Analytical Estimation of the Equivalent Elastic Compliance Tensor for Fractured Rock Masses

Abstract

The elastic compliance matrix is a key parameter for the stability analysis of engineering projects constructed in fractured rock masses. In this study, the energy equivalence and the superposition methods were used to estimate the elastic compliance matrix of rock masses containing persistent or nonpersistent fractures. For the energy equivalence method, two loading schemes were proposed to obtain the values of S16 and S26 for nonsymmetric fracture sets. The superposition method was proposed to estimate the compliance matrix of rock mass containing several fracture sets by summing the matrices of intact rock and each single fracture set. For a rock mass containing regular persistent fracture sets, the derived analytical results were consistent with closed-form results. The analytical results were also compared with the results of FEM for a rock mass containing two normally distributed nonpersistent fracture sets. The maximum deviations of the directional Young’s modulus, shear modulus, and Poisson’s ratio were 7.9, 11.3, and 21.3% respectively. The limitations of the proposed methods are discussed in this paper.