In many geomechanics applications, material boundaries are subjected to large displacements and deformation. Under these circumstances, the application of boundary conditions using particle methods, such as the material point method (MPM), becomes a challenging task since material boundaries do not coincide with the background mesh. This paper presents a formulation of penalty augmentation to impose nonhomogeneous, nonconforming Dirichlet boundary conditions in implicit MPM. The penalty augmentation is implemented utilizing boundary particles, which can move either according to or independently from the material deformation. Furthermore, releasing contact boundary condition, as well as the capability to accommodate slip boundaries, is introduced in the current work. The accuracy of the proposed method is assessed in both 2D and 3D cases, by convergence analysis reaching the analytical solution and by comparing the results of nonconforming and classical grid-conforming simulations.

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.

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