hahaha

Monotonic and dilatory pore-pressure decayduring piezocone tests in clay

S.E. Burns and P.W. Mayne

Abstract: During a pause in cone penetration in fine-grained soils, pore-water pressure dissipation tests are performedto evaluate the coefficient of consolidation. For standard piezocones with shoulder filter elements, soft clays and siltsshow a monotonically decreasing response with time; however, dissipation tests performed in heavily overconsolidatedsilts and clays show dilatory behavior, with the pore-pressure behavior increasing from the initial measured value to amaximum, and then decreasing to hydrostatic values. This paper presents a theoretical framework which combinescavity-expansion theory and critical-state soil mechanics with an analytical solution to the radial consolidation equation.The method is able to describe the pore-pressure response curve for dissipation tests performed in soils whichdemonstrate either monotonically decreasing or dilatory pore-pressure behavior.

Key words: cavity expansion, consolidation, piezocone, pore pressure.

Rsum : Durant une pose lors de la pntration du cne dans les grains fins, des essais de dissipation des pressionsinterstitielles sont raliss dans le but dvaluer le coefficient de consolidation. Pour les pizocnes standard avec leslments poreux au-dessus du cne, les argiles et les silts montrent une diminution monotonique en fonction du temps;cependant, les essais de dissipation raliss dans les silts et argiles fortement surconsolids, montrent un comportementen dilatation, avec un accroissement de pressions interstitielles partir de la valeur initiale mesure jusqu unmaximum, suivi dune diminution jusquaux valeurs hydrostatiques. Cet article prsente un cadre thorique quicombine la thorie dexpansion de cavit et la mcanique des sols ltat critique avec une solution analytique delquation de consolidation radiale. La mthode peut dcrire la courbe de rponse de pression interstitielle pour desessais de dissipation raliss dans des sols qui montrent soit un comportement de pression interstitielle en dilatation,soit dcroissant de faon monotonique.

Mots cls : expansion de cavit, consolidation, pizocne, pression interstitielle.

[Traduit par la Rdaction] Burns and Mayne 1073

Introduction

Piezocone penetration tests are a widely utilized technol-ogy for the in situ investigation of soil deposits, primarilyfor profiling stratigraphy and for distinguishing fine-grainedclayey soils from coarse-grained sandy soils. In addition,pore-pressure dissipation tests, which are performed during apause in the cone penetration, yield information about thecoefficient of consolidation and permeability of a soil de-posit. Dissipation tests performed in soft, fine-grained siltsand clays measure monotonically decreasing pore-waterpressures, similar to the behavior observed in the standardlaboratory one-dimensional consolidation test. However, dis-sipation tests performed in heavily overconsolidated siltsand clays often record dilatory pore-water pressure behavior,showing a temporary increase in pore-water pressure withtime followed by a decrease and return to hydrostatic pres-sure. Although several consolidationtime models are cur-

rently available to describe the dissipation behavior of softclays, none to date has been able to rationally explain thedilatory behavior of stiff clays.

This paper presents a theoretical framework based on cavity-expansion concepts and critical-state soil mechanics forevaluating the pore-pressure behavior observed in a range ofsoil consistencies, from normally to lightly to heavilyoverconsolidated fine-grained soils. The pore-pressure decaywith time next to the piezocone is modeled using an analyti-cal solution to the consolidation equation to evaluate the insitu value of the coefficient of consolidation of a soil de-posit.

Generation of excess pore pressure

The insertion of a cone penetrometer, or any penetratingprobe, into a soil deposit causes changes in the pore-fluidconditions surrounding the penetrometer. For soundings insaturated fine-grained soils with low hydraulic conductivity,these changes occur under undrained conditions. The alter-ation in pore-water pressure results from a combination ofthe changes in the octahedral normal stress, oct, which re-sults from the displacement of soil and fluid by the penetrat-ing cone, and in the octahedral shear stress, oct, which iscaused by the shear deformation of the soil adjacent to thecone body.

Can. Geotech. J. 35: 10631073 (1998) 1998 NRC Canada

1063

Received January 27, 1998. Accepted July 3, 1998.

S.E. Burns. Department of Civil Engineering, Thornton Hall,University of Virginia, Charlottesville, VA 229032442,U.S.A.P.W. Mayne. School of Civil and EnvironmentalEngineering, Georgia Institute of Technology, Atlanta, GA303320355, U.S.A.

Under the cone tip, the largest effect on the magnitude ofpore-water pressure is due to the changes in mean normalstress, and the relative changes in shear stress are small(

To account for the dilatory response, an empirical offsetmethod was suggested by Sully and Campanella (1994)whereby the curves were shifted to the maximum value ofmeasured pore pressure and then subjected to the monotonicdecay solution of Teh (1987). A theoretical basis has notbeen suggested until now.

Model development

The development of the model presented herein is basedon the premise that the excess pore pressures which developduring the penetration of a probe are due to changes in bothnormal and shear stresses. Compression-induced pore pres-sures from increasing normal stresses are always positive;however, shear-induced pore-water pressure may be either

positive (contractive) or negative (dilatant). Under the conetip, the shear stress component can be derived from stresspath analysis and always has positive values (Chen andMayne 1994); additionally, the magnitude of the normal-induced response is often much larger than that of the shear-induced response under the cone tip. However, along theshaft, the normal- and shear-induced components can becomparable in magnitude. While the normal component willalways remain positive, the shear-induced component can bepositive at low overconsolidation ratios (OCRs) or negativeat high OCRs.

The zone of influence of the octahedral normal stress is afunction of the rigidity index (Ir = G/su, where G is the un-drained shear modulus (typically, assumed G50), and su is theundrained shear strength) of the soil and is large (approxi-

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Burns and Mayne 1065

Reference Cavity type Soil model Initial pore pressure, ui CommentsSderberg 1962 Cylindrical,

radius RElastoplastic u/ui = R/r Consolidation surrounding

driven piles; finitedifference

Torstensson 1975, 1977 Cylindrical;spherical

Elastoplastic ui = 2su ln(rp/r); ui =4su ln(rp/r), where rp is theradius of the plasticized zone

No shear stresses; finitedifference

Randolph and Wroth 1979b Cylindrical Elastoplastic ui = 2su ln(rp/r) Consolidation surroundingdriven piles; analytical

Baligh and Levadoux 1980;Levadoux and Baligh 1986

Piezocone model Nonlinear From strain-path method Total stress soil model

Battaglio et al. 1981 Cylindrical;spherical

Elastoplastic ui = 2su ln(rp/r); ui =4su ln(rp/r)

Shear by empirical method;finite difference

Jones and Van Zyl 1981 Experimental Empiricalapproach

Measured Correlation between measuredtime for 50% consolidationt50 and oedometer-measured values of ch

Kavvadas 1982 Piezocone model Nonlinear From strain-path method Effective stressstrain modelSenneset et al. 1982 Cylindrical Elastoplastic ui = 2su ln(rp/r)Tumay et al. 1982 Piezocone model Linear From strain-path method Experimental dataGupta and Davidson 1986 Piezocone model Elastoplastic Modified cavity expansion;

dissipation as cone penetratesIsotropic and anisotropic

Soares et al. 1987 Piezocone model Nonlinear Corrected by visual examina-tion and regression analysis

Whittle 1987 Piezocone model Nonlinear From strain-path method Effective stressstrain modelHoulsby and Teh 1988;

Teh and Houlsby 1991Piezocone model Nonlinear Predicted by large-strain, finite-

element analysis and strain-path method

Finite difference

Elsworth 1990, 1993 Point-dislocationtheory

Elastoplastic From point-dislocation theory Not applicable for u2measurements

Aubeny 1992 Piezocone model Nonlinear From strain-path method Coupled consolidation; effec-tive stressstrain model

Sully and Campanella 1994 Piezocone model Nonlinear Predicted by large-strain, finite-element analysis and strain-path method

Empirical time shift to umaxfor overconsolidated (OC)dissipation

Burns and Mayne 1995 Spherical Elastoplastic uoct = 4su ln(rp/r); ushear =vo[1 (OCR/2)0.8]

Incorporates shear stresses;models OC dissipation;finite difference

Burns 1997 Spherical Elastoplastic uoct = 4su ln(rp/r); ushear =vo[1 (OCR/2)0.8]

Incorporates shear stresses;models OC dissipation;analytical

Note: Modified after Lunne et al. (1997) and Jamiolkowski (1995).

Table 1. Historical development of piezocone dissipation modeling.

mately 1020 diameters or 350700 mm), in comparisonwith the zone of influence of the shear stress (approximately110 mm). In contrast, the zone affected by interface shearstresses is limited to a thin annulus next to the body of thecone penetrometer. Because the volume affected by the nor-mal stress is much larger than that affected by the shearstress, the dissipation of the shear-induced pressures will oc-cur more rapidly than that of the normal-induced pore pres-sures.

The core of the model uses cavity-expansion theory torepresent the octahedral normal component of excess porepressure in combination with Modified CamClay to quan-tify both the shear-induced component of excess pore pres-sure and the variation of the undrained shear strength as afunction of OCR. In this simple model formulation, no at-tempt has been made to incorporate strain fields (Acar andTumay 1986) or strain paths (Baligh 1986) which wouldlead to a more rigorously correct, but significantly morecomplicated model formulation. The hybrid cavity-expansion critical-state formulation has successfully repre-sented penetration pore-water pressures in a variety of clayswith consistencies ranging from soft to stiff to hard (Mayne1991, 1993; Lunne et al. 1997). The model relies on an ana-lytical solution to the radial consolidation equation

[3]

=

+

u

tc

u

r

c

r

u

rh

h2

2

where ch is the horizontal coefficient of consolidation, u isthe pore pressure, r is the radius, and t is the time. Themethod is a rapid, compact solution and is easily pro-grammed into a personal computer. The procedure to modelboth lightly and heavily overconsolidated clay dissipationbehavior with time is outlined below.

The normal-induced pore pressures used in the modelwere based on derivations of cavity-expansion theory(Bishop et al. 1945; Vesic 1972). According to the conceptsof undrained cavity expansion, the following equations areapplicable for the generated pore pressure u in cone pene-tration testing (Torstensson 1977):

[4] u s Gs

=43 u u

spherical cavityln

[5] u s Gs

= u

u

cylindrical cavityln

Development of shear-induced pore pressures in un-drained loading is evaluated using a constant p stress pathfor isotropically consolidated soil in Cambridge qp space(Wroth 1984), where p is the mean effective stress, and q isthe deviator stress. The shear-induced pore stress can thenbe expressed as the difference between the initial and finaleffective mean stresses:

[6] u p pshear o f= where po is the initial mean principle effective stress, and pfis the mean principle effective stress at failure. For the pur-poses of this study, po is assumed equal to the effective ver-

tical stress vo (Wroth 1988), an approximation that neglectsthe effect of initial anisotropic stress state.

According to Modified CamClay, the final mean princi-ple effective stress can be represented by the following:

[7] = f vo

OCR2

is the plastic volumetric strain ratio = 1 Cs/Cc, where Csis the swelling index, and Cc is the compression index. Datacompiled by Mayne (1988) indicate that = 0.80 is appro-priate for many natural clays. For estimation of the shear-induced pore pressures along the cone shaft at the type 2 po-sition, a value of = 0.80 is used in this representation.

The linear partial differential equation that describes ra-dial consolidation surrounding a piezocone was solved toobtain an analytical solution for use in the model. Prior solu-tions to similar problems have related to heat-flow analysisand to consolidation surrounding driven piles (Carslaw andJaeger 1959; Randolph and Wroth 1979b). Derivation of thetwo different solutions, using the conditions imposed byspherical and cylindrical cavity expansion, is given in a sep-arate paper.1

In its most simple form, the dissipation model requires in-put values for the effective vertical stress ( vo), the hydro-static pore-water pressure (uo), cone radius (r), rigidity index(Ir), OCR, and effective stress friction angle () of the soil.The undrained shear strength was represented by the critical-state Modified CamClay model and corresponds to triaxialcompression loading in terms of effective stresses (Wrothand Houlsby 1985)

[8] s Muvo

OCR

=

2 2

where M is the slope of the critical-state line:

[9] M =

63

sinsin

Although isotropic triaxial compression is not necessarilythe most appropriate mode for both the octahedral and shearcomponents next to a penetrometer, the general trends areindicative and representative of soil behavior, particularlycontractive to dilatant pore-pressure response.

The undrained shear strength ratio (su/ vo) increases as afunction of overconsolidation ratio, which is reasonable andconsistent, except in cases where the clay becomes fissured.Fissures can occur at many scales within the soil, each ofwhich will affect the measurement of properties differently.Based on experimental data reported by Bishop (1972) andSkempton et al. (1969), a strength-reduction factor of 0.5was chosen as appropriate for the very heavily fissuredclays. However, it is noted that additional work in quantify-ing the strength-reduction factor due to fissuring is war-ranted.

The size of the induced plasticized zone generated by thecone sounding was calculated according to spherical cavityexpansion. The rigidity index affects both the size of the

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1066 Can. Geotech. J. Vol. 35, 1998

1 S.E. Burns and P.W. Mayne. Analytical Solutions for Consolidation Surrounding Cone Penetrometers. In preparation.

plasticized zone and the increase in excess pore pressure dueto changes in octahedral normal stresses. However, the ap-propriate value of the rigidity index is ill-defined and gener-ally quite difficult to assess due to the uncertainty associatedwith estimation of the stress level during testing (Mayne1995). Consequently, the rigidity index was taken as an in-put parameter and multiple dissipation curves are presentedbased on chosen values for the rigidity index. Alternately,when the initial generated pore pressure is measured, the ri-gidity index can be estimated because all other parameters(umeas, vo, , OCR, and uo) are known.

The next step in the model was to calculate the excesspore pressure generated due to cone penetration. The octahe-dral normal component of the pore pressure was calculatedusing spherical cavity expansion. In reality, the zone sur-rounding the type 2 filter is neither completely spherical norcylindrical, but represents a transitional area between thetwo. Pore pressure was assumed to increase only within theplastic zone; excess pore pressure outside the plastic zonewas set equal to zero.

Finally, the magnitude of shear-induced pore pressures fora piezocone with shoulder filter element was calculated us-ing the concepts of CamClay (Mayne and Bachus 1988):

[10]

ushear voOCR

=

1 2

The increases in excess pore pressure due to changes inshear stress were assumed to decrease linearly with distanceaway from the cone body. The sum of the squared errors, asdiscussed in detail later, was used to determine the most ap-propriate thickness of the shear zone. For the cases exam-ined, the shear zone width was set equal to 2 mm.

The final form of the equation for calculating the gener-ated excess pore pressure is as follows:

[11] u M Im vo rOCR=

43 2 2

ln

+

+ =vo o

OCRat1

20

u t

[12] um = uo at t = t100The initial distribution of the excess pore pressure within

the plastic zone was used as the initial condition to solve theone-dimensional, uncoupled partial differential consolidationequation for radial drainage. While the initial magnitude ofthe octahedral induced normal stress was calculated usingspherical cavity expansion, the consolidation equation for ra-dial drainage corresponding to cylindrical cavity expansionwas used to evaluate the change in pore pressure as a func-tion of time. The hybrid cavity-expansion solution was usedbecause spherical cavity expansion provided the most accu-rate evaluation of the initial generated pore pressure and evi-dence suggests that radial drainage most strongly governsconsolidation surrounding a penetrating probe (Bjerrum andJohannessen 1961; Koizumi and Ito 1967; Randolph andWroth 1979a).

Boundary conditions assume that there is no increase inexcess pore pressure outside the spherical cavity plastic zone(u = 0) and that the cone body was an impermeable bound-ary (Fig. 2). After the excess pore-pressure dissipation wascalculated, the values were added to the hydrostatic pore-pressure value at that depth. This was done because the

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Fig. 2. Zones affected by cone penetration. E, Youngs modulus; ro, cone radius; rp, radius of plasticized zone;v, Poissons ratio.

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piezocone measures total pore pressures (hydrostatic plusexcess).

The model was run iteratively with an input value of chchosen for the initial run. Based on the results of the first it-eration, a new value for ch was chosen until the deviation ofthe predicted dissipation curve was at a minimum from the

actual measured dissipation curve as determined using thesum of the squared errors. Previous versions of the modelused a finite-difference solution to the consolidation equa-tion (Burns and Mayne 1995); however, an analytical solu-tion was derived that required only 15 s of computer timecompared with approximately 1 h necessary for the finite-

SiteDepth(m) OCR

Ir(fit)

Piezoelementdata(this study),ch (mm2/s)

Lab-measuredcv (mm2/s) Comments Reference

Bothkennar, U.K. 12.0 1.4 33 100 0.2 0.32 Soft clay Nash et al. 1992Bothkennar, U.K. 12.0 1.4 33 100 0.2 0.080.13 Soft clay Jacobs and Coutts 1992Drammen, Norway 19.5 1.1 34 100 0.2 0.531.52 Marine clay Lacasse and Lunne 1982McDonald Farm, B.C. 20.0 1.1 35 200 1.9 1.85.5* Lean insensitive

clayey siltSully 1991

Saint Alban, Que. 4.6 1.2 27 200 0.6 0.30 Sensitive clay Roy et al. 1981Amherst, Mass. 3.0 7.0 30.5 15 0.4 0.070.10* Crust of soft clay DeGroot and Lutenegger

1994; Lally 1993Canons Park, U.K. 5.7 14.0 22.5 100 0.25 0.010.03* 102 mm pile in

London ClayJardine and Bond 1989

St. Lawrence Seaway,N.Y.

6.1 3.5 30 50 0.3 0.250.80 Crust of soft clay Lutenegger and Kabir 1987

Taranto, Italy 9.0 26.0 28 200 0.4 0.100.25 Cemented clay Battaglio et al. 1986; Bruzziand Battaglio 1987

*Data reported by Robertson et al. (1992) in a review of methods of coefficient of consolidation prediction from dissipation testing.

Table 2. Comparison of model predictions and laboratory values for modeled sites.

Fig. 3. Model predictions in soft clay with monotonic pore-water dissipations for (a) Bothkennar, United Kingdom; (b) Drammen,Norway; (c) McDonald Farm, British Columbia; and (d) Saint Alban, Quebec.

difference solution (Burns 1997).

Results from evaluated test sites

Documented pore-water pressure dissipation measurementsfrom piezocone soundings and instrumented driven pile testsites in both normally consolidated to lightly overconsoli-dated and heavily overconsolidated clays were chosen fromthe literature for comparison with the prediction of themodel. Four soft clay sites which exhibited monotonicallydecreasing dissipation curves and four stiff to hard clays thatexhibited dilatory pore-pressure behavior were chosen. Alisting of the eight sites with the input parameters used forevaluation is given in Table 2. All model predictions of thevalue of the coefficient of consolidation were performed byminimizing the sum of the squared errors, and without priorknowledge of either the laboratory-measured values or ofpreviously predicted field values.

Plots of the model results for the four lightly overcon-solidated sites are shown in Figs. 3a3d. The Bothkennarsite (Fig. 3a) is a postglacial silty clay deposit of intermedi-ate plasticity located in Scotland (experimental data fromJacobs and Coutts 1992). The coefficient of consolidationevaluated by the model was 0.2 mm2/s and the rigidity indexwas 100. The Drammen deposit (Fig. 3b) is a low-plasticity,low-sensitivity marine clay located in Norway (experimentaldata from Lacasse and Lunne 1982). Model-estimated pa-rameters were ch = 0.2 mm2/s and Ir = 100. McDonald Farm

(Fig. 3b) is a test site in soft, normally consolidated clayeysilt located in British Columbia (experimental data fromSully 1991) with a model-determined coefficient of consoli-dation of 1.9 mm2/s and a rigidity index of 200. Saint Alban(Fig. 3d) is a deposit of lightly overconsolidated sensitiveclay located in Quebec (experimental data from Roy et al.1982). Evaluated parameters were ch = 0.6 mm2/s and Ir =200. In all four cases involving soft clays, the predictedcurves match well with the measured responses.

The model was also used to evaluate dilatory pore-pressure response in heavily overconsolidated soils, with theresults shown in Figs. 4a4d. The Amherst dissipation test(Fig. 4a) was performed in an upper desiccated crustal re-gion of varved clay of low plasticity (experimental data fromLally 1993). Model-estimated results were ch = 0.4 mm2/sand Ir = 15. Instrumented pile data from Canons Park,United Kingdom, which exhibited dilatory pore-pressure re-sponse were also modeled (Fig. 4b). The 102 mm diameterdriven pile was located in the heavily overconsolidated Lon-don Clay (experimental data from Bond and Jardine 1991),with model-evaluated results of ch = 0.25 mm2/s and Ir =100. The Saint Lawrence Seaway dissipation test (Fig. 4c)was performed in the crust of a silty clay deposit in NewYork (experimental data from A.J. Lutenegger, personalcommunication, 1997). Slight dilatory pore-pressure re-sponse was observed at this site; the model-estimated valueof the coefficient of consolidation was 0.3 mm2/s and the ri-gidity index was 50. The Taranto deposit (Fig. 4d) is a

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Fig. 4. Model predictions in hard clay with dilatory pore-water decays for (a) Amherst, Massachusetts; (b) Canons Park, UnitedKingdom; (c) St. Lawrence Seaway, New York (SLS); and (d) Taranto, Italy.

heavily overconsolidated and cemented clay located insouthern Italy (experimental data from Bruzzi and Battaglio1987). For this site, the determined parameters were ch =0.4 mm2/s and Ir = 200 and matched well with the measuredpore-water measurements.

Examination of the evaluated versus measured dissipationcurves shows that the model is able to estimate the dissipa-tion curves for a shoulder position pore-pressure measure-ment fairly well. The compilation of the coefficient ofconsolidation data given in Table 2 shows that the value ofch determined by the model is within range of the values ofthe vertical coefficient of consolidation cv reported from lab-oratory consolidation tests conducted on companion samplestaken at similar test depths. Note that the evaluation of thecoefficient of consolidation in piezocone testing occurs inremolded soil, whereas the measurement in the laboratorytest does not. Additionally, the effects of soil sensitivity, ageof the deposit, and filter smearing might improve the predic-tion if included. Additional examples of monotonic and dila-tory responses are given by Burns (1997).

Error surfaces

A study was performed to identify the relative influenceof the model input parameters on the predicted results. Spe-cifically, the error ei (or residual) was calculated betweeneach predicted and actual measurement using the followingdefinition (Santamarina and Fratta 1998):

[13] e y yi i i= (meas) (pred)

where yi(meas) is the measured value, and yi(pred) is model-predicted value. The error norm L2 was then calculated asthe sum of the squared errors using the following equation:

[14] | |L eii

22

1 2

=

/

The best fit for the model parameters was then achievedby varying one parameter until the error converged to a min-imum. The L2 error norm uses a least-squares minimization,and assumes that the measured data follow a Gaussian distri-bution. The input parameters which were varied included thewidth of the shear zone, the coefficient of consolidation, therigidity index, the effective friction angle, and the OCR. Theerror norms are plotted versus a reasonable operating rangeof magnitude encountered in engineering practice.

Figures 5a and 5b show the resulting error norms causedby changing the width of the zone of soil affected by theshearing action due to the soil and penetrometer interactionin a soft clay (Bothkennar) and in a hard clay (Taranto), re-spectively. Each point on the graphs represents a differentrun of the model. The results show clearly that the width ofthe shear zone has little effect in the soft clay where the con-tribution of shear stresses is less significant than in the stiffclay. In the soft clay, the sum of the squared errors remainedessentially constant. However, the width of the shear zone in

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Fig. 5. Error norm for the width of shear zone in (a) soft clay,and (b) hard clay.

Fig. 6. Error norm for the effective stress friction angle in(a) soft clay, and (b) hard clay.

the hard clay apparently had a more significant effect, espe-cially as the width of the shear zone was increased over2 mm. The calculated error norm reached a minimum at2 mm, and increased as the width of the shear zone was in-creased. Variation of the input parameters including the co-efficient of consolidation and the rigidity index showedsimilar trends.

The error norms were also calculated for the effectivefriction angle and OCR, with the results for the friction an-

gle shown in Figs. 6a and 6b (similar trends were seen forthe OCR). Again, the data from the Bothkennar and Tarantosites were used for comparison to show soft clay versus hardclay responses. Of all the parameters examined for the hardclays, the changes produced by these two parameters werethe most significant. The error norms for the friction angleand OCR in the hard clay show steep gradients movingaway from the error minimum, showing that the model issensitive to the input value of these parameters. Similar tothe trends seen previously, the variation of the effectivestress angle and OCR are less significant for the soft clay,producing a smaller level of error than was seen in the hardclay for the same level of variation. The significant effect ofthe effective stress friction angle and OCR makes the initialevaluation of these parameters of critical importance in theestimation of the coefficient of consolidation, primarily be-cause they represent the undrained strength and initial pene-tration pore-water pressure regime used in the evaluation.

Normalized dissipation data

The evaluated dissipation results can also be presented asa series of normalized curves, similar to those given by Tehand Houlsby (1991). Figures 7a7c show the normalizeddissipation curves estimated for values of equal to 20, 30,and 40, respectively, all at Ir = 100. The data are presentedas the measured pore pressure normalized to the initial mea-sured value (u/ui). The coefficient of consolidation can beevaluated from the normalized curves by the following:

[15] c Trt

h =2

where T is the time factor. As seen in the figures, the lowervalue of leads to more significant differences in behaviorfor different values of OCR. This is because the lower valueof the friction angle leads to a smaller initial magnitude ofpore pressure, and a more rapid decay of the pressures whenthe values are normalized to the initial value.

Conclusions

A hybrid cavity-expansion critical-state representationof piezocone dissipation is presented as a rational interpreta-tion of the coefficient of consolidation in clays and silts thatexhibit either monotonically decreasing or dilatory pore-pressure response. The inclusion of components to accountfor both the normal- and shear-induced pore-water pressuresprovides a reasonable explanation for the initial drawdownobserved in the pore-pressure dissipation behavior ofoverconsolidated soils. The utilization of an analytical solu-tion for the consolidation equation provides a rapid and ro-bust approach for the evaluation of pore pressure as afunction of time. The model developed in this study requiredthe input parameters of rigidity index, effective stress fric-tion angle, overconsolidation ratio, effective vertical stress,cone radius, and hydrostatic pore pressure; it was evaluatedat a variety of sites, ranging from consistencies of soft tostiff clays, and gave estimates of the coefficient of consoli-dation which were within range of the laboratory-measuredvalues. Further laboratory and field evaluation of the methodis ongoing.

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Fig. 7. Normalized dissipation curves for u/ui versus timefactor T at different overconsolidation ratios (OCR) for effectivestress friction angles of (a) 20, (b) 30, and (c) 40.

Acknowledgments

The authors gratefully acknowledge the support of Na-tional Science Foundation grant MSS 9257642 throughwhich this project was funded. Diego LoPresti, AlanLutenegger, and John Powell are thanked for their provisionof experimental data.

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