Theoretical basis for evaluating the deformability of rock blocks

Abstract

AbstractA theoretical basis for evaluating the deformability of rock blocks is presented in this study and is used to derive an equation that governs the relationship between the normal force applied and the displacement produced. This relationship depends on the distribution of forces in the contact; therefore, it depends on the load process acting at the asperities of the rock block. Most previous studies do not take into account the crushing effect of the contact points and do not address large pressures. However, this effect is more crucial when the material is thicker. The interpretation of the deformability tests with coarse granular materials is difficult because the stresses within the material are not known but are estimated from boundary conditions. The load is distributed in a general situation between asperities in an elastic state, asperities in a plastic state and the body of the block. A mathematical model based on a suitable geometrical characterization of the roughness of the surface of the rock block, height and radius, and well‐known mechanical principles is developed. This model makes it possible to evaluate partially the force‐displacement relationship of particle breakage tests. The main objective is to obtain the stress‐strain relationship of rock blocks considering the influence of roughness on its surface. The described theoretical formulation is applied to the rockfill of the dock of the Minerales harbor (Huelva). Their strength characteristics and deformation modulus are known, and the distribution of roughness on its surface is obtained using a specialized scanner on one of the block samples. From these results, the arrangement of the irregularities and the parameters of this developed mathematical model are applied to obtain adequate predictions and behavior patterns of particle breakage tests. The developed model adequately reproduces the different behaviors of the force‐displacement relationship depending on the fragility index (FI). Realistic values of this index make it possible to obtain adequate predictions.