Updating Grasselli's 2D morphology parameter for estimating JRC of rock joints

The Grasselli's 2D morphology parameter ${\theta _{\rm G}}$ 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 ${\theta _{\rm G}}$, 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 ${\theta _{\rm G}}$ and the internal average slope angle ${\theta _{\rm H}}$ are superimposed to propose a new roughness parameter ${\theta _{\rm C}}$ for rock joints. The ${\theta _{C}}$ of ten standard JRC profiles is obtained, and its relationship to JRC is then analyzed to establish an estimation formula for JRC based on ${\theta _{\rm C}}$. The proposed parameter ${\theta _{\rm C}}$ under different sampling intervals and different sampling directions is calculated. The results show that ${\theta _{\rm C}}$ has fractal characteristics and can reflect the anisotropy of joint surface morphology. Further, the estimation formula for JRC is applied to the JRC-JCS model. By comparing the experimental results obtained from the existing researches and the predicted results under different shear strength models, it is verified that the estimated JRC based on ${\theta _{C}}$ can accurately predict the peak shear strength of joints. Finally, the new parameter ${\theta _{\rm C}}$ is extended to 3D form, and a 3D roughness parameter ${({\theta _{\rm C}})_{\rm 3D}}$ is proposed to capture the anisotropic characteristics of joint morphology.