Dynamic response and protection of RC piers under debris flow impact: an SPH-DEM-FEM coupled modeling approach

Debris flows critically threaten bridge safety by impacting reinforced concrete piers. This study develops a multi-scale SPH-DEM-FEM model to investigate the impact mechanisms, where SPH simulates the debris flow, DEM models boulders, and FEM constructs a refined pier model, with its accuracy validated experimentally. Results indicate that increasing the longitudinal reinforcement ratio reduces concrete spalling and transverse displacement, while decreasing hoop spacing helps suppress shear crack development, although additional protective measures remain necessary under high-velocity impacts. Furthermore, a higher debris flow height leads to a sharp increase in pier displacement, raising the risk of progressive collapse. A proposed steel shell-rubber composite structure demonstrates improved impact resistance through graded energy dissipation. Sensitivity analysis reveals that impact velocity is the dominant factor influencing impact force, while the impact angle significantly affects structural displacement. A modified impact force formula is proposed, providing accurate load predictions and theoretical support for the design and protection of piers in debris flow-prone regions.