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.

本文基于u -p推导了一种新颖的数学规划公式动态分析饱和多孔介质的形式。混合有限元用于场变量的插值，离散化后，将公式重塑为标准的二阶锥规划问题，可以使用现代优化引擎解决该问题。所提出的基于优化的计算方案已通过典型基准进行了验证，例如动态固结问题和饱和土中的波传播。为了解决诸如网格变形和由大变形引起的严重自由表面演变之类的问题，该方案被进一步实施到PFEM框架中。