A Quantitative Strain Energy Indicator for Predicting the Failure of Laboratory-Scale Rock Samples: Application to Shale Rock

Abstract

Strain energy is one of the key factors that control the brittle failure process of rock mass, such as the onset of accelerating displacement. The phenomenon of accelerating displacement is a necessary and important precursor to predict the brittle failure of rock, and it is attributed to the unstable propagation of micro-cracks when the load reaches or exceeds the crack damage stress threshold. Thus, for the design of underground rock engineering and to ensure proper safety practices, it is important to propose a suitable strain energy criterion that uses the strain energy at the crack damage stress threshold (Wcd) to predict the strain energy at final failure (Wucs). For this purpose, a quantitative strain energy indicator (Wucs/Wcd) was proposed based on two-dimensional renormalization group theory for the prediction of the brittle failure of laboratory-scale rock samples subjected to uniaxial pressure. The indicator is a function of the homogeneity index, m, of the Weibull distribution. The reliability of the strain energy indicator was verified by a series of uniaxial compression tests on 12 shale samples that had different homogeneity indices, m. The heterogeneity of the sample was dominated by different bedding dip angles. The experimental results showed that the quantitative indicator could be used to predict the brittle failure of samples of any type of rock at the laboratory scale using their m values. In addition, the effect of the bedding dip angle on the homogeneity index, m, and the strain energy indicator were discussed based on the experimental results to provide a better understanding of the relationships among heterogeneity, the strain energy indicator, and the other physical and mechanical properties of the shale samples that were tested. Also, the discussion included the effects of the homogeneity of the sample and the strain energy indicator on the physical and mechanical properties of the samples. As a result, some conclusions were obtained that might be applicable to laboratory-scale shale samples.