An experimental approach for determination of the Weibull homogeneity index of rock or rock-like materials

The spatial variation of the physical–mechanical properties of rock or rock-like materials is an intrinsic characteristic of the materials induced by multiscale material heterogeneities. The Weibull distribution is a widely used statistical model for the characterization of non-uniform mechanical property distribution of rock or rock-like materials at particle scale. The key parameter of the Weibull distribution is the homogeneity index, m. In the past, the m value is normally assumed. This paper proposes an experimental approach to obtain the m value through the establishment of a relationship between m and the ratio of the peak strain to the crack damage strain using the one-dimensional renormalization group theory. Using this relationship, the m value can be estimated once the peak strain and the crack damage strain have been measured during a uniaxial compression test. The reliability of using the m value in the Weibull distribution to characterize the micro-heterogeneity of the failure stress of rock or rock-like materials has been verified by a series of uniaxial compression tests carried out on cement-grouted sand specimens with three different ranges of particle sizes and three types of cement grouts. Furthermore, the effect of particle size, void ratio and water cement (W/C) ratio on the micro-heterogeneity of cement-grouted sand is discussed based on experimental results. The effect of micro-heterogeneity on the physical–mechanical properties of rock or rock-like materials and the relationships among the micro-heterogeneity and physical–mechanical properties at the specimen scale of the materials were also discussed.