Development a practical method for calculation of the block volume and block surface in a fractured rock mass

This study introduces a practical method for calculating the volume and surface area of blocks formed by the intersection of three persistent joint sets in a fractured rock mass. The proposed method considers the geometrical characteristics of these joint sets, demonstrating the relationship between block volume, surface area, true spacings of joint sets, and the angle between edge vectors and the normal to joint sets. The determination of required angles is facilitated through stereographic projections of joint sets using known spacing values. Validation is performed using 3DEC version 7.0 software and field data from a quarries mine, while response surface methodology (RSM) illustrates the parameter effects. Additionally, the analysis of errors from previous models identifies the reliability range of each method. The stereographic projection is further employed to analytically determine volumetric fracture intensity (P₃₂) by dividing block surface by block volume.