Determination of the geometrical REV based on fracture connectivity: a case study of an underground excavation at the Songta dam site, China

This paper presents a technique for estimating the geometrical representative elementary volume (REV) of a fractured rock mass based on fracture connectivity. A three-dimensional fracture network model, of dimensions 78 m × 50 m × 50 m, was generated and validated for a granite rock mass using joint data collected from an exploration tunnel at the Songta dam site in southwest China. Two hundred and forty cubic specimens with edge lengths ranging from 1 to 20 m were sampled from the model, and connectivity parameters of each specimen, including the number of intersections per unit volume (C ₁) and the intersection length per unit volume (L ₁), were calculated. The REV was determined using the connectivity parameters and a series of statistical tests. The results demonstrate that both the C ₁- and L ₁-based REVs are equal to 11 m × 11 m × 11 m. In this work, the volumetric fracture intensity (P₃₂) was also used to calculate the REV for comparison. The REV obtained by P₃₂ is 9 m × 9 m × 9 m, which is smaller than that calculated by C ₁ and L ₁. Finally, the geometrical REV for the rock mass by integrating C ₁, L ₁, and P₃₂ is 11 m × 11 m × 11 m.