An h-adaptive edge-based smoothed point interpolation method for elasto-plastic analysis of saturated porous media

This study presents the first application of the edge-based smoothed point interpolation method (ESPIM) for adaptive analysis of coupled elasto-plastic problems in saturated porous media. The original ESPIM is enhanced with an adaptive strategy involving an automated h-refinement scheme, a simple, yet effective, recovery-based error indicator, and an efficient data transfer scheme to analyse coupled elasto-plastic problems in geomechanics. The governing equations are presented and discretised in space and time to yield the fully coupled system of equations. The solution strategy is then discussed in terms of handling the material non-linearity, and accommodating the proposed adaptivity procedure in the numerical algorithm. Four numerical examples comprising two different bearing capacity problems, a two-dimensional consolidation problem, and a slope stability analysis are thoroughly investigated. Different adaptive analyses with a range of adaptivity control parameters are investigated in each example and the performances of different techniques are compared in terms of accuracy and the time of the analysis. The results show the ability of the proposed adaptive analyses in yielding accurate and efficient results. Conclusions are drawn in terms of the most efficient numerical set-up to solve non-linear problems in porous media using the proposed numerical scheme.