Hybrid and enhanced finite element methods for problems of soil consolidation.

*(English)*Zbl 1194.74494Summary: Hybrid 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 nonlinear consolidation problems.

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74L10 | Soil and rock mechanics |

##### Keywords:

hybrid finite element; enhanced finite element; pore pressure oscillation; consolidation of soils
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\textit{X. X. Zhou} et al., Int. J. Numer. Methods Eng. 69, No. 2, 221--249 (2007; Zbl 1194.74494)

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