A constitutive model of highly jointed rock masses

Abstract

Rock masses are characterized by the existence of distributed joints. The mechanical behavior of jointed rock masses is strongly affected by the properties and geometry of the joints. A constitutive model is proposed in this paper which can deal with a wide variety of joint distribution in rock masses. The stress-strain relations of the jointed rock mass are formulated by taking the volume average of the stress and strain inside a representative volume element where the evaluation of the relative displacement across the joints is required. The mechanical behavior of joints is represented by an elasto-plastic constitutive law that is based on the classical theory of plasticity. The relative displacement across the joints is calculated from the joint stiffness and the stress concentration tensor which gives a relationship between the overall stress and the traction acting on the joint. The stress concentration tensor depends on the ratio of the joint stiffness to the system stiffness which is the stiffness of the surroundings affected by the behavior of other joints and the joint connectivity. To evaluate the stress concentration tensor, a simple method is developed. The interaction effect between joints is considered in the model by using a homogenization method proposed in this study. The effect of joint connectivity, which results in the reduction of the system stiffness, is treated in the model with a connection coefficient. Some simple examples are solved by the proposed constitutive model, and the critical state at which the shear displacement on the joint reaches the peak value is captured in the calculation. The results are in agreement with the experimental data showing the characteristic features of the behavior of jointed rock masses.