The relevance of roundness to the crushing strength of granular materials

The prediction of the crushing strength of sands is still an unresolved problem in soil mechanics. For natural sand grains with a regular geometry, Weibull theory has long been adopted to explain the decay of a nominal crushing strength with increasing particle size. The Weibull parameters for a given soil relate strength to size, and, although useful, this is an empirical framework that does not consider the mechanics of crushing. This study aims to provide a more fundamental assessment of the relationship between size, roundness, the stresses induced within the particles, and their crushing strength. A new grain-scale failure criterion is proposed, based on physical experiments on artificial and natural particles, Hertzian analysis and numerical simulations. It considers the physical properties of the particles, including the shape of the grain, as described by the roundness, and both its elastic and plastic features in terms of Young's modulus, Poisson ratio and hardness. The new criterion is suitable for implementation in particle-scale crushing simulations of granular masses, using, for example, the discrete-element method, as well as in improved probabilistic frameworks.