Determination of Geometrical REVs Based on Volumetric Fracture Intensity and Statistical Tests.

This paper presents a method to estimate a representative element volume (REV) of a fractured rock mass based on the volumetric fracture intensity P₃₂ and statistical tests. A 150 m × 80 m × 50 m 3D fracture network model was generated based on field data collected at the Maji dam site by using the rectangular window sampling method. The volumetric fracture intensity P₃₂ of each cube was calculated by varying the cube location in the generated 3D fracture network model and varying the cube side length from 1 to 20 m, and the distribution of the P₃₂ values was described. The size effect and spatial effect of the fractured rock mass were studied; the P₃₂ values from the same cube sizes and different locations were significantly different, and the fluctuation in P₃₂ values clearly decreases as the cube side length increases. In this paper, a new method that comprehensively considers the anisotropy of rock masses, simplicity of calculation and differences between different methods was proposed to estimate the geometrical REV size. The geometrical REV size of the fractured rock mass was determined based on the volumetric fracture intensity P₃₂ and two statistical test methods, namely, the likelihood ratio test and the Wald–Wolfowitz runs test. The results of the two statistical tests were substantially different; critical cube sizes of 13 m and 12 m were estimated by the Wald–Wolfowitz runs test and the likelihood ratio test, respectively. Because the different test methods emphasize different considerations and impact factors, considering a result that these two tests accept, the larger cube size, 13 m, was selected as the geometrical REV size of the fractured rock mass at the Maji dam site in China. [ABSTRACT FROM AUTHOR]