Studying the normal stress influential factor on rock joint stiffness using CNL direct shear test

Abstract

The deformational behavior of jointed rock masses is greatly influenced by the geometrical and mechanical characteristics of joints. Shear (k_s) and normal (k_n) stiffness of joints not only are vital input factors in the dis-continuum numerical analysis but also use to calculate elastic constants of an equivalent continuous material in the finite element numerical modeling. In this study, based on eighty-nine laboratory direct shear tests under constant normal loading (CNL) conditions, the dependency of k_s and k_n on normal stress (σ_n) is evaluated by the regression models. All natural and saw-cut discontinuity specimens belong to the meta-sandstone and limestone rock types. The range of the normal stress and ratio of normal stress to joint compressive strength was from 0.34 to 7.5 MPa and 0.01 to 0.24, respectively. The data analysis led to the inevitable outcome; the k_s and k_n versus σ_n increased by the power-law and exponential-law relationship, respectively. The shear stiffness not only in a natural joint, in which joint roughness coefficient (JRC) has a direct effect on the stiffness but also in a saw-cut specimens shows a power-law relationship with normal stress. Besides, the normal to shear stiffness ratio ($\raisebox{1ex}{${k}_n$}\!\left/ \!\raisebox{-1ex}{${k}_s$}\right.$) against the σ_n exhibit a non-linear trend line; the meta-sandstone bedding and joint show the power and the exponential trend line, respectively; the stiffness ratio ($\raisebox{1ex}{${k}_n$}\!\left/ \!\raisebox{-1ex}{${k}_s$}\right.$) at lower normal stress (0.5 MPa) were from 1.5 to 5.6, but by increasing the σ_n up to 7.5 MPa the stiffness ratio raised to 14.4. Considering the effect of normal stress on joint stiffness while choosing the reliable input factors for numerical analysis can avoid conservative analysis.