Evolutive phase field modelling of fracture behavior of cemented paste backfill under Mode-I loading condition

An evolutive phase field model (PFM) that incorporates cement hydration process is developed to predict Mode-I fracture behavior in cemented paste backfill (CPB). The model seamlessly integrates hydration-dependent stiffness and toughness evolution into a standard finite element framework, regularizing sharp cracks through a diffusive phase field variable. In all three case studies, the PFM reproduces key experimental observations-narrow crack bands and stable propagation in single-edge notched bending (SENB) test, mode-I dominated crack paths and post-peak softening in semi-circular bending (SCB) test, and wide, diffuse fracture zones in splitting tensile tests. The coupled hydration damage formulation captures the time- and temperature-sensitive strengthening of CPB, successfully matching the delayed crack initiation and gradual load-bearing increases seen across varied curing ages and temperatures. The robustness of a single parameter set across multiple test configurations underscores the model potential for generalized CPB fracture prediction without geometry-specific calibration. By accurately forecasting crack patterns and load-displacement responses, this evolutive PFM offers a powerful tool for optimizing CPB mix design, service-life prediction, and curing protocol development in deep-mine applications.