SCIENCE SOCIETY OF AMERICA

PROCEEDINGSVOL. 34 NOVEMBER-DECEMBER 1970 No. 6

DIVISION S-l —SOIL PHYSICS

The Influence of Soil Water Matric Potential onthe Strength Properties of Unsaturated Soil1

JOHN WILLIAMS AND C. F. SHAYKEWICH-

ABSTRACTA study was made of the contribution that matric potential

makes to effective stress and therefore the strength propertiesof two unsaturated soils. From an evaluation of the effectivestress parameters C' and 0', and the unconfined strength, theshear strength, effective stress, and the x factor were estimatedas a function of soil water matric potential over the range-0.59 to -15.1 bars.

The strength properties of a Gretna clay increased rapidlywith decreasing matric potential. In a Wellwood loam, how-ever, the strength properties remained relatively constant overthe range —0.59 to —15.1 bars.

The influence of matric potential on the strength propertiesof an unsaturated soil can be described in terms of the con-tribution that matric potential makes to the effective stressoperating in the soil system. A measure of the proportion ofthe matric potential operative in the effective stress is givenby the x factor which is related to the degree of saturation.Therefore, the influence that matric potential has on thestrength of an unsaturated soil is related to the moisture reten-tion properties of the soil.

The implications arising from the contribution that matricpotential makes to the strength properties of an unsaturatedsoil are briefly discussed in terms of soil-plant relations.

Additional Key Words for Indexing: effective stress, shearstrength, unconfined compressive strength.

THE SOIL matric potential in terms of its contribution tothe free energy of soil water has been the subject for

active investigation in soil physics. Considerably lessemphasis, however, has been directed towards understand-ing the contribution that matric potential makes to the me-chanical behaviour of the soil system. The direct contribu-

1 Contribution from Dept. of Soil Science, Univ. of Manitoba,Winnipeg, Canada. Received May 29, 1970. Approved June24, 1970.

- Post-doctoral Fellow and Assistant Professor of Soil Physics,respectively.

tion that matric potential makes to soil strength is throughits contribution to the intergranular or effective stress oper-ating between the solid soil particles as is evident from theTerzaghi effective stress equation. In a saturated system,

= cr — U [1]where a', a, and u are the effective stress, the applied stress,and the pore water pressure, respectively. This relationshipis valid for negative pore water pressure provided the sys-tem remains saturated (Bishop and Eldin, 1950; Aitchisonand Donald, 1956). Thus a negative pore water pressurecontributes positively to the effective stress in the solidframework of the soil system. Since matric potential, T,expressed in units of stress is equivalent to negative porewater pressure, it is apparent that under saturated con-ditions an applied matric potential is equivalent to a me-chanically applied compressive stress. This can be writtenas,

[2]

if T ̂ 0 and is expressed in units of stress. This equiva-lence between matric potential and applied stress has beendemonstrated theoretically and experimentally by Childs(1955) and Towner (1961) for saturated sands and clays.Collis-George and Williams (1968) used this equivalenceto separate the influence of matric potential and effectivestress on the germination of lettuce. Deviations from equiv-alence, however, have been reported by McMurdie and Day(1960).

The effective stress equation has been modified for un-saturated conditions (Aitchison, 1961; Bishop, 1961; andJennings, 1961). For an unsaturated soil where the voidis continuous with the atmosphere, which is the case formost agricultural soils, the effective stress is given by

= cr + [3]

835

836 SOIL SCI. SOC. AMER. PROC., VOL. 34, 1970

where ^ is a factor which is some function of the degreeof saturation. The ^ factor represents the proportion of thematric potential that contributes to the effective stress. Insaturated soil x — 1 and equations [2] and [3] are identi-cal, however, as the soil drains ^ decreases with decreas-ing matric potential.

The mechanical strength of a soil may be described bythe shear strength at failure. The shear strength, S, in termsof effective stress and matric potential can be written as,

5 = C + [o- + x\r\]n tan [4]

where C' and <£' are the effective stress parameters, cohe-sion and angle of shearing resistance, respectively. Theterm [(J + ^|r|]n is the effective stress normal to the planeof failure. The relationship between shear strength andmatric potential for an unsaturated soil can be evaluatedby the direct measurement of shear strength as reported byCroney arid Coleman (1961) and Yong et al. (1970). Sucha determination, however, does not allow the evaluationof the terms in equation [4] through which matric potentialexerts its influence.

The purpose of this study was to investigate the contri-bution that matric potential makes to effective stress and,therefore, the strength properties of unsaturated soils. Theeffective stress at a given matric potential and bulk densitycan be estimated from the following analysis which treatsthe unconfined compression test in terms of effective stress.In this analysis it is necessary to assume that C' and <f>'for a given bulk density are independent of the degree ofsaturation and, therefore, independent of matric potential.This is an assumption which has been widely used in soilmechanics (Lee and Donald, 1968) and it is supported byexperimental evidence (Newlands, 1965; and Blight, 1966).If C and $ are evaluated in terms of total stress (Campand Gill, 1969) where the contribution that matric poten-tial makes to the stress in the system is neglected, then thisassumption cannot be made. The contribution that matricpotential makes to the shear strength of a soil system at agiven bulk density is reflected in the magnitude of the totalstress cohesion C. This may well account for the increasein C that Camp and Gill (1969) could not explain throughbulk density change. Newlands (1965) held bulk densityconstant and indicated that the cohesion in terms of effec-tive stress, C', represents only a small fraction of the totalstress cohesion C as determined by Camp and Gill (1969).

From an analysis of the triaxial compression test at fail-ure (Yong and Warkentin, 1966) for a soil at a given bulkdensity the stresses in the system can be described by

1C' cos <t>'1 — sin </>'

sin1 — sin 15]

where </, and (/3 are the major and minor principal effec-tive stresses, respectively. The unconfined compressive testis a special case of this where the applied minor principalstress 0-3 is zero. The analysis of the unconfined compres-sive test can be written for a soil system in equilibriumwith a given matric potential, T. From equation [3],

„> = o-, + v|r1 1 A I

as o-g = 0 then,

o-'i = xkl

, and a'3 =o-3 + X

, and (T\ — 0-3 = o-j .

Substitution and re-arranging equation [5] for this specialcase yields

2C' cos d>' 2 sin d>'1 - sin d>'

[6]

where a^ is the applied vertical stress at failure or the un-confined compressive strength and -%T K t'le effectivestress operating in the soil system. If C' and </>' are inde-pendent of the degree of saturation, then equation [a] isreadily solved for effective stress at a given matric poten-tial. It follows that as x r is the effective stress at a givenmatric potential, the x factor can be computed.

The shear strength at failure in the unconfined compres-sion test is given by

S = - cos [7]

Alternatively it can be shown that

S = C'(l + sine//) + X T | ( ! + sm<t>') tan < / > ' . [8]

At a given matric potential and bulk density, if C' and <j>'are known, it is therefore possible to evaluate the effec-tive stress, the x factor, and the shear strength operativein a soil system from the analysis of the unconfined com-pression test.

EXPERIMENTAL PROCEDURE

(i) The Drained Triaxial Compression TestThe effective stress parameters C' and </>' at a given bulk

density were evaluated by a series of drained triaxial compres-sion tests on a saturated soil sample. In this test it was essentialthat the pore water pressure, u, in equation [1] be zero such thatthe effective stress is equal to the applied stress. To ensurethat the rate of strain permitted the dissipation of pore waterpressure change, preliminary tests were conducted at a widerange of strain rates. The rate of strain was varied from 0.02 cmiwV1 to 0.002 cm min-1 for the Wellwood soil and from 0.02cm min-1 to 0.001 cm min-1 for the Gretna soil. For the Well-wood soil this tenfold difference in strain rate did not producea significant difference in the deviator stress at failure, hencea rate of strain of 0.02 cm min-1 was used for this soil. For theGretna soil, however, a rate of strain of 0.002 cm min-1 wasnecessary to meet this condition.

(a) Sample Preparation—A Wellwood loam (See Table 1for physical properties) and a Gretna clay were air dried andprepared to pass a 2.00 mm sieve. Perspex cylinders, 3.81 cmin diameter and 10 cm in length, coated internally with petro-leum jelly were filled with a mass of air dry soil which had beenpreviously steam sterilized to produce a bulk density of 1.15 gcm-3 for the Wellwood and 1.10 g cm-3 for the Gretna soils.The sample was saturated slowly via the cotton fabric base byplacing the cylinder to a depth of 9.0 cm in a container of dis-tilled water. The cylinders were transferred to tension plates andbrought to equilibrium with a matric potential of —0.05 bars.

WILLIAMS & SHAYKEWICH: INFLUENCE OF MATRIC POTENTIAL ON STRENGTH PROPERTIES OF SOIL 837

Table 1—Physical properties of the soil materialsMechanical analysis,

Bulk density, water content, and degree of saturation at matric potential, bars gravimetric percentageSoil property -0.25 -0.59 -0.98 -2.07 -3.95 -6.71 -15.10 OM Clay Silt Sand

Wellwcod LoamBulk density, g cm'3 1. 21 0. 02* 1. 21 0. 05 1. 22 ± 0. 02 1. 17 0. 04 - - 1. 18 ±Water content, g KXT1 30.3 0.4 23.3 0.7 21. 1 t 0. 6 18.5 0.7 - - 15.3±Degree of saturation 0. 67 0. 03 0. 52 0. 06 0. 47 ± 0. 02 0. 38 0. 03 - - 0. 33 ±

Gretna ClayBulk density, g cm"3 1. 07 0. 06* 1. 10 0. 03 - - 1. 11 0. 02 1. 09 0. 03 1. 19 ±Water content, g 100-' 38.7 0.6 33. 9 0. 4 - - 29.9 0.4 27.7 1.0 25. 8 ±Degree of saturation 0. 70 0. 07 0. 67 0. 03 - - 0. 57 0. 05 0. 52 0. 04 0. 55 t* Each value quoted is the mean and standard deviation of at least six replicates.

Mean bulk density over all replicates and matric potential for Wellwood Loam = 1. 19 ± 0. 07 g cm-Mean bulk density over all replicates and matric potential for Gretna Clay = 1. 10 ± 0. 07 g cm~

The soil sample was carefully slid from the cylinder to a splitmould and trimmed with sharp blade or wire saw to the stan-dard dimensions (3.81 cm in diameter by 7.64 cm in length)for the triaxial test.

(b) The Test Procedure — The sample was assembled in thetriaxial cell as described by Bishop and Henkel (1962) for thestandard drained test. Three tests at each of the three ambientcell pressures (68.9, 137.8, and 206.7 x 104 dyne cm-2) were (a)conducted for the Wellwood soil. The Gretna soil was tested atfive ambient pressures (34.5, 68.9, 102.0, 137.8, and 206.7 x104 dyne cirr2). The water flow from the saturated soil wasequated with volume change and the "corrected area" of thesample was computed from the relationship presented byMcMurdie and Day (1960). The maximum deviator stress wasconsidered to be the criterion of failure. The regression equationfor o-'j as a function of <r'3 was evaluated and equation [5] was

( i i ) The Unconfined Compression Test

(a) Sample Preparation — The air dry soils prepared as above (b)were placed in cotton based perspex cylinders (internal dimen-sions 5.0 X 16.0 cm) to a bulk density of 1.15 g cirr3 for theWellwood and 1.10 g cm-3 for the Gretna soil. The samplewas saturated and transferred to the dialysis membrane cylinder

5. 2 26. 9 44. 9 28. 20. 10 1. 25 ± 0. 030.4 13. 7 ±0.100. 05 0. 32 ± 0. 01

5. 4 55. 1 24. 0 20. 90. 06 1. 16 ± 0. 070.7 21.7 ± 0. 50. 01 0. 45 ± 0. 05

i

|

rx :

::: :_

(-5cmHr — Perspex Former

•;•••' -'••'•".•••"" ;;

'•'/:'" -:'-:^ :J :_'."•. "'- ••>'.' •"•'.;•.•. •''•v''-~\mm) '-•••.i-^1' ••••.>.'•;• ;;!£•%•*

'-'•"• n^-:'V^'?

— Soil Sample

• — Dialysis Tubing

^---Perspex Base!r -̂'O' Rings

r ——— ——— — Pump

^rfc^r^

IS^S::̂

fl^g — Soil Sample£i< — PE.G. Solution

£±S:>>SSft:;S; :/-Sas described below.

(b) Osmotic Control of Soil Water Matric Potential—Amodified form of an osmotic technique introduced by Zur(1966) was used to bring the soil sample to the desired matricpotential.

Two thicknesses of dialysis tubing (size identity 1%)(Manufactured by Union Carbide, Lindsay, Ont.) with aninternal diameter of approximately 5.0 cm were stretched overperspex formers and sealed with tightly fitting rubber bands toproduce a cylinder approximately 16.0 cm in length (Fig. la).

The cylinder containing the soil sample was fitted directly tothe top of the upper former and by means of a rubber plungerthe soil sample was pushed into the dialysis tube cylinder. Sixsuch cylinders of soil were then placed in a 10 liter reservoir ofpolyethylene glycol (P.E.G.) 6000 (Fig. Ib) . The concentra-tion of P.E.G. 6000 was regulated to provide the desired soilwater matric potential. The calibration curve for the P.E.G.solution was obtained from data presented by Williams andShaykewich (1969). To maintain the required concentrationthe solution was changed every 7 days and circulated by a suita-ble immersion pump for 5 min every hour through the use ofa simple switching circuit.

During preliminary work on this technique, soil water con-tent-time relationship for the two soils at 6.7 bars was investi-gated. At 5, 10, and 15 days the sample was sectioned radiallyand longitudinally to determine the water content variation. At15 days there was no significant longitudinal variation in watercontent and the radial variation had decreased to ± 0.25 g100-1 g. To prevent microbial decay of the membrane it wasnecessary to steam "sterilize" the soil and to add approximately100 ppm "Gammasam" (Manufactured by Chipman ChemicalLtd., Winnipeg, Manitoba.) to the soil system.

Fig. 1—Apparatus used in the osmotic control of soil watermatric potential.

(c) The Test Procedure—After 16 days the sample wasremoved from the solution. The membrane was cut away andthe sample placed in a split mould where it was trimmed witha sharp blade to the approximate dimensions of the mould(5.00 cm in diameter by 10.00 cm in length). Sample dimen-sions were determined with vernier calipers. The unconfinedtest apparatus was a Soil Test model U-130 (Manufactured bySoil Test, Chicago, 111.) on which the vertical stress was deter-mined by a proving ring and the strain determined (± .001 cm)by a good quality dial gauge. The rate of strain was controlledby a valve to an approximately constant rate of 0.05 cm min-1.From the calculated axial stress—strain relationship, the maxi-mum axial stress was considered as the criterion of failure.This maximum axial stress is the o-j of equation [6], the un-confined compressive strength for that soil condition.

At five matric potentials between —0.59 bars and —15.1 barsat least six replicates were tested. The maximum axial stress foreach soil replicate was used in the calculation of the mean un-confined compressive strength at a given matric potential.

RESULTS AND DISCUSSIONFrom the analysis of the drained triaxial compression test,

the effective stress parameters C' and <f>' f°r both soilswere evaluated. The C' for the Gretna and Wellwood werefound to be 8.5 and 10.0 X 104 dyne cm-2, respectively.The value of </>' for the Gretna was 15.5° and for the Well-

838 SOIL SCI. SOC. AMER. PROC., VOL. 34, 197060 r

50

40

1£30

20

10

A - SILICA SILTY LOAM• - COARSE ALUMINA SANDX - WELLWOOD LOAMO - GRETNA CLAY

-0.01 -10.0-O.I -1.0MATRIC POTENTIAL (BARS)

Fig. 2.—The relationship between shear strength and matric potential for four different soil systems.

wood 25.5°. The bulk density at which these estimationswere made was 1.07 ± 0.03 for the Gretna soil and 1.13± 0.04 for the Wellwood soil. A least significant differ-ference test (see Table 1) showed that there was no sig-nificant difference between the bulk density of all replicatesat all matric potentials tested in the unconfined test andthe bulk density in these triaxial tests. Therefore the valueof C' and <f>' so determined may be considered to be areasonable estimate of C' and </>' for the bulk densitiesstudied in the unconfined test.

The unconfined compressive strength, shear strength,effective stress, and the x factor were calculated as a func-tion of matric potential. In interpreting this data as a func-tion of matric potential, it was assumed that during the testno important changes occurred in the potential up to incipi-ent failure. For unsaturated soil at matric potentials lessthan —0.59 bars, this is a reasonable assumption and it hasbeen used by workers in soil mechanics and soil physics(Towner, 1961; Blight, 1966; Yong et al. 1970). Thisassumption is supported by Taylor & Box (1961) whofound at a matric potential of approximately —0.58 barsthat a confining stress of approximately 0.66 bars produceda change in matric potential of less than —0.03 bars. Thisconfining stress is in excess of the stress applied to theWellwood and Gretna soils at approximately the samematric potential. A confining stress applied over a consid-erable time period in the manner of Taylor and Box (1961)is not strictly analogous to the stress applied in the uncon-fined test; however, it does serve to indicate the magnitudeof change that may be expected at the high matric poten-tials. At more negative potentials the magnitude of thechange in potential would be presumably smaller. New-lands (1965) presents data for a sandy clay which doesindicate under similar unsaturated conditions that potentialcan be considered to be independent of applied stress.

The shear strength of both soils as a function of matricpotential is presented in Fig. 2. This data clearly indicatesthat over the range of matric potential studied (—0.59 to

— 15.1 bars) these two unsaturated soils are very different intheir strength properties. The shear strength of the Gretnaclay increased rapidly over the whole range of matric po-tential studied. In strong contrast the shear strength of theWellwood loam remained relatively constant. The uncon-fined compressive strength-matric potential relationshipw i l l fol low an identical pattern (see equation [7]). Forcomparison purposes the shear strength-matric potentialrelationships for two cohesionless materials (I. Williams,1968. Seed germination as influenced by soil water. Ph.D.Thesis. University of Sydney, Australia) are presentedalong with the two soils. The silica silty loam maintaineda high degree of saturation over the range of matric poten-tial studied, therefore, the shear strength increased veryrapidly with decreasing potential. The value of <£' for thismaterial is 38° hence contributing further to this rapidincrease in shear strength. This behaviour is similar to theGretna soil which has a high degree of saturation (seeTable 1) over a large range of matric potential. The coarsealumina sand increased in shear strength with decreasingmatric potential until drainage occurred (—0.03 bars). Fur-ther decrease in matric potential resulted in a slow decreasein shear strength. In qualitative terms this material be-haves in a manner similar to that of the Wellwood soil.The behaviour of the coehesionless materials indicates thatthe shear strength properties of a porous system dependson the degree of saturation associated with the decreasein matric potential.

The essential nature of the relationship between matricpotential and the strength properties can be understood interms of the contribution that matric potential makes toeffective stress. From Fig. 3 it is apparent that the effectivestress-matric potential relationship follows a pattern similarto that for the strength properties. This is anticipated fromequation [6] where C' and <f>' are constants for each soil.The effective stress operating in the Gretna clay increasedrapidly with decreasing matric potential such that at — 15.1bars the magnitude of the effective stress was 126 X 104

WILLIAMS & SHAYKEWICH: INFLUENCE OF MATRIC POTENTIAL ON STRENGTH PROPERTIES OF SOIL 839

0.6 r

120 -

100 -

S 80

60

40

20

O - GRETNA CLAYX - WELLWOOD LOAMA - SILICA SILTY LOAM

x-—-

-0.1 -1.0MATRIC POTENTIAL (BARS)

-10.0

Fig. 3 — The relationship between effective stress and matricpotential for a saturated silty loam and two unsaturated soils.

dyne cnr2. At the potentials studied, the effective stressin the Wellwood loam remained relatively constant, al-though there was a tendency to decrease with decreasingmatric potential. As anticipated, the effective stress in thesaturated silty loam increased rapidly with decreasingmatric potential. The nature of the relationship betweeneffective stress and matric potential was therefore differentfor each of the three soil systems. Consequently, the effec-tive stress term in equations [6] and [8] is basic to under-standing the influence that matric potential exerts on thestrength properties of an unsaturated soil.

The x factor which is similar to the k term introduced byby McMurdie and Day (1960) is a measure of the pro-portion of the matric potential that contributes to the effec-tive stress. At each potential the proportion of the matricpotential contributing to effective stress was very muchlarger in the Gretna than in the Wellwood (see Fig. 4).At potentials less than —3.95 bars there was a tenfold dif-ference between the soils.

The relationship between ^ and the degree of satura-tion for both soils is presented on Fig. 5. This form of therelationship is similar to data collected from nLtmeroussources and presented by Jennings and Burland (1962).It is unlikely that this is a unique relationship and fromsoil mechanics literature one would expect it to be differentfor different soils. The fact that both soils appear to fall ona similar curve could well be fortuitous. However, it mayreflect the similar sample preparation and bulk densitiesof the two soils. The regression equation for this relation-ship was

X = 6.99 Sr5-»5 (r2 = 0.947) . [9]

This empirical equation may serve as a practical tool in

-1.0 -10.0MATRIC POTENTIAL (BARS)

Fig. 4 — The relationship between thepotential for two unsaturated soils.

0.6 -

0.5 -

0.4

factor and matric

0.3

Q2

- O - GRETNA CLAYX - WELLWOOD LOAM

O.I 0.3 0.4DEGREE OF

0.5 0.6SATURATION Sf

0.7

Fig. 5—The relationship between the x factor and the degreeof saturation for two unsaturated soils.

estimating the contribution that matric potential makes tothe effective stress and therefore the strength properties ofsimilar soil systems.

From Table 1 it is apparent that at any matric potentialthe degree of saturation is greater in the Gretna than in theWellwood. From this and the ^ — Sr relationship in Fig.5 it is apparent that the effective stress, and hence strengthproperties of a soil, as a function of matric potentialdepend to a large extent on the water retention propertiesof the soil system.

The relationships which are of consequence in inter-preting the influence of matric potential on strength be-haviour in unsaturated conditions are (i) the relationship

840 SOIL SCI. SOC. AMER. PROC., VOL. 34, 1970

between the ^ factor and the degree of saturation, and (i i)the relationship between the degree of saturation and matricpotential. This is true for a given bulk density. However, asbulk density is some function of matric potential for swell-ing and shrinking materials, the resultant influence of bulkdensity is superimposed on the above concepts. A change inbulk density will influence the magnitude of both C' and </>',presumably change the nature of the relationship betweenX and Sr, and change the relationship between the degreeof saturation and matric potential. Therefore, matric poten-tial will exert its influence on the strength properties of anunsaturated swelling system through both the effectivestress and the effective stress parameters which will bebulk density dependent.

Measured effective stress and shear strength are withinthe range which has been shown to retard root elongationand development (Barley and Greacen, 1967). The influ-ence of matric potential has been shown, by Collis-Georgeand Williams (1968) for germinating seed and by Taylorand Ratliff (1969) for elongating roots, to exert its influ-ence through its contribution to the mechanical strengthof the soil system, rather than through its control of thefree energy of the soil water. The contribution that matricpotential makes to the effective stress and hence thestrength properties of an unsaturated soil, as discussedhere, is therefore a factor to be considered in the study ofsoil water-plant relations. For example, in the Gretna soila decrease in matric potential not only reduces the "availa-bility" of water but simultaneously increases the resistanceto root development. In the Wellwood, however, the resis-tance to root development is reasonably constant withdecreasing matric potential. Consequently, the comparisonof the two soils in terms of water "availability" at thesebulk densities could well be confounded unless the differ-ences in mechanical resistance to root development wereconsidered. In the interpretation of the influence of matricpotential on the behaviour of the plant system in unsatu-rated conditions, it is therefore necessary to consider thecontribution that matric potential makes to the mechanicalstrength of the soil system.

ACKNOWLEDGMENT

The authors are deeply indebted to Prof. A. Baracos, Depart-ment of Soil Mechanics, University of Manitoba, for his assist-ance in theoretical and practical aspects of this study. Financialassistance from the National Research Council of Canada isalso gratefully acknowledged.

3. Barley, K. P., and E. L. Greacen. 1967. Mechanical resis-tance as a soil factor influencing the growth of roots andunderground shoots. Advance. Agron. 19:1-40.

4. Bishop, A. W., and G. Eldin. 1950. Undrained triaxialtests on saturated sands and their significance in the gen-eral theory of shear strength. Geotechnique 2:1-13.

5. Bishop, A. W. 1961. The measurement of pore pressurein the triaxial test, p. 38-46. In Pore pressure and suctionin soils. Butterworth, London.

6. Bishop, A. W., and D. F. Henkel. 1962. The measurementof soil properties in the triaxial test. Edward Arnold Ltd.,London, p. 122-129.

7. Blight, G. E. 1966. Strength characteristics of desiccatedclays. J. of Soil Mech, and Foundations Division, A.S.C.E.Proc. no. SM6, Nov. 92:19-37.

8. Blight, G. E. 1967. Effective stress evaluation for unsatu-rated soils. J. of Soil Mech, and Foundations Division,A.S.C.E. Proc. SM2, March 93:125-148.

9. Camp, C. D., and W. R. Gill. 1969. The effect of dryingon soil strength parameters. Soil Sci. Soc. Amer. Proc.33:641-644.

10. Childs, E. C. 1955. The physical aspects of some conceptsin soil mechanics. Proc. Nat. Acad. Sci. India. 24A, 86-92.

11. Collis-George, N., and John Williams. 1968. Comparisonof soil matric potential and isotropic effective stress on thegermination of Lactuca sativa. Aust. J. Soil Res. 6:179-192.

12. Croney, D., and J. D. Coleman. 1961. Pore pressure andsuction in soils, p. 31-37. In Pore pressure and suction insoils. Butterworth, London.

13. Jennings, J. E. B. 1961. A revised effective stress law foruse in the prediction of the behaviour of unsaturated soils.In Pore pressure and suction in soils, p. 26-30. Butter-worth, London.

14. Jennings, J. E., and J. B. Burland. 1962. Limitations tothe effective stresses in partly saturated soils. Geotech-nique 12:125-144.

15. Lee, I. K., and I. B. Donald. 1968. Effective stress law forsaturated and unsaturated soil and rock, p. 53-69. InSoil Mechanics—Selected topics. American Elsevier Pub-lishing Co., New York.

16. McMurdie, J. L., and P. R. Day. 1960. Slow tests undersoil moisture suctions. Soil Sci. Soc. Amer. Proc. 24:441-444.

17. Newland, P. L. 1965. The behaviour of soils in terms oftwo kinds of effective stress. Engineering effects of mois-ture changes in soils. Texas A & M Press, College Station.78-92.

18. Taylor, H. M., and L. F. Ratliff. 1969. Root elongationrates on cotton and peanuts as a function of soil strengthand soil water content. Soil Sci. 108:113-119.

19. Taylor, Sterling A. and James E. Box. 1961. Influence ofconfining pressure and bulk density on soil water matricpotential. Soil Sci. 91:6-10.

20. Towner, G. D. 1961. Influence of soil water suction onsome mechanical properties of soils. J. Soil Sci. 12: ISO-187.

21. Williams, John, and C. F. Shaykewich. 1969. An evalua-tion of polyethylene glycol (P.E.G.) 6000 and P.E.G.20,000 in the osmotic control of soil water matric poten-tial. Can. J. Soil Sci. 49:397-401.

22. Yong, R. N., and B. P. Warkentin. 1966. Introduction tosoil behaviour. Macmillan, New York. p. 267-276.

23. Yong, R. N., R. D. Japp, and G. How. 1970. Shearingresistance and soil water potential of partially saturatedclays. Soil Mechanics Research Report No. 70-1 Dept, ofCivil Engineering and Applied Mechanics, McGill Univ.,Montreal, Canada. 1-11.

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