Back analysis of staged embankment failure: The … · Back analysis of staged embankment failure: ... the embankment was raised in a very short time to the crest level at 6.3 m above

Beyond 2000 in Computational Geotechnics – 10 Years of PLAXIS International © 1999 Balkema, Rotterdam, ISBN 90 5809 040 X

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Back analysis of staged embankment failure:The case study Streefkerk

C.M. BauduinBesix, Brussels, Belgium

M. De VosBelgian Building Research Institute, Brussels, Belgium

P.A. VermeerInstitut für Geotechnik, Stuttgart, Germany

Keywords: case history, clays, failure, soil models, undrained loading, consolidation, creep

ABSTRACT: In 1984 an embankment instability occured in a dike recently heightened in stages.After the instability, an extensive research program has been set up to back-analyse the settlementsand the pore pressures measured during construction, focussing especially on the effects of shearstress and plastic yielding. Back-calculations have been performed using two uncoupled FEMcodes in sequence : one to estimate initial stresses and the total stress increments at the undrainedloading phases and another to simulate the intermittent consolidation. A simplified cap model hasbeen introduced for undrained loading. The present paper presents the results of back-calculationsusing the Soft Soil and the Soft Soil with Creep models. Comparing them with those of the firstback-calculations allow to overlook the progress made in soil modelling, to indicate the remainingvital input of engineers judgement and to propose some directions for further development.

1 INTRODUCTION

In 1984 an embankment instability occured in a recently reinforced section of the river Lek Dikenear Streefkerk in the central west part of the Netherlands. As the foundation for the riverbanksconsist often of extremely weak clay and peat alluvial deposits, the heightening works are per-formed in stages allowing for in between consolidation. Usually, excess pore pressures generatedby loading and their decay due to consolidation are observed during construction using piezome-ters.

Following the instability, design type analyses, based on Bishop’s slip circle method and usingthe monitored pore pressures were performed. However, they were not able to provide satisfactoryexplanations to the occurrence of the accident. Furthermore, the prediction of excess pore pressuresgenerated during the previous loading sequences, using elastic soil models were shown to be ingreat error.

An extensive research program has therefor been set up in the months following the accident, toinvestigate the causes that have lead to failure. The method and the results of this research havebeen extensively reported elsewhere (Teunissen et al. 1986, Bauduin & Molenkamp 1991).

As the soil conditions were rather well known and the history of the settlements and of excesspore pressure generation and dissipation were well measured during the whole construction perioduntil failure, the accident may be used as a benchmark problem for the verification of the develop-ment of soil models and finite element calculation techniques for embankments on soft soil duringthe last 15 years.


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2 CROSS SECTION AND SEQUENCE OF EVENTS

The cross section of the original flood bank and the additional layers are shown in Figure 1. Verti-cal drainage (Colbond KF 350 triangular pattern d = 3.0 m) is used under the bank of the height-ened dike to accelerate consolidation in this area. The loading history is indicated in Figure 2. Thelocation of the piezometers and settlement gauges is shown in Figure 1.

The construction works started in August 1982 : the embankment was raised in four stages fromground level at 1 m below MSL up to 2.3 m above MSL and was then left to consolidate from Oc-tober 1982 to March 1983. The bank was than further raised in three stages to 4.5 m above MSLthat was reached in may 1983. Consolidation was then allowed until end of August 1983 ; at thisperiod, the embankment was raised in a very short time to the crest level at 6.3 m above MSL andthe bank and whole inner slope were covered by a 0.7 m thick clay layer. It was then left to con-solidate during one year until September 1984. In September and October 1984, the embankmentwas completed : basaltstone was lead for the outer slope protection and the temporary road on thecrest was replaced by the permanent one. Not so much load was added during these works. How-ever, soon after that, when the ditch at the bank bank was enlarged, the landside slope of the bankbegan to fail over a length of about 80 m. The observed cracks and soil movements indicated hori-zontal soil displacements up to 40 m beyond the toe of the bank without significant soil heave.

A schematic geotechnical soil profile is indicated on Figure 1. Table 1 summarises the values ofsoil properties as selected for the calculations in 1984. The values are mean values from a regionaldatabank, except that for the peat layer for which the additional information from local CD com-pression and extension triaxial tests at low confining stresses is implemented. Remark that the fric-tion parameters of the regional databank are deduced from cell tests. Elastic deformation moduli

Figure 1. Embankment cross section and schematic geotechnical profile.

Figure 2. Loading history.


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Figure 3. Measured excess pore pressures. Figure 4. Measured settlements.

are deduced from oedometer tests, complemented by pocket pressuremeter tests and by the triaxialtests for the peat layers. It is worthwhile to notice the distinction made between the preloaded soilin the area under the existing old dike and the soil outside its influence area. The soil is consideredto be normally consolidated. No reliable information on this is however available, so all calcula-tions will be performed considering OCR equal to 1.

The hydraulic heads of the excess pore pressures as measured by the piezometers are shown asfunction of time on Figure 3. The measured settlements are illustrated on Figure 4.

Table 1. Soil parameters.

Soil type Level

m-MSL

γkN/m³

w

%

wl

%

wp

%

c’

kN/m²

ϕ’

°

E

kN/m²

ν-

kv

m/day

Cp’

-

Cs’

-

Dike material -1.0/+4.0 18 8 22 2700 0.35 1.7E-3 100

Tiel clay under(preloaded)

-2.7/-1.0 15 90 35 10 20 689 0.35 1.3E-3 45 100

Tiel clay -2.7/-1.0 15 90 35 5 22 689 0.35 1.3E-3 45 100

Peat under(preloaded)

-9.6/-2.7 11 400 250 45 18 18 420 0.20 1.7E-3 11 55

Peat-9.6/-7.5-6.7/-2.7

11 400 250 45 5 26 420 0.20 1.7E-3 11 55

Gorkum clay 2 -7.5/-6.7 11.5 200 125 45 8 19 648 0.35 9E-5 12 60

Gorkum clay 1under (preloaded)

-13.0/-9.6 15 80 12 21 864 0.35 6E-5 27 120

Gorkum clay 1 -13.0/-9.6 15 80 5 21 864 0.35 6E-5 27 120

Pleistocene sand .../-13.0 20 1 33 10000 0.30 4.3E-2 NA


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3 ANALYSIS IN 1984: SOIL MODELS AND FINITE ELEMENT CALCULATIONS

It was recognised in 1984 that a proper prediction of the excess pore pressure due to undrained de-formation should take account of:− The increment of isotropic total stress, which is equal to the mean of the principal stresses as

long as the local shear stress is lower than the local undrained shear resistance and which be-comes close to the increment of major principal stress once the local undrained shear resistanceis reached (Hoëg et al. 1968, Burland 1971);

− The increment of deviatoric stress once the ESP reaches a yield surface;− Load transfer through the soil mass from areas of fully mobilised shear strength towards areas in

which there is still shear resistance available.It was considered that strain softening has a negligible effect. As creep provokes volumetric anddeviatoric irreversible strains, it can be also a contributing factor. Due to the lack of simple and re-liable creep models usable for FE calculation process at that time, creep effects were disregarded,although the consequences of this assumption were not fully understood.

An approximately formulation of undrained behaviour in terms of the stress invariant p’ and qwas established for plane strain deformation. It is illustrated on Figure 5:− Path A’B’ : ESP remains below the yield surface at the initial state; elastic behaviour,− Path B’F’ : ESP is directed outside the surface at the initial state; irreversible volumetric strain

occurs (densification; excess pore pressure ∆uα),− Path AF1 : TSP up to local state of failure; ∆uβ1 is the corresponding increase of isotropic stress,− Path F1F2 : TSP is modified to remain at deviatoric stress equal to undrained shear resistance at

the initial state; the total stress invariant p increases according to the increase of the principalstress, leading to an equal increase of excess pore pressure ∆uβ2.

As a consequence of this formulation, the undrained shear strength can be estimated by (Vermeer etal. 1985)

( ) ( )ϕ′+ϕ′′= sinpcoscc 'Fu (1)

in which c’ and ϕ’ are the effective shear resistance parameters and pF’ is the effective isotropicstress at undrained failure according to the undrained effective stress path through the current ef-fective stress state.

For the calculations in 1984, it was tentatively assumed that the yield surface is a straight linesloping at -45° from the Ko line until the failure line in the p-q plane ; below the Ko line the behav-iour was assumed to be elastic. This simple model was based on the concepts of the YLIGHTmodel (Tavenas & Leroueil 1977) and on observation of the results of a few CU triaxial tests onDutch organic clays and peat available at that moment. Remark that the described tentative modelfocuses only on the prediction of increase of excess pore pressure as a consequence of the increase

Figure 5. Stress paths at undrained loading.


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of the shear stress, but the volumetric strains, which are the « motor » of the excess pore pressuresdue to shearing, are not calculated.

To increase the insight into the effects of the plastic spreading of additional loads, it was at-tempted to back-analyse the behaviour of the embankment using two uncoupled FE codes in com-bination with relatively simple additions to simulate ESP as in Figure 5 (see e.g. Teunissen et al.1986). The main conclusions of the calculations were (see Bauduin & Molenkamp 1991):− For the loading stages up to the one of May 1993 an area of full shear strength mobilisation de-

veloped under the existing riverbank ; the behaviour at the toe of the embankment remainedbelow the failure line.

− The severe load of August-September 1983 produced a much larger area with full plastic flow.It was recognised that quite no safety against failure remained available from that moment.

− The excess pore pressures due to undrained loading could be well back calculated for all loadingstages until may 1983. Back calculated values of the excess pore pressure provoked by the se-vere loading stage of August-September remained significantly lower than the observed ones.

Although the use of non-linear FE analyses allowed to account for global stress transfer due toplastic flow and the very important improvement of the constitutive model compared to the onesapplied for design, it was considered that the applied constitutive model was still too rough to leadto an accurate simulation of « a near failure state » of the soil mass. Also the fact that creep has notbeen simulated may have contributed to the deficiency. Further on, the limitations due to the use ofuncoupled codes were pointed out.

4 DEVELOPMENTS OF SOIL MODELLING

Since the calculations of 1984 and the present date, enormous progress in the development and im-plementation of advanced constitutive models in finite elements codes have taken place, allowingfor coupled analyses of the undrained loading and consolidation of soil with appropriate realisticconstitutive models.

For loading of soft, normally or near normally consolidated soils, PLAXIS provides follow-ing improved models compared with the Mohr-Coulomb model :− The Soft Soil model,− The Soft Soil with Creep model.The Soft Soil model is extensively described in Vermeer & Brinkgreve (1998). It resembles to themodified Cam-Clay model, including a yield function but without softening behaviour. The yieldfunction models the irreversible volumetric straining in primary compression and is used as the capof the yield contour. The failure behaviour is modelled using a Mohr-Coulomb type yield function.A fixed Mohr-Coulomb failure surface and a cap, which may expand in primary compression (seeFig. 6), thus define the total yield contour.

Figure 6. Yield contour of the Soft Soil model.


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Stress paths within this boundary only give elastic (unloading or reloading) strain increments,whereas stress paths that tend to cross this boundary generally give both elastic and plastic strainincrements and corresponding excess pore pressures. Compared to the previous tentative model forthe prediction of excess pore pressures, the Soft Soil model proposes a proper formulation of thechanges in volumetric strains. The logarithmic compression law is described by the modified com-pression and swelling index λ* and κ*. The shear resistance at failure for undrained loading isagain given at the intersection of the effective stress path with the failure line and is thus deducedfrom the effective strength parameters c’ and ϕ’ and the effective isotropic stress at undrained fail-ure according to the undrained effective stress path through the current effective stress state, whichis usually located on the (expanding) cap for uniform loading problems at OCR equal to 1, such asthose treated in this paper.

The Soft Soil with Creep model is basically similar to the Soft Soil model, but includes the ef-fects of volumetric strains due to creep. It introduces time dependency of the plastic range in a SoftSoil model, having thus an ellipsoidal plastic potential and a Mohr-Coulomb type failure surface atthe dry side of critical state. The time dependent creep plastic strains are described by the modifiedcreep index µ*. The following rough estimates and interrelations for λ*, κ* and µ* might be used :

'pC

1=λ∗ (2)

pur

ur

C

3

1

1

ν+ν−≈κ∗ (3)

'sC

1≈µ∗ (4)

and:

10à515à10 =κλ=

µλ

∗

∗

∗

∗

(5,6)

5 BACK ANALYSIS OF THE FAILURE USING ADVANCED MODELS

To overlook the progress made in computational techniques since 15 years, back-calculation runshave been performed with PLAXIS 7.1 windows version, using the following models:− Mohr-Coulomb,− Soft Soil,− Soft Soil with Creep.The undrained loading stages and subsequent consolidation are coupled in one single calculationrun simulating the complete history of the embankment.

The Mohr-Coulomb analysis has been performed to compare the results of the more sophisti-cated models with this classical one. It was expected that no noticeable improvements in predictionof excess pore pressures should be gained compared to the analysis of 1984 as the Mohr-Coulombmodel does not account for generation of excess pore pressure due to shearing. This run howeverallows comparing the effectivity and consequences of enhanced soil modelling.

The shear strength and other soil parameters where firstly taken equal to those of the calcula-tions of 1983. The modified compression and swelling index λ* and κ* needed in the Soft Soilmodel were estimated from the available test result of one-dimensional oedometer tests and ob-served settlements of embankments on similar soil. Similarly, the creep deformation parameter µ*


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required for the creep model was deduced from values of the secondary compression modulus Cs’and from empirical relations between µ*, λ* and κ*. The OCR has been taken equal to 1.0 as noreliable quantified information is available. Clearly more appropriate laboratory testing should bewelcome to obtain more accurate values. The values of these parameters as used for the calcula-tions are indicated in Table 2.

The load sequence, geometry, soil layering etc. were taken fully identical to those reported forthe calculations performed in 1984. The same mesh has been used for all three calculations.

5.1 Results of Mohr-Coulomb analyses

The results of the Mohr-Coulomb analyses are shown in Figures 7, 9 and 10. The conclusions putforward for the 1984 calculations are confirmed by the use of this simple model.

5.2 Results of analyses using the Soft Soil model

The initial stress state before starting of the heightening of the dike was established using theMohr-Coulomb soil model ; further loading stages were analysed using the Soft Soil model.In a first run all strength and permeability parameters were maintained unchanged compared withthose of the Mohr-Coulomb analysis. The calculations lead to collapse of the soil for the loadingstage of August-September 1983. It appears that:− The excess pore pressures for the load stages of 1982 were well back calculated.− The Soft Soil calculations over-predict strongly the excess pore pressures induced by the load-

ing stage of March-May 1983.− Very intense shearing, with full plastic strength mobilisation was observed in the calculation re-

sults up to a few meters beyond the toe of the bank ; besides the effect of shearing, also an im-portant effect of stress transfer explains the high values of excess pore pressures calculated atthis stage.

− The excess pore pressures calculated by the Soft Soil model at the collapse of August 1983 aremuch higher than those calculated using previous models.

− The fact that failure was calculated for the loading stage August 1983 results from both the ef-fects of much larger strength mobilisation in the previous load steps compared to those calcu-lated previously and the higher excess pore pressure remaining after consolidation from Marchto August 1983.

Table 2. Modified or complementary values of soil properties for Soft Soil calculations without and withcreep.

Soil typeλ*

-κ*

-µ*

-c’

kN/m2ϕ’°

Dike material NA NA NA 8 30

Tiel clay under (preloaded) 0.07 0.015 0.003 12 23

Tiel clay 0.14 0.030 0.004 6 25

Peat under (preloaded) 0.14 0.03 0.005 21 21

Peat 0.25 0.05 0.008 6 29

Gorkum clay 2 0.17 0.03 0.006 10 22

Gorkum clay 1 under (preloaded) 0.08 0.02 0.003 14 24

Gorkum clay 1 0.13 0.03 0.005 6 24


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Based on the observation that the dike did not collapse in August 1983, a second run has beenperformed using slightly increased values of the internal friction angle and the cohesion. Thismight appear as illogical, but following argument supports this way of doing :

The original values of the shear strength parameters were based on the common use of cell testsand on a cautious estimate of the shear resistance as measured in the CD tests on peat ( failure cri-terion was rather a strain criterion than a maximum observed shear resistance in the test). It is wellknown that these approaches lead to an underestimate of the shear parameters of 10 to 15 % com-pared to values obtained at failure from triaxial tests. In terms of classical approaches there was agood reason to choose somewhat low values of shear strength parameters : slip circle methods,taking further account of the fact that a sufficient value of the safety factors against sliding calcu-lated using the c’ and ϕ’ from cell test lead to a design for which the displacements of the dikewere usually observed as acceptable. This avoided that the shear stresses should reach such a levelthat the densification produces very high increase of excess pore pressures. Thus, the use of ratherconservative estimates of the shear strength parameters avoided stress levels close to the sensitivenear plastic failure levels.

The results of the second run using the Soft Soil model are shown on Figures 7, 9 and 10 indi-cating the calculated excess pore pressures and settlements compared to the measured ones and theESP at piezometer 2. A good agreement is found. Especially the Soft Soil model gives much betterback-calculated values of the pore pressures at the severe loading stage of August 1983 comparedto the previous calculations. For the loading stages up to May 1983, the Soft Soil model tends tooverestimate slightly the excess pore pressures at undrained loading. This might be explained bythe fact that the slight overconsolidation of the soil has been neglected. The displacements at failure(September 1984) are shown in Figure 8. Remark that the permeability coefficients of the soil weretaken equal to the values used for the calculations performed in 1984, except after day 370. For thearea in which vertical drainage was applied, the vertical permeability coefficient was taken tentimes higher than the « natural » value up to day 370 ; after that the permeability coefficient wastaken slightly higher than the natural value : it was indeed considered that the decrease of observedconsolidation rate was to be ascribed to a decrease of effectivity of the drains.

5.3 Result of calculations using Soft Soil with Creep

The same input parameters were used as in the second Soft Soil run ; the value of the creep pa-rameter (see Table 2) has been estimated using rather simple correlations and needs to be refinedby appropriate laboratory testing. The results of some calculations are given in Figures 7 to 10.

Figure 7. Calculated and measured vertical displacements at the toe of the existing dike.


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Figure 8. Total displacement field according to the Soft Soil calculations.

Figure 9. Calculated and measured excess pore pressures.


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Figure 10. Stress paths at piezometer 2.

The main conclusions from the calculations are summarised below.− The excess pore pressures generated by undrained loading are lower than those calculated using

Soft Soil model ; undrained shear has a less effect on the shape of the ESP than in the Soft Soilmodel : in fact, in the Soft Soil with Creep model the ESP at undrained loading is close to theESP at undrained loading using the Mohr-Coulomb model. This is in agreement with Vermeer& Neher (1998).

− The creep model shows increase of excess pore pressure over a period after undrained loading.The value of these excess pore pressure is very sensitive to the value of µ* and of the soil per-meability :

− A good fitting between measurements and calculations was obtained for the loading stages up to


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370 days by using low estimates of the creep factor and the same values of the permeability co-efficients as in previous Mohr-Coulomb and Soft Soil calculations.

− The lowered values of the soil permeability in the area with vertical drainage, introduced after370 days in the Mohr-Coulomb and Soft Soil calculations to match the measured consolidationlead to completely erroneous calculated behaviour in the Soft Soil with Creep model ; a betterfitting shown in Figure 9 was obtained by introducing permeability coefficients after 370 daysequal to 50 % of the initial value in that area.

The effective stress paths at the piezometer 2 are compared in Figure 10. One notices the differ-ences, especially at undrained loading (Soft Soil clearly exhibits shear strain induced excess porepressures, while both other models do not) and during consolidation (Mohr-Coulomb consolidatesclose to the failure line, while both other models consolidate at more or less constant shear stress).

6 CONCLUSIONS

The following main conclusions may be put forward on base of this second back-analysis of theStreefkerk failure problem:− The use of the software has become incredibly more easy and user-friendly in the last 15 years,

allowing to concentrate on modelling and geotechnical matter rather than on computational dif-ficulties.

− The results of the calculations using sophisticated soil models validate most of the assumptionsand conclusions of the work performed in 1984.

− The Soft Soil model appeared to give very reliable results, even in the near failure stages, afterhaving somewhat upgraded the shear strength parameters compared to the previous analyses.

− Best fit of the total soil stability is found for slightly higher values of the shear strength pa-rameters in the Soft Soil model compared to the Mohr-Coulomb or simplistically improvedMohr-Coulomb model. One should be aware that transferring values of soil parameters fromone model to the other might lead to gross errors : for each model, there is an appropriate choiceof strength parameters. Further development in this should be welcome for design practice.

− Design at stress levels rather far from failure (thus at rather high values of the safety factor) isnot too much sensitive to the model used ; design at stress levels very close to failure is verysensitive to the choice of the soil model and of appropriate values of the soil parameters.

− More investigation on the sensitivity and on the values of creep and permeability coefficients isneeded for the Soft Soil with Creep model, together with a closer analysis of the model behav-iour at undrained loading as it seems to underestimate somewhat the excess pore pressures.

− The use of advanced Soft Soil and Creep models needs for quantified evaluation of the overcon-solidation ratio.

ACKNOWLEDGEMENTS

The authors are grateful to Mr. Brinkgreve and Mr. Bonnier for their advice and help during thecalculations presented.

REFERENCES

Bauduin, C.M. & Molenkamp, F. 1991. Evaluation of failure of embankment during heightening. Geotech-nique 41(3) : 426-435.

Burland, J.B. 1971. A method of estimating pore pressures and displacements beneath embankments of softnatural clay deposits. Proc. Roscoe Memorial Symp., Cambridge. Cambridge : University Press.

Hoëg, K.H., Christian, J.T. & Whitman, R.V. 1968. Settlement of a strip load on elastic-plasic soil. J. SoilMech. Fdns. Div. Am. Soc. Civ. Engrs. 94(SM2) : 431-445.


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Tavenas, F. & Leroueil, S. 1977. Effects of stresses and time on yielding of clays. Proc. 9th Int. Conf. SoilMech., Tokyo, 1977.

Teunissen, J.A.M., Bauduin, C.M. & Calle, E.O.F. 1986. Analysis of failure of an embankment on soft soil :a case study. 2nd International Symposium on Numerical Models in Geomechanics, Ghent : Redruth :Jackson.

Vermeer, P.A. & Brinkgreve, R.B.J. (ed.) 1998. PLAXIS Finite Element Code for Soil and Rock AnalysesVersion 7. Rotterdam : Balkema.

Vermeer, P.A. & Neher, H. 1998. A soft soil model that accounts for creep. PAO course Stability of em-bankments on soft soils, Delft, 28-29 May 1998.

Vermeer, P.A., Vergeer C.J.H. & Termaat, R.J. 1985. Failure by large plastic deformations. Proc. XIth Int.Conf. On Soil Mech. And Found Eng., San Francisco, 12-16 Aug. 1985. Rotterdam : Balkema.

Back analysis of staged embankment failure: The … · Back analysis of staged embankment failure: ... the embankment was raised in a very short time to the crest level at 6.3 m above

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