Plane-Strain Modelling for Unsaturated Soil
The general analytical formulation for the plane-strain deformation regime of an elasto-plastic unsaturated soil is presented and then applied to two types of stress path: wetting at constant in-plane net stress state and in-plane loading at constant suct
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D. Gallipoli, M. Karstunen and S.J. Wheeler University of Glasgow, Glasgow, UK
ABSTRACT: The general analytical formulation for the plane-strain deformation regime of an elasto-plastic unsaturated soil is presented and then applied to two types of stress path: wetting at constant in-plane net stress state and in-plane loading at constant suction. Two different implementations of the plane-strain deformation regime are compared. The first one is correct whereas the second one assumes improperly that each single component of the total out-of-plane strain has to be null. This incorrect formulation is believed to be implemented in some finite element codes due to historical reasons. Modelling the soil behaviour by the constitutive model proposed by Alonso et al.(1990), substantially different load-displacement relationships are obtained with the two different formulations for the wetting paths. In the case of loading at constant suction the results from the two different formulations coincide in the elastic field and small discrepancies are observed when plastic deformations occur.
1 INTRODUCTION In geotechnical engineering design the assumption. of a plane-strain deformation mode is often made in order to simplify the analysis of three-dimensional problems. In many cases the geometry of the problem and the boundary conditions applied are sensibly constant along one dimension and, for this reason, a plane strain assumption is reasonable. It is
A. Cividini (ed.), Application of Numerical Methods to Geotechnical Problems © Springer-Verlag Wien 1998
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D. Gallipoli, M. Karstunen and S.J. Wheeler
therefore crucial to model correctly the plane-strain deformation in design tools, such as finite element codes, which are widely used by geotechnical engineers. This paper addresses the plane-strain implementation for an unsaturated soil with elastoplastic mechanical behaviour. It shows the consequences arising from an incorrect modelling for some typical stress paths involving elasto-plastic deformation. For each of these stress paths the load-displacement behaviour has been predicted using two different approaches in modelling the plane-strain deformation regime: one is correct while the other introduces some further unnecessary constraints on the deformation mode of the soil. It is thought that due to historical reasons this incorrect implementation is present in some codes. A complete load-displacement relationship has been achieved by modelling the stress paths by means of a finite element code, "Compass" (Thomas and He in press 1998), which is able to perform fully coupled flow-deformation analyses in unsaturated soil. This code has been developed by Prof HR Thomas and colleagues at the University of Wales, Cardiff. Although the constitutive model of Alonso et al. (1990) has been assumed, the modelling of the plane-strain deformation regime discussed in the next section has general relevance for any unsaturated soil with an elasto-plastic mechanical response.
2 PLANE-STRAIN FORMULATION FOR UNSATURATED SOIL The stre
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