Steadily moving semi-infinite fracture in plane poroelasticity

Abstract

We present a fully coupled boundary integral formulation for modeling steadily propagating semi-infinite plane strain fractures in poroelastic media. By combining fundamental solutions of plain strain poroelasticity for instantaneous fluid source and edge dislocations (normal and slip modes) with temporal and spatial superposition principles, we derive boundary integral equations governing the tractions (normal and shear stresses) and pore fluid pressure on the fracture surfaces. Assuming prescribed tractions and pore fluid pressure profiles, we develop a numerical methodology to solve the governing equations for fracture opening, slip, and cumulative fluid exchange rate. The formulation is systematically verified on several relevant problems, including the case of a tensile fracture with exponential normal loading, a stress-free tensile fracture with an imposed exponential pore fluid pressure, and a shear fracture under uniform shear loading over a finite region, demonstrating excellent agreement with analytical solutions. The framework provides a robust tool for analyzing coupled fracture-fluid interactions in permeable poroelastic media and can be adapted to broader classes of elasto-diffusive problems by modifying the underlying physical parameters.