Minerals trapped inside diamonds during their formation deep within the Earth preserve high residual pressures — a natural record of their entrapment conditions. Accurately decoding these pressures is fundamental to geobarometry, the science of estimating the depth and conditions of rock formation. However, a persistent discrepancy exists: numerical models consistently overestimate residual pressures compared to natural observations. This thesis investigates fracture mechanisms as a key pressure-release pathway, combining two advanced computational frameworks: XFEM (Extended Finite Element Method) — simulating brittle fracture propagation Phase-Field Modeling (PFM) — capturing complex brittle and quasi-brittle fracture behaviour in 3D Results reveal that while fractures significantly influence pressure relaxation, they alone cannot fully reconcile models with nature. Key findings highlight the role of inclusion geometry, fracture coalescence in multi-inclusion systems, and quasi-brittle behaviour in enhancing relaxation. These findings point toward additional mechanisms — fluid-mediated weakening, viscous deformation, and pre-existing defects — as critical missing links, directly motivating ongoing research into hydro-mechanical modelling of these systems.