Scaling laws for rockfall impact fragmentation emerging from diverse lithologies

TL;DR

This study develops a universal statistical model for rockfall impact fragmentation across diverse lithologies, revealing consistent Weibull scaling laws and linking impact energy to debris evolution, with implications for hazard mitigation.

Contribution

Introduces a discrete element framework and a relative breakage index to unify fragmentation behavior across lithologies, connecting microscopic fracture mechanics to macroscopic debris patterns.

Findings

Fragment size distributions follow a universal Weibull law.

Fragmentation data collapse onto a single signature using the breakage index.

The Weibull signature indicates lithological sensitivity and energy partitioning.

Abstract

Impact-induced fragmentation is a fundamental dissipative process in geosciences, yet its stochastic nature makes predicting debris evolution a persistent challenge. Here, we introduce a discrete element framework to resolve fragmentation mechanics across a diverse lithological spectrum, from high-strength siliciclastic units to massive carbonates, validated against high-resolution field data from documented rockfall events. Our results reveal that, despite the inherent randomness of impact dynamics, fragment size distributions consistently follow a universal Weibull scaling law, independent of lithology or initial kinetic energy. By applying a relative breakage index, we demonstrate a remarkable collapse of fragmentation data onto a single statistical signature, bridging the gap between grain-scale fracture and macroscopic debris evolution. We find that this Weibullian signature acts as a proxy for lithological sensitivity, reflecting distinct efficiencies in converting kinetic energy into new fracture surfaces. This framework explicitly resolves the energy partitioning between surviving blocks and comminuted debris, providing a robust predictive link between impact mechanics and structural resilience. From an engineering perspective, our findings enable a shift from idealised single-block impact assumptions toward a realistic assessment of distributed energy in fragmented particle clouds, offering a physical basis for optimising protective galleries and hazard mitigation strategies in complex mountainous terrains.