Finite Element and Machine Learning Modeling of Autogenous Self-Healing Concrete

Abstract

A time-dependent modeling framework for autogenous self-healing concrete that couples moisture diffusion with damage evolution was developed. Water transport follows Fick's second law with a damage-dependent diffusivity obtained by power-law interpolation between intact concrete and crack space. Healing reduces damage in proportion to the product of local moisture and a smoothed cement availability field computed via a novel Helmholtz filtering approach that models the spatial extent over which cement clinker can travel and form crystals. Two finite element variants were implemented in FEniCSx: a Crack Diffusion Model (CDM) with standard diffusion and a Crack Membrane Model (CMM) that introduces a novel threshold-based gating mechanism to control cross-crack water transport until a critical moisture threshold is reached. Key control parameters are the initial crack orientation and size, the diffusion coefficients of intact and cracked concrete, the healing rate constant, and the cement availability smoothing parameter. Simulations show that healing time varies non-monotonically with crack orientation, peaking near $45^\circ$ and $135^\circ$ and minimizing near $90^\circ$. The dependence on crack width reverses with material parameters. The CMM reproduces staged moisture penetration with delayed gate activation but lengthens total healing time, whereas the CDM is efficient for parametric sweeps. Machine learning regression models were trained on finite element simulation data to predict healing times $H(\sigma,\gamma,\beta)$ with high accuracy ($R^2 > 0.999$), dramatically reducing computational time. SHAP analysis demonstrated that crack orientation influenced healing time the most, followed by crack width and cement availability smoothing. The modeling framework provides a versatile tool for guiding future laboratory studies and implementations of self-healing concrete.