In this paper, a new formulation of material point method (MPM) to model coupled soil deformation and pore fluid flow problems is presented within the framework of the theory of porous media. The saturated porous medium is assumed to be consisting of incompressible pore fluid and deformable soil skeleton made up of incompressible solid grains. The main difference of the proposed MPM algorithm is the implicit treatment of pore-water pressure which satisfies its incompressibility internal constraint. The resulting solid-fluid coupled equations are solved by using a splitting algorithm based on the Chorin's projection method. The splitting algorithm helps to mitigate numerical instabilities at the incompressibility limit when equal-order interpolation functions are used. The key strengths of the proposed semi-implicit coupled MPM formulation is its capability to reduce pressure oscillations as well as to increase the time step size, which is independent of the fluid incremental strain level and the soil permeability. The proposed semi-implicit MPM is validated by comparing the numerical results with the analytical solutions of several numerical tests, including 1D and 2D plane-strain consolidation problems. To demonstrate the capability of the proposed method in simulating practical engineering problems involving large deformations, a hydraulic process leading to slope failure is studied, and the numerical result is validated by the monitored data.

中文翻译：

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一种基于分步法的饱和土半隐式材料点法

在本文中，在多孔介质理论的框架内，提出了一种新的材料点法 (MPM) 模型，用于模拟耦合土壤变形和孔隙流体流动问题。假设饱和多孔介质由不可压缩的孔隙流体和由不可压缩的固体颗粒组成的可变形土骨架组成。所提出的MPM算法的主要区别在于对满足其不可压缩性内约束的孔隙水压力进行了隐式处理。通过使用基于 Chorin 投影方法的分裂算法求解得到的固-流耦合方程。当使用等阶插值函数时，分裂算法有助于缓解不可压缩极限处的数值不稳定性。所提出的半隐式耦合 MPM 公式的关键优势在于它能够减少压力振荡以及增加时间步长，这与流体增量应变水平和土壤渗透率无关。通过将数值结果与包括一维和二维平面应变固结问题在内的几种数值试验的解析解进行比较，对所提出的半隐式 MPM 进行了验证。为了证明所提出的方法在模拟涉及大变形的实际工程问题中的能力，研究了导致边坡破坏的水力过程，并通过监测数据验证了数值结果。这与流体增量应变水平和土壤渗透率无关。通过将数值结果与包括一维和二维平面应变固结问题在内的几种数值试验的解析解进行比较，对所提出的半隐式 MPM 进行了验证。为了证明所提出的方法在模拟涉及大变形的实际工程问题中的能力，研究了导致边坡破坏的水力过程，并通过监测数据验证了数值结果。这与流体增量应变水平和土壤渗透率无关。通过将数值结果与包括一维和二维平面应变固结问题在内的几种数值试验的解析解进行比较，对所提出的半隐式 MPM 进行了验证。为了证明所提出的方法在模拟涉及大变形的实际工程问题中的能力，研究了导致边坡破坏的水力过程，并通过监测数据验证了数值结果。