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  • Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond 99

    Figure 1. Stress-strain curves for sand.

    SHEARING STRENGTH OF SOILS

    SYMBOLS

    Notation Dimensional Analysis

    b = a length Lc = the cohesion intercept M L-1 T-2Ip = the plasticity index

    -P = a force M L T-2u = the pore fluid pressure ML-1 T-2 = an angle Angle1 = shear strength reduction factor related to time effects -2 = shear strength reduction factor related to fissuring - = the normal stress on a plane M L-1 T-2 = the shearing stress on a plane M L-1 T-2 = the angle of internal friction Angle = an angle related to cohesion Angle

    Subscripts etc. where not identified above = parameter measured in terms of intergranular or effective quantitiesc = preconsolidation valuescu = consolidated undrained parametersd = drained test parameters i.e. dissipated pore pressurese = so-called true parametersf = failure valuesmax = maximum valuesn = normal to plane valuesnc = normally consolidated valueso = overburden valuesu = unconsolidated undrained test parameters1 = major principal values2 = intermediate principal values3 = minor principal values

    1. INTRODUCTIONStability analysis in geotechnical engineering includes all studies which

    attempt to determine whether or not the average shearing strength of soilover the assumed failure surface has a sufficient factor of safety againstfailure. Basically such studies consist of comparisons between all theforces which are or may act to cause failure and the resisting forcesprovided by the soil's shearing strength.

    The shearing strength of a soil sample is generally defined as itsmaximum resistance to shearing forces. In special cases an ultimate,residual or post peak value is used. The peak and ultimate values areshown on the normal stress-strain plot of test results in Figure 1. Theresidual value (Skempton, 1964) may be taken as the value recorded on apresheared sample or on an intact sample which is subject to excessiveshearing, such as in a ring shear apparatus (Bishop et al, 1971), where thesoil particles can rearrange themselves into preferred orientations.Normally stability problems are solved by approximating the stress-strainbehaviour by an ideal rigid-plastic material as shown in Figure 2. Wheresuch an assumption is made the stability can be expressed in terms ofsome definition of the shearing strength f alone (this need not be amaximum value of ). In actual fact the failure strength varies with thenormal stress on the failure plane. Coulomb is credited with being thefirst person to express this variablefailure strength in terms of two engineering properties or parameters,namely:(1) cohesion (c), or the resistance due to the forces tending to bond or

    hold the soil particles together in a solid mass;(2) internal friction (), or the rate of change of the resistance due to an

    increase of normal stress (n) on the failure plane.

    Coulomb's original shearing strength equation or Law is shown onFigure 3 and was expressed in terms of total stresses by

    f ' c % n tan (1)

    It should be noted that unless = 0 the value of f is not equal to themaximum shearing strength stress max. This relationship expresses boththe variation of strength of a single sample to changing external stressesor the locus of test results using different samples of the same type soil.Another point worth noting is that the equation must have some limitationotherwise soil slopes with slope angles less than could theoretically beinfinitely high. Particle crushing will obviously occur first.

  • Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond 100

    Figure 2. Stress-strain curve for ideal rigid-plastic material.

    Figure 3. Coulomb's law.

    Figure 4. Hvorslev's concept of true cohesion and frictionangle (e.g. Gibson, 1953)

    2. EFFECTIVE STRESS CONCEPTUnfortunately the values of c and were not found to be constant

    values. Their usefulness was not universally accepted until Terzaghi'sconcept of effective intergranular stress () was postulated. This relatedthe soil's behaviour to the difference between the total stresses () and soilfluid pressure (u) by

    ' & u (2)In accordance with Terzaghi's concept the shearing strength of a soil maybe expressed as

    f ' c % (n & u) tan 'c % n tan (3)

    where the primes signify that the soil parameters are determined usingeffective stresses or equivalent intergranular stresses.

    3. TRUE PARAMETER CONCEPTHvorslev (e.g. Gibson, 1953) working with multiple samples of

    remoulded soils, showed that the cohesion intercept was dependent on themoisture or water content of the failing soil sample. This led to what hasbecome termed the true cohesion (ce) and true angle of internal friction(e) which are determined as shown in Figure 4 and a restatement ofequation (1) by

    f ' ce % n tan e (4)

    ce ' nc tan e (5)

    where nc is the effective intergranular pressure which would have to beapplied normally to the failure plane of a normally consolidated sample ofthe same soil to give a failure water content of the same value as thefailing sample, and e is an angle which relates the true cohesion to nc.Hvorslev's proposals are useful as an academic model for soil strength butare normally not used in practice.

    4. PRACTICAL CONSIDERATIONSIn nature soil has been affected by weathering and other phenomenon

    so that fundamental relationships, such as suggested by Hvorslev, have notfound general acceptance in practical engineering. In addition theshearing strength of soil is, like most other engineering material,dependent on factors such as creep and fatigue. For these and other morecomplex reasons the shearing strength parameters used in practice aregenerally based on simplifying conditions of determining the stabilityagainst immediate failure and (or) long term failure depending on the

  • Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond 101

    Figure 5. Elemental stresses on random plane.

    nature of the problem.

    In the analysis of immediate stability it is assumed that the soil has avery low permeability and the moisture content of the soil will remainunchanged during the course of the engineering works. For suchconditions the soil is tested rapidly enough to ensure undrained conditions.Interpretation of the test results is then based on considering the soil as asingle phase material much as most other engineering materials (i.e. steel,concrete and the like). Analysis is then performed by working in totalstresses. The shearing strength equation for immediate, total stress orundrained stability analysis for a soil at a given moisture content

    f ' cu % n tan u (6)

    where cu = the undrained cohesionu = the undrained angle of internal frictionIt has been shown by Skempton (1948a) and Bishop and Eden (1951)

    that when soil samples at the same moisture content and same stresshistory are fully saturated and the pore fluid and soil solids areincompressible in comparison with the soil skeleton

    u ' 0 (7)

    This result is extensively used when dealing with immediate stabilityproblems involving saturated or near saturated clays and relativelyimpermeable saturated silts for which, very simply (further correctionsmay be required prior to application) for the identical saturated samples

    f ' cu (8)

    For saturated samples with different moisture contents cu would, of course,vary. Thus in a natural soil deposit cu may vary with depth.

    On the other hand where the permeability of the soil is high and rapiddissipation of pore fluid pressures occur, such as with clean sands andgravel, or in low permeability soils where a change in moisture content islikely during loading, the shearing strength is expressed in terms ofeffective intergranular stresses as given by equation (3). The parametersare sometimes referred to as drained (more logically dissipated pore fluidpressure) parameters

    f ' cd % n tan d (9)

    In a drained test the pore fluid pressures are zero (or used as the zerodatum when not zero) so that

    cd ' c (10)

    n ' n (u ' 0) (11)

    d ' (12)

    Thus equation (9) becomes identical to equation (3) or

    f ' c % (n & u) tan (13)

    It should be clearly understood that the term "drained" refers to thedissipation of pore fluid pressures and not to the drainage under gravityof pore fluid from the soil. Basically what is being referred to is the openposition of the drainage cock leading to the pore water of the soil. Withthe cock open pore water may (drain) enter or leave the sample to maintainzero pore pressure. A fully saturated soil specimen subject to a drainedlaboratory test remains fully saturated. In clean sands, gravels andnormally consolidated clays c is generally close to and assumed to bezero.

    5. THEORY VERSUS APPLICATIONFrom a simple engineering mechanics point of view it is appropriate to

    develop theoretical engineering solutions in terms of Coulomb's

    expression for shearing strength (equation (1)) and then apply the resultto practical problems in terms of short term undrained or total stressparameters (equation (6)) or long term drained or effective stressparameters (equation (13)).

    6. RELATIONSHIP BETWEEN PRINCIPAL STRESSES ANDFAILURE SHEARING STRESS

    The relationship between the principal major and minor stress andfailure shearing stress using the Coulomb failure criteria is illustrated byresolution of the forces on the element shown in Figure 5. (Note that theintermediate principal stress has no theoretical effect on the Coulombfailure criteria).

    Resolving forces (P) normal to any assumed plane making an angle with the plane on which the major principal stress acts

    Pn ' P1 cos % P3 sin (14)

    nb

    cos ' 1 b cos % 3 b tan sin (15)

    n ' 1 cos2 % 3 sin2 (16)where subscripts 1 and 3 refer to major and minor principal values, and bis a length over which P1 acts.

    Resolving forces parallel to any assumed plane to find the shear forceP on the plane

    P ' P1 sin & P3 cos (17)

    bcos

    '1 b sin & 3 b tan cos

    (18)

    ' (1 & 3) sin cos (19)

    If the assumed plane is the failure plane and Coulomb's relationship istaken as being valid on the plane

    ' f ' c % n tan (20)

    Substituting equation (19) with suitable subscripts to indicate failure andequation (16) for n in equation (20)

    (1 & 3)f sin cos '

    c % [(1)f cos2 % (3)f sin2] tan (21)

    1 ' 3 %c % 3 tan

    sin cos & cos2 tan at failure

    (22)

  • Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond 102

    Figure 6. Failure stress interrelationships from Mohr'scircle.

    Figure 7. Principle of direct soil-shear testing apparatus.

    The plane of least resistance would make this value of 1 a minimumvalue to produce failure or

    sin cos & cos2 tan ' Maximum (23)

    To find the location of it is necessary to differentiate with respect to and equate to zero.

    dd

    (sin cos & cos2 tan ) ' 0 (24)

    cos2 ' sin2 % 2 cos sin tan ' 0

    (25)

    & cot 2 ' tan (26)

    9 ' 4%

    2' 45E %

    2 (27)

    Substituting back into equation (22) gives (at failure)

    1 ' 3 N % 2 c N (28)

    where

    N '1 % sin 1 & sin ' tan2 (45 %

    2)

    ' 1tan2 (45 &

    2)

    (29)

    Also substituting equation (27) in equation (19)

    f' (1&3)f sin (45%2

    )cos(45% 2

    ) (30)

    only when = 0 does the Coulomb failure shearing stress equal themaximum shearing stress. This may easily be seen on the Mohr circleshown in Figure 6. The Mohr circle is a useful method of verifying theabove equations. It may be seen that the radius of the Mohr circle whichmust touch the failure locus shown in Figure 6 is (at failure)

    1 & 32

    ' { ctan

    % 1 % 32

    } sin (31)

    which may be rearranged to give equation (28).

    For the case of a saturated soil tested in an undrained condition u = 0.The total stress criterion using equation (31) then gives

    f ' cu ' {1 & 3

    2}f (32)

    The other simple condition is for clean sands and gravels where c = 0.The effective stress criterion using equation (31) then gives

    13

    ' N (33)

    7. MEASUREMENT OF SHEARING STRENGTHThe shearing strength of a soil can be determined in situ or in the

    laboratory. In situ tests are often preferred in the practice of engineeringbecause great care and judgement are required in the sampling,transportation, storage and handling of laboratory samples prior to testing.Furthermore, cohesionless soils are badly disturbed during sampling andhandling. Such disturbance makes correlations between laboratory testingand field performance questionable. Fortunately for granular soil c maybe taken as zero and field testing is then correlated with only. The highpermeability of most granular soil generally means that undrained failureis unlikely. For cohesive soils, however, the long term parameters cannotbe satisfactorily determined in situ and these soils are often sampled andtested in the laboratory. Laboratory testing must also be relied on todetermine the parameters of placed and compacted soils where testing ofthese soils is required.

    Although c and are not true constants in practice they are generallyregarded as constant at any given point (or depth) over the stress rangelikely to be encountered in the field problem being analyzed.Consequently, testing should be carried out at stress magnitudesappropriate to the solution and location being considered. For example ina u = 0 analysis cu is constant at a given depth but may vary, oftenlinearly, with depth.

    The values of c and , if assumed constant may be determined bycarrying out two or more (generally three is considered minimum) testswith different normal pressures acting on the plane of shear failure. If theshearing strength on the failure plane is measured directly, as in the shearbox text shown in Figure 7, the shearing strength may be plotted directlyagainst the normal stress on the induced failure plane to give c and asshown in Figure 3.

    Alternatively where the external stresses are controlled, such as theprincipal stresses in the triaxial tests shown in Figure 8, the results maybe plotted on a Mohr circle as shown in Figure 9. Once two or morefailure circles are drawn a common tangent determines the values of c and.

    Normally the triaxial test is done in compression with 2 = 3 howeveran extension test is sometimes done in research or expensive projectswhere warranted. In such cases 1 = 2. In either case the value of 2 hasno theoretical effect on the Coulomb failure criteria, although in fact somedifferences have been noted (Bishop, 1966). Because of these differencesa number of different laboratory testing equipment are available forresearch and special projects. The shear box and triaxial test equipment

  • Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond 103

    Figure 8. Stresses acting on triaxial compression sample.

    Figure 11. Principle of vane shear apparatus.

    Figure 10. Experimental determination of c and .

    Figure 11. Main characteristics of standard penetration test.

    are the mainstay of a commercial laboratory particularly where both c and are required. A special form of triaxial test where 3 = 0 is known as theunconfined compression test.

    Where either c or is assumed several tests are available both for insitu and laboratory testing. The most common in situ tests are the vaneshear test shown in Figure 10 for use in soft clays to measure cu (u = 0)and the standard penetration test shown in Figure 11 for use in sandswhere the number of blows of a standard sampling spoon is related to (c = 0). Other common field equipment includes the static or dynamiccone penetrometer for sands (Sanglerot, 1972) and the pressure meter(Baguelin et al, 1978) for stiff clays and soft rocks. Numerous more

    complex equipment are also available (e.g. the plate test and in situ shearbox used by Marsland, 1971).

    8. TYPES OF SHEAR TESTINGThree main types of tests are performed on soils dependent on the

    dissipation of pore pressures (termed drainage) from the specimens undertest.

    (A) Immediate or Undrained Test (also known as Quick Test): thesamples are subject to an applied pressure (under conditions of nodrainage) and as quickly thereafter sheared. Care is taken to prevent (infact this is difficult) any dissipation of pore pressure since the resultsassume none has occurred. The test is most applicable to clays with lowpermeability where drainage is very slow and negligible if the test isperformed quickly. If the soil samples being tested have the same stresshistory and are fully saturated then at failure u = 0 as shown in Figure12. This is one way of establishing that a soil is fully saturated. Clayswith fine sand lenses where cavitation of air from the pore fluid oftenoccurs prior to failure and partially saturated soils with high degrees ofsaturation generally give low values of u. The undrained immediatestrength is also obtained in situ with the vane equipment. This test is mostapplicable to soft saturated soils. For such a result = 0 is assumed.Similarly in the laboratory when the unconfined compression test 3 = 0is done u = 0 is assumed and (1 - 3) = 2 cu. For different sets of samples(i.e. from different depths) different values of cu will obviously beobtained.

    (B) Consolidated Undrained Tests: the samples are allowed toconsolidate under an applied pressure. Once equilibrium is reached thedrainage cock is closed and they are then sheared at constant moisturecontent under conditions of no drainage. The total stress parameters,obtained by using different consolidation pressures, ccu, cu are of littlevalue in practice so pore fluid pressure is generally measured during thetest. Where the pore fluid pressures are measured the test must beperformed slow enough to allow equalisation of pore pressure (normally95%) since the sample may not be perfectly uniform in composition orexternal loading. This allows the effective or long term strengthparameters c and to be obtained as shown in Figure 13. Because ofthe slow rate of consolidation of soils having low permeability this test isgenerally preferred for obtaining the c and values of clays. There isno equivalent in situ test. The value of c and is affected by theconsolidation pressure used in relationship to the soil's preconsolidationpressure. When the consolidation pressure greatly exceeds thepreconsolidation pressure c is normally observed to be close to zerowhich is a characteristic of normally consolidated remoulded clays.

    (C) Drained Tests: the samples are allowed to consolidate as in theconsolidated undrained test and then sheared slowly enough that anyexcess pore pressures dissipate completely (normally 95% dissipation is

  • Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond 104

    Figure 12. Undrained results on saturated soils withidentical histories.

    Figure 13. Consolidated undrained test results.

    Figure 14. Triaxial compression tests on crock ballast(e.g. Raymond and Davies, 1978)

    Figure 15. Typical shearing strength of rockfill(e.g. Leps, 1970).

    acceptable). In highly permeable material this test is preferred because ofthe difficulty of ensuring no escape of water in the consolidated undrainedtest. In soils of low permeability such as clays the time required to ensure95% dissipation of all pore pressures becomes excessive. This test isparticularly suited for granular cohesionless materials. In the field it isperformed indirectly in the form of a standard penetration test (SPT) orcone penetration test in which case c = 0 is assumed and correlations existto establish . Since the effective and total stresses are the same, resultssimilar to the effective stress construction shown in Figure 13 areobtained. Small differences, which are generally neglected, sometimesexist.

    9. SHEARING STRENGTH OF COHESIONLESS SOILSThe mobilisation of shearing resistance of cohesionless soils is

    illustrated by the stress-strain curves shown in Figure 1. For densegranular materials the resistance increases to a peak value and thendecreases as the strain increases further to an ultimate value. During thispost peak period the soil particles gradually loosen to a conditionapproximately the same as that of the granular material in the loose state.The value of for loose granular soil often being called the angle ofrepose. Several tests conducted at different confining pressures on loose

    material generally result in c = 0. On dense material, as shown in Figure14, the anomaly c 0 is often obtained due to the fact that for densecohesionless soils tends to decrease with increasing confining pressure.Indeed if the confining pressure is excessively too high severe particlecrushing occurs. The decrease in is important for high earth dams andthe like. Under normal foundation engineering loads c = 0 is generallyassumed. Thus from one test result

    For dense clean granular soils, particularly gravel sized material andlarger, this often leads to the nonsensical result of > 45E. This isclearly not the friction between two surfaces but includes energy requiredfor dilation. Nevertheless, because of established usage of the c = 0approximation and the fact that the energy to cause dilation would berequired to cause failure in situ this convention is maintained herein. Anincrease in density (decrease in porosity or void ratio) at a constant valueof n thus causes an increase in The effect of increasing the confiningpressure on granular materials at a given density results in a decreasingvalue of as shown by Taylor (1948) for sands (Figure 15) and by Leps(1970) for larger size particles (Figure 16). Leslie (1963) has shown thatwell (or broadly) graded granular soil has a higher value of than auniformly graded (single sized or well sorted) soil with the samemaximum particle size. In addition a higher is recorded for the largerparticle sized soils of two similarly graded soils. Soils composed ofangular particles generally have higher values of than soils composedof rounded particles as shown in Table 1 (Sowers and Sowers 1951).Typical values of for granular soils loaded at normal engineeringfoundation stresses are given in Table 2. These values would decreaseunder the high pressures associated with high dams and the like.

    In the field values of are normally obtained from either the standardpenetration test (SPT) or cone penetrometer. Typical test correlationvalues for sands at n = 200 kPa are shown in Table 3. The values of should be decreased 5E for non-plastic (plastic index less than 6) silt sizesoils and silty sands and increased 5E for gravel sand mixtures. Silts andsands with plastic fines should be evaluated as cohesive soils.

    ' tan&1 ( fn

    ) (34)

    10. SHEARING STRENGTH OF COHESIVE SOILSThe selection of the shearing strength parameters appropriate to an

    engineering works built in cohesive soils is one of the most complex anddifficult decisions facing the Geotechnical engineer. It is the intent herein

  • Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond 105

    Table 1. Effect of Angularity and Grading on Peak EffectiveFriction Angle of Coarse Sand in Degrees

    (e.g. Sowers and Sowers, 1951).

    Shape and Grading Symbol Loose Dense

    Rounded, UniformRounded, Well Graded

    Angular, UniformAngular, Well Graded

    SPSWSPSW

    30343539

    37404345

    Figure 16. Typical friction angles from direct shear tests onsub-rounded sand (e.g. Taylor, 1948).

    Figure 17. Relation between sensitivity and saltconcentration in pore-water of marine clays

    (e.g. Skempton, 1953).

    to deal only with the strength of cohesive soils in a simplistic manner.Cohesive soil properties need selection for three types of common analysisdepending on the appropriateness of the problem

    (i) the total stress or undrained stability, which for a saturated soil, yieldssome appropriate proportion of cu 0 and u = 0,

    (ii) the peak effective stress analysis in terms of some appropriateproportion of c and

    (iii) the residual effective stress analysis in terms of cr and r.

    11. STRENGTH CLASSIFICATION OF COHESIVE SOILSBecause cohesive soils often present serious stability problems the

    further classification of these soils beyond that established using theUnified System is most common. Three main characteristics of immediateinterest in any stability analysis are(i) Variation of undrained shearing strength cu of the soil deposit(ii) Nature of fissuring within the soil deposit(iii) Sensitivity of the various soil layers within the deposit.

    Other factors such as anisotropy are also important but are generally notspecifically determined in routine commercial investigations.

    The undrained strength classification, often termed consistency, variesas shown in Table 4 from very soft to hard. These terms have norelationship to stress-strain properties since soft clays may, in some cases,be extremely brittle. It will be noted that the strength range covered byeach higher consistency level is twice the range and values of the directlylower level.

    Very soft and soft cohesive soils are generally intact and show little orno fissuring. Stiff to hard consistency clays, on the other hand, are veryfrequently fissured. Indeed as the strength increases some of the fissuresmay become classified as joints and these hard soils becomeindistinguishable from soft rocks. Clearly there is no clear cut divisionbetween these definitions and great care must be exercised in dealingwith problems where fissures or joints are likely to be important in anystability analysis. Medium strength clays are likely to be either intact,showing no signs of a fissured pattern, or be clearly fissured. Theirbehaviour will be very much dependent on their physical nature.

    The sensitivity of a cohesive soil is defined as the ratio of itsundisturbed undrained strength to the remoulded undrained strength of thesame soil. A sensitivity classification (Skempton and Northey, 1952) maybe made and is shown in Table 5. It should be clearly understood thatdetermination of a soil's sensitivity is not standardized. For the highervalues of sensitivity there will normally be considerable differences in thevalues determined in the laboratory and in the field. The value determinedby field vane is often less than that obtained by a laboratory triaxial or,more commonly, unconfined compression test. Further complicationsoccur due to the fact that sensitive clays show different degrees of strengthregain (known as thixotropic strength regain or thixotropy) afterremoulding. Thus the time between remoulding and testing may have anappreciable effect on the measured value of sensitivity.

    One of the best known type of clay deposits exhibiting highsensitivities are those deposited in a sea water environment and thenleached by fresh water. Sensitivity in these deposits are sometimes relatedto residual salt content (Figure 17).

  • Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond 106

    Table 4. Consistency of Saturated Clay Soils

    Consistency UnconfinedCompressiveStrength-kPa

    ShearingStrength

    (kPa)

    StandardPenetration

    Blows/300 mm

    Very SoftSoftMedium/FirmStiff Very StiffHard

    < 25 25 - 50 50 - 100100 - 200200 - 400

    > 400

    < 12.512.5 - 25 25 - 50

    50 - 100100 - 200

    > 200

    < 2 2 - 4 4 - 8 8 - 1515 - 30 > 30

    Table 5. Sensitivity of Clays(after Skempton and Northey, 1952).

    Classification Strength Ratio

    InsensitiveLow Sensitivity

    Medium SensitivitySensitive

    Extra SensitiveQuick

    < 11 - 22 - 44 - 88 - 16> 16

    Table 2. Typical Values of Frictional Angles for Granular Soils for n = 100 kPa

    Soil Type Symbol Loose Medium Dense

    Silt (non-plastic)Uniform Sand and Silty SandWell Graded SandGravel

    ML, MH (PI 0.8

    < 44 - 10

    10 - 3030 - 50

    > 50

    22 - 44 - 12

    12 - 20> 20

    < 2828 - 3030 - 3737 - 42

    > 42

    * Decreases 5E for non-plastic silts (ML,MH with PI < 6) and silty sands (SM)Increase 5E for gravel or gravel sand mixtures (GW,GP,GM)

    12. STRENGTH CHARACTERISTICS IN SOFT CLAYSVery soft and soft clays are generally intact, rarely exhibiting any

    fissures. They have a liquidity index over 0.5 depending on theirsensitivity and strength. Sensitive soils have a liquidity index close to orgreater than 1.0 and insensitive soils a liquidity index less than 1.0. Theliquidity index decreases as the strength (consistency) increases and forstiff and very stiff clays reduces to a value close to zero.

    In a new, fresh or young deposit of uniform, fully consolidated soil theeffective overburden pressure in most practical cases, increases relativelyuniformly with depth (Skempton, 1948a) though, due to positive ornegative artisan water pressure, this may be slower or faster than given bya static water table assumption. In such a normally consolidated soildeposit this uniform increase in effective overburden pressure (o) isassociated with a decrease in moisture content of the soil and a uniformincrease in undrained shearing strength (cu). Note that if three samples ofsoil from the same depth are tested in an unconsolidated undrained test u= 0, cu = constant for the given depth. On the other hand if a series ofsuch sets of tests are performed, each set from different depths, and thevalue of cu for each depth is compared with the effective overburden (o)then (in practice cu is obtained with an in situ vane test or unconfinedcompression test)

    cuo

    ' constant (35)

    This very important relationship is characteristic of young normallyconsolidated clay deposits. Where erosion of a young normallyconsolidated clay deposit has occurred the deposit becomes lightlyoverconsolidated. Because the expansion index of a soil is very muchsmaller than its compression index a small decrease in effective stress (duefor example to erosion) has little effect on the soil's moisture content andon its undrained shearing strength cu at a given depth. It does, howeverhave an effect on the effective overburden pressure. In lightlyoverconsolidated young deposits of clay equation (35) must be modifiedto

    cuc

    ' constant (36)

    where c = the preconsolidation pressure (in effective stresses)

    As the amount of erosion increases the assumption of no change in cuat a given depth becomes less valid and thus equation (36) decreases incorrectness.

  • Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond 107

    Figure 18. Example of 'aged' normally consolidated clay(e.g. Raymond, 1968).

    Figure 19. Typical characteristic values of glacial and postglacial normally to lightly overconsolidated clays

    (e.g. Bjerrum, 1973).

    Figure 20. Post failure factors of safety from undrained totalstress analysis using full values of cu (e.g. Bjerrum, 1973)

    Figure 21. Variation of ' with plasticity index for normallyconsolidated remoulded clays (e.g. Gibson, 1953).

    Normally consolidated clays may exhibit a continuing consolidation atapproximately constant effective stress (known as secondaryconsolidation). This causes a slow decrease in moisture content and aslow increase in shearing strength. This rate of increase in strength hasbeen shown by Bjerrum (1967) to be dependent on the effectiveoverburden pressure such that in some aged normally consolidated claysboth equations (35 and 36) are valid (the constants are different). Fornormally consolidated deposits aged and modified by secondaryconsolidation only, the induced preconsolidation pressure, known asquasi-preconsolidation, increases uniformly with depth so that

    co

    ' constant (37)

    Obviously both equations (35 and 36) will be valid although the constantswill be different. An example of a deposit exhibiting this quasi-preconsolidation due to aging is shown in Figure 18. For glacial and postglacial clays the constants of equations (35 and 36) generally range withthe limits shown in Figure 19.

    Normally consolidated deposits may also be aged by other factors suchas the bonding of particles by chemical action. These soils may also showa relationship expressed by equation (36) and it is common engineeringpractice in normally consolidated and lightly overconsolidated clay tocheck the validity of both equations (35) and (36).

    Very soft and soft clay deposits of saturated or near saturated soils aregenerally intact (do not exhibit fissures). Their short term undrainedstrength is based on u = 0, cu 0 with a correction for the difference inrate of testing (Casagrande and Wilson, 1951), soil anisotropy and otherfactors. The correction to be made to the value of cu has been the subjectof an extensive study by Bjerrum (1973). The correction factor wascorrelated, with sufficient accuracy for practical purposes, to the soil'sPlasticity Index (Ip). This is shown in Figure 20 and may be expressed by

  • Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond 108

    Figure 22. Typical results for fissure clay (e.g. Ward et al.).

    Figure 23. Strength-depth profile for london clay (e.g. Wardet al, 1965).

    1 '1

    0.84 % 0.08 Ip (38)

    where the engineering undrained stability strength is given by

    f ' 1 cu (39)

    It is recommended that 1 should not be taken as greater than 1.LaRochelle et al (1974) have suggested that the value of 1 may beobtained by using the post peak strength (termed, by them, the undrainedresidual) recorded at relatively low strains since this strength could dropdrastically on remoulding. Limited data is presently available on thisprocedure.

    The long term or effective stress stability of very soft and soft normallyconsolidated and lightly overconsolidated clays are based on the peakvalues of c and . Great care must be taken to determine the parametersover the stress range applicable to the field since in aged clays theparameters change quite abruptly if the soils are subject to in situ shearstresses close to failure or close to or above the preconsolidation pressure.According to Bjerrum (1973) the correction for rate of loading is similarin magnitude to that expressed by equation (39).

    f ' 1 (c % n tan ) (40)

    Gibson (1953) has given a tentative relationship for of normallyconsolidated remoulded clays, Figure 21. Further data confirming theguide has been presented by Kenney (1959).

    Sensitive soils are particularly prone to major changes in their longterm strength parameters if loaded close to their preconsolidationpressures along with major changes in their settlement parameters. Thesechanges may result in large long term deformations due to creep and (or)consolidation. Sensitive soils may be treated, in terms of stabilityanalysis, like insensitive soils except that higher factors of safety shouldbe required particularly where failures are likely to cause large andpossible catastrophic deformations.

    13. STRENGTH CHARACTERISTICS OF STIFF TO HARDCLAYS

    Intact, non-fissured very stiff to hard clays may be considered such ararity that where they are reported it is recommended that a careful checkbe undertaken or they be regarded as fissured. Fissured clays exhibitweaknesses along the fissures which in random testing depends on the sizeof specimen. Where selected testing is done results similar to those shownin Figure 22 are obtained. For random testing the strength decreases asthe specimen size increases since larger specimens are more likely toinclude more representative fissures of field scale. Considerable scattermust be expected in a testing program and this is illustrated in Figure 23which shows the strength profile for a deep deposit of very stiff to hardLondon clay.

    Provided that, in the field, water cannot enter the fissures and causerapid softening a total stress or undrained analysis in fissured clay may beperformed in the same way as any other undrained strength analysisexcept that a factor (2) for fissures needs to be included.

    Thus

    f ' 1 2 cu (41)

    Little information is available on the variation in values of 2 for differentsoil types. Generally local or regional information exists where a recordof case histories has been kept by local engineers. Quite often there areGovernmental records since Governments are the major clients dealingwith public works.

    In reality the undrained stability of stiff to hard clays is not generallya major consideration since the strength is more likely to decrease in thelong term. Short term considerations should be centred on preventing thefissures from opening. If the fissures do open then water enters thefissures and softens the clay adjacent to the fissures. The strength of the

  • Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond 109

    Figure 24. Comparison of drained strength of intact andfailed overconsolidated clay (e.g. Skempton, 1964)

    Figure 25. Decrease in r' with increasing clay fraction(e.g. Skempton, 1964)

    Figure 26. Properties of an overconsolidated clay(e.g. Skempton and Larochelle, 1965)

    soil adjacent to the fissures decreases and also controls the 'global'strength of the deposit. Under such conditions the strength drops to valuesclosely associated with the residual strength parameters. This may occurquite rapidly particularly where the prevention of fissure opening cannotbe or is not engineered.

    For long term stability involving increases in compressive lateral forcesit is reasonable to assume that any fissures would remain closed and thelong term stability may be based on peak effective stress parametersmodified for time effects and fissure spacing.

    ' 1 2 (c % n tan ) (42)

    On the other hand when considering the long term stability involvingdecreases in compressive lateral forces the possibility of fissure openingis of major concern. In such circumstances the long term strength shouldbe based on residual effective stress parameters. Since theses should beobtained at very slow rates of loading and along presheared failure planes,as illustrated in Figure 24, no time or fissure coefficients are necessaryand thus

    f ' cr % n tan r (43)

    A rough guide, shown in Figure 25, to the value of r has been presentedby Skempton (1964) who found the value to be very much affected by theclay content of a soil.

    14. STRENGTH CHARACTERISTICS OF MEDIUM TO STIFFCLAYS

    Medium to stiff intact clays should be treated in much the same way assoft and very soft clays. On the other hand medium to stiff fissured claysshould be treated in much the same way as stiff to hard clays. The scatterin strength data may be expected to increase as the strength increases andas the overconsolidation ratio increases. In a strength depth profile ageneral curve in the data, as shown in Figure 26, may be expected due tothe reduction in strength with loss of overburden or increase inoverconsolidation ratio.

    15. SOILS WITH STRUCTURALLY UNSTABLE SOIL FABRICAlthough not stated so far in the discussion of shearing strength it has

    been implicitly assumed that the soils under discussion have a soil fabricstructure which is sufficiently stable that it may be simplisticallymodelled. These soils are characteristic of those found in post glacialregions and in alluvial deposits. They are composed in the main ofrelatively inert, natural or artificially compacted materials which are over90% saturated. Of more complexity are the soils of diverse characteristicsoccurring in climatic regions which produce occasional or continuingaridity. Present fundamental knowledge of these soils is limited but hasbeen summarized by Aitchison and Tokar (1973) under the term knownas 'structurally unstable soils'. There is no clear definition of a'structurally unstable soil' however such soils have stress-strain responseswhich cannot be quantified simply in terms of the applied stress level andan applied stress dependent pore fluid response. The definition includeshigh void ratio sands, silts and clays which are unsaturated and lightlycemented and which collapse or expand on wetting or leaching in theunloaded or lightly loaded condition. They also include those high voidratio soils which may be subject to dynamic loading and respond byliquefaction.

    The solution to a problem on a 'structurally unstable soil' generallytakes on one of the following(a) to design for collapse (swelling) as quantified

  • Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond 110

    (b) to design for avoidance of collapse (swelling) by precluding theoperation of the triggering mechanism

    (c) to induce collapse (swelling) prior to construction(d) to apply soil stabilization processes to modify or remove the

    susceptibility of the soil to collapse (swelling).At the present time a practical scientific approach to the problems

    involving 'structurally unstable soils' has not been developed which isgenerally accepted. This is mainly due to the fact that the hazard to lifeand injury is largely absent in these soils and thus research funding hasbeen noticeably minor. Nevertheless it should be understood that propertydamage due to collapsing and swelling soils in terms of damage to houses,buildings, roads and pipelines is conservatively estimated for the U.S.A.by Jones and Holtz (1973) to be more than twice that due to damage fromfloods, hurricanes, tornadoes and earthquakes.

    These soils will not be dealt with herein but the interested reader isreferred to the State-of-the-Art statements in various Proceedings of theInternational Society of Soil Mechanics and Foundation EngineeringConferences as a suitable starting point.

    16. REFERENCESAitchison, G.D. and Tokar, R.A., (1973) "Problems of Soil Mechanics andConstruction on Soft Clays and Structurally Unstable Soils (Collapsible,Expansive and Others)", Proceedings of the Eighth InternationalConference on Soil Mechanics and Foundation Engineering, Moscow,August 1973, Volume 3, pp. 161-190. (TA710.I6t).

    Baguelin, F., Jezequel, J.F. and Shields, D.H., (1978), "The Pressuremeterand Foundation Engineering", Trans Tech Publications, Germany.(TA775.B22 1987t).

    Bishop, A.W., (1966) "The Strength of Soils as Engineering Materials",Geotechnique, The Institution of Civil Engineers, London, Volume 16,No. 2, June 1966, pp. 91-128. (TA1.G3).

    Bishop, A.W. and Eldin, G., (1950) "Undrained Triaxial Tests onSaturated Sands and Their Significance in the General Theory of ShearStrength", Geotechnique, The Institution of Civil Engineers, London,Volume 2, No. 1, June 1950, pp. 13-32. (TA1.G3).

    Bjerrum, L., (1967) "Engineering Geology of Norwegian Normally-Consolidated Marine Clays as Related to Settlements of Buildings",Geotechnique, The Institution of Civil Engineers, London, Volume 17,No. 2, June 1973, pp. 81-118. (TA1.G3).

    Bjerrum, L., (1973) "Problems of Soil Mechanics and Construction onSoft Clays and Structurally Unstable Soils (Collapsible, Expansive andOthers)", Proceedings of the Eighth International Conference on SoilMechanics and Foundation Engineering, Moscow, August 1973, Volume3, pp. 111-159. (TA710.I6t).

    Casagrande, A. and Wilson, S.D., (1951) "Effect of Rate of Loading onthe Strength of Clays and Shales at Constant Water Content",Geotechnique, The Institution of Civil Engineers, London, Volume 2, No.3, June 1951, pp. 251-263. (TA1.G3).

    Gibson, R.E., (1953) "Experimental Determination of the True Cohesionand True Angle of Internal Friction in Clays", Proceedings of the ThirdInternational Conference on Soil Mechanics and Foundation Engineering,Zurich, Volume 1, August 1953, pp. 126-130. (TA710.I6t).

    Jones, D.E. and Holtz, W.G., (1973) "Expansive Soils - the HiddenDisaster", Civil Engineering, American Society of Civil Engineers,Volume 43, No. 8, August 1973, pp. 49-51. (TA1.C58).

    Kenney, T.C., (1959) "Discussion on Geotechnical Properties of GlacialLake Clays", Journal of the Soil Mechanics and Foundation Division,

    American Society of Civil Engineers, Volume 85, No. SM3, June 1959,pp. 67-79. (TA710.A1 A57).

    LaRochelle, P., Trak, B., Tavenas, F. and Roy, M., (1974) "Failure of aTest Embankment on a Sensitive Champlain Clay Deposit", CanadianGeotechnical Journal, National Research Council of Canada, Ottawa,Volume 11, No. 1, February 1974, pp. 142-164. (TA1.C213).

    Leps, R.M., (1970) "Review of Shearing Strength of Rockfill", Journal ofthe Soil Mechanics and Foundation Division, American Society of CivilEngineers, Volume 96, No SM4, Proceedings Paper 7394, July 2970, pp.1159-1170. (TA710.A1 A57).

    Leslie, D.D., (1963) "Large Scale Triaxial Tests on Gravelly Soils",Proceedings of the Second Panamerican Conference of Soil Mechanicsand Foundation Engineering, Brazil, Volume 1, 1963, pp. 181-202.(TA710.P187).

    Marsland, A., (1971) "Large In situ Tests to Measure the Properties ofStiff Fissured Clays", Proceedings of the First Australian - New ZealandConference on Geomechanics, Melbourne, 1971, Volume 1, pp. 180-189.(TA710.A83t).

    Raymond, G.P. (1968) "Construction Method and Performance of anEmbankment on Deep Muskeg", Proceedings Third International PeatCongress, Quebec City, pp. 51-56. (TA710.A1 N27).

    Raymond, G.P. and Davies, J.R., (1978) "Triaxial Tests on DolomiteRailroad Ballast", Journal of the Geotechnical Engineering Division,American Society of Civil Engineers, Volume 104, No GT6, June 1978,pp. 737-751. (TA710.A1 A57).

    Sanglerat, G., (1972) "The Penetrometer and Soil Exploration", ElsevierPublication Co., Amsterdam. (TA710.5 S2523).

    Skempton, A.W., (1948a) "A Study of the Immediate Triaxial Test onCohesive Soils", Proceedings of the Second International Conference onSoil Mechanics and Foundation Engineering, Rotterdam, Volume 1, June1948, pp. 192-196. (TA710.I6t).

    Skempton, A.W., (1948b) "The Geotechnical Properties of a Deep Stratumof Post-Glacial Clay at Gosport", Proceedings of the Second InternationalConference on Soil Mechanics and Foundation Engineering, Rotterdam,Volume 1, June 1948, pp. 145-150. (TA710.I6t).

    Skempton, A.W., (1953) "Discussion on Theories and Hypotheses ofGeneral Character, Soil Properties, Soil Classification, EngineeringGeology", Proceedings of the Third International Conference on SoilMechanics and Foundation Engineering, Zurich, Volume 3, 1973, pp. 115-116. (TA710.I6t).

    Skempton, A.W., (1964) "Long Term Stability of Clay Slopes",Geotechnique, The Institution of Civil Engineers, London, Volume 14,No. 2, June 1964, pp. 77-101. (TA1.G3).

    Skempton, A.W. and LaRochelle, P., (1965) "The Bradwell Slip: A Short-Term Failure in London Clay", Geotechnique, The Institution of CivilEngineers, London, Volume 15, No. 3, September 1965, pp. 221-242.(TA1.G3).

    Skempton, A.W. and Northey, R.D., (1952) "The Sensitivity of Clays",Geotechnique, The Institution of Civil Engineers, London, Volume 3, No.1, June 1952, pp. 1-16. (TA1.G3).

    Sowers, G.B. and Sowers, G.F., (1970) "Introductory Soil Mechanics andFoundations", Third Edition, The MacMillan Co., New York, p. 556.(TA710.S67).

  • Shearing Strength of Soils -- GEOTECHNICAL ENGINEERING-1997 -- Prof. G.P. Raymond 111

    Taylor, D.W., (1948) "Fundamentals of Soil Mechanics", John Wiley andSons Inc., New York, p. 700. (TA710.T2).

    Ward, W.H., Marsland, A. and Samuels, S.G., (1965) "Properties of theLondon Clay at the Ashford Common Shaft: In situ and UndrainedStrength Tests", Geotechnique, The Institution of Civil Engineers,London, Volume 15, No. 4, December 1965, pp. 321-344. (TA1.G3).

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