Elastic models of rock masses having one, two and three sets of joints

Abstract

The theory of orthorhombic layers is successively applied to analyse the stress—deformation behaviour of rock masses containing one, two and three sets of joints. The joints in each set are assumed to be planar and to be approximately equally spaced. When more than one set of joints are present these are assumed to be mutually perpendicular. The stress—deformation properties of a particular jointed rock mass are described in terms of an ‘equivalent’ homogeneous orthorhombic material. The case where the rock and the joint materials are isotropic and have the same value of Poisson's ratio is examined. Simple expressions for the direct moduli occur for the two extreme values of ν = 0 and ν = 0.5. Consideration is given to the conditions produced when the joints are very thin and very soft relative to the dimensions and stiffness of the rock material. The expressions for the properties of the ‘equivalent’ material are consideration simplified, particularly in the limiting case where the jonts have zero thicknesses. These properties are defined as functions of nine ‘joint compliance’ terms, six relating to shear moduli and three relating to direct moduli and Poisson's ratios. It is concluded that, all other factors being equal, the reduction in shear moduli due to the presence of joints tends to be greater than corresponding reductions in direct moduli and Poisson's ratio.