2-D SPH modelling of poroelasticity: u-w-p and u-p formulations with absorbing boundary conditions and volumetric locking treatments

This paper presents a new simulation approach for modelling strongly-coupled processes in saturated porous media using the meshless method smoothed particle hydrodynamics (SPH). This paper proposes new SPH formulations for the  u-w-p and u-p versions of Biot’s model that address key challenges including accurate boundary conditions and numerical stability. Using corrected SPH gradient and Laplacian operators both absorbing and explicit treatment of free-surface conditions are achieved. The improved standard viscous boundary is then introduced into SPH as an absorbing boundary for problems involving dynamic loading. The volumetric locking issue is observed and a new countermeasure, named volumetric strain diffusion, is proposed, based on the well-established B-bar method and density diffusion technique. The proposed formulations are then systematically examined with six classical poroelastic problems spanning quasi-static and dynamic ranges. The simulated results agree with the reference solutions and display the desired order of convergence. The u-w-p and u-p models perform similarly under slow to moderate loading, but show distinct behaviour under highly dynamic loading. This observation matches existing understanding, thereby demonstrating the correctness of the proposed formulations. The introduced absorbing boundary condition and volumetric locking treatment also show promising results.