Numerical Methods in Geotechnical Engineering – Benz & Nordal (eds)© 2010 Taylor & Francis Group, London, ISBN 978-0-415-59239-0

Comparison of methods for calculation of settlements of soft clay

H.P. JostadNorwegian Geotechnical Institute (NGI), Oslo, NorwayNorwegian University of Science and Technology (NTNU), Trondheim, Norway

S.A. DegagoNorwegian University of Science and Technology (NTNU), Trondheim, Norway

ABSTRACT: Calculation of long-term settlements of soft clay generally consists of many uncertainties. Bystudying back-calculated field cases, from literatures, it is therefore generally very difficult to compare theperformance of different calculation tools due to varying interpretations and assumptions in the governing inputparameters. Therefore, as part of a series of creep workshops called CREBS, the participants were invited toanalyse a set of hypothetical cases using their material models and computer program. The cases involved a30 m thick homogeneous normally consolidated soft clay layer underlying a 10 m thick sand layer subjected to asurface stress of either 50 or 90 kPa. Six groups submitted their contributions to this exercise. This paper presentsthe main results from this exercise, compare the background of the different material models and discuss thereasons for the characteristic differences in the obtained results.

1 INTRODUCTION

The first CREBS (CREep Behaviour of Soft clay)workshop was held in January 2006, at NGI in Oslo.One of the conclusions from this workshop was thateven for material models based on the same frame-work it is very difficult to compare the differencesin assumptions and input data since all models usesomewhat different expressions. Hence, it was recom-mended to establish a common set of definitions and tosystematically compare existing calculation tools usedin long-term settlement analyses of soft soils.

The participants at the second CREBS workshop,held in September 2007 in Pisa (Italy), were invitedto analyse a set of well defined hypothetical casesby various calculation tools. The main purpose wasto compare variations in interpreted input data andobtained calculation results and not a competitionin predicting the most correct results. When study-ing published back-calculations of field cases (seefor instance Leroueil 2006) large differences may beobtained due to uncertainties in material properties,in situ pore pressure distribution, drainage conditionsand earlier load histories.

The results from the analyses of the hypotheticalcases were briefly presented at the third CREBS work-shop held in July 2009, in Gothenburg (Sweden). Thispaper gives a more detailed presentation and evalua-tion of some of the most characteristic results fromthis exercise.

2 HYPOTHETICAL CASES

All cases consist of a 30 m thick soft clay layer below a10 m thick sand layer as shown in Figure 1. A surfaceload of 50 kPa (light structure) or 90 kPa (heavy struc-ture) is distributed over an area that is large comparedto the thickness of the soft clay layer (1D condition),except for one case. Settlements below the clay layerare neglected. The ground water table (GWT) is at thetop of the sand layer. For the bottom boundary twoextreme assumptions are considered, either a perfectlydrained or an impervious surface. The following caseswere analysed (however, only some of the results arepresented here):

1. Normally consolidated (NC) behaviour where thepre-consolidation pressure is assumed to be equalto the in-situ effective vertical stress.

2. Normally consolidated behaviour with an appar-ent pre-consolidation pressure corresponding toa constant over-consolidation ratio of OCR =1.4.

3. A time history where the soil profile is pre-loadedin a period of 25 years before increasing the load.

4. The clay layer is divided into two sub-layers withsignificantly different permeabilities.

5. A load is applied on a strip foundation with limitedwidth of 20 m, that gives a decreasing excess stressdistribution with depth and induce some effect ofshear mobilisation.

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Figure 1. The hypothetical cases.

2.1 Soil conditions

2.1.1 Sand layerIn order to make it easier to compare the results,the main properties of the sand layer were directlygiven: Constrained modulus, M = 10 MPa, submergedunit weight of soil, γ ′ = 10 kN/m3 and permeability,k = 1 m/year.

2.1.2 Clay layerThe soft soil layer consists of a homogeneous, nor-mally consolidated, fully water saturated, plasticmarine clay with approximately the same age (10,000years). This means that the characteristic mechanicalbehaviour found at one depth is assumed to be validfor the entire depth of the layer.

The constitutive behaviour of the clay is found froma standard oedometer test with incremental loading(IL). The results from the different load incrementsare shown in Figure 2. The figure shows the verti-cal strain increment �εv = �δv/ho, where �δv is thevertical displacement at the top of the sample dur-ing the actual load increment and ho = 20 mm is theinitial sample height. Most of the load incrementshave a period of about 1440 minutes (1 day). How-ever, for load increment (180 − 280 kPa) the verticalstress of 280 kPa was kept for a period of about 5.5days (8000 minutes). Figure 2 shows the accumulatedvertical strain (εv = δv/ho) after 24 hours for all loadincrements.

The initial effective vertical stress σ ′vo was pur-

posely not provided for the actual test. The reasonis that because the actual over-consolidation ratioOCR = σ ′

vc/ σ ′vo was specified. The results should

therefore be representative for the given OCR and notaffected by the interpretation of the effective verticalpre-consolidation pressure σ ′

vc.For models based on void ratio, the initial void ratio

eo is 1.17.

Figure 2. Stress, strain and time relationships obtained froma standard IL-test.

3 PARTICIPANTS

The following participants have analyzed the givencases:

• Dr. Martino Leoni and Professor Pieter Vermeerfrom the University of Stuttgart.They used the com-puter program Plaxis (www.plaxis.nl) with the SoftSoil Creep (SSC) (Vermeer & Neher 1999) and theuser defined Anisotropic Creep model (Leoni et al.2008)

• Dr. Zhen-Yu Yin and Dr. Minna Karstunen fromEcole Centrale de Nantes and University of Strath-clyde. They used Plaxis with the user defined visco-plastic EVP-SCLAY1S model (Yin & Karstunen2008)

• Dr. David Nash from the University of Bristol.He used the computer program BRISCON with anisotache based model (Nash & Ryde 2001)

• Mats Olsson and Professor Claes Alén fromChalmers University of Technology. They usedthe GeoSuite Settlement Program (www.novapoint.com) with the Chalmers model Claesson(2003)

• Per-Evert Bengtsson and Rolf Larsson from theSwedish Geotechnical Institute (SGI). They usedthe settlement program EMBANKCO with a modelrather similar to the Chalmers model (Bengtsson &Larsson 1997)

• Professor Hans Petter Jostad from NGI and Nor-wegian University of Science and Technology(NTNU). He used the GeoSuite Settlement Pro-gram with the Krykon material model (Svanø et al.1991)

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4 BRIEF DESCRIPTIONS OF MODELS USED

In order to systematically compare the different mod-els used, their behaviours in uniaxial vertical straincondition (1D) are briefly presented.The vertical strainrate is then decomposed into a component due to effec-tive vertical stress changes (a reference strain) and acomponent only due to time (creep):

where Mt is an effective stress dependent tangentialconstrained or oedometer modulus; R = Ro + r · t isJanbu’s time resistance (Janbu 1969); Ro is the initialtime resistance; and r is the time resistance num-ber. Lines with constant R-values in vertical effectivestress–strain space are called isotaches (Šuklje 1957).

The values for the model parameters are presentedbased on the results submitted by the participants.

4.1 The Krykon model

The Krykon model, implemented in the GeoSuite Set-tlement program, is based on Janbu’s time resistanceconcept. A detailed description of the model can befound in Svanø et al. (1991).

The reference strain after 24 hr εo due to effectivestress changes, is given by a stress dependent tangen-tial constrained modulus: Mt = Moc for σ ′

v < σ ′vc and

Mt = m · (σ ′v − σ ′

vr) for σ ′v > σ ′

vc (where σ ′vr is reference

stress), with Moc = 5 · m · σ ′vc; m = 16 and σ ′

vr = 0 inthis case. The time resistance R is given as function ofthe vertical strain ε:

where Ro = 0.8 year is the time resistance at the ref-erence strain εo, and r is an effective vertical stressdependent time resistance number varying linearlybetween r = 1125 at σ ′

vo and r = 300 at σ ′vc. In the

NC-regime r is taken to be constant equal to 300.

4.2 The Chalmers model

The Chalmers model, implemented in the GeoSuiteSettlement program, is also based on Janbu’s timeresistance concept.A detailed description of the modelcan be found in Claesson (2003).

The 24 hr reference strain, due to stress changes,in this case is given by an initial stress depen-dent tangential constrained modulus, Mt = 12 MPa +0.5 MPa · (z − 10 m) for σ ′

v < σ ′vc and Mt = 13.5 ·

σ ′vo for σ ′

v > σ ′vc. The time resistance is given as:

R = Ro + r · t, where Ro = r · to; to = 24 hr and r isvarying linearly between r = 10, 000 atσ ′

vo and r = 300at σ ′

vc. In the NC-regime r = 300.

4.3 The Embankco model

The Embankco material model is very similar to theChalmers model; however, the model is implemented

in the finite difference program Embankco (Bengts-son & Larsson 1997).

The 24 hr reference strain, due to stresschanges, is given by the constrained modulus,Mt = Moc for σ ′

v < σ ′vc; Mt = ML for σ ′

vc < σ ′v < σ ′

vL;and Mt = ML + m · (σ ′

v − σ ′vL) for σ ′

vL < σ ′v; where

Moc = 50 · σ ′vc; ML = 3140 + m · (σ ′

vc − 192 kPa);σ ′

vL − σ ′vc = 78 kPa; and m = 16.5. The time resistance

is given as: R = Ro + r · t, where Ro = r · to, to = 24 hr;r is 261 at σ ′

vc and increases asymptotically to aninfinite value at OCR = 1.25. In the NC-regime, rincreases from 261 to about 365 at 10 % vertical strain.

4.4 The Briscon model

The material model used in the finite difference pro-gram BRISCON (Nash & Ryde 2001) is also based onthe isotache concept.

The 24 hr reference strain, due to stress changes, isgiven by: Mt = mr · σ ′

v for σ ′v < σ ′

vc, and Mt = m · σ ′v

for σ ′v > σ ′

vc, with m = 13.7 and mr = 8 · m = 110.The time resistance is given as R = Ro + r · teq,

where Ro = 0.95 year. The equivalent time teq is thetime required to obtain the increase in creep strain fromthe reference time line (RTL) to the current strain atthe actual effective vertical stress. The RTL in a εv −ln(σ ′

v) plot is a line that goes through the strain at σ ′vc

by a slope defined by the modified compression indexλ∗ = 1/m.The teq is then calculated from the equivalentcreep strain εeq:

In the over-consolidated (OC) regime the initialεeq,o is defined by the OCR (σ ′

vc/σ ′v) and the modulus

numbers m and mr :

The time resistance numbers for the load steps inthe IL test were found to be: r = 4000, 3000, 2000,1200, 700, 280, 400, 360 and 410. In addition, it isrealistic to assume that some of the creep observed inthe OC-regime is due to sample disturbance and thatthe in-situ creep rate for a 10,000 year old clay is negli-gible. The pre-consolidation pressure was found to beσ ′

vc = 152 kPa. Based on this, three different variationsof the r-value were considered: r = 343 (constant); ras function of σ ′

v/σ ′vc based on measured results; and a

case where r is gradually increased in the OC-regimeto an unlimited value at OCR = 1.4 (only constant r ispresented here).

4.5 The Soft Soil and Anisotropic Creep models

The Soft Soil Creep model (Vermeer & Neher 1999)in Plaxis, is similar to the BRISCON model; however,

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extended to a full 3D stress condition using the frame-work of the modified Cam-Clay model.The time resis-tance is defined as R = Ro + r · teq, where Ro = r · to,to = 24 hrs, r = 1/µ∗ = 333, and µ∗ is the modifiedcreep index used as input in Plaxis.

The volumetric creep strain is then related to theexpansion of the ellipse in the effective mean stress(p′) – deviatoric stress (q) space controlled by the mod-ified compression index, λ∗ = 1/m = 1/13.7 = 0.073.This means that the equivalent time teq and the corre-sponding creep strain is governed by the expansionsof the ellipse compared to the ellipse given by the cur-rent stress state (p′ and q). This gives the followingexpression for the time resistance:

where σ ′vy is the updated apparent pre-consolidation

stress due to creep. The elastic effective stress depen-dent constrained modulus is given as:

where νur = 0.2 is the unloading/reloading Poisson’sratio; Ko is the actual effective horizontal/verticalstress ratio; and mr = 7.85 · m = 108.

For the Anisotropic Creep Model (Leoni et al.2008), a rotated ellipse based on a fabric tensor(Wheeler et al. 2003) is used. However, ACM givesthe same results as the SSC model except for Case 5.

4.6 The EVP SCLAY-1S model

In differ to the other models that are based on theisotache concept, the anisotropic elasto-viscoplasticmodel EVP SCLAY-1S (Yin & Karstunen 2008) isbased on the overstress theory (Perzyna 1966) and arotated Cam-Clay surface as in ACM. In this case thetime resistance is give by a somewhat more complexexpression:

where µ is the fluidity parameter; N is the strain-ratecoefficient relating to the strain-rate effect on shearstrength and pre-consolidation stress; df 1 ∼ 0.7 for 1Dcondition; and OCRs is the ratio between the size of theellipse given by the current stress state (dynamic load-ing surface) and the size of an inner expanding ellipse(static yield surface).The expansion of the inner ellipseis controlled by the accumulated creep strain as for theSSC/ACM. From the above expression it is seen thatthe time resistance Ro at the 24 hr reference strainis controlled by OCRs– value and that the creep ratevanish when OCRs = 1.

By fitting the IL test the constants were found tobe µ = 5 · 10−16 (1/year) and N = 13.77. The OCRs

is taken to be 3.6 at the NC reference line. The cor-responding r-value at the NC-line is then 412. Themodulus numbers were taken equal to m = 13.7 andmr = 13.5 · 13.7 = 185.

4.7 Discussions

All models may give approximately the same 24 hr ref-erence strain and the time dependent strain. The actualresults are therefore dependent on how the participantsinterpreted the IL test.

The modulus number used in the NC-regime did notdiffer much since almost all participants based it onthe slope of the εv versus log(σv

′) plot at large effec-tive vertical stresses. The interpreted creep strain inthe NC-regime also did not differ much. Most of theparticipants found the time resistance factor r fromthe last part of the 8000 minutes creep phase at aneffective vertical stress above the pre-consolidationpressure. However, the parameters (N and µ) used inEVP-SCLAY1S were selected in order to fit the strainfor all load steps in the IL test. Consequently the modelunderestimated the strain during the 8000 minutes longcreep phase at 280 kPa.

The time resistance number in the NC-regime variesbetween 261 (Embankco) and 412 (EVP-SCLAY1S) atthe 24 hr reference time. Furthermore, for the N -valueused in EVP-SCLAY1S, the r-value increases withincreasing strain under a constant effective verticalstress.

The largest differences are found in the mod-elling of the creep in the OC-regime. In Embankcothe r-value asymptotically increases with increasingOCR to infinitely at OCR = 1.25. In the Chalmersmodelr-value increases with increasing OCR to a verylarge value (r = 10,000) at OCR = 1.4. In Krykon thecorresponding value at OCR = 1.4, is r = 1125. InSSC/ACM and Briscon the r-value is independent ofOCR. Instead it is the equivalent time teq that increaseswith OCR (see Eq. 3) which gives an increase in the ini-tial time resistance Ro = r · (to + teq). However, basedon the IL test all the r-values used in all the analysesmay be considered as reasonable.

The modulus used in the OC-regime depends onwhether it was based on the initial loading from thein-situ effective vertical stress to the pre-consolidationstresses (which may underestimate the stiffness dueto sample disturbance), taken from the unloadingsequence at the end of the test (starting from a largeeffective vertical stress) or based on in-house experi-ences. For instance in-house experiences were used forthe Chalmers model to extrapolate to larger effectivestresses.

Figure 3 shows the stress dependent 24 hr refer-ence strain and the time dependent strain at the topand bottom (with drainage boundary) of the clay layer(OCR = 1.4) given by the different models.The curvesare established based on the reported input parameters.

From these plots it is clear that the calculatedsettlements for Case 1 to 5 will be smallest byEVP-SCLAY1S and largest by SSC and Briscon. The

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Figure 3. Effective vertical stress-strain-time relationshipsderived from the different models at the top and the bottomwith open boundary of the clay layer. The time dependentstrains are for an excess load of 50 kPa.

results obtained by SSC and Briscon should be verysimilar.

5 RESULTS

Only the main results that demonstrate some charac-teristic differences are selected and presented here.

Figure 4 shows the calculated settlements versustime for Case 1. The plot demonstrates the effect ofdifferent time resistance numbers used, where EVP-SCLAY1S gives the smallest settlements (0.95 m) dueto a time resistance number r of more than 400, whileEmbancko gives the largest settlements (1.62 m) with

Figure 4. Calculated settlements versus time for Case 1 withopen bottom boundary.

Figure 5. Calculated settlements vs. time for Case 2 withopen bottom boundary and q = 50 kPa.

Figure 6. Excess pore pressure histories for Case 2 withq = 50 kPa and open bottom boundary.

r = 261. The settlements due to creep for r = 300 isabout 1 m after 100 years.

Figure 5 also shows the calculated settlements forCase 2 with q = 50 kPa and open bottom boundary.The results demonstrate the effect of different assump-tions of the constitutive behaviour in the OC-regime.Chalmers and EVP-SCLAY1S models give the small-est settlements (0.3 m) due to the smallest creep inthe OC-regime, while Krykon, Briscon and SSC giveroughly the same settlements (an average of 0.66 m).Embankco gives the largest settlements (0.89 m) and itseems that the solution has become somewhat unstableafter about 60 years.

From Figure 6, which shows the correspondingexcess pore pressure in the middle of the soft clay layerversus time, it is seen that the primary consolidationphase is finalized after 100 years for all cases (exceptfor Embankco). The differences in calculated pore

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Figure 7. Calculated strain profiles after 100 years forCase 2 with q = 50 kPa and open bottom boundary.

pressure during the first 20 years are significant, e.g.after 10 years the excess pore pressure varies between7 kPa or 14% (Chalmers) and 37 kPa or 74% (Krykon).It is also seen that the excess pore pressure for SSC andBriscon initially becomes larger than 50 kPa.This indi-cates that the initial creep strain rate in these modelsis unrealistically large at this depth. The creep rate isalso too large in Krykon, however, in GeoSuite Settle-ment the creep strain is not allowed to reduce the initialeffective vertical stresses.The excess pore pressure forEVP-SCLAY1S and Chalmers decreases very rapidlydue to stiffer behaviour and less creep.

Figure 7 shows the calculated total strain profilesafter 100 years, also for Case 2 with q = 50 kPa andopen bottom boundary. From this plot it is seen thatthe strain at the top and bottom of the clay layer gen-erally agree with the strains-time relationship givenin Figure 3. The differences in the obtained resultsare directly results of the differences in the inter-preted input data. However, the strain at the top ofthe clay layer is slightly larger for Embankco andslightly smaller for EVP-SCLAY1S than found fromthe curves in Figure 3.

6 CONCLUSIONS

The main conclusion from this study is that the dif-ferences in calculated settlements for the set of welldefined idealized hypothetical cases are rather large.The main reason for the differences is uncertaintiesand assumptions in the creep behaviour for stressconditions below the initial pre-consolidation stress(OC-regime). The differences could have been evenlarger for a real case where uncertainties related to theOCR profile are generally significant.

It is therefore recommended to continue the focuson the constitutive behaviour in the OC-regime, tofind suitable testing procedures and interpretationtechniques that can account for sample disturbance.

Furthermore, it would have been of large benefitif all creep models have used a common set of maininput parameters. It would then be easier to understanddifferences in obtained results by comparison of inputparameters and to establishing a common data base forcreep behaviour of soft clays.

ACKNOWLEDGEMENTS

The participants of the exercise are greatly acknowl-edged for their valuable contribution and allowing theauthors for publishing the results.

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