Mechanically informed three-dimensional wear inversion of stone stair treads under pedestrian loading

Repeated pedestrian loading produces measurable wear on stone staircase treads, but its mechanical interpretation remains challenging because present surface morphology results from coupled contact loading, material loss, environmental aging, and measurement uncertainty. This study proposes a mechanically informed, non-destructive framework for three-dimensional wear analysis and service age inversion of stone stair treads. The framework integrates point-cloud-based surface reconstruction, polynomial profile fitting, finite-element (FE) contact simulation, and an environment-adaptive Archard wear model. Three-dimensional tread morphology is first reconstructed from field scanning data and converted into wear depth profiles. FE analysis is then used to evaluate stress concentration and loading-path differences during ascent, descent, and multi-person use. The improved Archard model incorporates time-dependent material degradation and environmental correction terms to relate accumulated wear to pedestrian loading and service duration. The method is evaluated using four stone staircases with different ages and traffic intensities. The results show that the framework captures spatial wear morphology, explains the mechanical origin of localized tread depressions, and distinguishes loading signatures associated with different movement modes. The inverse wear model estimates service ages with a mean accuracy of 94.4 %, while sensitivity and Monte Carlo tests indicate low sensitivity to material-aging perturbations and robust performance under 5 % point cloud noise. This work provides an applied mechanics approach for linking measured surface morphology, contact stress, and time-dependent wear evolution in stone stair structures.