Back analysis of staged embankment failure: The case study Streefkerk

Back analysis of staged embankment failure: The case study Streefkerk C.M. Bauduin Besix, Brussels, Belgium M. De Vos Belgian Building Research Institute, Brussels, Belgium P.A. Vermeer Institut 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 settlements and the pore pressures measured during construction, focussing especially on the effects of shear stress and plastic yielding. Back-calculations have been performed using two uncoupled FEM codes in sequence : one to estimate initial stresses and the total stress increments at the undrained loading phases and another to simulate the intermittent consolidation. A simplified cap model has been introduced for undrained loading. The present paper presents the results of back-calculations using the Soft Soil and the Soft Soil with Creep models. Comparing them with those of the first back-calculations allow to overlook the progress made in soil modelling, to indicate the remaining vital 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 Dike near Streefkerk in the central west part of the Netherlands. As the foundation for the riverbanks consist often of extremely weak clay and peat alluvial deposits, the heightening works are performed in stages allowing for in between consolidation. Usually, excess pore pressures generated by loading and their decay due to consolidation are observed during construction using piezometers. Following the instability, design type analyses, based on Bishop s slip circle method and using the monitored pore pressures were performed. However, they were not able to provide satisfactory explanations to the occurrence of the accident. Furthermore, the prediction of excess pore pressures generated during the previous loading sequences, using elastic soil models were shown to be in great error. An extensive research program has therefor been set up in the months following the accident, to investigate the causes that have lead to failure. The method and the results of this research have been 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 excess pore pressure generation and dissipation were well measured during the whole construction period until failure, the accident may be used as a benchmark problem for the verification of the development of soil models and finite element calculation techniques for embankments on soft soil during the last 15 years. 1

2 CROSS SECTION AND SEQUENCE OF EVENTS The cross section of the original flood bank and the additional layers are shown in Figure 1. Vertical drainage (Colbond KF 350 triangular pattern d = 3.0 m) is used under the bank of the heightened dike to accelerate consolidation in this area. The loading history is indicated in Figure 2. The location 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 from ground level at 1 m below MSL up to 2.3 m above MSL and was then left to consolidate from October 1982 to March 1983. The bank was than further raised in three stages to 4.5 m above MSL that was reached in may 1983. Consolidation was then allowed until end of August 1983 ; at this period, the embankment was raised in a very short time to the crest level at 6.3 m above MSL and the bank and whole inner slope were covered by a 0.7 m thick clay layer. It was then left to consolidate during one year until September 1984. In September and October 1984, the embankment was completed : basaltstone was lead for the outer slope protection and the temporary road on the crest was replaced by the permanent one. Not so much load was added during these works. However, soon after that, when the ditch at the bank bank was enlarged, the landside slope of the bank began to fail over a length of about 80 m. The observed cracks and soil movements indicated horizontal 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 of soil properties as selected for the calculations in 1984. The values are mean values from a regional databank, except that for the peat layer for which the additional information from local CD compression and extension triaxial tests at low confining stresses is implemented. Remark that the friction 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. 2

Table 1. Soil parameters. Soil type Level m-msl γ kn/m³ w % w l % w p % c kn/m² ϕ E kn/m² ν - k v m/day C p - C s - 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) Peat -9.6/-2.7 11 400 250 45 18 18 420 0.20 1.7E-3 11 55-9.6/-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 1 under (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 Figure 3. Measured excess pore pressures. Figure 4. Measured settlements. are deduced from oedometer tests, complemented by pocket pressuremeter tests and by the triaxial tests for the peat layers. It is worthwhile to notice the distinction made between the preloaded soil in the area under the existing old dike and the soil outside its influence area. The soil is considered to be normally consolidated. No reliable information on this is however available, so all calculations will be performed considering OCR equal to 1. The hydraulic heads of the excess pore pressures as measured by the piezometers are shown as function of time on Figure 3. The measured settlements are illustrated on Figure 4. 3

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 deformation 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 becomes close to the increment of major principal stress once the local undrained shear resistance is 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 and deviatoric irreversible strains, it can be also a contributing factor. Due to the lack of simple and reliable 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 q was 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 u α ), Path AF 1 : TSP up to local state of failure; u β1 is the corresponding increase of isotropic stress, Path F 1 F 2 : 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 principal stress, leading to an equal increase of excess pore pressure u β2. As a consequence of this formulation, the undrained shear strength can be estimated by (Vermeer et al. 1985) ' cu = c cos ( ϕ ) + p F sin ( ϕ ) (1) in which c and ϕ are the effective shear resistance parameters and p F is the effective isotropic stress at undrained failure according to the undrained effective stress path through the current effective stress state. For the calculations in 1984, it was tentatively assumed that the yield surface is a straight line sloping at -45 from the K o line until the failure line in the p-q plane ; below the K o line the behaviour was assumed to be elastic. This simple model was based on the concepts of the YLIGHT model (Tavenas & Leroueil 1977) and on observation of the results of a few CU triaxial tests on Dutch organic clays and peat available at that moment. Remark that the described tentative model focuses only on the prediction of increase of excess pore pressure as a consequence of the increase Figure 5. Stress paths at undrained loading. 4

of the shear stress, but the volumetric strains, which are the «motor» of the excess pore pressures due to shearing, are not calculated. To increase the insight into the effects of the plastic spreading of additional loads, it was attempted to back-analyse the behaviour of the embankment using two uncoupled FE codes in combination 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 developed under the existing riverbank ; the behaviour at the toe of the embankment remained below 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 loading stages until may 1983. Back calculated values of the excess pore pressure provoked by the severe 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 to plastic flow and the very important improvement of the constitutive model compared to the ones applied for design, it was considered that the applied constitutive model was still too rough to lead to an accurate simulation of «a near failure state» of the soil mass. Also the fact that creep has not been simulated may have contributed to the deficiency. Further on, the limitations due to the use of uncoupled codes were pointed out. 4 DEVELOPMENTS OF SOIL MODELLING Since the calculations of 1984 and the present date, enormous progress in the development and implementation of advanced constitutive models in finite elements codes have taken place, allowing for coupled analyses of the undrained loading and consolidation of soil with appropriate realistic constitutive models. For loading of soft, normally or near normally consolidated soils, PLAXIS provides following 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 the modified Cam-Clay model, including a yield function but without softening behaviour. The yield function models the irreversible volumetric straining in primary compression and is used as the cap of 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 (see Fig. 6), thus define the total yield contour. Figure 6. Yield contour of the Soft Soil model. 5

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 strain increments and corresponding excess pore pressures. Compared to the previous tentative model for the prediction of excess pore pressures, the Soft Soil model proposes a proper formulation of the changes in volumetric strains. The logarithmic compression law is described by the modified compression and swelling index λ* and κ*. The shear resistance at failure for undrained loading is again given at the intersection of the effective stress path with the failure line and is thus deduced from the effective strength parameters c and ϕ and the effective isotropic stress at undrained failure according to the undrained effective stress path through the current effective stress state, which is usually located on the (expanding) cap for uniform loading problems at OCR equal to 1, such as those treated in this paper. The Soft Soil with Creep model is basically similar to the Soft Soil model, but includes the effects of volumetric strains due to creep. It introduces time dependency of the plastic range in a Soft Soil model, having thus an ellipsoidal plastic potential and a Mohr-Coulomb type failure surface at the dry side of critical state. The time dependent creep plastic strains are described by the modified creep index µ*. The following rough estimates and interrelations for λ*, κ* and µ* might be used : 1 λ = ' C p (2) κ 1 ν 1+ ν 1 µ ' C s ur ur 3 C p (3) (4) and: λ µ λ = 10 à 15 = 5 à 10 κ (5,6) 5 BACK ANALYSIS OF THE FAILURE USING ADVANCED MODELS To overlook the progress made in computational techniques since 15 years, back-calculation runs have 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 calculation run simulating the complete history of the embankment. The Mohr-Coulomb analysis has been performed to compare the results of the more sophisticated models with this classical one. It was expected that no noticeable improvements in prediction of excess pore pressures should be gained compared to the analysis of 1984 as the Mohr-Coulomb model does not account for generation of excess pore pressure due to shearing. This run however allows comparing the effectivity and consequences of enhanced soil modelling. The shear strength and other soil parameters where firstly taken equal to those of the calculations of 1983. The modified compression and swelling index λ* and κ* needed in the Soft Soil model were estimated from the available test result of one-dimensional oedometer tests and observed settlements of embankments on similar soil. Similarly, the creep deformation parameter µ* 6

required for the creep model was deduced from values of the secondary compression modulus C s and from empirical relations between µ*, λ* and κ*. The OCR has been taken equal to 1.0 as no reliable quantified information is available. Clearly more appropriate laboratory testing should be welcome to obtain more accurate values. The values of these parameters as used for the calculations are indicated in Table 2. The load sequence, geometry, soil layering etc. were taken fully identical to those reported for the 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 put forward 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 the Mohr-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 with those of the Mohr-Coulomb analysis. The calculations lead to collapse of the soil for the loading stage 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 loading stage of March-May 1983. Very intense shearing, with full plastic strength mobilisation was observed in the calculation results up to a few meters beyond the toe of the bank ; besides the effect of shearing, also an important effect of stress transfer explains the high values of excess pore pressures calculated at this stage. The excess pore pressures calculated by the Soft Soil model at the collapse of August 1983 are much higher than those calculated using previous models. The fact that failure was calculated for the loading stage August 1983 results from both the effects of much larger strength mobilisation in the previous load steps compared to those calculated previously and the higher excess pore pressure remaining after consolidation from March to August 1983. Table 2. Modified or complementary values of soil properties for Soft Soil calculations without and with creep. Soil type λ* - κ* - µ* - c kn/m 2 ϕ 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 7

Based on the observation that the dike did not collapse in August 1983, a second run has been performed using slightly increased values of the internal friction angle and the cohesion. This might 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 tests and on a cautious estimate of the shear resistance as measured in the CD tests on peat ( failure criterion was rather a strain criterion than a maximum observed shear resistance in the test). It is well known that these approaches lead to an underestimate of the shear parameters of 10 to 15 % compared to values obtained at failure from triaxial tests. In terms of classical approaches there was a good 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 calculated using the c and ϕ from cell test lead to a design for which the displacements of the dike were usually observed as acceptable. This avoided that the shear stresses should reach such a level that the densification produces very high increase of excess pore pressures. Thus, the use of rather conservative estimates of the shear strength parameters avoided stress levels close to the sensitive near plastic failure levels. The results of the second run using the Soft Soil model are shown on Figures 7, 9 and 10 indicating the calculated excess pore pressures and settlements compared to the measured ones and the ESP at piezometer 2. A good agreement is found. Especially the Soft Soil model gives much better back-calculated values of the pore pressures at the severe loading stage of August 1983 compared to the previous calculations. For the loading stages up to May 1983, the Soft Soil model tends to overestimate slightly the excess pore pressures at undrained loading. This might be explained by the 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 were taken equal to the values used for the calculations performed in 1984, except after day 370. For the area in which vertical drainage was applied, the vertical permeability coefficient was taken ten times higher than the «natural» value up to day 370 ; after that the permeability coefficient was taken slightly higher than the natural value : it was indeed considered that the decrease of observed consolidation 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 parameter (see Table 2) has been estimated using rather simple correlations and needs to be refined by 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. 8

Figure 8. Total displacement field according to the Soft Soil calculations. Figure 9. Calculated and measured excess pore pressures. 9

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 Soil model : in fact, in the Soft Soil with Creep model the ESP at undrained loading is close to the ESP 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 permeability : A good fitting between measurements and calculations was obtained for the loading stages up to 10

370 days by using low estimates of the creep factor and the same values of the permeability coefficients as in previous Mohr-Coulomb and Soft Soil calculations. The lowered values of the soil permeability in the area with vertical drainage, introduced after 370 days in the Mohr-Coulomb and Soft Soil calculations to match the measured consolidation lead to completely erroneous calculated behaviour in the Soft Soil with Creep model ; a better fitting shown in Figure 9 was obtained by introducing permeability coefficients after 370 days equal 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 differences, especially at undrained loading (Soft Soil clearly exhibits shear strain induced excess pore pressures, while both other models do not) and during consolidation (Mohr-Coulomb consolidates close 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 the Streefkerk 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 difficulties. The results of the calculations using sophisticated soil models validate most of the assumptions and conclusions of the work performed in 1984. The Soft Soil model appeared to give very reliable results, even in the near failure stages, after having 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 parameters in the Soft Soil model compared to the Mohr-Coulomb or simplistically improved Mohr-Coulomb model. One should be aware that transferring values of soil parameters from one model to the other might lead to gross errors : for each model, there is an appropriate choice of 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) is not too much sensitive to the model used ; design at stress levels very close to failure is very sensitive 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 is needed for the Soft Soil with Creep model, together with a closer analysis of the model behaviour 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 overconsolidation ratio. ACKNOWLEDGEMENTS The authors are grateful to Mr. Brinkgreve and Mr. Bonnier for their advice and help during the calculations presented. REFERENCES Bauduin, C.M. & Molenkamp, F. 1991. Evaluation of failure of embankment during heightening. Geotechnique 41(3) : 426-435. Burland, J.B. 1971. A method of estimating pore pressures and displacements beneath embankments of soft natural 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. Soil Mech. Fdns. Div. Am. Soc. Civ. Engrs. 94(SM2) : 431-445. 11

Tavenas, F. & Leroueil, S. 1977. Effects of stresses and time on yielding of clays. Proc. 9 th Int. Conf. Soil Mech., 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. 2 nd 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 Analyses Version 7. Rotterdam : Balkema. Vermeer, P.A. & Neher, H. 1998. A soft soil model that accounts for creep. PAO course Stability of embankments 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. 12