Enhanced finite element formulation for geometrically linear fluid-saturated porous media

SUMMARYIn this contribution an algorithm for parameter identi"cation of geometrically linear Terzaghi}Biot-type #uid-saturated porous media is proposed, in which non-uniform distributions of the state variables such as stresses, strains and #uid pore pressure are taken into account. To this end a least-squares functional consisting of experimental data and simulated data is minimized, whereby the latter are obtained with the "nite element method. This strategy allows parameter identi"cation based on in situ experiments. In order to improve the e$ciency of the minimization process, a gradient-based optimization algorithm is applied, and therefore the corresponding sensitivity analysis for the coupled two-phase problem is described in a systematic manner. For illustrative purpose, the performance of the algorithm is demonstrated for a slope stability problem, in which a quadratic Drucker}Prager plasticity model for the solid and a linear Darcy law for the #uid are combined.

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A finite element algorithm for parameter identification of material models for fluid saturated porous media

Mahnken

Steinmann

2001

Num Anal Meth Geomechanics

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Mixed finite element method for coupled thermo-hydro-mechanical process in poro-elasto-plastic media at large strains

Liu

Lewis

2005

Int. J. Numer. Meth. Engng

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SUMMARYA mixed finite element for coupled thermo-hydro-mechanical (THM) analysis in unsaturated porous media is proposed. Displacements, strains, the net stresses for the solid phase; pressures, pressure gradients, Darcy velocities for pore water and pore air phases; temperature, temperature gradients, the total heat flux are interpolated as independent variables. The weak form of the governing equations of coupled THM problems in porous media within the element is given on the basis of the Hu-Washizu three-filed variational principle. The proposed mixed finite element formulation is derived. The non-linear version of the element formulation is further derived with particular consideration of the THM constitutive model for unsaturated porous media based on the CAP model. The return mapping algorithm for the integration of the rate constitutive equation, the consistent elasto-plastic tangent modulus matrix and the element tangent stiffness matrix are developed. For geometrical non-linearity, the co-rotational formulation approach is utilized. Numerical results demonstrate the capability and the performance of the proposed element in modelling progressive failure characterized by strain localization and the softening behaviours caused by thermal and chemical effects.

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Hybrid and enhanced finite element methods for problems of soil consolidation

Zhou

Chow

Leung

2006

Numerical Meth Engineering

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SUMMARYHybrid and enhanced finite element methods with bi-linear interpolations for both the solid displacements and the pore fluid pressures are derived based on mixed variational principles for problems of elastic soil consolidation. Both plane strain and axisymmetric problems are studied. It is found that by choosing appropriate interpolation of enhanced strains in the enhanced method, and by choosing appropriate interpolations of strains, effective stresses and enhanced strains in the hybrid method, the oscillations of nodal pore pressures can be eliminated. Several numerical examples demonstrating the capability and performance of the enhanced and hybrid finite element methods are presented. It is also shown that for some situations, such as problems involving high Poisson's ratio and in other related problems where bending effects are evident, the performance of the enhanced and hybrid methods are superior to that of the conventional displacement-based method. The results from the hybrid method are better than those from the enhanced method for some situations, such as problems in which soil permeability is variable or discontinuous within elements. Since all the element parameters except the nodal displacements and nodal pore pressures are assumed in the element level and can be eliminated by static condensation, the implementations of the enhanced method and the hybrid method are basically the same as the conventional displacement-based finite element method. The present enhanced method and hybrid method can be easily extended to non-linear consolidation problems.

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Enhanced finite element formulation for geometrically linear fluid-saturated porous media

Cited by 12 publications

References 24 publications

A finite element algorithm for parameter identification of material models for fluid saturated porous media

A finite element algorithm for parameter identification of material models for fluid saturated porous media

Mixed finite element method for coupled thermo-hydro-mechanical process in poro-elasto-plastic media at large strains

Hybrid and enhanced finite element methods for problems of soil consolidation

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