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ANDERSLAND, 0. R. and AK ILI , w. 1967. GLobt echni que, 17:.?7-39

STRESS EFFECT ON CREEP RATES OF A FROZEN CLAY SOIL0. B. ANDERSLAND* and WADDAH AK IL I~

SYNOPSISDifferential creep tests have been carried out onfrozen cylindrical clay soil samples to examine theinfluence of stress on creep rates. Concurrently,information was obtained concerning temperatureand structure effects on the stress/creep raterelationship.

On a fait des essais de fluage differentiels sur desBchantil lons de sol argileux cylindriques gel& pourexaminer linfluence de la contrainte sur les co-efficients de fluage. En m&me temps, on a obtenudes renseignements sur les effets de temperature etde structure sur le rapport de coefficient contrainte-Approximate linearity between logarithm ofaxial creep rate and axial stress (u), for stressesgreater than two-thirds the ultimate compressive

strength and constant temperature, support an ex-ponential law (exp Be) for predicting the effect ofstress on creep rates. The hyperbolic sine law(sinh Bu) closely approximates the exponential lawfor the high stresses used. The data and analysisindicate that thermal activation is involved inthe creep of this frozen clay soil and that tempera-ture (T) should appear through an expression ofthe form exp (-d F/RT). An observed activationenergy (dF) close to 93.6 kcal/mole appears to re-main constant over a range of axial stresses (600-800 lb/sq. in.) and temperatures (- 12C to - 18C).This constant activation energy supports the ideathat one creep mechanism predominates for thesestresses and temperatures.Experimental data show that a linear relationshipappears to exist between axial stress and reciprocalof temperature for constant creep rates and tempera-tures lower than - 6C. This provides a means forpredicting creep rates at other axial stresses andtemperatures based on limited creep data.

fluage.Une linearite approximative entre le logarithmede coefficient de fluage axial et de contrainte axiale(u), pour des contraintes depassant les deux tiers dela force de compression limite et B temperature con-stante, supporte la loi exponentielle (exp Bo) pourprevoir leffet de contrainte sur les coefficients defluage. La loi sinusoIdale hyperbolique (sinh Bo)sapproche de p&s de la loi exponentielle pour lesfortes contraintes utilisees. Les releves et lanalyseindiquent que lactivation thermique agit dans lefluage de ce sol argileux geld et que la temperature(T) doit apparaitre dans une expression de la formeexp - dF/RT). Une dnergie dactivation observee(dF) proche de 93,6 k Cal/mole semble rester con-stante sur une certaine gamme de contraintes axiales(600 livres/poucea a 800 livres/pouces) et de tem-peratures (- 12C a - 18C). Cette Bnergie dactiva-tion constante confi rme quun mecanisme de fluageest predominant pour ces contraintes et ces tem-peratures.Des releves experimentaux montrent quunrapport lineaire semble exister entre la contrainteaxiale et la reciproque de temperature pour descoefficients de fluage et des temperatures inferieuresa -6C. Ceci permet de prevoir les coefficients defluage pour dautres contraintes axiales et tempera-tures bashes sur des releves de fluage limit&.

INTRODUCTIOKThe creep of frozen soil depends on two external variables of stress and temperature and theinternal variable of structure. Although creep data are now available on frozen soil (Sangar,

1963 ; Vyalov, 1963, 1962), the relationship between these variables is as yet only vaguelyunderstood. Attempts have been made to formulate theories for creep, but their agreementwith fact has been disappointing. It appears that new types of definitive creep data areneeded to provide the essential knowledge for formulating better and more realistic creeptheories for frozen soil.

Perhaps one source of the failure to uncover an adequate theory arises from the fact thatnearly all analyses of experimental data on creep in the past have disregarded the observations,by Vyalov (1962), Tsytovich (1963) and others, that structure of frozen soil changes during creep.For example, it is customary in evaluating the effect of stress on the creep rate to correlate thesecondary creep rate with the applied stress. Vyalov (1962) states that at low stressesstrengthening (strain hardening) of the frozen soil leads to damped creep deformations,whereas at higher stresses structural weakening (recovery) leads to increasing creep rates and

* Associate Professor of Civil Engineering, Michigan State University, East Lansing, Michigan, U .S.A.t Assistant Professor, Department of Civil Engineering and Mechanics, Drexel Institute of Technology,Philadelphia, Pennsylvania, U.S._4.27

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28

EiIoktsBCC, CRTVrAFAU

0. B. ANDERSLAND ANDNOTATION

l-l,conventional strain = - I0true (or logarithmic) axial strain

W. AKILI

= Jog.4 0true (or logarithmic) axial creep rate = de/&axial stressinstantaneous length of specimenoriginal length of specimenBoltzmanns constant = 133 x lo-la ergs/mole/Ytimefrozen soil structurestress factorfrequency factorconstantsgas constant = 1.986 cal/mole/Cabsolute temperatureflow volumeactivation energyreduction in axial stress

subsequent failure. Consequently the stress/secondary creep rate relationship found in theusual way reveals not only the effect of stress but also the effect of differences in structure onthe secondary creep rate.It was the purpose of the study reported here to isolate the effect on the creep rate of stressalone, in an attempt to provide new data for possible formulation of a better creep theory forfrozen soils. In addition, an attempt was made to ascertain how temperature, structure, andice contained in the soil pores might affect the stress/creep rate relationship.

METHODThe procedure adopted was simple. A cylindrical frozen soil specimen (approximately1.4 in. dia. x 2 in. high) was pre-crept at a given axial stress (u) and temperature T) to aselected conventional strain (change in sample length divided by initial length) at which time

the stress was reduced to some lower value. The instantaneous true creep rate (gr) (withor, the logarithmic strain, i.e. the natural logarithm of the ratio of instantaneous length toinitial sample length) was determined after reduction of the axial stress by da,. Second, third,etc., tests were conducted on duplicate soil specimens under identical conditions except thatthe axial stress was reduced by larger values, Aaz, A+, yielding yet lower instantaneous creeprates, i, and is. Inasmuch as the pre-creep conditions were identical in each series of tests, theinstantaneous structures obtained immediately after reducing the stress were presumed to beidentical. This would not have been true if the stresses were raised above the pre-creep stressbecause changes in structure would be introduced by the rapid additional straining occurringwhen the stress was raised. Data for samples A-2(6) and A-2(7) shown on Fig. l(a) illustratethis method.After a number of specimens had been tested by the single stress reduction method, amodified version including successive stress reductions was tried which provided more data persample. Figure l(b) illustrates this method for sample A-3(3) in which comparable results

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STRESS E FFECT ON CREE P RATES OF FROZEN CLAY SOIL 29

0.14 - a)

E 0.12 -Ini t i al xi al stress= 675 I b/ rq. i n.

2 0 Sampl e A- 2(6)2

AC, = 75 I b/sq. n0. 10 -

aE, = 0,00262/ m n.

5 k, =O- 000361/ m n.5e

008 Cl Sampl e A- 2(7) Ag, = 50 Ib/rq. i n.- / E. = O. O0270/ m n.

0. 06~ 8 E, = O. O0078/ m n.% d I I I I I0 I O 20 30 43 50 60

TI ME i t) M N.

/El Sampl e A - 3 ,315

Temperat ure- l 2' C

2 u =675 Ib/sq.n. E, = 0 00403l m n.;cd ncr, =40 E, = O- 00164fm n.ti

au, i i 36 10 E, = 0 000 205l m n.

0 r 20 43 60 89 I O0 120TIME ( 1, M N

Fig. 1. Typical examples of a) single stress reduction and b) successive stressreductions

were obtained. The good agreement of the stress-creep rate data (Fig. 6) obtained by the twotechniques at - 12C encouraged the use of successive stress reductions at other temperatures.Although the method was simple, certain factors were considered in order to obtainaccurate results.(a) It might be thought that creep recovery immediately following the reduction in stresswould interfere with accurate evaluation of the instantaneous true creep rate. Pre-liminary data indicated that such recovery was not measurable for frozen soil specimenspre-crept at high stresses if stress reductions were limited to about one-sixth of the totalstress.

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30 0. B. ANDERSLAND AND W. AKILIb) A major objection to the procedure arises from the fact that each point for the stress-creep rate relationship must be obtained from a new specimen, in which samplingvariations can be appreciable for creep tests. To minimize this factor, duplicate soilspecimens were prepared in the manner described by Leonards (1955). Good agree-

ment between samples A-2(6) and A-2(7) is illustrated on Fig. 4.(c) Data reported by Leonards and Andersland (1960) showed that temperature historymay influence the ice content of a frozen clay soil at a given temperature. This factorwas minimized by cooling all samples to at least three degrees below and then warmingthem to test temperature. Unfrozen water contents should then fall on or near thewarming curve shown on Fig. 2.SOIL STUDIED

The soil used in this study was a red clay obtained from a glacial lake deposit approxi-mately 15 miles south of Sault St. Marie, Michigan. I t is pedologically classified as Ontonagan.Soil samples were taken in a fairly recent highway cut, about 4-5 ft below the original groundsurface. The results of identification and mineralogical tests on the clay soil are summarizedin Table 1. Unfrozen water contents for the compacted clay soil, determined by the calori-metric method (Lovell, 1957), are given in Fig. 2 for the temperature range used in this study.Table 1. Soil identification and mineralogical data

Description Sault St. Marie clayLiquid limitPlastic limitPlasticity indexSpecific gravityGr;d;on ( finer by weight)

0.06 mm.002 mmSpecific surface area ( < 2 I I )C.E .C. ( < 2 p)MiE;;l content ( < 2 p)VermiculiteChloriteQuartz, feldspar, andmontmorillonite

t:362.78100::290-360 sq. m/gm3650251510

-

Sample preparationEXPERIMENTAL PROGRAMME

The clay soil obtained from the lake deposit was allowed to dry in the air. This materialwas processed by crushing and sieving until the material passed a 4 in. sieve, and was thenplaced in a galvanized can for storage. Preparation of the 11 in. diameter by 34 in. high cakeof soil involved taking sufficient air-dry soil, uniformly mixing it with a selected amount ofdistilled water, and permitting the moistened soil to stand for two days in a covered containerto ensure a uniform water content distribution.The prepared soil was placed in the mould and statically compacted following the procedurereported by Leonards (1955). After extruding from the mould, the soil cake was cut into 21rectangular shaped pieces. Each piece was covered with aluminium foil, coated with wax, andtemporari ly stored under water. Samples were trimmed to approximately 1.4 in. dia. x 23 in.high using a motorized soil lathe. Each sample was weighed, and height and diameters

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STRESS EFFECT ON CREEP RATES OF A FROZEN CLAY SOIL 31Moulded dry density - 100 lb/u. fiMoulded water content - 25 xDegree saturation - 95

Freezing point

Warming

.-deprsssion- 1I

TEMPERATURE : CFig. 2. Unfrozen water contents, Sault St. Marie clay (after Dillon)

(top, middle, and bottom) were measured. Friction reducers and lucite disks (with theirsides covered by a film of silicone grease) were placed on each end of the sample. A rubbermembrane was placed over the sample and disks, and tight-fitting rubber bands wereplaced on each lucite disk. The friction reducers consisted of a perforated sheet of aluminiumfoil coated with a mixture of silicone lubricant and graphite powder covered with a thinpolyethylene sheet at top and bottom. A layer of silicone lubricant was spread over themembrane and a second membrane was placed over the sample with additional tight-fittingrubber bands placed on the lucite disks.A paratus and test procedure

The prepared sample was mounted in the triaxial cell, which was quickly filled with coolantand immersed in a larger coolant bath (Fig. 3) at a temperature of at least 3 below testtemperature. The coolant was a mixture of ethylene glycol and water. Rapid sample freez-ing minimized any redistribution of soil moisture. Temperatures adjacent to the sample andwithin the cell were measured using copper-constantan thermocouples. After reachingequilibrium, sample temperature fluctuation was limited to a range of about 5 0~05C due todelayed temperature response in the triaxial cell as compared to greater variations in the largercoolant bath.Axial loads up to the selected unit stress were applied to the specimen using an electricallypowered mechanical jack to lower dead weights at a rate close to 1.0 in./min. The loadingsetup, coolant bath, and triaxial cell are shown schematically in Fig. 3. Upon sample de-formation, a constant unit stress was maintained by adding lead shot to dead weights tocompensate for the small increase in sample area. Preliminary measurements showed novolume change ( + 0.01 cu. cm) during deformation, hence constant volume deformation wasassumed. Part of the initial dead load consisted of preselected amounts of lead shot in bucketswith funnel shaped bottoms and a 1 in. dia. clamped hose. Stress reduction was accomplished

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32 0. B. ANDERSLAND AND W. AKILI

PLE

Fig. 3 (above). Schematic diagram showing loading setup, coolant tank, and triaxial cell

Fig. 4 (top right). Typical creep curves obtained concurrent to stress reduction tests on Sault St.Marie clay

Fig. 5 (right). Effect of axial stress on true axial creep rates at constant structure, SaultMarie clay St.

simply by removing the hose clamp and allowing the lead shot to drain from the bucketsinto containers in a matter of seconds. For smaller stress reductions, a small container withlead shot could be easily lifted from the dead weights. Confining pressures were limited toabout a 6 in. head of coolant liquid on all samples. Time and axial deformations ( t_O 0001 n.accuracy) were visually observed and recorded as needed for each test. On completion ofeach test and after removal from the cell, the appearance of the sample was noted and the finalwater content taken.RESULTS

Several typical creep curves, obtained concurrently with the stress reduction tests, areplotted in Fig. 4. Curves shown are for a constant axial stress of 675 lb/sq. in. and tempera-tures of - 12C, - 15C, and - 18C. Since these creep tests were not continued to rupture,

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STRESS EFFECT ON CREEP RATES OF A FROZEN CLAY SOIL 33

@I2112OCA - 2 6)-15OC - IEOC

Axial :res = 675b/ q. in.Moulded dry density -9&l lb/a. fcMoulded water content - 261 xDegree saturation - 960 * 1 1 1 f 1 1 f k-1 I I I

0 20 40 60 80 100 I20 140 600 800TIME (/I : MIN

Pre-creep strucfure~ obtainedunder the fol lowing condationr :

650

Smgle stress reductionTemperature- 12CMoulded dry denmy - 98-l lb/a. fc

6 8 ,o-, 2 4 IO.3 2 4 6 8TRUE AXIAL CREEP RATE (; ) : N./IN./MIN.

only three stages are shown : stage 1, termed instantaneous strain, represents the strain whichoccurs upon loading; stage 2, termed primary or transient creep, represents the initial region ofdecreasing creep rate; and stage 3, termed secondary creep, represents the region of relativelyconstant creep rate. The final region of increasing creep rate, leading to eventual failure ofthe specimen, was omitted because of stress reductions.Creep data, obtained by the single stress reduction method for axial stresses greater thantwo-thirds the ultimate compressive strength and a temperature of - 12C are plotted in Fig5. Specimens were pre-crept to different strains at several stress levels in order to gaininformation on the effect of stress on the creep rate at constant structure. The last two seriesplotted on Fig. 5, pre-crept to 6 conventional strain, show a different behaviour from the

2

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0. B. ANDERSLAND AND W. AKILIMoulded dry density - 981 lb/w. ItMoulded water ccntcnr - 261,sDegree saturation - 96 g -18CA-3(4) 2

2CQ-0I , ,...n., I *.I I ..I 1 * I.,10-b 2 4 6 8 10-5 2 4 6 8 IO.4 2 4 6 8 10.3 2 4 6

TRUE AXIAL CREEP RATE (;) : IN./lN./MIN

Relationship of true axial creep rate to axial stress for several temperatures, Sault St.Marie clay

other samples because of the existence of a different structure. The stress reduction was madeduring primary creep.structure The data for the secondary creep stage suggest that for this soili = CexpBo . . . . . . . . * (1)

where i is the true axial creep rate, (T s the axial stress, C is a constant, and 2*303/B is the slopeof the lines shown on Fig. 5. But since the creep rate must vanish when the stress is zero, itis possible that the stress/creep rate relationship is given byg = C (eB-e-B) = C sinh B.2 . . . . . . (2)

since eeBO is negligible for the relatively high stresses used above.More creep data for a larger range of stresses and several temperatures, obtained by meansof successive stress reductions, are plotted in Fig. 6. Good correlation between the singlestress reduction and the successive stress reductions methods, at the - 12C temperature, sup-port the use of the latter method. More creep information was obtained from fewer frozensoil samples. These data show that changing soil structure related to strain hardening appearsto influence creep rates at the lower stresses. Lower temperatures shift the curve upward(larger stresses) and to the left (slower creep rates). This may be due to the influence oftemperature on structure or to its effect on the deformation mechanism.than 5 x 10e3/min. quickly lead to sample failure. Strain rates greaterInformation on the influence of stress-strain history on the true axial creep rates for sampleA-3(10) at a temperature of - 12C is plotted in Fig. 7. The reloading portion of the curveappears to parallel the unloading part except for being shifted to the left (slower creep rates).For the larger stresses, results from the single stress reduction method have been plotted for

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STRESS EFFECT ON CREEP RATES OF FROZEN CLAY SOIL 35

600

5 I , , , I I I I I L 1 I I I,,,1 I I I111111 I 1 I,1 4 6 8 10.6 2 4 6 8 ,0-s 2 4 6 a ,I). 2 4 6 ,8

TRUE AXIAL CREEP RATE (e) : N./IN./MIN.Fig. 7. Influence of stress-strain history on true axial creep rates

comparison. It appears that structure changes related to strain hardening are responsiblefor the slower creep rates on reloading for comparable stress levels. This same effect holdsfor other temperatures as shown by Akili (1966).

DISCUSSIONUsing data from Fig. 6, axial stress was plotted against the reciprocal of temperature forselected creep rates in Fig. 8. For temperatures lower than -6C and a constant axial strainrate, the data show a linear relationship between stress and reciprocal of temperature. Thisbehaviour and the data supporting equation (2) both point to a genera1 equation (Conrad,1961; Kauzmann, 1941) which has been useful for a large group of materials. The general

equation for the true creep rate (i) has the formda- = i = ,ZCi a, T ) exp -AF,(a, T , s)dl RT 1inh [B, T, s)o] . .t

where C, is the frequency factor, AF, is the activation energy, and B, is the stress factor.These terms may correspond to one of i number of deformation mechanisms. The frequencyfactor and activation energy may depend on stress (a), temperature T), and frozen soilstructure (s). The stress factor may depend on temperature and structure. R is the uni-versal gas content.Although a number of deformation mechanisms may be operating simultaneously, usuallyone is rate-controlling so that an evaluation of equation (3) is possible by gross mechanicalmeasurements. If the mechanisms are in series (i.e., the operation of one depends on theoperation of others), the slowest mechanism will control; if they are in parallel, the fastestmechanism will be controlling (Conrad, 1961). In certain temperature or stress ranges two or

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0. B. ANDERSLAND AND W. AKILI

830 -

700zj 600 -

22.-/ 500 -t:25.;i 400 -a

Moulded dry density - 981 lb/a. ftMoulded water conrenr - 261Degree saturation - 96

- 12oc - ISOC -WCI , 1 4 1 I I ,)B I I 1 ? I

0~00375 000380 @00385 0-00390Reciprocal of f temperarure (I/T) : aK-1

Fig. 8. Relationship of reciprocal of temperature to axial stress for selected creep rates

more mechanisms may be contributing significantly to deformation, in which case it would bevery difficult to evaluate the exact form of equation (3).For one deformation mechanism controlling, and stress conditions such that sinh Ba N expBu, equation (3) may be written

expBa . . . . . .where the reciprocal of temperature and stress are linearly related as indicated in Fig. 8. Theexponential relationship for stress, supported by Fig. 5, has been included. Taking thelogarithm of equation (4) gives

BU AF 1log,, d = log,, c f- - - 0-2.303 2.303 R T * * Equation (5) suggests a straight line relationship between log,, i veY.su.s/T with [-AF/2.303 R)] equal to the slope and [log,, Cf Ba/(2.303)] equal to the intercept. Using datafrom Fig. 6 for the lower temperatures (- 12C to - 18C) and higher stresses (600 lb/sq. in. to600 lb/sq. in.), the plot of reciprocal of temperature vwsus the logarithm of true axial creeprate does give straight lines as shown on Fig. 9. Reasonably parallel lines for different stresslevels are in accord with a thermally activated process and indicate the predominance of onecreep mechanism. Activation energies obtained from the slopes are shown on Fig. 9 andhave an average value close to 93.6 k Cal/mole.Similar values for the activation energy may be obtained from creep curves, for constantstress and temperatures T1 and T,, if times t, and t, are selected for a total strain falling in theregion of secondary creep (Dorn, 1954). Integrating equation (4) and using the two sets ofvalues for time and temperature gives the relation

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STRESS EFFECT ON CREEP RATES OF A FROZEN CLAY SOIL 37Fig. 9 left). Reciprocal of temperature

A F= 94 SOOcr l mo l eversus true axial creep rate

Fig. 10 below). Variation of the observedactivation energy with axial stress,SauIt St. Marie clay

AXIAL STRESS (b, : LB/=. IN.

dF = 2.303R l~g,o(Vz)T,- T,) . . . . . . . (6)TIT,Now using data from the creep curves plotted on Fig. 4, the average observed activationenergy at 9 strain is equal to 93.1 k Cal/mole. This value is not greatly different from theprevious average value of 93.6 k Cal/mole obtained from Fig. 9.A plot of axial stress verstis observed activation energy is shown on Fig. 10. Reasonablyconstant values of the observed activation energy in the range of 600-800 lb/sq. in. indicate thepredominance of one deformation mechanism. Higher values of activation energy for stressesbelow 600 lb/sq. in. suggest the existence of a transition region where two or more mechanismscontribute significantly to the creep deformation. It may be that, if more data at smallertemperature intervals were available, one could show the predominance of another creepmechanism in the stress range of 350-550 lb/sq. in.The stress factor B may be obtained from equation (4) by writing

=B * (7)Considering Fig. 6, the slope at a particular stress and temperature equals 2*303/B. Asshown in Fig. 5, for the - 12C temperature and higher stresses, the stress factor appears to beindependent of stress during secondary creep. At lower temperatures of - 15C and - 18Cand higher stresses there is only a small decrease in the stress factor. This may be caused bythe influence of temperature on structure, corresponding to a small decrease in unfrozen watercontent. With higher temperatures the stress factor increases, the largest value at -3Cbeing only about 10 times larger than the smallest value at - 18C.

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38 0. B. ANDERSLAND AND W. AKILIIf we utilize chemical rate theory Kauzmann, 1941), a flow volume may be computed

from the stress factor. The flow volume may be thought of as the area of the flow unit in themicro-shear plane multiplied by the distance through which the micro-shear stress acts incarrying the unit of flow from the normal to the activated state. In theory, the flow unitmay be a single molecule or a group of molecules which migrate under the action of an appliedmicro-stress. The gradual movement of water molecules around a clay particle will permit theparticle to rotate or translate. In addition, there is probably a continuous yielding or slidingof clay particles and/or ice grains at their contact points, due to the creep process.

The theoretical volume V,) of the flow unit Herrin and Jones, 1963; Kauzmann, 1941)may be estimated from the equation

v, 2/2B=r T3 . . . . . . . . . 8)where k s Boltzmanns constant and B, V,, and T are as previously defined. 42The constant 3converts the axial stress to an octahedral shear stress if uniform strains are assumed for thetriaxial test conditions. Here, one must assume that macro-stresses are proportional tomicro-stresses. For the -12C temperature and an axial stress close to 650 lb/sq. in. theflow volume is approximately equal to 1.1 x lo5 cubic angstroms cu. A).spherical particle 0.001 mm in diameter has a volume close to 10la cu. A. For comparison, aThese values, ifapproximately correct, support the idea that creep mechanisms involved are limited to par-ticle and/or ice contact points rather than entire soil particles.

The frequency factor C may be evaluated from equation 4) using the measured creeprate, axial stress, and temperature with the observed activation energy and stress factor.For a constant temperature - 12C) the frequency factor appears to remain constant at thehigh stresses. Computed values at - 18C may be slightly larger. The data are inadequateto provide information on the frequency factor for lower stresses and the lower creep rates. Itmay be that changes in C would correlate to changes in structure.

SUMMARY AND CONCLUSIONSIt is apparent from the data and analysis that thermal activation is involved in creep of

this frozen clay soil and that temperature should appear through an expression of the formThe observed activation energy 93.6 k Cal/mole) appears to remain constant

over a range of axial stresses 600800 Ib/sq. in.) and temperatures - 12C to - 18C) sup-porting the idea that one deformation mechanism predominates. The larger activationenergy observed at 550 lb/sq. in. probably indicates a transition region where two or morecreep mechanisms contribute to creep rates. Significant changes in the unfrozen watercontent at temperatures higher than -6C would handicap any creep analysis in this region.

The approximate straight line relationship between the logarithm of true axial creep rateand axial stress at high stresses, shown on Fig. 5, supports an expression including axial stressof the form exp Ba). Small changes in B at lower temperatures may be due to a change infrozen soil structure, i.e. slightly less unfrozen water. Higher temperatures increase thestress factor. An estimate of the volume of the flow unit, based on chemical rate theoryand using the observed stress factor, indicates that the creep mechanisms are probablylimited to particle and/or ice contact points rather than to entire particles.

The frequency factor appears to remain reasonably constant at the higher stresses 600800lb/sq. in.) and lower temperatures (- 12C to - 18OC).

The plot of axial stress versus reciprocal of temperature provides a graphical means for

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STRESS EFF ECT ON CREEP RATES OF A FROZEN CLAY SOIL 39predicting creep rates for selected stresses and temperatures. The failure region for the claysoil as used in this study would be approximated by the region above the line representing atrue creep rate equal to 5 x IOe3/min. The region below the line representing a true creeprate close to 10-5/min. corresponds to damped creep strain hardening predominates).

More research is needed to evaluate the nature of the frequency factor, activation energy,and stress factor. Information is not available on how other soil densities, moisture contents,or other soils influence these parameters.

ACKNOWLEDGEMENTSThe research described in this Paper represents a portion of the work supported by Re-search Grant No. GP-1198 of the National Science Foundation, U.S.A.

REFERENCESAKILI , W., 1966. Stress effect on creep rates of a frozen clay soil from the standpoint of rate process theory.

Ph.D. Thesis, Mich. State Univ., E. Laming, Mich.CONRAD H., 1961. Experimental evaluation of creep and stress rupture. M echanical behavi or of mat evi alsat elevat ed t emperatur es (J ohn E. Dom, ed.), pp. 149-217. McGraw Hil l , New York, 149-217.DILLON, H. B. (in preparation). Temperature effect on creep rates of a frozen clay soil . Ph.D. Thesis,Mich. State Univ., E. Lansing, Mich.DORN, J . E., 1954. Some fundamental experiments on high temperature creep. J . M ech. Phys. Sol i ds,3:85-l 16.HERRIN, M. and G. E. J ONES, 1963. The behavior of bituminous materials from the viewpoint of the abso-lute rate theory. Proc. tech. Sess. Ass. Asph. Pav . Technol ., 32:82-105KAUZMAN, W., 1941. Flow of solid metals from the standpoint of the chemical-rate theory. Trans. Am.I nst. Mi n. metal l . Engrs, 143:57-81.LEONARDS, G. A., 1955. Strength characteristics of compacted clays. Trans. Am. Sot . civ . Engrs, 120:1420-1454.LEONARDS, G. A. and 0. B. ANDERSLAND, 1960. The clay water system and the shearing resistance of clays.Proc. Res. Conf. Shear Strength Cohesive Soils, pp. 793-818. American Society of Civ il Engineers.L~VELL, C. W., 1957. Temperature effects on phase composition and strength of partially frozen soil.H ighs. Res. Bul l . 168:74-95.SANGAR, F. J . and C. W. KAPLAR, 1963. Plastic deformation of frozen soils. Pvoc. 1st I nt . Conf. 0 Per-mafvost, pp. 305-315. National Academy of Sciences, Nat. Res. Council publi cati on No. 1287.TSYTOVICH, N. A., 1963. Instability of mechanical properties of frozen and thawing soils. PYOC. st Int .Conf. on Permafrost, pp. 325-330. Nat i onal Academy of Sciences, Nat . Res. Council publi cati on No.1287.VYALOV, S. S., 1963. Rheology of frozen soils. Proc. 1st I nt . Conf. on Permafrost, pp. 332337 NationalAcademy of Sci ences, hat . Res. Counci l publication No. 1287.VYALOV, S. S., 1962. Mechanism of rheological processes. The st rengt h and creep of r ozen soil s and calcula -ti ons for ice-soil retaining structures (Chap 2) (S. S. Vyalov, ed.) U.S. Army Col d Regi ons Research andEngineering Labor at ory Tr. 76, 1965.