Loading rate dependence of granular cushion under rockfall impact and proposal of an analytical model for impact force estimation

The cushioning behaviour of granular materials, such as sand and gravel, has been studied for the rational design and performance evaluation of a rock shed intended for rockfall protection. The shape of the collision surface of a falling mass strongly affects the impact force waveform of the falling mass. However, the control factors for generating impact force waveform have not been fully clarified. Previous studies have shown that the maximum transmitted impact force acting on the top plate of a rock shed through a cushioning material depends not only on the maximum impact force acting on the falling mass but also on its duration. To accurately predict the maximum transmitted impact force acting on a structure, understanding the generation mechanism of the impact force waveform acting on the falling mass is necessary. These control factors were investigated through the two-dimensional (2D) discrete element method (DEM) analysis. It was shown that the mean principal stress of particles around a falling mass increased with the loading velocity of the falling mass. Based on this result, an analytical model for estimation the impact force waveform of the falling mass was proposed. The validity of the proposed method and the control factors estimated via simulations was confirmed by comparing the results obtained by the proposed method with 2D DEM simulation results and experimental results. This study contributes to the elucidation of the deformation mechanism of soil under high-speed loading and development of rational countermeasures considering the deformation behaviour of a sand cushion.