Ge 490603

On the mechanics of structured sands

T. CUCCOVILLO and M. R. COOP{

To date the effect of structure on the behaviourof natural sands has focused almost exclusivelyon the component of bonding, and the effect offabric has been largely overlooked. The paperdescribes a detailed investigation of the beha-viour of two natural sands by means of triaxialtesting over a wide range of pressures. Onematerial had bonding as the principal elementof its structure and the other fabric. Followingon from a paper of Cuccovillo and Coop whichexamined the inuence of the two structuralelements on the small-strain stiffness, the cur-rent paper develops a new framework for theyielding and large-strain behaviour. It is sug-gested that structure should be considered as anelement of the nature of a sand in addition toproperties such as mineralogy, particle shapeand grading. The resulting framework is thencapable of encompassing the patterns of beha-viour seen for both bonding- and fabric-domi-nated sands. While bonding results in a cohesivemode of shearing, it is demonstrated that whenfabric dominates, the shearing behaviour re-mains predominantly frictional, although therates of dilation and peak strengths may be verymuch higher than for the reconstituted soil atthe same stressvolume state. It is shown that itis not necessarily the position of the state of thesoil relative to the critical-state line that distin-guishes strain-hardening and strain-softening be-haviour, but the proximity to the boundarydetermined in isotropic compression.

KEYWORDS: fabric/structure of soils; laboratorytests; sands; soft rocks.

Jusqu'ici, l'effet de structure sur le comporte-ment des sables naturels s'est axe presque ex-clusivement sur le composant de liaison; l'effetde la texture a ete le plus souvent oublie. Cetexpose decrit une etude detaillee du comporte-ment de deux sables naturels au moyen d'essaistriaxiaux dans une vaste fourchette de pressions.Pour l'un des materiaux, le composant de liaisonetait l'element principal de sa structure et pourl'autre, c'etait sa texture. Faisant suite a uneetude de Cuccovillo et Coop qui avaient examinel'inuence des deux elements structuraux sur larigidite de petite deformation, cet expose devel-oppe un nouveau cadre de travail pour l'elasti-cite et le comportement de grande deformation.Nous suggerons que la structure devrait etreconsideree comme un element de la nature d'unsable en plus des proprietes comme la mineralo-gie, la forme et la taille des particules. Le cadrede travail qui en resulte est alors capable detenir compte des modeles de comportement con-states pour les sables domines par le composantde liaison et les sables domines par la texture.Alors que la liaison donne un mode cohesif decisaillement, nous demontrons que lorsque latexture domine, le comportement au cisaillementdemeure en predominance frictionnel bien queles taux de dilatation et les resistances de pointepuissent etre beaucoup plus eleves que dans lecas de sols reconstitues et ramenes au memeetat de tension-volume. Nous montrons que cen'est pas necessairement la position de l'etat dusol par rapport a la ligne d'etat critique quidistingue le comportement de durcissement al'effort et de ramollissement a l'effort mais laproximite de la frontiere determinee en com-pression isotrope.

INTRODUCTION

The behaviour of sands in laboratory or eld testshas traditionally been related to their relative den-

sity (Dr), but more recent work has highlighted thedeciencies of this approach. Experimental studiesin the triaxial apparatus (e.g. Coop & Lee, 1993;Lade & Yamamuro, 1996) have shown that, pro-vided sufciently high pressures are reached, it ispossible to identify a normal compression line(NCL) which lies parallel to the critical state line(CSL). It was then shown that strain-softening andstrain-hardening modes of behaviour were denednot by Dr but by the combination of the specicvolume (v), mean effective stress ( p9) and deviato-

Cuccovillo, T. & Coop, M. R. (1999). Geotechnique 49, No. 6, 741760

741

Manuscript received 30 July 1998; revised manuscriptaccepted 30 June 1999.Discussion on this paper closes 30 June 2000; for furtherdetails see p. ii. South Bank University, London; formerly City Uni-versity, London.{ City University, London.

ric stress (q9) that denes the location of the stateof the soil relative to the NCL or CSL. This wasin accordance with a critical state framework and,when associated with an analysis of the volumetricchanges in stressdilatancy terms, could be used todescribe accurately the peak states observed. Thelocations of the CSL and NCL were found to bedifferent for different sands (Coop & Cuccovillo,1998) and were shown to be related to the amountof particle breakage that the soil underwent duringloading and hence to the nature of the soil parti-cles. This nature was considered to be the grading,together with the mineralogy of the particles andtheir shapes. One of the principal drawbacks ofthis work was that it was almost all carried out onreconstituted sands. Studies of the behaviour ofnatural sands have, in contrast, been relatively rare,particularly as a result of the difculty of retrievingundisturbed samples.

Structure in sands has often been simply identi-ed with the bonding which arises from inter-particle cementing, since interparticle forces arenegligible, and it is on this component of structurethat most recent research has been focused (e.g.Clough et al., 1981). Cemented sands have beenseen to have patterns of behaviour that resemblethose observed for structured clays and which arerelated to the elements of the soil structure createdby the geological processes experienced by the soilsince its deposition. State alone has therefore beenconsidered insufcient to account for those patternsof behaviour which do not conform to the criticalstate framework. To distinguish features of beha-viour arising from structure from those related tochanges in state, an approach that has been widelyadopted has been to compare the response of thenatural soil to that of the corresponding reconsti-tuted soil (e.g. Leroueil & Vaughan, 1990). Triaxialtest data for shearing of structured soils have oftenbeen normalized with respect to the NCL and/orthe CSL of the reconstituted soil. Although thisapproach has been very useful in highlightingqualitatively many features deriving from structure,it has failed to provide a unied framework thatcould identify and fully describe mechanicalfeatures such as yielding, strength and a stateboundary surface for structured soils. Further de-velopment of a consistent framework for naturalsands has been prevented by the difculty inidentifying a variable which could quantify struc-ture, as p9, q9 and v do for state, and it is thisaspect of the mechanics of structured sands that isa central theme of this paper.

For some cemented sands, in particular thecarbonates, the usual comparisons with the beha-viour of reconstituted soils were not initially possi-ble, rstly because it was difcult to reconstitutethe cemented soil without breaking its delicateshell particles and secondly because the interpreta-

tion of the data was often complicated by largevariations in the properties of the intact samples.This led some researchers to test articially ce-mented sands, making comparisons not with thereconstituted soil but with soils made up of thesame constituents in which bonding had not beenallowed to develop (e.g. Huang & Airey, 1993;Coop & Atkinson, 1993). Using this method,Cuccovillo & Coop (1993) examined the inuenceof the strength of the cement bonds by varying theamount of cement added to an articially cementedcarbonate sand. Fig. 1 shows a schematic represen-tation of the isotropic compression behaviour theyobserved. The effect of the cement was to makethe initial stressstrain behaviour stiffer and elas-tic, so that the gradual yield seen for the loosesand, which was attributed to the onset of particlebreakage, was not seen for the cemented sand. Thekey difference in the behaviour of the strongly andweakly cemented soils was that the former reachedstates outside the intrinsic NCL dened by theuncemented soil, while the weakly bonded soilyielded before reaching the NCL. During shearing,three modes of behaviour could be identied, asillustrated in Fig. 2, depending on the initial stateof the sample relative to the yield curve of thecement bonds. At conning pressures which werelow relative to the strength of the bonds, thebehaviour was elastic up to a well-dened yield,followed by strain-softening towards a critical state.At intermediate pressures, yield occurred beforereaching the critical state, so no peak strength wasseen and the failure was essentially frictional. Theonly effect of the bonding at these intermediatepressures was therefore a stiffening of the initialstressstrain behaviour. At the highest pressures,the behaviour was ductile from the start as the

Intrinsic isotropicnormal compression line

sw

v

ln p

w

s

UncementedCementedWeakStrong

Fig. 1. Schematic comparison of the isotropic com-pression of weakly and strongly cemented carbonatesand

742 CUCCOVILLO AND COOP

bonding had been broken during compression, andthe stressstrain behaviour tended towards that ofthe uncemented soil. The effect of an increase inthe cement content was to expand the yield curveof the cement bonds.

The type of framework shown in Figs 1 and 2has been developed considering only the compo-nent of soil structure arising from bonding. Theinuence of fabric has, however, been largely over-looked, either because of a lack of data for intactsands with their intact fabric preserved or becauseof the belief that, unlike clays, this inuence wasnot important for sands, even if Barton (1993)identied that for many coarse-grained soft rocksthe transition from a loose sand to a sandstoneinvolved not only the creation of bonding but alsochanges to the fabric. This paper will discuss theinuence of both aspects of structure on the mech-anics of sands, comparing and contrasting thebehaviour of two sands, a calcarenite which hasbonding as the dominant structural feature and asilica sandstone for which fabric is more impor-tant. Cuccovillo & Coop (1997b) examined thesmall-strain behaviour of the two materials, andthe current paper now extends that work to exam-ine the behaviour at larger strains. In this investi-gation some of the data for the calcarenite arethose from Coop & Atkinson (1993), which havebeen reinterpreted in the light of the new methodsof analysis.

Yield surfaceof cement

Critical-state line

1 2 3

Yield pointCritical state

1

23

q /p

M

q

p

a

Fig. 2. Schematic diagram showing modes of shearingbehaviour for cemented carbonate sands (after Coop& Atkinson, 1993)

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ON THE MECHANICS OF STRUCTURED SANDS 743

SOIL DESCRIPTIONS

Table 1 gives a summary of the principalcharacteristics of the two structured sands. Thesilica sandstone was from the Lower Greensandseries and was recovered as a block sample fromabout 5 m depth in a quarry near Maidstone, Kent.The soil is characterized by strong particles bondedby a weak cement. It was deposited during theCretaceous in a shallow marine environment(Casey, 1961) and in its geological history it hasbeen subjected to deep burial followed by theerosion of the overlying strata, so that it has beenoverconsolidated, with a past maximum verticaleffective stress estimated to be around 9 MPa. Aniron oxide cement was then deposited around thequartz grains at a late stage in the geologicalhistory from groundwater owing through the sand(Warren, 1995). A scanning electron micrograph(SEM) of a polished section is shown in Fig. 3.The cement is the white material which appears toweld the particles together. There is only a smallamount of cement present, and so the low specicvolume v of 145 is clearly related to the particlepacking, or fabric, and not to the inlling of thevoid spaces with cement. Apart from the relativelysmall amount of cement, Dapples (1972) has iden-tied that the weakness of this type of bondingresults from the poor adhesion of the iron oxide tothe quartz.

Reconstituted samples of both the silica sand-

stone and the calcarenite were created by gentlybreaking the cement bonds while avoiding damageto the particles. For the silica sandstone Cuccovillo& Coop (1997b) found it to be impossible torecreate the intact specic volume by compaction ofthe reconstituted soil. The only way that this couldbe achieved was to overconsolidate the sample byisotropic compression in the triaxial apparatus, butthe maximum stress of 70 MPa required to do thiswas far in excess of that ever experienced by thenatural soil. The reason for the high density of thesilica sandstone in situ was identied from anexamination of the thin section shown in Fig. 4,which shows a well-developed interlocking fabric.Dusseault & Morgenstern (1979) and Maxwell(1964) have attributed the development of this typeof `locked' fabric in geologically old silica sands(pre-Quaternary) to pressure solution at the particlecontacts, where the contact stresses are very muchhigher than the overburden stress. This then allowsthe particles to rearrange relative to one another,creating large grain contact areas and achievingparticle packings which cannot be recreated whenthe soil is reconstituted, as the original interparticlecontacts have been lost. This well-dened fabricwas therefore created while the soil was buried

Fig. 3. Scanning electron micrograph of the silicasandstone (after Cuccovillo & Coop, 1997b)

Fig. 4. Thin section of the silica sandstone (width ofphoto equivalent to 07 mm; plain white light andstained void spaces)


deeply and long before the cement was deposited.The deposition of the iron oxide after the geologicaloverconsolidation and the development of the fabricis then the reason why the bonds are still intact, asthe strains experienced by the soil subsequent tothese events were small. Although there is a naturalvariation in the degree of bonding of the LowerGreensand, all the samples used in the current studywere taken from the same block and so had auniform specic volume and degree of bonding.

The calcarenite samples were retrieved by triple-tube rotary coring and come from the site of theNorth Rankin offshore platform in Western Austra-lia. By comparison with the silica sandstone thiscalcarenite may be characterized as having weakparticles and a strong interparticle cement. The soilis a biogenic carbonate sand comprising shellsdeposited in a warm coastal sea environment duringthe Pleistocene. Thin sections of two of the samplesare shown in Fig. 5. The particles are angular,resulting in an open fabric. Under the cross-polar-ized light used to take the photographs, the voidspaces are black and the white fringe that surroundseach particle is the cementing, which is calciumcarbonate deposited soon after the time of deposi-tion of the particles. The type of shells and the

amount of cement deposited are both sensitive tothe precise depositional environment (Fookes, 1988;Apthorpe et al., 1988), and since the rates ofdeposition are slow, there are large and apparentlyrandom variations in the nature of the soils oversmall intervals of depth.

Most of the calcarenite samples were fromdepths between 127 and 142 m. The variationswithin this range of depths of both the particlenatures and the amount of cement deposited areevident in Fig. 5 and result in a wide range ofspecic volumes for the samples tested (168 to203). Despite these differences, the soils, whenreconstituted, were found to have remarkably simi-lar properties. Cuccovillo & Coop (1993) foundthat a single state boundary surface could bedened for all of the reconstituted samples tested.Another important feature that can be seen qualita-tively in Fig. 5 is the relationship between specicvolume and degree of cementing. The more heavilycemented sample is much denser, partly as a resultof the inlling of the void spaces with the cement.The geological loading history of the soils hasbeen one of rst loading only, and since the in situstresses are well below those at yield, the cementhas preserved the depositional fabric.

Fig. 5. Thin sections of the calcarenites (width of photos equivalent to 14 mm; cross-polarized light): (a) loose andweakly bonded; (b) dense and strongly bonded


LABORATORY EQUIPMENT AND PROCEDURES

Triaxial tests were carried out in a variety ofapparatuses covering a range of stresses from50 kPa to 70 MPa. Each of the apparatuses wascomputer controlled and data-logged and is de-scribed in detail by Cuccovillo & Coop (1999).Most tests were instrumented with a new systemfor the local measurement of the axial strain of thesample based on miniature linear variable differen-tial transformers (Cuccovillo & Coop, 1997a).Combined with new sample preparation methodsand modications to the setting-up procedure inthe apparatus to ensure the coaxiality of the axialloading system with the sample (Cuccovillo &Coop, 1997b), it was possible to resolve the stiff-ness of the materials tested down to strains of00001%. Although the data examined in this paperare for larger strain levels, it was found that theseimprovements were also necessary for a correctdenition of the yield point during shearing.

ISOTROPIC COMPRESSION

When isotropically compressed, the intact calcar-enite reached states which were impossible for thereconstituted soil (Fig. 6(a)) and from this point ofview the bonding may be characterized as strongwithin the scheme shown in Fig. 1. A clear rela-tionship existed between the specic volumes andmean effective stresses at yielding, which resultedin the identication of an isotropic yield locus.This was found to be substantially coincident withthe postyield compression curves and thus denedthe boundary for the possible states attainable inisotropic compression. The offset between the iso-tropic boundaries of the intact and reconstitutedsoils reduced as the specic volume decreased,until the two boundaries became coincident. Theisotropic boundary of the intact soil has thereforebeen modelled as bilinear, as indicated. One groupof four samples, from a narrow depth range(13371355 m), was found, however, to haveyield points which lay signicantly below those ofall the other samples (Fig. 6(b)) and closer to theintrinsic NCL dened by the reconstituted samples.This is characteristic of a weaker bonding, whichis likely to have resulted from a depositionalenvironment that was signicantly different fromthose in which the other calcarenites were created.As none of these weaker samples was loaded farbeyond yield, the postyield compression line whichis shown, and will be used in later analyses, hasbeen assumed to converge with the intrinsic NCLat the same point as for the stronger-bonded soils.

For the silica sandstone, isotropic yielding oc-curred inside the permissible space of the reconsti-tuted soil (Fig. 7) and this material may thereforebe classied as a weakly bonded material. Theisotropic boundary of the silica sandstone, there-

fore, is likely to coincide with the NCL of theoriginal uncemented soil as it was deposited in theground. However, the soil as deposited would havehad a slightly different initial grading from that ofthe current reconstituted soil because of the parti-cle breakage that the soil underwent under the highoverburden pressure which this soil, unlike thecalcarenite, had experienced before it became ce-mented. As was shown by Coop & Atkinson(1993), the location of the NCL of a soil iscontrolled by the initial grading, not the current,and a correct comparison between the compressionbehaviour of the intact soil and reconstituted sam-ples should, ideally, account for this small differ-ence in their initial gradings. In any case, theconvergence of the compression data of the intactsoil towards a slightly different NCL from thatfound for the reconstituted soil could not be con-rmed because of the limitation on the conningstress in the apparatus.

SHEARING

When sheared, the calcarenite was found toreach the same critical states as the reconstitutedsoil, dening a CSL in vln p9 space that wasparallel to the NCL of the reconstituted soil (Coop& Atkinson, 1993). The silica sandstone reachedsimilar stress ratios at the ultimate states to thereconstituted soil but localized failure of the intactsoil prevented the identication of critical states interms of volume. For the reconstituted soil theCSL was again parallel to the NCL.

An increase in conning pressure transformedthe shear behaviour of both structured sands fromstrain-softening to strain-hardening. Typical stressstrain curves are shown in Figs 8 and 9. Here,except for one undrained test on the calcarenite,the data are all from drained tests following con-stant- p9 stress paths. At the start of each test thevalues of axial strain were those from the internalmeasurements, whereas at large strains the externalmeasurements have been used.

The strain-softening mode of behaviour wascharacterized for both soils by an initially linearstressstrain relationship and no change in volume.Cuccovillo & Coop (1997b) demonstrated that thelinear stressstrain behaviour was also elastic andinterpreted the end of this linear elastic response,which identied yielding, as being the onset ofbond degradation. Despite this common feature thetwo soils achieved their peak strength through dif-ferent modes of shearing. For the calcarenite thepeak states were practically coincident with yield-ing and were followed by a rapid loss of strengthand volumetric compression. Conversely, for thesilica sandstone, at all but the very lowest conn-ing stresses, which are not considered here, thepeak states were accompanied by dilation and


plastic strains which developed after the soil hadyielded and the bonds had started to degrade. Forthe calcarenite the near coincidence of the peakstates with yielding is a clear indication of thecohesive nature of the peak strength of this struc-tured sand and the patterns of behaviour may beadequately described by Fig. 2. For the silicasandstone, however, the peak strengths were foundto be frictional, as the stressdilatancy analysispresented later will show, and the framework

shown in Fig. 2 cannot therefore describe thebehaviour observed.

For both soils, strain-hardening was accompa-nied by volumetric compression. In the case of thesilica sandstone this was associated solely with abehaviour that was non-linear from the start ofshearing, indicating that at these conning pres-sures the bonds had been degraded during isotropiccompression and had no further inuence on shear-ing. For the calcarenite, in contrast, at some inter-

Fig. 6. Isotropic compression of the calcarenite: (a) stronger-bondedsamples (after Cuccovillo & Coop, 1997b); (b) weaker-bonded samples

IntactReconstituted

4 5 6 7 8 9 10 11 12ln p : kPa

(a)

1.20

1.40

1.60

1.80

2.00

2.20

v

100 1000 10000 100000p : kPa

Intact IB

NCL

CSL

4 5 6 7 8 9 10 11 12ln p : kPa

(b)

1.20

1.40

1.60

1.80

2.00

2.20

v

100 1000 10000 100000p : kPa

Intact (data from Coop& Atkinson (1993))Reconstituted

CSL

NCL

RAN3-RAN4

Intact IBStronger bonding

Intact IBWeaker bonding


mediate stress levels, strain-hardening was alsoseen to be associated with an initially linearresponse. In this case the strength was thereforefrictional and the bonds only contributed to anincrease in the initial stiffness.

At their critical states the intact samples ofcalcarenite and silica sandstone reached similarstress ratios to those of the corresponding reconsti-tuted soils as shown in Fig. 10. It is believed thatin both cases the CSL is straight and that anytendency to curve at the high pressures is morelikely to be due to incomplete testing.

The peak strengths of both materials were foundto increase with increasing p9 (Fig. 11). The varia-tions of the specic volumes at the peak for theintact samples of both soils were small (within0:01) and these differences therefore could onlyhave had a negligible inuence on the peakstrengths observed. For the silica sandstone aunique envelope can be identied which convergestowards the CSL at higher values of p9. The datafor the calcarenite are insufcient to identify peakfailure envelopes, but the much lower strength ofsample RAN6 compared to the other intact samplesof calcarenite seems likely to be not only becauseof the lower p9 but also, and perhaps predominantly,because this was one of the four weaker-bondedsamples.

Figure 11 also shows that the peak states denedby the two intact soils lie well above those denedby the reconstituted soils. However, a correct com-parison needs to account for the inuence ofdifferences in the specic volumes between the

intact and reconstituted soils, and this will be donelater by means of a normalization of the data withrespect to an equivalent pressure.

STRESS DILATANCY OF A NATURAL SILICA

SANDSTONE

As for the reconstituted soil, the peak stressratios of the intact silica sandstone were achievedwhen the rate of dilation was at its maximum. Thisindicates that the peak strength of this structuredsand was purely frictional, in contrast to the cohe-sive nature of the peak strength of the calcarenite.In the following analyses of these states, the dila-tancy d has been dened as

d pv

ps(1)

where pv and ps are the plastic components of

the volumetric and shear strains. The dilatancy hasonly been calculated for the higher values of thestress ratio ( q9= p9), for which the elastic com-ponent of both strains is negligible, as are thebedding errors in pv, which was measured usingan external volume gauge.

In Fig. 12 the peak stress ratio (p) is plottedagainst the maximum dilatancy (dmax). The intactsoil reached a dilatancy of 17, which is very muchhigher than either the maximum value of 03 forthe reconstituted soil or that of 075 reported byRowe (1969) for reconstituted silica sands with thedensest possible packing. Despite these remarkabledifferences, the intact and reconstituted soils fol-

R9

R10

IntactReconstituted

NCL

4 5 6 7 8 9 10 11 12ln p : kPa

1.20

v

1.45

1.60

1.75

1.90 100 1000 10000 100000p : kPa

Fig. 7. Isotropic compression of the silica sandstone (afterCuccovillo & Coop, 1997b)


lowed the same stressdilatancy relationship,which may be described by an equation of thesame form as the ow rule used in Cam Clay(Roscoe & Schoeld, 1963), and which was alsochosen by Nova & Wood (1979) for their modelfor sands sheared in triaxial compression:

p M dmax (2)where M is the value of at the critical state and is a constant. The gure shows, however, thatbecause of a relatively low value of for this soil,ow rules such as that of the original Cam Clay orthat proposed by Rowe (1962) cannot be used, asthey signicantly overestimate the peak strength.

A large difference between the dilatancies wasstill seen when comparisons were made between

the behaviours of the intact and reconstituted soilsat volumetric states which were similar relative tothe CSL. Fig. 13(a) shows values of p9=p9cs at thepeak stress ratio, indicated as ( p9=p9cs)p, plottedagainst dmax, where p9cs is an equivalent pressuretaken on the CSL and is dened in Fig. 14. For thesame normalized state the dilatancy at peak of theintact soil is still very much higher than that ofthe reconstituted soil. The trend of the data for theintact soil seems to indicate a linear relationship asfor the reconstituted soil. However, an extrapola-tion of the line for the intact soil gives an interceptwith a value of ( p9=p9cs)p greater than unity. Thissuggests that the CSL of the intact soil in vln p9space is located to the right of that which wasfound for the reconstituted soil, although this could

Fig. 8. Typical stressstrain curves for shearing of the calcarenite: (a)undrained test at p9init 255 kPa; (b) test at constant p9 of 1400 kPa; (c)test at constant p9 of 4910 kPa

Yield point

q

u

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0 5 10 15 20 25 30a: %

(a)

q: k

Pa

0

500

1000

1500

2000

2500

3000

0

500

1000

1500

2000

2500

3000

u

: kP

a

Yield pointN3p 5 1400 kPa

0 5 10 15 20 25 30a: %

(b)

q: k

Pa

0

500

1000

1500

2000

2500

3000

25

0

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not be conrmed experimentally, because of strainlocalization in some tests and premature ending ofothers due to the strain limit of the radial strainbelt. It is possible that the differences in the initialgrading of the intact and reconstituted soils mayhave been responsible for the different locations oftheir CSLs, as discussed above. Fig. 13(b) shows,however, that even when the states of the intactsoil are normalized with respect to an offset CSL,assumed to be parallel to that of the reconstitutedsoil, although the intercept is now the same, alarge difference is still seen in the dilatancy of theintact and reconstituted soils. Even if the high peakstrengths of the natural silica sandstone are fric-tional, they are therefore only in part a conse-quence of the high density of the intact soil. Itsinterlocked fabric and the presence of some re-maining interparticle cementing are therefore be-lieved to be responsible for the higher strengths ofthe intact soil. The values of dilatancy for thesilica sandstone were of a similar order to thoseobserved in shear box tests by Dusseault & Mor-genstern (1979) for three natural silica sands whichhad several features in common with that testedhere, notably that they were geologically old andhad a quartz composition with a high density andinterlocked fabric.

Qualitative considerations of energy balancesuggest that the dilation of the intact soil afteryielding is inhibited by the interlocked fabric andby the continued presence of some of the bonding.Fig. 15 shows that prior to peak the dilatancyexperienced by the intact samples at a given stressratio is smaller than that of the reconstitutedsamples and that the rate of dilation for the intactsoil decreases as the p9 at which the samples weresheared reduces. This initial delay is later compen-sated for by a faster dilation that culminates at

peak. In terms of energy, the total work done bythe stresses at the boundary of the soil element(W ) is partly dissipated in friction (Wfric) andpartly spent in disrupting the structure of the soil(Wstruc), so that

W Wfric Wstruc (3)For axisymmetry and for a unit volume, equation(3) can be written as

q9 ps p9pv Mp9ps Wstruc (4)or

q9

p9 M

pv

ps Wstruc

p9ps(5)

To maintain a balance in equation (5), since M isa constant, at a given stress ratio, if work is spentin degrading the bonding and disrupting the soilfabric the rate of dilation has to decrease. Up toyielding, the presence of bonding prevents theintact soil from dilating. After yielding, the gradualdegradation of the bonds and the disruption of thefabric inhibit the dilation of the soil, which is laterrecovered by a more rapid increase of the dilatancyuntil a maximum is reached, which both corre-sponds to and causes the higher peak strength.

A FRAMEWORK FOR THE BEHAVIOUR OF

STRUCTURED SANDS

To account for the effect that the presence ofcementing has on the volumetric state Cuccovillo& Coop (1993) normalized the stress paths forboth the intact and the reconstituted samples ofcalcarenite by means of p9cs. Fig. 16(a) shows thatfor the samples of intact calcarenite that had notyielded during isotropic compression, neither a

0 5 10 15 20 25 30a: %

(c)

q: k

Pa

0

2000

4000

6000

8000

10000

25

0

5

10

15

v: %

v

q

N2p 5 4910 kPa

Fig. 8. (Cont.)


Fig. 9. Typical stressstrain curves for constant- p9 shearing of the silicasandstone: (a) p9 900 kPa; (b) p9 14 400 kPa; (c) p9 60 000 kPa

D1p 5 900 kPa

0 5 10 15 20 25 30a: %

(a)

q: k

Pa

0 210

v: %q

500

1000

1500

2000

2500

25

0

5

10

v

0 5 10 15 20 25 30a: %

(b)

q: k

Pa

0 210

v:

%6000

12000

18000

24000

30000

25

0

5

10

v

q

A2p 5 14400 kPa

0 5 10 15 20 25 30a: %

(c)

q: k

Pa

0 210

v: %

15000

30000

45000

60000

75000

25

0

5

10

v

qA1p 5 60000 kPa


unique yield surface nor a state boundary surface(SBS) could be identied. In Fig. 16(b) it can beseen that for the samples that had been compressedbeyond yield, the normalized stress paths contractprogressively towards the SBS of the reconstituted

soil until the isotropic boundary of the intact soilbecomes coincident with the NCL of the reconsti-tuted soil.

The method of analysis was therefore re-exam-ined and it was found that by taking an equivalent

Fig. 10. Critical states: (a) calcarenite; (b) silica sandstone

IntactReconstitutedCSL

0 10000 20000 30000 40000 50000p : kPa

(a)

0

10000

20000

30000

40000

50000

q: k

Pa

IntactReconstitutedCSL

0 15000 30000 45000 60000 75000p : kPa

(b)

0

15000

30000

45000

60000

75000

q: k

Pa

?

?


pressure on the isotropic boundary of the intactsoil ( p9IB; see Fig. 14) it was possible to identifyboth yielding and state boundary surfaces. Theapproach taken was that of considering the struc-ture to be an intrinsic property characterizing thenature of the soil, in the same way that grading,

particle mineralogy and particle shape are forreconstituted sands. The intact and the reconsti-tuted calcarenite therefore have different natures,or, in other words, they are different soils. Thechange in nature due to the presence of interparti-cle bonding in the intact calcarenite is reected by

Fig. 11. Peak states: (a) calcarenite; (b) silica sandstone

N3 (1.74)C1 (1.75)

RAN6 (1.76)R1 (1.71)

R2 (1.72)(1.74)

Ultimate state intactUltimate state reconstitutedPeak state intactPeak state reconstitutedCSLv at peak

0 1000 2000 3000 4000 5000p : kPa

(a)

0

1000

2000

3000

4000

5000

q: k

Pa

0 6000 12000 18000 24000 30000p : kPa

(b)

0

6000

12000

18000

24000

30000

q: k

Pa

Ultimate state intactUltimate state reconstitutedPeak state intactPeak state reconstitutedCSLPeak envelope intact


the change in the location of the isotropic bound-ary. The shearing data for each soil should then benormalized with respect to the isotropic boundaryfor the particular soil. Whereas for the reconsti-tuted soil, normalizations with respect to either theNCL or CSL are equivalent because the two linesare parallel, for the intact soil this is not the case.

The isotropic boundary of the calcarenite invln p9 space will be referred to in the followingas the intact isotropic boundary (intact IB). This isrepresented by two straight lines in Fig. 6: asteeper initial portion representing the postyieldcompression of the intact samples and then, forvalues of specic volume less than 1465, a part

Original Cam Clay Rowe

IntactReconstituted

p 5 0.53dmax 1 1.29

20.5 0 0.5 1 1.5 2 2.5dmax

0

0.5

1

1.5

2

2.5

p

Fig. 12. Stressdilatancy relationship for peak statesof the silica sandstone

Fig. 13. Inuence of state on dilatancy for the intactand reconstituted silica sandstone: (a) using the sameCSL location; (b) using an offset CSL for the intactsoil

IntactReconstituted

0 0.5 1 1.5 2dmax(b)

0

0.5

1

1.5

(p/p

cs) p

(p /p cs)p 5 22.06 dmax 1 1

(p /p cs)p 5 20.49 dmax 1 1

IntactReconstituted

0 0.5 1 1.5 2dmax(a)

0

0.5

1

1.5

(p/p

cs) p

(p /p cs)p 5 22.06 dmax 1 1

(p /p cs)p 5 20.78 dmax 1 1.59

v

CSL

Intrinsic NCL

Compressionof intactsample

Currentstate

pcs pe pIB ln p

Fig. 14. Denition of the normalizing parameters usedin this paper

D3

D5

A2

IntactReconstituted

5 0.53d 1 1.29

TestD3D5A2

p : kPa3460560014400

20.5 0 0.5 1 1.5 2d

0

0.5

1

1.5

2

2.5

Fig. 15. Comparison between the stressdilatancy re-lationships of the intact and reconstituted samples ofthe silica sandstone


which is coincident with the NCL of the reconsti-tuted soil. As previously discussed, for the fourweaker-bonded calcarenite samples, a lower intactIB was used than for the other samples (Fig. 6(b)).Values of an equivalent pressure p9IB were thencalculated for each sample on the appropriateintact IB. For the reconstituted soil the values ofp9IB were taken on the intrinsic NCL for allvolumes. It should be pointed out that in this typeof normalization the critical states of the intact

soils are identied by a single point only for valuesof the specic volume smaller than 1465. Criticalstates reached at higher specic volumes are lo-cated along the line represented by a value of thestress ratio equal to M and by values of p9= p9IBsmaller than 034. This method of analysis wasused by Cuccovillo & Coop (1997b) to examinethe inuence of state on the small-strain stiffnessof the calcarenite.

Figure 17 shows the yield surface for the calcar-

Fig. 16. Normalized stress paths for the calcarenite (adapted fromCuccovillo & Coop, 1993): (a) samples that did not yield in isotropiccompression; (b) samples that yielded in isotropic compression

RAN

Stress path intactAfter Coop &Atkinson (1993)Yield pointISBS

RAN5

RAN6

N3C1

C3

5 M

0 3 6 9p /pcs(a)

0

3

6

q/p c

s

RAN1

RAN4

RAN3

N5

N7

N4

N2

5 M

RAN

Stress path intact (weaker bonding)Stress path intact (stronger bonding)ISBSAfter Coop & Atkinson (1993)

0 1.5 3 4.5 6 7.50

1.5

3

4.5

6

p /pcs(b)

q/p c

s


enite that may be identied using this normaliza-tion. The yield points in isotropic compressionwere located to the left of the isotropic boundary,resulting in a value of p9=p9IB of less than unity. Itcan be seen that, using this approach, the yieldpoints of the calcarenite now dene the same yieldsurface irrespective of their degree of bonding. Forthe calcarenite, this normalization proved to be ofgreat importance in accounting for the large varia-bility of both the specic volume and the degreeof bonding of the samples tested and hence for theinuence of both of these factors on the yieldstress.

Figure 18 shows the normalized stress paths ofthe intact samples of calcarenite sheared afterisotropic yielding. Superimposed are the stresspaths of the reconstituted samples which dene theintrinsic state boundary surface (ISBS). For theintact samples sheared from states located on theportion of the intact IB convergent with the NCL,the stress paths lie above the ISBS. As the state ofthe intact soil prior to shearing approaches theNCL, the stress path becomes coincident with theISBS as shown by sample N5. The normalizationtherefore identies the space of permissible statesof the intact soil, which could not be achieved bythe p9cs normalization used in Fig. 16. The sampleswith weaker bonding reached states which areabove the ISBS but within the space limited by thestress paths of the more strongly cemented sam-ples.

In Fig. 19 the stress paths of the calcarenitesamples sheared before isotropic yielding and theyield surface are superimposed on the ISBS and onthe outer boundary surface dened in Fig. 18. Inthis representation the values of the state variablep9=p9IB can now be used to distinguish modes of

shear behaviour of the intact soil. For the calcar-enite the yield surface, which denes the domainof normalized states in which the shear behaviouris controlled by bonding, occupies a large portionof the permissible space. This means that over thewhole pressure range and for the large range ofdensities of the calcarenite, the shear behaviourwas mainly cohesive. Frictional behaviour for thecalcarenite, which is behaviour associated withstates beyond the yield surface but still within theintact SBS, was accompanied by volumetric com-pression and controlled by a progressive mechan-ism of bond degradation and particle breakage.The transition between the cohesive and frictionalmodes of behaviour corresponds to a value ofp9=p9IB of 042, which is where the yield surfacemeets the line of gradient M . For values of p9=p9IBsmaller than 042 the calcarenite reached peakstates which were all located on the yield surface,so that the peak strength was solely cohesive. Forvalues of p9= p9IB greater than 042, the strengthwas frictional and coincident with the critical state.In these cases, however, the interparticle bondingcontributed to an increased stiffness of the soilprior to yielding (Cuccovillo & Coop, 1997b).Moving the state of the soil towards the intact IBdoes not change the value of stiffness determinedby the bonds but decreases the range of strainsover which bonding enhances stiffness, until forstates on the intact IB the behaviour becomes non-linear from the start of shearing.

For the silica sandstone, yield and state bound-ary surfaces were identied by taking an equivalentpressure on the critical-state line. Because of thehigh initial density of the silica sandstone and theweak bonding its behaviour in isotropic compres-sion was seen to be similar to that of an uncemen-

C1

D1

5 M Yield point (stronger bonding)Yield point (weaker bonding)Yield surface

0 0.5 10

0.5

p /p IB

q/p I

B

Fig. 17. Yield surface for the calcarenite


ted sand, for which the critical-state line and theisotropic boundary are parallel. Therefore, for thesilica sandstone the appropriate line of referencefor the normalization can be either the isotropicboundary or the CSL. In Fig. 20 the states of theintact soil have been normalized with respect tovalues of p9cs taken on a different critical-state linefrom that of the reconstituted soil, as was indicatedby the stressdilatancy data in Fig. 13. The yieldpoints again identify a clear yield surface, which,for the silica sandstone, occupies only a smallportion of the permissible space of the intact soil

and is entirely contained within the ISBS. Thisdemonstrates that the shear behaviour of the silicasandstone was mainly frictional. States between theyield and state boundary surfaces were associatedwith bond degradation and were accompanied bydilation on the dry side of the critical state, orcompression on the wet side of the critical state. Apeak strength resulting from cohesion was observedonly at the very lowest pressures. Otherwise thepeak strengths were frictional and substantiallyhigher than those of the reconstituted soil becauseof the greater dilatancy.

Fig. 18. Normalized stress paths for reconstituted and intact samples ofthe calcarenite sheared after isotropic yielding: (a) stronger-bondedsamples; (b) weaker-bonded samples

5 M

0 0.5 10

0.5

p /p IB(a)

q/p I

B N5

1.52

1.54

1.521.66 1.66

Intact (stronger bonding)reconstitutedv at the start ofshearing

5 M

0 0.5 10

0.5

p /p IB(b)

q/p I

B

1.52

1.54

1.521.661.66

Intact (weaker bonding)Intact (stronger bonding)v at the start ofshearingISBS

1.73

1.73


CONCLUSIONS

The shear behaviour of natural sands has beenshown to be controlled by mechanisms which differfrom those for reconstituted sands and which resultfrom their structure. These mechanisms can beeasily understood once it is recognized that thenature of a sand is dened not only by the type ofthe material constituents but also by the processes

experienced in the ground during its geologicalhistory. These processes are reected in the soilstructure, which, it is suggested here, should beconsidered as an additional element of the soilnature. It is then possible to interpret the shearbehaviour of two substantially different structuredsands in the light of the differences in their nature,which leads to the development of a general frame-

5 M

0 0.5 10

0.5

p /p IB

q/p I

B

Stress pathYield surfaceOuter intact SBSISBS

Fig. 19. Normalized stress paths for calcarenite samples sheared prior toisotropic yielding

0 0.50

0.5

Yield surface

Stress path reconstitutedStress path intactYield point intactISBS

Hvorslev surfaces

Roscoe surface

Yield surface

0 1 2 3 4 50

1

2

3

4

5

5 M

p /pcs

q/p c

s

Fig. 20. Normalized shear behaviour of the silica sandstone


work in which the various features of the behaviourof the two soils are explained in terms of thestressvolume state of the soil.

As shown by the calcarenite and the silicasandstone, the isotropic boundary of a structuredsand is controlled by its nature and therefore,among other things, by its structure. Differentmodes of shear behaviour have been shown to becontrolled by the location of the state relative tothe isotropic boundary of the soil. It is only whenthe isotropic boundary happens to be parallel tothe critical-state line that reference to either one ofthem is equivalent. An isotropic boundary parallelto the critical-state line was seen for the silicasandstone, where fabric was the most importantstructural feature and for which bonding was weak.For the calcarenite, in which the structure aroseprincipally from a strong bonding, the isotropicboundary was not parallel to the critical-state line,and references to states on the `dry' or `wet' sideof the critical state become meaningless for distin-guishing different modes of shear behaviour.

Sands in which structure arises predominantlyfrom bonding would have shear behaviour which islargely cohesive and would follow the patterns ofbehaviour set out in Fig. 2. As is shown by thecalcarenite, the peak strength would be solelycohesive and the soil would show brittle failure.Frictional behaviour would only be seen at conn-ing pressures that are sufciently high and/or atdensities that are sufciently low to cause thedisruption of the bonds owing to yielding. Thefrictional behaviour would then be dominated bycompression and particle crushing and the strengthwould be achieved through strain-hardening to anultimate state. The principal problems for engineer-ing design in such materials might arise from pro-gressive failure mechanisms because of the strain-softening behaviour or from the large volumetriccompression that might occur, which might giverise to large settlements or reduce the boundarystresses acting on an engineering structure such asa pile.

Sands in which the structure arises predomi-nantly from an interlocking fabric and in which thebonding is weak would have a shear behaviour thatis largely frictional. This behaviour cannot bedescribed adequately either by a conventional soilmechanics framework based on the behaviour ofreconstituted materials or by the patterns of beha-viour shown in Fig. 2. Fig. 21 identies schemati-cally the main features of behaviour for a fabric-dominated sand. As shown by the silica sandstone,the shear mechanisms would be dominated bydilation, which would be the cause of the peakstrengths. The stressstrain behaviour would benon-linear for much of the range of conningstresses (case 2b) and, if seen, linearity would beconned to the initial part of shearing (case 2a).

Compression and particle crushing would be lim-ited to only the very highest stresses (case 3), andif the sand has a small degree of bonding, cohesivepeaks would only be seen at the lowest conningstresses (case 1). Because of the dilation thesesands would give particularly high bearing capaci-ties, and design methods for this type of soil couldfollow those normally applied to dense sands,although a determination of the peak strength fromreconstituted samples would greatly underestimatethe strength of the soil in the ground because ofthe much greater dilation of the natural material.

To develop a general framework which is validfor both frictional and cohesive behaviour, it isproposed that the strain-softening and strain-hard-ening modes of shear behaviour should be distin-guished on the basis of the location of the state ofthe soil relative to its isotropic boundary ratherthan to its critical-state or intrinsic normal com-pression line.

ACKNOWLEDGEMENTS

The research was funded by the EPSRC, towhom the authors are grateful. Support was alsogiven by the Nufeld Foundation through a grantto the rst author. The calcarenite samples werekindly provided by BP International.

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2b3

M

a

q/p

p

q

1 2a 2b 3Yield surfaceof cement

Peakenvelope

Critical-state line

Fig. 21. Schematic diagram showing modes of shearingbehaviour for the silica sandstone


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INTRODUCTIONSOIL DESCRIPTIONSLABORATORY EQUIPMENT AND PROCEDURESISOTROPIC COMPRESSIONSHEARINGSTRESS DILATANCY OF A NATURAL SILICA SANDSTONEA FRAMEWORK FOR THE BEHAVIOUR OF STRUCTURED SANDSCONCLUSIONSACKNOWLEDGEMENTSREFERENCES

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