An Analytical Solution of the Elastic Compliance Matrix and Its Parameter Characteristics for Jointed Rock Masses
摘要
Accurately assessing the deformation of jointed rock masses is of great significance for engineering construction. Currently, the analytical solution of the elastic compliance matrix for jointed rock masses still has shortcomings in considering the joint sets structure and stiffness parameters. This paper derives a general formula of the joint structure deformation tensor (JD) based on tensor theory. Subsequently, the analytical solution of the elastic compliance matrix of jointed rock masses is derived, and its performance is validated using numerical tests and field triaxial tests. Additionally, the anisotropic characteristics of elastic deformation of jointed rock masses and the spatial characteristics of the main elastic parameters in the compliance matrix are analyzed. The results show that the general formula for the JD can comprehensively reflect the influence of the intersection angle and stiffness parameters of joint sets on the elastic deformation of joint structures. By utilizing the principal values of the JD and stiffness parameters of the reference joint set in the principal vector space, the elastic compliance matrix can be constructed. The analytical solution shows good consistency with both numerical test and field test results. The proposed structural elastic deformation anisotropy indices (SEDAI) can accurately reflect the degree of anisotropy and the true anisotropic characteristics of the elastic deformation capacity of jointed rock masses. The spatial characteristics of the elastic parameters in the compliance matrix are significantly influenced by the number and relative magnitudes of non-zero principal values of the JD and the stiffness ratio of the reference joint set.