Hardening Soil Model Research Articles

Input parameters of Transdanubian Clay for the Hardening Soil and Soft Soil models

In recent years, finite element modeling has become an important design tool. Advanced programs make it possible to use more complex soil models in addition to standard elasto-plastic models with Mohr-Coulomb failure criteria. These new models can follow nonlinear behavior and complicated loading sequences. The two most promising new models are: the Hardening Soil Model (HS) and the Soft Soil Model (SS).This paper focuses on the behavior of Transdanubian Clay, common in Hungary. Sampling, laboratory testing, and evaluation of data aiming at determining parameters for HS and SS models are described. Results based on oedometer tests using unloading/reloading sequences proved to be adequate for input to these models.

Validation of models and empirical equations to estimate deformations in jointed rock through the monitoring of a 40-storey tower foundation

There is a pressing need in Rock Mechanics for the calculation of deformations and stresses of structures in rock. With this aim, the rock mass modulus must be estimated and a model chosen to perform the calculations. Monitoring the foundation of twin towers in Tenerife Island has allowed validating both the rock mass modulus estimated from empirical equations and the model. In this paper, only the second tower (tower N) with a structural height of 137.4 m above foundation has been studied, because the first tower had been previously presented by Justo et al. [Int J Rock Mech Min Sci 2006;43;267–81]. The foundations of both towers are supported by jointed, vesicular and weathered basalt, and scoria. The parameters have been deduced from the simple empirical equations proposed by several authors as a function of geological strength index (GSI) or rock mass rating (RMR). Three-dimensional, elastic and advanced elasto-plastic finite element (FE) programs have permitted calculation of the displacements of tower N, the stresses in the slab and the factor of safety (FOS) of the excavation. The installation of rod extensometers at different depths below the slab has permitted comparison between measured and calculated displacements. Good fit has been obtained in this type of rock. These results increase our confidence in the use of classification schemes to estimate the deformations in jointed rock. In construction processes that involve unloading–reloading, it is important to use a material model that considers these processes. The use of advanced elasto-plastic methods increases the calculated settlements even if there are no failure points, as the pre-consolidation stress and the mobilized angle reached during the excavation phase are exceeded at many points during the loading phase. Tension cut-off points also increase deformations with respect to linear-elastic behaviour. The hardening-soil model improves fit between measured and calculated settlements as well.

Capturing strain localization in reinforced soils

Lade’s single hardening soil model with Cosserat rotation embodied in the finite element method is employed to investigate the behavior of geosynthetic reinforced soils with special attention to the development of shear banding. The ability of the finite element model to detect shear banding in a reinforced soil is examined against three high quality small-scale laboratory plane strain tests on Toyoura sand with and without reinforcement. These three tests were chosen because of the clear failure surfaces that developed in the soil during loading. The FEM analyses were able to reasonably simulate the plane strain laboratory tests including both unreinforced and reinforced cases. The FEM analyses gave reasonably good agreement with the experimental results in terms of global stress–strain relationships and shear band occurrences. Furthermore, and based on FE analyses of a hypothetical geosynthetic reinforced soil (GRS) retaining wall, it is shown that the geosynthetic reinforcements are very effective in hindering the formation of shear bands in GRS retaining walls when small spacing between the reinforcement layers was used. When used properly, the geosynthetic reinforcements made the soil behave as a truly reinforced mass of considerable stiffness and strength.

Impact of constitutive models on the numerical analysis of underground constructions

The constitutive model frequently used in numerical calculations of tunnel excavation is linear-elastic perfectly plastic with a Mohr–Coulomb (MC) failure criterion. Generally, this leads to shallower and wider surface settlement troughs than those observed experimentally. It is therefore necessary to use adapted constitutive models for the design of underground works. In this paper, three constitutive models are implemented in a two-dimensional simulation of an underground excavation in plane strain: a linear-elastic perfectly plastic model (the MC model), an elastoplastic model with isotropic hardening [the hardening soil (HS) model, Schanz et al., Beyond 2000 in computational geotechnics, Balkema, Rotterdam, pp. 281–290, 1999] and an extension of this model which implies an evolution of the stiffness modulus in the small-strain range according to the strain level (the HS model with small-strain stiffness “HS-Small”, Benz, Small-strain stiffness of soils and its numerical consequences. Ph.D. thesis, Universitat Stuttgart, 189 pp., 2007). The study is based on the results of drained triaxial compression tests representing an overconsolidated clay (Gasparre, Advanced laboratory characterisation of London clay. Ph.D. thesis, Imperial College London, 598 pp., 2005); and is then applied to a shallow tunnel. The impact of the constitutive model is highlighted as well as the limits of the simplest constitutive model.

Numerical studies of ring foundations on geogrid-reinforced sand

Numerical predictions of the ultimate bearing capacity of ring foundations supported by a sand bed with and without geogrid reinforcement are presented. Numerical analyses of the test models were carried out using the finite element package Plaxis. It is shown that the behaviour of ring foundations on sand beds may be reasonably well represented by the hardening soil model available in the Plaxis package. The hardening soil model parameters were derived from the results of drained triaxial tests. The parameters investigated are the effect of depth of first reinforcement layer, the number of reinforcement layers and reinforcement layer size on the ultimate bearing capacity of ring foundations. The results from the finite element analysis are in very good agreement with the experimental observations. The results of this study showed that the reinforcement had a considerable effect on the ultimate bearing capacity of the ring foundations. It was also shown that ultimate bearing capacity values can, depending on the reinforcement geogrid arrangement, be improved by up to three times that of the unreinforced case for the model arrangements investigated.

Uplift response of strip anchors in cohesionless soil

Physical and computational studies investigating the uplift response of 1 m wide strip anchors in sand show that maximum resistances increase with anchor embedment ratio and sand packing. Agreement between uplift capacities from centrifuge and finite element modelling using PLAXIS, based on 0.2 m computed maximum displacements, is excellent for anchors up to embedment ratios of 6. Some divergence occurs for deeper anchors. Pre-peak response is reasonably well reproduced using the Hardening Soil Model available in PLAXIS, although the characteristic post-peak softening in some physical model tests requires a more sophisticated soil model. PLAXIS also produces breakout factors which compare reasonably well with established limit state and finite element based theories.

Settlement behaviour of a concrete faced rock-fill dam

Settlement behaviour of a concrete faced rock-fill dam (CFRD), Kurtun dam, located in the East Black Sea Region, Turkey, is investigated. This is the first instrumented CRDF in the Country. Two dimensional plane strain finite element analyses were carried out to assess the total stresses and displacements in the dam both for construction and reservoir filling stages by using computer program PLAXIS. Predicted stresses and settlements are compared with those observed and overall the results are found to be in good agreement for the construction stage. Due to the relatively steep abutment slopes, cross-valley arching has a significant effect on stresses and displacements in the dam body. For the reservoir filling condition, it is seen that, predicted settlements are larger than the observed values, which indicates that during reservoir filling the rock-fill embankment responds more stiffly than it does during the construction stage. The hardening soil model is used to represent the non-linear, inelastic and stress dependent behaviour of rock-fill material. The model parameters are selected from the appropriate values in the literature investigating comparable cases.

Behavior of strip footing on geogrid-reinforced sand over a soft clay slope

The potential benefits of reinforcing a replaced layer of sand constructed on near a slope crest was studied. Model tests were carried out using model footing of 75 mm width and geogrids. Several parameters including the depth of replaced sand layer and the location of footing relative to the slope crest were studied. Particular emphasis is paid on the reinforcement configurations including number of layers, spacing, layer length and depth to ground surface. A series of finite element analyses were performed on a prototype slope using two-dimensional plane strain model using the computer code Plaxis. The soil was represented by non-linear hardening soil model, which is an elasto-plastic hyperbolic stress–strain model while reinforcement was represented by elastic elements. A close agreement between the experimental and numerical results is observed. Test results indicate that the inclusion of geogrid layers in the replaced sand not only significantly improves the footing performance but also leads to great reduction in the depth of reinforced sand layer required to achieve the allowable settlement. However, the efficiency of the sand–geogrid system increases with increasing number of geogrid layers and layer length. Based on the theoretical and experimental results, critical values of the geogrid parameters for maximum reinforcing effects are established.

Selecting parameters to optimize in model calibration by inverse analysis

A study evaluating the benefits of using inverse analysis techniques to select the appropriate parameters to optimize when calibrating a soil constitutive model is presented. The factors that affect proper calibration are discussed with reference to the optimization of the elasto-plastic Hardening-Soil model for four layers of Chicago glacial clays. The models are initially calibrated using results from triaxial compression tests performed on specimens from four clay layers and subsequently re-calibrated using inclinometer data that recorded the displacements of a supported excavation in these clays. Finite element simulations of both the triaxial tests and the supported excavation are performed. A parameter optimization algorithm is used to fit the computed results and observed data, expressed in the form of stress–strain curves and inclinometer readings, respectively. A procedure is presented which uses the results of sensitivity analyses conducted on the soil model parameters for the identification of the relevant and uncorrelated parameters to calibrate. In both cases the inverse analysis methodology effectively calibrates the soil parameters considered, which numerically converge to realistic values that minimize the errors between computed responses and experimental observations.

Arching effects behind a soldier pile wall

A wall consisting of anchored steel piles with horizontal timber laggings was selected to support a 16 m deep excavation with a length of more than three kilometres near Cologne in Germany. Vertical holes were bored on the wall line, at 4 m centres, and steel piles were placed within these holes. Good contact between the piles and the surrounding soil was ensured by concreting the remaining space in the holes. In this way the earth pressure behind the wall was transferred to the piles through horizontal arching, so relieving the timber laggings. As a result, lighter timber laggings could be used and the economy of the wall construction could be increased. In situ tests as well as non-linear 3D finite element (FE) analyses were carried out. Horizontal arching was promoted by means of flexible horizontal lagging timbers and solid contact between the piles and the surrounding soil. Vertical arching was induced by high pre-stress forces in the upper ground anchors. FE analyses were based on both the elasto-plastic Mohr–Coulomb model and a more advanced hardening-soil model.