Phase field modeling of crack self-healing kinetics in wet rock salt: Theory, numerical implementation, and micro-CT validation

This study proposes a theoretical phase field-based model to quantitatively capture the kinetic process of crack self-healing driven by diffusion mass transfer in wet rock salt. The model defines the rock-crack system’s free energy using the Kim-Kim-Suzuki (KKS) model to quantify the thermodynamic driving forces of structural evolution. A phase field order parameter is introduced to characterize the solid-aqueous interface’s evolution. The mechanisms coupled in the self-healing process, including salt transport, dissolution-precipitation reactions, and activity degradation, are governed by two equations: (i) the Allen-Cahn equation for interface evolution and (ii) the matter conservation equation for phase field-dependent salt diffusion. The model’s theoretical consistency and numerical stability were first validated through simulations on simplified two-dimensional (2-D) cracks. The model was then applied to a three-dimensional (3-D) crack structure reconstructed from micro-CT scans. A comparison between simulation results and post-healing CT scans demonstrated the model’s ability to capture key self-healing behaviors, including crack fragmentation and spherization. These findings highlight the model’s potential as a theoretical approach for investigating the self-healing dynamics of complex crack structures in rock salt. In addition, the comparison also identifies this model’s limitations, including insufficient capture of healing on microscale curvature and the absence of distortion energy-driven recrystallization. Feasible enhancement strategies were proposed to address these limitations and enhance the model’s applicability and predictive accuracy.