Enriched mixed numerical manifold formulation with continuous nodal gradients for dynamics of fractured poroelasticity

Abstract

Based on the three-variable Biot model, a numerical manifold model is presented to investigate dynamic responses of the fractured poroelasticity, especially the interaction between hydro-mechanical wave and fracture. The most flexible 3-node triangular mesh serves as the mathematical cover (MC) of the present model regardless of the problem types, shunning difficulties in qualified mesh generation. Continuous nodal gradients and Kronecker-delta property are achieved for the global approximations by constructing the local approximations with a constrained and orthonormalized least square (CO-LS) scheme, presenting more precise effective stress fields and more convenience in implementing boundary conditions for both solid and fluid phases. Incorporating a stick-slip frictional contact model via the augmented Lagrange multiplier method, the present model is capable of accurately predicting the contact phenomenon in fractured poroelasticity. In terms of the energy balance condition, precision and stability of the proposed model in time integration are verified. Fractured porous media involved multiple cracks can be addressed more naturally and conveniently with the present model relative to extended finite element method (XFEM) and phantom node method (PNM). By solving a set of typical porous media problems, the superiority, accuracy and robustness of the present model are verified.