the water was frozen. Mold extensions were first removed and the exposed sample surface was trimmed with a sharpened paint scraper giving a uniform seating area for the loading platens. Samples were then removed from the molds, weighed, and enclosed in rubber membranes to prevent sublimation during storage. 3.1 Uniaxial Compression Test Samples Uniaxial constant strain rate compression tests conducted at —6°C and at a strain rate of approximately 1.2 x 10_4sec_l on cylindrical samples (diameters of 1.13, 1.41, 1.94 and 2.40 inches with a 2:1 height to diameter ratio) were used to investigate the influence of sample size on the mechanical properties of frozen sand. The effects 0f strain rate and temperature were determined from tests conducted at constant strain rates ranging from 5.69 x 10_7sec_l to 1.78 x 10-3sec—l and at temperatures of —2, —6, —10, and -15°C using 1.41 inch diameter samples. Constant axial stress compression creep tests were conducted at -6°C using samples 1.13 inches in diameter. These sample diameters were se for 001 availal mas was ap‘ ventio necess stress tertia P (disk) of the reduce sample The l. of the Plate: sampl Conta trans Water for t What t0 t1 attae 10ad‘ 63 were selected to stay within the capacity of the test equipment and for convenience, since molds in most of these sizes were already available in the laboratory. The 1.41-inch diameter sample was chosen as a standard for comparison of rate and temperature effects since it was approximately the same diameter as samples normally tested in con— ventional triaxial cells. For the constant stress creep tests, it was necessary to use the smaller 1.13-inch diameter sample size to obtain stress levels (using a dead weight hanger system) high enough to reach tertiary creep in less than eight hours. Prior to mounting samples in the triaxial cell, stainless steel (disk) loading platens were placed on each end of the sample. Surfaces of the loading platens were coated with a thin layer of Teflon to reduce end effects. Two protective membranes were placed over the samples and fastened securely to the loading platens with rubber bands. The 1.13 and 1.41-inch diameter samples were then mounted on the base of the triaxial cell (inside a cold box) by screwing the bottom loading platen onto the loading pedestal. The triaxial cell was placed over the sample, attached to the cell base, and the loading ram was brought into contact with the top loading platen. The entire triaxial cell was then transferred to a low temperature circulating bath of ethylene glycol and water and the cell was allowed to fill with coolant. In order to use aVailable equipment, the mounting procedure required for the larger diameter samples (1.94 and 2.40 inch diameters) was some— What different. After the loading platens and membranes had been applied to the samples, they were transferred to the low temperature bath and attached to the base of the cell by screwing the bottom platen onto the loading pedestal. A cylindrical aluminum cell was placed over the sample and th loadin l with I trim: expose trans: ature the 5‘ hours (1.94 leaks samp] data base I...) N froz film 1.94 and Vere Stre i[We 64 and the ram of the loading frame was lowered into contact with the top loading platen. These mounting procedures protected the samples from any contact with the coolant fluid which contained ethylene glycol. While sample trimming and mounting took approximately one hour, the samples were exposed to temperatures above 0°C for only a few seconds while being transferred from the cold box to the low temperature bath. Sample temperatures were allowed to adjust to the cold bath temper- ature prior to testing. A period of at least 6 hours was allowed for.. the smaller samples (1.13 and 1.41-inch diameters) and at least 12 hours was allowed for temperature equilibration for the larger samples (1.94 and 2.40—inch diameters). After the sample had been tested the triaxial cell was disassembled and the sample removed. The membrane and sample were inspected for leaks and the failure mode was noted and sketched (in most cases the samples were also photographed). The oven dry weights were then determined and the volume fraction and degree of ice saturation computed based on the mold volume. 3.2 Split Cylinder Test Samples The influence of sample size on the indirect tensile strength of the frozen sand was determined using disk shaped samples prepared in split aluminum molds with a height to diameter ratio of 0.5 and diameters of 1.94, 2.40 and 4.00 inches. The test temperature was maintained at -6°C and the applied vertical deformation rate was adjusted to give an average vertical strain rate of 6 x 10_4sec'-l for each size sample (average strain rate = vertical deformation rate é sample diameter). Samples for investigation of rate and temperature effects were prepared in the lI.00- rangi and - for u devic The 4 later of th loade' eonsi the 5 low rubbe loweI clam] rods stre' defo- lust then lees brie was was weig and Val ‘3 I 65 4.00-inch diameter molds and tested at vertical deformation rates ranging from 0.002 to 0.280 in/min at temperatures of —2, —6, e10, and -15°C. The 1.94 and 2.40-inch diameter samples were selected for use since they compared roughly with the diameters of coring devices (BX and MK sizes) normally used in field investigations. The 4.00 inch diameter sample provided a convenient size for measuring lateral deformations and represented an upper bound on the dimensions of the samples to remain within the testing capacity of the available loading frame and load transducer. The mounting procedure for the split cylinder samples was considerably simpler than for the uniaxial compression tests. After the samples had been trimmed and weighed, they were mounted on the lower half of the loading jig (described in Chapter IV). A' rubber membrane was placed over the sample and fastened securely to the lower circular loading plate with a rubber o—ring and a steel hose clamp. The top half of the loading jig was then aligned with the guide rods and brought into contact with the sample. The membrane was stretched over the top loading plate and secured as before. The lateral deformation transducer was then attached to the jig assembly and ad- justed to rest against the sample sides. The loading jig assembly was then transferred from the cold box to the low temperature bath. At least 12 hours was allowed for the sample temperature to reach equili- brium with the bath before testing. Immediately after testing the jig was disassembled and the sample inspected for leaks. The failure mode was sketched and the sample was oven dried at 110°C to determine the weight of sand. As with the uniaxial tests, the sand volume fraction and the degree of ice saturation were computed based on the mold volume and the weight of the sand. ll of the from l triaxi accomp for us used t was de Preset deter: and ; cell Plat. Stud g! CHAPTER IV EQUIPMENT AND TEST PROCEDURES The influence of sample diameter on the compressive strength of the frozen sand was investigated using samples varying in size from 1.13 inch to 2.40 inches in diameter. Since conventional triaxial cells available in the laboratory were not large enough to accompany the larger sample sizes, existing equipment was modified for use in the testing program. Similarly, the loading apparatus used to determine the indirect tensile behavior of the frozen sand was designed and built expressly for this investigation. This chapter presents a description of the equipment and test procedures used to determine the mechanical properties of the sand-ice material. 4.1 Equipment A standard triaxial cell was used for the uniaxial compression tests and for the constant strain rate compression tests conducted on the 1.13 and 1.41-inch diameter samples. The samples rested on a stainless steel platen which screwed onto the end of a loading pedestal attached directly to a Strainsert Model FL5U-ZSPKT flat load cell (rated capacity of 5,000 pounds). Figure 4—1 presents a schematic diagram of the triaxial cell assembly. The uniaxial compression tests (constant strain rate) on the 1.94 and 2.40—inch diameter samples were conducted using the modified triaxial cell shown in Figure 4.2. The samples rested on a stainless steel platen which screwed directly onto the end of a 15,000 pound capacity stud type load transducer (Strainsert Model Q—1096). The cell consisted 66 of a 5.0 The loadJ' cell. Si due to c: construcI ram of t] directly ahemisp‘ lubricat and the The lig show opposite With a 1 was adj. of the 5 Sample I Model E A co: the tes Circula miXture Using a with se hath. samples '01tmel 67 of a 5.0 inch 0.D. aluminum pipe capped with a circular aluminum plate. The loading ram of the test frame served as the piston for the triaxial cell. Since the cell served only to reduce the temperature variation, due to cycling of the refrigeration coolant bath, the cell was not constructed to apply confining pressures. The sample and the loading ram of the test frame were aligned by centering the base of the cell directly under the ram. The load was transmitted to the sample through a hemispherical piston cap attached to the upper loading platen. A lubricated hardened steel washer was placed between the loading ram and the piston cap in an attempt to minimize any eccentricity. The indirect tensile strength was determined using the loading jig shown schematically in Figure 4-3. The load was applied to opposite sides of the sample through two stainless steel loading strips with a radius matching that of the Sample. The width of the loading strips was adjusted such that the angle at the origin subtended by.the Width of the strips was approximately 15 degrees. The load applied to the sample was measured using a 10,000 pound capacity load cell (Strainsert Model FLlOU—ZSPKT) attached to the end of the loading ram. A constant temperature was maintained during testing by immersion of the test apparatus (triaxial cell or split cylinder loading jig) in a circulating low temperature bath of ethylene glycol and water (50—50 mixture). The temperature of the coolant fluid was maintained to i_0.l°C using a micro-regulated refrigeration unit and circulator. A thermometer with scale divisions of 0.1°C was used to monitor the temperature of the bath. The temperature of the coolant immediately adjacent to the samples was determined to :_0.05°C using a thermistor and digital voltmeter. Figure 4-4 shows a diagram of the testing equipment and coolam TI All COI using . with a loadin Result slight load I tests a10,( displ: split screw testi that rates adea bath. the 1 (for the Sam fom eith atte 68 coolant circulation system. Two different load frames were used during the testing program. All constant strain rate uniaxial compression tests were conducted using a WykehamrFarrance (Model WF 10050) variable speed testing machine with a 10,000 pound capacity. This frame had a 30 speed gear box with loading rates varying from 0.225 to 0.00024 inches per minute. Results indicate that the cross—head displacement rate increased slightly during testing, reaching the selected rate only after the peak load had been reached. The uniaxial creep tests and the split cylinder tests were conducted using a Soiltest load frame (Model T—llS-X) with a 10,000 pound capacity and Graham variable speed gear box. The displacement rates were also observed to vary slightly during the split cylinder test. The transmission on this test frame was of the screw type which permitted displacement rates to be corrected during testing, but the split cylinder tests were of such short duration that insufficient time was available for correction of the displacement rates. The uniaxial constant stress creep tests were performed using a dead—weight hanger which straddled the test frame and low temperature bath. The electric motor and gear box were used to raise and lower the hanger. = Axial displacement of the uniaxial compression test samples (for both constant strain rate and constant stress creep tests) and the deformation across the loaded diameter of the split cylinder sampleswerenmnitored using a Sanborn Linearsyn differential trans- former (Model 585DT—1000). When used with the triaxial cells to conduct either the creep or constant strain rate tests, the transformer was attached to the loading ram with the core element bearing on the top of the was al tests: loadi1 ohtai1 mm. the t the a by su to th speci Consi gages ”heat of u the Fig“ diff (mm and tes thi dif 69 of the triaxial cell as shown in Figures 4—1 and 4-2. The transformer was also attached to the loading ram during the split cylinder tests, with the core element resting on a stationary portion of the loading apparatus as shown in Figure 4—3. All deformation measurements obtained in this fashion contained elastic deflections of the loading ram. These deflections were determined by placing steel cylinders in the test equipment and monitoring the deflections as a function of the applied loads. The measured sample deformations were than corrected by subtracting the elastic deflection of the ram. The lateral deformation along the diametrical axis perpendicular to the axis of the split cylinder samples was recorded using a specially designed transducer. The Lateral Deformation Transducer (LADT) consisted of two cantilever bars fitted with four resistance strain gages (Micro—Measurements, Type EA—O6-125PC-350) arranged in a full Wheatstone bridge circuit. The cantilever bars were fixed to the sides of two aluminum adjustment blocks resting on a rack and pinion device. Movements or deflections of the beams at the points of contact with the specimen were calibrated with the output of the bridge circuit. Figure 4-5 shows a photograph of the split cylinder loading jig and LADT with a sample in place. The outputs from the various transducers were recorded using two different strip chart recorders. A Sanborn 2 channel recorder (model 7702B) and preamplifier (Model 8805A) was used to record the load and axial deformation for all constant strain rate uniaxial compression tests. At maximum sensitivity, one centimeter needle deflection on this recorder represented 0.0053 inches axial deflection for the differential transformer, 99.26 pounds for the 5,000 pound capacity flat stud and u Sanbo 1100) needl diffs defor capat strai abui bum in t1 volu bure than test the tea oft 8qu 1:~‘2';& r 70 flat load cell, and 150.18 pounds for the 10,000 pound capacity stud transducer. The load and deformation data from the split cylinder and uniaxial constant stress creep tests was recorded using a Sanborn 4 channel recorder (Model 150) and preamplifiers (Model 150— 1100). At maximum sensitivity for this recorder one centimeter of needle deflection represented 0.0032 inches deflection for the differential transformer, 0.0066 inches deflection for the lateral deformation transducer, and 138.21 pounds for the 10,000 pound capacity flat load cell. Sample volume change measurements were obtained for 8 constant strain rate compression tests and 3 constant stress creep tests, using a burette and flexible tube connected to the triaxial cell. The burrette was fixed to the side of the coolant tank. The fluid level in the burette was only slightly above the coolant surface to minimize volume changes in the fluid due to any temperature differential. The burette, calibrated with scale divisions of 0.1 cm3, permitted volume changes to be estimated to the nearest 0.01 cm3. 4.2 Test Procedures Test procedures for the constant strain rate uniaxial compression tests and the split cylinder tests were essentually the same. After the sample had been mounted in the triaxial cell or loading jig, the test apparatus was submerged in the cold bath. When a sufficient period of time had elapsed for temperature stabilization, the following test sequence was followed: 1. The transducer circuits were connected to the recorder, which was allowed to warm up for approximately one—half hour prior to testing. After the warm—up period, the transducers were 71 adjusted to a zero reading. The loading ram of the test frame was brought into contact with the test apparatus, but with no applied load. For constant strain rate uniaxial compression samples 27 through 90, a small seating stress of approximately 100 psi was applied to the samples prior to testing. The manual loading feature of the Wykeham—Farrance test frame was used to apply the seating load and the magnitude was monitored with the .1oad transducer. The speciman was not tested until the seating stress had been decreased to nearly zero by sample relaxation. This procedure was intended to provide a more uniform contact surface between the sample and the loading platens and served to minimize data scatter. Prior to use of this procedure, several samples (23 through 26) exhibited failure surfaces through the trimmed end of the sample, indicating the presence of small surface irregularities. The temperature of the cold bath adjacent to the sample (inside the triaxial cell for the uniaxial compression tests) was observed and recorded. The gear box controls for the loading ram were adjusted to give the desired loading rate and the loading ram was engaged. The deflection of the stylus needles on the recorder were observed as the test progressed. The attenuation of the recorder was adjusted, as needed, to keep the trace on the ,recording paper. All constant strain rate uniaxial compression samples were strained to at least 7 percent (failure or peak stresses T couduc 0f lea 100 pg 12 hou Sa1111316 seatir the he max; frtune “Omit inter for t remai caSES 72 normally occurred at less than 5 percent axial strain). Failure in the split cylinder tests was usually quite sudden, with the load dropping immediately to zero. The drive mechanisms for the recorder and test frame were then stopped and the temperature of the bath recorded. 7. Circuits from the transducers were then disconnected from the recorder and the test apparatus was removed from the cold bath. Samples were oven dried at 110°C to determine the dry weight of sand. 8. Recorder strips were labeled and filed until the data could be transcribed to data sheets. The constant stress uniaxial compression (creep) tests were conducted using static loads applied by a hanger supporting a dead weight of lead bricks. Prior to testing, a seating stress of approximately 100 psi was applied and the samples allowed to creep for approximately 12 hours to minimize surface irregularities at the trimmed end of the samples. Axial strains observed in the samples, as a result of this seating stress, were less than 0.2 percent. To apply the test load, the hanger (and lead bricks) was lowered onto the loading ram of the triaxial cell using the fastest rate possible with the Soiltest loading frame. After the load was applied the deflection of the sample was monitored with the differential transformer and, at predetermined intervals, small increments of weight were added to the hanger to correct for the increased sample cross—sectional area. Weights were allowed to remain on the sample until initiation of tertiary creep (and in.some cases, until rupture). The sample was then unloaded and the triaxial cell sketc of sa 73 cell removed from the cold bath and disassembled. The failure mode was sketched and the sample was oven dried at 110°C to determine the weight of sand. Figur 74 LVDT I“ fil Burette Steel Loading a / / Platen /Sample Rubber Thermistor /// Membranes Loading RUbber Pedestal Bands \\\\\\\\ <:ffiylene . J Glycol-Water ///////////////////// \ Figure 4-1: Diagram of Triaxial Cell Used for Uniaxial Compression Tests. 7w: ‘=.:_ 4._;_ _< 75 Loading Ram LVDT Lubricated \ Washer F: Steel Loading // cap :« (— I Thermistor f-IIW 5. s — _'_____—Sample \Nl ' -" '..-.5 Rubber Membranes Transducer \\ '...‘H."% Rubber Bands stud I // Ethylene Glycol— \\\\\} l Water ijlant) ////////// // / /////// Figure 4—2: Modified Triaxial Cell. Spl Cyl L034 Jig Gly Coc Fig, 76 Load Cell 55’! \Yr ’~\ Split L S -'2 Cylinder , Loading —\\‘{: Jig I l I F . Thermistor (J Ethylene GlyC01—Water Coolgn:::> f I 1% ////////////////////////////// & Membrane Jacket ////’_ Hose Clamp Figure 4-3: Diagram of Split Cylinder Test Equipment. 77 Electric Motor [:1, ::f////'— Loading Ram Triaxial Cell Test Frame or Loading Jig —-—“\ \\\\ A'jI///.__ Insulation _ En” [ Coolant Out Cold Bath r. _____.- l 1 Recorder I Coolant ' I l —" l l Coolant In L_____J omlfl Refrigeration Unit Figure 4-4: Diagram of Test System. , .mumHm SH AHA—4.; HwODfimflmHn—u GOHUNEHOMGQ HGHUUNH JuHB MHH. 5H U.S.—H n ,4 . . w .vmo .Hw ,1, A .H 0 mm "mlq wusmflm 78 PIC SflI am adu CHAPTER V EXPERIMENTAL RESULTS Experimental results along with a brief discussion of implications of these results are given in Chapter V. This material is presented in three parts: constant strain rate uniaxial compression tests, constant stress uniaxial compression creep tests, and split cylinder tests . 5.1 Constant Strain Rate Uniaxial Compression Tests The constant strain rate (unconfined) uniaxial compression test provided information on the mechanical properties of frozen Wedron sand. Several investigators have noted that strain rate, temperature, and sample shape influence the compressive strength of frozen sand. In addition, constant strain rate compression tests have been suggested for determination of the creep parameters needed to predict time dependent deformation of frozen soils subject to constant stress loading condi— tions. However, the influence of temperature, strain rate, and sample diameter on the stress—strain behavior of frozen sand has not been fully assessed. Data is not available for a direct comparison between creep parameters obtained from constant stress creep tests and constant strain rate tests. This section presents results from a series of constant strain rate uniaxial compression tests conducted to determine the influence of sample diameter, temperature, and strain rate on the stress-strain behavior of frozen Wedron sand. Table 5—1 summarizes the physical properties (dry density, sand volume fraction, and degree of ice saturation) of samples 79 mate stra 5. 6S app] shc duI aft 80 used for the constant strain rate compression tests. Table 5-2 summarizes test results with respect to mechanical properties of the frozen sand in compression. 5.1.1 Strain Rate Effects The strain rate effect on the stress—strain behavior of sand-ice materials in compression was investigated using a series of constant strain rate tests conducted at nominal strain rates between _1 and 1.78 x 10_3sec—l and a sand volume fraction of 5.69 x 10'7sec approximately 64 percent. Temperatures were held constant at -2, —6, -10 and -15°C. A Wykeham—Farrance variable speed testing machine was used to conduct all of the constant strain rate compression tests. Figures 5-1 and 5-2 present plots of stress versus time and strain versus time for samples 44 and 45 tested at —6°C and nominal strain rates (en) of _l and 8.89 x lO-4sec_l, respectively. These figures 1.19 x 10‘4sec show that the strain rate (or cross-head displacement rate) increased during testing, approaching the selected or nominal strain rate only after the peak stress was obtained. The variation in the strain rate was due to stiffness of the test apparatus and appears to be typical of all tests conducted on the Wykeham-Farrance loading frame. The average strain rate (save) for each test was determined as shown in Figures 5-1 and 5-2; by dividing the axial strain at failure by the time to reach the peak stress (failure was assumed at the peak stress). The stress—strain behavior and deformation modes for the frozen sand appear to be governed by the applied axial strain rate. Figure 5-3 presents stress-strain Curves for samples 58, 59, and 63 tested 4t at -10°C and at average strain rates ranging from 2.52 x 10— o 4.82 modes froze of fa obseu sand by a was the 81 4.82 x lO—7sec—l. The photographs in Figure 5-4 illustrate the failure modes associated with these samples. The deformation behavior of the' frozen sand was observed to change from a ductile to a brittle type of failure as the strain rate increased. This general trend was also observed for samples tested at —2, -6, and -15°C. At low average strain rates (less than 7 x lO—6sec-l), the frozen sand deformed elastically in the early stages of deformation followed by an initial yield or rapid change in slope. The initial yield point was followed by a prominent region of plastic strain hardening up to the peak stress (defined as failure). As the strain rate increased, the value of the initial yield stress increased and the region of strain hardening became less pronounced. At high average strain rates (above 4 2 x 10_ sec-l), the stress-strain curves remained nearly linear up to the peak stress. I In most cases, the initial yield point was not as clearly defined at the higher strain rates, as for average strain rates below 2 x lO-4sec_l. Consequently, the construction shown in Figure 5—6 was used to systematically estimate the initial yield stress and strain for all samples tested. A line parallel to the initial linear portion of the stress-strain curve (below the yield stress) was offset by a small strain value. The intersection of the offset line and the stress-strain curve was defined as the initial yield point. The value of the strain offset for each test temperature was selected to provide points of intersection near the visable yield in the stress-strain curves. A strain offset of 0.1 percent was used for samples tested at —2, —6 and -lO°C, while a value of 0.2 percent was found to be more appropriate for samples tested at —15°C. The presente strain 1 a strai; the eff nateria where 0 strain rate as Se remains at strz moderat the sa1 approx At hig nultip imatel surfac that t for tt (10mph Strai. Val-Sn Plot m 82 The results obtained from this construction procedure are presented on a log—log plot of initial yield stress versus average strain rate (save) to failure in Figure 5-6. This plot implies that a straight—line relationship may be the most appropriate to describe the effect of strain rate on the initial yield stress (0y) of the material; suggesting a power expression of the form: _ . m oy — Uc(€ave) (5—1) where 0c and m are defined as in Equation (2—20). The initial yield strain was observed to be nearly independent of the applied strain rate as shown by Figures 5-3 and 5-7. Samples tested at average strain rates less than 7 x 10_6sec_l . remained nearly cylindrical, with no visible shear planes or cracking, at strains well in excess of the peak stress (Figure 5-4a). For '1 and 2 x 10'4sec71, ’ moderate average strain rates, between 7 x 10_6Sec the samples exhibited well defined shear planes inclined at an angle of approximately 60 degrees to the horizontal as shown in Figure 5—4b. At higher strain rates (save 3_ 2 x 10_4sec-l), the samples developed multiple conjugate slip—lines or fractures inclined at angles of approx— imately 60 degrees to the horizontal. The inclination of the failure surfaces for both the moderate and high nominal strain rates suggests that the mobilized angle of internal friction was close to 30 degrees for these tests. For average strain rates below 7 x 10—6sec-l, the peak stress or compressive strength (of) was observed to be a function of the applied strain rate. Figure 5—8 shows a log-log plot of compressive strength versus the nominal axial strain rate and Figure 5—9 presents a log—log Plot of the compressive strength versus the average strain rate up to failr sive str law of l where o: Eave are def 7xro' strengt rate fc ll decree: Curves Versus l strain is nea As the britt] than ] below rate deter analy bElow iuir line . E 83 to failure. At average strain rates below 7 x 10"6sec_l the compres- sive strength increased linearly with strain rate according to a power law of the form: ) _ . m I 0f _ oc(eave) (5-2) where of is the compressive strength, save is the average strain rate (é ve may be replaced by én for é §_ 1 x lO_Ssec_l) and 0c and m a n are defined as in Equation (2—20). For average strain rates above 7 x 10—6 sec-1 (nominal strain rates above 1 x lO-Ssec_l),the compressive t strength appears to be relatively independent of the applied strain rate for the range of strain rates considered. The axial strain at failure (at peak stress) was observed to . decrease with increasing strain rate as shown by the stress-strain curves in Figure 5-3. A log-log plot of the axial strain at failure versus the average axial strain rate, Figure 5-10, indicates that for strain rates less than about lO_Ssec_l the axial strain at failure .v4 v4 v is nearly independent of strain rate and roughly equal to 4.5 percent. As the strain rate increased and the material behavior became more brittle, the axial strain at failure decreased rapidly to values less than 1 percent. The slope of the initial linear portion of the stress—strain curves, below the initial yield stress, was observed to increase as the strain rate increased (see Figure 5—3). The initial tangent modulus was determined, for each sample tested, by a linear regression least squares analysis of the nearly straight—line portion of the stress—strain curves below the yield point. Figure 5-11 presents a log-log summary of the initial tangent modulus versus the average strain rate to failure. The linear increase in the initial tangent modulus with increasing strain rate Equa? wher were the show -1T pom ind app obt ini met m 84 rate on the log—log plot suggests a power law relationship similar to Equations (5-1) and (5—2): b E1 = B(éave) (5—3) where B and b are temperature dependent constants. Eight tests were conducted in Which volume change measurements were made to examine the influence of strain rate and temperature on the volumetric strain of the frozen sand. Figures 5-12, 5-13 and 5-14 show the stress—strain curves for the tests conducted at —2, -6 and —15°C, respectively. Figures 5—15, 5—16 and 5—17 present the corres— ponding plots of volumetric strain versus axial strain. Initially, at low axial strain values, the volumetric strain was negative . indicating a net decrease in the sample volume. As the axial strain approaches the initial yield strain value, the volumetric strain obtains its minimum value. As the axial strain increased beyond the initial yield strain and toward the axial strain at failure, the volu—. metric strain increases at an accelerating rate. The initial reduction in volume appears to be associated with pressure melting of the ice, a simultaneous densification of the sand particles, and compression of the ice matrix. As dilatancy and interparticle friction begin to contribute to the volumetric strain, the sample volume reaches its minimum value and begins to increase. The increase in sample volume appears to continue at axial strains in excess of the failure strain corresponding to the peak stress. Poisson's ratio was computed (as a function of the axial strain) from the volumetric strain data as discussed by Duncan and Chang (1970) and Daniel and Olson (1974): wher axis in 1 str: les: inc 85 —A(sV - e) “t = __2As_ (5‘4) where v is the tangent Poisson's ratio computed for increments of axial stress applied to the sample, Ev is the volumetric strain, and s is the axial strain (positive for compression). Figures 5-18, 5-19 and 5-20 present plots of the tangent Poisson's ratio versus axial strain for the samples corresponding to the stress-strain curves in Figures 5—12 through 5—13. As would be expected from the volumetric strain data, the value of the tangent Poisson's ratio was initially less than 0.5, indicating that the volume was decreasing with increasing strain. Poisson's ratio then increased rapidly to a value of approximately 0.5 at or near the initial yield strain, indicating a point of zero volume change in the stress—strain process. Beyond the initial yield strain, the value of Poisson's Ratio continued to increase at a somewhat slower rate with increasing axial strain. At axial strains in excess of the peak stress the value of tangent Poisson's ratio appears to approach a value of 1.0. Both the volumetric strain and the tangent Poisson's ratio appear to increase somewhat with increasing strain rate. Figure 5—17 illustrates the apparent influence of strain rate on the volumetric strain. Samples 82 and 83 compare very favorably with respect to dry density and degree of ice saturation (dry densities equal to 105.8 and 106.2 pcf, respectively, and degree of ice saturation equal to 96.4 97.3 percent, respectively). However, sample 82, tested at an average strain rate of 8.34 X 10_55ec_l, experienced a greater volume reduc— tion at low strain values as compared to sample 83 tested at anew -6 -1 average strain rate of 5.63 x 10 sec and at the same temperature of -15° volu stra tang stra tang (te: in' val COD . sup awe rm st at re Sa SE m 86 —15°C. Sample 82 also exhibited a significantly greater increase in volume at axial strain values equal to or greater than the failure strain. The same trend is also observed in Figure 5—20 for tangent Poisson's ratio as a function of axial strain. At the higher strain rate (Sample 82, save = 8.34 x lO_Ssec-l), the value of tangent Poisson's ratio initially is less than that for Sample 83 6sec-l), indicating a more rapid decrease (tested at e = 5.63 x 10— ave in volume. Above the initial yield point on the stress—strain curves (Figure 5—14), the higher strain rate results in significantly greater values of Poisson's ratio for Sample 82 than for Sample 83, as is consistent with the volume change data presented in Figure 5—17. The data shown in Figures 5—17 and 5—18 at a temperature of —2°C supports the general trend described above. Sample 87 tested at an average strain rate of 9.42 x lO—Ssec_;:experienced'greater‘volume reduction prior to initial yield and greater volumetric expansion at strains above this initial yield point than Samples 88 and 89, tested . ' —6 —1 -7 —1 at average strain rates of 6.19 x 10 sec and 8.74 x 10 sec , res ectivel . However a reater volume increase was observed for y a g Sample 89 than for Sample 88. Figure 5-18 indicates that the values of the tangent Poisson's ratio for these two samples are very close for the same strain levels. Since the sand volume fractions for the two samples are nearly the same (64.05 percent for Sample 88 and 64.10 percent for Sample 89) this would suggest that volumetric strain is less dependent on strain rate as the applied strain rate decreases. 5.1.2 Temperature Effects The influence of test temperature on the compression mechanical Preperties of the frozen sand was investigated by conducting a series of of t] This froz the war dat yie ave law 87 constant strain rate compression tests at constant temperaturessof —2, —6, —IO and —15°C. Figure 5—21 illustrates the effect of temperature on the stress-strain behavior of frozen Wedron sand. For samples tested at the same nominal strain rate, but different temperatures, there was no significant change in the general shape of the stress—strain curves. However, as may be noted in Figure 5—21 and Figure 5—5, the value of the initial yield stress increases with decreasing temperature. This phenomenon suggests that the ice matrix within the frozen sand increases in strength as the temperature decreases, since the soil structure and density of the samples tested was held relatively constant. Figure 5—22 presents a log-log plot of the initial yield stress versus the number of degrees below freezing (freezing assumed at 0°C) for several strain rates. To eliminate data scatter at the selected strain rates, values of the initial yield stress for a given strain rate were obtained from a least squares linear regression analysis of the data shown in Figure 5—5. For temperatures below —2°C, the initial yield stress increased linearly with decreasing temperature for a given average strain rate on the log—log plot (Figure 5—22). Thus, a power law of the form: 0 = c(e)‘°’ (5—5) Y would be appropriate to relate the number of degrees below freezing (e) to the initial yield stress (oy); where s is a strain rate dependent constant. The initial yield strain was observed to remain relatively inde- pendent of the test temperature as shown in Figure 5—7 and 5—21. Since the initial yield stress increased with decreasing temperature, the net effect was to increase the initial tangent modulus as the temperature decre to th inure init: tempt of t temp modu stra pro1 the mod in: 111 is ‘_'_‘_‘_—_"""'_"""""_""'"""-—"'_'_—‘!IE§EEE’ 88 decreased. Because the stress-strain curves remained nearly linear up to the yield point, an increase in the yield stress results in an increase in the tangent modulus. This temperature dependence of the initial tangent modulus may be clearly observed from Figure 5-11. For temperatures below —2°C, there is a significant increase in the value of the initial tangent modulus, at a given strain rate, with decreasing temperature. Figure 5—23 presents a log-log plot of the initial tangent modulus versus the number of degrees below freezing for several average strain rates. A power expression similar to Equation (5-5) appears to provide a reasonable relationship between the initial tangent modulus (E1) and the number of degrees below freezing (6) for temperatures less than or equal to —6°C. There was no apparent decrease in the tangent modulus between 46°C and -2°C. The compressive strength or peak stress was also observed to increase with decreasing temperature (see Figures 5-9 and 5-21). A linear increase in the compressive strength with decreasing temperature is shown on a log-log plot in Figure 2—24. This suggests the applica- tion of an expression of the form given by Equation (5-5) and similar to Equation (2—25): of = C(e)s (5—6) where of is the compressive strength and the constants C and s are strain rate dependent. The influence of temperature on the volumetric strain may be observed in Figure 5-25. There appears to be a greater initial decrease in volume (for axial strains below the initial yield strain) as the temperature decreases. For axial strains above about 1.5 percent, the volumetric strain appears to be relatively independent of the test tempera may be inspect strain tempera strain closely 5.1.3 it ties in nominal sample ratio . 0n the diamet A leas Only a ofsw Stress 14 pet Stuart Sizes the d dePEI] temperature. The net effect on the value of the tangent Poisson's ratio may be deduced from the above observation and verified from a close inspection of Figures 5—18, 5-19 and 5-20. At low values of the axial strain (< 1.0 percent) tangent Poisson's ratio is less at the lower temperatures, as a result of the greater volume decrease. As the axial strain increased, values of tangent Poisson's ratio appear to more closely agree. 5.1.3 Sample Size Effects The influence of sample size (diameter) on the mechanical proper- ties in compression was investigated at a temperature of —6°C and a nominal strain rate of approximately 1.2 x 10‘43ec—l using cylindrical samples 1.13, 1.41, 1.94 and 2.40 inches in diameter (length: diameter ratio of 2.0). Figure 5—26 summarizes the influence of sample diameter on the initial yield stress and strain. The initial yield stress obtained for the 1.41, 1.94 and 2.40 inch diameter samples appears to be relatively independent of sample diameter. A least squares linear regression analysis (Figure 5-26a) indicates only a 0.23 percent decrease in the initial yield stress over a range of sample sizes from 1.41 to 2.40 inches. However, the average yield stress obtained from the 1.13 inch diameter samples is approximately 14 percent less than the value predicted from an extension of the least squares line fitted through the data points for the three larger sample sizes (Figure 5—26a). Figure 5—26b presents the initial yield strain as a function of sample diameter. A least squares linear regression analysis through the data points indicates that the initial yield strain is somewhat dependent on the sample diameter. There is approximately a 9.30 percent deer: test: for of t This Prio seat the samw rel; uni sam is lit 1.1 Fig in CO' 90 decrease in the initial yield strain over the range of sample sizes tested (1.13 inches to 1.41 inches in diameter). However, the data for the 1.41 inch diameter sample gives a significantly higher value of the initial yield strain, as may be observed from Figure 5—26b. This probably results from higher strains associated with sample seating- Prior to testing the 1.13, 1.94 and 2.40 inch diameter samples, a small seating stress of approximately 100 psi was placed on each sample using the manual loading option of the Wykeham—Farrance test machine. The sample was then allowed to creep for a sufficient period of time to relax the applied load. This procedure was intended to provide a more uniform application of lead to the sample. The 1.41 inch diameter samples were tested without the application of a seating stress. Thus, is would seem reasonable to expect somewhat higher yield strains. A linear regression analysis through the data points, neglecting the 1.41 inch diameter samples, results in a slope reversal, as shown in Figure 5-26b. Consequently, there appears to be an 11 percent increase in 8y over a range in sample diameters from 1.13 to 2.40 inches. Figure 5-27 summarizes the effect of sample diameter on the compressive strength (peak stress) and the axial strain at failure. A least squares line through the strength data in Figure 5—27a shows that an increase in sample diameter from 1.13 inches to 2.40 inches results in a 0.65 percent decrease in the compressive strength. The axial strain at failure (shown in Figure 5—27b) appears to be independent 0f the sample size for the range in diameters considered. The initial tangent modulus, summarized in Figure 5—28, shows Significant data scatter at each sample diameter. A linear regression .nalysis of the data indicates a 31 percent increase in Ei for sample diame sampi stre: comp froz stre tes1 1101 ohy deg sum of th of 31 ————-———-——fi 91 diameters over the range considered. This data suggests that the sample diameter significantly influences the initial slope of the stress—strain curve. 5.2 Constant Stress Uniaxial Compression Creep Tests To investigate the suitability of constant strain rate uniaxial compression tests to determine the time dependent behavior of the frozen sand under constant stress conditions, a series of constant stress creep tests were conducted for comparison. A.total of seven tests were conducted at -6°C and at uniaxial stresses ranging from 1100 psi to approximately 1500 psi. Table 5—3 summarizes the samples’ physical properties (including volume fraction, dry unit weight and degree of ice saturation) for the constant stress creep tests. A summary of the test results related to the time dependent deformation of the frozen sand is contained in Table 5—4. The creep curves are summarized in Figure 5-29. Each curve shows an instantaneous strain immediately after load application followed by a region of decreasing strain rate (primary creep). Beyond this region the curves approach linearity (secondary creep) prior to development of instability or an accelerating creep rate (tertiary creep). The lepe of the linear or constant strain rate portion of the creep curve (secondary creep rate) was observed to increase with increasing stress level as shown in Figures 5-29. This increase appears to be linear when plotted on a log—log scale, as suggested by Ladanyi (1972) and as shown in Figure 5—20. An expression of the form presented by Equation (2—6) appears appropriate to relate the secondary creep rate and the uniaxial stress. The total axial strain at failure (at the initiation of instability 1w, or te Figur the b Howey with proce the: 5-32 wers volu in F DIOC was 8am: $3111 aPP the dat 0f 0f to in 92 or tertiary creep) was determined from the creep curves shown in Figure 5-29. As shown in Figure 5-31, the total axial strain at the beginning of tertiary creep increased as the stress level increased. However, the time required to reach tertiary creep decreased rapidly with increasing stress (Figure 5-29). To investigate the volumetric strain behavior during the creep process, volume change data was obtained using a burette to measure the fluid expelled from the triaxial cell during testing. Figure 5—32 presents a plot of volumetric strain (5V) and volume change (AV) versus time for samples 3c, 5c, and 6c. The result is a series of volumetric creep curves similar in shape to the creep curves presented in Figure 5—29. The increase in sample volume during the creep processes denotes the influence of dilatancy and interparticle friction in resisting deformation. The failure mode for those samples reaching instability or rupture was similar to that observed in the constant strain rate tests for samples tested at moderate strain rates. Once in tertiary creep the samples generally developed a well defined shear plane oriented at -approximately 60 degrees to the horizontal; suggesting as before that the mobilized angle of internal friction was close to 30 degrees. The tangent Poisson's ratio was computed from the volumetric strain data using Equation (5—4). Tangent Poisson's ratio (Vt) as a function ‘Of time is summarized in Figure 5—33. Immediately after application 0f the uniaxial stress, Poisson's ratio is approximately equal to 0.5. However, as the creep process proceeds the value of Vt increases grapidly as dilatancy contributes to the volumetric strain. The rate of increase in Vt is greatest at the higher stress levels as would be com 38‘ C0111 the 5.3 in 10: in 1116' di ra m 93 expected from the volume change data presented in Figure 5—32. 5.3 Split Cylinder Tests The influence of temperature, deformation rate (or strain rate), and sample diameter on the mechanical properties of frozen wedron ‘sand in tension was evaluated from a series of indirect tensile tests conducted using the split cylinder test method. Table 5-5 presents a summary of sample densities, ice saturation, and dimensions. A complete summary of test results related to the tensile behavior of the sand—ice material is presented in Table 5-6. 5.3.1 Strain Rate Effects The split cylinder tests were conducted as shown schematically in Figures 2-11 and 2—12. A compressive load was applied over a narrow ' 1 loading arc and across the vertical diameter of the sample. To ‘ finvestigate the influence of the vertical deformation rate (ET) on the mechanical properties in tension, 4.00 inch diameter samples (height: diameter ratio of 0.5) were tested at constant vertical deformation rates varying from 0.002 in/min to approximately 0.28 in/min (at constant temperatures of —2, —6, -10, and —15°C). Figure 5-34 presents typical vertical deformation (YT) versus time plots for the split cylinder tests conducted using the Soiltest loading frame. The deformation rate varies slightly with time up to the point of rupture. Therefore, the deformael tion rates were computed using a least squares linear regression analysis of the vertical deformation versus time curve for each test conducted. This procedure results in the straight-time approximation for the deformation—time plots shown in Figure 5-34. The maximum deformation rate achieved by the test machine was also observed to decrease with decr the Cons appa at- and our tYP shi was of 1&1 de 3P ra be e geareazat , . i 94 decreasing test temperature. As the stiffness of the sample increased the recorded deformation rate at a selected transmission speed decreased. Consequently, the maximum deformation rate possible with the test apparatus varied from approximately 0.28 in/min at —2°C to 0.22 in/min at —15°C. Typical load versus vertical deformation curves for the split cylinder tests are given in Figure 5—35 for a temperature of —10°C and several different vertical deformation rates. The load—deformation curves remain nearly linear up to the rupture load, indicating a brittle type of deformation behavior and a nearly linear stress—strain relation— ship for the frozen sand up to failure. The indirect tensile strength (at) or the tensile stress at rupture was computed using Equation (2—36) given by Hondros (1959). The value of 0t was observed to increase with increasing vertical deformation rate, as shown in Figure 5—36. The rate of increase in at appears to decrease as the deformation rate increases and may asymtotically approach a constant value for some deformation rate above the maximum rate achieved in the present study. A linear relationship dog—log p100 between deformation rate and indirect tensile strength may be appropriate for the range of deformation rates shown in Figure 5-37. For vertical deformation rates above 0.002 in/min the samples failed by splitting along the loaded diametrical axis, with wedges formed at each loading strip as shown in Figure 2—l4c. A total of four samples were tested at a deformation rate of 0.002 in/min and temperatures of -6°C and —15°C. Both of the samples tested at —6°C failed to develop tensile splits even at large vertical deformations. Only a local compression deformation adjacent to the steel loading strip was observed. At -1 while This sand trans defo: waS' Chap tota plot P015 in 1 The appi val cer hot by to eh Th 81 95 At —15°C, one sample split at tensile stress (computed) of 407 psi, while the second deformed plastically under the applied loading. This implies that the split cylinder test may be applicable to frozen sand only at high deformation rates and that a ductile-brittle transition occurs with respect to the split cylinder test at a deformation rate of approximately 0.002 in/min. The total horizontal deformation of most samples (4-inch diameter) was measured using the horizontal deformation device described in Chapter IV (see Figure 4-5). Figure 5-38 shows typical load versus total horizontal deformation (XT) plots and Figure 5—39 gives typical plots of total vertical deformation versus total horizontal deformation. Poisson's ratio for each sample was computed using the expression given in Table 2—1, where DR is deformation ratio (YT/KT) determined from a least squares linear regression analysis as shown in Figure 5—39. The computed values of Poisson's ratio are plotted as a function of the applied vertical deformation in Figure 5-40. The computed numerical values varied from approximately —0.21 to 0.03. There was no dise C cernable dependence of Poisson's ratio on the vertical deformation rate. The total tensile strain at rupture was computed from the total Lhorizontal deformation at failure (XTF) and Poisson's ratio as indicated .by the appropriate equation in Table 2-1. The tensile strain rate up to rupture was also computed by taking the time derivative of this ‘expression as shown below: . = ~ O.1l85v+0.03896 <54) €t T 0.2491“) 10.06730 where v is considered constant with time and KT is the slope of the least squares line fitted through the total horizontal deformation versus time curves (shown in Figure 5—41). Over the range of dc to be VETST of - wher date from The aS‘ 10a: rup in lin in tn tyj 5. St ——w 96 deformation rates considered, the tensile strain at failure appears be independent of the computed tensile strain rate (Figure 5—42). Figure 5—43 presents a log-log plot of indirect tensile strength rsus the computed tensile strain rate. The data at temperatures -15°C and —lO°C seems to indicate a linear relationship between and st (on a log—log scale) of similar form as Equation (2e20): at = oc(é ) (5—8) .ere 0c and m are material constants defined as before. The limited rta at —2°C and —6°C also appear to support this observation. The modulus of elasticity, Et’ (Young's modulus) was computed tom the expression given in Table 2—1 for the 4-inch diameter samples. re value of SH’ the horizontal tangent modulus (P/XT) was determined ; the slope of the least squares line of best fit between the applied )ad (P) and the total horizontal deformation (XT) for the loads up to pture (typical load versus horizontal deformation plots are shown 1 Figure 5-38). The modulus of elasticity was observed to vary . nearly (log-log plot) with increasing tensile strain rate as shown 1 Figure 5—44. 3.2 Temperature Effects The influence of test temperature on the mechanical properties of ozen Wedron sand in tension was obtained from a series of split linder tests conducted at —2, —6, —10, and —15°C. Figures 5—40 and 42 suggest that the computed values of Poisson's ratio and the tensile rain at failure are relatively independent of test temperature. Both Operties exhibited considerable data scatter and there was no cernable relationship with the test temperature. from chan: Log- the seve show and whe 5.3 of cyl £01 was OJ th or re te WE 97 Both the indirect tensile strength and Young's modulus, determined from the split cylinder test, appear to be significantly influenced by changes in temperature, as seen in Figures 5-43 and 5—44, respectively. Log-log plots of indirect tensile strength and Young's modulus versus the number of degrees below freezing (0°C) are presented in Figures 5-45 and 5-46, respectively. The data points shown were computed for several strain rates from the equations for the least squares lines shown in Figures 5—43 and 5—44. Both the indirect tensile strength and Young's modulus may be expressed as a power function of temperature: 5 0 or E = C(e) (5-9) where C and s are constants for a given strain rate. 5.3.3 Sample Size Effects The influences of sample diameter on the indirect tensile strength of the frozen sand was determined from tests conducted at —6°C on ‘cylindrical samples with diameters of 1.94, 2.40, and 4.00 inches _(with a height to diameter ratio of 0.5). Two specimens were tested for each sample diameter. The deformation rate for each sample diameter was selected to give an average vertical compression strain rate of 0,035 min.l (vertical deformation rate divided by sample diameter) over the loaded diameter of the speciman. For no variation in YOung's modulus .or Poisson's ratio, this procedure would produce the same tensile strain rate for all sample diameters. As indicated in Figure 5—47, the indirect tensile strength was observed to be independent of the sample diameter over the range of sample sizes considered. The lateral deformation of the 1.94 and 2.40 inch diameter samples was not measured. Based on results obtained from the 4.00 inch diameter samples, the horizontal deformation in the 1.94 and 2.40 inch diameter samples of the mation tensile 98 samples was estimated to be approximately equal to the resolution (of the LADT and Sanborn 4 channel recorder. Consequently, no infor— mation was obtained related to the effect of sample diameter on the tensile strain at failure, Young's modulus, or Poisson's ratio. Table _— —— Sample No. oo\|o-‘n [>10th 99 Table 5—1: Physical Properties Summary for Constant Strain Rate Uniaxial Compression Test Samples Sample Percent Dry Degree Ice Sample Diameter Sand by Unit Wt. Saturation No. (in) Volume (pcf) (Z) 1 1.40 63.26 104.4 98.27 2 1.40 63.17 104.3 99.22 3 1.40 63.97 105.6 98.83 4 1.40 64.44 106.4 97.03 5 1.40 63.39 104.7 99.99 6 1.40 63.69 105.2 98.56 7 1.40 63.69 105.2 98.79 8 1.40 63.78 105.3 98.16 9 1.40 64.91 107.2 98.39 10 1.40 63.50 105.3 98.50 11 1.40 63.73 105.2 97.91 12 1.40 63.37 104.6 98.80 13 1.40 63.01 104.0 99.03 14 1.40 63.62 105.0 97.88 15 1.40 63.39 104.7 97.24 16 1.40 63.73 105.2 97.78 17 1.40 63.40 1 104.7 97.75 18 1.40 63.61 105.0 98.23 19 1.40 63.94 105.6 98.99 20 1.40 63.88 105.5 98.88 21 1.40 63.80 105.3 97.78 22 1.40 ———————— Membrane Leak ———-—~-—-;— ‘23 1.13 63.54 104.9 98.29 24 1.13 63.39 104.7 97.82 25 1.13 63.37 104.6 98.14 _26 1.13 63.34 104.6 98.06 27 1.94 64.81 107.0 98.75 ‘28 1.94 63.35 104.6 98.48 ‘29 - 1.94 64.28 106.1 98.11 30 1.94 64.16 105.9 99.07 ‘31 1.94 63.44 104.7 98.38 132 1.94 63.38 104.6 98.53 _33 1.94 63.38 104 6 98.54 34 1.13 63.42 104.7 98.04 .35 1.13 -------- Membrane Leak ——————————— .36 1.13 63.62 105.0 98.27 37 1.13 64.51 106.6 98.60 .38 1.13 63.83 105.4 98.36 39 1.13 63.45 104.8 98.04 40 1.13 63.92 105.5 99.15 ,41 1.40 63.81 105.3 99.71 :42 . 1.40 63.93 105 6 97.32 .43 1.40 63.68 105.1 98.19 44 1.40 63.54 104.9 97.03 .45 1.40 64.07 105.8 97.43 100 )le S—l (cont'd.) Sample Percent Dry Degree Ice nple Diameter Sand by Unit Wt. Saturation Jo. (in) Volume (pcf) (%) #6 2.40 64.33 106.2 98.15 57 2.40 63.91 105.5 98.13 18 2.40 63.98 105.6 97.57 19 2.40 63.99 105.7 98.36 50 2.40 63.86 105.4 98.66 51 2.40 64.05 105.7 98.42 52 1.94 64.23 106.0 98.27 33 1.94 64.31 106.2 98.33 54 1.94 64.27 106.1 96.11 55 1.94 64.29 106.1 99.41 36 1.94 63.96 105.6 98.04 57 1.40 64.03 105.7 97.41 58 1.40 64.12 105.9 96.69 39 1.40 64.17 105.9 97.39 30 1.40 63.65 105.1 97.06 31 1.40 64.18 106.0 97.40 32 1.40 64.18 105.9 97.05 53 1.40 63.60 105.0 96.96 34 1.40 64.10 105.7 98.90 55 1.40 64.10 105.7 98.06 36 1.40 63.28 104.5 99.43 37 1.40 63.08 104.2 99.30 58 1.40 64.00 105.7 96.99 §9 1.40 63.57 105.0 98.96 '0 1.40 64.45 106.4 98.39 Tl 1.40 64.80 107.7 97.66 72 1.40 64.70 106.9 97.00 j3 1.40 63.81 105.4 97.22 f4 1.40 64.18 106.0 97.88 .5 1.40 64.20 106 0 97.22 16 1.40 63.96 105.6 98.51 ‘7 1.40 64.26 106.1 98.98 ‘8 1.40 64.02 105 7 96.16 ;9 1.40 64.25 106.1 98.98 D 1.40 64.85 107.1 97.37 ‘1 1.40 63.56 105.0 98.77 12 1.40 64.10 105.8 97.30 -3 1.40 64.32 106.2 96.40 4 1.40 63.89 105.5 96.69 5 1.40 64.41 106.4 . 96.39 6 1.40 64.16 105.9 99.69 .7 1.40 64.22 106.0 96.13 8 1.40 64.05 105.8 98.30 9 1.40 64.10 105.8 98.90 0 1.40 64.92 107.2 96.20 Fe uvlt-P‘LI WUMUH. 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A.w v Aow\cflv AHmm m om Anflv .02 man o . V co 0 u v uswwmmm uwmwmw mmouuw :Omuum mmwuum AHIoumm AHqumw .mama .OOQ oHdEmm HwOanH .w pamflw munafiwmIo xmom nOmHum cflmuum some madamm mmmgm>¢ln andflaozlm Table I Sample No. 1c 2c 30 40 Se 6e 7e Table Sample 105 Table 5—3: Physical Properties Summary for Constant Stress Uniaxial Creep Tests Percent Dry Degree Ice Sample Sand by Unit Wt. Saturation No. Volume (pcf) (Z) lc 63.69 105.2 98.22 2c 63.08 104.1 97.42 3c 63.62 105.0 97.30 4c 63.74 105.2 97.30 5c 63.58 104.9 96.87 6c 63.57 104.9 97.16 7c 63.89 105.5 98.36 able 5-4: Uniaxial Compression Constant Stress Creep Test Secondary Immediate *Failure ample Stress Creep Rate Strain, s 1) Strain, a NO- (psi) (seC'Vl) (in/in) (in/in) 1c 1350 5.55 x 10'6 0.0246 0.060 2c 1350 1.08 x 10'5 0.0242 0.061 ‘3c 1140 7.55 x 10‘7 0.0209 ,——_ 4c 1503 3.53 x 10‘4 0.0125 0.060 5c 1244 1.58 x 10‘6 0.0231 0,050 60 1296 3.60 x 10‘6 0.0228 0.055 7c 1100 6.02 x 10'7 0.0213 0.051 Failure Strain taken as strain at beginning of tertiary creep period All samples were tested at —6°C, 106 able 5-5: Physical Properties Summary for the Split—Cylinder Samples Test Percent Degree Ice Dry Sample ample Temp. Sand by Saturation Unit Wt. Dia. No. °C Volume (Z) (pcf) (in) ls —6.06 64.57 97.90 106.6 4.00 28 -5.96 63.68 96.56 105.1 4.00 33 —5.99 65.21 97.10 107.6 4.00 43 -5.96 65.27 97.66 107.8 4.00 53 -5.99 64.58 97.18 106.6 4.00 65 -5.99 64.53 97.63 106.5 4.00 75 —5.96 65.29 97.49 107.8 4.00 83 ~5.93 65.70 97.58 108.5 4.00 93 —5.93 65.21 97.48 107.6 4.00 10S —6.00 63.86 97.14 105.4 4.00 118 —5.90 64.17 96.65 105.9 .4.00 128 -5.90 64.49 97.01 106.5 4.00 135 —6.09 64.58 97.00 106.6 4.00 145 -10.09 64.63 97.23 106.7 4.00 158 -10.09 64.54 97.53 106.6 4.00 165 —10.10 64.67 97.19 106.7 4.00 178 -9.99 64.93 98.45 107.2 4.00 185 —9.99 64.18 97.42 105.9 4.00 193 —10.08 64.95 98.37 107.2 4.00 203 -10.01 64.45 97.13 106.4 4.00 213 —15.05 64.15 96.89 105.9 4.00 223 —15.05 64.81 98.09 106.9 4.00 233 -15.05 64.58 97.61 106.6 4.00 243 —l4.95 64.75 N100 106.9 4.00 258 ~14.93 64.69 98.02 106.8 4.00 263 —14.95 64.67 96.92 106.8 4.00 275 -14.95 64.69 98.44 106.8 4.00 283 —14.95 64.80 98.09 106.9 4.00 298 —1.96 64.28 96.95 106.1 4.00 303 —l.96 65.31 98.55 107.8 4.00 315 -1.98 64.88 99.37 107.1 4.00 328 -6.03 64.42 99.36 106.3 2.40 338 —5.99 64.07 98.48 105.7 2.40 343 —6.00 64.04 97.72 105.7 1.94 355 —5.96 64.10 98.75 105.8 1.94 WUMQH. 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I mw 8 ._ O AN .4 I < 4 4 Q Q G H I- 0 .OO Aw m>m u H I- . an wvm u m OOH “ocHH moumsvm ammoq I OHOHON 1‘ PC I OoNooNl r t r l n QHDUNMMQEQH 120 Cool ..0 ca TC.“ -mm-hx «mafia—Wm LOW mmPHHHU GHwHumlwmmHu—m HNOOHOHOO HOHOO . _ v xii o a Q!.. 1.1V 1 U o I HI mmmIOH x «N w I 00m . 00w . l H- m.OH O OO O I w>m (\l H O a o w mm 02 mHQEmm_lfiWl O .OO .02 OHOaOO :AVI. O .OO .02 OHOEOO.IAVI. Uomo.ml "musumumaEwH “NHIm muanm O. S ,.O. n 3 S S ..O. Mm a 7m. OIO.H ..O.H ..O.H IO.H 121 .UoOI um om wcm .mw .qw mmHaEmm Oom mm>uso :Hmuumlmmmuum "mHIm muanm AOO OHOOOO HOOOO w m o m c m N H o rrr . . _ . _ _ m I 2 J: N. Ia .m>m . _ HlowmthH x HH.m n w em .02 MHQEMWIU' I 4 q. m>w I O cu HlomeIOH x OH.O u m .mw .oz mHQEmmILGYI. _ l .4 OI n H-OOOO-OH O OO.O n m>OO .OO .oz OHOOOO.IOYI. - 4 O m cool "wunumumaama u.w. WW Him-\- ..O.H I T O l N H ‘_ I I 0 OH 4 0 rl. ‘I. ©0H .L‘ o .. o ..O.H 1O.O Vofl w v mmmvhu vH A.OOO Figux 122 2.6 2.4 H . 2.2 H 2.0 - 1.8 1.6 _ 1.4 d 1.0 _ r Temperature: -15°C . _ -5 -l (3 Sample No. 82, Save — 8.34 x 10 sec -1 a o —6 .6 L (3 Sample No. 83, gave 5.63 x 10 sec Stress (ksi) 2O ‘. Axial Strain (Z) .gure 5-14: Stress-Strain Curves for Samples 82 and 83 at -15°C. 0“ 123 .UoNI um OO OOO .OO .OO OOHOOOO .7 HNO OOOOOO HOOOO O m q n N H .- o-amefla o .u 0 Id\\ 0 . I I 4 o 4 I 4 o 4 I O 4 , I 4 IN) 0 um mmmuum xmmm .< I daomm OH x ¢~.w I m>mw .m .o m mam HI ml I . w 2 H m lAull . m>m . HIUQOOIOH x OH O u m mm .02 mHQSMm IIAYII O>w : H-OOOOIOH x O0.0 u O .OO .02 OHOeOO.IIarI. Oomo.ml "musumuwmawe HI H+ N+ m+ How :Hmuum HaHx< mamum> QHMHum UHHumEDHo> ”mHIm wustm (Z) ursxns OIJJBWDIOA COW] o<\IunIIlIII 0001 um ow mam .mw .qw moHaEMm How cHwHum HMHx< mnmuw> deHum UHnumEDHo>.uoHIm 124 wpstm I HI ONO .O .OHOOOO HOOOO c m 1H m N H _ _ _ A m. I n - O + 4 n 4 I H n. O 1p! um mwmuum xmwm S n I m. 4 ‘u A3 0 N ,. 4 M/u w>m H-OOOTOH x HH.O n O .OO .02 «HOOO.O [DI uwm OH x 0H6 95m O .02 w new '0’ l. ‘. HI. 0| .I a mm H m m H owmm OH x «05 nw>.mw I% .02 meEMm 1.? Oool "wusumuwmfime \ UOWHI. "NHL—us NIPQCEQLI .UomHI um mm paw Nw mmHmEMm How :Hmuum HmHN< wsmuw> chHum UHHumEDHo> ANV.OHOOOO HOOO< 125 TV um mmmuum xmwm >m HIOOOOIOH x OO.O n O O .OO .02 OHOEOO.IOHIII HlowmmIOH x qm.w u m .Nw .oz mHaEmm IAQIII OomHI "OHSumHomeH unHlm HO- whstm (z) urexns orxnamnIoA .UoNI um mm cam .ww .mw mmHmEmm How aHmuum HNHx< mumpw> owumm m.:ommHom uawwSMH "wHIm mgstm A5 53% Hmfia m c m q m N H o rII . _ _ _ _ _ N.o w>m HlowwNIOH x «m.w n m .mw .oz mHmEMm IlflWI.III I.m.o HlommoIOH x OH.O n w>wm .ww .oz mHaEmm IIAYIII.I H-OOOOIOH x O0.0 u OZOO .OO .02 OHOEOO IQII. IOO UoNI "mudumeQEMH 126 1A ‘orneg s‘uossrod nuaSuel .OoO- OO OO OOO .OO .OO OOHOOOO .How chuum HMHN< msmums OHumm m.nommHonH uawwcmé umHIm mustm _ HOO OHOOOO HOHOO O O O O O . O H O H H H H H H H O.O ®>Hw HIOOOOIOH x HH.O n O .OO .02 OHOEOO I1UII-II. HIOOOOIOH x OH.O u O>OO .OO .oz OHOEOO IIOOII.... f O.O HIOOOOIOH O OO.O u O>OO .OO .02 OHOEOO .LarIIIII m u OoOI ”wusuwuwafimm. l¢.o ea n m 1.. fl 1... I. O \m m.o .m. S D O O.O s m .4 I I H 0.0 ‘o O I 3O nu O.O I.O.O .OomHI um mm mam Nw mmHQEMm How chHuw HNHN¢ mswpw> OHumm m.aommHom anMGMH HNO OHOHOO Hme< m>m HlummOIOH x mo.m u m .mw .oz wHQEmm.IAUIll HlowmmIOH x qm.w u w>mM ONw .oz mHaEMm IAVIII 128 vomHI ”musumuwmamH "ONIm mustm 3A ‘orneu s‘uossroa nuafiuel II OOONN 129 .GOHmwmeaoo :H vcmm amuoum mo HoH>mnwm :HmuumImmeum wsu do uowwwm wusumwmmawfi HNO.O .OHOOOO HOHOO nHOIO OOOOHO O n O O O m N H o . _ H H H H H _ H : OON .Invmm VA 0 H HI OIOH OH H w "wumm chHum HmaHEoz I ooq O O OOO I OoNI "OHDOmummeH . 3 rl O . m HIommmIOH x NO m n m>m w cow m OO..Oz OOOOOO I OOOH m UoOI ”wusumuwaEwH m OOO OH x OO.O u I OOOH n HI ml 1 HN .oz mHmzm OOOH cum x . u m \/ HI OIOH OO O . m mm oz MHmzmw HI OI O I O I NO .02 mqmzmw U O W; IIIIAU (\|I‘ I. 00m w>mnw HI TOH I . O I owm OH w>mm HI OI I . nu I OO w>m 1 UUW H w HI OIOH . nu I 0mm 0 m>mw 1 HI I H I . "waHH mwumsvm umme wHSMHm OH (rsd) ‘13 ‘snInpow quaBueL IEIJIUI 132 .nuwamuum m>flmmwuaaoo so uumwwm OHSuNMmQEmH Acov .O .mGHwaum BOHmm mwmuwmo OCH OH H __H__ H H __HHH_H H _ NOm.o H m Hmm mam I OO0.0 n m HOO OOO I mm¢.0 H m Hmn Nwm mwmvo H we I# nmwcHH mmhmsvn JnUUJ OON ooq OOO oow OOOH OOON "OOIO OBOE. (rsd) ‘39 ‘q38u9133 GAISSBIdmOQ .GHMIHum UHIHumEHHHo> Go uummwm mudumumaEmH ”ONIO OOOOOO fl HI HNO .O .OOOOOO HOHOO O O O O O O H _[ _ _ _ II A o O m 8 H4 1 I. 3 % S I. O 3 A‘ I O O.OHI .OO OHOEOO O ICII 0oOI .OO anHEmm IIIIOII. O.OI .OO OHOOOO III.IIIAOIII \\\\ O II O HIOOO IOH x OH.H I O "mama HHHOIHum HmcHEoz 134 1600 — :3 Temperature: -6°C m -5 -l f} = 9.5 x 10 sec ‘ave _4 -l I» an '= 1.2 x 10 sec O a; 1400 _ 8 g 0 I: 8 J R "U I g g >4 1200 _ o 8 z: 0 0' I} 0 Least Squares Line: EI e (Neglects 1.13 in.Dia.) H = 1298 2 33D O 0y ' 1000 I l 1 fl 0.5 l 1.5 2 2.5 Sample Diameter, D, (in) (a) 0.8 C) Temperature: -6°C é = 9.5 x 10_SSec_l ave 0 En = 1.2 x 10-4sec_l IQ \’ 0.6 __ c) No seating load on 1.41 25 in.dia. samples. ” ey=(0.0046-0.0003D)100 _g C) O :3 _ o g 9 m ~ ~ ~ _ - 'U 0.4 __ E5 -— ::;::;:33:::;==——-::‘::: E W - j o o t“ Least Squares Line: 0 8 Q (Neglects 1.41 in.Dia.) '5‘ e = (0.00293 + 0.0004D)100 ‘g‘ 0.2 y O H I I I 0.5 l 1.5 2.5 2 Sample Diameter, D, (in) (b) ;ure 5-26: Sample Diameter Effect on (a) Initial Yield Stress (b) Initial Yield Strain 135 1900 H E. Least Squares Line: of = 1749 — 8.876D i Temperature: —6°C 6H 2': = 1.2 x 10_4sec_l . 1800 n '5 — 2° © 0 Q q) . b O 9 o (D W I» 5 1700 8 g 8 o o ’8. o O E O O o o 1600 . I I 1 2 3 Sample Diameter, D,(in) (a) 4— Temperature: —6°C 0 g 2': = 1.2 x 10_4sec A 8 D. N 1'5 v g g Q g I: «H -I-I (I) 3— S . g 0 © H cu U! H = g H H 3;: Least Squares Line: ef=100(0.0307 + 0.000140) i 2 I I l 3 Sample Diameter, D,(in) gure 5—27: Sample Diameter Effect on;(a) Compressive Strength, (b) Failure S train. -1 136 .mHQ O OH x OO0.0 + nu .mSHDOoZ ucmwcmH HmHquH mau no uummwm uwquMHQ mHmEmm uwNIm wustm HcHO HmumEmHa mHasmm O.N m.H _ _ ) H x O ” | H OOH HO N u C)C> mmmuum m>mewOOEou HOmeHsD vow. u .quM mmmuo Oumwaoumm HI HOO. OI OIOH _ . OIOH uOOIO OOOOHO OH flfiH H H H _ H H _ HH H H H H H H _ HH H H H H H H OOOO I O . s I HOO. 8 OO OH 3 1 HO w H OOO.OHHOO.O OOOO s OHHm umwm mo QGHH meandvm uwmmH oOI "musumummama OOH OOO OOO I OOO OOOH I OOON ooom OOOO (rsd) ‘ssexng eArsseidmoglxerxerun III-III? 139 .muwwH mmwwo mmmuum uamumaoo How mmmuum HMHx< msmuo> Aamwuo zumHuHmHv mODHHmm um AHwOv .o .mmmuum HNHK< OOOH OOOH OOMH OOOH OOHH H H OOHHOOOOOO.O + OHO.OO I HOOOO “uHm ummm mo maHH mwumsvm umme OoOI u wusumquEwH_ OOOOOO HOOOO OHOIO OOOOHO (Z) ‘J3 ‘alntreg as urexns {er 140 ‘urezns orxnamnIoA A ‘ 3 .mume mmmuo mmmyum uamumaou wnu How QEHH mdmuo> chHum UHHumESHo> ”lem mustm ASHEV .u .mEHH OOO OOO OOO OOm OON OOH H . H H _ H H HOO OOHH I O um .02 wHOHamw II II .I N 1 OOO OOOH u s m I um .02 wHaEmm O I. OOO OOOH I O 0O .02 mHaEmm m I I UoOI ”wudumumOEmH O OO.OI OO.H OO.H ( mo) ‘AV ‘afiueqo emnIOA E .mummm. ammuo mmmuum unnumaoo OHHH How QEHH mSmIHQO/ OHH.O.M m.domeoOH uawwEOH "MMIO mustm ASHSV . u . mEHH OOO OOO OOO O0.0 OOm OON OOH O H H H H , H H H H.O lN.O O.O HmOH OONH u 6 .OO .02 wHOHEmm IIUII Im.O am a me OONH u 0 .OO .02 wHOHEmw IIQIII W Hwa OOHH n O .om .oz mHOHEmm IIOII. AIOO Q m. H a. 1 O OoOI "ousumumafima O lm.O MI O T0.0 Hm. A F .4 0.0 IO.O Q .wmumm aOHumaHommO HOUHun> mo :OHumcHauwumm Mom OGOHumEHNouOO< deHIucmeuum waHzonm Amumma HOOGHHOO uHHOmv muOHm wEHH msmum> sOHumfisowwm HOUHuHm> HOUHOOH uOOIO OOOOHO Auwmv.u .wEHH OO Om OO I Om 0.0 OH [ _ H H _ _ \ O \ \ \ \ \ \ O 1 OOO OOOO . \ \ I m. “HO meHHH wmeDHum uwmwd \\ \ \ H0.0 OHM. \ \ A 2 \ O \ m M \ v D D H w \ IOO.O M \ \ I. \ O o \ H m H4 \ I. O O .u \ SEE OO0.0 I HO .OH .oz OHOEOO IIUI ISO 11 \ 353 OOH.O I HO .OH .02 OHOOOO IQ] . \ OEOOH OOH.O I OO.O .OH .02 OHOEOO IO] M. \ ( OoOHI "wusumsmmame [O0.0 143 mume HOOGHHOO uHHQm How wm>uso GOHumEHowmo HNUHuHm> mswum> OOOH HOUHth "mmlm MHSmHm Ach .H» .EOHumEpowmo HOUHuuw> HOuOH O0.0 O0.0 OO.O H0.0 H . H H H O I O IOOOH OoOHI “muaumummame wuauasm IIIIwA I OOEOOO OO0.0 n HO .OH .02 OHOEOO IIIImeIII IOOOO GHE\CH OOH.O n H% .NH .02 MHQEmm IIIIAYIIII OOOOOH OOH.O I HO .OH .02 OHOaOm IIIIOIIII I IOOOO I O I ‘ II o OOOO I .M. ‘ II OOOO O 4 fix ’ IOOOO (qt) ‘a ‘peoq paIIddv ' Jun.- “ 144 .nuwcwuum wHHman uuwHHOGH mnu no uomwmm mumm COHumEhomwo HNUHuHm> ”Onlm wustm AcHE\:Hv .Hw .wumm :OHumeuowwm HOUHuuw> Om.O .. . ON.O OH.O O H H H OOH u IOOO m IIAvIIIIIIIIIIIIIIIIIIIIIIAVIII m D DON! T _ 3 TH . 8 . I w com I HO a N O E G O O a O.O- AT . o IOOO Ow MO AV 9 O.OHI G U 2. IOOO MO 0 a O. 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NNN.O 1 m .NmN.N u H1owm u .11Hw1 L 1 00¢ 1 coo AGVo 1 Ho 1 m 1 HmmcHH mwumsvm umme 1 OOO OOOH umqlm mustm sd) ‘39 ‘q38ualns aIIsual SDBIIPUI I ( .mummH HmudHH%O uHHmm Eoum OmaHEumuwn msHawoz mHmdsow do uumwwm wusumuwaSmH "OGIM WHDMHM AOov .o .waHNwmum 3onm mmmuwmm O.OOH ow ow oq ON O.OH m o H N o.H _ u q _ — — — _ H1 — u — —1Jlll] _ OH m % mHoOo u m HuHm ummm mo mwaHH mwumnvm uwme 1 N a. .b HHo.o 1 m .NmN.m n H1uwm¢1OH x q u 1 mmo.o " w oWNO-m H HIUUmHVIOH um .H H mqo.o u m .Hoo.m u Hlummm1OH x m 1 1 \T (18d) ‘33 ‘AJIOIJSBIH JO snrnpow OH Q? .fimfimuum wHHmama uumnHHEH web :0 uowwwm HoumEmHm wHNHHHwa qulm QMSMHQ 33 .n .3353 3956 m N H H . _ TEN . u ES o + an n o OOm HuHm ummm mo waHH moumsvm umMQH 1am [.OOq Oocl "wusumuomamH #1OOm O/r1 of [1 + rco/of>11/2 <6-3) where r is the ratio of uniaxial compressive creep strength to uniaxial tensile creep strength, both of which are time and temperature dependent, and s = (r + l)l/2 (6-4) Equation (2-28) suggests that for long time intervals the uniaxial compressive creep strength may be written as: “‘1 f(e) (.6—5) of(t,e) = o:o(éf/sc) where 0:; is the compression creep proof stress extrapolated to 0°C and f(6) is a temperature correction factor similar to Equation (2—25). From the data for Wedron sand, it seems reasonable to express the time dependent tensile stress from split cylinder tests in the same form: ot(t,e) = 0:0(éf/ec)l/n f (6—6) where 620 denotes the proof stress obtained from tensile data extra- polated to 0°C and f(6) is also a temperature correction factor similar to Equation (2-25). If the value of m (m = l/n) is the same for tension and compression and the same temperature—strength relationship applies, r will remain constant with time and temperature: C o m G. r = fl _—_ M = ofl = a constant (6 7) Ut(t’e) ot (é /e )m f(9) at co f c co 193 Equation (6—3) may now be rewritten as: 1/2 -1 1317—). of(t,0) l + r [Fish] (6—8) The data presented in Figure 6-15 would suggest a value of r of approximately 1/5 for frozen Wedron sand. 6.4 Simplified Analysis Ground freezing projects which involve frozen sand as a structural material include many diverse open excavations. One special application related to natural gas pipeline construction in discontinuous permafrost regions is illustrated in Figure 6—18. Operating temperatures for the natural gas pipeline will be in the range of -8 to—lZflC. thus, granular bedding soils adjacent to the pipeline will remain continuously frozen. In areas where ground water and soil conditions are favorable, this procedure could result in the formation of ice lenses in the underlying unfrozen soil. Frozen sand backfill, simulating an unreinforced concrete beam, could provide some support for the pipeline in areas subject to differential frost heave. A simple analogy to this application of frozen sand as a struc— tural element considers the simply supported beam shown in Figure 6-19. To illustrate baSic design concepts pertaining to time dependent strength and deflection behavior, an analysis of the beam response to the applied load P is presented in the following section. Beam dimen- sions and loading conditions have been selected to permit laboratory verification and use of analytical solutions for stress distribution and deflection. 194 6.4.1 Stress Distribution The time dependent response of a beam subjected to pure bending, outlined in Section 2.5.2, was based on the assumption that the time dependent material behavior was the same in tension and compression. The frozen sand tensile strength (from the split cylinder tests) was approximately 1/5 the compressive strength from conStant strain rate uniaxial compression tests. The parameter n in Equation (2—6) appears to be approximately the same for tension and compression. Therefore, the proof stress for tension (0:) should be approximately 1/5 the proof stress for compression (0:) determined from the constant strain rate uniaxial compression tests. Different Stress—strain—time relationships for tension and compression requires that the stress distribution due to bending, given by Equation (2—5), be re—examined since the neutral axis will no longer be located at the centroid of the cross—section. Applying the elastic analog described in Section 2.5.2, the strain rate is made to correspond to the elastic strain as given below: n z > O . a = cc 0 sgn(0) c o n z < O : s — éc t sgn(o) (6—8) 0 c z = 0 : s = 0 where z is the distance from the neutral axis (shown in Figure 6—20) and s = -z/p (Q is the radius of curvature of the beam). The beam of the neutral axis may then be determined from equilibrium requirements: 2F = o fodA = 0 = ‘21 t z 1/n h'zl c z n . 0c pé sgn(z)bdy + cc pé sgn(z)bdy = 0 o o C (6-9) where 21 is defined in Figure 6-20a and expressions for 0 were obtained from Equations (6-8) in terms of the radius of curvature of the beam. Assuming the strain distribution shown;in Figure 6-20a, 9 may be expressed as: z p = _l (6-11) 61 where 81 is the strain in the bottom fibers of the beam at some time t1. Substituting Equation (6—10) into Equation (6—9) and integrating yields: 1 b t 1+l/n c 1+l/n . ————— -——— — + h — = 0 6:12 [z s ] l+n ' Oc lzll 0c I zll ( ) l c If 0: = 50:, Equation 6-ll may be solved for zl in terms of h: — h (6—12) 2 _ _________ + l 1 + (0.2)1/(l ll“) For the beam shown in Figure 6-19, (h = 2.Sin. and n = ll) 21 may be determined to be 2.035 in.. Since Equation (6—12) is independent of the strain, the location of the neutral axis is independent of time for stationary creep conditions. The spatial stress distribution may now be determined by considering equilibrium at a given cross—section in terms of the applied bending moment: EM = 0: M = fzodA (6-13) 196 Substituting Equations 6-8 for o and integrating yields: 1 z > O: o = -M Izl /n O": b c . 2 + 1 2 + 2 + l/n _c (Z1) /n + (h ‘ 21) “H 0'C (6—14) l/n z < 0: o = M '2' C . b 2 + l/n 0c 2 + l/n 2 + l/n (Z1) + at (h ‘ 7‘1) C for the rectangular cross-section shown in Figure 6-20a. The maximum stresses in the beam due to bending are located in the outer fibers of the beam at x—coordinate where the bending moment is a maximum. For the simply supported beam shown in Figure 6—19, the maximum bending moment occurs at mid-span and equals Mmax = (PL/4). Figure 2-20b presents a plot of normal stress due to bending versus distance from the neutral axis in terms of the applied load P. 6.4.2 Time Dependent Deformation The magnitude of the applied load may be determined so as to limit the maximum strain in the beam or the maximum deflection to an allowable value over the service life of the structure. Consider the beam shown in Figure 6—19 at a temperature of -20°C. Assume that the load is applied to the beam pseudo—instantaneously and that the dynamic response may be ignored. Assume also that a condition of stationary creep is developed in the beam within a short period of time and that plane sections through the beam remain plane during creep. If, as suggested by Vyalov (1959), the creep strain tends to dominate the deformation process, the total strain at any point in the beam 197 may be estimated from the stress distribution using Equation (2-6) as a function of time. The time dependent strength of the frozen sand may then be expressed in terms of a failure strain (or allowable strain) and a service life for the beam. With these conditions in mind; the allowable load P for a designated service life of the structure may be computed. As shown in Figure 2—20a, the maximum strain in the beam occurs at z = —zl. If the strain at failure in tension equals the failure strain in compression at the same applied strain rate, as suggested by Perkins and Ruedrich (1973), the allowable stress based on the failure strain and service life may be computed from Equations 6—8. The stress in the frozen sand beam at z = —zl based on the appropriate expression from Equations (6—14) becomes: 0(z = —zl) = 1.128P (6-15) If the failure strain (sf) in tension is taken as approximately 0.045 (Figure 5-10) and the service life (tf) as 7 days (convenient for laboratory testing), the tensile stress required to reach the failure strain at t may be computed as: f e l/n -% 0C [ g ] f(e) C Q ll co (6—16) 0.045 10‘6(6.05 x 105) 0.053 (1 + 20) = 409 psi ' 0.091 = %—(516)[ ] where Oco is the compression proof stress extrapolated to 0°C and f(e) and w are determined from a log-log plot (Figure 6—21) of CC C versus the normalized temperature (1 + e/ec). The allowable load P 198 may be determined from Equations (6-15) and (6-16): 409 1.128 = 363 lbs. (6-17) The creep deflection at tf may be obtained in a similar fashion to that presented by Odqvist (1966). The deflection rate w may be related to the radius of curvature and the strain rate as: dzw -c éc o n = n = _ = __ z>0 ——2 w z z(c]sgn(0) dx 0 c (6-18) dzw -e ' Sc 0 n' z<0: —-Q- = w" = —z- = -z—- 7 sgn (0) ’dx ‘Oc where w is the deflection rate. Solving for o in terms of w" and substituting into Equation (6-13) one obtains: (6-19) M = f(o)sz . -l/n _ If: C ____lL_____ 2+l/n. __ll____ 2+1/n ' ‘ [gel 0c [3(2 + 1/n) (21) + 2 + l/n (h ‘ 21) ] ." l/n = - [El] CC In a c c Solving for w" and integrating, the deflection rate at mid-span may be computed as: n 2 . PL L a (6-20) c 40: In 4(n + 2) g. ll 10-6 364(22) 111 (22)2 4(2591)(1.038)J 4(11 + 2) 3.62 x lO—7in/sec 199 At the anticipated service life of 7 days (6.05 x lossec) the deflection at mid-span is 0.219 inches. This deflection is only 0.99 percent of the length of the beam. Popov (1968) indicates that for elastic deflections less than approximately l/lO of the beam length, the assumption of small deformations may be considered valid. If this criteria may be applied to the creep deflections, then the small deflection estimated would be consistant with the assumption of small deformations used in the development of creep equations (Odqvist, 1966). The elastic and plastic deformations described by the first two terms of Equation (2—7) may also be included in an analysis similar to the one presented above. However, to avoid complexity in integrating Equation (6—19), these.terms have been neglected in the example presented. The example does serve to demonstrate that small beams composed of frozen sand should support significant loads for limited periods of time and that the sand-ice material will resist bending moments (in agreement with field observations). 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I 88 oh I o 3: H . o- I o>m 0 AH mv Avov Avov I ooom m n u , Hloo oIOH x H m um voaHMuno b ouoz vb Acm\m + Hv .aEwH IQ uOOOH (rsd) ‘39 ‘559133 Joela CHAPTER VII SUMMARY AND CONCLUSIONS The results and conclusions derived from this investigation are summarized in the following sections: material behavior, standardization and evaluation of test methods, material property selection, and recommended additional research. 7.l Material Behavior The material behavior of frozen Wedron sand was examined with respect to mechanical properties required for design of frozen soil structural elements subject to bending meoments. Of primary interst was the stress-strain—time relationships governing deformation in tension and compression. Constant strain rate uniaxial compression tests conducted on the sand—ice material indicated that the stress-strain behavior of the material was governed by the applied strain rate. The deformation behavior changed from a plastic to a brittle failure as the applied strain rate increased. At average strain rates below 2 x lO-4sec_l, the stress—strain curves exhibited an initial yield followed by a period of plastic strain hardening. At high strain rates (average above 2 x lO_4sec-l), the stress—strain curves were nearly linear up to the failure, with the initial yield stress approximately equal to the peak“ stress. The initial portion of the stress-strain curves appears to be dominated by the behavior of the ice matrix. Yield in the ice is believed to be responsible for theinitialyield point Observed in the stress-strain curves. The plastic strain hardening occuring after the initial yield, has been attributed to dilatancy and mobilization» 226 227 of interparticle friction (as supported by the volume change measurements). The compressive strength of the frozen sand obtained,from the constant strain rate tests,was observed to increase uniformly with increasing strain rates, up to an average strain rate of about 7 x lO-6sec_l. At higher strain rates the compressive strength appears to be independent of the applied strain rate. This transition was observed to occur close to the strain rate at which the mode of failure changed from plastic (no visable cracking) to brittle (shear planes or multiple cracks). The decrease in plasticity coupled with surface irregularities at the sample ends may have produced premature failure at the higher strain rates. Data obtained at low strain rates increased uniformly with increasing strain rate according to a power law which, in turn, permits computation of the long term strength. A similar relationship was observed for the indirect tensile strength determined from the split cylinder tests. The exponents in the two power law relationships were observed to be approximately the same. However, the indirect tensile strength appears to be roughly l/5 the compressive strength of the frozen sand and approximately equal to the tensile strength of ice. There was some evidence which suggests that the split cylinder test may significantly underestimate the true tensile strength. However, data obtained by other investigators does seem to confirm that the tensile strength (as a functionof strain rate) is much less than the compresSive strength for frozen sand. Both indirect tensile strengths and uniaxial compressive strengths increased with decreasing temperature (for temperatures less than -6°) according to a power law-similar to that given by Ladanyi (1972). The indirect tensile strength increased in proportion to the compre551ve 228 strength with decreasing temperatures in such a fashion as to maintain a compressionztension strength ratio of approximately 5. At higher temperatures the compressive strength was observed to be more dependent on the applied strain rate. The axial strain at failure in compression increased from less than one percent at high strain rates to greater than 4 percent at low strain rates. The slower rates appear to permit more pressure melting and-water migration,refreezing and particle readjustments to occur prior to the develOpment of the peak load. The computed tensile strains reported for the split cylinder tests were in most cases less than 0.1 percent, which compares favorably with the failure strain in tension reported for ice by other investigators. However, data presented for direct tensile tests on frozen sand (Perkins and Reudrich, 1973) indicates that the tensile strain at failure is approximately equal to the compressive failure strain, at the same strain rates. The failure strains observed for both the indirect tensile tests and the constant strain rate compression tests were determined to be independent of temperature. The initial tangent modulus for constant strain rate compression tests was observed to be approximately equal to the computed value of Young's modulus from the split cylinder tests. Both values were observed to increase uniformly with strain rate and temperature. This suggests that power expressions similar to those used to relate temperature and strain rate to the strength of the frozen sand might be applied to the elastic modulus. 229 7.2 Standardization and Evaluation Of Test Methods The applied strain rate during the so-called constant strain rate compression tests was observed to vary over the duration of the test. Variation in the applied strain rate may be attributed directly to the stiffness of the test apparatus. Elastic strain energy stored in the test system was released as the sample reached the initial yield and peak stress, accounting for the increase in strain rates observed at these points. The observed strain rates did not reach the nominal strain rate until after the sample had reached the peak stress. Differences between material constants obtained from analyses using the average strain rate to failure and the nominal strain were not considered to be significant in this study. The differences do. indicate that the test system stiffness will influence test results. The effect of machine stiffness on test results would obviously increase as the stiffness of the test system decreases. In addition, if the same test system were used, changes in the sample geometry, which influences the stiffness of the sample, will also effect the response of the test system during testing. Differences in test frames or sample geometry could result in significant differences in test results obtained by various investigators, if nominal strain rates were used by some for analysis. The effect of sample diameter on the mechanical properties in tension and compression was observed for the same average strain rate to failure. The indirect tensile strength was observed to be independent of sample diameter for the range of sample sizes (1.94 to 4.00 inches) tested. The mechanical properties of the frozen sand determined from the constant strain rate compression tests were also observed to be 230 independent of the sample diameter, with the possible exception of the initial tangent modulus. Data obtained suggests that the initial tangent modulus increased by approximately 31 percent over a range of sample diameters (1.13 to 2.40 inches) which could be encountered in field investigations. The explanation for this apparent increase in Ei can not be ascertained from available data. A reasonable requirement, based on theoretical considerations, is that the minimum linear dimension of the sample Should be 10 to 20 times the maximum particle diameter (Hawkes and Mellor, 197). The sample length should be at least twice the diameter for uniaxial compression tests (Baker, 1978a). Comparison of results obtained from constant strain rate and constant stress compression (creep) tests indicates that the constant strain rate compression tests may be used to provide a reasonable estimate of the time dependent deformation during secondary creep. The material parameters necessary to define the creep strain prior to secondary creep can not be obtained from the constant strain rate tests. If the service life of a structure were less than the duration of primary creep, then constant stress creep tests are needed to define the parameters necessary for predication of the creep strain as a function of time. Application of constant strain rate tests are limited to situations where the elastic and primary creep deformations are small in comparison to the secondary creep strain. It would also seem reasonable that constant strain rate compression tests could be used to determine the time dependent strength of the frozen sand. The failure strain obtained from the constant strain rate 5sec—l) was observed compression tests (for strain rates less than 10- to be approximately equal to the strain at the onset of tertiary creep in the constant stress creep tests. The long term strength of the 231 frozen sand may be determined as indicated by Equation 2—10. Several problems were observed with respect to applying the split cylinder test to frozen sand. At low vertical deformation rates tensile failures did not occur in the samples,only an apparent compression in the area of the loading strips. As a result, it was not possible to obtain data for tensile strain rates below about 1.4 x lO—Ssec_l. The computed values of Poisson's ratio were usually less than zero. Since Poisson's ratio was used to compute Young's modulus, the tensile strain at failure, and the tensile strain rate, there is some question as to the accuracy of the relationships between tensile strength or Young's modulus and tensile rate. In addition, there is some evidence to indicate that the split cylinder test may significantly underestimate the true tensile strength. These problems would suggest that emphasis should be placed on developing another test method to determine the material properties of frozen sand in tension. 7.3 Material Property Selecti0n_ Selection of material properties defining the stress—strain—time behavior of frozen sand in tension and compression is required for engineering design of sand—ice structural elements. The constitutive equations governing the time dependent strain of frozen sand in tension or compression appears to be reasonably approximated by power law relationships which are functions of stress and time. Data obtained in this investigation and supported by the work of other researchers, indicates that the uniaxial constant strain rate compression test may be used to estimate the creep parameters in compression and tension. The creep parameter n (the exponent in the power law) appears to be approximately the same for tension and 232 compression (with respect to the uncertainty' of computing tensile strain rates for the split cylinder test). The tensile strength of frozen Wedron sand was observed to be approximately l/S the compres— sive strength of the same range of strain rates. It appears that the creep proof stress 0: for tension may be obtained from the constant strain rate compression tests as 1/5 the value of compression creep proof stress 0:. Young's modulus from the split cylinder tests was found to be in close agreement with values obtained from constant strain rate compression tests at the same temperature and strain rate. Values of the elastic modulus for tension and compression may be obtained as a function of strain rate from the constant strain rate compression test. Both the elastic modulus and strength were observed to increase withdecreasing temperature according to similar power expressions, which may be evaluated from the constant strain rate compression data. Extension of the uniaxial creep (power) expression to multiaxial states of stress has been considered by several other investigators. The von Mises flow law and the assumption of volume constantancy have usually been assumed. Volume change data obtained from uniaxial compression creep tests at zero confining pressure indicates that dila— tancy results in a significant volume increase during the creep process. The value of Poisson's ratio during creep was computed to be greater than 0.5 (constant volume value) and was observed to vary with strain according to a power law relationship. Influence of confining pressure on Poisson's ratio was not investigated and may justify using a value of approximately 0.5 for design. The Mohr—Coulomb failure theory may be extended to multiaxial states 233 of stress (ignoring the possible influence of the intermediate principal stress on failure) and to consider the time dependent strength of frozen sand. Assuming that the tensile strength of frozen sand may be estimated from the uniaxial compressive strength, a parabolic representation of the time dependent Mohr envelopes may be developed in terms of the compression:tension strength ratio. A simiplified analysis of a simply supported.beam was presented to illustrate flexural analysis concepts pertaining to the time dependent rupture and deflection of the beam. The analysis also serves to illustrate the ability of frozen sand to resist flexural defor- mation and the applicatidn Of constitutive creep equations (and corresponding temperature corrections) for design or analysis of a frozen soil structural element. 7.4 Recommended Additidnal Research Additional research is needed in several areas related to the mechanical properties of frozen sand and the design of frozen soil structures. Several specific problems are outlined below: 1. Due to uncertainty and difficulties in interpreting results for the split cylinder tests, additional tensile tests on sand-ice ma- terials are needed. Direct tensile tests would help verify the results of indirect test methods. Constant strain rate and/or constant stress uniaxial tension tests would seem appropriate. 2. The influence of confining pressure on the volumetric strain of frozen soils should also be investigated. It is suspected that confining pressures would reduce the dilatancy of frozen sand during creep or constant strain rate compression tests, resulting in a decrease 234 in the value of Poisson's ratio. Data obtained from unconfined compression tests in this investigation suggest that Poisson's ratio may be significantly greater than 0.5 due to dilatancy effects. Data related to the interaction of confining pressure, strain,, and Poisson's ratio would permit a more realistic evaluation of current methods of considering creep under multi-axial stress conditions. 3. The ability of frozen sand to function as a structural element (even temporarily) suggests an analogy to concrete. Steel reinforcement is normally used in concrete structures to compensate for the low tensile strength of the material. Similar use of reinforcement may also be helpful in many applications of frozen soil structures. The bond strength as a function of time and temperature would be required to define the interaction between the reinforcement and the frozen sand for structural design. 4. Laboratory investigation of the performance of simple beams would provide verification of the analysis presented in this investi- gation. Properly instrumented beams would help define strain distri- bution in the beam and permit computation of the creep parameters in tension (provided the compression creep parameters are known in advance). Laboratory tests on model beams could also be extended to consider the effect of reinforcement on the time dependent response. Such information would be a valuable contribution to developing design procedures for field application of reinforced frozen earth structural elements for construction purposes. APPENDIX kmld 235 Table A—l:. Constant Strain Rate Uniaxial Compression Test Data SAMPLE NO. 1 SAMPLE NO. 2 (cont'd.) Temperature = -6.08°C _4 -1 0.374 294 Nom. Strain Rate = 1.19 x 10_ sec_l 0.399 389 Ave. Strain Rate = 9.46 x 10 sec 0.442 491 Sample Diameter = 1.405" 0.480 625 Initial Length = 2.81" 0.597 878 Percent Sand (by Vol.) = 63.26 0.755 1099 Degree Ice Saturation (Z) = 98.27 0.924 1237 Time to Failure = 310 sec 1.114 1311 Strain Stress 1'376 1358 a . 1.613 1405 (A) (281) 1.961 1457 0.027 77 2.310 1501 0.049 192 2.680 1527 0.092 301 3.033 1540 0.131 435 3.220 1543 0.179 492 3.407 1546 1 0.192 543 I 3.784 1521 I 0.229 684 W 4.181 1485 . 0.326 945 4.561 1442 0.625 1241 4.979 1387 1.036 1382 5.379 1333 1.474 1464 2 5.777 1291 1°952 15 5 6.311 1218 2.431 1574 ‘ 6.862 1151 2.934 1585 7.431 1091 3.423 1565 _ 3'933 1519 SAMPLE NO. 3 4.429 1450 —‘—"———‘_“‘ 4.943 1376 Temperature = —6.05°C _4 -1 5.496 1295 Nom. Strain Rate = 1.19 x 10_ sec_l 6.013 1204 Ave. Strain Rate = 9.76 x 10 sec 6.547 1131 Sample Diameter = 1.405" 7.346 1032 Initial Length =~2.81" Percent Sand (by Vol.) = 63.97_ SAMPLE N0. 2 Degree Ice Saturation (Z) = 98.83 0 Time to Failure = 282 sec Temperature = -6.05 C _4 —l Nom. Strain Rate = 1.19 x 10_4sec_l Strain Stress I Ave. Strain Rate = 1.02 x 10 sec (Z) £B§11_ Sample Diameter = 1.405" 0.069 44 Initial Length = 2.81" 0-122 236 Percent Sand (by Vol.) = 63.17 0.194 428 Degree Ice Saturation (%) = 99.22 0.261 651 Time to Failure = 335 sec 0-380 912 . 0.521 1145 ‘ Strain Stress 0.672 1298 (4) (ps1) 0.906 1377 0-083 83 1.143 1418 0.135 109 1.305 1473 0-224 147 1.844 1508 0-241 179 - 2.213 1547 0.307 230 236 Table A-1 (cont'd.) SAMPLE NO. 3 (cont'd.) SAMPLE NO. 5 2.566 1565 Temperature = —6.05°C 2.752; 1569 Nom. Strain Rate = 1.19 x 10 sec 2.939 1566 Ave. Strain Rate = 9.92 x 10 sec 3.316 1548 Sample Diameter = 1.405" 3.676 1498 Initial Length = 2.81" 4.210 1410 Percent Sand (by Vol.) = 63.39 4.803 1304 Degree Ice Saturation (Z) = 99.99 5.358 1200 Time to Failure = 370 sec 5°9ll 1108 Strain Stress 6.618 987 (Z) ( si) 7.307 866 O 011 —B§E—_ 0.087 211 W 0.159 403 Temperature = —6.05°C _4 -1 0.230 594 Nom. Strain Rate = 1.19 x 10_ sec_l 0.319 798 Ave. Strain Rate = 9.29 x 10 sec 0.409 982 Sample Diameter = 1.405" 0.575 1165 Initial Length = 2.81" 0.841 1289 Percent Sand (by V01.) = 64.44 1.112 1368 Degree Ice Saturation (Z) = 97.03 1.567 1475 Time to Failure = 290 sec 2.023 1575 . 2.481 1649 Strain Stress 3.053 1707 —441—— ififiil— 3.558 1716 0'027 89 3.668 1727 0'063 262 4.175 1700 0°133 461 4.819 1627 0'202 677 5.484 1543 0'271 888 . 6.322 1415 0.343 1072 7.254 1289 0.456 1224 0.685 1342 SAMPLE NO. 6 1.032 1413 ——-———"—‘—“ o 1.491 1483. Temperature = —6.08 C _3. —1 1.970 1544 Nom. Strain Rate = 1.34,x 10_ sec_'l 2.452 1580 Ave. Strain Rate = 3.69 x 10 sec 2.695 1582 Sample Diameter = 1.405" 2.939 1572 Initial Length = 2.81" 3.449 1527 Percent Sand (by Vol.) = 63.69 3.945 1440 Degree Ice Saturation (Z) = 98.56 4.499 1339 Time to Failure = 11.1 sec 3 881 1052 Strain Stress ° (2) (psi) . 0.003 134 0.017 332 0.033 678 0.080 921 Table A-1 (cont'd.) SAMPLE N0. 6 (cont'd.) 0.107 1170 0.171 1423 0.244 1597 0.290 1685 0.360 1723 0.414 1741 0.489 1739 0.624 1705 0.823 1600 1.136 1482 1.579 1374 2.096 1272 2.593 1178 3.375 1051 4.268 938 SAMPLE NO. 7 Temperature = -6.05°C Nom. Strain Rate = 5.93 x lo—Zsec: Ave. Strain Rate 2.68 x 10- sec Sample Diameter = 1.405" . Initial Length = 4.81" Percent and (by Vol.) = 63.69 Degree Ice Saturation (Z) = 98.79 Time to Failure = 28 sec Strain Stress (Z) (psi) 0.037 83 0.074 166 0.120 333 0.172 531 0.240 754 0.298 977 0.366 1193 0.463 1403 0.568 1541 0.749 1589 0.928 1586 1.249 1556 1.617 1525 1.996 1481 2.628 1359 3.281 1214 4.303 956 SAMPLE N0. 8 Temperature = —6.10°C Nom. Strain Rate - 2.77 x 10::sec:i Ave. Strain Rate = 2.04 x 10 sec Sample Diameter = 1.405" Initial Length = 2.81" Percent Sand (by Vol.) = 63.78 Degree Ice Saturation (Z) = 98.16 Time to Failure = 143 sec Strain Stress (Z) (psi) 0.098 205 0.186 492 0.229 684 0.301 868 0.373 1052 0.449 1199 0.621 1330 0.811 1391 1.012 1426 1.213 1468 1.414 1502 1.624 1544 1.826 1578 2.028 1606 2.287 1633 2.592 1659 2.917 1679 3.396 1658 3.979 1617 4.553 1516 5.201 1415 6.134 1274 6.893 1180 7.729 1076 SAMPLE NO. 9 Temperature = —6.05°C _5 Nom. Strain Rate = 5.34 x 10_55ec Ave. Strain Rate 2.57 x 10 sec Sample Diameter = 1.41" Initial Length = 2.81” Percent Sand (by Vol.) = 64.91 Degree Ice Saturation (Z) = 98.39 Time to Failure = 1317 sec Strain Stress (2) (psi) 0.007 64 0.063 103 0.110 179 I I I I -1 -l 238 Table Arl (cont'd.) SAMPLE NO. 9 (cont'd.) SAMPLE NO. 10 (cont'd.) 0.157 288 4.184 1632 0.208 467 4.619 1588 0.263 632 5.054 1544 0.336 804 5.396 1497 0.450 975 0.018 83 0.582 1107 0.103 320 0.774 1220 0.195 575 0.990 1293 0.039 147 1.223 1379 0.465 1071 1.458 1451 0.633 1234 1.746 1542 2.073 1624 SAMPLE NO. 11 2'419 1699 1 Temperature = -6.05°C 2.785 1761 . _ 3.175 1785 Nom. Strain Rate - 1.07 x 10 sec Ave. Strain Rate = 9.23 x 10 sec 3.379 1795 Sample Diameter = 1.405" 3.587 1778 . . _ u . 8 1719 Initial Length — 2.81 2 216 1612 Percent Sand (by V01.) = 63.73 ‘ Degree Ice Saturation (Z) = 97.91 6:18: iii: Time to Failure = 4590 sec 7.059 904 Strain Stress (Z) (psi) SAMPLE NO.-10 0.023 39 o 0.031 57 Temperature = —6.05 C _5 -1 0.055 86 Non. Strain Rate = 5.34 x 10_ sec_l 0.079 119 Ave. Strain Rate = 4.36 x 10 sec 0.126 205 Sample Diameter = 1.405" 0'219 374 Initial Length = 2.81" 0.339 536 Percent Sand (by V01.) = 63.50 0.455 676 Degree Ice Saturation (Z) = 98.50 0.600 793 Time to Failure = 753 sec 0.811 911 Strain Stress 1.095 1036 (7.) (psi) 1.434 1174 0.069 211 1.784 1299 0.154 448 2.032 1336 0.263 716 2.331 1420 0.382 976 2.650 1483 0.546 1172 2.961 1541 0.747 1297 3.338 1603 0.963 1364 3.809 1638 1.201 1411 4.237 1656 1.438 1464 4.649 1642 1.822 1527 5.139 1616 2.217 1584 5.649 1571 2.614 1628 6.159 1520 3.031 1658 6.917 1442 3.280 1660 3.715 1646 239 Table A-1 (cont'd.) SAMPLE N0. 12 Temperature = —6.05°C _5 Nom. Strain Rate = 2.37 x 10__5 Ave. Strain Rate = 2.01 x 10 sec Sample Diameter = 1.405" Initial Length = 2.81" Percent Sand (by Vol.) = 63.37 Degree Ice Saturation (Z) = 98.80 sec-1 -1 Time to Failure = 1950 sec Strain Stress (Z) (psi) 0.004 32 0.019 96 0.067 233 0.139 381 0.198 495 0.255 600 0.352 740 0.506 7 911 0.734 1068 0.996 1182 1.258 1271 1.536 1343 1.891 1426 2.378 1500 2.987 1572 3.558 1606 3.924 1618 4.850 1597 5.655 1528 6.498 1455 7.434 1363 7.415 1346 SAMPLE NO. 13 Temperature = -6.05 _3 -1 Nom. Strain Rate = 1.78 x 10_ sec_l Ave. Strain Rate = 6.46 x 10 sec Sample Diameter = 1.405" Initial Length = 2.81" Percent Sand (by V01.) = 63.01 Degree Ice Saturation (Z) = 99.03 Time to Failure = 7.85 sec Strain Stress (Z) (psi) 0.002 67 0.002 224 0.003 393 0.054 582 0.096 780 SAMPLE NO. 13 (cont'd.) 0.138 985 0.179 1195 0.238 1406 0.303 1577 0.382 1697 0.507 1746 0.693 1673 1.036 1458 1.402 1288 2.075 1129 2.812 989 3.733 875 4.755 780 5.659 725 SAMPLE NO. 14 Temperature = —6.10°C -6 Nom. Strain Rate = 4.75 x 10_ sec Ave. Strain Rate = 4.05 x 10 sec Sample Diameter = 1.405" Initial Length = 2.81" Percent Sand (by Vol.) = 63.62 Degree Ice Saturation (Z) = 97.88 Time to Failure = 11,280 sec -1 —1 Strain Stress (Z) (psi) 0.026 16 0.042 42 0.066 73 0.107 128 0.153 211 0.246 303 0.310 391 0.375 474 0.586 659 0.916 809 1.359 954 1.599 1119 2.066 1286 2.455 1399 2.889 1511 3.422 1596 4.051 1647 4.293 1655 4.572 1662 4.986 1643 5.477 1604 5.761 1569 5.987 1559 6.366 1517 240 Table A—1 (cont'd.) SAMPLE N0. 15 SAMPLE N0. 16 (cont'd.) Temperature = -6.05°C —6 -1 1.133 560 Nom. Strain Rate = 1.42 x 10_6sec_l 1.582 712 Ave. Strain Rate = 1.23 x 10 sec 2.123 887 Sample Diameter = 1.405" 2.593 1023 Initial Length = 2.81" 3.103 1138 Percent Sand (by Vol.) = 63.39 3.707 1242 Degree Ice Saturation (Z) = 97.24 4.337 1289 Time to Failure = 37,080 sec 4.580 1292 Strain Stress Time 4'767 1290 a . . 5.219 1266 _QL. fl ELI-L) 5 709 1229 0.077 61 8 ' 6.333 1170 0.118 112 18 6.921 1111 0.133 144 25 7.470 1052 0.166 243 48 8 019 1001 0.296 351 73 ' 0.545 465 108 1.010 646 173 §é§3§§—394—41 1.565 851 248 Temperature = —6.13°C _4 —1 2.123 1047 323 Nom. Strain Rate = 4.45 x 10_4sec_l 2.719 1215 398 Ave. Strain Rate = 2.26 x 10 sec 3.357 1356 478 Sample Diameter = 1.405" 4.022 1432 558 Initial Length = 2.81" 4.561 1442 618 Percent Sand (by Vol.) = 63.40 v5.162 1421 683 . Degree Ice Saturation (Z) = 97.75 5.936 1355 768 I Time to Failure = 36 sec 6.714 1272 848 . ' 7.377 1204 913 SEE§1n iggiis 7.534 1143 993 ELIEEI— -—5II—- 0.059 137 §A¥§E§.EQ_1§ 0,035 237 Temperature = —0.06°C _7 —1 0-143 445 Nom. Strain Rate = 5.69 x 10_ sec_1 0.222 732 Ave. Strain Rate = 4.90 x 10 sec 0.310 1031 Sample Diameter = 1.405" 0-399 1263 Initial Length = 2.81" 0-479 1415 Percent Sand (by Vol.) = 63.73 0.575 1521 Degree Ice Saturation (Z) = 97.78 0.651 1572 Time to Failure = 93,540 Sec 0.731 1589 . 0.812 1600 Straln Stress 0.997 1585 —£42__. $B§11_ 1.322 1561 0.017 10 1.682 1530 0,033 39 2.287 1471 0.049 61 2.944 1374 0.084 83 3.611 1265 0,135 131 4.392 1145 0.202 192 5.31 995 0.359 294 0.737 426 241 Table A—1 (cont'd.) SAMPLE NO. 18 SAMPLE N0. 19 (cont'd.) Temperature = —6.06°C. -6 —1 0.185 182 Nom. Strain Rate = 2.14 x 10_6sec_l 0.255 306 Ave. Strain Rate = 1.87 x 10 sec 0.398 463 Sample Diameter = 1.405" 0.415 612 Initial Length = 2.81” 0.589 802 Percent Sand (by Vol.) = 63.61 0.913 996 Degree Ice Saturation (Z) = 98.23 1.197 1126 Time to Failure = 2.622 x 104 sec 1.482 1249 Strain Stress i 931 i221 (Z) (281) ' 0.003 10 0.015 32 §A¥El§11fllai§2 0.032 51 Temperature = -6.08°C _4 —1 0.055 74 Nom. Strain Rate = 1.19 x 10_ sec_l 0.070 106 Ave. Strain Rate = 8.88 x 10 sec 0.167 239 Sample Diameter = 1.405" I 0.557 522 Initial Length = 2.81" I 1.007 672 Percent Sand (by Vol.) = 63.88 1.654 900 ' Degree Ice Saturation (Z) = 98.88 2.284 1101 Time to Failure = 354 sec 3’82; 13:; ‘ - Strain ‘ Stress 3.607 1451 546%5— 3§§%l- 4.104 1517 0.091 262 4.548 1552 0.159 396 4.903 1559 0.225 559 5.522 1537 0_297 747 6-692 1446 0.472 1090 7-792 1322 0.639 1260 0-105 160 0.889 1358 0.224 326 1.161 1430 0-291 396 1.427 1477 0°379 447 1.701 1523 0.449 478 1.985 1569 ' 2.317 1614 §AME£§_EQI_12 2.779 1650 Temperature = —6.08°C _5 —1 3-144 1656 Nom. Strain Rate = 1.42 x 10_Ssec_l 3.567 1630 Ave. Strain Rate = 1.16 x 10 sec 4.209 1576 Sample Diameter = 1.405" 4.837 1487 Initial Length = 2.81" , 5~712 1358 Percent Sand (by V01.) = 63.94 6.908 1216 Degree Ice Saturation (Z) = 98.99 Time to Failure = 3456 sec Strain Stress (Z) (psi) 0.063 23 0.131 , 83 242 Table A—1 (cont'd.) SAMPLE N0. 21 SAMPLE NO. 23 (cont'd.) Temperature = -6.08°C _4 —1 0.403 524 Nom. Strain Rate = 1.19 x 10_ sec_l 0.487 794 Ave. Strain Rate = 9.59 x 10 sec 0.549 973 Sample Diameter = 1.405" 0.615 1144 Initial Length = 2.81" 0.698 1271 Percent Sand (by Vol.) = 63.80 0.798 1369 Degree Ice Saturation (Z) = 97.78 0.917 1421 Time to Failure = 335 sec 1.186 1486 Strain Stress 1°54l 1514 (7) ( Si) 1.882 1558 —-—L-- -lL-—-— 2.318 1590 0.019 70 2.756 1606 0.095 233 3.281 1594 0.168 406 3.893 1541 0.259 587 4.832 1412 0.341 772 . 6.073 1226 H 0.441 953 7 833 992 0.553 1114 ' I 0.678 1249 1,099, 1476 Temperature = —6.08°C _4 -1 1.395 1509 Nom. Strain Rate = 1.11 x 10_ sec__1 1.797 1584 Ave. Strain Rate = 9.32 x 10 sec 2.194 1629 Sample Diameter = 1.13" 2,729 1682 ’ Initial Length = 2.26" 3.212 1705 Percent Sand (by Vol.) = 63.39 3.839 1694 Degree Ice Saturation (Z) = 97.82 4.538 1638 Time to Failure = 341 sec 5'315 1546 Strain Stress 6.132 1443 (1) (psi) 7.195 1308 0.048 ‘“§§—‘ 0.078 179 SAMPLE NO. 22 0.152 322 Data Invalid - Membrane Leak 0.235 485 0.320 643 SAMPLE NO. 23 0-395 841 o 0.465 1037 Temperature = —6.08 C _4 —1 0.554 1199 Nom. Strain Rate = 1.11 x 10_43ec_l 0.661 1316 Ave. Strain Rate = 1.13 x 10 sec 0.793 1398 Sample Diameter = 1.13" 1 221 1481 Initial Length = 2.26" 1.689 1532 Percent Sand (by Vol.) = 63.54 1.835 1559 Degree Ice Saturation = 98.29 2.096 1594 Time to Failure = 243 sec 2.450 1631 Strain Stress 2°63: $223 (7.) (128i) 3-1 0.133 109 3.821 1622 0.201 194 4.696 1532 0.287 307 5.621 1419 7.002 1223 Table A—1 (cont'd.) SAMPLE NO. 25 SAMPLE N0. 26 (cont'd.) Temperature = -6.09°C _4 -1 0.369 514 Nom. Strain Rate = 1.11 x 10_ sec_l 0.416 682 Ave. Strain Rate = 8.23 x 10 sec 0.493 835 Sample Diameter = 1.13" 0.574 992 Initial Length = 2.26" 0.707 1148 Percent Sand (by Vol.) = 63.37 1.141 1260 Degree Ice Saturation (Z) = 98.14 1.472 1369 Time to Failure = 341 sec 1.822 1428 Strain Stress 2'458 1510 a . 3.146 1567 (A) (281) 3.735 1582 0.027 174 4.343 1557 0.057 303 5.310 1466 0.094 392 6.498 1317 0'134 490 7 966 1160 0.189 664 ' I 0.225 782 I 0.303 960 PAMEE§_E9;_EZ 0 0.364 1068 Temperature = -6.03°C _4 -1 0.468 1200 Nom. Strain Rate = 1.29 x 10_4sec_l 0.606 1297 Ave. Strain Rate = 1.00 x 10 sec 0.838 1353 Sample Diameter = 1.94'' 1.196 1407 Initial Length = 3.88" 1.663 1479 Percent Sand (by. Vol.) = 64.81 2.175 1589 Degree Ice Saturation (Z) = 98.75 2.807 1582 Time to Failure"= 247 sec 3'426 1558 Strain Stress 4.195 1473 . . 5 193 1341 (A) ABEEA— ' 0.034 133 6'397 1226. 0.077 260 7 880 987 0.119 406 0.155 574 §£§EE£1£EZL_§§ 0,193 752 Temperature = -6.08°C _4 _1 0.274 1028 Nom. Strain Rate = 1.11 x 10_ sec_l 0.402 1220 Ave. Strain Rate = 9.78 x 10 sec 0.570 1331 Sample Diameter = 1.13" 0.825 1411 Initial Length = 2.26" 1.118 1474 Percent Sand (by Vol.) = 63.34 1.472 1558 Degree Ice Saturation (Z) = 98.06 1.830 1624 Time to Failure = 382 sec 2.326 1682 _ 2.579 1694 Strain Stress 2.908 1678 _iél___ £2211_ 3.452 1570 0,030 101 4.011 1414 0.050 162 4.838 1134 0.082 238 5.355 946 0.117 318 0.228 456 0.304 502 244 Table A-1 (cont'd.) SAMPLE NO. 28 SAMPLE NO. 29 (cont'd.) Temperature = —6.00°C _4 —1 0,344 1311 Nom. Strain Rate = 1.29 x 10_4sec_l 0.505 1427 Ave. Strain Rate = 1.01 x 10 sec 0.726 1497 Sample Diameter = 1.94" 0.956 1544 Initial Length = 3.88" 1.299 1616 Percnet Sand (by Vol.) = 63.35 1.692 1704 Degree Ice Saturation (Z) = 98.48 2.179 1790 Time to Failure = 267 sec 2.539 1783 Strain Stress 2'990 1764 (Z) ( Si) 3.611 1671 —————— —lL—-—- 4.643 1378 0.046 93 0.068 234 5.117 1018 6.291 624 0.092 398 0.117 564 0.183 936 Temperature = —6.00°C _4 -1 0.219 1132 Nom. Strain Rate = 1.29 x 10_ sec_1 0.284 1295 Ave. Strain Rate = 1.02 x 10 sec 0.438 1473 Sample Diameter = 1.94" 0.631 1571 Initial Length = 3.88" 1.093 1653 Percent Sand (by Vol.) = 64.16 1.619 1722 Degree Ice Saturation (Z) = 99.07 2.161 1785 Time to Failure = 303 sec 2'696 1802 Strain Stress 3.382 1762 . . 4 477 1618 (A) £2911_ ' 0.031 53 5.418 1361 0 056 182 6.893 1130 0.078 322 0.105 473 W 0,131 637 Temperature = -6.05°C _4 -1 0-164 806 Nom. Strain Rate = 1.29 x 10_ sec_l 0.208 972 Ave. Strain Rate = 9.30 x 10 sec 0.265 1115 Sample Diameter = 1.94" 0.335 1227 Initial Length = 3.88" 0.461 1315 Percent Sand (by Vol.) = 64.28 0.637 1380 Degree Ice Saturation (Z) = 98.11 0.817 1426 Time to Failure — 273 sec 1.039 1464 , 1.327 1521 Strain Stress 1.684 1593 _$Zl__ SBEIL. 2.004 1654 0~027 79 2.438 1713 0-043 147 2.915 1743 0-079 283 3.088 1751 0°145 325 3.527 1727 0.142 601 4.071 1668 0.168 792 4.615 1519 0.201 989 5.599 1301 0.266 1166 Table Arl (cont'd.) SAMPLE NO. 31 SAMPLE NO. 32 (cont'd.) Temperature = —6.05°C _4 —1 0.216 1188 Nom. Strain Rate = 1.29 x 10_ sec_l 0.309 1374 Ave. Strain Rate = 9.39 x 10 sec 0.483 1494 Sample Diameter = 1.94” 0.663 1531 Initial Length = 3.88" 0.895 1567 Percent Sand (by Vol.) = 63.44 1.162 1602 Degree Ice Saturation (Z) = 98.38 1.505 1652 Time to Failure = 282 sec 1.928 1706 Strain Stress 2’391 1736 . . 2.849 1738 A 95;)— 3 389 1691 0.003 96 ' O 009 274 3.810 1591 4.717 1447 0.016 426 6 079 1230 0.033 649 ' 0.053 860 0, 082 1069 W 0.180 1319 Temperature = —6.08°C _4 _1 0.270 1425 Nom. Strain Rate = 1.29 x 10_ sec_l 70.382 1496 Ave. Strain Rate = 9.67 x 10 sec 0.636 1554 Sample Diameter = 1.94" 0.970 1610 Initial Length = 3.88" 1.441 1686 Percent Sand (by Vol.) = 63.38 2.075 1758 Degree Ice Saturation (Z) = 98.53 2.649 1775 Time to Failure = 268 sec 2.586 1598 Strain Stress 5.339 1352 02/330 L 3(1)) 6.761 1121 0.033 234 8.243 787 0.054 398 0.073 567 §AEEEEL1511_§E 0,091 748 Temperature = -6.02°C _4 —1 0.117 939 Nom. Strain Rate = 1.29 x 10_4sec_l 0.155 1122 Ave. Strain Rate = 1.04 x 10 sec 0.223 1324 Sample Diameter = 1.94" 0-330 1452 Initial Length = 3.88" 0-540 1539 Percent Sand (by Vol.) = 63.38 0.984 1610 Degree Ice Saturation (Z) = 98.53 1.492 1696 Time to Failure = 275 sec 1.895 1750 2.298 1776 Strain Stress 2.592 1788 (Z) (PS—i) 3.224 1749 0.014 56 4.276 1567 0.027 149 4.741 1366 0°046 245 5.671 1150 0.072 412 6.661 917 0.097 579 7.449 732 0.133 821 0.224 935 Table A—1 (cont'd.) SAMPLE NO. 34 Temperature = -6.08°C Nom. Strain Rate - 1.11 x 10_4sec- Ave. Strain Rate = 8.63 x 10_ sec Sample Diameter = 1.13" Initial Length = 2.26" Percent Sand (by Vol.) = 63.42 Degree Ice Saturation (Z) = 98.04 Time to Failure = 379 sec SAMPLE N0. 0.076 0.121 0.169 0.255 0.368 0.506 0.707 0.907 1.113 1.482 2.181 2.682 3.191 3.836 5.256 6.757 8.018 36 (cont'd.) 586 741 868 1054 1186 1278 1360 1411 1463 1534 1645 1700 1711 1670 1514 1296 1128 37 SAMPLE NO. Strain Stress (Z) (psi) 0.009 87 0.013 173 0.039 296 0.066 421 0.095 553 0.121 684 0.150 758 0.208 917 0.308 1074 0.451 1191 0.703 1296 1.196 1466 1.845 1637 2.707 1762 3.272 1780 4.000 1729 4.699 1646 5.748 1487 6.986 1315 SAMPLE NO. 35 Data Invalid — Membrane Leak SAMPLE NO. 36 Temperature = —6.08°C _4 _ Nom. Strain Rate = 1.11 x 10_ sec Ave. Strain Rate = 8.62 x 10 sec Sample Diameter = 1.13" Initial Length = 2.26" Percent Sand (by Vol.) = 64.51 Degree Ice Saturation (Z) = 98.60 Time to Failure = 331 sec Temperature = —6.06°C —4 —1 Nom. Strain Rate — 1.11 x 10_ sec_l Ave. Strain Rate = 9.12 x 10 sec Sample Diameter = 1.13" Initial Length = 2.26" Percent Sand (by Vol.) = 63.62 Degree Ice Saturation (Z) = 98.27 Time to Failure = 350 sec Strain Stress (Z) (psi) 0.001 46 0.001 113 0.021 266 0.046 431 Strain Stress (Z) (psi) 0.003 64 0.010 137 0.015 218 0.032 343 0.058 468 0.088 599 0.123 728 0.145 817 0.179 867 0.208 946 0.279 1079 0.409 1221 0.603 1312 0.904 1406 1.785 1609 2.358 1691 2.852 1721 3.805 1647 5.129 1446 6.425 1202 8.172 916 247 Table A—1 (cont'd.) SAMPLE NO. 38 SAMPLE NO. 39 (cont'd.) Temperature = -6.05°C _4 -1 0.549 1273 Nom. Strain Rate = 1.11 x 10_Ssec_l 0.828 1383 Ave. Strain Rate = 8.66 x 10 sec 1.313 1508 Sample Diameter = 1.13" 1.848 1622 Initial Length = 2.26" 2.369 1701 Percent Sand (by Vol.) = 63.83 2.907 1745 Degree Ice Saturation (Z) = 98.36 3.819 1704 Time to Failure = 345 sec 5.016 1556 Strain Stress 6'026 1339 (Z) ( si) 7.484 1125 0:025_ _P03_— 8.765 851 0.041 262 0.069 405 W 0.122 620 Temperature = -6.03°C 0.158 765 Nom. Strain Rate = 1.11 x 10 sec 0.205 876 Ave. Strain Rate = 8.88 x 10 sec 0.259 1004 Sample Diameter = 1.13" 0.361 1147 Initial Length = 2.26" 0.612 1317 Percent Sand (by Vol.) = 63.92 0.902 1416 Degree Ice Saturation (Z) = 99.15 1.302 1528 Time to Failure = 354 sec % 329 1:25 Strain Stress 2.986 1757 ‘ L 1&' ° 0.035 143 3.715 1701, . 0.084 268 4.879 1544 0.142 408 6.000 1362 0.167 541 7.096 1212 0.225 683 8.615 1034 0.285 814 0.351 910 W 0.455 1052 Temperature = —6.08°C _4 —1 0-677 1188 Nom. Strain Rate = 1.11 x 10_ sec__l 1.003 1327 Ave. Strain Rate = 8.43 x 10 sec 1.523 1481 Sample Diameter = 1.13" 2~236 1664 Initial Length = 2.26" 3.145 1778 Percent Sand (by Vol.) = 63.45 4.134 1693 Degree Ice Saturation (Z) = 98.04 5.376 1493 Time to Failure = 345 sec 6.579 1247 . 7.807 1007 Strain Stress 8.862 827 (Z) (psi) 0.021 181 ’ 0.045 322 0.071 447 0.110 575 0.153 712 0.253 956 0.347 1118 248 Table A—1 (cont'd.) SAMPLE NO. 41 SAMPLE N0. 42 (cont'd.) Temperature = —6.06°C _4 -1 1.122 .1476 Nom. Strain Rate = 1.19 x 10_ sec_l 1.602 1576 Ave. Strain Rate = 9.42 x 10 sec 2.209 1659 Sample Diameter = 1.405" 2.886 1698 Initial Length = 2.81" 3.667 1653 Percent Sand (by Vol.) = 63.81 4.513 1535 Degree Ice Saturation (Z) = 99.71 5.385 1436 Time to Failure = 347 sec 6.213 1237 Strain Stress 7'226 1064 (Z) (psi) 0.012 154 W 0.040 299 Temperature = -6.06°C _4 -1 0.075 448 Nom. Strain Rate = 1.19 x 10_ sec_l 0.125 598 Ave. Strain Rate = 9.13 x 10 sec 0.167 748 Sample Diameter = 1.405" 0.203 856 Initial Length = 2.81" 0.344 1031 Percent Sand (by Vol.) = 63.68 0.385 1193 Degree Ice Saturation (Z) = 98.19 0.522 1299 . Time to Failure = 335 sec 3 1:: i232 Strain Stress 1.845 1647 (Z) L Si) ' 0.018 129 2.627 1758 0.051 270 3.279 1778 0.083 412 4.347 1672 0.125 566 5.470 1501 0.167 719 6.693 1291 0.214 863 7.686 1123 0.239 936 0.328 1139 ____SAMPLE N0. 42 0.443 1301 Temperature = —6.10°C _4 -1 0.579 1419 Nom. Strain Rate = 1.19 x 10_Ssec_l 1.056 1533 Ave. Strain Rate = 9.02 x 10 sec 1.597 1619 Sample Diameter = 1.405" 2-151 1673 Initial Length = 2.81" 3.059 1732 Percent Sand (by Vol.) = 63.93 4.071 1640 Degree Ice Saturation (Z) = 97.32 5.256 1419 Time to Failure = 320 sec 6.636 1148 Strain Stress (Z) (psi) 0.019 122 0.047 268 0.087 412 0.125 566 0.172 713 0.218 856 0.341 1117 0.498 1284 0.696 1380 Table A-1 (cont'd.) W SAMPLE NO. 45 (cont'd.) Temperature = —6.06°C ‘_4 -1 0.209 1198 9,4 Nom. Strain Rate = 1.19 x 10_ sec__l 0.288 1449 11.4 Ave. Strain Rate = 9.59 x 10 sec 0.337 1570 12.4 Sample Diameter = 1.405" 0.387 1659 13.4 Initial Length = 2.81" 0.453 1734 14.4 Percent Sand (by Vol.) = 63.54 0.527 1771 15.4 Degree Ice Saturation (Z) = 97.03 0.623 1781 16.4 Time to Failure = 343 sec 0.809 1747 18-4 Strain Stress Time 1'353 1629 23°4 (Z) ( Si) (sec) 2.096 1511 21.: _0.006 _P__105 __8 3.278 1313 3. 0.035 246 18 4.658 1111 55-4 6.386 899 73~4 0.075 386 28 0.125 536 38 0.169 668 48 w 0.253 878 63 Temperature = —6.09°C 4 1 0.343 1076 78 Nom. Strain Rate = 1.04 x 10' sec— 0.419 1189 88 Ave. Strain Rate = 8.62 x 10‘ sec—1 0.503 1274 93 Sample Diameter = 2.40" 0.703 1354 118 Initial Length = 4.80" 1.035 1419 148 Percent Sand (by Vol.) = 64.33 1.490 1495 188 Degree Ice Saturation (Z) = 98.15 2.049 1587 238 Time to Failure = 368 sec 2'639 1652 288 Strain Stress 3.290 1678 343_ . (7) ( si) 3.957 1648 393 0 501 16—6— 4.717 1549 453 0'027 177 5.476 1453 513 0'040 294 6.615 1316 603 0‘056 416 7.941 1173 703 0:078 557 0.105 696 w 0.133 845 Temperature = —6.09°C 1 0-175 981 .229 1100 .299 1195 .389 1263 552 1324 .813 1403 285 1501 Nom. Strain Rate = 8.90 x 10:4sec_l Ave. Strain Rate = 3.80 x 10 sec Sample Diameter = 1.405" IMthlegfl1=2£F' Percent Sand (by Vol.) = 64.07 Degree Ice Saturation (Z) = 97.43 \IO‘U’l-J-‘UJUJNI-‘l-‘OOOOO 00 O \J Time to Failure = 16.4 sec 1610 . . 552 1721 Strain Stress Time .170 1754 ———“> L 51) ——(Se°) .658 1733 0.019 157 1.4 483 1623 0.035 275 2 4 249 1497 0.055 400 3 4 .225 1339 0.077 531 4.4 .243 1182 0.096 659 5.4 ' 0.120 800 6 4 0.147 927 7 4 Table A—1 (cont'd.) SAMPLE NO. 47 SAMPLE N0. 48 (cont'd.) Temperature = -6.06°C _4 -1 0.054 280 Nom. Strain Rate = 1.04 x 10_4sec_l 0.071 398 Ave. Strain Rate = 8.71 x 10 sec 0.089 532 Sample Diameter = 2.40" 0.121 756 Initial Length = 4.80" 0.157 895 Percent Sand (by Vol.) = 63.91 0.199 1030 Degree Ice Saturation (Z) = 98.13 0.257 1142 Time to Failure = 354 sec 0.325 1247 Strain Stress 0'424 1316 (Z) ( si) 0.602 1414 -lL———- 0.959 1481 0.008 50 1.374 1541 0.010 114 1 961 1636 0.018 183 ' 2.560 1697 0.024 254 3 035 1708 0.032 329 ° 0 046 443 3.443 1725 ' 3.880 1661 0.062 577 4.829 1569 0'093 756 6 109 1410 8.161 1333 7:990 1223 0.206 1126 0.287 1256 W 0.362 1326 Temperature = -6.03°C _4 -1 0.497 1434 Nom. Strain Rate = 1.04 x 10_5sec_l 0.724 1483 Ave. Strain Rate = 9.24 x 10 sec 0.957 1519 Sample Diameter = 2.40" 1.209 1561 Initial Length = 4.80" 1.518 1595 Percent Sand (by Vol.) = 63.99 1,944 1653 Degree Ice Saturation (Z) = 98.36 2.513 1709 Time to Failure = 361 sec 3‘33: 1:3; Strain Stress ' (Z) (psi) 4.281 1639 0.018 42 5.906 1487 0.033 161 7.787 1298 0.055 282 0.083 407 W 0,119 548 Temperature = —6.09°C _2 —1 0-184 756 Nom. Strain Rate = 1.04 x 10_53ec_l 0.239 892 Ave. Strain Rate = 8.72 x 10 sec 0.305 1014 Sample Diameter = 2.40" 0.381 1119 Initial Length = 4.80" 0.515 1243 Percent Sand (by Vol.) = 63.98 0.661 1324 Degree Ice Saturation (Z) = 97.57 0.872 1374 Time to Failure = 395 sec 1.124 1446 1.382 1488 Strain Stress 1.653 1523 _£ZI__ IP§11_ 1.996 1570 0°019 76 2.384 1609 0.034 176 251 Table A—1 (cont'd.) SAMPLE N0. 49 Ccont'd.) SAMPLE NO. 51 (cont'd.) 2.856 1633 Strain Stress 3.337 1656 (Z) (psi) 3.612 1621 0.004 50 4.641 1490 0.008 105 6.617 1310 0.014 170 7.697 1135 0.028 243 0.037 322 SAMPLE N0. 50 0.039 402 Temperature = —6.00°C 4 1 0'058 490 Nom. Strain Rate = 1.04 x 10_ sec- O°O6l 580 . —5 —1 0.076 668 Ave. Strain Rate = 8.95 x 10 sec 0 105 797 Sample Diameter = 2.40" 0'132 929 Initial Length = 4.80" 0'173 1041 Percent Sand (by Vol.) = 63.86 0 226 1157 Degree Ice Saturation (Z) = 98.66 0°279 1259 Time to Failure = 335 sec 0:349 1331 Strain Stress 0.418 1410 (Z) (psi) 0.588 1457 0.019 80 0.748 1497 0.042 184 1.041 1559 0.069 297 ' 1.372 1593 0.099 428 1.592 1669 0.130 571 2.452 1724 0.169 713 3.095 1724 0.217 849 3.847 1661 0,305 1034 4.182 1611 0.421 1185 5.053 1553 0.560 1286 8.171 1434 0.713 1347 0.903 1410 §AMPLE_§QL_52 1'106 1453 Temperature = —5.99°C _ —1 1'479 1520 Nom. Strain Rate = 1.29 x 10 4sec 1 1°936 1584 Ave. Strain Rate = 1.02 x 10_ sec— 2’472 1640 Sample Diameter = 1.94" 2'998 1662 Initial Length = 3.88" 3'570 1615 Percent Sand (by Vol.) = 64.23 4'680 1502 Degree Ice Saturation (Z) = 98.27 6'296 1321 Time to Failure = 315 sec 7.542 1199 Strain Stress SAMPLE NO. 51 (Z) 331)— "‘__——_“——___ o 0.065 42 Temperature = —6.05 C _4 -1 0_104 132 Nom. Strain Rate = 1.04 x 10_Ssec_l 0.142 241 Ave. Strain Rate = 8.74 x 10 sec 0.184 370 Sample Diameter = 2.40" 0.228 512 Initial Length = 4.80" 0.275 674 Percent Sand (by Vol.) = 64.05 0.364 929 Degree Ice Saturation (Z) = 98.42 0.502 1127 Time to Failure = 354 sec 252 Table A—1 (cont'd.) SAMPLE N0. 52 (cont'd.) SAMPLE N0. 54 0.711 1291 Temperature = -6.06°C _4 _1 1.047 1367 Nom. Strain Rate = 1.29 x 10_4sec_l 1.465 1461 Ave. Strain Rate = 1.04 x 10 sec 1.978 1559 Sample Diameter = 1.94" 2.416 1650 Initial Length = 3.88" ~2.881 1677 Percent Sand (by Vol.) = 64.27 3.218 1677 Degree Ice Saturation (Z) = 96.11 3.754 1592 Time to Failure = 296 sec 2:83i 1255 Strain Stress (A) (281) 0.035 132 mm 0.062 274 Temperature = —6.03°C _4 —1 0.098 431 Nom. Strain Rate = 1.29 x 10_ sec_l 0.133 601 Ave. Strain Rate = 1.04 x 10 sec 0.174 789 Sample Diameter = 1.94" 0.229 973 Initial Length = 3.88" 0.296 1140 Percent Sand (by Vol.) = 64.31 0.386 1275 Degree Ice Saturation (Z) = 98.33 0.490 1375 Time to Failure = 270 sec . 0.617 1439 . 0.731 1478 Strain Stress 0.857 1511 —$41—— ififiil— 1.041 1554 °°034 127 - 1.280 1590 0'061 277 1.526 1626 0'096 437 1.769 1671 0'140 578 2.020 1707 0°176 794 2.283 1738 0'236 978 2.696 1755 0.305 1145 3.088 1753 0.398 1280 3.641 1709 0.516 1369 4.264 1610 0.787 1452 5.838 1134 0.908 1475 1'139 1517 SAMPLE NO. 55 1.445 1557 ‘—___"—_’—"‘ 1.878 1620 Temperature = —6.16°C _4 _1 2.335 1652 Nom. Strain Rate = 1.04 x 10_ sec_l 2.817 1664 Ave. Strain Rate = 1.08 x 10 sec 3.286 1631 Sample Diameter = 1.94" 3.835 1554 Initial Length = 3.88" 4.543 1397 Percent Sand (by V01.) = 64.29 4.894 1218 Degree Ice Saturation (Z) = 99.41 5.605 1012 Time to Failure = 333 sec Strain Stress (Z) (Psi) 0.049 101 0.082 195 0.119 342 253 Table A—1 (cont'd.) SAMPLE N0. 55 (cont'd.) SAMPLE NO. 56 (cont'd.) 0.159 512 4.230 1766 0.212 697 4.429 1689 0.308 954 5.147 1542 0.433 1160 6.002 1306 0.593 1291 6.804 1068 0.779 1362 0.959 1414 SAMPLE NO. 57 1'142 1460 Temperature = -10.05°C 1.325 1501 . -3 —1 Nom. Strain Rate = 1.78 x 10 sec 1.561 1552 . — —1 Ave. Strain Rate = 7.20 x 10 sec 1.879 1619 . n Sample Diameter = 1.405 1.898 1692 . . n Initial Length = 2.81 2.776 1759 _ Percent Sand (by Vol.) — 64.03 3.226 1789 . o _ Degree Ice Saturation (A) - 97.41 3'601 1796 Time to Failure = 9.9 sec 4.129 1744 4.756 1633 Strain Stress 4.983 1460 (Z) (281) 5.998 1142 0.003 66 7.023 797 0.021 207 0.056 448 SAMPLE NO. 56 ’ 0.086 611 o 0.141 883 Temperature = -6.16 C _4 -1 0.203 1185 Nom. Strain Rate = 1.04 x 10 sec . — —1 0.264 1495 Ave. Strain Rate = 1.10 x 10 sec 0.336 1800 Sample Diameter = 1.94" 0.422 2092 Initial Length = 3.88" 0.514 2325 Percent Sand (by Vol.) = 63.96 0 645 2456 Degree Ice Saturation (Z) = 98.04 0'713 2480 Time to Failure = 331 sec 0:849 2400 Strain Stress 1.139 2064 (Z) (psi) 1.618 1600 0.090 130 2.041 1418 0.115 243 2.449 1287 0.149 403 2.873 1182 0.200 586 3.671 999 0.288 853 4.633 855 0.364 1016 6-035 710 0 403 1085 7 622 592 0.450 1147 0.555 1252 0.676 1329 1.138 1451 1.451 1514 1.799 1592 2.155 1669 2.775 1762 3.290 1802 3.641 1798 254 Table A—1 (cont'd.) SAMPLE N0. 58 SAMPLE N0. 59 (cont'd.) Temperature = -10.05°C _4 —1 0.091 569 Nom. Strain Rate = 5.93 x 10_ sec_l 0.124 735 Ave. Strain Rate = 2.52 x 10 sec 0.168 904 Sample Diameter = 1.405" 0.211 1077 Initial Length = 2.81" 0.266 1252 Percent Sand (by Vol.) = 64.12 0.359 1474 Degree Ice Saturation (Z) = 96.69 0.430 1607 Time to Failure = 28.8 sec 0.511 1714 Strain Stress 0'603 1795 a . 0.856 1892 (4) (281) 1.137 1918 0.004 57 1.603 1959 0.011 224 2.054 2019 0.037 388 2.516 2060 0.056 544 2.945 2063 0.094 701 3.381 2011 0.131 870 4.116 1879 0.175 1071 4.894 1626 0.219 1265 5.688 1401 0.269 1475 6 592 1196 0.360 1659 ' 0.384 1837 0.539 2114 Temperature = —10.05°C _5 -1 0.627 2195 Nom. Strain Rate = 2.37 x 10_55ec_l 0.727 2231 Ave. Strain Rate = 2.15 x 10 sec 0.914 2202 Sample Diameter = 1.405" 1.117 2089 Initial Length = 2.81" 1.371 1952 Percent Sand (by V01.) = 63.56 1.830 1779 Degree Ice Saturation (Z) = 97.06 2.586 1553 Time to Failure = 1914 sec 2'33: 13:; Strain Stress - 2 (psi) 6.724 741 —(—)—- 0.010 43 SAMPLE NO. 59 0-024 114 _—_"—______‘_ o 0.029 196 Temperature = —10.05 C -1 050 277 Nom. Strain Rate = 1.19 x 10_45ec_l Ave. Strain Rate = 9.06 x 10 sec Sample Diameter = 1.405" Initial Length = 2.81" Percent Sand (by Vol.) = 64.17 075 349 102 440 132 537 179 652 253 820 F‘F‘P‘C>C>O c>c>c>c>o o c 05 .D a) Degree Ice Satruation (Z) = 97.39 992 Time to Failure = 324 sec 452 1128 Strain Stress 209 1537 (Z) (psi) 0.006 112 199 1518 0.022 259 613 1638 0.049 413 974 1751 255 Table A-1 (cont'd.) SAMPLE NO. 60 (cont'd.) SAMPLE NO. 62 (cont'd.) 2.325 1864 Percent Sand (by Vol.) = 64.18 2.784 2004 Degree Ice Saturation (Z) = 97.05 3.147 2090 Time to Failure = 37,920 sec 3.764 2163 . 4.113 2210 Strain Stress 4.244 2213 (4) m 0.008 60 4.786 2210 0.019 95 5.183 2167 0.031 154 5.582 2116 0.041 197 6.019 2052 0.062 240 6.517 1951 6.993 1882 0'083 284 0.105 325 0.126 366 Temperature = -10.05°C -6 —1 0.180 442 Nom. Strain Rate = 4.75 x 10_6sec_l 0.329 581 Ave. Strain Rate = 4.35 x 10 sec 0.613 710 Sample Diameter = 1.405" 1.425 1016 Initial Length = 2.81" 2.531 1466 Percent Sand (by Vol.) = 64.18 3.898 1828 Degree Ice Saturation (Z) = 97.40 4.843 1894 Time to Failure = 12,204 sec 6.261 1759 . 7.769 1500 Strain Stress (Z) (psi) 0.007 44 SAMPLE NO. 63 0.013 109 Temperature = —10.00°C _7 —1 0.029 172 Nom. Strain Rate = 5.69 x 10_7sec__l 0.048 233 Ave. Strain Rate = 4.82 x 10 sec 0.071 292 Sample Diameter = 1.405" 0.109 380 Initial Length = 2.81" 0.132 441 Percent Sand (by Vol.) = 63.60 0.161 .480 Degree Ice Saturation (Z) = 96.96 0.188 505 Time to Failure = 91,680 sec 0'239 584 Strain Stress 0.404 740 (Z) (psi) 0.722 900 0.016 ——I§__ 2.709 1688 0.049 93 5.313 2177 0_099 174 6.771 2012 0.129 214 7.897 1817 0.169 281 0.223 336 §éyP£§_§9;_9§ 0,379 440 Temperature = ~10.05°C —6 -1 0.616 531 Nom. Strain Rate = 1.42 x 10_6sec_l 0.992 672 Ave. Strain Rate = 1.28 x 10 sec 1.489 870 Sample Diameter = 1.405" 2.259 1151 Initial Length = 2.81” 3-144 1414 256 Table A—1 (cont'd.) SAMPLE NO. 63 (cont'd.) SAMPLE NO. 65 (cont'd.) 4.419 1542 0.149 652 5.136 1488 0.178 722 0.216 792 SAMPLE NO. 64 0.378 1014 Temperature = —10.05°C —6 —1 8'32: 1351 Nom. Strain Rate = 2.14 x 10_6 sec_l 1°795 1685 Ave. Strain Rate = 1.84 x 10 sec ' . _ H 2.966 2051 Sample Diameter — 1.405 Initial Length = 2 81" 4'275 2188 ' 6.044 2004 Percent Sand (by Vol.) = 64.10 Degree Ice Saturation (Z) = 98.90 Time to Failure = 25,680 sec §AEELELEQL—§é . Temperature = -10.09°C _ _ 52;?1n it:::s Nom. Strain Rate = 5.34 x 10_Ssec_i ° -lL~——— Ave. Strain Rate = 4.18 x 10 sec 0-007 36 Sample Diameter = 1.405" 0'013 116 Initial Length = 2.81" 0'027 188 P d b V 1 ) = 63 28 0.052 259 ercent San ( y o . a . 0.190 294 Degree Ice Saturation (Z) = 99.43 0.202 358 Time to Failure — 322 sec 0.251 415 Strain Stress 0.283 466 (Z) (psi) 0.334 504 ' 0.003 36 0.439 574 0.013 138 0.705 699 0.025 236 1.275 942 0.047 338 2.361 1400 0.068 442 3.674 1832 0.123 649 4.728 1916 0.179 873 6.151 1743 0.255 1092 7.449 1517 0.343 1296 0.564 1547 SAMPLE NO. 65 0.845 1669 o 1.396 1819 Temperature = —10.00 C _ -1 2.349 2044 Nom. Strain Rate = 1.07 x 10_6sec_l 3.437 2170 Ave. Strain Rate = 8.77 x 10 sec 5.222 2003 Sample Diameter = 1.405" 7 244 1663 Initial Length = 2.81" Percent Sand (by V01.) = 64.10 Degree Ice Saturation = 98.06 Time to Failure = 4872 sec Strain Stress (Z) (psi) 0.001 92 0.006 174 0.018 260 0.031 339 0.076 506 257 Table A—1 (cont'd.) SAMPLE NO. 67 SAMPLE N0. 68 (cont'd.) Temperature = —10.06°C _4 -1 0.309 1902 Nom. Strain Rate = 2.67 x 10_4sec_l 0.379 2169 Ave. Strain Rate = 1.30 x 10 sec 0.479 2403 Sample Diameter = 1.405" 0.655 2500 Initial Length = 2.81" 1.063 2173 Percent Sand (by Vol.) = 63.08 1.553 1753 Degree Ice Saturation (Z) = 99.30 2.435 ' 1406 Time to Failure = 67.40 sec SAMPLE NO. 69 Strain Stress (Z) (psi) Temperature = —15.00°C _3 -1 0.003 63 Nom. Strain Rate = 1.34 x 10_4sec_l 0.014 137 Ave. Strain Rate = 4.75 x 10 sec 0.020 214 Sample Diameter = 1.405" 0.033 292 Initial Length = 2.81" 0.047 369 Percent Sand (by Vol.) = 63.57 0.064 447 Degree Ice Saturation (Z) = 98.96 0.097 481 Time to Failure = 13.60 sec 0'116 675 Strain Stress 0.141 783 a . (A) (231) 0.196 987 -———-- 0.003 68 0.251 1188 0.004 190 0.378 1569 0.015 324 0.452 1740 0.023 415 0.614 1947 ' 0.059 682 0.873 2038 0.086 870 1.777 1906 0_112 1062 4.096 1277 .146 1253 .189 1489 SAMPLE N0. 68 .266 1897 0 0 0 Temperature = —10.00°C 1 0.355 2316 0 0 1 Nom. Strain Rate = 1.34 x 10:3sec:l .468 2626 Ave. Strain Rate = 5.04 x 10 sec .646 2863 Sample Diameter = 1.405” .008 2384 Initial Length = 2.81" 1.512 1703 Percent Sand (by V01.) = 64.00 2.011 1355 Degree Ice Saturation (Z) = 96.99 3.237 954 Time to Failure = 13 sec SAMPLE NO. 70 Strain Stress '_—‘“*——"-—‘ Z psi Temperature = —15.00°C _ _ 0f0i9 ( 61) Non. Strain Rate = 5.93 x 10_:sec_i 0.028 175 Ave. Strain Rate = 1.95 x 10 sec 0.036 306 Sample Diameter = 1.405" 0.053 442 Initial Length = 2.81" 0.068 570 Percent Sand (by Vol.) = 64.45 0.085 717 Degree Ice Saturation (Z) = 98.39 0.102 860 Time to Failure = 23 sec 0.163 1202 0.231 1584 258 Table A—1 (cont'd.) SAMPLE N0. 70 (cont'd.) SAMPLE N0. 71 (cont'd.) Stfain Stress 0,339 1838 (4) (281) 0.422 2060 0.021 73 0.565 2343 0.029 163 0.765 2453 0.037 259 1.439 2083 0.044 364 2.820 1779 0.053 474 0.064 576 SAMPLE NO. 72 0.073 691 _ o 0.085 809 gemperature — —15;00 C _5 -1 0.095 921 om. Strain Rate — 7.12 x 10_Ssec_l 0.107 1039 Ave. Strain Rate = 5.32 x 10 sec 0.119 1158 Sample Diameter = 1.405" 50.139 1279 Initial Length : 2.81" 0.152 1394 Percent Sand (by Vol.) = 64.70 0.187 1636 Degree Ice Saturation (Z) = 97.00 0 230 1878 Time to Failure = 549 sec 0.272 2101 Strain Stress 0.321 2317 (Z) ( Si) P 0.383 2494 0.004 64 0.545 2700 0.011 163 1.047 2180 0.018 266 2.291 1514 0.038 374 0.049 484 SAMPLE N0. 71 0.071 ”582 Temperature = -15.00°C 0.076 633 , —4 —1 0.088 694 Nom. Strain Rate = 2.67 x 10 sec . —4 -1 0.112 803 Ave. Strain Rate = 1.14 x 10 sec 0 128 860 Sample Diameter = 1.405" 0.152 975 Initial Length = 2.81" ' 0.176 1093 Percent Sand (by Vol.) = 64.80 . . 0.224 1259 Degree Ice Saturation (Z) = 97.66 0 329 1545 Time to Failure = 67 sec 0.458 1745 Strain Stress 0.733 1990 (Z) (psi) 1.437 2102 0.005 53 2.248 2266 0.008 126 2.920 2350 0.013 205 4.295 2102 0.019 289 6.599 1435 0.031 374 0.036 458 SAMPLE NO. 73 8'82: 2:: Temperature = —15.00°C _5 —1 ' Nom. Strain Rate = 5.34 x 10_ sec_l 0'082 713 Ave. Strain Rate = 4.02 X 10 sec 0‘098 800 Sample Diameter = 1.405" 0'123 937 Initial Length = 2.81" 0‘171 1169 Percent Sand (by Vol.) = 63.81 0'224 1386 De ree Ice Saturation (Z) = 97.22 0 276 1616 g ' Time to Failure = 789 sec 259 Table A—1 (cont'd.) SAMPLE NO. 73 (cont'd.) SAMPLE NO. 74 (cont'd.) Strain Stress 2.772 2422 (Z) (psi) 3.703 2522 0.005 81 4.803 2378 0.012 152 6.149 2055 0.017 233 ‘ 0.027 315 SAMPLE NO. 75 0.036 402 o 0.045 485 Temperature = -15.00 C _5 —1 0.068 608 Nom. Strain Rate = 2.38 x 10_Ssec_l Ave. Strain Rate 1.79 x 10 sec 8:25; £39 Sample Diameter = 1.405" 0.142 994 Initial Length = 2.81" O 197 1198 Percent Sand (by Vol.) = 64.20 0.271 1424 Degree Ice Saturation (Z) = 97.22 0.381 1646 Time to Failure = 1971 sec 0.483 1791 Strain Stress 0.745 1951 (Z) (psi) 1.446 2108 0.008 95 2.201 2273 0.018 200 3.171 2362 0.031 310 4.338 2205 0.046 422 6.096 1732 0.057 529 0.089 707 SAMPLE NO. 74 . 0.127 873 Temperature = -14.98°C _5 -1 8.5:: :22: Nom. Strain Rate = 3.56 x 10_ sec_l 0:307 1411 Ave. Strain Rate = 2.86 x 10 sec 0.426 1575 Sample Diameter = 1.405" 0.559 1681 Initial Length = 2.81" 0.880 1847 Percent Sand (by Vol.) = 64.18 1 352 2028 Degree Ice Saturation (Z) = 97.88 1.881 2218 Time to Failure = 1297 sec 2.393 2388 Strain Stress 3~004 2503 (Z) (psi) 3.530 2558 0P002_' _.73T__ 4.249 2477 0,003 132 5.094 2285 0.013 210 ‘ 5.907 2049 0.015 292 7.267 1781 0.028 374 0.040 458 0.052 543 0.073 659 1 0.097 771 0.122 882 0.150 994 0.179 1093 0.407 1550 0.963 1877 1.786 2151 260 Table A-1 (cont'd.) SAMPLE N0. 76 SAMPLE NO. 77 (cont'd.) Temperature = —15.00°C _5 _1 0.459 880 Nom. Strain Rate = 1.42 x 10_ sec_1 0.741 1030 Ave. Strain Rate = 1.15 x 10 sec 1.239 1240 Sample Diameter = 1.405" 2.003 1581 Initial Length = 2.81" 2.428 1781 Percent Sand (by Vol.) = 63.96 2.838 1948 Degree Ice Saturation (Z) = 98.51 3.485 2151 Time to Failure = 3345 sec 4.088 2266 Strain Stress 4'607 2297 a . 5.038 2280 -$42——- $2§$l—- 5 589 2207 0.004 64 ° 6.162 2103 0'005 147 6 872 1950 0.013 242 ' 0.024 337 0.036 433 mm 0.055 526 Temperature = -15.00°C _5 -1 0.070 617 Nom. Strain Rate = 1.07 x 10_ sec_l 0.094 707 Ave. Strain Rate = 8.53 x 10 sec 0.121 796 Sample Diameter = 1.405" 0.148 882 Initial Length = 2.81" 0.263 1175 Percent Sand (by V01.) = 64.02 0.758 1582 Degree Ice Saturation (Z) = 96.16 1.7635 1950 ‘ Time to Failure = 4452 sec 5.39: 322% Strain Stress ' (2) (Esi) 4.479 2428 0.013 336 5.164 2326 0.032 429 i 0.052 518 1 SAMPLE NO. 77 0 071 614 1 Temperature = —14.98°C -6 —1 0-093 707 Nom. Strain Rate = 2.14 x 10_6sec_l 0.149 873 Ave. Strain Rate = 1.82 x 10 sec 0.209 1029 Sample Diameter = 1.405" 0-283 1172 Initial Length = 2.81” . 0.411 1320 Percent Sand (by Vol.) = 64.26 0.556 1427 Degree Ice Saturation (Z) = 98.98 0.818 1549 Time to Failure = 25,260 sec 1.260 1701 1.645 1845 Strain Stress 2.209 2048 (2) (psi) 2.733 2199 0-001 83 3.318 2303 0-009 173 3.799 2341 0.022 263 4.324 2322 0-042 349 ' 5 256 2184 0-062 433 6.156 2001 0-090 513 7.567 1769 0.142 550 0.189 620 0.295 683 0.356 798 Table A—1 (cont'd.) SAMPLE NO. 79 Temperature = —15.00°C —6 1 Nom. Strain Rate 1.42 x 10_6sec:l Ave. Strain Rate = 1.21 x 10 sec Sample Diameter = 1.405" Initial Length = 2.81" Percent Sand (by Vol.) = 64.25 Degree Ice Saturation (Z) = 98.98 Time to Failure - 34,080 sec Strain Stress (Z) (Psi) 0.002 207 0.027 311 0.053 417 0.082 517 0.106 565 0.336 811 0.403 874 0.505 962 0.628 1031 0.770 1099 1.015 1242 1.384 1439 1.810 1635 2.272 1833 2.775 2005 3.321 2124 3.781 2181 4.115 2198 4.697 2173 5.383 2060 6.322 1872 7.488 1659 SAMPLE N0. 80 Temperature = —14.98°C ' _7 —1 Nom. Strain Rate = 5.69 x 10_ sec_l Ave. Strain Rate = 4.83 x 10 sec Sample Diameter = 1.405" Initial Length = 2.81" Percent Sand (by Vol.) = 64.85 Degree Ice Saturation (Z) = 97.37 Time to Failure = 90,900 sec Strain Stress (Z) (psi) 0.003 68 0.004 96 0.009 151 0.053 192 0.066 237 SAMPLE N0. 80 (cont'd.) 0.071 0.073 0.104 0.157 0.222 0.483 0.858 1.335 1.829 2.308 2.839 3.382 3.856 .394 .848 .437 .067 .699 .540 \IO\O\UIJ-\4-\ 275 333 390 499 588 752 908 1144 1389 1608- 1779 1930 2019 2051 2010 1926 1801 1684 1539 w Temperature Nom. Strain Rate Ave. Strain Rate = —14.98°C Sample Diameter 1.405" Initial Length = 2.81" Percent Sand (by V01.) = 63.56 *1 4.75 x lO-6sec_l 3.77 x 10_ sec Degree Ice Saturation (Z) = 98.77 1 Time to Failure Strain (Z) .005 015 016 025 045 076 00000000 Stress (psi) 54 129 214 297 416 538 652 761 875 977 1072 1237 1438 1598 1751 1968 2176 2279 9240 sec { 262 Table Arl (cont'd.) SAMPLE N0. 81 (cont'd.) SAMPLE N0. 83 (cont'd.) 3.126 2345 Time to Failure = 7200 sec 3.479 2361 Strain St A V 1 4.081 2322 , “335 ° - 4.750 2196 (A) 931—) @ 0.035 246 -0.01 5.424 2029 6.518 1790 0.073 495 -0.01 0.166 828 —0.02 0.298 1105 -0.03 §AMEL§_E9;_§£ 0.438 1282 -0.02 Temperature = —14.96°C _4 -1 0.572 1388 -0.02 Nom. Strain Rate = 1.19 X 10_53ec_l 0.759 1481 -0.01 Ave. Strain Rate = 8.34 x 10 sec 0.936 1567 +0.01 Sample Diameter = 1.405" 1.128 1646 +0.04 Initial Length = 2.81" 1.323 1725 +0.06 Percent Sand (by Vol.) = 64.10 1.553 1828 +0.08 Degree Ice Saturation (Z) = 97.30 1.655 1920 +0.10 Time to Failure = 307 sec 1.907 1998 +0.12 Strain Stress A V31. 3.3:: :32: :g.§g (Z) (P31) (cm ) 3.299 2458 +0.40 0.039 274 -0.01 4,054 2550 ___ 0.064 579 -0-02 4.675 2509 +0.79 0.101 873 -0.03 5.363 2376 +1.25 0.155 1176 —0.06 6.707 2079 +1.85 0.220 1482 —0.09 0.302 1743 —0.09 SAMPLE N0. 84 0.409 1951 -O.11 o 0.528 2109 -0.11 Temperature — —5.96 C _4 —1 0.678 2207 -0.08 Nom. Strain Rate — 1.19 x 10_ sec_l 0 839 2235 —0 04 Ave. Strain Rate = 9.64 x 10 sec ' ' Sample Diameter = 1.405" 1.021 2237 -0.01 . . n Initial Length = 2.81 1.291 2231 +0.05 _ Percent Sand (by Vol.) - 63.89 1.366 2230 +0.12 . a _ Degree Ice Saturation (Z) — 96.69 1°543 2232 +0.18 T' t F ilure = 330 sec 1.710 2241 +0.24 me ° a 1.885 2262 +0-30 Strain Stress A Vol. 2.219 2286 +0.43 (7,) (psi) (cm3) 2.561 2309 +0.60 ‘ 0,003 73 —0.01 2.930 2269 +0.78 0.016 220 —0.01 3.714 2115 +1.02 0,053 509 —o.02 4.507 1896 +1.49 0.107 752 —0.04 6.470 1426 +2.84 0.191 994 —0.05 0.304 1178 -0.06 SAMPLE N0. 83 0.440 1294 -0.04 o , -0.02 Temperature = 414.96 C -6 —1 O 586 1362 - _ 0.739 1430 +0.01 Nom. Strain Rate — 7.12 x 10_ sec_l 0 897 1479 +0 03 Ave. Strain Rate = 5.63 x 10 sec 1'053 1527 +0:06 Sample Diameter = 1.405" 1'212 1569 +0 09 P t Sand (by Vol.) = 64.32 1' ' ercen 1.736 1705 +0.20 Degree Ice Saturation = 96.40 263 Table A—1 (cont'd.) SAMPLE N0. 84 (cont'd.) SAMPLE N0. 86 2.055 1775 +0.29 Temperature = —5.95°C 7 1 2.394 1831 +0.40 Nom. Strain Rate = 9.94 x 10: sec-l 2.744 1875 +0.50 Ave. Strain Rate = 8.12 x 10 sec- 3.199 1890 +0.64 Sample Diameter = 1.405" 3.556 1877 +0.79 Initial Length = 2.81" 4.274 1808 +1.19 Percent Sand (by V01.) = 64.16 5.053 1702 +1.64 Degree Ice Saturation (Z) = 99.69 5.948 1566 +2.22 Time to Failure = 53,340 sec 6.557 1484 +2.58 , . Strain Stress A V31. (Z) (psi) (cm ) W 0.002 14 _0.01 Temperature = —5.95°C —6 -1 0.004 33 -0.01 Nom. Strain Rate = 7.12 x 10_ sec_l 0.005 56 -0.01 Ave. Strain Rate = 6.10 x 10 sec 0.008 91 -0.01 Sample Diameter = 1.405" 0.022 168 -0.01 Initial Length = 2.81" 0.093 292 +0.01 Percent Sand (by Vol.) = 64.41 0.184 346 +0.01 Degree Ice Saturation (Z) = 96.39 0.401 415 +0.02 Time to Failure = 7380 sec 0.517 446 +0.03 Strain . Stress A V61. 0'770 524 +0'07 , _ 3 0.914 574 +0.07 (4) (ps1) (cm ) 1.051 615 +0.08 0.037 294 +0.03 1.149 652 +0.08 0.121, 508 +0.07 1.331 698 +0.11 0.269 610 +0.10 1.690 828 +0.15 0.434 708 +0.13 1.797 871 +0.17 0.613 780 +0.15 2.024 929 +0.19 0.787 855 +0.17 2.096 953 +0.19 0'976 932 "‘0'” 3.182 1259 +0.30 1.166 1006 +0.19 4 433 1426 +0.52 L350 1064 “"20 5:635 1378 +1.12 1-605 1153 “3'21 6.354 1307 +1.61 1-748 1208 ”'22 7.341 1187 +2.30 1.927 1275 +0.23 2-198 1353 +014 SAMPLE NO 87 2.725 1483 +0.27 -——-—-——4——— 2,992 1553 +0.30 . Temperature = —2.03°C _4 _1 3.178 1606 +0.32 Nom. Strain Rate = 1.19 x 10_ sec_l 3.579 1686 +0.40 Ave. Strain Rate = 9.42 x 10 sec 4.506 1749 +0.83 Sample Diameter = 1.405" 5.296 1704 +1.46 Initial Length = 2.81" 6.456 1539 +2.32 Percent Sand (by V01.) = 64.22 7.218 1426 +2.84 Degree Ice Saturation (Z) = 96.13 Time to Failure = 351 sec Strain Stress A Vol. 0.033 101 —0.01 0.096 303 —0.01 0.154 479 -0.01 264 Table A-1 (cont'd.) SAMPLE NO. 87 (cont'd.) SAMPLE N0. 88 (cont'dt) 0.241 696 -0.02 3.609 1284 +0.55 0.336 839 -0.01 4.054 1315 +0.70 0.468 959 -0.01 4.483 1321 +0.88 0.607 1018 +0.01 4.897 1297 +1.10 0.745 1058 +0.04 6.411 1148 +1.93 1.037 1119 +0.10 6.734 1111 +2.14 1.308 1166 +0.15 1.691 1221 +0.26 SAMPLE N0. 89 §:g33 i223 :g:2g Temperature = -2.02°C _7 —1 2.729 1296 +0.60 Nom. Strain Rate : 9.94 x 10_ sec_l Ave. Strain Rate — 8.74 x 10 sec 3.063 1316 +0.72 1 D' t = 1 405" 3.306 1319 -—— $1113.61 lame :1 2 81" 3.437 ‘ 1317 +0.88 Pnltla Lengt ' ‘ _ ercent Sance (by Vol.) - 64.10 3.830 1306 +1.06 D . , = egree Ice Saturation (A) 98.90 4'169 1289 +l’26 Time to Failure = 98.90 4.907 1218 +1.70 5.305 1176 +1.93 Strain Stress A Vol. 5.663 1148 +2.18 (Z) (psi) (cm3) 6.440 1066 +2.87 0.019 29 —0.01 0.035 50 ~0.01 SAMPLE NO. 88 0.055 67 -0.01 o 0.069 82 —0.01 ' Temperature = —2.02 C _ 0.104 107 - +0;01 Nom. Strain Rate = 7.12 x 10 sec 0.236 164 +0.02 Ave. Strain Rate = 6.19 x 10 sec 0.366 199 +0.03 Sample Diameter — 1.405" 0.519 232 +0.03 Initial Length = 2.81" 0.669 265 +0.07 Percent Sand (by Vol.) = 64.05 0.823 298 +0.08 Degree Ice Saturation (Z) = 98.30 1 023 343 +0.12 Time to Failure = 7248 sec 1 231 388 +0 13 Strain Stress A V31. 1.456 :37 +0.1: Z psi (cm ) 1.706 56 +0. 0f031 ( 88) —0.01 1.796 481 +0.22 0.082 199 —0.01 2.163 548 +0.29 0.245 342 +0.01 2.586 614 +0.40 0.394 411 +0.03 ~ 3.213 688 +0.58 0.589 468 +0.03 3.807 730 +0.80 0.766 527 +0.05 4.311 738 +1.02 0.949 590 +0.05 4.968 718 +1.37 1.133 652 +0.07 6.493 638 +2.31 1.346 733 +0.11 7.569 562 +3.05 1.472 779 +0.12 I 1.661 834 +0.14 1.860 896 +0.16 2.049 950 +0.19 2.230 1002 +0.22 2.430 1056 +0.25 2.819 1161 +0.32 3.232 1233 +0.43 265 Table A—1 (cont'd.) SAMPLE NO. 90 Temperature = —2.02°C —6 -1 Nom. Strain Rate 3.56 x 10 6sec 1 Ave. Strain Rate _ = 3.02 x 10‘ sec Sample Diameter = 1.405" Initial Length = 2.81" Percent Sand (by V01.) = 64.92 Degree Ice Saturation (Z) = 96.20 Time to Failure = 13,380 sec Strain Stress (Z) (psi) 0.007 38 0.018 70 0.029 104 0.052 ' 131 0.067 159 0.095 183 0.136 219 0.161 253 0.303 294 0.444 337 0.669 391 0.925 476 1.169 563 1.531 672 2.065 825 2.562 967 3.147 1085 3.645 1142 4.035 1161 4.597 1155 5.293 1116 6.259 1020 6.998 941 7.718 868 266 Table A—2: Constant Stress Uniaxial Compression Creep Test Data SAMPLE N0. 1C SAMPLE N0. 2C (cont'd.) Stress = 1350 psi 2.173 5.00 Temperature = —6.10°C 2.629 8.00 Sample Diameter = 1.13" 3.027 11.00 Initial Length = 2.26" 3.426 16.00 Percent Sand (by Vol.) = 63.69 3.783 21.00 Degree Ice Saturation (Z) = 98.22 4.096 26.00 . . 4.395 31.00 St T 331“ 196 4.851 36.00 (4) (nun), 0.876 1.00 5.393 46.00 1 239 2.00 5.677 51.00 1.489 3 00 6.076 56.00 ° 6.931 66.00 1.702 4.00 7.729 76.00 1.845 5.00 - 8.613 86.00 1.987 6.00 9.354 96.00 2.194 8.00 9.553 106.00 2.358 10.00 10 978 114 67 2.643 12.00 ° ' 2.928 17.00 3.184 22_00 §9E2L§_EQL_§E 3.384 27.00 Stress = 1140 psi 3.711 37.00 Temperature = —6.08°C 4.039 47.00 Sample Diameter = 1.13" 4.324 57.00 Initial Length = 2.26" 4.595 67.00 Percent Sand (by V01.) = 63.62 4.922 87.00 - Degree Ice Saturation (Z) = 97.30 5'236 97'00 Strain Time A Vol. 6.048 107.00 a . 3 (4) (mm) (cm ) 6.361 117.00 '—“-‘ 0.000 0.00 +0.00 6.789 127.00 0.119 1.00 +0.01 7'245 137'00 0.283 . 2.00 +0.01 7'815 147'00 0.639 5.00 +0.02 8'580 157'00 1.024 11.00 +0.03 9°496 166'33 1.388, 20.00 +0.04 1.644 30.00 +0.06 §AMBL§_E91_Z£ 1.794 39.00 +0.06 Stress = 1350 psi 2.029 59-00 +0.07 Temperature = —6.03°C 2.199 79.00 +0.07 Sample Diameter = 1.13" 2.392 99.00 +0.09 Initial Length = 2.26" 2.663 129-00 +0-ll Percent Sand (by v61.) = 63.08 2.833 159.00 +0.13 Degree Ice Saturation (Z) = 97.47 2.948 189.00 +0.15 . . 3.048 219.00 +0.16 Stfaln T183 3.233 249.00 +0.18 _Sél__. fifllfll 3.318 279.00. +0.18 0-491 0-13 3.461 309.00 +0.18 0-783 0-50 3.660 339.00 +0.23 1.118 1.00 _ 1.524 2.00 1.795 3.00 267 Table Ar2 (cont'd.) SAMPLE N0. 4c SAMPLE N0. 5c (cont'd.) Stress = 1503 psi 4.099 185.00 --- Temperature = —6.10°C 4.428 215.00 +0.41 Sample Diameter = 1.13" 4.641 236.00 -—- Initial Length = 2.26" 5.083 290.00 +0.56 Percent Sand (by Vol.) = 63.74 5.781 327.00 -—- Degree Ice Saturation (Z) = 97.30 6.152 357.00 +0.71 Strain Time 6.519 387.00 --- (Z) (min) 8.431 500.00 +1.26 0.466 0.167 10.141 557.00 +1.66 0.922 0.333 1.777 0.399 §AMEEE—E9;—é£ 2.169 0,499 Stress = 1296 psi 2,497 0,599 Temperature = —6.03°C 2.604 0,799 Sample Diameter = 1.13" 3,173 0,999 Initial Length = 2.26" 3.601 1,199 Percent Sand (by Vol.) = 63.57 4.028 1,399 Degree Ice Saturation (Z) = 97.16 4'684 1'599 Strain Time A Vol. 4.969 1.799 (Z) (min) (cm3) 5.325 1.999 0_022 _0700 _:::-— 5-667 2-199 0.485 1.00 +0 04 79020 2-332 0.799 2.00 +0.05 7-875 2 399 - 1.176 4.00 +0.08 1.561 7.00 +0.09 832 10.00 +0.13 152 15.00 +0.17 437 20.00 +0.19 ; , 822 30.00 +0.24 5 121 . 40.00 +0.27 1 363 50.00 +0.32 691 65.00 +0.38 SAMPLE N0. 5c Stress = 1244 psi Temperature = -6.10°C Sample Diameter = 1.13" Initial Length = 2.26" Percent Sand (by Vol.) = 63.58 Degree Ice Saturation (Z) = 96.87 O®N®MU14>J>J>WWQONNNH .l.\ .l.\ O\ 005 80.00 +0.44 Strain Time A V31. 100.00 +0.53 (2) (min) isa_2_ 973 120.00 +0.63 0.068 0.00 --- 439 140.00 +0.73 0.417 0.50 -0-03 999 160.00 +0.85 0.538 1.00 —0 01 655 180.00 +1.00 0.730 2.00 -0.01 481 200.00 +1.15 1.008 4.00 +0-01 564 220.00 +1.37 1.464 9.00 +0.04 1 .160 237.33 +1.58 1.806 15.00 +0-05 2.148 25.00 +0-09 2.476 35.00 +0.12 2.689 45.00 +0-13 2.903 60.00 +0-15 3.159 80.00 +0 18 3.501 110.00 +0-22 3.786 140.00 --- 3.915 160.00 +0-32 268 Table Ar2 (cont'd.) SAMPLE N0. 7c Stress = 1100 psi Temperature = -6.03°C Sample Diameter = 1.13" Initial Length = 2.26" Percent Sand (by Vol.) = 63.89 Degree Ice Saturation (Z) = 98.36 Strain Time (Z) (min) 0.091 0.00 0.454 2.00 0.896 7.00 1.380 17.00 1.815 37.00 2.142 67.00 2.370 97.00 2.598 137.00 2.698 160.00 3.068 249.00 3.239 300.00 3.453 359.00 3.667 411.00 3.852 472.00 4.094 533.00 4.237 583.00 4.365 615.00 4.507 667.00 5.030 734.00 5.092 806.00 5.319 865.00 5.576 923.00 5.804 975.00 6.231 1033.00 6.601 1069.00 269 Table Ar3: Split Cylinder Test Data SAMPLE N0. ls SAMPLE N0. 35 (cont'd.) Vertical Def. Rate = 0.250 in/min 553 0.0123 0.00013 14.00 Temperature = —6.06°C 898 0.0146 0.00013 18.00 Sample Height = 2.00" 1410 0.0172 0.00019 22.00 Sample Diameter = 4.00" 1935 0.0201 0.00027 26.00 Percent Sand (by Vol.) = 64.57 2405 0.0232 0.00047 30.00 Degree Ice Saturation (Z) = 97.90 2723 0.0256 0.00060 34.00 . 3137 0.0283 0.00079 38.00 vert' H°rlz‘ . 3510 0.0319 0.00113 42.00 Load Def. Def. Time (lbs.) (in.) (in.) (sec) 3787 0.0361 0.00139 46.00 —1770_ 0.0800 -—:::T_ -:::— 4119 0.0444 0.00233 53.00 Recorder Malfunction — No SAMPLE N0. 45 Additional Data P01nts. Vertical Def. Rate = 0.002 in/min Temperature = -5.96°C §AEEL§—EQL—g§ Sample Height = 2.00" Vertical Def. Rate = 0.250 in/min Sample Diameter = 4.00" Temperature = —5.96°C Percent Sand (by Vol.) = 65.27 Sample Height = 2.00" Degree Ice Saturation (Z) = 97.66 Sample Diameter = 4.00" . Percent Sand (by v61.) : 63.68 Load 3:77. ngéf' Time Degree Ice Saturation (Z) = 96.57 (lbs.) (in.) (in.) (sec) Vert. Horiz. 54 0.0004 0.00027 32.00 'Load Def. Def. - Time 256 0.0033 0.00087 152.00 (lbs.) (in.) (in.) (sec) 408 0.0063 0.00133 242.00 276 0.0045 0.00000 0.60 492 0.0121 0.00220 292.00 539 0.0071 0.00000 1.20 871 0.0213 0.00373 517.00 843 0.0097 0.00000 1.80 1382 0.0339 0.00733 742.00 1189 0.0113 0.00000 2.40 1714 0.0469 0.01092 967.00 1617 0.0138 0.00000 3.00 1824 0.0552 0.01239 1092.00 1907 0.0161 0.00010 3.60 2211 0.0798 0.02224 1892.00 2474 0.0189 0.00010 4.20 2681 0.1143 0.04229 2342.00. 2902 0.0213 0.00030 4.80 3096 0.1771 0.08658 2792.00 3317 0.0235 0.00040 5.40 2764 0.2366 0.11655 3172.00 3718 0‘0258 0'00070 6'00? —— No Tensile Split Developed —- 4229 0.0289 0.00080 6.76 SAMPLE N0. 58 SAMPLE NO. 35 —_____“___—__' _ _ , Vertical Def. Rate = 0.002 in/min Vertical Def. Rate = 0.050 in/min Temperature = _5'996C Temperature = —5.99°C Sample Height = 2.00" Sample Height = 2'00" Sample Diameter = 4.00" Sample Diameter = 4'00” Percent Sand (by Vol.) = 64.58 Percent Sand (by VOl') = 65'21 Degree Ice Saturation (Z) = 97.18 Degree ICe Saturation (Z) = 97.10 . Vert. Horiz. Vert. Horiz. Load Def. Def. Time Load Def. Def. Time (lbs.) (in.) (in.) (SEC) (lbs.) (in.) (in.) iéssl "55"' 0.0004 0.00020 32.00 76 0-0059 0-00007 6'00 253 0.0034 0.00073 151.00 228 0-0101 0-00007 10-0 409 0.0063 0.00140 241.00 Table A—2 (cont'd.) SAMPLE N0. 53 (cont'd.) 477 0.0123 0.00206 293.00 871 0.0214 0.00366 516.00 1409 0.0337 0.00733 741.00 1699 0.0468 0.01079 966.00 1838 0.0551 0.01252 1093.00 2267 0.0794 0.02211 1894.00 2654 0.1139 0.04196 2340.00 3096 0.1765 0.08725 2791.00 2792 0.2359 0.11790 3170.00 -- No Tensile Split Developed -— SAMPLE NO. 63 Vertical Def. Rate = 0.083 in/min Temperature —5.99°C Sample Height 2.00" Sample Diameter 4.00" Percent Sand (by Vol.) = 64.53 Degree Ice Saturation (Z) = 97.63 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 202 0.0003 0.00036 1.00 663 0.0018 0.00073 3.00 1265 0.0036 0.00102 5.00 1831 0.0058 0.00113 7.00 2370 0.0083 0.00128 9.00 2930 0.0107 0.00135 11.00 3497 0.0137 0.00135 13.00 4036 0.0171 0.00139 15.00 4464 0.0214 0.00146 17.00 4671 0.0250 0.00154 18.40 SAMPLE NO. 78 Vertical Def. Rate = 0.143 in/min Temperature —5.96°C Sample Height 2.00" Sample Diameter 4.00" Percent Sand (by Vol.) = 65.29 Degree Ice Saturation (Z) = 97.49 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 380 0.0010 ——- 1.00 843 0.0033 —-— 2.00 1424 0.0050 ——— 3.00 1976 0.0070 —-— 4.00 2640 0.0092 —-— 5.00 3206 0.0116 -—- 6.00 270 SAMPLE N0. 73 (contYd.) 3842 0.0143 ——- 7.00 4312 0.0174 -—- 8.00 4948 0.0217 --- 9.10 —-— LADT Not Operating ——- SAMPLE NO. 85 Vertical Def. Rate Temperature = -5.93°C Sample Height 2.00" Sample Diameter 4.00" Percent Sand (by Vol.) = 65.70 0.144 in/min Degree Ice Saturation (Z) = 97.58 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 58 0.0018 ——— 0.74 130 0.0044 --- 1.82 224 0.0069 -—— 2.88 423 0.0080 --— 3.36 830 0.0096 -—- 4.02 1189 0.0109 —-- 4.54 1652 0.0126 —-— 5.28 2156 0.0147.‘ —-- 6.14 2778 0.0172 —-— 7.19 3372 0.0198 -—— 8.28 3980 0.0228 --— 9.55 4450 0.0253 --- 10.56 4782 0.0275 -—— 11.50 5058 0.0296 ——— 12 40 ——— LADT Not Operating ——— SAMPLE N0. 95 Vertical Def. Rate = 0.092 in/min Temperature -5.93°C Sample Height = 2.00" Sample Diameter 4.00" Percent Sand (by V01.) = 65.21 Degree Ice Saturation (Z) = 97.48 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 102 0.0031 -—- 2.00 213 0.0081 —-— 4.00 539 0.0108 —-- 6.00 1030 0.0128 —-— 8.00 1589 0.0147 --— 10.00 2211 0.0170 ——— 12.00 Table A—3 (cont'd.) SAMPLE NO. 93 (cont'd.) 2792 0.0192 -—— 14.00 3399 0.0220 --— 16.00 3953 0.0251 --- 18.00 4395 0.0293 —-- 20.00 4699 0.0335 —-- 21.80 ——— LADT Not Operating --— SAMPLE N0. 105 Vertical Def. Rate = -0.053 in/min Temperature = -6.00°C _Sample Height = 2.00” Sample Diameter = 4.00" Percent Sand (by V01.) = 63.86 Degree Ice Saturation (Z) = 97.14 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 91 0.0045 --— 4.00 362 0.0076 —-- 9.00 658 0.0100 ——— 13.00 961 0.0118 ——— 17.00 1299 0.0146 -—— 21.00 1659 0.0178 ——— 25.00 2128 0.0220 —-- 29.00 2626 0.0272 ~—- 34.00 3054 0.0319 --- 39.00 3455 0.0368 ——- 44.00 3897 0.0425 --— 49.00 4146 0.0466 —-— 54.00 4174 0.0489 —~- 55.00 -—— LADT Not Operating ——- SAMPLE NO. 11s Vertical Def. Rate = 0.100 in/min Temperature = -5.90°C Sample Height = 2.00" Sample Diameter = 4.00" Percent Sand (by Vol.) = 64.17 Degree Ice Saturation (Z) = 96.65 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 160 0.0046 —-- 3.40 362 0.0100 -—- 7.40 636 0.0153 —-— ' 11.40 1126 0.0204 -—— 15.40 1652 0.0262 ——— 19.40 SAMPLE NO. 115 (cont'd.) 2169 0.0352 ——— 23.40 2688 0.0434 --- 27.40 3441 0.0500 ——- 31.41 4146 0.0564 -—— 35.41 4824 0.0646 —-— 39.41 4948 0.0671 -—— 40.41 -—— LADT Not Operating -—— SAMPLE NO. 125 Vertical Def. Rate = 0.192 in/min Temperature = —5.90°C Sample Height = 2.00" Sample Diameter = 4.00" Percent Sand (by Vol.) = 64.49 Degree Ice Saturation(Z) = 97.01 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 66 0.0031 —-— 0.72 196 0.0067 -—- 1.52 547 0.0077 —-— 2.32 974 0.0089 --- 3.12 1548 0.0107 -—- 3.92 2128 0.0134 --- 4.72 2750 0.0158 —-- 5.52 3372 0.0179 --- 6.32 3939 0.0206 ——— 7.12 4478 0.0239 -—- 7.92 4920 0.0277 ——- 8.64 —-— LADT Not Operating --- W Vertical Def. Rate = 0.256 in/min Temperature = —6.09°C Sample Height = 2.00" Sample Diameter = 4.00" Percent Sand (by V01.) = 64.58 Degree Ice Saturation (Z) = 97.00 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 332 0.0028 --— 0.54 815 0.0040 ——— 0.99 1306 0.0051 -—- I1.45 1838 0.0064 --- 1.90 2335 0.0080 ——— 2.36 Table A-3 (cont'd.) SAMPLE NO. 133 (cont'd.) 2861 0.0098 -—— 2.81 3552 0.0118 -—— 3.26 4063 0.0138 ——— ,3.72 4644 0.0165 ——- 4.17 5114 0.0196 —-— 4.59 ———LADT Not Operating SAMPLE N0. 145 Vertical Def. Rate = Temperature = —10.09° ~Sample Height = 2.00" Sample Diameter = 4.00" Percent Sand (by Vol.) = 64.63 Degree Ice Saturation (Z) = 97.23 0.250 in/min C Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 166 0.0038 0.00036 0.60 357 0.0071 0.00089 1.07 699 0.0093 0.00089 1.54 1126 0.0114 0 00080 2.02 1652 0.0126 0.00071 2.49 2211 0.0142 0.00062 2.96 2737 0.0159 0.00062 3.92 3289 0.0180 0.00071 .4.39 3870 0.0201 0.00089 4.86 4395 0.0223 0.00098 5.33 4699 0.0234 0.00107 5.62 SAMPLE NO. 155 Vertical Def. Rate = 0.185 in/min Temperature = -10.09°C Sample Height = 2.00" Sample Diameter = 2.00” Percent Sand (by Vol.) = 64.54 Degree Ice Saturation (Z) = 97.53 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 464 0.0011 0.00009 0.67 1030 0.0025 0.00018 1.29 1603 0.0040 0.00036 1.91 2198 0.0053 0.00053 2.52 2819 0.0071 0.00071 3.14 3441 0.0091 0.00089 3.76 4174 0.0107 0.00098 4.37 4754 0.0130 0.00116 4.98 272 SAMPLE NO. 153 (cont'd.) 5363 0.0153 0.00124 5.60 5888 0.0178 0.00133 6.22 6164 0.0194 0.00169 6.56 SAMPLE NO. 168 Vertical Def. Rate = 0.146 in/min Temperature = -10.10°C Sample Height = 2.00" Sample Diameter = 4.00" Percent Sand (by Vol.) = 64.67 Sample Diameter = 4.00" Degree Ice Saturation (Z) = 97.19 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 235 0.0002 0.00044 ,1.10 500 0.0002 0.00071 2.10 1009 0.0011 0.00089 3.10 1506 0.0028 0.00098 4.10 2128 0.0045 0.00133 5.10 2889 0.0065 0.00160 6.10 3524 0.0086 0.00160 7.10 4132 0.0112 0.00160 8.10 4948' 0.0138 0.00160 9.10 5473 0.0245 0.00160 10.10 5860 0.0263 0.00160 10.80 SAMPLE NO. 178 Vertical Def. Rate = 0.100 in/min Temperature = —9.99°C Sample Height = 2.00" Percent Sand (by V01.) = 64.93 Degree Ice Saturation (Z) Vert. Horiz. Load Def. Def. (lbs.) (in.) (in.) 246 0 0036 0.00009 556 0 0051 0.00018 1057 0 0064 0.00027 1652 0 0088 0.00053 2529 0 0112 0.00080 3262' 0 0137 0.00089 3967 0.0164 0.00098 4865 0 0192 0.00116 5501 0 0227 0.00124 5832 0.0242 0.00133 98.45 Table A-3 (cont'd.) SAMPLE NO. 183 Vertical Def. Rate = 0.072 in/min Temperature = -9.99°C Sample Height = 2.00" Sample Diameter = 4.00" Percent Sand (by Vol.) = 64.18 Degree Ice Saturation (Z) = 97.42 Vert. Horiz. Load Def. Def Time (lbs.) (in.) (in.) (sec)- 268 0.0012 0 00000 2.30 603 0.0022 0 00000 4.30 962 0.0038 0.00009 6.30 1569 0.0064 0 00018 8.30 2170 0.0085 0 00027 10.30 2999 0.0110 0 00036 12.30 3455 0.0137 0.00044 14.30 4050 0.0165 0 00071 16.30 4754 0.0198 0 00089 18.30 5252 0.0240 0.00098 20.30 5528 0.0261 0.00107 21.60 SAMPLE N0. 195 Vertical Def. Rate = Temperature = —10.08 Sample Height = 2.00" Sample Diameter = 4.00" Percent Sand (by Vol.) = 64.95 Degree Ice Saturation (Z) = 98.37 0.043 in/min °C Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 340 0.0011 0.00000 5.30 702 0.0041 0.00000 10.30 1189 0.0069 0.00009 15.30 1721 0.0100 0.00027 20.30 2253 0.0135 0.00036 25.30 2778 0.0171 0.00071 30.30 3317 0.0211 0.00089 35.30 3842 0.0248 0.00098 40.30 4298 0.0294 0.00116 45.30 4658 0.0325 0.00142 49.20 SAMPLE NO. 205 Vertical Def. Rate = 0.230 in/min Temperature = —10.01°C Sample Height = 2.00" Sample Diameter = 4.00" Percent Sand (by Vol.) = 64.45 273 SAMPLE NO. 203 (cont'd.) Degree Ice Saturation (Z) = 97.13 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 254 0.0019 0.00044 0.48 586 0.0029 0.00062 0.76 1106 0.0047 0.00080 1.21 1728 0.0056 0.00080 1.46 2336 0.0069 0.00089 1.80 2902 0.0084 0.00098 2.20 3455 0.0102 0.00107 2.64 4036 0.0119 0.00116 3.09 4561 0.0137 0.00142 3.58 5667 0.0179 0.00160 4.66 SAMPLE NO. 218 Vertical Def. Rate = 0.222 in/min Temperature = —15.05°C Sample Height = 2.00" Sample Diameter = 4.00" Percent Sand (by Vol.) = 64.15 Degree Ice Saturation (Z) = 96.89 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 177 0.0034 0.00009 0.92 608 0.0059 0.00018 1.59 1099 0.0077 0.00027 2.08 1797 0.00931 0.00027 2.52 2571 0.0112 0.00036 3.11 3359 0.0132 0.00044 3.56 4146 0.0152 0.00053 4.11 5058 0.0173 0.00071 4.66 5750 0.0198 0.00080 5.35 6634 0.0236 0.00089 6.37 W Vertical Def. Rate = 0.133 in/min Temperature = -15.05°C Sample Height = 2.00' Sample Diameter = 4.00" Percent Sand (by V01.) = 64.81 Degree Ice Saturation (Z) = 98.09 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 149 0.00184 0.00009 0.80 470 0.00254 0.00018 1.60 Table A—3 (cont'd.) SAMPLE NO. 223 (cont'd.) 961 0.0034 0.00018 2.40 1500 0.0046 0.00027 3.20 2377 0.0070 0.00036 4.20 3220 0.0091 0.00044 5.20 4050 0.0115 0.00053 6.20 5031 0.0141 0.00062 7.20 5998 0.0174 0.00080 8.40 6828 0.0212 0.00098 9.60 SAMPLE NO. 233 Vertical Def. Rate = 0.160 in/min Temperature = —15.05°C Sample Height = 2.00" Sample Diameter 4.00" Percent Sand (by Vol.) = 64.58 Degree Ice Saturation (Z) = 97.61 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 304 0.0056 0.00018 1.31 967 0.0078 0.00027 2.13 1520 0.0096 0 00044 2.94 2080 0.0113 0 00071 3.76 3013 0.0131 0.00089 4.58 3455 0.0149 0 00107 5.39 4008 0.0172 0 00116 6.21 4602 0.0192 0 00124 7.03 5667 0.0212 0 00142 7.85 6496 0.0240 0.00169 8.99 SAMPLE NO. 245 Vertical Def. Rate = 0.106 in/min Temperature = —14.95°C Sample Height = 2.00" Sample Diameter = 4.00" Percent Sand (by Vol.) = 64.75 274 Degree Ice Saturation (Z) = m100.00 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 207 0.0030 0.00000 1.00 504 0.0054 0.00000 1.80 1140 0.0077 0.00000 3.00 1769 0.0089 0.00000 4.20 2709 "0.0100 0.00000 5.40 3869 0.0118 0.00000 6.60 4948 0.0141 0.00000 7.80 5943 0.0157 0.00000 8.80 SAMPLE NO. 243 (cont'd.) 6496 0.0172 0.00000 6634 0.0175 0.00000 SAMPLE NO. 255 Vertical Def. Rate = 0.034 in/min Temperature = —14.93°C Sample Height = 2.00" Sample Diameter = 4.00" Percent Sand (by Vol.) = 64.69 Degree Ice Saturation (Z) = 98.02 Vert. Horiz. Load Def. Def Time (lbs.) (in.) (in.) (sec) 111 0.0020 0.00009 3.60 243 0.0051 0.00027 7.60 451 0.0078 0.00036 11.60 829 0.0090 0.00044 15.60 1341 0.0106 0.00053 19.60 1852 0.0126 0.00062 21.70 2972 0.0164 0.00080 29.70 4050 0.0208 0.00098 37.70 5141 0.0251 0.00107 45.70 6026 0.0312 0.00124 54.30 SAMPLE NO. 265 Vertical Def. Rate = 0.075 in/min Temperature = -l4.95°C Sample Height = 2.00" Sample Diameter = 4.00" Percent Sand (by Vol.) = 64.67 Degree Ice Saturation (Z) = 96.92 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 80 0.0021 0.00036 1.00 285 0.0058 0.00053 ,3.00 1023 0.0081 0.00071 6.00 1935 0.0112 0.00080 9.00 2944 0.0141 0.00089 12.00 3967 0.0174 0.00089 15.00 4906 0.0212 0.00098 18.00 5832 0.0257 0.00107 21.00 6219 0.0283 0.00116 22.80 Table A—3 (cont'd.) SAMPLE NO. 275 SAMPLE NO. 29s (cont'd.) Vertical Def. Rate = 0.002 in/min Percent Sand (by V01.) = 64.28 Temperature = -14.95°C Degree Ice Saturation (Z) = 96.95 Sample Height = 2.00" . Sample Diameter = 4.00" Vert. Horiz. Percent Sand (by Vol.) = 64.69 (2:2d) ?::') (22f; Time) . . _ . . . sec Degree Ice saturatmn (A) ' 98’“ 133 0.0012 0.00009 W Vert. Horiz. 376 0.0031 0.00018 2.00 Load Def. Def. Time 670 0.0055 0.00036 3.00 (lbs.) (in.) (in.) (sec) .967 0.0084 0.00053 4.00 207 0.0000- 0.00000 85.00 1272 0.0113 0.00071 5.00 558 0.0003 0.00000 190.00 1576 0.0140 0.00089 6.00 1216 0.0028 0.00000 305.00 1852 0.0168 0.00098 7.00 1949 0.0059 0.00000 425.00 2156 0.0207 0.00116 8.00 2902 0.0099 0.00062 590.00 2460 0.0236 0.00142 9.00 3635 0.0142 0.00151 740.00 2737 0.0270 0.00151 10.00 4533 0.0184 0.00409 905.00 3040 0.0283 0.00160 10.44 4920 0.0243 0.00480 1025.00 5169 0.0317 0.00640 1155.00 SAMPLE N0. 308 5224 0'0394 0'00738 1275'00 Vertical Def. Rate = 0.280 in/min Temperature = -1.96°C §é§3§§_§9;_g§§ Sample Height = 2.00" Vertical Def. Rate = 0,002 in/min Sample Diameter = 4.00" Temperature = —14.95°C Percent Sand (by Vol.) = 65.31 Sample Height = 2.00" Degree Ice Saturation (Z) = 98.55 Sample Diameter = 4.00" ' ' . Percent Sand (by V91') : Load g8f5- HDZfS. Time Degree Ice Saturation (Z) = 98.09 (lbs.) (in.) (in.) (Sec) 1 ? Vert. Horiz. 188 0.0037 0.00009 1.11 { Load Def. Def. Time 406 0.0077 0.00018 2.23 ’ (lbs.) (in.) (in.) (sec) 545 0.0131 0.00027 3.35 210 0.0028 0.00044 85.00 643 0.0200 0.00053 4.47 556 0.0058 0.00089 191.00 967 0.0257 0.00071 5.58 1223 0.0092 0.00151 305.00 1320 0.0324 0.00089 6.70 1956 0.0128 0.00213 426.00 1755 0.0372 0.00098 7182 2916 0.0180 0.00293 592.00 2280 0.0443 0.00107 9.49 3607 0.0226 0.00373 742.00 2806 0.0504 0.00124 10.88 4561 0.0273 0.00453 907.00 3110 0.0560 0.00142 12.01 4920 0.0314 0.00616 1028.00 5197 0.0356 0.00587 1160.00 W 5252 0-0397 0'00622 1280'00 Vertical Def. Rate = 0.058 in/min 5197 0.0436 0.00702 1400.00 Temperature = —1.96°C 5141 0.0477 0.00782 1520.00 Sample Height = 2.00.. Sample Diameter = 4.00" W Percent Sand (by Vol.) = 64.88 Vertical Def. Rate = 0.016 in/min Degree Ice Saturation (Z) =99.37 Temperature = -1.96°C Sample Height = 2.00" Sample Diameter = 4.00" Table Ar3 (cont'd.) SAMPLE NO. 318 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 64 0.0021 0.00000 2.00 199 0.0049 0.00007 6.00 486 0.0073 0.00007 10.00 760 0.0097 0.00007 14.00 1050 0.0129 0.00013 18.00 1465 0.0185 0.00020 24.00 1886 0.0246 0.00033 30.00 2301 0.0311 0.00053 36.00 2640 0.0383 0.00067 42.00 2833 0.0469 0.00073 48.00 2902 0.0484 0.00073 49.40 SAMPLE NO. 325 Vertical Def. Rate = 0.085 in/min Temperature = —6.03°C Sample Height = 1.20" Sample Diameter = 2.40" Percent Sand (by Vol.) = 64.42 Degree Ice Saturation (Z) = 99.36 Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 55 0.0017 -—- 1.00 97 0.0029 —-- 2.00 366 0.0057 -—- 4.00 518 0.0072 —-— 5.00 677 0.0084 -—— 6.00 802 0.0093 -—- 7.00 926 0.0113 —-— 8.00 1223 0.0138 ——- 10.00 1499 0.0165 ——- 12.00 1811 0.0198 ——— 14.00 ———LADT Not Used ——- SAMPLE NO. 338 Vertical Def. Rate = 0.070 in/min Temperature = -5.99°C Sample Height 1.20" Sample Diameter = 2.40" Percent Sand (by Vol.) = 64.07 Degree Ice Saturation (Z) = 98.48 276 SAMPLE NO. 335 (cont'd.) Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 283 0.0022 —-- 2.00 428 0.0032 ——— 3.00 539 0.0044 —-— 4.00 753 0.0058 ——— 5.50 954 0.0076 -—- 7.00 1133 0.0092 ——— 8.50 1340 0.0108 —-— 10.00 1527 0.0118 ——— 11.00 1672 0.0127 -—— 12.00 1817 0.0139 —-— 12.80 ——— LADT Not Used SAMPLE NO. 345 Vertical Def. Rate = Temperature = -5.96°C Sample Height = 0.97" Sample Diameter = 1.94" Percent Sand (by Vol.) = 64.04 Degree Ice Saturation (Z) = 97.72 0.069 in/min Vert. Horiz. Load Def. Def. Time (lbs.) (in.) (in.) (sec) 97 0.0014 —-- 1.00 200 0.0028 ——- 2.00 297 0.0043 ——- 3.00 401 0.0057 --- 4.00 498 0.0072 --— 5.00 594 0.0086 --- 6.00 698 0.0100 -—— 7.00 795 0.0115 -—— 8.00 995 0.0143 -—— 10.00 1175 0.0137 —-— 11.90 --- LADT Not Used W Vertical Def. Rate = Temperature = —6.03°C Sample Height = 0.97" Sample Diameter = 1.94" Percent Sand (by Vol.) = 64.10 Degree Ice Saturation (Z) = 98.75 0.066 in/min Table Ar3 (cont'd.) SAMPLE NO. 35 (cont'd.) Load (lbs.) 97 200 297 401 498 609 698 802 1002 1133 Vert. Def. (in.) 0.0014 0.0028 0.0042 0.0056 0.0069 0.0083 0.0097 0.0111 0.0139 0.0125 Horiz. Def. (in.) Time (sec) 1 00 2.00 3.00 4 00 5.00 6.00 7.00 10.00 11.33 277 BIBLIOGRAPHY BIBLIOGRAPHY Akazawa, T., "Tension Test Method for Concrete”, Bulletin No. 16, Int. Assoc. of Testing and Research Lab. for Mat. and Struct., Paris, (November 1953), pp. 11—23. , Unpub- Alkire, B. D., "Mechanical Properties of Sand—Ice Materials" lished Ph.D. Dissertation, Michigan State University, East Lansing, 1972. Alkire, B. D., and Andersland, O. B., "The Effect of Confining Pressure on the Mechanical Properties of Sand—Ice Materials", J. Glaciology, 12(16), 1972. Anagnos, J. N , and Kennedy, T. W., "Practical Method of Conducting the Indirect Tensile Test", Research Report'98—10, Center for Highway Research, The University of Texas at Austin, August 1972. Andersland, 0. B., and AlNouri, I., "Time-Dependent Strength Behavior of Frozen Soil", J. Soil Mech. Found. Div. Am. Soc. Civ. Eng., 96(SM4), 1970. Andersland, O. B., Sayles, F. H., and Ladanyi, B., "Chapter 5: Mechanical Properties of Frozen Ground”, Geotechnical Engineering for Cold Regions, 0. B. Andersland and D. M. Anderson, eds., New York: McGraw-Hill Book Co., Inc., 1978. "Ice Nucleation and the Substrate—Ice Interface," Anderson, D. M., Nature, CCXVI (November, 1967). Anderson, D. M., Pusch, R. and Penner, E., "Chapter 2; Physical and Thermal Properties of Frozen Ground", Geotechnical Engineering For Cold Regions, O.B. Andersland and D. M. Anderson, eds., New York: McGraw-Hill Book Co., Inc., 1978. Anderson, D. M. and Tice, A . R. "Predicting Unfrozen Water Contents in Frozen Soils from Surface Area Measurements," Highway Research Record, No. 393, 1972, 12—18. Baker, T. H. W., "Effect of End Conditions on the Uniaxial Compressive Strength of Frozen Sand", Proc. 3rd Int. Conf. on PermafrostL Ed mouton, Alberta, 1978a, Vol. 1: pp.608-614. Baker, T. H. W., Strain Rate Effects on the Compressive Strength of Frozen Sand", Engineering Geology, 13 (1978b) 223—231. 278 279 Carniero, F. and Barcellos, A., "Concrete Tensile Strength", Bulletin No. 13, Int. Assoc. of Testing and Research Lab. for Mat. and Struct., Paris, (March 1953). pp. 97—127. Chen, W. and Chang, T., "Plasticity Solution of uConcrete Splitting Tests", J. Eng. Mech. Div. Am. Soc. Civ. Eng., 104(EM3), 1978. Daniel, E. E., and Olson, R. E., "Stress-Strain Properties of Compacted Clays", J. Geotech. Eng. Div. Am. Soc. Civ. Eng., 100(GT10), 1974. Dillion, H. B. and Andersland, O. B., "Predicting Unfrozen Water Contents in Frozen Soils," Canadian Geotechnical Journal, III, (February 1966), 53—60. Duncan, J. M., and Chang, C. Y., "Nonlinear Analysis of Stress and Strain in Soils", J. Soil Mech. and Found. Div. Soc. Civ. Egg., 96(SM5), 1970. Fairhurst, C., "On the Validity of the Brazilian Test for Brittle Mateirals", Int. J. Rock Mech. Mining Sci., 1 (1964) pp. 535—546. Frocht, M. M., Photoelasticity, Vol. 2, New York: John Wiley and Sons, Inc., 1957. Goughnour, R. R., "The Soil—Ice System and the Shear Strength of Frozen Soils", Unpublished Ph.D. Dissertation, Michigan State University, East Lansing, 1967. Goughnour, R. R., and Andersland, 0.B., "Mechanical Properties of a Sand—Ice7system”, J. Soil Mech. Found. Div. Am. Soc. Civ. Engg, 94(SM4), 1968. Grieb, W. E. and Werner, G., "Comparison of the Splitting Tensile Strength of Concrete with Flexural and Compressive Strengths", Public Roads, Vol. 32 (December 1962). pp. 97—106. Hadley, W. 0., Hudson, W. R., and Kennedy, T. W., "Evaluation and Predication of the Tensile Properties of Asphalt-Treated Materials", Research Repgrt 98—9, Center for Highway Research, The University Of Texas at Austin, May 1971. Hawkes, I., and Mellor, M., "Deformation and Fracture of Ice Under Uniaxial Stress", J. of Glaciology, Vol. 11, No. 71, 1972. Hawkes, I., and Mellor, M., "Uniaxial Testing in Rock Mechanics Laboratories", Eng. Geology, Vol, 4, 1970. Haynes, F. D., "Tensile Strength of Ice Under Triaxial Stresses", Technical Note, U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, 1973. Haynes, F. D., Karalius, J. A., and Kalafut, J., "Strain RAte Effect on the Strength of Frozen Silt", Research Report 350, U. S. Army Cold Region Research and Engineering Laboratory, Hanover, New Hampshire, 1975. 280 Houdros, G., "The Evaluation of Poisson's Ratio and the Modulus of Materials of a Low Tensile Resistance by the Brazilian Indirect Tensile Test with Particular Reference to Concrete", Australian J. Applied Sci., 10 (1959), pp. 243—268. Hudson, W. R, and Kennedy, T. W., "An Indirect Tensile Test for Stabilized Materials", Research Report 98—1, Center for Highway Research, The University of Texas at Austin, January 1968. Hult, J. A. H., Creep in Engineering Structures. Waltham, Mass: Blaisdell Publishing Company, 1966. Klein, J. and Jessberger, H. L., "Creep Stress Analysis of Frozen Soils under Multiaxial States of Stress", Proc. 1st Int. Symp. on Ground Freezing, Bochum, Germany, 1978. Ladanyi, B., "An Engineering Theory of Creep of Frozen Soils," Canadian Geotechnical Journal, Vol. 9, No. 1 (February 1972), 63—80. Ladanyi, B. and Arteau, J., "Effect of Specimen Shape on Creep Response of a Frozen Sand", Proc. lst Int. Symp. on Ground Freezing, Bochum, Germany,1978. Leonards, G. A. and Andersland, O. B., "The Clay-Water System and the Shearing Resistance of Clays", Proc.'COnf. on Shear Strength of Cohesive Soils, ASCE, University of Colorado, Boulder, Colorado, 1960, pp. 793—818. Lovell, C. S. "Temperature Effects on Phase Composition and Strength of Partially Frozen Soil", Bulletin 168, Highway Research Board, Washington, D.C., 1957. Mellor, M. and Hawkes, I., "Measurements of Tensile Strength by Diametrical Compression of Disk and Annuli", Eng. Geology, Vol. 5, No. 3, (1971), pp. 173-225. Mitchell, N. B., "The Indirect Tension Test for Concrete", Materials Research and Standards, (October 1961), pp. 780—787. Offensend, F. L., "The Tensile Strength of Frozen Soils", Technicial Note, U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, 1966. Odqvist, F. K. G., Mathematical Theory of Creep and Creep Rupture London: Oxford University Press, 1966. Parameswaran, V. R., "Deformation Behavior and Strength of Frozen Sand", Canadian Geotechnical J., 17 (1980), 74—88. Perkins, T. K. and Ruedrich, R. A "The Mechanical Behavior of Synthetic Permafrost", Soc. Petrol. Eng. J., (Aug 1973), 211-220. 281 Perloff, W. H. and Baron, W., Soil Mechanics, New York: The Ronald Press Company, 1976. Popov, E. P., Introduction to Mechanics of Solids, Englewood Cliffs: Prentice-Hall, Inc., 1968. Pounder, E. R., The Physics of Ice, Oxford: Sayles, F. H., "Creep of Frozen Sand", Technical Report 190, U. S. Army Cold Regions Research and Engineering Laboratory, Hanover, Pergamon Press, 1967. New Hampshire, 1968. Sayles, F. H., "Low Temperature Soil Mechanics",Technica1 Note, U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, 1966. Sayles, F. H., "Triaxial and Creep Test on Frozen Ottawa Sand", Technical Repggt 253, U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, 1974. Sayles, F. H. and Epanchin, N. V., "Rate of Strain Compression Tests on Frozen Ottawa Sand and Ice", Technical NOte, U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, 1966. Timoshenko, S. and Goodier, J. N., "Stresses in a Circular Disk", Theory of Elasticity, 2nd E., McGraw—Hill Book Co., Inc., New York, 1951. Tsytovich, N. A., "Bases and Foundations on Frozen Soils", Highway Research Board, Tr. Spec. Rpt, 58, 1955. ,Vyalov, S. S., "Rheological Properties and Bearing Capacity of Frozen Soils", Translation 74, U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, 1959. Vyalov, S. S. "Rheology of Frozen Soils," Proc. lst Int. Conf. Permafrost, Lafayette, Ind., 1963, NAS-NRC Pub. 1287, pp. 332-337. vyalov, S. S., "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, 1962. Williams, P. J., ”Unfrozen Water Content of Frozen Soils and Soil MOisture Suction", Geotechnique, XIV (March 1964), pp. 231-246. Wright, P. J. F., "Comments on the Indirect Tensile Test on Concrete Cylinders", Magazine of Concrete Research, July 1955. \ 7% J‘ farm—rug... a 7"er 1 -. ‘2: " “H.345“; ““43.- :i" :41. “SEQ-£415.! 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