The effects of sample size on mechanical properties of fractured rocks are investigated considering the correlation between distributions of fracture aperture and trace length. A recently developed nonlinear algorithm is used for predicting the normal stress-normal displacement behavior of fractures when the initial stiffness of the fractures is correlated to the fracture length. The influence of correlated fracture aperture-length on the existence of Representative Elementary Volume (REV) of the fractured rock concerned, representative mechanical properties and strength envelopes of the fractured rock mass, is examined using a large number of stochastic Discrete Element Method (DEM) models of varying sizes and varying fracture properties. The results show that REV size of the stochastically generated DEM models for correlated models is larger than uncorrelated models. Calculated elastic modulus and strength show significant differences between the models with un-correlated and correlated fracture apertures and trace lengths.

Introduction and background

The strength and elastic modulus of rock masses in-situ are considerably different with the laboratory results, using small samples without large-sized fractures, would indicate. Larger samples volumes of rocks in-situ contain much more fractures of varying sizes and inclusions which contribute to the changes, often as reduction, in strength and elastic modulus [1,2,3] of the fractured rock masses. One useful technique to represent the overall equivalent (or effective) properties of fractured rocks at field scales is to use the concept of the Representative Elementary Volume (REV), beyond which the concerned properties of the rock mass, such as Young's modulus, Poisson's ratio or strength, become constant in principle. Using in situ tests for determination of field scale mechanical properties are very difficult, time consuming and expensive, with largely unknown effects of the fractures nearby the test site. Therefore indirect estimation methods are often applied, such as various rock classification systems that cannot predict stress and size dependence of the fractured rocks objectively and quantitatively because no constitutive models are involved in such estimation schemes based largely on experience. Numerical method is able to investigate the deformability and strength parameters of fractured rocks considering the interactions between the intact rock matrix and fractures, when their constitutive behaviors are well understood. The Discrete Element Method (DEM) is a very attractive method which simulates very complicate fracture system geometrical models using the Discrete Fracture Network (DFN) approach, with complicate constitutive behavior of rock fractures and rock matrix [4]. In the DEM modeling using UDEC the deformation evolutions can be considered by simulating processes of motion and deformation of the discrete blocks formed by the fractures [5]. In the earlier studies about calculating the deformability parameters and strength of fractured rock mass, they either considered regular fracture systems which are often not 1348 good representation of rock reality in the field or they did not consider the size and stress effects of mechanical properties of fractures and interactions between the fracture parameters [6, 7, 8].

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