Investigation of geometrical representative elementary volumes based on sampling directions and fracture sets

This paper reports that the geometrical representative elementary volume (REV) of fractured rock masses is anisotropic, and the geometric shape of an REV is of a complex, irregular geometry. A 3D fracture network model of 98 m × 80 m × 80 m was created using the field information collected from tunnel PD254 at the Maji dam site in China. One hundred random cubes of various sizes with the same sampling direction were selected to assess the volumetric fracture intensity (P₃₂). Changing the sampling direction along the dip direction and dip angle at a 10° increment, the REV size of each sampling direction was inferred using the Wald–Wolfowitz runs test and P₃₂ values. The REV sizes of entire rock masses and each fracture set were calculated, and the results indicated that the REV sizes varied with the different sampling directions. The anisotropy ratio and standard deviation were employed to quantify the degree of the anisotropy of REVs. Based on the results, the anisotropy of REVs for fracture set 2 is the most significant, and that of fracture set 3 is the worst. The relationship between the anisotropy of REVs and fracture sets was discussed; one fracture set, two fracture sets, and three fracture sets were selected randomly from these simulated rock masses to evaluate the characteristics of the anisotropy of REVs. The mean value and the anisotropy of REVs increased with the number of fracture sets. The maximum REV size with a sampling direction was selected as an REV for each fracture set. Four cubes with different directions and different sizes were assembled into an irregular geometry. This geometry can represent the geometric shape of the REV of entire rock masses.