Hybrid time integration and coupled solution methods for nonlinear finite element analysis of partially saturated deformable porous media at small strain

作者：Kim Jaehong; Wang Wei; Regueiro Richard A^*

来源：International Journal for Numerical and Analytical Methods in Geomechanics, 2015, 39(10): 1073-1103.

DOI：10.1002/nag.2350

• partially saturated nonlinear elasticity
• coupled pore fluid flow and solid skeleton deformation small strain finite element analysis
• fully implicit
• semi-implicit
• and explicit time integrations
• mixed quadrilateral finite elements
• monolithically coupled nonlinear solution method versus staggered-coupled nonlinear solution method

The goal of the paper is to determine the most efficient, yet accurate and stable, finite element nonlinear solution method for analysis of partially saturated deformable porous media at small strain. This involves a comparison between fully implicit, semi-implicit, and explicit time integration schemes, with monolithically coupled and staggered-coupled nonlinear solution methods and the hybrid combination thereof. The pore air pressure p(a) is assumed atmospheric, that is, p(a)=0 at reference pressure. The solid skeleton is assumed to be pressure-sensitive nonlinear isotropic elastic. Coupled partially saturated consolidation' in the presence of surface infiltration and traction is simulated for a simple one-dimensional uniaxial strain example and a more complicated plane strain slope example with gravity loading. Three mixed plane strain quadrilateral elements are considered: (i) Q4P4; (ii) stabilized Q4P4S; and (iii) Q9P4; Q refers to the number of solid skeleton displacement nodes, and P refers to the number of pore fluid pressure nodes. The verification of the implementation against an analytical solution for partially saturated pore water flow (no solid skeleton deformation) and comparison between the three time integration schemes (fully implicit, semi-implicit, and explicit) are presented. It is observed that one of the staggered-coupled semi-implicit schemes (SIS(b)), combined with the fully implicit monolithically coupled scheme to resolve sharp transients, is the most efficient computationally.

• 出版日期2015-7