Estimation of the elastic properties of fractured rock masses

The discontinuities in rock masses in the form of joints, fissures and interface separations are crucial to the design of various excavations. The effects of such discontinuities can often be characterized by the effective moduli of the fractured rock masses. In the present paper, an estimation of the effective moduli is presented by modeling these discontinuities as planar tunnel cracks. The interaction among the cracks is accounted for within the framework of self-consistent mechanics. Three geometries-randomly distributed cracks, parallel cracks and two orthogonal sets of cracks-are used to simulate the discontinuities in rock masses where all tunnel cracks are parallel to a certain direction. The uncracked material is assumed isotropic, while the cracked solid behaves as an orthotropic material. The damaged elastic moduli, in-plane and out-of-plane, are presented in terms of a defined planar crack density, which can be easily densities at which the in-plane effective moduli vanish is established for each geometry. For all three cases, the out-of-plane moduli decay much slower than the in-plane moduli as the crack density increases. Also addressed in detail is the effect of the interaction between the two orthogonal sets of cracks on the damaged elastic properties. Some applications to geomechanics are discussed, and an investigation is made of the scale dependence of the modulus.