Beckeretal 1987 CGJ Work Criterion

8/3/2019 Beckeretal 1987 CGJ Work Criterion

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Work as a criterion for determining in situ and yield stresses in claysD. E. BECKER

Golder Associates, 3151 Wharton Way , Mississauga, O nt., Canada L4X 2B 6J . H. A. CROOKSN D K. BEEN

Golder Associates, 701 Farrell Road S. E., Calgary, Alta., Canada 7ZH OT3A N DM . G . JEFFERIES

Gulf Canada Corporation, 401 9th Avenue S.W., Calgary, Alta., Canada 7ZP OH7Received March 13, 1987

Accepted July 7, 1987A method of interpreting conventional oedometer test data using work per unit volume as a criterion for determining bothin situ effective and yield stresses in clay is presented. T his technique was applied to the results of oedom eter tests carried outon samples of natural clay deposits and on specimens consolidated anisotropically from a sluny to a known effective stressstate. The work per unit volume - effective stress relationship, using arithmetic scale s, can be approximated or fitted usinglinear relationships. The intersections of these fitted lines are demonstrated to provide accurate values for in situ current andyield (preconsolidation) stresses. T he yield stress is defined as the intersection of the initial fitted line and the linear relation-ship observed at higher stresses. The current effective stress is indicated by the first significant divergence of the data from theinitial fitted line. The se relationships apply to both conventionally (horizontally) trimmed specimens and to vertically trimmed

oedom eter samples. It is hypothesized that the in situ effective and yield stresses (in both the vertical and horizontal directions)in a natural clay can be determined by the work per unit volum e interpretation of oedome ter tests carried out on horizontallyand vertically trimmed specimens.Key words: in situ, stress, yield, oedometer, interpretation, clays, work, state, KO ,preconsolidation pressure.U nt mtt hode d'interprktation des donnCes d'essais oedomCtriques conventionnels basCe sur le travail par unit6 de volume e stprCsentCe comme critkre pour determiner les contraintes effectives et les contraintes limites en place dans les argiles. Cettetechniqu e a CtC utilisCe pour les rCsultats d'ess ais oedom Ctrique s rCalisCs sur des Cchantillons de dCpBts d'argile s naturelle s e tsur des specimens consolidCs dans un Ctat anisotrope en partant d'u n coulis, jusqu'h un Ctat connu de contrainte effective. Larelation travail par unit6 de volume en fonction de la contrainte effective peut &treCvaluCe sur des Cchelles arithmktiques outracee en utilisant des relations linCaires. I1 est dCmontrC que les intersections de ces courbes tracCes foumissent des valeurspricises des contraintes actuelles ou des contraintes limites (de prC-consolidation). La contrainte limite est dCfinie parl'intersection de la c ourbe initiale tr ac te, avec la relation 1inCaire observCe h plus forte contrainte. La contrainte e ffectiveactuelle est donnCe par la premikre divergence significative d es donnCes par rapport B la ligne initiale. Ces relations sont appli-cables tant aux sp ecime ns conventionnels taillCs horizontalement q u'aux Cchantillons oedomCtriques taillCs verticalement.

L'on pose comm e hypothkse que les contraintes effectives en place et les contraintes limites (dans les deux directions horizon-tale et verticale) dans use argile naturelle peut &tredCterminCe par llinterprCtation basCe sur le travail par unit6 d e volume desessais oedom Ctriques rCalisCs sur de s s ptci me ns taillCs horizontalement et verticalement.Mots cl6s : in situ, contrainte , limite tlastiq ue, oedomktre, interprCtation, argiles, travail, Ctat, KO, ression de prC-consoli-dation.

[Traduit par la revue]Can. Geotech. J. 24, 549-564 (1987)

IntroductionThe behaviour of a clay is governed by the conditions underwhich it exists. As is the case with other soils, the most signifi-cant conditions are void ratio and current geostatic stresses;

these together describe the current state of a soil and can berepresented as a point on the state diagram (i.e., in e - logstress space, Fig. I). It is convenient to quantify current statein terms of distance from a reference state that can also beexpressed as a unique relationship on the state diagram. Forclays, the virgin consolidation line (VCL) has traditionallybeen used, either implicitly or explicitly, for this purpose.Current state has been quantified as the stress differencebetween the current state (a;) and the state on the VCL follow-ing recompression (a;), which is equivalent to log (a;/a;) onthe state diagram. It is noted that a;, the preconsolidation pres-sure, reflects the void ratio of the material. Thus, the currentstate of a clay can be expressed in terms of its overconsolida-tion ratio (OCR). It has been clearly demonstrated that the

behavioural properties of clays correlate well with overconsoli-dation ratio (Roscoe and Burland 1968; Ladd and Foott 1974;Ladd et al. 1977; Wroth 1984). Further, the well-appreciateddependence of the ratio of undrained strength to preconsolida-tion pressure for various test types (see, e .g., Larsson 1980) isa manifestation of the same phenomenon. Finally, the effectivestress path and yield behaviour of clays under field loading hasbeen shown to be controlled by the in situ state and yield envel-ope; the latter is directly controlled by the maximum past pres-sure (Folkes and Crooks 1985; Crooks et al. 1984; Beckeret al. 1984).It is appreciated that factors other than void ratio and currentstress regime (e.g., physical, chemical, and mineralogicalconditions) affect clay behaviour. However, a clear apprecia-tion of the first-order conditions is necessary to provide arational framework within which the influence of other factorscan be evaluated. Further, the current stresses existing within aclay are not adequately represented solely by the vertical stress

Printed in Canada I Imprim6 au Canada


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550 C A N GEOTECH. J. VOL. 24, 1987

FIG. 1. Quantifying the current state of a clay.(a:,); the horizontal stress (uAo) is also important. It is prefer-able that both the current and yield stresses in a clay aredescribed in terms of the first stress invariant ( II). Although itis a simplification of the general three-dimensional stress case,current effective stress can be described as I; = (a!,, + 2 uAo)/3where a,!,, = Koa!,o and mean yield stress I; can be described as(a:, + 20,!,,)/3. Becker et al. (1987) have demonstrated thatfield vane strength data can be well rationalized using I; and I;.However, existing data and experience related to clay behavi-our are almost universally expressed in terms of verticalstresses alone (i.e., OCR = a;/u~,).Based on the above and assuming that the vertical and hori-zontal directions coincide with the principal stress directions,quantification of clay behaviour in terms of the state of thematerial requires knowledge of the vertical and horizontaleffective in situ and yield stresses. In situ vertical effectivestress can readily be determined; however, the determinationof KO and yield stresses is more difficult. Several laboratoryand field techniques to measure or infer KO have been pro-posed, such as instrumented oedometer cells to measure lateralstresses, triaxial consolidation under conditions of no lateralstrain, hydraulic fracturing, installation of total pressure cellsin situ, self-boring pressuremeters, and dilatometers (Brookerand Ireland 1965; Bishop and Henkel 1962; Bjerrum andAnderson 1972; Hughes 1973; Massarsch et al. 1975;Tavenas et al. 1975; Marchetti 1975, 1980). The advantagesand limitations of these methods have been the subject of muchdiscussion and controversy (American Society of Civil Engi-neers 1975; Ladd et al. 1977; Soos and Sallfors 1981; Mori1981; Wroth 1984; Chan and Morgenstern 1986; Jefferieset al. 1987).Traditionally, a; has been determined from the results of theoedometer test. Various methods for interpretation of a; fromoedometer test data are available (Casagrande 1936; Schmert-mann 1955; Burmister 1942 and 1951; Janbu et al. 1981). Ingeneral, these methods are satisfactory for clays that exhibit ane - og stress curve with a well-defined break in the vicinity ofa;. However, for soils that exhibit more "rounded" e - logstress curves, the above methods do not always provide anunambiguous definition of a;. In these cases, a; determined us-ing conventional methods 1s usually reported in terms of aprobable value with an associated range of possible values.Therefore, prediction of clay behaviour is also subject to asimilar range of interpretation, which is not always adequate

for analyses and design. It is often the case that the roundnature of e - og stress curves is taken as evidence of soil dturbance during sampling and specimen preparation. This mnot always be the case and rounded e - og stress curves mequally represent real soil behaviour. Regardless of which the dominant effect, the interpretation of these test data still rquires the accurate definition of yield stresses.

This paper presents an alternative approach for interpretinoedometer test data using work done per unit volume ascriterion to determine both in situ and yield stresses. Confirmtion of this method is provided by the results of controlllaboratory testing of a reconstituted, slurried Beaufort Sea cland samples of various natural clays. Comparisons of in sistresses determined in the laboratory with computed in sivertical stresses and horizontal stresses measured in self-borpressuremeter tests are presented. The advantages of the woper unit volume approach for oedometer test interpretatiover other conventional approaches are also discussed.Oedometer test data interpretation in terms of work punit volumeGeneral approachRegardless of how carefully sampling operations are peformed and physical disturbance minimized, the stress regimacting on the clay is changed during sample retrieval. Consquently, the behaviour of the material in laboratory tests is alchanged. The main issue, then, is to assess the in situ state the material from the results of laboratory tests on specimethat have experienced a stress disturbance effect of unknowmagnitude.

In the field, stresses start at a! but in the laboratory, applistresses are initially less than a!,,. Because of sampling distubance and changed stress conditions, a small deformatiresponse occurs in the stress range below a!,, Therefore, tlaboratory e - log stress curve determination from oedometer test on an overconsolidated clay should reflect thrdifferent deformation responses: one response for a!, < a!,,, second response for a!,, < a: < a;, and a third response fa!, >a;. Similarly, for a normally consolidated clay, two madeformation responses should be observed. Typical e - lstress curves indicate that changes in deformation response occur at these reference stresses but the demarcation at a!,onot well pronounced. Because a!,, can be readily calculatethe utility of a technique to determine a!,, from the results oedometer tests is not immediately apparent. However, tsignificance of this capability will become obvious in later setions of this paper.

When a material under an existing state of stress is subjectto an incremental stress tensor and deforms by strains del, dde3, the work done per unit volume (W) to the material can expressed as[ l ] W = j (aldel + a2dez+ u 3 d 4In soils, deformations are governed by changes in effectistresses and the stress -strain relationship is not linear. Therfore, for test interpretation, [I.] must be written in terms effective stresses, and work per unit volume computed incrmentally.

The use of work per unit volume as a yield criterion to defithe change from small strain response to large strain responto loading was introduced by Crooks and Graham (1976)define yield envelopes for Belfast clays using drained triaxstress probe tests. This approach has also been adopted f


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BECKER ET AL. 551


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552 C A N . GEOTECH. J . VOL. 24, 1987

V E R T I C A L E FFE CT IVE S T R E S S , u"' k P a )

I I I I IPOSTYIELD LlNE

4 - -3 -

n\- 7 2 - --3

I - P R E Y I E LD L I N E-

0. " I0 5 0 1 0 0 1 5 0

S TR E S S i k P o J-

-

-se e deta i l

-

20 0 40 0 600 800 1000V E R T I C A L E FFE CT IVE STRESS ( k P 0 )

FIG.3. Oedometer test on normally consolidated Wallaceburg clay: (a) void ratio - og stress relationship; (b) work per unit volume interptation.defining yield from triaxial test data for other clays (Tavenaset al. 1979; Graham et al. 1983). Although this criterion hasbeen found to work w ell for interpreting triaxial test data, it hasnot been used to interpret oedometer test data. S ince yield canbe defined as a change from small strain to large strainresponse, it is postulated that yield in the oedom eter test is syn-onym ous with a;. Lateral strains are prevented in oedom etertests and therefore the work per unit volume associated with agiven load increment can be computed as follows:

The strains used to define AW in [2] are incremented naturalstrains (i.e., the deformation within each increment is refer-enced to the sample height at the start of each increment). Tointerpret yield from an oedo meter test, the cumu lated work perunit volume is plotted against the applied vertical effectivestress at the end of the relevant load increm ent using arithmeticscales.A typical e - og stress curve obtained from a conventionaloedometer test with a load increment ratio (LIR) of 1 on anatural, almost normally consolidated Beaufort Sea claysample is presented in Fig. 2a . As is typical of these materials,the e - og stress curve appears to be rounded, which makesthe accurate determination of a; very uncertain. Th e probablevalue of a;, using the Casagrand e construction, is indicatedtogether with a range of possible a; values. Figu re 2b showsthe same oedometer test data interpreted using the work perunit volume approach as described above. The data at lowstress levels are show n on an expanded scale (inset in Fig. 2 b)and, as indicated, a linear approxim ation of these data seem s to

be reasonable. The linear relationship formed by the postyiedata is clearly evident. The intersection of the preyield apostyield lines indicates the vertical yield stress (a:,).The oedometer stress-strain curve is show n in Fig . 2c illustrate that the computed work per unit volume corresponto the area beneath the stress -strain curve. T he linear approimation between the individual loads inherent in [2] is quadequate for calculating the work p er unit volume during toedom eter test. Th e major discrepancy in calculating work punit volume using [2] lies with the last two load incremenThe AWod values computed for these last two increments31.1 and 56.6 kJ/m3 respectively: the AWoed eneath the act

a' - E curve for the same stress intervals are 30.3 a55.0 kJ/m3. Therefore, [2] overestimates work per uvolume by about 2 % , which is negligible.Normally consolidated clays

Although oedometer test data interpretation using the woper unit volume approach resu lts in an unam biguou s definitiof a:,, it remains to be demonstra ted that the yield stress idenfied by this approach is the same as the preconsolidatipressure a; interpreted using the more conventional approacTo examine this issue, e - og stress curves with a reasonabwell-defined break in the vicinity of a; were interpreted usithe work per unit volume approach. Figure 3a presents tresults of an oed ometer test on a natural undisturbed specimof soft, almost normally consolidated clay from WallacebuOntario (Becker 1981). The e - og stress curve has a reasoably well-defined break and the determination of a; by tCasagrande construction can be camed out with some condence. W ork per unit volume interpretation of the same da


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BECKER ET AL. 55 3I I I I I I I I I -

I I

-- -

a

- 0 4 I I -STRESS ( k P a )

- -

- -

LOADING0 ( INLOADING

V E R T I C A L E F F E C T I V E S T R E S S ( k P a )FIG.4. Oedome ter test on remoulded clay.

is shown in Fig. 3b. The postyield W-stress relationshipis clearly linear, whereas the preyield data points can bereasonably represented by a straight line. The intersection ofthese fitted lines indicates a yield stress, a:,, equal to 120 kPa.This value is in close agreement with the a; value of 115 kPadetermined from the e - log stress plot using Casagrande'sconstruction.The work per unit volume approach has also been applied tothe results of an oedometer test on a sample of Beaufort Seaclay that was remoulded at its in situ water content prior to test-ing (Fig. 4). The sample was subjected to two full loadingcycles with off-loading at 61 and 487 kPa. Each load incre-ment was applied only for a sufficient time period to permitprimary consolidation (i.e., negligible secondary compressionwas allowed). The test data were interpreted using the workper unit volume approach. For each loading cycle, pre- andpost-yield lines can be readily defined. The intersections ofthese relationships define yield stresses of 63 and 490 kPa.The above examples demonstrate that the yield stress deter-mined by the work per unit volume approach corresponds tothe preconsolidation pressure defined by the conventionalCasagrande construction. Further, the distinct intersection ofthe fitted lines representing the pre- and post-yield W-stressdata provides an unambiguous definition of a:

Overconsolidated claysThe results of an oedometer test performed on a naturalundisturbed specimen of an overconsolidated clay fromWallaceburg are shown in Fig. 5. The e - log stress curve(Fig. 5a) exhibits a well-defined break that enables a; to beconfidently determined by conventional methods. The workper unit volume interpretation of the same test data againpermits approximation of the preyield data as a linear relation-ship; the postyield data form a distinctly linear relationship(Fig. 5b). The intersection of these lines (a:,) occurs at a stressof 145 kPa, which agrees well with the a; value of 150 kPadetermined by the Casagrande construction.Close examination of the W- stress plots presented in Figs.2-5 together with the results of an oedometer test on a typicaloverconsolidated Beaufort Sea clay sample (Fig. 6) indicates aconsistent difference between normally consolidated and over-consolidated samples. In the case of essentially normally con-solidated clays (Figs. 2 -4), the pre- and post-yield fitted linespass through almost all data points. However, in the case ofoverconsolidated samples (Figs. 5 and 6), the W - stress datapoints in the stress range from uCo to slightly beyond a; lieabove the preyield (a: < and postyield (a: > a;) lines.The intersection of the short dashed line connecting pointsslightly beyond aio and the preyield linear approximation of


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554 CAN. GEOTECH. J. VOL. 24. 1987

1.2

1 . 1

P O S S I B L E R A N G E O F m b

1.0

WALLACEBURG CLAYD E P TH : . 01 rn0 . 9

*0 0 . 8+a(r

09 0.7

0 . 6

0.5

10 r 00 1 0 0 0 1 0 0 0 0VER T IC AL EF F EC T IVE STR ESS ( k P a

1 6 0 I I I I0 LO A D I N G

VERTICAL EFFECTIVE STRESS ( k P o )FIG.5. Oedometer test on overconsolidated Wallaceburg clay: (a)void ratio - og stress relationship; (b) work per unit volume interpretatio

the data at stresses below coincides closely with the com-puted vertical effective stress. The intersection of these fittedlines allows for demarcation of the stress level at which achange in deformation response occurs. This observation isconsistent with previous discussions and suggests that a changein deformation response in the oedometer test occurs at oJo.The work per unit volume approach identifies this change.To demonstrate the validity of defining as the stress levelat which significant departure from the initial linear approxi-mation of the test data is observed, values for the TarsiutP45 site in the Beaufort Sea were interpreted using the workper unit volume interpretation of oedometer tests at variousdepths (Fig. 7). These compare favourably with the computedvalues at the same depths based on measured unit weights.Similar agreement between computed and measured oo valueshas been achieved at a large number of sites.Horizontal stress (KO)The successful application of the work per unit volumeapproach for interpreting in situ vertical effective stresses fromthe results of oedometer tests on conventional "horizontallytrimmed oedometer" (HTO) specimens encouraged the use ofthe same approach to interpret the results of tests on "verti-cally trimmed oedometer" (VTO) specimens (Fig. 8). Typicaltest results from a VTO test on an overconsolidated BeaufortSea clay are shown in Fig. 9 and indicate the same response aswas observed for the HTO specimens. The obvious inferenceis that the first intersection (point A) defines the current in situhorizontal effective stress (aho), whereas point B defines thehorizontal yield stress (oh,). This implies that work per unitvolume interpretation of VTO tests provides a relatively simplemethod for determining KO as well as the horizontal yield

stress. However, unlike the value of oho in situ cannot computed to allow direct validation.Thus, it is necessary to rely on comparison with othmeasurements of KO. n this respect, an adequate data base KOvalues determined by in situ self-bored pressuremeter (SBtests is available for the Tarsiut P45 site offshore in tBeaufort Sea (Jefferies et al. 1987). The KO values obtainfrom the SBP tests are compared with those obtained frowork per unit volume interpretations of oedometer tests samples from the same depths at this site in Fig. 10. indicated, there is reasonable agreement between the twapproaches.It is appreciated that the agreement indicated in Fig. 10 donot prove that the work per unit volume interpretation oedometer data provides the correct value of KO;both methoof measurement could be wrong. However, it is considerunlikely that both methods would be wrong by the sammagnitude. Further, the fact that good agreement is achievdespite the very different natures of the two test types compelling. Nevertheless, further validation of the work punit volume approach is necessary as discussed below.

Laboratory verification of work per unit volumeinterpretationTo confirm the validity of the work per unit volumapproach, HTO and VTO tests were carried out on csamples with known stress histories. To "build in" a knostress history into a clay mass, a clay slurry was consolidain a large triaxial cell to a specific stress state. It was necessato consolidate from a slurry rather than remould a sample atnatural water content to ensure that the behaviour reflected


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BECKER ET AL

COMPUTED r;b ( = Y z ) ( k ~ a )

2 0 0

160-mE\

FIG. 7. Computed and measured in situ vertical stresses atTarsiut P45.the work per unit volume approach was the result of the knownstress history and did not reflect any inherent relict stress orfabric effects. The removal of the consolidated clay mass fromthe triaxial chamber would essentially simulate release of total

7Y.../

1 2 0 - --

8 0 - -BEAU F OR T SEA C L A Y- s e e d e t a i l -DEPTH = 25.9 m BELOW SEABEDW = 2 7 . 2 %

40 - e , = 0.74 -PI = 2 2 %CT ' = 4 0 0 kP a-

0 I I0 400 800 1 2 0 0 1600 2 0 0 0 2 4 0 0 2 8 0 0V E R T I C A L E F F EC T I V E S T RE S S ( k P a )

FIG. 6. Work per unit volume interpretation of oedometer test data for overconsolidated Beaufort Sea clay.

- 8 --Ir)

Ground S u r f a c e7 T r em m ~ ng Oedameter Tesl

0Y> 2 3 8 k P a -0 01 0I

F I G . 8. Definition of horizontally trimmed (HTO) and verticallytrimmed (VT O) oedom eter tests.

< 6 - 0- 7 -Y-q 4 -- -

2 -- -

J0 5 0 100 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0- S T R E S S ( k P a ) -

stresses associated with sampling. In triaxial testing, it isnormally assumed that axisymmetric conditions exist and thatthe stress conditions are uniform throughout the sample. How-ever, an examination of the actual stress conditions in a triaxialspecimen indicates that these assumptions are not necessarilytrue (Perloff and Baron 1976; Saada and Townsend 1980). Toavoid the influence of possible stress concentrations and toensure a reasonable approximation of the assumed triaxialstress conditions, small (50 mm diameter) oedometer speci-mens were trimmed from the central portions of 150 mm diam-eter triaxial samples that had a length-to-diameter ratio of two.Sample preparationThe clay slurry was manufactured from samples of BeaufortSea clay obtained from a depth range of 0-6.6 m below sea-bed. A grain size analysis performed on the prepared sample


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/

/o/ -16- ///

- -12- / -E\

--

-S T R E S S ( k P o )-

- -B E A U FO R T S E A C L A Y- -D E P T H y 2 5 . 8 m B E L O W

S E A B E Ds ee d e l o ~ i b o ve- -- V E R T I C A L L YO E D O M E T E R -S A M P L E I IE F F E C T I V E S T R E S S ( k P a )FIG.9. Work per unit volume interpretation of VTO test on overconsolidated Beaufort Sea clay.ri, DET ERMI NE D F ROM I N S l T US E L F - BORED PRESSUREMET ER T ES T S ( k P o )

FIG. 10. Comparison of u;, values from self-bored pressuremetertests and work per unit volume interpretation of VT O tests atTarsiut P45.indicated that the material consisted of 37% silt sizes and 63 %clay sizes by weight. The liquid and plastic limits were 57%and 27% respectively.The natural clay samples were manually remoulded and cutinto small pieces, which were then mixed with tap water in ablender to produce a thin smooth slurry. The sluny was

allowed to cure for several days in a humid room to permit thsample to "bleed" water. The excess clear water was thedecanted and the slurry transferred to a large mechanical mixing bowl. As mixing continued, small pieces of remouldeclay were added to thicken the slurry. Mechanical mixinoperations and manual manipulation of lumps continued untilsmooth paste-like consistency was achieved. The water content of the resultant slurry was 89%.Because the slurry possessed minimal shear strength, thinitial stage of consolidation required the confinement of aouter split mould. The purpose of this initial consolidatiostage was to impart sufficient strength to the material so that could support its self-weight and the top loading platen. Aftenominal strength gain occurred, consolidation in the triaxiachamber was completed using standard procedures.A partial vacuum was employed in conjunction with peripheral filter paper strips to impose an isotropic consolidatiopressure of 80 kPa. After consolidation under this stress wacomplete, as indicated by volume change measurement, thsplit mould was removed and the filter paper, porous stoneand loading platen were placed on the prepared top surface othe specimen. The 80 kPa vacuum was again applied (drainagvalves open) and maintained until the triaxial chamber was iplace and filled with water. Isotropic consolidation unde100 kPa was then effected followed by incremental anisotropconsolidation. The use of small consolidation increments wanecessary to maintain the cylindrical shape of the consolidatin


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ET AL. 557

0 20 40 60 80 100 120 1 4 0I I 1 I I

U N D E R 2 4 x P o Y A C U U MA

-

-- U N 3 E R 8 0 r P l l V A C U U M

h E U 0 V E G h lO U L D AN D S E TI NS ID E T 9 ' A X l A i C E L L

U l i L E R 1 0 0 *? > I I S 0 7 R O P I C II N T R ! A X l A . C E L i

FIG. 11 . Typical volume change - square root time relationshipduring triaxial consolidation of clay sluny.3 0 0 0

sample. The duration of each load increment was sufficient toallow primary consolidation to occur as defined by conven-tional curve-fitting techniques. A geing du e to secondary com-pression was negligible. For each increment, volume changeand pore pressure were monitored so that the end of primaryconsolidation, and thus the achievement of a specific effective

JNLE-: 0 k ~ i l :~~OTROPICJ11 T R l A X l A L C E L L A N D ATuTAL OF 1275N DN1 I I I H 4 N G E R I

stress state, was known. A volume change - ime relationshipfor all consolidation increments on a typical slurry sample isshown in Fig. 11. In total, approximately 2.7 L (volumetricstrain of 48% ) of water was expelled, over a period of 165 h,from the slurry during consolidation to the desired effectiveaxial and radial stresses. It is noted that 75% of the totalvolume ch ange occurred during the initial consolidation incre-ment in the split mould. Although the subsequent volumechange resulted in the mem brane becoming wrinkled, the sur-face of the consolidated sample was observed to be relativelysmooth after the filter paper strips were removed.Th e test program involved "manufacturing" and testing anormally consolidated (NC) sample and an overconsolidated(OC) samp le. The stress history fo r each sample is summarizedas follows:

"Current" effective Yield (maximum)stress (P a ) stress (kPa)Axial Radial Axial RadialType (40) (40) a:o/o;o (miy )

For the case of the NC clay specimen, the 150 mm diametersample of clay slurry was consolidated to an effective stressstate corresponding to a:/uA equal to 0.63. The maximumimposed axial and radial effective stresses were 223 and

140 kPa respectively. On completion of primary consolidationat these stresses, the sample was completely off-loaded(drainage valves closed), removed from the triaxial chamber,and stored in a humid room.T o prepare the OC sample with an OCR of about two, theclay slurry was consolidated under maximum axial and radialstresses of 215 and 140 kPa, respectively. The sample wasthen off-loaded and allowed to undergo primary swelling (withdrainage valves open) to "current" axial and radial stresses of104 and 70 kP a respectively. Th e samp le was then completelyoff-loaded (no swelling) and stored in a humid room.Oedorneter test programFour oedometer specimens (50 mm diameter, 12 mm high)were trimmed from the central portions of each of the 150 mmdiameter samples. Two specimens were trimmed from a hori-zontal plane (HTO) and two were trimmed vertically (VTO),one each from two perpendicular vertical planes. The oedom-eter tests were carried out using conventional equipment withfixed oedometer rings and double drainage. The oedometerrings were greased to reduce side friction. Both conventionalload increment ratio (LIR = 1) and smaller load incrementratio (LIR < 1) tests were carried out. T he LIR < 1 tests wererequired to better define the W-stress relationships in thevicinity of both the current and yield stresses. During theoedometer tests, each individual load increment was appliedfor a sufficient period to permit primary consolidation to occu rand to minimize secondary compression effects. Typica lly, theloading duration varied between 3 0 and 90 min. To this end,plots of dial reading versus log tim e and (or) square root timewere maintained during testing. In some tests involving smallload increment ratios, the resulting dial reading - log timecurves were not of the classical "S" shape, thereby making thedetermination of the end of primary consolidation by conven-tional methods ambiguous and uncertain. In these cases, therectangular hyperbola fitting method (RH M) proposed by Srid-haran and Sreepada Rao (1981) and Sridharan and Prakash(1985) was utilized (Fig. 12a). The relationship between t/6and for t for a load increment is plotted using arithmetic scalesuntil a straight line with a slope "rn" can be defined. A line isthen drawn from th e origin at a slope equal to 1.24 rn; the inter-section of this line with the actual laboratory curve defines theelapsed time required for an average degree of consolidationequal to 98% (i.e., ts8).To confirm the validity of this method, the RHM-predictedtimes to end of primary consolidation for natural andremoulded Beaufort Sea clay samples were compared withthose obtained by conventional interpretation of dial reading -log time curves with a well-defined "S" shape. The resultsobtained using the two methods are shown in Fig. 126 andgood correspondence is eviden t. Figu re 13 presents typicalRHM results obtained whenever a small load increment ratiowas used. The log time plot (Fig. 130) indicates no deviationfrom a straight-line relationship and thus determinination ofthe end to primary consolidation is not possible. On the otherhand, the characteristic plot associated with the rectangularhyperbola fitting method is still evident (Fig. 13b). Therefore,the rectangular hyperbola fitting method was found to beextremely useful in defining the end of primary consolidationfor small load increment ratios.Results of tests on no rmally consolidated clayTh e known stress history and results of work per unit volumeinterpretation of the oedometer test data for normally consoli-


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55 8 CAN. GEOTECH. J. VOL. 24, 1987t = e l a p s e d t k me6 d e f o i m o l l o n d u r i n g t c m e 1

T lME (mini

l im e (min iL O G t M E T H O D

FIG . 12. (a) T he rectangular hyperbola fitting method (RH M) forthe determination of end of primary con solidation (after Sridharan andSreepada Rao 1981). (b) Comparison of the time to end of primaryconso lidation determined by RHM with log time technique for"S"-shaped deformation - ime relationships.dated samples are summarized in Table 1. The initial watercontents and void ratios of the individual specimens are verysimilar, indicating reasonable homogeneity in terms of stresshistory. Repeat tests were carried out: one using a conven-tional LIR equal to one and the other using sm aller load incre-ment ratios. T he data fo r these tests (Fig. 14) exhibit distinctlylinear postyield W -stress relationships. A lso, the preyielddata can be reasonably ap proxima ted by linear relationships inall tests. The intersections of the lines were approximatelyequal to the known maximum stresses in the axial and radialdirections. There is little difference in the yield stress valuesdetermined from the LIR = 1 and LIR < 1 tests; both indicatepredicted yield stresses within f % of the known yieldstresses. Howe ver, the re is a tendency f or the test results asso-ciated with the LIR < 1 tests to provide m ore accurate pre-dictions.Results of tests on overconsolidated clayThe stress history and results of the work per unit volumeinterpretation of the oedometer test data on the overconsoli-dated samples are also summarized in Table 1 . The imposedmaximum axial and radial effective stresses were 215 and140 kPa respectively. The sample was unloaded and allowedto undergo primary swelling to "current" axial and radial

TlME ( m i n i

T l M E lminlFIG . 13. Deformation- ime relationships for small load incremenratios: (a) conventional dial reading - log time relationshi( b ) rectangular hyperbola fitting method.

TA BL E . Summary of oedometer test resultsCurrent and yield stresses (kPa

W"Test (% I eo 40 4, 0 4,N/C specimenHTO- 1HTO-2VTO-1VTO-2O/C specimenHTO-1HTO-2VTO-1VTO-2

*Imposed stress.

effective stresses of 104and 70 kPa respectively. Four oedometer tests were performed on specimens trimmed in the sammanner as described for the normally consolidated clay. Thesfour samples had very similar initial void ratios. A LIR


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BECKER ET A L. 559

E F F E C T I V E S T R E S S ( k P a ) E F F E C T I V E S T R E SS ( k P a )

4 = 140 k P oRl - R o= (0.045rn

u W 6 0 kP /I //'0 50 100 150

a/

Y- STRESS ( k P o ) /120- !

TO- IW = 36.3 %e = 0 . 9 8 7

s e e d e t a ~ l urn = ury' 140 kP aabove LI R = 1.0

00 500 1000 1500 2000 2500 3030

STRESS ( k P o )

e, = 0.982see deta~labove ur , ' = c r y ' = 40 kP oL I R < I

500 1000 1500 X)OO 2500 3000E F F E C T I V E S T R E S S ( k P a ) E F F E C T I V E S T R ES S ( k P a )

FIG.14. Work per unit volume interpretation of oedometer tests on reconstituted normally consolidated samples.

defined at low stress levels (a' < a;) and the lines defined athigh stress levels (a' > a;) accurately reflect the maximumapplied (yield) stresses. The inset figures showing the linearapproximation to the data points at low stress levels clearlyindicate distinct changes in response at stresses correspondingquite closely to the known "current" stresses. Thus, bothVTO tests reflect a distinct break at a stress of approximately70 Wa (i.e., and both HTO tests indicate a change atabout 104 kPa (i .e ., aLo).

DiscussionA comparison between the known "current" and yieldstresses and those determined using the work per unit volumeapproach for all of the control test data is shown in Fig. 16a.The agreement between the known stresses and those inter-preted using the work per unit volume approach is good, withthe latter values all lying within 10% of the known stresses.Also shown in Fig. 16b is a typical e - og stress curve forone of these tests. The apparently rounded nature of the curve

would cause some difficulty in the application of the Casa-grande approach to achieve the same degree of corre-spondence.As shown in Figs. 14 and 15, the computed W values atstresses greater than approximately 1200 Wa in some casesplot slightly above the postyield line that passes through thepreceding three to four data points. In other instances, the post-yield line passes through all the computed W-stress points(Fig. 17). This difference is associated with "flow or squeez-ing out" of the clay between the loading cap - porous stoneand the oedometer ring at high stress levels. The width of thisannulus was not the same for all of the oedometer equipmentand flow of the clay at high stress levels was more predominantin cells with a wider annulus. The magnitude of the yield stressof the clay is also a factor: at the same stress level, clays with alower yield stress will have a greater tendency to flow giventhe same annulus dimension. Because of this phenomenon, themeasured vertical strain is larger and hence the computed workper unit volume is higher than would be the case if no flow


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560 CAN. GEOTECH. J . VOL. 24, 1987

STRESS (kPa1

W = 40.6% W : 40.5%

E F F E C T I V E S T R E S S ( k P o ) E F F E C T I V E S T R E S S ( k P a )

S T R E S S I k P a ) /// i

2 0- Oror*; = 75 P 0L /

S T R E S S I k P o I //

see detol labove

E F F E C T I V E S T R E S S ( k P o ) E F F E C T I V E S T R E S S ( k P a )FIG. 15. Work per unit volume interpretation of oedometer tests on reconstituted overconsolidation samples.

occurred. The effect can be partially quantified by determiningthe magnitude of (Ri - Ro) for each point, where Ri is theactual initial dial gauge reading at the beginning of a givenloading increment and Ro is the "theoretical" initial dial gaugereading based on conventional log time or square root timeconstructions. Small values of (Ri - Ro) indicate negligibleflow of the clay into the annular space; large values of (Ri -Ro) indicate significant flow. The magnitude of (Ri - Ro) forsome loading increments is indicated beside the correspondingpoint in W-stress space in Figs. 14 and 15. In general, thevalue of (Ri - Ro) increases with increasing vertical stress. Forcomparatively small values of (Ri - Ro), the postyield linepasses directly through all computed W-stress points; how-ever, for larger values of (Ri - Ro) the computed W-stresspoints start to diverge (i.e., lie above) the postyield line. It isnoted that for cases in which (Ri - Ro) generally exceeded0.04 mm, flow of the clay into the annulus was visuallyobserved when the test equipment was dismantled. These

observations greatly enhanced the "fitting" of the postyielddata by indicating which points should be considered suspectthe postyield line being defined on the basis of points havinglow values of (Ri - Ro). In general, the postyield line idefined by the computed W-stress points corresponding to thlower stress portion of the line (Fig. 17).The determination of yield based on the work criterion is nogreatly influenced by LIR, since yield is accurately defined bythe intersection of the initial portion of the W-stress relationship at low stress levels (approximated by a straight line) anthe line defined at higher stress levels. The points defined byLIR = 1 are therefore adequate for the determination of yieldHowever, definition of current effective stresses generallrequires more loading increments in the vicinity of this streslevel than is provided by LIR = 1. Variation in the load increment ratio, however, has been reported to have a significaneffect on the interpretation made regarding the shape of thvoid ratio - og stress curve (Leonards 1962). At stress level


13/16

BECKER ET AL

nZ

L E G E N D0 Y I E L D S T R E S S5 0 A CURRENT STRESS

(0)0 8 I50 100 150 ZOO 25 0 3 0 0

A C T U A L S T R E S S I M P O S E D ( k P o 1

NC S P E C I M E NM T O - 2

021 ' " " ' 1 ' ' " " " I ' ' " ' ' ' 1 ' ' ' 1100 1000E F F E C T I V E S T R E S S L k P o l

FIG. 16. (a)Comparison of stresses determined from work per unitvolume interpretation of oedometer tests with the known stressesimposed on reconstituted samples. (b) Example of void ratio - logstress relationship from oedometer tests on reconstituted clay.below and well beyond a;, the difference in void ratio obtainedfrom an oedometer test using LIR = 1 and from a test usingLIR < 1 is small. However, in the vicinity of the preconsoli-dation (yield) pressure, the interpretation of the shape of thecurve between measured points can be different particularly iflong load durations are used, which allows greater secondarycompression deformations to occur. This is particularly truefor "structured" clays, which undergo very distinct "struc-tural breakdown" and exhibit an e - log stress curve with awell-defined break. For less structured clays, the interpretationof the actual curve between actually measured points is subjectto less variation. For example, Fig. 18 presents the results ofoedometer tests conducted on reconstituted clay specimenstrimmed from adjacent locations in the same triaxial sample.One test series used a LIR of unity and the other employedsmaller, varying load increment ratios. The results are pre-sented in terms of both e - log stress and W-stressThere is essentially no effect of LIR on the resultant relation-ships, even in the vicinity of yield. This agreement suggeststhat additional W-stress data points can be accuratelyobtained by discretizing the e - log stress curves obtainedusing LIR = 1.In the field, the vertical and horizontal directions are associ-ated with stress- and strain-controlled boundary conditionsrespectively. In the conventional oedometer test (HTO) the

E F F E C T I V E S T R E S S

E F F E C T I V E S T R E S SFIG. 17 . Criterion for the determination of the postyield line.

imposed boundary conditions reflect in situ boundary condi-tions and, as such, the inferred stresses from the work per unitvolume interpretation should accurately reflect uio and a;.However. in the case of a VTO test. the boundan, conditionsduring the test are not those that would exist in situ. Theinfluence of this boundary condition change on the accuracy ofmeasured horizontal stresses (aAo and ak,) is not known at thistime; for the reasons discussed below, the effect may not besignificant. In the triaxial cell, both the axial and radial bound-aries are stress controlled. The oedometer tests. which wereconducted on reconstituted samples consolidated in the triaxialcell, did not satisfy these boundary conditions. However, thework per unit volume interpretation of the HTO and VTO testdata accurately defined the-imposed current and yield stressesin both the vertical and radial directions. Further work isrequired to fully assess the significance of boundary condi-tions. For example, a clay slurry could be consolidated in alarge oedometer cell with instrumented walls to known stressconditions, followed by HTO and VTO testing with subse-quent work per unit volume interpretation.Comparison with other oedometer data interpretation tech-niquesIn the absence of a fully formulated comprehensive stress-strain-time model for clays, the interpretation of significantsoil properties from the results of laboratory tests must rely onempirical plotting techniques (e.g ., yield stresses in oedometertests). Therefore, it is not a question of which technique is"correct"; rather the issue is which technique provides themost repeatable result and is least ambiguous. In the case of


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562 CAN. GEOTECH. J . VOL. 24 , 1987

EFFECTIVE VERTI CAL STRESS ( k P a )

1.2 I I I I I I 1 1 1 I 1 1 1 1 \ 1 1 I 1 1 1 1 1 1 1 ~L E G E N D

H TO S E R I E S U'by = 223 kPa L IR =0 L I R c

V T O S E R I E S

N C S P E C I M E N /c o o ' c ay = 2 23 l tpa

I I 1 1 1 1 1 1 I I I 1 I 1 l l I I 1 1 1 1 1 1 I I I 1 I t 1 1 0. 4I 10 100 1000 10000

EFFECTIVE STRESS ( k P a )FIG.18. Effect of load increment ratio (LIR) on oedometer test results.

oedometer test interpretation, it can be readily demonstratedthat the same relationship between the stress -strain data willbe preserved regardless of whether the data are plotted in termsof void ratio - og stress, log specific volume - og stress, orwork per unit volume - stress. However, natural strains mustbe used if the same form of relationships is to be preserved instrain - og stress plots; the use of engineering strains causesdistortion of the test data particularly at high strains. It is alsonoted that the oedometer test data should be based on primaryconsolidation strains only; inclusion of arbitrary amounts ofsecondary compression strain is not acceptable if a repeatablereference line is to be developed.Based on the above, it is evident that the only differencebetween the plotting techniques will be the enhancement ofdata presentation. It is considered that the work per unitvolume approach provides this advantage for the following

reasons. Firstly, the quantities-work per unit volume anstress-are plotted on arithmetic scales. Thus, the potential foerror in defining the stresses at which changes in strairesponse occur is greatly minimized. The use of logarithmiscales for plotting stress data normally introduces significanuncertainty. Secondly, the effect of integration, which is inherent in the work per unit volume approach, is to enhance thdata presentation. As illustrated by the postyield data for thtests presented in this paper, linear relationships are clearlevident. In the preyield range, the effect of integration is treduce the curvature of the relationship, particularly in thstress range between a; and a;. This facilitates approximatioof the data as linear relationships, which allows a reliablmeasure of the in situ stress state to be made.It is normally the case that the W-stress data below ah forma reasonably well-defined linear approximation, whereas th


15/16

BECKER ET AL . 563postyield data exhibit a distinctly linear relationship. There-fore, definition of yield stresses using the work per unitvolume approach can be used with a high degree of confi-dence.In som e cases the data in the stress range between a; and a;form a more pronounced curved relationship an d as such som edegree of subjectivity is involved in approximating these dataas a linear relationship. Thu s, in these cases the deg ree of con-fidence involved in predicting current in situ stresses is lessthan is the case for yield stress predictions. It is possible thatfurther examination of the work p er unit volume app roach willresult in a better selection of the optimum test conditions tominimize this uncertainty. Th e degree of subjectivity involvedin defining a; can be reduced by placing less emphasis on databelow 30 kPa and by u sing the data included in the stress rangeimmed iately beyond a; whe re a; is indicated by the firstsignificant divergence of the data from the initial linearapproximation of the data below a;. Further, da ta points corre-sponding to stresses approaching the yield stress shouldreceive less attention while fitting this intermed iate line.

ConclusionsA method of interpreting oedom eter test data using w ork perunit volume as a criterion is presented. For normally consoli-dated clays, the relationship between w ork per unit volume andstress, when plotted using arithmetic scales, can be approx-imated by two straight lines, the intersection of which definesthe yield stress. Fo r overconsolidated samples, the data belowa; form a reasonably well-defined linear approximation to theactual curved relationship, whereas the postyield (i.e. , abovea;) data exhibit a distinctly linear relationship. T he intersectionof these two fitted lines represents the yield stress. The datapoints corresponding to stresses slightly abo ve ah are observedto diverge in another linear approximation from the initial

linear approximation of the data below a;. The point of thisdeparture, defined as the intersection of these tw o lines, repre-sents the current effective stress, a;.The above forms of work per unit volume relationshipsapply to both conventionally (horizontally) trimmed samplesand to vertically trimmed oedometer samples. Therefore, therespective vertical and horizontal in situ effective stresses andyield stresses can be determined. The accuracy with whichin situ effective and yield stresses are determined was d emo n-strated to be within 10% of known stresses based on thefollowing testing:for natural clays by comparing with computed values(i.e., y'z).aAo-for natural clays based o n com pariso n with self-bored

pressuremeter test data.a(,,-for natu ral clay s wit h wel l-defin ed "knees" on th e e -log stress curves, w ork per unit volum e predictions agreed wellwith predictions of preconsolidation based o n the Casagrand econstruction.-for remoulded clays in an oedometer test subjected to twooff-loading cycles; the maximum loads were accurately pre-dicted in each case.@Ao, a:,, aj -a remo ulded clay w as cons olida ted aniso -tropically from a sluny in a triaxial chamber to known effec-tive axial and radial stresses (normally consolidated sample).A second sample was overconsolidated by allowing the sam pleto swell to a know n "current" effective stress state. Th e"current" effective and yield stresses on horizontal and verti-

cal planes through the sample were accurately determinedusing the work per unit volume method.

AcknowledgementsTh e authors wish to express their appreciation to Mr. W. R.Livingstone (Gulf Canada Corporation) for his interest and

support of this research w ork. T he autho rs are also grateful toR. M . C . Ng, who provided m any helpful suggestions, and toG. A. Leonards, D. Negussey, Y . Vaid, and L. Rothenburgfor their comments on initial drafts of this paper. T he drawingswere prepared by R. Kroeker and C. Gibson , and the manu-script was typed by K. Koch.AMERICANOCIETYF CIVIL NGINEERS.975. In situ measurementof soil properties. Proceed ings, ASCE Specialty Conference of theGeotechnical Engineering Division, Raleigh, NC.BE CK ER , . E. 1981. Settlement analysis of intermittently-loadedstructures founded on clay subsoils. Ph.D . thesis, Faculty of Engi-neering Science, University of Western Ontario, London, Ont.BECKER,D. E., CROOK S, . H. A., JEFFE RIES, . G ., andMCKENZIE,. 1984. Yield beh aviour and consolidation . Part 2.

Strength gain. Proceedings, ASCE G eotechnical Engine ering Divi-sion Symposium on Sedimentation Consolidation Models, Predic-tions and Validation. San Francisco. Edited b y R. N . Yong andF. C. Townsend. pp. 382-398.BECKER,. E., CROOKS,. H. A., and BEEN , . 1987. Interpretationof the field vane test in terms of in situ and yield stresses. AmericanSociety for Testing and Materials. International Symposium onLaboratory and Field Vane Shear Strength Testing, Tampa, FL.BISHO P, . W., and HE N KE L, . J. 1962. The measurement of soilproperties in the triaxial test. 2nd ed. Edward Arnold (Publishers)Ltd., London, England.BJERRUM,., and ANDERSON,. H. 1972. In situ measurement oflateral pressures in clay. Procee dings, 5th European C onference onSoil Mechanics and Foundation Engineering, Madrid, Vol. 1, pp.11 -20.BROOKER,. W., and IRELAND,. 0. 1965. Earth pressures at restrealted to stress history. Canadian Geotechnical Journal, 2; 1- 5.BURMISTER,. M. 1942. Laboratory investigations of soils at Flush-ing Meadow Park. Transactions of the American Society of CivilEngineers, 107: 187.1951. The application of con trolled test methods in consoli-dation testing. Symposium on Consolidation Testing of Soils.American Society for Testing and Materials, Special TechnicalPublication 126, p. 83.C AS AGR ANDE,. 1936. The determination of the preconsolidationload and its practical significance. Proceedings, First InternationalConference on Soil Mechanics and Foundation Engine ering, Cam-bridge, Vol. 3, pp. 60-64.CHA N, . C. Y., and MORGENSTERN ,. R. 1986. Measurement oflateral stress in a lacustrine clay deposit. Proceedings, 39th Cana-dian Geotechnical Conference, Ottawa, pp. 285-290 .CROOKS,. H. A., and GRAHAM,. 1976. Geotechnical properties ofthe Belfast estuarine deposits. GCotechnique, 26: 293 -315.CROOKS,. H. A., BECKER,D. E., JE FFER IES, . G ., andMC KE NZ IE, . 1984. Yield behaviour and consolidation. Part 1.Pore pressure response. Proceedings, ASCE Geotechnical Engi-neering Division Symposium on Sedimentation ConsolidationModels Predictions and Validation, San Francisco. Edited b y R. N.Yong and F. C. Townsend. pp. 356-381.FOLKES, . J. , and CROOK S,. H . A. 1985. Effective stress paths andyielding in soft clays below embankments. Canadian GeotechnicalJournal, 22: 357 -374.G R A H A M ,., NO ONA N, . L., and LEW ,K. V. 1983. Yield statesand stress-s train relationships in a natural plastic clay. CanadianGeotechnical Journal, 20: 502 -516.HUGHES,. M . 0 . 1973. An instrument for in situ measurement of


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564 CAN. GEOTECH. I . VOL. 24, 1987soft clays. Ph.D. thesis, University of Cambridge, Cambridge,England.JAN BU , ., TOKH EI M, . , and SENNESET,. 1981. Consolidationtest with continuous loading. Proceedings, 10th International Con-ference on Soil Mechanics and Foundation Engineering, Stock-holm, Vol. 1, pp. 645 -654.JEFFERIES, . G., CROOK S, . H . A. , BECKER , . E. , and HILL ,P. R. 1987. Independence of geostatic stress from overconsolida-tion in some B eaufort Sea clays. C anadian Geotechnical Journal,24: 342-356.LADD,C. C., and FOOTT,R. 1974. New design procedure for stabil-ity of soft clays. ASCE Journal of the Geotechnical EngineeringDivision, lOO(GT7): 763-786 .LADD , C. C. , FOOTT, R. , ISHIHAR A, . , SCHLOSSER,., andP o u ~ o s , . G. 1977. Stress-deformation and strength character-istics. State-of-the-Art Repo rt, 9th International Conference o n SoilMechanics and Foundation Engineering, Tok yo, pp 421 -494.LARSSON,. 1980. Undrained shear strength in stability calculationof embankments and foundations on soft clays. Canadian Geotech-nical Jorunal, 17: 5 91 -602.LEONARDS,. A. 1962. Engineering properties of soils. In Founda-tion engineering. Edited by G. A. Leonards. McGraw-Hill BookCompany, Inc., New York, NY, chap. 2, pp. 66-240.MARCHETTI,. 1975. A new in situ test for the measurement of hori-zontal soil deformation. Proceedings, ASCE Specialty C onferenceon In Situ Measurement of Soil Properties. Raleigh, NC, Vol. 2,pp. 255-259.1980. In situ tests by flat dilatometer. ASCE Journal of theGeotechnical Engineering Division, 106 (GT3): 299- 2 1.MASSARSCH,. R. , HOLTZ,R. D. , HOLM,B. G. , and FREDRIKSSON,A. 1975. Measurement of horizontal in situ stresses. Proceedings,ASCE Specialty Conference on In Situ Measurement of SoilProperties, Raleigh, N C, Vol. 1, pp. 266-285 .MORI ,H. 1 981. Soil exploration and sampling-General report. Pro-ceedings, 10th International Conference on Soil Mechanics andFoundation Engineering, Stockholm, Vol. 4, pp. 399-412.PERLOFF,W. H. , and BARON,W. 1976. Soil mechanics: Princiolesand applications. Ronald Press Company, New York, NY, Ipp.26-91.

ROSCOE,K. H. , and BURLAND,. B. 1968. On the generalizedstress-strain behaviour of wet clay. In Engineering plasticity.Cambridge University Press, London, England, pp. 535-609.SAAD A, . S . , and TOWNSEN D,. C. 1980. State-of-the-art: Labora-tory strength testing of soils. In Laboratory shear strength of soil.American Society for Testing and Materials, Special TechnicalPublication 740, pp. 7-77.S C H M E R T M A N N ,. M . 1955. The undisturbed consolidation of clay.Transactions of the American Society of Civil Engineers, 120:1201.Soo s, P. V., and SA LLFO RS, . 1981. Laboratory testing-Generalreport. Proceedings, 10th International Conference on SoilMechanics and Foundation Engineering, Stockholm, Vol. 4, pp.291 -305.SRI DHARAN,. , and PRAKASH, . 1985. Improved rectangularhyperbola method for the determination of coefficient of consolida-tion by rectangular hyperbola. Geotechnical Testing Joumal, 8(1):37-40.SRI DHARAN,., and SREEPADAA O ,A. 1981. Rectangular hyper-bola fitting method for one dimensional consolidation. Geotech-nical Testing Joum al, 4(4): 161- 68 .

TAVENAS,. A. , BLANCHETTE,. , LEROUEI L,. , ROY , M. , anLAROCHELLE,. 1975. Difficulties in the in situ determination oKO n soft sensitive clays. Proceedings, ASCE Specialty Conference on In Situ Measurement of Soil Properties, Raleigh, N C, Vo1, pp. 450-476 .T A V E N A S ,. , DES ROSIERS ,. P ., LEROU EI L,. , LA ROCHELLEand ROY,M . 1979. The use of strain energy as a yield and creecriterion for lightly overconsolidated clays. GCotechnique, 29285 -303.WR OT H, . P. 1984. The interpretation of in situ soil tests. The 24tRankine Lecture. GCotechnique, 34: 449-489.

List of symbolsHoHiHi- I

HTOI;,I;KOLIRNCOCOCRRH MRiRoVTOVCLWl98, l100w4 0

in i ti a l he igh t o f oedom ete r t es t spec ime ns p e c i m e n h e ig h t a t e n d o f i load ing inc r emens p e c i m e n h e i g h t a t e n d o f i - 1 loading increm e n t o r t h e h e i g ht o f s p e c i m e n a t b e g in n i n g o fload ing inc r ementhor izonta lly t r immed o edom ete r ( convent ionauJo( l + 2Ko) /3(a:, + 2aky) /3r a t io of in situ hor izon tal s tress to ver t ical ef fect i v e st r es s , o ~ o l u ( oload inc r ement r a t io in oedo mete r t e s tnor mal ly conso l ida tedover consol ida tedove rcon solid ated ratio , ab!aJor ec tangula r hyper bola f i t t ing methodac tua l in i ti a l d ia l gaug e r ead ing a t beg inning oa load ing inc r ement" theor e t ica l" in i ti a l d ia l gauge r ead ing abeginning of a load ing inc r ementver t ica l ly t r immed oedomete r ( r o ta ted 90" tconvent iona l )v i r g in conso l ida t ion l inew o r k d o n e p e r u n it v o l u m et i m e f o r 98% a n d 1 0 0 % p r i m a ry c o n s o li d a ti owate r conten tini t ia l ver t ical overburden ef fect ive s tress

40 ini t ia l hor izontal ef fect ive s tressy ie ld s t r e s s in th e ve r t i ca l d i r ec t ion

sky yie ld s t r e s s in th e hor izonta l d i r ec t iona;, pr econsol ida t ion pr es sur e4' ver t ical ef fect ive s tressa;, ini t ia l ef fect ive s tressaxial ef fect ive s tressa; radial ef fect ive s tressa t , a2 , 03, pr incipal s tressesa! a!I r I + I e f f ec t ive s t r e s s a t end of i a n d i + 1 load ininc r ementd q , d e2 , d f 3 inc r ementa l p r inc ipa l s t r a insei, ei+l na tura l s t r a ins a t end o f i a n d i + 1 load ini nc re m en t ( E ~ ( Ho - Hi) lHi - l )

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Beckeretal 1987 CGJ Work Criterion