Superposition-based concurrent multiscale approaches for porodynamics

Abstract

The current study presents superposition-based concurrent multiscale approaches for porodynamics, capable of capturing related physical phenomena, such as soil liquefaction and dynamic hydraulic fracture branching, across different spatial length scales. Two scenarios are considered: superposition of finite element discretizations with varying mesh densities, and superposition of peridynamics (PD) and finite element method (FEM) to handle discontinuities like strain localization and cracks. The approach decomposes the acceleration and the rate of change in pore water pressure into subdomain solutions approximated by different models, allowing high-fidelity models to be used locally in regions of interest, such as crack tips or shear bands, without neglecting the far-field influence represented by low-fidelity models. The coupled stiffness, mass, compressibility, permeability, and damping matrices were derived based on the superposition-based current multiscale framework. The proposed FEM-FEM porodynamic coupling approach was validated against analytical or numerical solutions for one- and two-dimensional dynamic consolidation problems. The PD-FEM porodynamic coupling model was applied to scenarios like soil liquefaction-induced shear strain accumulation near a low-permeability interlayer in a layered deposit and dynamic hydraulic fracturing branching. It has been shown that the coupled porodynamic model offers modeling flexibility and efficiency by taking advantage of FEM in modeling complex domains and the PD ability to resolve discontinuities.