Geo-Interface Modeling in the Material Point Method

Abstract

Interface methods, particularly nonconforming interfaces, are an important aspect of modeling in the Material Point Method (MPM). The Material Point Method (MPM) is a numerical method developed for large-deformations, such as geotechnical runout analyses. MPM features moving material points (MPs) and a fixed computational grid which are not geometrically aligned. Material information is stored in the MPs, then mapped back and forth to the computational grid to solve the governing equations. The extra mapping steps, compared to FEM, make MPM relatively expensive. Certain boundary conditions can help reduce the extents of the model, thus reducing computational cost. However, application of boundary conditions or contact methods becomes challenging due to the misalignment of the material domain relative to the computational domain. Nonconforming interfaces address this challenge (rather than using mesh-conforming interfaces which require irregular mesh to capture complex geometry) allowing for regular mesh and, subsequently, decreasing MPM cell-crossing error.

An improved levelset-barrier method is proposed in MPM, considering specific applications to geotechnical engineering problems. The method includes novel contact conditions, a geotechnical MPM parameterization, and the addition of adhesional resistance given its importance in undrained analysis. The improved levelset-barrier method is validated using several benchmark cases, showing improvements in accuracy, precision, and convergence rate relative to the original method.

Two large-scale geotechnical case studies are covered: the Lower San Fernando Dam failure and the Oso Landslide. The former makes use of the virtual stress boundary condition, for nonconforming and adaptive reservoir pressure on the deforming embankment, and a conforming adhesive boundary condition for basal materials and the special interface with the reservoir bottom. The latter uses the improved levelset-barrier method to replace static background material, defined by LEM slip surfaces, for two stages of runout. Both case studies represent improvements relative to previous studies.

Realistic visualizations of geotechnical MPM results are created in the VFX software Houdini. Processes are presented for incorporating scientific results, including one-way coupling of visual features. Results include a visualization of the Lower San Fernando Dam with animated water, concrete features, and grass. The goal is to intuitively understand model context and aid in interpretation of the results. These enhanced visualizations are a valuable tool for scientific communication with adjacent fields and non-technical audiences.