A constitutive model and FEM analysis of jointed rock masses

Abstract

In the present study, a constitutive model of jointed rock masses is presented which reflects the size, density, orientation and connectivity of joints as well as their mechanical properties. Following the continuum approach, the incremental stress-strain relation of the jointed rock mass is formulated by taking the volume average of stress and strain inside a representative volume element where the evaluation of the relative displacement across the joints is required. Employing an elasto-plastic constitutive model of the joint behavior, the relative displacement across the joint can be obtained once the stress acting on the joint is known. The fundamental difficulty in the constitutive modeling of jointed rock masses is due to the fact that the stress acting on a joint is different from the average stress since a joint does not cut through the rock mass but terminates within the rock mass, possibly connecting with other joints. The lower the stiffness of the surrounding matrix is, due to the existence of other joints or the connection of joints, the higher the stress acting on the joint will be. In the present study, the stress concentration tensor, which gives a relation between average stress and the stress acting on the joint, is introduced and a simple method to evaluate it is developed. The interaction effect between joints and the effect of joint connection are properly considered in the model. Some simple examples are solved by the proposed constitutive model. The results are in agreement with experimental data showing the characteristic features of the behavior of jointed rock masses. The proposed constitutive model for jointed rock masses is implemental into a finite element analysis program with a 3-D isoparametric element to analyze actual engineering problems. As an example, the program is used to analyze a plate-loading test problem and the results of the 3-D finite element analysis of the problem are compared with the test data. For highly jointed rock masses, the continuum model offers a powerful analytical method.