Size-dependence of fracture processes in intact rocks

Abstract

In brittle heterogeneous materials, the ultimate stress carries information on the material’s load-bearing capacity and, for this reason, this stress is an important engineering quantity. However, this stress is just a point in the sequence of stress–strain responses, each of them reflects the current state of damage in the material. Initially, isolated cracks grow, sense each other, and form multiple crack networks. The networks enable dilatational shear and facilitate further growth of damage. Large samples contain a broad spectrum of the crack-enabling defects and, therefore, the sample size becomes an irrelevant factor. However, when the defect population is limited, the damage process is constrained and, as a result, the peak stress is rising. According to the central limit theorem, the defect’s propensity for generating cracks should obey the rules of normal distribution. It turns out that the normal distribution of defects becomes a Weibull-like distribution of strength, where shape of the distribution is affected by the sample size and, also, is sensitive to hydrostatic pressure. The size-dependence of fracture processes is the main objective of the study.