Phase-field modeling of dynamic rock fracture with non-intrusive uncertainty quantification

The dynamic fracture of brittle geomaterials shows strong heterogeneity and stochastic variability, challenging safety assessment in hydraulic fracturing, underground energy extraction, and large-scale structures. This study develops a non-intrusive polynomial chaos expansion (PCE) framework coupled with a dynamic phase-field model to quantify the effects of material and geometric randomness on crack initiation and propagation. Two cases are studied: (i) hydraulic fracturing of sandstone and limestone with varying pre-crack inclinations, and (ii) crack evolution in a concrete dam under rising reservoir pressure. The results show the fracture energy as the dominant factor, with Young’s modulus having secondary interaction effects, while density and Poisson’s ratio are marginal. Sandstone fractures via stress concentration and gradual dissipation; limestone exhibits energy accumulation and sudden release. The PCE–phase-field framework reproduces experimental crack paths and dynamic responses with an order-of-magnitude reduction in computational cost, offering a robust tool for uncertainty quantification and reliability assessment in dynamic rock fracture.