How Does The Shape of A Falling Rock Affect Its Impact Force On Sand Cushions: A Computer-Aided Statistical Analysis

Adequate consideration of the three-dimensional geometry of falling rocks in impact force evaluation remains a major challenge. Currently, the prevailing assumption treats falling rocks as perfect spheres. To address this issue from a statistical perspective, we developed (1) a novel algorithm (Irregular Block Generator, IBG) for rapidly generating large numbers of random irregular blocks, which innovatively employs shape descriptors (e.g., elongation, flatness, sphericity, and convexity) to control block geometry mathematically; and (2) an efficient computational framework (Impact Force Solver, IFS) for determining impact forces of irregular blocks on sand cushions, successfully resolving the critical challenge of achieving both efficiency and accuracy in irregular block impact analysis. The reliability of IBG and IFS was validated by comparing their outputs with real natural blocks in terms of geometry and numerical impact forces. We introduce the concept of block-sphere impact-force ratio (BSIR), defined as the ratio of the peak impact force of an irregular block (in a given impact pose) to that of an equal-mass sphere under identical conditions. BSIR was found to be independent of block mass and insensitive to other potential influence factors. Thus, it can serve as a correction factor to scale the impact force of a spherical falling rock, allowing a straightforward evaluation of the impact force incorporating shape effects. Statistical results from IBG and IFS revealed that both the maximum value and quartiles of BSIR for an irregular block strongly correlate with its sphericity. Based on this observation, we enabled the quantitative estimation of the impact force of an arbitrary irregular block with known sphericity via an equal-mass sphere. Our findings affirm the non-negligible contribution of 3D shape to the impact force of natural rockfalls and provide a simple way to incorporate complex geometries into impact force calculations.