Estimating the Volumetric Fracture Intensity P₃₂ Through a New Analytical Approach

In the geomechanical characterisation practice of jointed rock masses, the volumetric fracture intensity P₃₂, defined as the total area of discontinuities per unit volume, is becoming increasingly popular as one of the most suitable three-dimensional estimators of the fracture abundance. 3D discrete fracture network (DFN) modelling is currently the most rigorous approach to estimate P₃₂. However, considering the practical difficulties of many practitioners in using DFN technology routinely, it seemed advantageous to search for alternative methods suitable to assess this parameter from common discontinuity measures of rock mass exposures. In order to address this practical need, the paper presents a new analytical approach based on the Monte Carlo method that can be used, with acceptable accuracy, to estimate P₃₂ of fractured rock masses. The computational strategy developed requires the knowledge of few orientation bias-free measures of the fracture abundance, namely the “true” (orthogonal) spacing distribution and persistence of each relevant fracture set comprised in the rock mass. Key advantages of the proposed methodology are the mathematical simplicity with which it can be implemented in standard spreadsheet and its applicability to rock masses with both persistent and non-persistent discontinuities. These features make the new analytical approach a valuable practical tool to complement the existing P₃₂ estimation methods in different rock engineering and geological applications.