Updates to the Grasselli’s 2D morphology parameter for estimating the JRC of rock joint

The Grasselli’s 2D morphology parameter θG used to estimate the joint roughness coefficient (JRC) is questionable, because it only considers the apparent inclination of the shear side and ignores the internal undulation angle. From the physical meaning of θG, it is found that the contribution of internal bulge height in the climbing area to surface roughness can be expressed as the slope angle at the total climbing horizontal distance. The sum of the slope angles provided by all climbing areas is defined as the roughness of joint internal undulating. The apparent average inclination angle θG and the internal average slope angle θH are superimposed to propose a new roughness parameter θC for rock joint. The θC of ten standard JRC profiles is obtained, and its relationship to JRC is then analyzed to establish JRC estimation formula based on ?C. The proposed parameter θC under different sampling intervals and different sampling directions is calculated. Results show that θC has fractal characteristics and can reflect the anisotropy of joint surface morphology. Further, the JRC estimation formula is applied to the JRC-JCS model. By comparing the experimental results obtained from the existing research and the prediction results under different shear strength models, it is verified that the estimated JRC based on θC can accurately predict the joint peak shear strength. Finally, the new parameter θC is extended to 3D form, and a 3D roughness parameter (θC)3D is proposed to capture the anisotropic characteristics of joint morphology.