A generalized Hellinger-Reissner variational principle and its PFEM formulation for dynamic analysis of saturated porous media

In this paper, a novel mathematical programming formulation is derived based on the u-p form for the dynamic analysis of saturated porous media. A mixed finite element is used for the interpolation of field variables and after discretization the formulation is remolded into a standard second-order cone programming problem that can be resolved using modern optimization engines. The proposed optimization-based computational scheme is verified against typical benchmarks such as the dynamic consolidation problem and the wave propagation in saturated soils. To tackle issues such as mesh distortions and severe free-surface evolutions resulting from large deformations, the scheme is further implemented into the PFEM framework. The capability of the proposed method for analyzing porous media with large deformations is illustrated by modelling the collapse of a saturated granular column in air and the post-failure process of an embankment due to seepage with results compared to the ones from lab tests and numerical simulations using other approaches such as the material point method and the smoothed particle hydrodynamics method.

Automated summary

A novel mathematical programming formulation is developed for the dynamic analysis of saturated porous media, which can be solved using modern optimization engines. The proposed computational scheme is verified against typical benchmarks and further implemented into the PFEM framework to address issues caused by large deformations. Several case studies illustrate the capability of the method for analyzing porous media with large deformations.