Mathematical Modeling and Simulation of Energy-Constrained Pavement Crack Maintenance Using XFEM-Based Crack Evolution and AI-Driven Repair Strategy Optimization

This study presents a mathematical modeling and simulation framework for pavement crack maintenance under limited work zone energy availability. The framework combines crack evolution, thermal repair, interface behavior, and maintenance decision-making within a unified structural–thermal–energy formulation. A three-dimensional multilayer flexible pavement model is developed with an XFEM-enriched region in the aged asphalt surface layer, a localized repair zone, cohesive interface behavior, and wheel-loading stages before and after maintenance. Rather than assuming constant heating, the repair heat flux is governed by a photovoltaic battery-dependent amplitude function, allowing the model to reflect practical variations in available energy. The simulation generated a dataset containing crack geometry, pavement properties, repair zone dimensions, loading conditions, heat flux intensity, heating duration, bonding quality, XFEM damage status, stress response, temperature distribution, interface damage, energy feasibility, durability, and service life gain. These variables were used to develop the Crack–Energy–Repair Interaction Graph Network (CERIG-Net), which represents each maintenance case as a physics-guided heterogeneous graph and ranks delayed repair, crack sealing, localized patching, thin overlay, and deep repair. The thin overlay strategy reduced final crack length from 94.7 mm to 53.8 mm, lowered maximum stress from 3.85 MPa to 2.22 MPa, achieved a durability index of 0.86, and extended service life by 6.7 years.