Investigation of the representative elementary volume of fractured rock mass using the homogeneity index

Representative elementary volume (REV) is a fundamental concept in rock mechanics and its existence is a prerequisite for estimating the equivalent parameters of rock mass and applying the continuum method to investigating the rock mass. To comprehensively consider the effects of fracture size, orientation and density on the REV of rock mass, the heterogeneity index (HI) is presented to estimate the REV. The concept and meaning of HI are elaborated and 20 random realizations of fracture network models with moderate spacing and medium persistence are implemented using the General Block software. For each realization, ten rock mass models with different sizes are selected to calculate the HI. The results show an obvious size effect of the homogeneity index. The mean value and standard deviation of the homogeneity index are 0.5 and 0.14, respectively, when the size of the rock mass is not less than 8 m, and the REV for the rock mass is determined to 8 m. The investigation of the surrounding rock mass of the underground powerhouse in the Three Gorges using the HI shows a REV size of 60 m, which can be used as a criterion for the applicability of the discontinuous method. HI is a new index proposed from the perspective of rock mass structure, which is suitable for determining the REV and statistical range of rock masses. It is of great significance for the statistical analysis and investigation of the equivalent parameters of rock masses.