Assessing Stress Variability in Fractured Rock Masses with Frictional Properties and Power Law Fracture Size Distributions

The presence of fractures in rock masses plays a major role in its stress state and its variability. Each fracture potentially induces a stress perturbation, which is correlated to its geometrical and mechanical properties. This work aims to understand and quantitatively predict the relationship between fractured systems and the associated stress fluctuations distribution, considering any regional stress conditions. The approach considers the rock mass as an elastic rock matrix into which a population of discrete fractures is embedded-known as a Discrete Fracture Network (DFN) modeling approach. We develop relevant indicators and analytical solutions to quantify stress perturbations at the fracture network scale, supported by 3D numerical simulations, using various fracture size distributions. We show that stress fluctuations increase with fracture density and decrease as a function of the so-called stiffness length, a characteristic length that can be defined as the ratio between Young's modulus of the matrix and fracture stiffness. Based on these considerations we discuss, depending on DFN parameters, which range of fractures should be modeled explicitly to account for major stress perturbations in fractured rock masses. Stress fluctuations in fractured rocks are predicted quantitatively from a tensorial approach.At the fracture scale, stress fluctuations depend on fracture size, orientation with respect to the applied remote stress field, and mechanical properties.At the network scale, stress fluctuations depend on fracture density, as well as size, orientation and mechanical property distributions.