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We present a mixed dimensional model for a fractured poro-elasic mediumincluding contact mechanics. The fracture is a lower dimensional surfaceembedded in a bulk poro-elastic matrix. The flow equation on the fracture is aDarcy type model that follows the cubic law for permeability. The bulkporo-elasticity is governed by fully dynamic Biot equations. The resultingmodel is a mixed dimensional type where the fracture flow on a surface iscoupled to a bulk flow and geomechanics model. The particularity of the workhere is in considering fully dynamic Biot equation, that is, including aninertia term, and the contact mechanics including friction for the fracturesurface. We prove the well-posedness of the continuous model.

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