Mathematical modelling of jointed rock masses

Sammanfattning: In this thesis, a theoretical model of the mechanical behaviour of jointed rock masses is developed. An equivalent material approach is used to formulate the constitutive equations, where the structural components, intact rock and joints are assigned continuous material properties. The elastic and inelastic properties of the joints are modelled by an elasto-viscoplastic formulation. The model can be used to study general stress and strain paths for both two- and three-dimensional structures based on constitutive equations, i.e. stress-strain relations or in finite element codes. The rock mass model using the equivalent material approach can be applied to hard rock masses with several sets of intersecting continuous joints. The theoretical model developed for a single joint can also be used for discrete formulation of joint elements in finite element codes, cf. chapter 3. The intact rock is treated as a linearly elastic material. The elastic behaviour of the joint is modelled with a constant stiffness matrix. The onset of plastic flow is initiated when the normal stress exceeds the normal compressive strength of the joint asperities or the tensile normal strength of the joint. the shear stress exceeds the cohesive strength and frictional resistance of the joint surface. The normal tensile strength and the cohesion of the joints are assumed to be constant material properties. The frictional parameters the dilation rate, and the shear asperity angle, and the compressive normal strength are functions of the the compressive normal strength are functions of the applied stress field and joint displacement. Simple relations based on Barton's constants joint roughness coefficient, JRC, joint compressive strength, JCS, and the residual friction angle, 0r, simple relations are fitted to these parameters. This implies that input data to the model can be extracted from the Rock Mechanics literature for a wide variety of joints. Results from laboratory shear box test and numerical calculations has been made for a number of different joints. Good agreement was obtained. It shows, that peak shear strength behaviour of joint in principal is a function of dilation rate. Further, the calculations indicated that the elastic off-diagonal behaviour of joints, reported in the rock mechanics literature, is related to the dilation angle at the asperities in contact. By means of finite element technique the model is applied to a circular opening in a jointed rock mass. It is concluded that the model offers several advantages over a discrete formulation.