A flux based approximation to simulate coupled hydromechanical problems for mines with heterogeneous rock types using the material point method

Advances in numerical simulation techniques play an important role in helping mining engineers understand those parts of the rock mass that cannot be readily observed. The Material Point Method (MPM) is an example of such a tool that is gaining popularity for studying geotechnical problems. In recent years, the original formulation of MPM has been extended to not only account for simulating the mechanical behaviour of rock under different loading conditions, but also to describe the coupled interaction of pore water and solid phases in materials. These methods assume that the permeability of mediums is homogeneous, and we show that these MPM techniques fail to accurately capture the correct behaviour of the fluid phase if the permeability of the material is heterogeneous. In this work, we propose a novel implementation of the coupled MPM to address this problem. We employ an approach commonly used in coupled Finite Volume Methods, known as the Two Point Flux Approximation (TPFA). Our new method is benchmarked against two well-known analytical expressions (a one-dimensional geostatic consolidation and the so-called Mandel-Cryer effect). Its performance is compared to existing coupled MPM approaches for homogeneous materials. In order to gauge the possible effectiveness of our technique in the field, we apply our method to a case study relating to a mine known to experience severe problems with pore water.