This study presents a semi‐implicit MPM to adequately characterize the mechanical behavior of unsaturated soil based on Biot's mixture theory. To represent the dependency of the degree of saturation on the suction, we employ the VG model along with a soil‐water characteristic curve, which determines a functional form of permeability called the Mualem model. Hencky's hyperelastic model and the Drucker‐Prager model assuming nonassociativity are adopted for elastic and plastic deformations, respectively. The novelty of this study is the incorporation of the fractional‐step method into the MPM framework so that the pore water pressure is obtained by implicitly solving the pressure Poisson's equation, which reduces numerical instability and improves computational efficiency. Also, because the drag force between solid and liquid phases is evaluated using the intermediate velocity of pore water relative to the intermediate velocity of solid skeleton, the time increment can be chosen without considering the magnitude of water permeability. In addition, to suppress “odd‐even” oscillation, we employ a sub‐grid method in which two grids with different spatial resolutions are used for the velocities and pore water pressure. Furthermore, considering the advantages and disadvantages of two different interpolation schemes for pore water pressure, we suggest switching the schemes depending on the model conditions. Several numerical examples are presented to demonstrate the performance of the proposed method. Specifically, unidirectional consolidation and leak flow analyses are performed for verification purposes, followed by validation analysis of a model experiment of infiltration‐induced landslides.

中文翻译：

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模拟非饱和土结构入渗破坏的半隐式质点法

本研究提出了一种半隐式 MPM，以基于 Biot 混合理论充分表征非饱和土的力学行为。为了表示饱和度对吸力的依赖性，我们采用 VG 模型以及土水特征曲线，该曲线确定了称为 Mualem 模型的渗透率函数形式。弹性变形和塑性变形分别采用假设非关联性的 Hencky 超弹性模型和 Drucker-Prager 模型。本研究的新颖之处在于将分步法纳入MPM框架中，通过隐式求解压力泊松方程来获得孔隙水压力，从而降低了数值不稳定性并提高了计算效率。此外，由于固相和液相之间的阻力是使用孔隙水的中间速度相对于固体骨架的中间速度来评估的，因此可以在不考虑水渗透率大小的情况下选择时间增量。此外，为了抑制“奇偶”振荡，我们采用了子网格方法，其中两个具有不同空间分辨率的网格用于速度和孔隙水压力。此外，考虑到两种不同的孔隙水压力插值方案的优缺点，我们建议根据模型条件切换方案。给出了几个数值例子来证明所提出方法的性能。具体来说，进行单向固结和渗漏流分析以进行验证，然后对渗透引起的滑坡模型实验进行验证分析。