Static and dynamic behaviour of soils: a rational approach to quantitative solutions. II. Semi-saturated problems

SUMMARYThis paper addresses various issues concerning the modelling of solid-liquid-air coupling in multiphase porous media with an application to unsaturated soils. General considerations based on thermodynamics permit the derivation and discussion of the general form of field equations; two cases are considered: a three phase porous material with solid, liquid and gas, and a two phase porous material with solid, liquid and empty space. Emphasis is placed on the presentation of differences in the formulation and on the role of the gas phase. The finite element method is used for the discrete approximation of the partial differential equations governing the problem. The two formulations are then analysed with respect to a documented drainage experiment carried out by the authors. The merits and shortcomings of the two approaches are shown.

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“…The Liakopoulos drainage experiment was simulated by various authors with different approaches [37][38][39]36] to check their numerical models.…”

Section: Comparison Between Experiments and Modellingmentioning

confidence: 99%

Solid–liquid–air coupling in multiphase porous media

Laloui¹,

Klubertanz²,

Vulliet³

2003

Num Anal Meth Geomechanics

113

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“…Finally, it is remarked that the region with negative excess water pressures, which occur and are shown in the numerical results of the present examples, is already partially saturated. With the passive air assumption [33,34], by which air pressure is assumed constant (or zero for convenience) at each point in the region of interest, the u −p formulations to govern the behaviour of saturated porous media can be simply extended to the partially saturated ones [33,34]. The Drucker-Prager model used for describing the elastoplastic constitutive behaviour of the solid skeleton at local integration point can also be simply extended to the unsaturated zone, but the cohesion parameter of the Drucker-Prager model also depends on the value of Figure 10.…”

Section: Numerical Examplesmentioning

confidence: 99%

Mixed finite element method for saturated poroelastoplastic media at large strains

Liu

Lewis

et al. 2003

Numerical Meth Engineering

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SUMMARYA mixed ÿnite element for hydro-dynamic analysis in saturated porous media in the frame of the Biot theory is proposed. Displacements, e ective stresses, strains for the solid phase and pressure, pressure gradients, and Darcy velocities for the uid phase are interpolated as independent variables. The weak form of the governing equations of coupled hydro-dynamic problems in saturated porous media within the element are given on the basis of the Hu-Washizu three-ÿeld variational principle. In light of the stabilized one point quadrature super-convergent element developed in solid continuum, the interpolation approximation modes for the primary unknowns and their spatial derivatives of the solid and the uid phases within the element are assumed independently. The proposed mixed ÿnite element formulation is derived. The non-linear version of the element formulation is further derived with particular consideration of pressure-dependent non-associated plasticity. The return mapping algorithm for the integration of the rate constitutive equation, the consistent elastoplastic tangent modulus matrix and the element tangent sti ness matrix are developed. For geometrical non-linearity, the co-rotational formulation approach is used. Numerical results demonstrate the capability and the performance of the proposed element in modelling progressive failure characterized by strain localization due to strain softening in poroelastoplastic media subjected to dynamic loading at large strain.

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“…This work eventually led to the development of various non-linear finite element procedures for the analysis of dynamic phenomena for saturated and partially saturated soil, including liquefaction and cyclic mobility. These were summarised in two papers in the Proceedings of the Royal Society in 1990 (Zienkiewicz et al, 1990a(Zienkiewicz et al, , 1990b. Such procedures had great success in the predictions at the VELACS project organised by the US National Science Foundation in 1993, establishing the fact that the use of effective stress is imperative in the analysis of such phenomena.…”

Section: Obituarymentioning

confidence: 99%

Olgierd Cecil Zienkiewicz 1921—2009

Chan¹

2010

Géotechnique

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Static and dynamic behaviour of soils: a rational approach to quantitative solutions. II. Semi-saturated problems

Cited by 148 publications

References 12 publications

Solid–liquid–air coupling in multiphase porous media

Solid–liquid–air coupling in multiphase porous media

Mixed finite element method for saturated poroelastoplastic media at large strains

Olgierd Cecil Zienkiewicz 1921—2009

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