Bending and Buckling of Slender Rock-Socketed Piles Under Vertical and Lateral Load in Liquefiable Soils

This study proposes a unified framework for assessing bending-buckling failure of slender rock-socketed piles in liquefiable soils. Using a validated beam on nonlinear Winkler foundation (BNWF) model, it quantifies how axial loads amplify p-Δ effects, causing significant stiffness degradation. Study employs Receiver Operating Characteristic (ROC) analysis to establish a displacement-based buckling threshold and derives a novel governing equation incorporating embedment and slenderness ratios. Unified with the plastic hinge equation, it creates a failure mode partition diagram. Validated through case histories of Showa Bridge and Gaiko Warehouse, this approach offers a practical design tool for seismic pile foundations in liquefiable sites.