Numerical determination of scale effect and anisotropy of strength and deformability in jointed rock masses

Rock masses are inherently discontinuous and anisotropic due to the presence of joints, and their equivalent mechanical behaviour exhibits strong scale dependence. A key challenge is to determine the representative elementary volume (REV) at which mechanical properties stabilise. This study numerically investigates the effect of joint dip angle on the REV and equivalent parameters of jointed rock masses using three-dimensional discrete element models, with loading applied independently along the three principal directions. Cubic specimens with sizes ranging from 0.5 to 16 m were analysed under isotropic confinement followed by axial loading in the principal directions. Seven joint orientations from 0° to 90° were examined. The results reveal that REV is strongly dependent on both the considered parameter and joint orientation. For peak strength, the most unfavourable orientation occurred at 45°, where the representative strength was only 9 MPa, corresponding to a 94% reduction compared with intact rock, and the REV reached about 8 m. By contrast, parallel and perpendicular orientations yielded near-intact strengths of approximately 128.5 MPa with REVs of only 0.5 m. For deformation modulus, the minimum value occurred at 30°, where the modulus decreased to 20 GPa, a 46% reduction. The maximum modulus-based REV reached 10 m, larger than the strength-based case. Overall, the findings highlight that REV must be defined in a parameter-specific manner, and that joint orientations of 30°– 45° represent the most unfavourable conditions for mechanical stability. These insights provide a robust framework for incorporating anisotropy and scale effects into the engineering design of slopes, tunnels, and underground excavations.