Coupling of flow, contact mechanics and friction, generating waves in a fractured porous medium

TL;DR

This paper develops a comprehensive mixed-dimensional model for fractured poro-elastic media, integrating flow, contact mechanics, friction, and dynamic Biot equations to better understand wave generation in such systems.

Contribution

It introduces a novel coupled model that includes fully dynamic Biot equations and contact mechanics with friction for fractures, and proves its well-posedness.

Findings

Model captures wave generation in fractured media.

Incorporates inertia and friction in fracture contact mechanics.

Provides mathematical proof of model well-posedness.

Abstract

We present a mixed dimensional model for a fractured poro-elasic medium including contact mechanics. The fracture is a lower dimensional surface embedded in a bulk poro-elastic matrix. The flow equation on the fracture is a Darcy type model that follows the cubic law for permeability. The bulk poro-elasticity is governed by fully dynamic Biot equations. The resulting model is a mixed dimensional type where the fracture flow on a surface is coupled to a bulk flow and geomechanics model. The particularity of the work here is in considering fully dynamic Biot equation, that is, including an inertia term, and the contact mechanics including friction for the fracture surface. We prove the well-posedness of the continuous model.