A Study on the Peak Strength of Brittle Rocks

Abstract

A study on the peak strength of brittle rock materials having random strength distributions was carried out using the re-normalization group theory approach. A major advantage of the approach is that it is scale invariant, and therefore, one can relate the micro-fractures with macro-fractures of rocks at the critical state. The stress transfer from the broken sub-sections to the unbroken sub-sections is defined by a conditional probability. The critical probability P * and the relation between the peak strength and the mean strength of the elements have been obtained theoretically. On the other hand, the whole process of rock brittle fracture has also been simulated numerically from micro-fracture to macro-fracture by using the Rock Failure Process Analysis (RFPA) code. The peak strengths obtained by the numerical model agree fairly well with those obtained by the re-normalisation group theory. Due to the stress transfer from the broken subsections to the unbroken subsections, the peak strength is considerably less than the mean strength of the elements.