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Relationship between soil cohesion and shear

strengthHajime Yokoi

a

aNational Institute of Agricultural Sciences, Tokyo, Japan

Version of record first published: 29 Mar 2012.

To cite this article: Hajime Yokoi (1968): Relationship between soil cohesion and shear strength, Soil Science

and Plant Nutrition, 14:3, 89-93

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(Soil Science and Plant Nutrition, Vol. 14, No.3, 1968)

RELATIONSHIP BETWEEN SOIL COHESIONAND SHEAR STRENGTH

Hajime YOKOINational lnsfltute of Agricultural Sciences, Tokyo, Japan

RECEIVED NOVEMBER 6, 1967

IntroductionCohesion of soil is an important factor ofsoil consistency. The word cohesion, however,has acquired two connotations. In soil physics,

BA VER (2), for example, defines it as "thecohesive force that takes place between adjacent particles". On the other hand, in soilmechanics, cohesion means "the shear strengthwhen the compressive stresses are equal tozero". It is apparent that these two meaningsdiffer. For convenience in this report "soilcohesion" refers to the soil physics definition,while "shear cohesion" refers to that of soilmechanics.Theoretical concepts of soil cohesion inan ideal soil composed of uniform sphericalparticles have been developed by HAINES (4),FISHER (3), YAMANAKA (10), and others onthe basis of surface-tension force due to waterfilms between particles. Furthermore, ATTERBERG (1), NICHOLS (6), YAMANAKA (10),and others have carried out experimental studies on soil cohesion. However, the relationshipbetween soil cohesion and shear cohesion wasnot investigated. In the meeting repor t of theSociety of Soil Mechanics and FoundationEngineering, YAMANAKA and others (11)emphasized the urgent need of investigatingthe effect of soil internal stress on shearstrength. Furthermore, TSCHEBOTARIOFF (9)considered soil cohesion as true cohesion. Theauthor investigated field soil resistance totractor tillage and found a positive relationshipbetween soil cohesion and shear cohesion.

Theoretical ConsiderationsIt is generally assumed that in cohesive soils

the relationship between compressive stress (p)and the corresponding shear strength (s) canbe represented by an empirical equation, which

89

is known as COULOMB's equation:s=c+p tan cp (1)where c: shear cohesion as a constantcp: angle of shear resistance (internal friction)

The symbol c represents shear cohesion asa constant, which is equal to the shear strengthwhen the compressive stress is equal to zero.In the equation 0), if s=O, then C=-Po tan cpor Po = -c/tan cp, where Po is equivalent to thesoil internal stress at the shear surface. Sucha relation is illustrated in Figure 1.

..c.

c

; Shear strength line1(/ )Shear Tcohesion(C

L 0 Compressive stress (P)Initial stress(Po)Fig. 1. Shear strength factors.

It is thought that there is no force which isable to act as internal stress without soil cohesion. Such an internal stress correspondingto OL in Figure 1 was described as initial stressby JUMJKI(5). Consequentry, it is reasonable toassume that soil cohesion is equal to initialstress calculated from shear test under the samesoil condition. The assumption may be confirmed by two kinds of experiments. First. sincesieved soil does not develop soil cohesion undersaturated condition according to the soil cohesion theory based on surface-tension force,shear strength may be almost the same as thatof cohesionless soil. Therefore, the correspond-

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H. YOKOI

ing equation of the shear strength undersaturated condition may be expressed in thefollowing formula:

s=p tan tpSuch a problem was described by TERZAGHI(8) as an interesting phenomenon associatedwith change of water content and with degreeof permeability. In the second place, underunsaturated condition, soil cohesion directlymeasured by the metal-wedge method shouldhave a firm relation to initial stress calculatedfrom the shear test. However, as will be discussed later, it is very difficult to measure theabsolute value of soil cohesion by the metalwedge method.

Materials and MethodsSoil Samples1. Kibushi clay is porcelain clay taken fromTajimi city, in Gifu Prefecture. This sample is

expected to have rather strong soil cohesion.2. Kashima soil is Ando soil (volcanic ash soil)

from Ibaragi Prefecture. This sample is expectedto have weak soil cohesion, according to YAMANAKA'sstudies (10).

Some soil properties ar e shown in Table 1. Th esoil samples were previously air-dried and passedthrough a 2 mm sieve.

Table I. Properties of samplesSamples Mechanical composition Soil Organic

Coarse Fine Siltsand sandtexture carbonClay

0',0

Kibushi 0.2clay 7.S 27.6 64.4 HC 0.4Kashi 6.0 31. 4 44.3 IS.3 C L 7.0rna soil

Experimental methodsShear strength: Th e apparatus used was a one

dimentional shear apparatus (direct shear apparatus).The trimming case was a cylindrical metal, 5 cm ininside diameter, and 1. 2 cm in height. Th e area ofshear surface was about 20 cm'. Th e experimentalprocedure was carried out with reference to Methodsof Soil Analysis (7). Th e compressive stresses ap plied were from 1 Kg/cm' to 5 Kg, cm'. Th e moisture contents of the tested samples were determined

90

after the experiments.Soil cohesion: Th e force necessary to cause a

metal-wedge to penetrate th e soil mass was d e -termnied with the apparatus devised by YAMANAKA(10). Th e trimming case was a sectional metal boxwith inside dimensions of 6x 2x 1 ems. The area o fth e surface of rupture was about 2 cm 2 an d wasmeasured after each experiment. Th e moisture contents of th e tested samples were also determinedafter the experiments.

Pre-treatment of soil sample: The air-dried soilswere wetted near to the moisture content of th eupper plastic limit an d were allowed to stand fo rabout a day and then after sufficient paddling thesoil were taken in th e trimming cases fo r eacbexperiment.

Results and DiscussionSaturated conditionThe trimmed soil was wetted sufficiently byupward capillary movement of water an d the

shear strength was measured. Th e shearstrengths and the soil moisture contents areshown in Table 2 and Figure 2. As a matter of

432

VI o -::;::.:0 1 2 3 4 5

p (kg/em')Fig. 2. Shear strength lines under saturated

condition.Table 2. Shear strength under saturated

conditionCompressive Kibushi clay Kashima soilstress Shear Moisture Shear Moisturekg/em2 strength content strength contentkg/ern' % kg/ern' ~ t " - ~ - - - - - - ~ 1 0.59 33.5 0.64 71. 3

2 1.11 32.7 1. 23 68.03 l.64 31. 5 l. 75 67.24 2.14 29.6 2.31 65.45 2.65 29.1 2.74 64.2

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SOIL COHESION AND SHEAR STRENGTH

Table 3. Shear strength of Kibushi clay under unsaturated condition----- -- - - - ----------- - - --------Compressive Shear Moisturestress strength contentkg/em' kg/em' %-----2.01 30.02 2. 75 29.83 1. 69 29.44 2.05 29.05 2.52 28.8

course, soil moisture content decreased with theincrease of compressive stress, and bulk densityof the sheared soils increased with the increaseof compressive stress, because excess waterwas drained through porous plate. As shownin Figure 2, the shear strength lines obtainedare almost straight for both soils, and it isfound that the shear strength lines pass throughvery near the point of origin on the abscissa.This fact shows that initial stresses calculatedfrom shear experiments under saturated condi-tion are almost equal to zero, and does supportthe assumption mentioned above; that is, shearstrength of sieved soil under saturated condi-tion is almost the same as that of cohesion lesssoil.In connection with this problem, it was foundthat many soils except for very coarse soilsgave almost the same value of shear strengthunder saturated condition; the average shearstrength obtained under the stress of 1 kg/cm2was 0.627 kg/cm2 and the coefficient of varia-tion was about 7 % (2). Although shear strengthwas expected to be affected by soil propertiessuch as clay mineral composition, humus con-tent, etc., even under saturated condition, theresultes showed no apparent difference amongsoils. For this reason, it is assumed that shearstrength which is regarded as frictional resist-ance, is affected mainly by water films exist-ing between adjacent particles and there is noapparent difference in frictional resistance owingto water conditions of saturated soils that con-tain considerable amount of colloidal materialssuch as clay, humus, etc . Based on theseviews, further investigations are now carriedouL

Unsaturated conditionTrimmed soil was dried slowly in a glass

Shear Moisture Shear Moisturestrength content strength contentkg/em' ~ ' O kg/em' %1. 702.262.823.293.86

-------25.7 3.68 19.625.2 4.21 20.624.8 4.81 20.325.0 5.43 19.925.5 6.21 20.1

Table 4. Shear strength of Kashima soilunder unsaturated condition

Compressive Shear Moisture Shear Moisturestress strength content strength content

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kg/cm' kg/em' % kg/cm' %12345

'"'eu"--bI)C-UI

5432

0 0

O. 75 62.6 0.861. 25 59.6 1. 621. 73 61.1 2.392.40 58.6 2.992.79 58.5 3.51

/' .'

..: v.::(0/ : ./v:.,..-234 5

p (kg/em')

37.535.637.138.839.6

Fig. 3. Shear strength lines of Kibushi clayunder unsaturated condition.

432

00 2 3 4 5p (kg/cm')

Fig. 4. Shear strength lines of Kashima soilunder unsaturated condition.

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H. YOKOI

Table 5. Soil cohesionKibushi clay Kashima soil-- - - - - - ~ Moisture Soil Moisture Soilcontent cohesion content cohesion

00 kgcm2 0',0 kg/cm2- ----------------0.0 6.5 0.0

2.6 .t.8 8.35.3 4.3 25.0 0.2

17.5 3.8 38.5 0.219.9 2.6 48.7 0.422.3 1.4 60.4 0.425.1 l. 1 67.0 0.527.4 0.7 69.6 0.230.4 0.6Soil cohesion was calculated by the followingformula.c = W where W: measured weightA A: surface area.

desiccator without any desiccant to prevent theformation of cracks owing to rapid drying.Furthermore, by this treatment, the authorminimized the error due to the variation ofmoisture content of the samples tested at thesame time. The results obtained from the shearexperiments are shown in Tables 3 and 4, andFigures 3 and 4 respectively, and those fromsoil cohesion experiments are shown in Table5. As shown in Figures 3 and 4, the shearstrength lines are almost straight with theexception of line C-2. Line C-2 representingslightly unsaturated Kibushi clay before theexperiment, seems to be composed of twostraight lines. The part of line C-2 to the rightunder compressive stresses more than 3 kg/cm 2is very similar to the line obtained undersaturated condition. I t is understood for thisreason, from the results of moisture contentsshown in Table 3, that an application of strongcompression brought the soil sample to saturatedcondition.Simply speaking, both soil cohesion and shearstrength of Kibushi clay are stronger than thoseof Kashima soil. In other words, it is highlyprobable, as previously suggested, that Kibushiclay which has strong soil cohesion under driedcondition has strong shear strength, and thatKashima soil which has only weak soil cohesioneven under dried condition, owing to the property of volcanic ash soil, has rather weak shear

92

strength. From those results, the theoreticalassumption mentioned above seems to be con-firmed qualitatively.The shear cohesion and initial stress calcu-lated from the results of the shear experiments

are shown in Table 6. In the case of KashimaTable 6. Comparison between soil cohesionand shear constant

Sample Exp. No Soil Shear Initialsoil cohesion cohesion stress2 0.6 1.2 1.3Kibushi 3 1.1 1.1 2.0clay 4 2.6 3.1 5.3

soil, both soil cohesion and shear cohesion areso weak that it is impossible to compare themexactly. As a matter of course, shear strengthlines S-2 and S-3 pass through very near thepoint of origin owing to weak soil cohesion asin the case of saturated soils. In the case ofKibushi clay, it is found that soil cohesion isclosely related to initial stress; however, thesoil cohesion values were about half of theinitial stresses. For this reason, it was presum-ed that the angle of extreme edge affected.the experimental results of soil cohesion, andthe following tests were carried out.Although the metal-Wedge method is basedupon the dynamics of the wedge, the angle o fextreme edge is very important for experimentaldetermination and one can not determine ex-actly the effective angle of extreme edge. Theeffective angle of extreme edge may not be 80sharp as the angle of the whole wedge bodybut rather blunt, and perhaps, the force nec-essary to cause the metal-wedge to penetratethe soil mass could not be equal to the forcecalculated from using the angle of the wholewedge body. The necessary force is expressedin the following formula on the basis of thedynamics of the wedge in general:Wc= 2A tan fJ/2

where c: soil cohesionW: measured weightA: surface areafJ: angle of wedge

The results obtained from the experiments

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SOIL COHESION AND SHEAR STRENGTHTable 7. Comparison of soil cohesion in

relation to angle of wedgeSoil cohesionoilmoisturecontent

013 wedge 30 wedge 60 wedge

5.520.430.8

kg/cm2 kg/cm2 kg/cm 24.21.80.5

4.41. 90.6

6.12. 80. 9

for reference; tan 13/2=0.114tan 30/2=0.268 tan 60/2=0.577.

of soil cohesion by the use of three kinds ofwedges are shown in Table 7. The force determined by the use of 13 wedge is theoreticallyexpected to be two times larger than that measured by the use of 30 wedge. As shown inTable 7, however, the differences between theforces measured by the use of 13 wedge andthose of 30 wedge are very small, bu t theforces measured by the use of 60 wedge aremuch larger. From these results and otherresults described above, it is thought that theeffective angle of extreme edge of 13 wedge,which has been used up to the present time,is larger than 13, and that the correspondingtan 0/2 may be nearly equal to 0.25, at leastfor this test. However, it is necessary to notethat the use of a blunt wedge is no t alwaysprofitable for the measurement of soil cohesionbecause the adhesion of soil to the wedge andthe compression by a blunt wedge affect themeasurement of soil cohesion. For the present,therefore, it is experimentally feasible thatsoil cohesion measured by 13 metal-wedgecould be calculated by the following formula:

KWc=--p;where K is constant owing to the effectiveangle of th e used wedge. From these results,the soil cohesion values determined by themetal-wedge method can not be compared exactly with the initial stresses. However, it ispossible to assume that soil cohesion acts asinitial stress equivalent to compressive stress.For further determinations, detailed studiesusing many kinds of artifical and natural soilsare being carried out.

SummaryThe definition of cohesion used in soil physics

93

has not been the same as that in soil mechanics,and it is assumed that there is a firm relationship between soil cohesion and shear cohesion;that is, soil cohesion is equiva lent to initialstress which acts as a compressive stress tothe corresponding shear cohesion.From the experimental results, it is foundthat shear lines under saturated condition passthrough very near the point of origin, becausesieved soils under saturated condition have little soil cohesion, and that soil which hasstrong soil cohesion has strong shear strength.Although the absolute value of soil cohesioncan not be measured owing to the effectiveangle of extreme edge, soil cohesion measuredby the metal-wedge method is closely relatedto initial stress. Consequently, it is probablethat soil cohesion acts as a compressive stressto the corresponding shear cohesion.

AcknowledgmentThe auther is indebted to Dr. K. YAMANA

KA for his theoretical suggestion, and thanksDr. S. MOTOMURA, Mr. Y. AKIYAMA, andMr. S. FUKUZAKURA of the Institute for thehelp they rendered in this investigation.

References1) ATTERBERG, A.: Intern. Mitt. Bodenk., 2, 149(1912)2) BAVER, L. D.: Soil Physics, 3rd ed., John

Wiley & Sons, Inc., New York, 1959, p. 99.3) FISHER, R. A.: j . Agr. Sci., 16, 492 (1926)4) HAINES, W. B. : j . Agr. Sci., 15, 529 (1925)5) JUMIKIS, A. R. : Soil Mechanics, D. Van Nos

trand Company, Inc., New York, 1962, p. 477.6) NICHOLS, M. L. : Agr. Eng., 12, 259 (1931)7) SALLBERG, J. R. : Methods of Soil Analysis,

Part 1, Amer. Soc. of Agr., Inc., USA, 1965,p. 4318) TERZAGHI, K.: Theoretical Soil Mechanics,

John Wiley & Sons, Inc., New York, 1959, p. 7.9) TSCHEBOTARIOFF, G. P.: Soil Mechanics,Foundations, and Earth Structures, Me GrawHill Book Company, Inc., New York, 1951,p. 126

10) YAMANAKA, K.: Bul. Nat. Inst. Agr. Sci.(Japan) Ser. B. No. 6 (1955)

11) YAMANAKA, K. et a!.: Soil Mechanics andFoundation Engineering (japan), 12, 40 (1964)12) YOKOI, H. and FUKUZAKURA, S.: Abstracts of

Annual Meeting, Soc. Sci. Soil and Manui'e,japall., No. 13, 6 (1967)