The effect of sampling volume size on the apparent stiffness of jointed rock mass

Abstract

Overall mechanical properties of a jointed rock mass are strongly affected by discontinuities – fractures – that naturally occur in rocks. Stochastically-generated discrete fracture network (DFN) modeling, which uses a probabilistic approach to describe the spatial distribution of fractures, such as position, size, or orientation, offers an explicit way to describe geometry of the fracture system. Many in-situ measurements and analyses presented in literature indicate that fractures’ sizes can be adequately represented by the power law probability distribution. The parallel plate model of individual fractures combined with an averaging technique makes it possible to estimate the overall compliance or stiffness of jointed rock mass (Oda et al. [1]). In the present study, a series of numerical simulations of jointed rock mass modeled by DFN and Oda’s approach were conducted to analyze the effect of different sizes of the sampling volume on the overall elastic moduli. The results of the numerical study show that the variance as well as the average of the apparent stiffness decrease as the size of sampling element grows.