SPH-Based Numerical Investigation of Energy Transformation and Prediction of Wave Characteristics in Granular Landslide–Generated Impulsive Waves

Landslide-generated waves (LGWs) are hydrodynamic fluctuations triggered by landslides impacting water bodies, posing significant threats to life and property along shorelines. To enhance understanding and improve certainty regarding the energy transformation processes of impulsive waves induced by granular landslides, this study presents a numerical investigation utilizing the smoothed particle hydrodynamics (SPH) method, incorporating the Herschel–Bulkley–Papanastasiou (HBP) rheological model. A two-dimensional (2D) generalized LGW model was developed, comprising 27 numerical tests that considered three factors at three levels each. The study thoroughly analyzed the effects of slope angle, water depth, and the length-to-thickness ratio of the landslide on the energy transformation rate before impact, as well as the landslide–water energy transformation rate after impact. A series of equations were derived to estimate the energy transformation rate and the maximum wave amplitude through dimensional analysis. Based on these findings, a practical solution for the rapid estimation of maximum wave amplitude for granular LGW is proposed. To validate the performance and accuracy of this solution, a practical case study of the Baige LGW was conducted. The results indicate that the impact velocity and maximum wave amplitude obtained from the proposed method are in good agreement with previous studies, thereby demonstrating the effectiveness and accuracy of the solution.