Dominant factors and prediction model of toppling collapse for steep cliffs in strong earthquake zones

Earthquake-induced collapses of steep cliffs with hazardous rock masses are a prevalent geological hazard in mountainous regions. Current methods for assessing the stability of grouped rock failures under seismic loading exhibit significant limitations. This study introduces an integrated multi-scale methodology combining scaled shaking table tests with 3DEC discrete element numerical modeling to systematically investigate the failure modes, critical collapse thresholds, and risk factors for hazardous rock formations along the China-Pakistan Highway. The approach uniquely bridges physical experimentation, numerical mechanistic analysis, and data-driven prediction to decipher complex failure mechanisms, with a focused analysis on toppling collapse. Key findings include: (1) a displacement angle threshold of ≈ 15° serves as a robust collapse indicator, outperforming conventional metrics; (2) the degree of rock weathering (fragmentation) exerts a dominant control on stability compared to joint inclination, height, and strength; (3) a developed BP neural network model effectively identifies toppling and sliding as the two predominant failure modes, utilizing joint inclination as a key discriminant; (4) collapse initiation shows a nonlinear dependence on rock geometry, where failure is accelerated by increased joint inclination or decreased rock size. Furthermore, a critical vibration velocity is established as a practical criterion for predicting toppling collapse. Factor importance analysis ranks the influencing parameters in the order: rock size > joint inclination > shape > layering configuration. The proposed thresholds, predictive criterion, and neural network model provide directly applicable tools for early warning and risk assessment, offering a refined theoretical and practical framework for mitigating seismic rockfall hazards in earthquake-prone regions.