Hydrodynamic-Induced Deformation Prediction of a Toppling Rock Slope Based on the Cantilever Beam Theory

Toppling failure is a common instability mode of rock slopes in hydropower engineering projects in China. A comprehensive understanding of its mechanical response is crucial for evaluating slope stability and mitigating geological hazards. Based on the cantilever beam theory, this study focused on cases in which the base of a typical toppling rock slope consists of an altered rock mass prone to toppling. A load reduction–transfer model for rock slabs was developed to more accurately simulate progressive deformation from the slope front to the rear. This study also introduced a method for calculating hydrodynamic pressure during fluctuations in reservoir level. An analytical model was established to predict the deformation of toppling rock slopes. This model was applied to a large reservoir bank slope at a hydropower station on the upper reaches of the Yellow River. Calculations were conducted for various reference-plane dip angles to systematically analyze their influence on deformation characteristics and computational accuracy. The results were compared with field monitoring data, and deviations were systematically analyzed to identify the dip angle that most closely aligns with the slope’s engineering characteristics. The findings demonstrate that the analytical model agrees with engineering practice, providing a reliable theoretical basis and a practical tool for predicting toppling deformation in similar complex geological conditions.