A statistical index indicating the degree and mechanical effects of grain size heterogeneity in rocks

Abstract

Mineral grain size heterogeneity is one of the fundamental reasons leading to differences in rock mechanical behaviours. Several indices have been proposed to quantify grain size heterogeneity, however, the applicability of the existing indices is limited due to various preconditions. An improved grain size heterogeneity index He was proposed in this study. By comparing with the previous index, the improved index was proved to be more applicable for analysing rock mechanical properties. Through a series of grain-based model (GBM), the grain size heterogeneity effect, material heterogeneity effect and mineral content effect were further discussed. For a simple grain size heterogeneity effect, the crack initiation stress, damage stress, peak stress and crack initiation stress ratio of rock decreased linearly as the improved index He increased. After accounting for the material heterogeneity effect, the above characteristic stresses and elastic modulus decreased. A significant material heterogeneity effect and mineral content effect will impact the linear correlation between the rock macro-mechanical parameters and the He index. When the axial stress was low, the grain size heterogeneity had little effect on the number of microcracks, but this heterogeneity became the main factor affecting the evolution of microcracks as the axial stress increased. The number of intragrain tensile cracks increases and the number of intergrain shear cracks decreases with increasing He, when the axial stress reached the rock peak strength. Besides, the combined effects of material heterogeneity and mineral content may control the type and number of microcracks, further weakening the effect of grain size heterogeneity.