Effects of fracture distribution and length scale on the equivalent continuum elastic compliance of fractured rock masses

Fracture systems have strong influence on the overall mechanical behavior of fractured rock masses due to their relatively lower stiffness and shear strength than those of the rock matrix. Understanding the effects of fracture geometrical distribution, such as length, spacing, persistence and orientation, is important for quantifying the mechanical behavior of fractured rock masses. The relation between fracture geometry and the mechanical characteristics of the fractured rock mass is complicated due to the fact that the fracture geometry and mechanical behaviors of fractured rock mass are strongly dependent on the length scale. In this paper, a comprehensive study was conducted to determine the effects of fracture distribution on the equivalent continuum elastic compliance of fractured rock masses over a wide range of fracture lengths. To account for the stochastic nature of fracture distributions, three different simulation techniques involving Oda's elastic compliance tensor, Monte Carlo simulation (MCS), and suitable probability density functions (PDFs) were employed to represent the elastic compliance of fractured rock masses. To yield geologically realistic results, parameters for defining fracture distributions were obtained from different geological fields. The influence of the key fracture parameters and their relations to the overall elastic behavior of the fractured rock mass were studied and discussed. A detailed study was also carried out to investigate the validity of the use of a representative element volume (REV) in the equivalent continuum representation of fractured rock masses. A criterion was also proposed to determine the appropriate REV given the fracture distribution of the rock mass.