4_4. Real Soil Behaviour

4. Real soil behaviour

4.1 SynopsisThis chapter reviews real soil behaviour. It considers clay and sand soils and thensoils containing a range of particle sizes. The main facets of soil behaviour areidentified by considering results from laboratory tests. Data are presented withoutprejudice from any theoretical framework, and can therefore be used to verify andcompare with the theoretical constitutive models described in subsequent chapters.

4.2 IntroductionThe finite element theory presented in Chapter 2 assumed material behaviour to belinear elastic. Unfortunately, real soils do not behave in such an ideal and simplemanner. If they did, failure would never occur and geotechnical engineers wouldprobably not be needed. Real soil behaviour is highly nonlinear, with both strengthand stiffness depending on stress and strain levels. For realistic predictions to bemade of practical geotechnical problems, a more complex constitutive model istherefore required. As this involves nonlinear behaviour, further developments arerequired to the finite element theory. These developments are presented anddiscussed in Chapter 9.

Due to the complexity of real soil behaviour, a single constitutive model thatcan describe all facets of behaviour, with a reasonable number of input parameters,does not yet exist. Consequently, there are many models available, each of whichhas strengths and weaknesses. In Chapters 5, 7 and 8 a variety of constitutivemodels that have been, and still are, used to represent soil behaviour are described.However, before delving into the complex theory behind these mathematicalmodels, it is useful to consider real soils and identify the important aspects of theirbehaviour. Such information provides a framework which can then be used toassess and compare the various different constitutive models.

Soil behaviour is a complex subject and it is not possible to cover every aspectin a single chapter. Consequently, only the most important issues are discussedhere. It is assumed that the reader is familiar with soil mechanics and in particularwith conventional laboratory testing of soil samples and the manner in which theresults from such tests are presented. The aim is to summarise the more importantcharacteristics of soil behaviour as observed in laboratory tests, rather than tointroduce new concepts to the reader. The chapter begins by considering the

Real soil behaviour / 91

behaviour of clay soils. Behaviour under one dimensional compression and whensubjected to shear under triaxial stress and strain conditions is presented. Theeffects of the magnitude of the intermediate principal stress, the orientation of theprincipal stresses and shearing to large strains on clay behaviour are thendiscussed. Sand soils are considered in the same way and the differences inbehaviour noted. Although pure clay and sand soils do exist, many soils contain arange of particle sizes from clay to sand, with their behaviour reflecting theircomposition. In the last part of this chapter the behaviour of several of these soilsis compared. The chapter ends by summarising the more important facets of soilbehaviour which, ideally, should be reproduced by constitutive models.

1.4

1.2:

1.0

0.8

0.6

0.410 100

(kPa)1000 10000

4.3 Behaviour of clay soils4.3.1 Behaviour under one dimensional compressionThe behaviour of clays under onedimensional compression is usuallyinvestigated in an oedometer.Typically a cylindrical sample of soil60mm in diameter and 20mm high issubjected to vertical compression,while movement in the radialdirection is prevented. Results from atest on reconstituted Pappadai clay(Cotecchia (1996)) are shown Figure4.1, where the vertical effective stress,av', is plotted against the void ratio, e.As is the custom, the vertical effectivestress is plotted on a logarithmicscale. The soil sample has beensubjected to compression with twocycles of unloading/reloading.

In its initial condition, whenplaced in the oedometer, the reconstituted clay is in a normally consolidated staterepresented by point A in Figure 4.1. On loading (increasing av') the samplecompresses and its void ratio reduces travelling down the virgin consolidation line(VCL) (i.e. A to B). At B the sample is unloaded and swells travelling along theswelling line BC. On reloading the sample moves along the line CDE. At point Dit rejoins the VCL and remains on this line with any further increase in verticalstress. If unloaded again the soil will move along another swelling curve. Forexample, when unloaded from point E the soil follows the line EF. It is generallyassumed that swelling loops, such as BCD and EFG ,are parallel.

Soil which is on the VCL is said to be normally consolidated because it hasnever been subjected to a higher vertical stress. Soil on a swelling loop is definedas overconsolidated, with an overconsolidation ratio (OCR) defined as cr,/max /cr,/,

Figure 4.1: One dimensionalconsolidation of Pappadai clay

(Cotecchia (1996))

92 / Finite element analysis in geotechnical engineering: Theory

1.2

1.0

0.8

0.6

04

Swelling line

-

i

\VCL

ok

\10 100

crv' (kPa)1000 10000

where cr/max and av' are the maximumvertical effective stress the sample hasever experienced and the currentvertical effective stress, respectively.For an increment of vertical stressnormally consolidated soil suffers amuch larger change in void ratio thanan overconsolidated soil. This impliesthat overconsolidated soils are muchstiffer than normally consolidatedsoils. Overconsolidated soilssubjected to reloading experience arapid reduction in stiffness as theirstress state approaches the VCL.

To use results like those shown inFigure 4.1 for design purposessimplifications are often introduced. For example, it is often assumed that the VCLis a straight line in e-loglo0v' space, with a gradient Cc, and that the swelling loopcan be replaced with a single line of gradient Cy, see Figure 4.2. However, such anapproach is not universally accepted. For example, some geotechnical engineersadvocate plotting the results in \og]0e-\og]0(jv' space before making the idealisationsfor the VCL and swelling loops, while others prefer to plot results in terms of meaneffective stress instead of vertical effective stress and/or to use natural logarithms.Some of these idealisation are discussed in greater depth in subsequent chapters.

Figure 4.2: Idealised behaviour ofclays in one dimensional

consolidation

4.3.2 Behaviour when shearedThe behaviour of soil when subjected to shear can be investigated in a range ofapparatuses (e.g. triaxial, true triaxial, direct shear, simple shear, torsional shear,hollow cylinder etc.). However, the most common test performed on soils is theconventional triaxial test, in which a cylindrical sample is subjected to a constantradial stress, or, and then sheared by either increasing (triaxial compression), orreducing (triaxial extension) the axial stress, oa . Most tests are performed onsamples with a diameter of 38mm and a height of 76mm, although tests on largersamples with diameters of 50mm or 100mm and heights of 100m or 200mm aresometimes performed (especially when the effects of macrofabric are of interest).However, the latter tests are not popular for clay soils as pore pressure equalisationwithin the sample takes more time and therefore the tests take much longer toperform. Although there are loading platens at the top and bottom of the sampleswhich can affect the stress distribution within the sample, uniform stress and strainconditions are assumed when interpreting the results.

Typical results from a series of tests performed on Ko consolidated samples ofclay from Pentre in Shropshire are shown in Figure 4.3 (Connolly (1999)). Allsamples were Ko (i.e. no radial strain) normally consolidated from A to B, seeFigure 4.3. The samples were then Ko unloaded to a particular value of


overconsolidation ratio, with eachsample having a different OCR. Atthis point all drainage valves wereclosed and the samples were shearedundrained to failure, by eitherincreasing or decreasing the axialstress. The resulting effective stresspaths are shown in Figure 4.3. Severalimportant facets of soil behaviour areevident in this plot. Firstly, theeffective stress paths for samples withan 0CR<3 bend to the left, having asmaller mean effective stress at theend of the test than they had at thebeginning. This implies that, whensheared, the samples tried to contract,however, as undrained conditionswere enforced this resulted in thegeneration of compressive (positive)pore water pressures. In contrast, thestress paths for the heavilyoverconsolidated samples (0CR>3)bend to the right. This implies dilatantbehaviour and the generation oftensile (negative) pore waterpressures.

The stress states of all samples atfailure tend to plot on a straight linewhich passes through the origin. Thisline is often referred to as the criticalstate line and is defined by an angleof shearing resistance, cpj. Therelevant cpj angles for the stress pathsshown in Figure 4.3 are 32° and 28°for compression and extensionrespectively. Although not evident inFigure 4.3, sometimes for heavilyoverconsolidated clay the stress pathspass above the critical state linebefore they reach failure. This impliesa peak effective strength, in terms ofa cohesion, c1, and an angle ofshearing resistance, cp'', greater thanthat at ultimate failure.

400r

-200L

Figure 4.3: Effective triaxial stresspaths for laminated Pent re clay

(Connolly (1999))

0.001 0.01 0.1 1Axial strain (%)

Figure 4.4: Undrained Young'smoduli for Pent re clay

(Connolly (1999))


For lightly overconsolidated samples the deviator stress (=(cra'-o/ )) reachesa peak value and then reduces as ultimate failure is approached. This implies thatthe undrained strength, Su, which is defined as half the maximum deviator stress,occurs before the full angle of shearing resistance has been mobilised. In contrast,for the heavily overconsolidated samples the deviator stress obtains its highestvalue at ultimate failure.

The variation of secant Young's modulus Eu {r{oa-Ga^l{ea-eaX (where oao andeao are the axial total stress and the axial strain just prior to undrained shearingrespectively) with change in axial strain, sa~eao, are shown in Figures 4.4a and4.4b, for the compression and extension tests respectively. These plots clearly showthat the soil becomes progressively less stiff as it is sheared. This occurs for allsamples, but is particularly marked for the lightly overconsolidated samples wherethe stiffness drops by more than an order of magnitude.

It is also evident from Figure 4.4that the stiffness magnitude dependson OCR. However, it should be notedthat both OCR and the mean effectivestress,// {=(ax'+a2'+0^)13), vary foreach test. It is therefore not possibleto identify the influence of each ofthese parameters from the datapresented. The effect on stiffness ofstress level alone is shown in Figure4.5 (Soga et al (1995)), where theresults from four torsional tests onisotropically normally consolidatedkaolin are presented. The tests differonly in that the magnitude of theconsolidation stress changes. Theresults indicate the typical decay ofstiffness with strain as shown in Figures 4.4a and 4.4b, but more importantly theyindicate a nonlinear relationship between stiffness and mean effective stress, /?'.

From the above observations it is clear that the overconsolidation ratio and themagnitude of the mean effective stress have a large influence on soil behaviour.

10"5 10"3 10'2 10'1

Shear strain (%)

Figure 4.5: Dependence of kaolinstiffness on stress level

(Soga etal. (1995))

4.3.3 Effect of stress path directionThe direction of the stress path also affects the stiffness characteristics of the soil.This has been investigated by Smith (1992) who performed a set of triaxial probingtests on Bothkennar clay, see Figure 4.6. All samples were first consolidated alongpath ABC and then swelled to D. Ko conditions were applied over portions BC andCD of this stress path. At point D the samples were allowed to age before beingsheared drained along a variety of stress path directions. The variation of stiffnesswith strain for the probing stages of these tests is shown in Figures 4.7 and 4.8. In


LCD30

Figure 4.7 the equivalent tangent bulkmodulus, KtJ (=Apf/Aev), normalisedby the mean effective stress, p\ isplotted against accumulatedvolumetric strain from the start of theprobing stage, ev . The equivalenttangent shear modulus, Gtan(=A(aa

f-arf)/3Aes), normalised hyp'

is plotted against accumulated triaxialdeviatoric strain from the start of theprobing stage, es (=2/3 (ea-er))9 inFigure 4.8. Both of these plotsindicate that the soil stiffnessdecreases as the sample is strained Figure 4.6: Probing stress paths forand in this respect agree with the data Bothkennar clay (Smith (1992))given in Figure 4.4 for Pentre clay.However, they also show that the magnitude of the stiffness and the manner inwhich it decays with strain depend on the direction of the probing stress path. Alsoshown on Figure 4.8 is the value of the shear modulus, Gsejsmic, obtained fromseismic tests performed at Bothkennar.

1500

30 40p' (fcPa)

IVUV

800

a, 600

«5 400

200

0

-

" LCD70

LCD315

0.001 1.0

Figure 4. 7: Bulk stiffness forBothkennar clay (Smith (1992))

Figure 4.8: Shear stiffness forBothkennar clay (Smith (1992))

4.3.4 Effect of the magnitude of the intermediateprincipal stress

As noted above, the drained strength parameters of Pentre clay vary depending onwhether the clay is subjected to triaxial compression or extension. The differencesbetween these two types of test are that in the compression tests the intermediateprincipal stress, a2, is equal to the minor principal stress, cr3, and the major principalstress, cr,, is vertical (i.e. a = 0°, where a is the angle between the direction of the


major principal stress and the direction of deposition of the soil). In contrast, in theextension tests the intermediate principal stress, G2, equals the major principalstress, o",, and the latter stress now acts radially (i.e. a = 90°). Consequently, thestrength difference could result from the magnitude of the intermediate principalstress, a2, or the orientation, a, of ah or a combination of both. To separate theeffects of each of these differences, special tests must be performed. Results fromtests to quantify the effect of the orientation of the major principal stress arediscussed in the next section. The influence of the magnitude of the intermediateprincipal stress, a2, is considered below.

In order to isolate the effect of the intermediate principal stress, a series of testsshould be performed in which only this quantity is varied, with all other parametersremaining the same. However, it is not possible to satisfy this requirement inconventional testing equipment and therefore tests must be performed in specialistequipment (i.e. true triaxial, directional shear cell or hollow cylinder apparatuses).To date, a comprehensive set of tests on a clay soil have yet to be performed,however data exist for sands and for clay-sand mixtures and these are discussedsubsequently.

For clays, data exist from conventional triaxial and plane strain tests on thesame soil and it is of interest to compare such results. As noted above, for triaxialcompression a2 = o2 and a = 0°, while for plane strain compression a = 0° and theintermediate stress a2 is somewhere between ax and a3. Its exact value is difficultto measure in plane strain tests, but the test data that are available suggest that0A5<[(G2-(J3)/(G]-G3)]<0.35. Vaid and Campanella (1974) tested similar samplesof Ko normally consolidated undisturbed Haney clay in both triaxial and planestrain compression. In terms of undrained strength, S1t9 these tests indicated that inplane strain the strength was some 10% higher than in triaxial compression (i.e.SJGJ values of 0.296 and 0.268 were obtained in plane strain and triaxialcompression respectively, where GVC' is the vertical effective consolidation stress).In terms of the peak angle of shearing resistance, cp\ little difference was observed,with plane strain and triaxial compression giving values of 31.6° and 29.8°.

Vaid and Campanella also performed plane strain and triaxial extension testson the same Haney clay. In triaxial extension G2 = GX and a = 90°, while for planestrain extension a = 90° and the intermediate stress G2 is again somewhere betweenox and a3. These results indicated that in plane strain Su was about 25% higher thanin triaxial extension (i.e. Su loV(! values of 0.211 and 0.168 were obtained in planestrain and triaxial extension respectively). Again, there were only small differencesin the peak angle of shearing resistance, with the plane strain and triaxial testsgiving 34.3° and 33.8° respectively.

A tentative conclusion from the above results from tests on clay is that thevalue of the intermediate principal stress has a modest effect on Su, but little effecton cp'. For sands and sand-clay mixtures the effects on <p' appear to be greater, asis discussed in later sections of this chapter. The above results also indicate that themode of shearing, compression or extension, and therefore the value of a has amuch larger effect on both Su and <p'.


4.3.5 AnisotropyFor convenience, laboratory test data are usually interpreted assuming that the claybehaves in an isotropic manner. This is evident in the data presented above, whereequivalent isotropic measures of stiffness have been used. In general, soil isunlikely to be completely isotropic, because of the way in which it was originallydeposited. In fact, it is only likely to be isotropic in the plane normal to its directionof deposition. Such a material is usually called 'cross anisotropic' or 'transverselyisotropic'. In such a material both strength and stiffness depend on both themagnitude and orientation of the applied stresses. However, it is not easy toinvestigate the anisotropic behaviour of clays in conventional laboratory triaxialand shear box tests. This is one of the reasons why anisotropic effects have beenneglected in the past. However, in recent years special testing devices (e.g.directional shear cell and hollow cylinder apparatus) have been developed toinvestigate anisotropic effects and, consequently, limited data exist.

Data on the undrained shear0 4

0.3

0.2

o.i

0.0

O OCR=1• OCR=4

r-J I I I L

onstrength of Ko consolidatedreconstituted Boston Blue clay aregiven in Figure 4.9. These data comefrom a series of tests performed in adirectional shear cell by Seah (1990),in which similar samples weresheared with different orientations ofthe major principal stress to thedirection of deposition, a (see insertin Figure 4.9). In Figure 4.9 theundrained shear strength, Su,normalised by the verticalconsolidation stress, ap (i.e. verticalstress after Ko consolidation/swelling), is plotted against a, fornormally consolidated clay and claywith an OCR=4. It can be seen thatthe undrained strength drops significantly, by up to 50%, as a increases, indicatinga strong anisotropic effect. If the clay was isotropic, the undrained strength wouldbe unaffected by the value of a.

There is also limited evidence that clay has an anisotropic stiffness. Forexample, the ratios of horizontal to vertical Young's modulus, Eh'IEv', for a rangeof clay soils are tabulated in Table 4.1. The data suggest that this ratio depends onthe clay type and its OCR, and varies with strain level during shearing.

0 15 30 45 60 75 90Direction of the major principal stress, a0

Figure 4.9: Undrained strengthanisotropy of Boston Biue clay

(Seah (1990))

4.3.6 Behaviour at large strainsMost laboratory testing devices cannot provide reliable data at large strains (>20%)due to the existence of non-uniformities occurring in the sample. For example,


Table 4.1: Review of stiffness ratio for natural and reconstituted clays

Reference

Ward et al(1959)

Kirkpatric andRennie(1972)

Franklin andMattson(1972)

Atkinson(1975)

Lo et al.(1977)

Saada et al.(1978)

Yong andSilvestri(1979)

Graham andHoulsby(1983)

Kirkgard andLade (1991)

Soil

London clay

Reconstitutedkaolin

Reconstitutedkaolin

London clay

Leda clay

ReconstitutedEdgar kaolin

Champlain clay

Winnipeg clay

S.Franciscobay mud

Strain level (%)

0.20.6

very large

very small

~ 1

0.4 - 0.6

0.00010.007

0.5-1.0

large

Eh'/Ev'

1.42.4

0.6 - 0.84

1.8-4.0

2

0.55

1.251.35

0.62

1.78

1.2- 1.8

samples tend to develop localised failure zones at large strains, within which thestresses and strains cannot be reliably determined from the instrumentation.

The ring shear device was developed to overcome these shortcomings. In theversion of this apparatus developed by Bishop et al. (1971), a ring of soil with anouter diameter of 152.4mm, an inner diameter of 101.6mm, and an initial thicknessof 19mm, is sheared torsionally by rotating the top of the sample, while keepingthe bottom fixed. During this process the vertical stress is usually maintainedconstant. The results from such tests indicate that, for many clays, strengthdecreases with large strains, dropping well below the peak strength observed atsmall strains in triaxial tests, until a residual value is reached. A typical result fromsuch a test is shown in Figure 4.10 for London clay (Parathiras (1994)). It can beseen that at large strains the residual shear stress that the soil can sustain isapproximately 50% of the peak value mobilised at much smaller strains. In termsof drained strength this residual condition corresponds to a cohesion, c/=2 kPa,and an angle of shearing resistance, <p/=12°. Typically, peak strength parameters


s50 - Peak shear stress = 45 kPaLondon clay normallyconsolidated to av = 100 kPa

of cp'=l kPa and (pp'=20° are quotedfor London clay (Potts et al (1997)).The reduction from peak to residual 1 2 5

conditions is usually associated withthe clay particles in the shear zone re- " % ts~ 90aligning themselves in the direction of Displacement (mm)shearing.

Clearly, residual strength and the Figure 4.10: Residual strength ofrate of loss of strength from peak to London clay (Parathiras (1994))residual can be very important inproblems involving progressive failure and in situations where established failuresurfaces already exist (e.g due to geological processes), see Potts et al. (1990).

4.4 Behaviour of sandsMany of the features described above for clays also apply to sands. However, sandspossess additional complexities in their behaviour due their particulate nature andmode of deposition. Sands are more permeable than clays and therefore requireshorter testing times. Consequently, more extensive testing of sands has beenperformed. The results from these tests enable the effects of the magnitude of theintermediate principal stress and of the anisotropic properties to be investigated indetail.

4.4.1 Behaviour under one dimensional compressionWhen considering the behaviour of a deposit of sedimentary clay, it is recognisedthat the clay begins its existence in the form of a slurry and that its current stateresults from a combination of consolidation and swelling stages. It may thereforebe considered that all parts of the deposit have a unique starting point, namely, theclay slurry. However, such an assumption is not valid for sands, as sands can bedeposited at different rates, resulting in a range of initial densities which influencesubsequent behaviour.

Figure 4.11 shows the compression characteristics of two samples of Ticinosand (Pestana (1994)): one initially in a dense state with eo = 0.6, the other in aloose state with eo = 0.8. It should be noted that when attempting to set up identicalsand samples, it is difficult to achieve exactly the same initial void ratio every time,either for a loose or a dense state. There is, therefore, a multiplicity of initial voidratios of sand for the same stress point. When the two samples are compressed onedimensionally, they follow normal compression lines (NCLs) which, at high valuesof effective stress, approach a unique virgin compression line (VCL). As thesamples have different initial void ratios, the NCLs are not coincident. The VCLis approached when the sand particles start to crush. The magnitude of the verticalstress at which this occurs is dependent on the strength of the soil particles (Coop(1990)). For example, for the loose Ticino sand, shown in Figure 4.11, the VCLis reached only when the vertical effective stress exceeds 10 MPa. For the dense


sample an even higher vertical stressis required, due to the greater numberof contact points compared to theloose sample. Consequently, the stresslevels and behaviour associated withmost geotechnical structures usuallyrelate to the early parts of the normalcompression curves (NCLs).Unloading/reloading results inhysteresis loops as discussed abovefor clay, and, although not shown inFigure 4.11, it is commonly observedthat unload/reload loops are parallelwhen the data is plotted in e-logwav'space.

NCL

VCL

100 1000

Figure 4.11: One dimensionalbehaviour of Tic in o sand

(Pestana (1994))

4.4.2 Behaviour when shearedAs with the behaviour under one dimensional compression, the behaviour of sandsubjected to shearing is also affected by its initial density. Stress paths from triaxialcompression and extension tests performed on loose Ham River sand (Kuwano(1998)) and dense Dunkirk sand (Kuwano (1998)) are shown in Figures 4.12 and4.13 respectively. Both of these plotsshow results from a series of tests inwhich the sand was one dimensionallycompressed and then unloaded from itsinitial state to a series of OCR values,before being sheared undrained in eithertriaxial compression or extension. Thetwo figures, although for different sands,indicate typical trends observed in sandsoils.

Considering the results from theloose Ham River sand shown in Figure4.12, the following trends are noted. Forall OCRs the stress paths for both thecompression and extension tests initiallybend to the left, indicating a contractanttendency, which manifests itself inpositive (compressive) pore water

600 r

400 -

200 -

-2001-

pressures. However, with further loadingthis compressive tendency reduces andbecomes dilative, imposing negativepore water pressures which bend the

Figure 4.12: Effective triaxialstress paths for loose Ham River

sand {Kuwano (1998))


stress path to the right. The kink in thestress path at which soil behaviourchanges from a compressive to a dilativetendency is often referred to as the'phase transformation point'. As theOCR increases the initial contractivetendency reduces and the dilativetendency increases.

For the dense Dunkirk sand, shownin Figure 4.13, a similar contractivefollowed by dilative tendency is onlyobserved in the extension tests onsamples with OCRs of 1 and 2. Forextension tests on samples with a higherOCR and for all compressive tests only adilative tendency is observed.

For both the loose and dense sandsthe compression and extension testsapproach a respective common failureline at large strains. Once this line is

400 r

J400

(kPa)

-200 L

Figure 4.13: Effective triaxialstress paths for dense Dunkirk

sand (Kuwano (1998))

reached both the loose and dense sands have a tendency to dilate and thereforegenerate negative pore water pressures, which push the stress state further up thefailure line. Consequently, the samples keep on taking higher and higher deviatorstress and do not indicate a critical state condition as is usually observed for clays.The tests are usually stopped when either the pore water cavitates, the testapparatus reaches its load capacity, or when the samples become so non-uniformthat measurements of stress and strain are unreliable. It is conceivable that a criticalstate does exist at higher stress levels, but that this can only be reached in specialhigh pressure test apparatus. Such a hypothesis has been put forward by Coop(1990) and is consistent with the existence of a unique VCL at high stresses.

For both the loose and dense sands the failure lines are well defined in bothtriaxial compression and extension. These can be represented by straight lines inFigure 4.12 and 4.13 which pass through the origin of stress space (i.e. c'= 0.0),giving compression and extension strengths of cpc'= 33° and (pe'= 22° for loose HamRiver sand, and cpc'= 37° and (pe'= 25° for dense Dunkirk sand. At low stress levelsthere is some experimental evidence to indicate that the failure lines are curvedrather than straight giving angles of shearing resistance cpc' and <pe' that vary withmean effective stress (Stroud (1971)).

It can be concluded from Figures 4.12 and 4.13 that the looser the sand and thelower the OCR, the greater the initial contractive tendency on shearing. However,at large strains this tendency reduces and is replaced by a dilatant one which pushesthe stress path along the failure line.

If the above tests had been performed drained, instead of undrained, the stresspaths would have been straight and failure would have occurred when they


intersected the Mohr-Coulomb failure line. The stress state would then remain atthis intersection point, regardless of any further straining. During further strainingdilation would continue to occur with the rate of dilation being dependent on theinitial void ratio and OCR of the sample. Such dilation appears to continue untillarge strains, when the sample becomes non-uniform and the measurementsbecome unreliable.

The existence and location of a critical state for sand, while of academicinterest, is only relevant in practice to undrained problems, or where the sand iskinematically constrained. As sands are usually highly permeable, undrainedconditions only occur when the loading is extremely fast, such as under seismicloading. Kinematically constrained conditions might occur at the base of deepfoundations, such as piles, and for penetration problems such as interpreting theresults from cone penetrometers. For many geotechnical structures, such as shallowfoundations and retaining walls, sand behaves in a drained manner and the volumechanges at failure do not have a large influence on collapse loads and it is only theinclination of the failure line (i.e. cp') that is important. This problem is discussedfurther in Volume 2 of this book, when the analyses of boundary value problemsare considered.

The variation of secantYoung's modulus, Eu, with axialstrain, sa-sao, for the triaxialcompression and extension testson loose Ham River sand areshown in Figure 4.14a and 4.14brespectively. Similar plots for thedense Dunkirk sand are shown inFigures 4.15a and 4.15b. Theseplots show similar trends to thosefor Pentre clay given in Figure4.4.

The effect on stiffness of stresslevel alone is shown in Figure4.16, where results from threetorsional shear tests on Konormally compressed loose HamRiver sand are presented. Thetests differ only in that thecompression stress changes. Theresults indicate a nonlinearrelationship between stiffness and Figure 4.14: Undrained Young's modulistress level. For further for loose Ham River sandinterpretation of these tests the (Kuwano (1998))reader is referred to Porovic andJardine(1994).

0.001 0.01 0.1 1Axial strain (%)

0.001 0.1Axial strain (%)


750

600Triaxial compression

0.001 0.01 0.1 1 10Axial strain, sa, (%)

0.001 0.01 0.1 1 10Axial strain, ea, (%)

Figure 4.15: Undrained Young's moduli for dense Dunkirk sand(Kuwano (1998))

5 -40

Pc'- Pc'

Pc'

-

= 600kPa= 400kPa—^^= 200kPa ^ " ^ ^

^ \

i i i

OCR =1.0eo = 0.77

i ^ —

10"5 KT* 103 102 10'Shear strain, y, (%)

10° 10

Figure 4.16: Dependence of sandstiffness on stress level

(Porovic and Jardine (1994))

4.4.3 Effect of the magnitude of the intermediate principalstress

As noted above, the drained strength parameters of sand differ depending onwhether the sand is subjected to triaxial compression or extension. As stated inSection 4.3.4, in compression tests the intermediate principal stress, a2, is equal tothe minor principal stress, cr3, and the major principal stress, a}, is vertical (i.e. a =0°). In contrast, in extension tests the intermediate principal stress, <r2, equals themajor principal stress, au and the latter stress now acts horizontally (i.e. a = 90°).Consequently, the strength difference could result from the magnitude of theintermediate principal stress, a2, or the orientation, a, of au or a combination ofboth. In order to investigate the influence of the magnitude of the intermediateprincipal stress, a29 results from isotropically compressed drained true triaxial tests


55

50

,45

Cumbria sandRelative density: 93%Cell pressure: 100 kPa

on dense Cumbria sand areconsidered in Figure 4.17 (Ochiai andLade (1983)). In these tests theorientation of the sample wasmaintained the same and the majorprincipal stress always acted in thevertical direction (i.e. a = 0°). Thesamples were all sheared in a similarmanner, with the exception that therelative magnitude of the intermediateprincipal stress differed from test totest. In Figure 4.17 the relativemagnitude of the intermediate stressis expressed by the value of b(=(o'2~(73y((J\~(J3)) a n d is plottedagainst the effective angle of shearing resistance, cp'. It can be seen that there is anincrease of up to 9° in cp' as the intermediate principal stress increases from beingequal to a3 (b = 0) towards ox (b= 1).

350.2 0.4 0.6 0.8 1.0

Figure 4.17: Effect of 'b' on cp'forsand (Ochiai and Lade (1983))

4AA AnisotropyAs noted for clays, the behaviour of isotropic soils is independent of the orientationof the major principal stress, all other things being equal. Conversely, differencesin behaviour observed in tests performed with different values of a (i.e. orientationof the direction of ox with respect to the direction of deposition) provide anindication of the degree of anisotropy. Several sands have been tested in this way.

Results from a series of hollowcylinder tests performed on Konormally compressed Ham River sandare presented in Figure 4.18, in theform of the peak angle of shearingresistance, q>p, against a (Hight(1998)). All the tests had b = 0.3 andwere similar except for the value of a.The results indicate a markedvariation of cpp' with a. The effect ofchanging a is large, indicating a highdegree of anisotropy in the sand,much larger than that observed forclay soils.

Sands also exhibit anisotropicstiffness behaviour. This can be seenin Figure 4.19 which shows resultsfrom Kohata et al. (1997), who tested

Ko compressed Ham River sand

1080 90

Figure 4.18: Effect of 'a' on cp' forsand (Hight (1998))

•- k.

m SLB sand

• • "

•ft/4I

• ••

I

• •

1 |


prismatic samples of a range of sands 2 5

and gravels. For each soil type aseries of samples were normally ^compressed with different ratios of r;i.5the vertical and horizontal effectivestress, ov'loh'. The samples were then 10 ~subjected to small cycles of bothvertical and horizontal loading from o.o 0.5 1.0 1.5 2.0 2.5which small strain values of Ev' andEh' could be calculated. The resultsfrom three sands, Toyoura, SLB and Fi9^e 4.19: Stiffness anisotropy ofTicino, are shown in Figure 4.19 sands (Konata et aL "997»where the ratio Ev

r/Eh' is plotted against the ratio ov'loh'. If the samples wereisotropic Ev'/Eh'=\, the greater the departure from this value the larger theanisotropy.

The results show that for all three sands the degree of anisotropy changes withov'/oh'. The results also show that the amount of anisotropy is much larger for SLBsand than for both Toyoura and Ticino sand.

4.4.5 Behaviour at large strainsSands do not appear to suffer large reductions in their strength properties whensubjected to large strains. In this respect they differ from the behaviour of manyclay soils.

4.5 Behaviour of soils containing both clay and sandWhile clays and sands have many facets of behaviour in common, there are severalimportant areas where they differ. In reality, soils seldom contain either all clay orall sand sized particles. In fact, many soils contain a range of particle sizes andtheir behaviour varies depending on their constitution. In this section the behaviourof some of these soils will be compared and some of the controlling factorsidentified.

4.5.1 Comparison of sedimentary soilsIn this section the behaviour of the following nine sedimentary soils is compared:

1. Ham River sand (HRS) (Kuwano (1998)). This is a quartz based sand that wasprepared in a loose state with an initial void ratio eo = 0.8.

2. Dunkirk sand (DKS) (Kuwano (1998)). This is a quartz based sand withapproximately 10% calcareous shell fragments, prepared in a dense state withan initial void ratio, eo = 0.65.

3. HRS + 10% (by weight) kaolin (HK) (Georgiannou (1988)). This was preparedin a loose state with an initial void ratio en = 0.8.


4. Silica silt (HPF4) (Ovando-Shelley (1986)). This is an angular silt, obtainedfrom pure quartz, which was prepared in a loose state with an initial void ratioeo = 0.95.

5. Silica silt (HPF4) (Zdravkovic (1996)). This is the same silt as above, butprepared in a dense state, with an initial void ratio e0 = 0.65.

6. Artificial clay (KSS) (Rossato (1992)). This material was prepared by mixing50% kaolin with 25% fine sand and 25% silt and consolidating it from a slurry.The percentages quoted refer to proportion by weight.

7. Lower Cromer till (LCT) (Gens (1982)). This is reconstituted low plasticity tillwhich was consolidated from a slurry.

8. Pentre clay (PEN) (Connolly (1999)). This is a natural silty clay.9. Bothkennar clay (BC) (Smith (1992)). This is a natural high plasticity clay.

The grading curves for thesematerials are compared in Figure4.20. All soils have been tested in thelaboratory in a standard triaxialapparatus (Bishop and Wesley(1975)). The samples were shearedundrained in either compression orextension after Ko consolidation,followed by Ko swelling to a range ofOCRs. In all cases, tests wereperformed covering a typical range ofstresses encountered in engineeringpractice.

Figure 4.21 compares thecompressibility of some of the abovesoils under Ko conditions. It is evidentfrom this figure that the sands havethe lowest compressibility and thatcompressibility increases with claycontent. The Pentre clay, whichconsists of both clay and silt sizedparticles, shows a spread of volumechange behaviour, depending onwhether the samples were relativelysilty or clayey, or had laminated ormarbled macro-structures. Toemphasize the effect of clay contenton compressibility the results for HRS (0% kaolin), HK (10% kaolin), KSS (50%kaolin) and kaolin (100% kaolin) are compared in Figure 4.22.

The effective stress paths observed in undrained triaxial compression andextension, following Ko consolidation to a range of OCRs, are presented in Figure4.23 for eight of the soils listed above. The results for LCT, KSS and Pentre clays

Psrtide sis? (mm)

Figure 4.20: Grading curves fordifferent soils

Figure 4.21: Compressibility ofdifferent soils


10 50 100av

( (kPa)200 500

Figure 4.22: Effect of clay contenton compressibility of soil

show the typical behaviour associatedwith clay soils. The stress paths fornormally consolidated samples allindicate a contractive tendency givingrise to positive, shear induced, porewater pressures. This contractivetendency diminishes with increase inOCR and after a critical OCR of about3 is exceeded, the samples show atendency to try to dilate producingnegative, shear induced, pore waterpressures. All stress paths indicate awell defined final state whichcorresponds to critical stateconditions.

The behaviour of sand is illustrated by the results from HRS and DKS. Withdense DKS the shearing in compression leads to the mean effective stressincreasing for all OCRs, indicating a tendency to try to dilate and therefore thegeneration of negative shear induced pore water pressures. The same behaviour isobserved at high OCRs when the sand is sheared in extension. However at lowOCRs the extension tests indicate an initial contractive tendency (positive shearinduced pore water pressures) followed by a tendency to try to dilate, and thereforethe generation of negative shear induced pore water pressures. For both thecompression and extension tests the effective stress paths travel along an inclinedfailure line to high values of mean effective stress. Within a range of stressestypically associated with geotechnical structures, they show no sign of reaching awell defined final stress state. The large strain behaviour of loose HRS is similarto that of the dense DKS. However, all the loose samples sheared in compressionshow a tendency to try to contract with the generation of positive shear inducedpore water pressures on first shearing. On further shearing these samples revert toa tendency to dilate, resulting in the generation of negative shear induced porewater pressures.

It is interesting to compare the results from the tests on HRS and HK in moredetail. HK consists of 90% HRS mixed with 10% kaolin. Both soils had an initialvoid ratio of 0.8. It is evident that the addition of the small quantity of kaolin hasa marked effect on the shape of the stress paths. For the HK compression tests, theonset of a tendency to try to compress and therefore generate positive excess porewater pressures is abrupt and so intense that it results in a drop in deviatoric stress.Quite large positive shear induced pore water pressures are generated before thematerial undergoes phase transformation and begins to try to dilate. The effectivestress paths then travel up the failure line to large values of mean effective stressin a similar manner to loose sands. Further tests were performed by Georgiannou(1988) with different amounts of kaolin. Some of the results for Ko normallyconsolidated samples are shown in Figure 4.24. Both triaxial compression and


(a.'-a,1) (kPa)600

(kPa)

-200

(kPa)

Loose Ham River sand (HRS)

(o.'-o,1) (kPa)

Dense Dunkirk sand (DKS)

Loose Ham River sand +kaolin (HK)

P' (kPa)100 200

Loose silica silt (HPF4)

(a,1-*,1) (kPa)400

200

-200

a,'-a3') (kPa)200 r

100

p ' (kPa)

Dense silica silt (HPF4)

( « ) (kPa)300 r

200

100

0

-100

-200

-100 I

(CT/-cy3') (kPa)

p ' (kPa)200

Lower Cromer till (LCT)

' (kPa)100 200, 300

Natural Pentre clay (PEN)

3UU

200

100

0

-100

-200

100N"'200 3 0 0 / 4 0 0

Kaolin-silt-sand (KSS)

)

p' (KPa)

500

Figure 4.23: Effective stress paths in undrained triaxiai compressionand extension for different soil types


200

-200

300 400(a;+cT,')/2 (kPa)

extension tests on HRS/kaolin 400

mixtures, with 7.5% and 3.5% (byweight) kaolin, are shown. Forcomparison, results from tests on pureHRS are also shown. Clearly theaddition of only a small quantity ofclay can have a major effect on soilbehaviour.

Comparing the behaviour of thesilt HPF4 with the other materials it isevident that it follows the generalpattern established for sands. Loosesamples of HPF4 behave similarly toloose HRS, and dense HPF4 respondsin the same way as dense DKS. Thedense HPF4 shows a strongly dilative tendency in compression and does not reacha clear peak resistance or critical state in either compression or extension. A farmore contractive tendency is observed in extension, with the mean effective stressfalling by up to 50% before reaching the phase transformation point. In a similarfashion to that observed for dense sands, the dense HPF4 exhibits a weaker'memory' of its past stress history than do most clay soils. Consequently, whentested in an overconsolidated state, its yielding characteristics appear to be lessclearly associated with those shown by normally consolidated samples.

Zdravkovic (1996) also performed250

Figure 4.24: Effect of clay contenton effective stress paths

(Georgiannou (1988))

200

complex hollow cylinder tests ondense HPF4 silt. From some of thesetests it was possible to determine theanisotropic stiffness properties.Results for Ko consolidated silt withan OCR=\3 are shown in Figure 4.25in the form of the variation of verticaland horizontal Young's moduli, Ev'and Eh', and shear modulus, Gvh, withincrease in deviatoric strain, Ed. Thelarge differences between Ev' and Eh'clearly indicate a strong anisotropicbehaviour. The decrease in stiffnesswith increase in strain is typical ofmost soils as discussed in the previoussections of this chapter.

Hollow cylinder tests have also been performed on KSS and HK (Menkiti(1995)) and HRS (Hight (1998)). One objective of these tests was to investigatestrength anisotropy. The variation of the angle of shearing resistance, (p\ with a forall these materials and the dense HPF4 are given in Figure 4.26. All tests were

0.01 0.1 1.0Deviatoric strain, Ed, (%)

Figure 4.25: Anisotropic stiffnessproperties of silt

(Zdravkovic (1996))

110/ Finite element analysis in geotechnical engineering: Theory

performed with the intermediatestress, cr2, having a value between oxand cr3. The results show that cp' isaffected by the value of a andtherefore that the soils are anisotropic.They also indicate that the degree ofanisotropy reduces as the clay contentincreases. For example, there is amuch larger variation in cp' for HRSthan there is for KSS.

4.5.2 Residual soilsSo far the discussion and datapresented in this chapter have beenconcerned with sedimentary soils.Such soils are essentially eroded fromparent rock, transported by eitherwater or wind and then deposited ina new location. In contrast, residualsoils are formed in-situ by weatheringof parent rock. The initial parent rockis often quite strong, having a bondedstructure and therefore possessingconsiderable cohesion. Theweathering process reduces thenumber and the strength of the bonds.As weathering is not a uniformprocess, residual soils have a widevariation in cohesive strength.Clearly, the bonded structure of thesesoils affects their behaviour. Due tothe highly variable nature of manyresidual soils it is often difficult toobtain an accurate picture of theeffects of bonding. This has led someresearchers to manufacture artificialbonded soils (Maccarini (1987),Bressani(1990).

As an example of the behaviour ofa residual soil, results from twotriaxial compression tests on Gravinadi Puglia calcarenite are shown inFigure 4.27 (Lagioia (1994) and

0 10 20 30 40 50 60 70 80 90a0

Figure 4.26: Variation of (p' with afor some soils

1000-

CT3' = 200 kPa a)

10 20Axial strain (%)

10 20Axial strain (%)

Figure 4.27: Stress-strain behaviourof calcarenite (Lagioia (1994))


Lagioia and Nova (1995)). Both samples were isotropically consolidated and thensheared drained. The results shown in Figure 4.27a are for a sample consolidatedto a mean effective stress of 200kPa. When sheared the soil is initially very stiff,but when the deviatoric stress reaches 1200 kPa the bonds begin to break and thesample is unable to sustain further deviatoric stress and therefore the stress straincurve shows a softening effect. At first, this softening is quite steep but with furtherstraining it becomes more moderate. After approximately 15% axial strain thedevaitoric stress increases and the material begins to harden. The behaviour fromthen on resembles that of an unbonded sample of the same material. Differentbehaviour can be observed in Figure 4.27b which shows the results for a similarsample but this time isotropically consolidated to 1300 kPa before being sheared.Again, the sample is initially very stiff. However, when the deviatoric stressreaches nearly 1200 kPa and bond degradation begins, the deviator stress does notreduce but remains constant. This behaviour continues until the axial strain reachesapproximately 10% at which point the material begins to harden again and behavelike an unbonded sample. The spiky nature of the stress strain curve up to an axialstrain of 10% is believed to reflect the erratic process involved in bonddegradation. The behaviour during this process is clearly dependent on the levelof the mean effective stress.

In both samples the stress-strain behaviour is approximately linear until bonddegradation begins in earnest when the deviator stress reaches 1200 kPa. Closerinspection of this part of the loading curve indicates that the samples are behavingin an approximately isotropic linear elastic manner.

4.5.3 Residual strengthIt was noted in Section 4.3.6 that when clays are sheared to very large strains theirstrength decreases from a peak value to a residual value. In terms of an angle ofshearing resistance, <p, it is not unusual for the residual value to be half of the peakvalue for clays. Such a drop in strength at large strains is not observed for sands.For soils containing both sand and clay sized particles the behaviour depends ontheir clay content. This is illustrated in Figure 4.28a, which shows how the residualangle of shearing resistance, <p/9 varies with clay fraction (% of clay in terms ofvolume) for several real soils. For low clay fractions (< 20%) cpr' is high, havinga value similar to the peak angle of shearing resistance. However, at clay fractionsgreater than 40%, cpr' is relatively small and much lower than the peak value. Forclay fractions between 20% and 40%, <p/ is sensitive to the clay content.

Further data on residual strength is given in Figure 4.28b, where q>r' are plottedagainst plasticity index, Ip. As the value of the plasticity index reflects the clayfraction this data indicate a similar trend to the data observed in Figure 4.28a.

The effect of clay fraction on residual strength has been considered in detail byLupini et al. (1981). They show that at low clay fractions turbulent shearinginvolves rolling and translation of soil particles, rather than direct sliding. Incontrast, for high clay fractions shearing can involve sliding between clay particles

112/ Finite element analysis in geotechnical engineering: Theory

and that with straining the clayparticles become aligned. It is thissliding and realignment that explainsthe low residual strengths.

4.6 Concluding remarksIdeally any constitutive model shouldbe able to simulate all the abovefacets of soil behaviour. However,only very advanced models are ableto do this. Some of these arediscussed in Chapter 8 where it isshown that, although they have theability to accurately reproduce soilbehaviour, they require many inputparameters, some of which are noteasily obtained from conventional siteinvestigation or laboratory test data.Consequently, in practice acompromise has to be made betweenusing an advanced model, whichrequires the results from speciallaboratory tests to define itsparameters, and simple models, whichmay not reproduce all facets of soilbehaviour, but can be readily definedfrom the available data. If the

40

30 =---,

120 -

10 -

_

a)i i

Skempton(1964)Borowicka(1965)

-•• Binnie etal. (1967)(a) Mangla(b) Jari

Blondeau &Josseaume (1976)

• " " - - - " • " " '

I i

20 40 60 80Clay fraction (%)

100

0 20 40 60 80 100Plasticity index*/^ {%}

Figure 4.28: Effect of clay fractionand plasticity index on residual

angle of shearing resistance(Lupinietal. (1981))

compromise is towards using the simpler models, which is often the case, it isimportant that the model can at least reproduce the soil behaviour that is dominantin the problem under investigation. For example, if the problem is likely to involvesoil instability, then clearly it is important to model correctly the soil strength, forexample in slope stability and retaining wall design. However, if the concern isover soil movements, it is more important to model accurately the stiffnessbehaviour of the soil, for example when assessing movements adjacent to a multi-strutted excavation.

4.7 SummaryFrom the preceding discussions the following important facets of soil behaviourcan be identified:1. The stiffness, both bulk and shear, of a soil element increases as the soil

particles are pressed closer together, i.e. as the mean effective stress, p\increases and/or the void ratio reduces.


2. Overconsolidated soils experience a rapid reduction in stiffness when a stressstate associated with the pre-consolidation stress is reached.

3. On a change in the stress path direction the stiffness of the soil is likely toincrease. This increase depends on the amount that the stress path changesdirection. It is particularly noticeable if there is a complete reversal in directionand the soil is unloaded.

4. Generally, heavily overconsolidated clays and dense sands attempt to dilate(expand) on shearing, whereas lightly overconsolidated clays and loose sandsattempt to compress. However, loose sands may revert to a tendency to dilateas failure is approached. The tendency to dilate also depends on mean effectivestress. At low stress levels there is a greater tendency to dilate, whereas at veryhigh stress levels even dense sands compress. If a fully saturated soil is shearedundrained, volume changes are suppressed. However, the volume changetendencies are still there and therefore negative shear induced pore waterpressures are generated in dilatant phases of soil behaviour and positive shearinduced pore water pressures occur during the compressive phases.

5. The shear stiffness reduces as the soil is sheared, i.e. due to an increase indeviator stress and strain. This change in stiffness is particularly marked at thebeginning of shearing when the deviatoric strains are quite small.

6. A soil element fails when a certain stress state is reached. Such a stress stateforms part of a failure criterion. In conventional soil mechanics a Mohr-Coulomb failure criterion is usually adopted. Undrained failure is not as welldefined for sands as for clays. Some soils show brittle behaviour, where theircapacity to sustain deviatoric stress reduces with further straining, afterreaching the failure criterion.

7. Many real soils contain a range of particle sizes and their behaviour dependson their composition. A small amount of clay particles can have a largeinfluence on the behaviour of sands.

8. Most soils show some tendency to behave in an anisotropic manner.

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4_4. Real Soil Behaviour