Non-Circular Rock-Fall Motion Behavior Modeling by the Eccentric Circle Model

The geometry of a block is a major factor affecting its rock-fall motion. A two-dimensional disc or three-dimensional sphere is often used to numerically simulate rock-fall motion, though circular or spherical blocks poorly represent the real geometry of rock falls. An eccentric circle model is specifically proposed to simulate the behavior of non-circular blocks in rock-fall motion using the distinct element method. In the eccentric circle model, the moment originates from the eccentricity. Three types of block shape, circle, ellipse, and eccentric circle, were used to simulate the fall of a single block through four different slope shapes to impact on a defense wall. The results of the simulation revealed that when the eccentricity falls below 0.5, the rock-fall motion is close to that of the ellipse model. As eccentricity grows, the rock-fall motion is closer to that of a flat piece, more stable, and tending to slide. When the block impacts the defensive wall using the circle model, a higher force and energy head in the wall is obtained. This case tends to be conservative, with the exception of the high slope angle case. The bouncing height using the circle model falls just between those of the ellipse and the eccentric circle models and tends to be unconservative. In conclusion, the rock-fall motion simulation using the proposed eccentric circle model appears to approach the non-circular block trajectory and energy loss, making it useful for rock-fall risk prevention and mitigation.