Hydro-mechanical phase-field modeling of fluid-driven fracture in diamond-olivine systems: Reassessing the role of time-dependent inelastic deformation

The entrapment pressure of mineral inclusions in diamonds is a key proxy for investigating Earth's interior conditions. Elastic geobarometry methods assume that the diamond host behaves purely elastically during exhumation. However, observations from the Udachnaya kimberlite challenge this assumption, as olivine inclusions exhibit anomalously low residual pressures. Reconciling these observations with entrapment conditions requires a non-elastic pressure relaxation of approximately 30%, which cannot be explained by purely elastic models. In previous work, we investigated whether brittle fracture alone could account for this relaxation. Using extended finite element methods and dry phase-field modeling, we showed that brittle fracture under dry conditions provides insufficient pressure relaxation, leaving a gap between numerical predictions and natural observations. A promising candidate to explain this discrepancy is the presence of fluid rims at the inclusion–host interface, which may promote fluid-driven ("hydraulic") fracturing at reduced stress thresholds. To investigate this mechanism, we developed a coupled hydro-mechanical phase-field formulation implemented in Abaqus via a user-defined element, building on porous-media-based damage frameworks. This framework enables coupled simulations of fluid pressure build-up and fracture propagation, allowing direct comparison between dry and fluid-assisted relaxation scenarios. Preliminary results indicate that although fluid rims enhance fracture nucleation compared to the dry case, the resulting pressure relaxation remains insufficient to reach the ~30% threshold required for Udachnaya samples. These findings suggest that brittle mechanisms alone cannot fully account for the observed pressure deficits. Our results suggest that time-dependent inelastic deformation, involving both plastic and viscous components, may also contribute to post-entrapment stress relaxation under lithospheric conditions.