Improving the Accuracy and Efficiency of Hydro-mechanical Coupled MPM in Modeling Small and Large Deformation Geomechanical Problems

Bodhinanda Chandra, Kenichi Soga

Keywords: Material Point Method, Fluid-Soil Interaction, Mining Engineering, Geotechnical Engineering

Abstract:

Understanding the hydro-mechanical interaction of porous flow and the deformation of a geomechanical medium has been a challenging topic and receive tremendous attention in computational mechanics research in the past decades. A clear understanding of this coupled phenomena is essential for designing many geotechnical infrastructures, as well as for many oil/gas and energy-related applications. Numerical methods to efficiently and accurately model the behavior of these complex systems, in both small and large deformation and within different dynamic regimes, are indeed in great economic and environmental demand.

In the current work, the Material Point Methods (MPM) is chosen as the numerical method to simulate the multiphase fluid-soil coupled problems. Even though the original formulation of the MPM, which assumes explicit dynamic time integration, has been proven to be successful in simulating many large-deformation problems, the method still suffers several drawbacks in efficiency accuracy. The semi-implicit version of MPM has been developed to circumvent these issues \cite{twophase}, which reduces pressure oscillations and increases the allowable time step size. Furthermore, several techniques to improve the accuracy of the results have been proposed, such as by re-evaluation of quadrature weight, usage of B-Spline basis functions, and appropriate treatments of nonconforming and nonhomogenous boundary conditions \cite{penalty}. On top of that, a parallelization scheme utilizing OpenMP and MPI has been introduced to improve computational efficiency. By incorporating these techniques to model two layers of materials, i.e. the immiscible solid skeleton and the fluid phase, the proposed method can produce significantly accurate and efficient results, yet easy implementation for advanced material models to tackle the problems of interest. Practical examples of this approach in mining engineering applications and geotechnical slope stability analysis have been studied to assess and quantify the results of the proposed methods.