Rockfall simulation via spherical harmonic based discrete element method

Abstract

The trajectory of falling rock is significantly affected by its shape. In order to capture the falling rock shape, spherical harmonic function expansion method is used. The reasonable order of spherical harmonic function expansion items is determined according to the error analysis. Spherical harmonic based discrete element method is utilized to simulate the rockfall process of cylindrical and irregular shape rocks. The influences of the rock and terrain shapes on the rockfall trajectory are analyzed. The results show that the shape of falling rock can be described precisely by spherical harmonic function expansion method, and only a little data should be stored. The predicted trajectory of cylindrical rockfall is close to the experimental result. Spherical and block falling rocks usually show more regular horizontal displacement, lateral offset and jump height during the motion process. Those motion quantities for long strip and flaky falling rocks are more sensitive to their initial rotations. Terrain has a strong influence on rockfall trajectory, falling rocks are prone to move along or rest at mountain valleys.