Spectral-based peak-shear-strength criterion for rock joints

In general, roughness profiles of rock joints consist of nonstationary and stationary components. At the simplest level, only one parameter is necessary to quantify nonstationary joint roughness. To capture the nonstationary roughness, it is suggested that the average inclination angle I, along with the direction considered for the joint surface, be used. Most natural rock-joint surface profiles do not belong to the selfsimilar fractal category. However, they may be modeled by self-affine fractals. It is shown that even though the fractal dimension D is a useful parameter, it alone is insufficient to quantify the stationary roughness of non-self-similar profiles. A new strength criterion, which includes three roughness parameters (D, I, and a spectral coefficient, Ks)' is suggested for modeling the anisotropic peak shear strength of rock joints at low normal effective stresses. Joint roughness data should be used to estimate the roughness parameters in different directions on the joint surface. Parameter D reflects the rate of change in length of the profile in response to a change in the scale of measurement r. Parameter Ks may be used to model the scale effect. A validation study shows that the new equation has good capability to predict the anisotropic peak shear strength of joints. In practice, to allow for modeling uncertainties, the new equation should be used with a factor of safety of about 1.5. Comparisons are also shown between the predicted shear strengths based on Barton's equation and the measured peak shear strengths.