A semi-implicit two-phase double-point Material Point Method (MPM) formulation, based on the incremental fractional-step method to model large deformation geotechnical problems has been derived. The semi-implicit formulation has two advantages compared with the explicit approach: the time step is independent of the water phase, and the pore pressure field is more stable. The semi-implicit MPM models based on the incremental fractional-step method available in the literature consist of modelling the soil and water mixture using a single set of material points only, in order to save computational time. In this study, we further derive this formulation with two sets of material points to represent the soil and water phases separately. The stress oscillations that are frequently found in the water and soil phases are stabilised with this approach. A new stabilisation method is developed based on the modified F-bar method. The proposed method is validated with two numerical examples under small and large deformations, respectively. After that, Nor-Sand constitutive soil model is used to simulate landslides. Numerical examples show an excellent performance of the proposed coupled MPM and the stabilisation method. The formulation with two sets of material points yields significantly different but more reliable results in the landslides analysis, compared with the single-point approach. Additionally, this research shows that the additional computational cost caused by the additional water material points is acceptable. Therefore, it is recommended to use two sets of material points for certain large deformation geotechnical problems.

翻译：基于增量分步法的半隐式两相双点物质点法（MPM）公式被推导，用于模拟大变形岩土工程问题。与显式方法相比，半隐式公式具有两个优势：时间步长与水相无关，且孔隙压力场更稳定。现有文献中基于增量分步法的半隐式MPM模型仅使用单套物质点来模拟水土混合物，以节省计算时间。在本研究中，我们进一步推导了该公式，采用两套物质点分别表示土相和水相。该方法能够稳定水土相中常见应力振荡现象，并基于改进的F-bar方法提出了一种新的稳定化方法。通过两个小变形和大变形数值算例对所提方法进行了验证。随后，采用Nor-Sand本构土体模型模拟滑坡。数值算例表明，所提出的耦合MPM及其稳定化方法具有优异性能。与单点方法相比，采用两套物质点的公式在滑坡分析中产生了显著不同且更可靠的结果。此外，本研究表明，因增加水相物质点而产生的额外计算成本是可接受的。因此，针对某些大变形岩土工程问题，推荐使用两套物质点。