mechanical behaviour of a natural soft clay

Mechanical behaviour of a natural soft clay

L. CALLISTO� and G. CALABRESI�

The results of an experimental study on themechanical behaviour of the natural soft clayfound at Pisa are discussed. Triaxial and truetriaxial stress path-controlled tests were carriedout, in which the soil was subjected to a varietyof drained stress paths, each starting from thein situ stresses. The stress-strain behaviour wasobserved to be substantially non-linear from thevery beginning of the loading process. The ob-served results are interpreted using concepts ofhardening plasticity. The in¯uence of the da-mage produced in the clay microstructure dur-ing loading is evaluated through a normalizationtechnique. A comparison between the behaviourof the natural and the reconstituted clay is alsopresented. The results of the true triaxial testsshow strength anisotropy. In both the triaxialand the true triaxial tests, the observed stiffnesswas found to depend strongly on the direction ofthe stress path.

KEYWORDS: anisotropy; clays; compressibility; lab-oratory tests; plasticity; stiffness.

Dans cet exposeÂ, nous preÂsentons les reÂsultatsd'une eÂtude expeÂrimentale sur le comportementmeÂcanique de l'argile tendre naturelle trouveÂedans la reÂgion de Pise. Nous avons effectueÂ desessais de contrainte triaxiale et de contraintetriaxiale reÂelle aÁ trajectoire controÃleÂe, essais aucours desquels le sol a eÂteÂ soumis aÁ une varieÂteÂde trajectoires de contrainte draineÂes, chacunecommencËant aÁ partir des contraintes in situ.Nous avons observeÂ que le comportement con-trainte-deÂformation eÂtait substantiellement nonlineÂaire depuis le commencement du processusde charge. Nous appliquons des concepts deplasticiteÂ durcissante pour interpreÂter les reÂsul-tats observeÂs. Nous eÂvaluons l'in¯uence des deÂ-gaÃts in¯igeÂs aÁ la microstructure de l'argilependant la charge graÃce aÁ une technique denormalisation. Nous comparons aussi le compor-tement de l'argile naturelle et de l'argile recon-stitueÂe. Les reÂsultats des essais triaxiaux reÂelsont mis en eÂvidence une anisotropie de reÂsis-tance. Dans les essais triaxiaux tout comme dansles essais triaxiaux reÂels, il est apparu que larigiditeÂ observeÂe deÂpendait fortement de la di-rection de la trajectoire de la contrainte.

INTRODUCTION

A number of experimental data obtained on recon-stituted isotropically consolidated clays allowed theCambridge Group to formulate a uni®ed frame-work, namely critical state soil mechanics, for themechanical behaviour of such clays (Roscoe et al.,1958; Scho®eld & Wroth, 1968). Since then, mucheffort has been put into the formulation of consti-tutive relationships, mostly based on hardeningplasticity, that are capable of accurately modellingthe behaviour of clayey soils subjected to bothmonotonic and cyclic loading (e.g. Scott, 1984;Burghignoli et al., 1991). However, such modelsare still largely based on experimental results ob-tained on reconstituted clays.

Most geotechnical engineering problems dealwith natural soils, and it is well known that the

mechanical behaviour of natural clays can differsubstantially from the behaviour of reconstitutedclays, due to the depositional conditions and post-depositional events that have occurred to the natur-al clayey deposit.

Since the 1970s, many authors have attemptedto use the notion of hardening plasticity in order todescribe the mechanical behaviour of natural softclays. It has been observed that natural clays, whensubjected to changes in effective stress, show arather stiff behaviour, while the stress vector re-mains within a domain in stress space, the bound-ary of which is called the `yield locus' (e.g.Mitchell, 1970; Wong & Mitchell, 1975; Crooks &Graham, 1976). For instance, Mitchell (1970) per-formed a series of tests in the triaxial cell, applyingdifferent effective stress paths to lightly overconso-lidated undisturbed samples; yield conditions wereassumed to correspond to more or less abruptchanges in stiffness, observed along different stresspaths. In this perspective, the yield locus was seenas a boundary between stress states that cause arelatively stiff, pseudo-elastic behaviour, and stress

Callisto, L. & Calabresi, G. (1998). GeÂotechnique 48, No. 4, 495±513

495

Manuscript received 17 December 1996; revised manu-script accepted 15 December 1997.Discussion on this paper closes 6 November 1998; forfurther details see p. ii.� University of Rome `La Sapienza'.

states inducing large deformability. Thus, the con-cept of yielding was not directly related to theonset of irreversible (that is, plastic) strains, butrather to the occurrence of a substantial decrease instiffness. Therefore, the notion of yield locus forsuch clays can be regarded as an extension of thetraditional concept of `preconsolidation pressure' tostress conditions more general than those asso-ciated with one-dimensional compression.

Although strains of natural clays for stress statescontained within the yield locus have frequentlybeen regarded as elastic (e.g. Wong & Mitchell,1975; Graham et al., 1983) it is now clear thatlinear elasticity is only a rough approximation to thepre-yield behaviour of such soils. Plastic (irreversi-ble) strains have been observed for stress changesmuch smaller than those required to reach the yieldlocus (e.g. Smith et al., 1992), and non-linearity hasbeen evidenced even for very small strains. How-ever, the assumption of linear elasticity within theyield locus may still be useful, depending on theparticular clayey soil examined, and on the peculia-rities of the engineering problems relating to soil.

In this paper we present the mechanical beha-viour of the natural soft clay found at Pisa, asobserved in stress-path controlled triaxial and truetriaxial laboratory tests. Such tests allowed obser-vations of the response of the clay to a largevariety of stess paths, and are therefore regarded asvaluable in extending the knowledge of the mech-anical behaviour of natural clayey soils. The beha-viour of the natural soil was also contrasted withthat of the reconstituted clay.

In interpreting the experimental results, the con-cept of yielding, as discussed above, has beenused. Plasticity and critical state concepts are oftenreferred to; elasticity is also used in discussing theobserved stiffness of the clay. In neither case is itintended that the `true' mechanical behaviour iseither plastic or elastic. Plasticity and elasticitytheories are used as tools in order to interpret theresults and to suggest possible ways to model theclay behaviour.

SOIL DESCRIPTION

The soil tested comes from the upper clayeydeposit found below the Tower of Pisa, in the depthrange 10´4±20´8 m. Soil samples were retrievedalong a borehole located south-west of the Tower,using the large-diameter tube sampler developed at

the Laval University (La Rochelle et al., 1981). Inorder to reduce the effect of soil heterogeneity andto test samples that were subjected to the samestress history in the ®eld, tests on natural clay wereperformed on two almost contiguous samples (18Aand 19B) retrieved from the same borehole be-tween depths of 12´3 and 12´8 m. At this depth, thevalues of the overconsolidation ratio (OCR) deter-mined through oedometer tests, vary between 1´5and 2 (Rampello et al., 1996).

Some of the tests described in this work wereperformed on reconstituted clay; this was preparedusing sample 29B, which was similar in gradingand index properties to samples 18A and 19B, butwas retrieved from 18´13±18´33 m below groundlevel. The reconstituted clay was prepared by thor-oughly mixing the clay with distilled water, to awater content equal to 1´5 times the liquid limitwL. The slurry was then consolidated in a largeoedometer up to a vertical effective stress of200 kPa, and subsequently allowed to swell up toOCR � 1:5. The material was then extruded fromthe oedometer, and the clay samples were trimmedand set up in the cell.

Some physical and index properties of the testedsamples are listed in Table 1. The clay has acontent in calcium carbonate of about 10%; theclayey minerals are mostly vermiculite and illite,with a small percentage of kaolinite. The undrainedshear strength is about 50 kPa, and the critical stateangle of friction, found in triaxial tests carried outby Rampello et al. (1996), is about 268.

EXPERIMENTAL APPARATUSES AND PROCEDURES

The tests discussed here were carried out usingtwo pieces of equipment: a stress-path triaxial cell,located at the University of Rome `La Sapienza',and a true triaxial apparatus, located at the Geo-technical Engineering Research Centre (GERC) ofthe City University, London.

The triaxial cell is similar to the one devised byBishop & Wesley (1975). As the cell is computercontrolled, fully automated, feedback-controlledstress path tests can be done (Toll & Ackerley,1988). Axial displacements were measured exter-nally, and corrections were applied to take intoaccount the compliance of the internal load cell.Pore pressures were measured at the base and atmidheight of the specimen, in the latter case usinga pore pressure probe (Hight, 1982). Drainage was

Table 1. Physical and index properties of the tested samples

Specimen Depth: m w0: % wL: % Ip: % CF: % CaCO3: %

18B 12´28±12´48 60 73´1 40´8 65 9´919A 12´61±12´81 62 80´6 49´2 65 10´429B 18´13±18´33 57 74´2 42´7 66 9´2

496 CALLISTO AND CALABRESI

allowed from the base and the top of the specimen(i.e. no radial drains were used).

The true triaxial apparatus (TTA) was designedby Dr. P. I. Lewin of the City University, London;it has been brie¯y described by Abbiss & Lewin(1990); Fig. 1 shows a schematic layout of theapparatus. The cell is of the ¯exible boundary type®rst developed by Ko & Scott (1967), allowingthree independent principal total stresses to beapplied on the three mutually orthogonal pairs offaces of a 60 mm cubic specimen.

The TTA (Fig. 1) is made of a brass frame,externally closed by six Perspex walls. The totalstresses are applied to the specimen by pressurizingthe gaps formed by the walls and by six rubbermembranes. The membranes are hat-shaped, withthe rim of the hat clamped between the brass frameand the Perspex walls. Next to the rim, the mem-branes have a concertina section, which is intendedto reduce any restraint offered by the wall of themembrane.

The membranes carry in their central part a1´4 mm steel pin, which is taken through the cellwall so that displacements of the centre of eachface of the specimen can be conveyed to anexternal displacement transducer.

Drainage channels are provided by three sets ofsmall holes drilled into orthogonal sections of thebrass frame. These channels are joined together sothat any drainage emerges at a single corner of theframe, where a drainage valve is mounted. Drai-

nage from the specimen is allowed by connectingthe drainage channel to three faces of the sampleby means of Terram ®lter strips.

Operation of the apparatus is completely auto-mated, and is controlled in feedback through apersonal computer.

TESTING PROGRAMME

The testing programme consisted of eight triax-ial tests and seven true triaxial tests on the naturalclay, plus ®ve triaxial tests on the reconstitutedclay.

Cylindrical samples for triaxial tests were cutwith their axes parallel to the vertical direction inthe ®eld (Fig. 2(a)). Similarly, cubic true triaxialtest samples were oriented in such a way that oneof the principal directions of stress was parallel tothe vertical direction (Fig. 2(b)). Throughout thepaper the assumption is made that cross-anisotropy,with a vertical principal axis of isotropy, is themaximum possible degree of anisotropy for boththe natural and the reconstituted samples in theirinitial conditions. This hypothesis is related to theone-dimensional stress history of the clay.

All the samples were reconsolidated, along pathABO in Fig. 3, to the in situ stress state O. The insitu horizontal effective stress ó 9h0 was evaluatedby carrying out stress-controlled K0 compressiontests to the in situ vertical effective stress ó 9a0

(Callisto, 1994), as well as using the empirical

Perspex walland side-plateMembrane

Steel pin formeasurement ofdisplacements

Filter paper

Drainage channelsPressurized chamber

Brass frame

Sample

Fig. 1. Schematic layout of the true triaxial apparatus

MECHANICAL BEHAVIOUR OF A NATURAL SOFT CLAY 497

relationship for evaluating K0 proposed by Mayne& Kulhawy (1982). Stresses at point O (ó 9a �113:5 kPa and ó 9h � 75:5 kPa) were maintained for40 h; thereafter the volumetric strain rate wasfound to be less than 0:002%=h. Volumetric strainsobserved after reconsolidation were generally lessthan 1´5%.

From point O, drained probing tests were per-formed, with rectilinear stress paths having differ-ent orientations in stress space. In Fig. 3, stresspaths for the triaxial tests are depicted in the qp9plane. Tests are labelled with a pre®x `A' or `R',referring to natural and reconstituted samples, re-spectively, followed by the relevant value of angleù in Fig. 3. The triaxial stress paths are replottedin Fig. 4 in Rendulic plane ó 9a,

p2ó 9h; here, the

trace of the octahedral plane Ð0, passing throughpoint O, is marked by a bold broken line. Eachstress point lying on Ð0 is characterized by thesame value of the mean effective stress p90 �88:2 kPa acting in the ®eld. In the true triaxialtests, stress paths were all contained in plane Ð0;these are shown in Fig. 5, where an octahedral

Fig. 2. Orientation of the cylindrical and cubic specimens

(vertical direction)a

h1

h2

(b)

σ ′h1, εh1

σ ′a, εa

σ ′h2, εh2

(vertical direction)

a

h

h

(a)

40

80

0

240

q: k

Pa

40 80 120 160 p′: kPa

A90,R90A60,R60

A30,R30

A0,R0A180

A135

O

B

ω

A

A315,R315

A280

Fig. 3. Triaxial stress paths in the qp9 plane0 100 200

0

100

200

√2 σ ′h: kPa

σ′ a:

kP

a

Diagonal(isotropic conditions)

A

B

A180

A135

(octahedral planethrough O)

ΠO

A90,R90

A60,R60A30,R30

A0,R0

A315,R315

A280

O

Fig. 4. Triaxial stress paths in the Rendulic plane

T0T30

T60

T90

T120

T150T180

T*150

T*120

T*90

T*60

T*30

σ ′a

σ ′h2σ ′h1

α

O

Fig. 5. True triaxial stress paths in the octahedralplane


view of the principal stress space is shown. Truetriaxial tests are labelled with the pre®x `T', fol-lowed by the relevant value of angle á in Fig. 5.Although tests marked T�, were not actually per-formed, the hypothesis of cross-anisotropy impliesthat soil response along such paths may be obtainedfrom that observed in the corresponding `T' paths,by interchanging the directions h1 and h2.

All tests were carried out under stress-controlledconditions. In tests A0, A30, A135, A180, A315,R0, R30 and R315 (where changes in p9 weregreater than or equal to the corresponding changesin q), the rate of variation in the mean effectivestress was equal to 1 kPa=h. In the remaining tests,a rate of variation in the deviatoric stress equal to1:5 kPa=h was applied. In the ®nal stages of testsA60, A90, A280, R60 and R90 the control wasswitched to the axial displacement, using an axialstrain rate of 0:1%=h.

During the early stages of test T180, the pres-sure supply at GERC failed, so that only a smallpart of stress path T180 was actually carried out(up to ås � 0:12%). Also, at the end of test T30 itwas observed that opposite faces of the specimenwere no longer parallel, and this occurrence wasascribed to an inclusion of organic matter in theclay. Therefore, deformations measured during suchtests were judged to be unreliable. However, thestress state at failure observed in such tests wasfound to be consistent with results from the othertests done using the TTA.

COMPARISON BETWEEN THE TRIAXIAL AND TRUE

TRIAXIAL RESULTS

In Fig. 6(a) a comparison is presented betweenthe results obtained in the axisymmetric test T0and in test A0b; this latter test was performed inthe triaxial cell, on the same sample (18B) used intest T0, following the same constant p9 stress-path.

It can be seen from Fig. 6(a) that only in theearly stages of the tests, up to deviatoric strains ås

of about 1%, do the q versus ås curves for the twotests coincide; at larger strains the curves diverge,showing different values of the shear strength.Speci®cally, the shear strength measured in thetriaxial cell is smaller by about 24% than thatmeasured in the TTA. If a logarithmic scale is usedfor the strains (Fig. 6(b)) it can be seen that thesame curve is indeed described by samples T0 andA0b for ås , 1%.

Differences in the values of the shear strengthwere also observed by Ko & Scott (1967) whentesting a medium dense sand in a triaxial cell andin their ¯exible boundaries TTA. They reported anangle of internal friction of 38´58 for a constant p9test carried out in the triaxial cell, and in excess of468 for the same test carried out in the TTA.

Green (1967), Bell (1968) and Arthur & Men-zies (1968) argued that the difference in shearstrength observed by Ko & Scott (1967) was pos-sibly due to a constraining action of the metalframe surrounding the specimen, while Ko & Scott(1968) ascribed the phenomenon to the non-uni-form stress distribution imposed in the conventionaltriaxial apparatus at the ends of the specimen.

More recently, differences in the shear strengthof a natural soft clay measured in the triaxial celland in a TTA with ¯exible boundaries have beenreported by Boudali (1995). The shear strengthobtained by Boudali in the TTA was greater thanthat observed in the triaxial cell, by as much as10±12%. Possible explanations for this anomalyput forward by Boudali (1995) include non-unifor-mity in the stress state applied by the rigid platensof the conventional triaxial apparatus, and the one-to-one shape of the TTA sample, which does notfacilitate the development of slip surfaces.

To investigate the latter point, constant p9

Fig. 6. Comparison between results obtained in theTTA and in the triaxial apparatus

true triaxial

triaxial (axisymmetric)

0 2 4 6 8 10 12 14εs: %

(a)

0

20

40

60

80

100

120

q: k

Pa

0

20

40

60

80

100

120

q: k

Pa

0.001 0.01 0.1 1 10εs: %

(b)


triaxial tests were carried out on two samples ofPisa clay, retrieved from a depth range 13´83±14´03 m. Test 21BN was performed on a specimenwith the conventional 2:1 height/diameter ratioand with rough ends, whereas test 21BR wascarried out on a 1:1 specimen with lubricatedends. Specimen 21BN failed along well-de®nedslip surfaces, as is always the case with Pisa claytested along a p9 � p90 path. For specimen 21BR,the development of the usual slip surfaces was notkinematically possible, and the deformation patternat failure appeared to be more uniform. Theresulting stress±strain curves are shown in Fig. 7.It is evident that, although the initial part of the qversus ås curves are very similar (for ås , 1%),the strengths measured in the two tests are quitedifferent, and the difference is consistent with thatobserved in Fig. 6, where results from the TTAand the conventional triaxial apparatus are com-pared. It was therefore inferred that the geometryof the TTA does not allow the development ofslip surfaces, which were never clearly observedon TTA samples, and therefore causes the samplesto fail in a different mode. It is worth mentioningat this stage that Lewin & Allman (1993) com-pared results from triaxial tests performed onreconstituted normally consolidated Bothkennarclay with results from TTA tests carried out usingthe same apparatus described herein. The compari-son proved satisfactory, in terms of both shearstrength and pre-failure deformability. The hypoth-esis can be made that the tendency of the recon-stituted clay sample used by Lewin & Allman todevelop slip planes was less signi®cant.

As a consequence of the comparison shown inFig. 6, it is concluded that results obtained on theconventional triaxial cell and in the TTA used inthis study can be directly compared only for devia-toric strains smaller than about 1%. None the less,results of TTA tests for strains in excess of 1%

will be discussed as well, as they are seen to forma consistent set of data for the mechanical beha-viour of the clay.

FAILURE IN THE TTA APPARATUS

The failure envelope determined from TTA testsis shown in Fig. 8 by the bold line. For compari-son, the failure curves resulting from the Mohr±Coulomb and the Lade & Duncan (1975) failurecriteria are also plotted; these match the strengthsin triaxial compression.

The experimental failure envelope is symmetri-cal about the ó 9a axis because of the hypothesis ofcross-anisotropy. Still, it is not endowed with six-fold symmetry, as it should be for an isotropicmaterial. The shear strength observed in triaxialcompression is in fact higher for ó 9h1 � ó 9h2 thanfor ó 9a � ó 9h1 or ó 9a � ó 9h2. In triaxial extension,the strength for ó 9h1 � ó 9h2 appears to be lowerthan that for ó 9a � ó 9h1 and ó 9a � ó 9h2. As a con-sequence, both the Mohr±Coulomb and the Lade& Duncan (1975) criteria, ®tted in triaxial com-pression to the experimental data, underpredict theshear strength for loading directions á in therange of (0, 1208), and overpredict it for á in therange of about (1208, 1508). Therefore, the clay iscross-anisotropic with respect to the strength,since a rotation of 908 of the principal stressdirections with respect to the specimen produces achange in shear strength. Similar deviations fromsix-fold symmetry were observed by Kirkgard &Lade (1993) for the failure envelope of a naturalsoft clay obtained from undrained true triaxialtests.

1:1 specimen

Standard specimen

0 2 4 6 8 10 12 14 16εs: %

0

20

40

60

80

100

120

q: k

Pa

21BR

21BN

Fig. 7. Effect of the shape of the specimen on theresults obtained from constant p9 triaxial tests

Failure envelopes

This study

Lade & Duncan

Mohr–Coulomb T0T30

T60

T90

120T120

T150

402402120220

2100

60

140

xσ: kPa

σ ′h2σ ′h1

σ ′a, yσ: kPa

Fig. 8. Failure envelope determined from tests in theTTA


YIELDING OF THE NATURAL CLAY

Triaxial testsIn each triaxial test carried out on the natural

clay, stress states at yield were identi®ed through atechnique similar to that used by Mitchell (1970)and by Graham et al. (1983), i.e. by locating thepoints at which the experimental stress±straincurves showed a marked bend. Since, for Pisa clay,yielding turned out to be a gradual phenomenon,care was used in identifying the start of yielding.The graphical technique used for this purpose hasbeen described in detail by Callisto & Calabresi(1995); it consists basically in locating the yieldstrains at the intersection of the rectilinear extra-polations of the pre- and post-yield portions of thestress±strain curves (Fig. 9). As the curves werenon-linear from the early stages of each test, somesubjectivity was unavoidable in locating the yieldpoints. Nevertheless, in some tests the pore pres-sure measured at the midheight of the samplesshowed, on reaching the yield stresses, small,though abrupt, changes, thus providing some addi-tional con®dence in positioning the yield points.The q versus ås and p9 versus åv curves obtainedfrom the triaxial tests on the natural samples andthe corresponding yield points are shown in Figs10 and 11.

The yield locus located from the triaxial testsresults is plotted in the qp9 plane in Fig. 12(a);roughly elliptic in shape, it is not symmetric aboutthe p9 axis. In Fig. 12(a) the contours of equalspeci®c strain energy W are also plotted. W isde®ned as

W ��

(ó 9a dåa � 2ó 9h dåh) (1)

where the integral is calculated along each stresspath, from the in situ stress point up to the pointrepresenting the current stress state. This was donein order to check the hypothesis that the strainenergy at yield is constant (Crooks & Graham,1976). In fact, it can be seen that this is not thecase for Pisa clay, since the yield locus crossesseveral strain energy contours. Therefore, strainenergy at yield appears to depend on the stresspath direction; this has also been shown for easternCanadian clays by Tavenas et al. (1979).

Also shown in Fig. 12(a) are the directions ofthe plastic strain increment vectors, plotted bothat yield and at a reference state W � 4 kJ=m3.The directions of the vectors were determined byassuming isotropic elastic behaviour for stressesinside the yield locus, and constant elastic para-

Yield point

Strain at yield

Strain

Str

ess

at y

ield

Effe

ctiv

e st

ress

Fig. 9. Location of yield points in triaxial tests onnatural Pisa clay

Yield points

A90

A60A30

A135

A180OA0

A315

A280

28 24 0 4 8 12 16

εs: %

280

240

0

40

80

120

160

q: k

Pa

Fig. 10. Plot of q versus ås obtained from triaxial testson natural Pisa clay

0 100 200 300p′: kPa

12

10

8

6

4

2

0

22

24ε v:

%

Yield points

A180

A135

O

A90

A280

A60A315

A30

A0

Fig. 11. Plot of p9 versus åv obtained from triaxialtests on natural Pisa clay


meters after yield. Increments of plastic strain werecalculated by subtracting from the increments oftotal strain the corresponding increments of `elas-tic' strains; these were evaluated using the tangentmoduli at yield (see Stiffness, below). In Fig. 12(a)some discrepancies from normality can be ob-served, especially for tests A90 and A280, althoughthe general picture seems consistent with an asso-ciated plastic ¯ow.

In Fig. 12(b) the yield points, plotted in the(e, log p9) plane, were ®tted using a logarithmiccurve:

e � 2:01ÿ 0:15 log10 p9 (2)

The coef®cient 0´15 of the logarithmic term inequation (2) is very close to the swelling indexproposed by Calabresi et al. (1993) for the upperclay deposit at Pisa. Therefore, if behaviour is tobe interpreted in terms of classic critical stateconcepts, it can be assumed that the yield locus inFig. 12(a) lies on an `elastic wall'.

True triaxial testsThe stress±strain curves observed in the true

triaxial tests are shown in Fig. 13 in terms of thelength of the stress path plotted against the devia-toric strain ås. The curves show an extremelysmooth and gradual transition towards failure, sothat a bilinear construction, like that shown in Fig.9, is of little use to locate yielding. However, acloser inspection of the curves in Fig. 13 revealsthat the curvatures of the different stress±straincurves can be related to the length of the stresspath required for each specimen to fail. Speci®-cally, when a long stress path is required to reachthe failure envelope (as for tests T120 and T150),the corresponding stress-strain curve is verysmooth and the yield conditions, detected as thebending of the curve, appear to occur separatelyfrom failure. Conversely, if the stress path length atfailure is relatively short (as in tests T60 and T0),the stress±strain curve shows a sharper bend, at astress state very close to that causing failure.

0 100 200p′: kPa

(b)1.6

1.8

e Cs 5 0.15

2100

0

100(a)

Yieldlocus

O

0.1 W contours

200

0.51.02.0

W 5 4.0 kJ/m3

p′: kPa, δεpv

q: k

Pa,

δεp s

Fig. 12. Yield locus plotted in the qp9 plane (a) and inthe ep9 plane (b)

Assumed yield points

0 2 4 6 8 10 12

εs: %

0

20

40

60

80

100

LSP

: kP

a

T150 T120

T60

T90

T0

T60

T0

T90

T120

T150

40 120

σ 9h2

xσ: kPa

σ9ayσ: kPa

Fig. 13. Stress±strain curves obtained in true triaxial tests. LSP, lengthof stress path


This point can be substantiated by looking atthe contours of equal shear strain plotted in Fig.14; here, shear strains range from 1% to 10% andthe contour spacing is 1%. In such a plot thedistance between the contours, taken along thestress paths, is proportional to the slope of thestress±strain curves, while the rate of variation insuch a distance is proportional to the curvature.The contour plot shows that, along paths such as

T60 and T0, the contours become suddenly veryclose to each other (i.e. the stress±strain curvatureis pronounced) in a zone near the failure envelope,whereas for paths like T120 and T150 the distancebetween the contours decreases in a very gradualfashion, and the maximum curvature can be identi-®ed long before the failure envelope is attained.

A possible way of de®ning conventionally ayield envelope is to associate yielding with acertain arbitrary value of the deviatoric strain(e.g. Alawaji et al., 1990). In Fig. 14 the ås � 4%contour has been highlighted, and it is possible tosee that this contour satis®es the requirement of

T0

T30

T60

T90

T120

T150

1%2342120 240 40 120

220

2100

260

140

O

Failureenvelope

σ ′h1σ ′h2

xσ: kPa

σ ′a, yσ: kPa

Fig. 14. Shear strain contours in the octahedral plane,for 1 , ås , 10%

T0T30

T60

T90

T120

T150Failureenvelope

140

60

220

2100

2402100

σ ′h1σ ′h2

xσ: kPa40 120

σ ′a, xσ: kPa

Parabolic interpolations

εs 5 4.0%

Fig. 15. Comparison between the ås � 4% contour andthe yield locus obtained by interpolating the stress±strain curves with parabolas

T0

T30

T60

T90

T120

T150

T180

0

4

8

12

16

20

212

28

24

216

4 8 12 16

εh1

εh2

xε: %

yε:

%ε a,

Fig. 16. Projection of the strain paths on to theoctahedral plane of strains

T0

T60

T90

T120

T150

140

60

220

2100

2120 240 40 120

σ ′h1, δεph1

σ ′h2, δεph2

σ ′a, yσ: kPa, δεph1

Fig. 17. Directions of strain increment vectors in theoctahedral plane


80 120 160 200 240 280 320 360

9

8

7

6

5

4

3

2

1

0

10

p ′: kPa

ε v: %

ω 5 08

(a)

0 2 4 6 8 10 12εs: %

(d)

20

30

40

50

60

70

80

90

q: k

Pa

ω 5 908

80 120 160 200 240 280 320

10

9

8

7

6

5

4

3

2

1

0

11

p ′: kPa

ε v: %

(b)

ω 5 308

0 2 4 6 820

40

60

80

100

120

140

160

q: k

Pa

εs: %

(c)

ω 5 308

Natural

Reconstituted

80 100 120 140p ′: kPa

5

4

3

2

1

0

6

ε v: %

(e)

ω 5 608

0 4 8 12 16 20εs: %

(f)

20

40

60

80

100

120

q: k

Pa

ω 5 608


being close to the failure envelope for tests with ashort path to failure, and quite far from it for testswith a relatively long path to failure.

An alternative way of de®ning yield points onthe curves in Fig. 13 is that used by Yong &McKyes (1971), which basically consists of ®ndingthe intersection of two parabolas interpolating theinitial and ®nal part of each curve. The yieldpoints marked in Fig. 13 were in fact located usingthis procedure, although it should be noted that thismethod is affected by strong subjective judgement.Fig. 15 shows a comparison of the yield locuslocated in this way and the ås � 4% contour. It canbe seen that the two curves are quite similar toeach other: differences are observed in the part ofthe curves mapped through tests T120 and T150,for which yield conditions are very dif®cult tolocate anyhow. It is clear that yield loci shown inFig. 15 are quite loosely de®ned, their relevancelying in proposing a possible shape for the initialyield locus of Pisa clay in the octahedral plane.

Figure 16 shows a view of the octahedral strainplane, on which the deviatoric strain paths havebeen drawn. (Strain path T30 is showed by adashed line because, as mentioned above, strainsobserved in such a test are not entirely reliable.)Arrows indicate the directions of the correspondingstress paths. As a general result, strain paths andstress paths have different directions from the verybeginning of each test, and this shows that the pre-yield behaviour is not isotropic elastic. However,stress and strain paths are parallel for test T0; thisis also true for the initial part of test T180 which,having been prematurely interrupted at ås � 0:12%,is hardly visible in Fig. 16. The occurrence thatstress paths T0 and T180, endowed with axialsymmetry about the ó 9a axis, yield strain paths with

the same symmetry, is consistent with the hypoth-esis of cross (transverse) anisotropy. The angleformed by each deviatoric strain path with thecorresponding stress path appears to increase withangle á, up to á � 608, and to decrease forá. 608, attaining lower values as á approaches1808.

Figure 17 shows the directions of the strainincrement vectors at yield and at failure. Elasticstrain increments were not subtracted from the totalstrain increments, since it was not possible to useisotropic elasticity for describing the pre-yield be-haviour, as the stress and strain paths are notparallel. It can be argued, however, that elasticstrains should be much smaller than plastic strainsfor stress paths directed as those in Fig. 5.

The strain increment vectors in Fig. 17 seem tobe approximately normal to both the yield and thefailure curve. However, a signi®cant deviation fromnormality can be seen for test T60, in which thedeviatoric strain path (Fig. 16) shows a kink as thestress path approaches failure.

HARDENING AND DESTRUCTURATION

Behaviour of the natural and the reconstituted soilsThe stress±strain behaviour observed in the

natural clay was compared with that observed inthe reconstituted soil, comparing pairs of testswith identical stress paths (see Fig. 3). As the re-constituted clay had been given a slight overcon-solidation ratio, some substantial changes in themechanical behaviour were expected on reachingthe yield locus of the reconstituted soil. The results(Fig. 18) show that this was not always the case.Let us de®ne as `deviatoric' those stress paths forwhich changes in the deviatoric stress q are greater

Fig. 18. (opposite and above) Comparison between results of triaxial tests done on natural and reconstituted clay

80

7

120 160 200 240 280

p ′: kPa

6

5

4

3

2

1

0

8

ε v: %

(g)

ω 5 3158

210 28 26 24 22 0εs: %

(h)

2160

2140

2120

2100

280

260

240

220

0

20

40

2180

q: k

Pa

ω 5 3158


than changes in p9, and as `spherical' those pathsfor which the reverse applies. It can be seen fromFigs 18(d,e,f ) that along the deviatoric paths (ù �908 and 608) the stress±strain curves of the recon-stituted clay show marked bends, and the behaviouris qualitatively similar to that of the natural soil.Conversely (Fig. 18(a,b,c)) along spherical paths(ù � 08 and 308) the behaviour of the reconstitutedclay is quite different from that of the natural soil;the initial portions of the stress±strain curves aresimilar for the two materials, but, as the stresspaths proceed, the reconstituted soil does not showsubstantial decreases in stiffness the way the natur-al clay does, and yielding, as de®ned in theprevious sections, does not seem to be a clearlyvisible phenomenon. Stress paths with ù � 3158are neither deviatoric nor spherical paths, sinceabsolute changes in q are equal to changes in p9.For such paths (Fig. 18(g,h)) the stress±straincurves of the reconstituted clay show some signi®-cant decrease in stiffness, although not quite asmuch as that occurring for the natural soil.

Evidence of destructuration in oedometer testsIn Fig. 19, the odeometer compression curve for

the natural clay is compared with that for areconstituted sample and with the sedimentationcompression curve (SCC) of the upper clayeydeposit at Pisa. The SCC (Terzaghi, 1941) de-scribes the compression of a soil element withinthe deposit, due to the increase in weight of theoverlying material as deposition continues. TheSCC can be found by plotting the relationshipbetween the natural void ratio and the in situvertical effective stress for samples retrieved from

different depths in a homogeneous deposit(Skempton, 1970); to this purpose, the depositshould be normally consolidated, in the sense thatthe soil has never been subjected to greater effec-tive stresses than those acting at the present time.The implicit assumptions in this procedure are thatthe increases in effective stress are the dominantcause of the compression of the clay, and thatinterparticle bonds, essentially of tixotropic origin,develop gradually during deposition, while factorssuch as cementation, cold-welding, coali®cation,etc., play a minor role.

The SCC for the Pisa deposit was determinedby interpolating, using a logarithmic curve, the fullcircles shown in Fig. 19, which represent thenatural void ratio of Laval samples retrieved fromthe strata labelled B1 and B3 by Calabresi et al.(1993), that is, from depths of 10´4±13´9 and15´9±20´8 m. The SCC is then described by theequation

e � 2:72ÿ 0:49 log10 ó 9v (3)

The slope of the SCC (equation (3)) is assumedto represent the compressibility of the upper clayeydeposit at Pisa. (Decrease of the overconsolidationratio (OCR) with depth within the deposit ledCalabresi et al. (1993) to the hypothesis that somemechanical overconsolidation in the deposit couldhave been due to super®cial erosion. If this hypoth-esis held true, the deposit could not be strictlyregarded as normally consolidated in the sensementioned above. However, Callisto (1996) showedthat, by taking into account the OCR distributionwith depth deduced from this hypothesis, the re-sulting changes in the slope of the SCC is negli-gible.) Uncertainties in the evaluation of the SCCare related to the scatter in the distribution of thevoid ratio values within the deposit and to theextrapolation of equation (3) to stresses larger thanthose for which the equation was obtained. Usingresults from the investigations carried out in thelate 1960s at Pisa, and correcting the void ratios toallow for small changes in the Atterberg limitswith depth, Skempton (1970) published a SCC forthe Pisa deposit which has, for all practical pur-poses, the same slope as the one presented in Fig.19, but spans a larger effective stress interval. Thisprovides some additional con®dence on the SCCdescribed by equation (3).

Figure 19 shows that the post-yield odeometercompression curve of the natural clay is initiallyvery close to the SCC, but is characterized bygreater compressibility: the compression index Cc

is about 1´3, whereas the value of Cc for the SCCfrom equation (3) is 0´49. Thus, the compressibil-ity estimated for the deposit during the sedimenta-tion is lower than that observed in the laboratoryfor the natural clay, since in the latter case loadingis carried out using much higher stress rates than

In situ void ratioSCC

Oedometer test, natural clayOedometer test, reconstituted clay

10 100 1000σ ′a: kPa

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

e

Fig. 19. One-dimensional compression tests on naturaland reconstituted clay, and the sedimentation com-pression curve of the deposit for comparison


those resulting from sedimentation (Leonards &Altschaef¯, 1964). (For the clayey deposit at Pisa,Skempton (1970) has given an estimate of the rateof deposition of about 2:5 m=1000 yr, correspond-ing to a vertical effective stress rate of about0:002 kPa=yr:) The resulting increase in compres-sibility can be ascribed to a progressive change inthe microstructure of the clay, that is, to destruc-turation (Leroueil et al., 1979; Burland, 1990).Effects of destructuration on the compressibilityappear similar to those caused by reconstitutingthe clay, since the compression curve of thenatural clay is seen to converge with that of thereconstituted clay, as the vertical effective stressincreases.

SBS and destructuration in triaxial testsCommonly, in critical state models the hypo-

thesis is made that plastic hardening is onlyvolumetric, the hardening law being linked tothe compressibility of the clay. This results in aunique relationship between effective stress com-ponents and void ratio (the state boundary surface(SBS)), which the soil obeys after yield has oc-curred (see e.g. Scho®eld & Wroth, 1968). As aconsequence, by normalizing the stresses withrespect to an èquivalent' pressure determined onthe compression curve at the current void ratio,the normalized stress paths should describe aunique surface, which separates attainable fromunattainable states.

For a natural clay, the question arises as towhich of the compression curves in Fig. 19 shouldbe used in normalizing the stress paths, that is, indescribing volumetric hardening. Smith et al.(1992) argued that the compression curve of anatural clay should not be used for normalizingdata, since it merely represents a transition fromthe sedimentary state (identi®ed by the SCC) tothe reconstituted (destructured) state. They choseto normalize their triaxial stress paths, carried outon Bothkennar clay, with respect to equivalentpressures read from the compression curve of thereconstituted clay, which was assumed to representthe ìntrinsic' (i.e. structure independent) compres-sion properties of the clay.

In studying the behaviour of Pisa clay, Callisto& Calabresi (1995) normalized the stress pathswith respect to the equivalent mean effective stressp9SCC, determined from the SCC of Fig. 19, using aK0 value of 0´67; they obtained the normalizedplot shown in Fig. 20. In this ®gure it is possibleto identify a boundary to the attainable states. Mostof the normalized stress paths, however, once hav-ing touched this envelope, bend and point inwards,rather than describe a single surface. Hence it isnot possible to locate a proper SBS in the normal-ized plane in Fig. 20, and the boundary to all

possible states was termed the ìnitial SBS'. Sucha boundary coincides with the normalized yieldlocus only in the portion mapped by tests A60 andA30, while elsewhere the initial SBS lies beyondthe yield locus.

It is possible to regard the SCC as the com-pression curve that the soil would describe if itwere allowed to keep its interparticle arrangementand bonds, i.e. if no disruption of its micro-structure were caused by too fast a loading, or bystress paths signi®cantly different from those fol-lowed during sedimentation. The fact that in thenormalization presented in Fig. 20 no unique SBSis obtained signi®es that the SCC cannot describevolumetric hardening for the clay; this circum-stance is seen as a signal that substantial changesare taking place in the microstructure of the clay.Consequently, points from which the normalizedpaths are re-directed towards the inside of theyield surface can be regarded as marking theonset of destructuration. This is thought to be away to de®ne destructuration in a quantitative,although conventional, way. Remarkably, as poin-ted out by Callisto & Calabresi (1995), the onsetof destructuration is seen to occur at a nearlyconstant value of the speci®c strain energy (W �2:0 kJ=m3). This is shown in Fig. 20, in whichthe contour W � 2:0 kJ=m3 is superimposed onthe destructuration envelope, and suggests thatdestructuration could be associated with a thresh-old energy value.

It is worth mentioning that, although the onlynormalization discussed here is the one shown inFig. 20, other normalizations were attempted forthe triaxial stress paths, in which the equivalentpressure was calculated using either the normalcompression curve of the natural clay or that ofthe reconstituted clay (Callisto, 1996). In neither

Initial SBS

W 5 2 kJ/m3

Yield locus

0.4 0.8 1.2 1.6

20.8

20.6

20.4

20.2

0

0.2

0.4

0.6

0.8

1

q/p

′ SC

C

p ′/p ′SCC

Tens

ion

O

A180

A135A90

A60

A30

A0

A315

A280

Fig. 20. Normalized triaxial stress paths


case was a unique SBS obtained. This occurrencesuggests that plastic volumetric strains alone arenot suf®cient to describe hardening, i.e. a uniqueSBS could exist only in a space containing, inaddition to the stress components, one or morehardening parameters in which the plastic devia-toric strains should be incorporated as well (e.g.Kavvadas, 1994; Muir Wood, 1995).

STIFFNESS

In this section, the stiffness of Pisa clay, deter-mined for small stress increments starting from thein situ stresses, is discussed. To this purpose, thetangent shear and bulk moduli, de®ned as if thesoil were an isotropic elastic material, were used.However, it has been argued previously that theclay can undergo irreversible deformations, evenfor very small stress increments; in addition, themechanical behaviour may be anisotropic. There-fore, elastic moduli should be regarded as a toolwith which to conventionally describe the soilstiffness, while it is not intended that, even forvery small stress increments, the clay behaves in apurely elastic manner.

Stiffness in the triaxial testsFigure 21 shows the values of the tangent bulk

and shear moduli K and G, determined as

K � d p9

dåv

G � dq

3 dås

(4)

plotted against the direction of the stress path ù(see Fig. 3), for three different values of the stresspath length LSP (5, 10 and 20 kPa). The corre-sponding volumetric and shear strains were in therange of 0´01±0´3%, depending on the stress pathdirection.

For a ®xed value of ù, values of K and G areseen to diminish as LSP increases, thus evidencinga non-linear behaviour starting from very smallstress increments.

For a constant value of LSP the moduli dependsubstantially on the stress path direction. The bulkmodulus K (Fig. 21(a)) is maximum for ù � 1808,while the shear modulus G is maximum forù � 3158 (Fig. 21(b)). The dependence of K andG, for a ®xed stress path length, on the directionof the stress paths ù can be interpreted either interms of coupled elasticity, or as evidence ofplastic behaviour, even for very small stress incre-ments. The former interpretation has been dis-cussed by, for instance, Graham & Houlsby (1983),who proposed a form of cross-anisotropic elasticity

restricted to triaxial conditions. If the behaviourshown in Fig. 21 is to be interpreted through sucha model, then the quantities K and G calculatedthrough equations (4) and shown in Fig. 21 shouldbe regarded as `equivalent' moduli. According toGraham & Houlsby (1983), the `equivalent' moduliKeq and Geq are given by

Keq � 3K�G� ÿ J 2

3G� ÿ J (dq=d p9)

Geq � 1

3

3K�G� ÿ J2

K� ÿ J (d p9=dq)

" # (5)

The parameters of the model are K�, G� and J,while Keq and Geq are not material parameters, asthey depend on the stress path direction d q=d p9.In addition, dq=d p9 � tanù, and hence Keq andGeq in equation (5) are periodic functions of ù, theperiod being 1808 (see e.g. Wheeler & Houlsby(1994)). It can be seen from Fig. 21 that theobserved variation of K and G with ù does notshow a period of 1808; for instance, the valuesof K (ù � 08) and G (ù � 908) are very differentfrom the values of K (ù � 1808) and G(ù � 2708), respectively. Therefore, it appears that

Fig. 21. Bulk and shear tangent moduli, determined intriaxial tests on natural clay, plotted as a function ofthe stress path direction ù. The direction of thereconsolidation path is shown by the arrow

30 90 150 210 270 330 30ω: deg.

(b)

0

2000

4000

6000

8000

10000

12000

G: k

Pa

LSP5 kPa10 kPa15 kPa

0 60 120 180 240 300 360ω: deg.

(a)

0

2000

4000

6000

8000

10000

12000

K: k

Pa


the dependence of K and G on the stress pathdirection cannot be satisfactorily interpreted interms of cross-anisotropic elasticity; the interpreta-tion of such a dependence in terms of plasticbehaviour appears more promising.

A comparison between the tangent moduli ofthe natural and the reconstituted soil, for LSP � 10and 20 kPa, is shown in Fig. 22, in which thestiffness of the reconstituted clay for small incre-ments seems to be in fair agreement with that ofthe natural clay.

During test A90, the shear wave velocity in thesample was measured using the bender elementstechnique (Viggiani, 1992). The shear modulus G0

at the in situ stress state, calculated from the shearwave velocity, is equal to 23 MPa. This value ismuch larger than those shown in Fig. 21, since themaximum shear strain in a bender element test,occurring near the transmitter, can be estimated tobe smaller than 0´001% (Dyvik & Madshus,1985).

Stiffness in the true triaxial testsFigure 23 shows the contours of equal shear

strains in the octahedral plane, for 0:1% , ås , 1%.In this plot, the distance of a contour from point

O, gauged along a stress path, is a measure of theincrement in the deviatoric stress required in orderto produce a ®xed shear strain, and is thereforeproportional to the secant shear stiffness of the soilat a given strain. It can be seen from Fig. 23 thatsuch a distance varies with the stress path direc-tion, being minimum for á � 0 and maximum forá � 1808, thus suggesting a signi®cant dependenceon the stiffness on the stress path direction.

This point can be emphasized by looking at thetangent shear modulus plotted as a function of á.For general stress conditions, as q and ås are bothnon-linear functions of the stress and strain compo-nents respectively, the tangent shear modulus G iscalculated as

G � 1

23

[(dó 9a ÿ dó 9hl)2 � (dó 9hl ÿ dó 9h2)2 � (dó 9h2 ÿ dó 9a)2]1=2

[(dåa ÿ dåhl)2 � (dåhl ÿ dåh2)2 � (dåh2 ÿ dåa)2]1=2

(6)

In Fig. 24, G is plotted against the stress pathdirection á for LSP � 5, 10 and 20 kPa; suchvalues of LSP correspond to shear strains in therange 0´008±0´5%. This plot shows that G ishighly dependent on á: it increases progressivelyas the stress path deviates from the conditions oftriaxial compression (á � 0), and reaches a maxi-mum under the conditions of triaxial extension(á � 1808). For á � 0 the values of G are approxi-mately equal to those observed in the triaxial testA90 (see Fig. 21(b)), as it should be, since testsT0 and A90 followed identical stress paths. Thenon-linearity of the observed behaviour is evi-

Fig. 22. Comparison between tangent moduli of thenatural and the reconstituted clay

0 60 120 180 240 300 360ω: deg.

(a)

0

2000

4000

6000

8000

12000

10000

K: k

Pa

10 kPa, natural10 kPa, reconstituted20 kPa, natural20 kPa, reconstituted

30 90 150 210 270 330 30ω: deg.

(b)

0

2000

4000

6000

8000

10000

G: k

Pa

LSP

T0

T60

T90

T120

T150T180

0.1%0.20.31.0

O

80

40

0

240

260 220 20 60

σ ′h1 σ ′h2

xσ: kPa

σ ′a, yσ: kPa

Fig. 23. Shear strain contours in the octahedral plane,for 0:1 , ås , 1%


denced by the rapid decrease in G along a singlestress path (i.e. for a constant value of á) as LSPincreases.

As discussed for the triaxial tests, the depen-dence of G on the stress path direction can beinterpreted in terms of anisotropic elasticity or interms of plastic behaviour. Cross-anisotropic elasti-city for the true triaxial tests can no longer bedescribed by the three-constants model proposedby Graham & Houlsby (1983) (see above). Across-anisotropic model is characterized by ®veparameters that, assuming that the direction ofmaterial symmetry is vertical, can be chosen asfollows: the Young's moduli in the vertical andhorizontal directions Ea and Eh, the horizontal±horizontal and horizontal±vertical Poisson ratiosíhh and íah, and the horizontal±vertical shearmodulus Gah. The latter modulus links shear strainsbetween the vertical and horizontal directions tothe corresponding shear stresses; such shear strainsand stresses are not applied in the TTA, so that novalues of Gah can be deduced for the present tests,and the relevant parameters of the model reduce tofour.

If the behaviour shown by Fig. 25 is to inter-preted in terms of cross-anisotropic elasticity, thenthe values of G calculated using equation (6) mustbe regarded as `equivalent moduli', G no longerbeing a material parameter. By inserting thestress±strain relationships for a cross-anisotropicelastic material in equation (6) and using thefollowing parameters:

Ea � 5000 kPaEa

Eh

� 4

íhh � 0:2íah

íhh

� 0:2 (7)

the values of Geq shown in Fig. 25 are obtained. Inthe same ®gure, the values of G observed forLSP � 5 kPa are plotted for comparison. It can be

seen that the observed and predicted values of theshear moduli are in good agreement for 0 ,á, 908. However, for 908 ,á, 1808 the twocurves in Fig. 25 diverge, the response of thecross-anisotropic elastic model being symmetricabout the direction á � 908. Hence, also for thetrue triaxial results, interpretation of the pre-yieldresponse through a cross-anisotropic elastic modelis not entirely satisfactorily, since such a model iscapable of reproducing the observed behaviouronly for a limited range of stress path direction.Such behaviour should probably be interpreted interms of plasticity. In this sense, the occurrencethat in both the triaxial and the true triaxial teststhe lowest stiffness is observed for stress pathdirections close to that of the reconsolidation path(indicated in Figs 21 and 24 by arrows, ù � 71:68and á � 08), seems to evidence a possible effect ofthe previous stress history of the samples on theirbehaviour for small stress increments. Results qua-litatively similar to those shown in Figs 23 and 24were obtained analytically by Darve et al. (1995)through their incrementally non-linear model.

CONCLUSIONS

Different aspects of the mechanical behaviour ofthe natural soft clay found at Pisa were observedthrough drained stress path controlled tests, per-formed both in the triaxial cell and in the truetriaxial apparatus.

A direct comparison between the results ob-tained in the two apparatus in testing a samplealong the same constant p9 path showed that theshear strength measured in the triaxial cell issmaller by about 24% than that measured in thetrue triaxial apparatus. However, for deviatoricstrains smaller than 1% the results obtained in thetwo apparatus were quite consistent.

The failure envelope obtained from the truetriaxial tests showed that the clay is cross-anisotro-pic with respect to the shear strength properties.

LSP5 kPa10 kPa20 kPa

0 60 120 180α: deg.

0

3000

6000

9000

12000

15000

18000

G: k

Pa

Fig. 24. Variation in the tangent shear modulus G as afunction of the direction of the stress path in theoctahedral plane á. The direction of the reconsolida-tion path is shown by the arrow

0 30 60 90 120 150 180α: deg.

0

3000

6000

9000

12000

15000

18000

G: k

Pa

Cross-anisotropicelastic model

LSP 5 5 kPa

Fig. 25. Comparison of the experimental G versus ácurve (for LSP � 5 kPa) with the curve predic- tedusing a cross-anisotropic elastic model


The Mohr±Coulomb and Lade & Duncan (1975)criteria, if ®tted to the experimental data in triaxialcompression with ó 9h1 � ó 9h2, overestimate theshear strength in triaxial compression with ó 9a �ó 9h1 or ó 9a � ó 9h2.

Yielding of natural Pisa clay was found to bequite a gradual phenomenon, so that a somewhatarbitrary procedure was needed in order to locatethe yield locus. Speci®cally, the yield locus wasidenti®ed with some reliability in the triaxial plane,using the procedures outlined previously, while itwas rather loosely de®ned in the octahedral plane,where two tentative, slightly different yield lociwere proposed.

It was seen that in the octahedral plane plastic¯ow is essentially associated, whereas some devia-tions from normality were observed in the triaxialplane.

In the triaxial tests on the natural clay, speci®cstrain energy at yield was found to depend on thedirection of the stress path.

For the natural clay it was not possible to obtaina unique state boundary surface by normalizing thetriaxial stress paths with respect to an equivalentpressure, probably because of the occurrence ofsigni®cant changes in the microstructure of theclay. Normalization of the stress paths with respectto the equivalent mean effective stress read fromthe sedimentation compression curve at the currentvoid ratio allowed the de®nition of a destructura-tion locus. Destructuration was seen to occur whena nearly constant value of the speci®c strain energywas reached.

The stiffness of the clay was conventionallyquanti®ed by means of `elastic' tangent moduli.Shear and bulk moduli were observed to decreasealong a single stress path, because of non-linearity,and to depend strongly on the direction of thestress path. Neither for axisymmetric stress paths,nor for stress paths lying on the octahedral plane,were the variations of the tangent moduli with thestress path direction entirely consistent with thehypothesis of cross-anisotropic elastic behaviour;however, such hypothesis allowed the observedbehaviour to be described for a limited range ofstress path directions. Plasticity-based models,which can take into account irreversible strainsoccurring for stresses within the yield locus, couldbetter describe the observed behaviour.

ACKNOWLEDGEMENTS

The authors are indebted to Dr P. I. Lewin, whokindly made available the true triaxial apparatusand his own considerable experience. Dr R. N.Taylor allowed one of us (L.C.) to work in thelaboratory at GERC. Dr S. Rampello revised themanuscript and helped with fruitful discussions.

NOTATIONE Young's modulusG shear modulusK bulk modulus

K0 coef®cient of earth pressure at restLSP length of stress path

(��(ó 9a ÿ ó 9a0)2 � (ó 9h1 ÿ ó 9h10)2 � (ó 9h2 ÿ ó 9h20)2

p)

p9 mean effective stress (� 13(ó 9a � ó 9h1 � ó 9h2))

p9 mean effective stress in axisymmetric conditions(� 1

3(ó 9a � 2ó 9h))

p9SCC equivalent mean effective stress determined onthe sedimentation compression curve at thecurrent void ratio

q deviatoric stress invariant(� 1=

��2p

[(ó 9a ÿ ó 9h1)2 � (ó 9h1 ÿ ó 9h2)2 � (ó 9h2ÿó 9a)2]1=2)

q deviatoric stress invariant in axisymmetricconditions (� (ó 9a ÿ ó 9h))

W strain energy per unit volume(� � (ó 9a dåa � ó 9h1 dåh1 � ó 9h2 dåh2))

xå, yå coordinates of strain point in the octahedralplane of strain (distances from the origin in theoctahedral plane are set equal to ås)

xó , yó coordinates of stress point in the octahedralplane of stress (distances from the origin in theoctahedral plane are set equal to q)

á direction of a true triaxial stress path in theoctahedral plane

ås deviatoric strain invariant(� (

��2=3

p)[(åa ÿ åh1)2 � (åh1 ÿ åh2)2

�(åh2 ÿ åa)2]1=2)ås deviatoric strain invariant in axisymmetric

conditions (� 23(åa ÿ åh))

åv volumetric strain (åa � åh1 � åh2)åv volumetric strain in axisymmetric conditions

(åa � 2åh)ó 9 effective normal stress componentsù direction of a triaxial stress path in the qp9 planeí Poisson's ratio

Subscripts0 relative to the in situ statea vertical direction in the ®eld, or axial direction

in the triaxial apparatuseq equivalent modulush horizontal direction in the ®eld, or radial

direction in the triaxial apparatush1, h2 two mutually orthogonal directions in the ®eld,

or two principal directions in the true triaxialapparatus

Superscriptsp plastic component

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ised theory of visco-elasticity in London clay. GeÂo-technique 40, No. 2, 641±646.

Alawaji, H., Alawi, M., Ko, H. Y., Sture, S., Peters, J. F.& Wood, D. M. (1990). Experimental observations ofanisotropy in some stress-controlled tests on dry sand.In Yielding, Damage and Failure of Anisotropic Solids


(ed. J. P. Boehler), EGFS, pp. 251±264. London:Mechanical Engineering Publications.

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