Boundary conditions for the weak formulation of the mixed (u,p) poroelasticity problem

This paper presents the boundary conditions that apply to the weak integral formulation of the Biot mixed (u_,p) poroelasticity equations. These boundary conditions are derived from the classical boundary conditions of the Biot displacement (u_,U_) poroelasticity equations. They are applied to the surface integrals of the associated weak form to account for exterior excitations, supports, and couplings with exterior elastic, acoustic, poroelastic media, and a septum. It will be shown that the derived boundary conditions for the (u_,p) formulation lead to simpler finite element equations compared to those obtained from the (u_,U_) formulation. Finally, two numerical examples are presented to validate the poroelastic-septum coupling condition, and to highlight the limitations of the free edge condition on a poroelastic medium.