A Fully Conservative Formulation of Hydromechanical Processes in Deforming Porous Media

Hydromechanical coupling in fluid-saturated porous media governs a wide range of geological processes, including compaction-driven fluid flow, strain localization, and fault activation. Many existing numerical approaches rely on non-conservative formulations expressed in terms of fluid and total pressures. While effective for smooth solutions, such formulations become inconsistent in the presence of sharp porosity gradients, compaction fronts, and shock-like structures, which promote strain localization into shear bands, where mass conservation and correct jump conditions are essential.

Here, we present a fully conservative hydromechanical formulation based on the conservation of fluid mass, total mass, and an explicit porosity evolution equation. This framework provides a physically consistent description of coupled flow–deformation processes, making it particularly suited for problems involving discontinuities, porosity waves, and localized deformation. We demonstrate that classical solitary porosity waves arise directly from the conservative equations and that fluid overpressure associated with channelized flow can trigger shear band formation through poro-visco-elasto-plastic yielding. We further extend the conservative formulation to two-phase flow with capillary pressure, showing that strain localization fundamentally alters phase pressure evolution and fluid distribution. The formulation is implemented in a GPU-accelerated framework, enabling high-resolution three-dimensional simulations of strongly nonlinear hydromechanical instabilities.

These results establish conservative hydromechanics as a foundation for modeling flow-driven localization, porosity waves, and multiphase transport in deforming geological media, with implications for fluid-induced seismicity and fault mechanics.