Abstract: Based on the formulae of normal displacement and shear displacement of crack faces from linear elastic fracture mechanics, this paper aims to investigate the stored excessive elastic strain energy during the fracturing process of a rock with a single crack by applying external loading. The normal stiffness and shear stiffness of the crack are assumed be constant rather than traction-free. Two deformation models, i.e. the non-uniform deformation mode and the uniform deformation mode, are applied to calculate normal and shear displacements. In addition, based on equivalence of elastic strain energy, the analytical expressions of equivalent Young’s modulus and shear modulus of 2D fractured rock mass containing regularly distributed non-persistent cracks are studied. The comparison between the analytical expression and a closed-form solution derived by Amadei and Goodman (1981) shows that the uniform deformation mode provides the same result. The comparison of normally distributed cracks between the analytical expressions and FEM shows that the non-uniform deformation mode considering crack interactions obviously underestimates the elastic moduli, while the uniform deformation mode predicts directional moduli within 10% deviation of FEM results. The obtained analytical expression can be used as one of effective methods to estimate the equivalent elastic modulus of rock mass under specific conditions.

Key words: fractured rock mass, equivalent elastic moduli, analytical method, elastic strain energy