Analytical Prediction of the Shear Behaviour of Rock Joints with Quantified Waviness and Unevenness Through Wavelet Analysis

We present an analytical model for the shear behaviour of a rock joint with waviness and unevenness. The waviness and unevenness of a natural joint profile are quantitatively separated through wavelet analysis. The critical waviness and critical unevenness of a joint profile are subsequently determined. The degradation process of each-order asperity is predicted by considering the role of plastic tangential work in shear, by which the sheared-off asperity area and the dilation angle are quantified. Both the dilation angles of critical waviness and critical unevenness decay, as plastic tangential work accumulates. The analytical predictions are compared with the experimental data from direct shear tests on both regular- and irregular-shaped joints. Good agreement between analytical predictions and laboratory-measured curves demonstrates the capability of the developed model. Therefore, the model is capable of assessing the stability of rock-engineering structures with ubiquitous joints.