This paper presents a single-point Material Point Method (MPM) for large deformation problems in two-phase porous media such as soils. Many MPM formulations are known to produce numerical oscillations and inaccuracies in the simulated results, largely due to numerical integration and stress recovery performed at non-ideal locations, cell crossing errors, and mass moving from one background grid cell to another. The same drawbacks lead to even worse consequences in the presence of an interstitial fluid phase, especially when undrained/incompressible conditions are approached. In this study, an explicit stabilised MPM, based on the Generalised Interpolation Material Point (GIMP) method with Selective Reduced Integration (SRI), is proposed to mitigate typical numerical oscillations in (nearly) incompressible coupled problems. It includes two additional features to improve stress and pore pressure recovery, namely (i) patch recovery of pore pressure increments based on a Moving Least Squares Approximation, and (ii) two-phase extension of the Composite Material Point Method for effective stress recovery. The combination of components leads to a new method named GC-SRI-patch. After a detailed description of the approach, its effectiveness is verified through analysing various consolidation problems, with emphasis on the representation of pore pressures in time and space.

本文提出了一种针对两相多孔介质（如土壤）中大变形问题的单点材料点法（MPM）。众所周知，许多MPM公式会在模拟结果中产生数值振荡和不准确性，这在很大程度上是由于在非理想位置执行的数值积分和应力恢复，单元交叉误差以及质量从一个背景网格单元移动到另一个背景网格单元所致。相同的缺点在存在组织液相的情况下甚至导致更糟的后果，尤其是在接近不排水/不可压缩的条件时。在这项研究中，提出了一种基于具有选择性减少积分（SRI）的广义插值材料点（GIMP）方法的显式稳定MPM，以减轻（几乎）不可压缩耦合问题中的典型数值振动。它包括两个额外的功能来改善应力和孔隙压力的恢复，即（i）基于移动最小二乘近似的孔隙压力增量的补丁恢复，以及（ii）复合材料点方法的两阶段扩展，以实现有效的应力恢复。组件的组合导致了一种名为GC-SRI-patch的新方法。在对该方法进行了详细描述之后，通过分析各种固结问题，重点是在时间和空间上表示孔隙压力，从而验证了该方法的有效性。组件的组合导致了一种名为GC-SRI-patch的新方法。在对该方法进行了详细描述之后，通过分析各种固结问题，重点是在时间和空间上表示孔隙压力，从而验证了其有效性。组件的组合导致了一种名为GC-SRI-patch的新方法。在对该方法进行了详细描述之后，通过分析各种固结问题，重点是在时间和空间上表示孔隙压力，从而验证了其有效性。