Analytical boundary integral solutions for cracks and thin fluid-filled layers in a 3D poroelastic solid in time and wavenumber domain

Abstract

The spectral boundary integral (SBI) method has been widely employed in the study of fractures and friction within elastic and elastodynamic media, given its natural applicability to thin or infinitesimal interfaces. Many such interfaces and layers are also prevalent in porous, fluid-filled media. In this work, we introduce analytical SBI equations for cracks and thin layers in a 3D medium, with a particular focus on fluid presence within these interfaces or layers. We present three distinct solutions, each based on different assumptions: arbitrary pressure boundary conditions, arbitrary flux boundary conditions, or a bi-linear pressure profile within the layer. The bi-linear pressure solution models the flux through a thin, potentially pressurized, leaky layer. We highlight conditions under which the bi-linear SBI equations simplify to either the arbitrary flux or arbitrary pressure SBI equations, contingent on a specific non-dimensional parameter. We then delve into the in-plane pressure effects arising from a shear crack in a poroelastic solid. While such pressurization has been suggested to influence frictional strength in various ways and only occurs in mode II sliding, our findings indicate that a significant portion of the crack face is affected in 3D scenarios. Additionally, we investigate non-dimensional timescales governing the potential migration of this pressurization beyond the crack tip, which could induce strength alterations beyond the initially ruptured area.