Theoretical formulation and seamless discrete approximation for localized failure of saturated poro-plastic structure interacting with reservoir

Abstract

Abstract This paper deals with nonlinear fluid-structure problems brought about by progressive localized failure of a dam structure built of porous cohesive material in interaction with reservoir under extreme static and/or dynamic loads. The theoretical formulation for structure is based upon Biot’s porous media theory extended to localized poro-plasticity that provides a sharp representation of cracks saturated with fluid. The fluid-structure interaction is handled by a seamless discretization between structure and fluid achieved by using a judicious combination of Voronoi cell approximation for structure, finite element approximation for fluid saturating cracks and finite element approximation for outside fluid. This is achieved by exploiting the duality of Voronoi cell and Delaunay triangle representations to allow exchanging information between mechanics and pore pressure fields at the numerical integration points to account for internal fluid-structure interaction, as well as with the external fluid motion in the reservoir being limited to small (irrotational) motion, described by Lagrangian description and mixed discrete approximation. Numerical simulations illustrate an excellent performance of the proposed model, capable to provide the overall safety assessment for pore-saturated structures, with outside fluid acting as the source of pore saturation and the external loading, in both quasi-static and dynamic setting.