Predictive Modelling of Residual Axial Capacity in Rockfall-Damaged Hollow RC Piers: A State-of-the-Art Review

Hollow reinforced concrete piers in mountainous bridges face severe rockfall hazards causing localized panel damage and global instability, yet current design codes lack rockfall assessment protocols. This review synthesizes recent research on residual vertical load-carrying capacity prediction following rockfall impact. A critical finding is the dual failure mechanism: small rockfalls (diameter less than 1.8 meters) induce front-panel slab-action rupture with width approximately 947 mm, while large rockfalls (diameter 1.8 meters or greater) activate side-panel shear with width approximately 1388 mm. Advanced machine learning surrogates achieve exceptional accuracy (coefficient of determination 0.996) with computational speedup of one million times compared to traditional finite element analysis. Earthquake-rockfall cascade hazards reduce residual capacity by 83 percent in a non-additive manner, reflecting synergistic damage interaction. Parametric studies identify residual normalized deflection at the impact location as the optimal engineering demand parameter with correlation coefficient 0.92 to residual capacity. Performance-based design frameworks incorporating Monte Carlo vulnerability assessment enable practical rockfall-resistant pier design. Critical gaps remain in machine learning generalization to new geometries, standardization of damage indices, and integration of geological hazard characterization with structural analysis.