Accurately modeling contact and interface behavior in faulted and fractured media is essential for applications such as subsurface energy storage, carbon sequestration, and the assessment of induced seismicity. These problems involve complex hydro-mechanical couplings, strong nonlinearities, and evolving contact conditions, including unilateral contact and frictional sliding along faults and fractures. A key numerical challenge lies in the coupling of non-conforming subdomains that may rely on different discretization schemes and physical models. In this contribution, we present a mortar-based approach [1] for the simulation of contact and discontinuous mechanics in coupled multi-physics problems. The method enables the weak enforcement of interface constraints between independently discretized subdomains, allowing, for instance, finite element formulations for momentum balance to be coupled with finite volume schemes for fluid flow. Contact conditions at faults and fractures naturally fit within the mortar framework and are modeled using Karush-Kuhn-Tucker conditions, accounting for non-penetration and frictional sliding, The approach is implemented in the open-source modular platform GReS and supports fully coupled hydro-mechanical simulations in fractured geological media. Benchmark examples illustrate the accuracy and robustness of the method in handling contact, sliding, and multi-field coupling across non-matching meshes. The results demonstrate the potential of mortar methods as a flexible and scalable tool for contact mechanics in complex multi-physics and multi-domain settings, with perspectives toward large-scale industrial and geoscientific applications. REFERENCES [1] D. Moretto, A. Franceschini, and M. Ferronato, A novel mortar method integration using radial basis functions, Computers & Mathematics with Applications, 189, pp. 38–58, 2025.