A Peak Dilation Angle Model Considering the Real Contact Area for Rock Joints

The area ratio content of the asperities with different apparent dip angles is studied based on Grasselli’s apparent dip angle distribution function. An approximate expression of the minimum dip angle of the asperities in contact is further obtained according to the contact theory. For regular joints, the peak dilation angle is the average dip angle of all asperities on the contact part. Extending the above idea to the peak dilation angle of rough joints, the peak dilation angle model is derived based on the apparent dip angle distribution of the real contact asperities. In the derivation process, the peak dilation angle of an arbitrary stress state is directly obtained, instead of obtaining the initial dilation angle first and then defining the relation between the peak dilation angle and the initial dilation angle. The more important innovation is that all the parameters in the new model are of physical significance and easy to obtain; furthermore, they are not obtained by fitting test results. Based on 89 sets of test data, the predicted values of the new model are compared with those of the other 4 existing models. The results show that the prediction accuracy of the new model is the best. Besides, the mesh scales of rock joint are discussed, and the size range of the triangle mesh is obtained. It is proposed to remove the isolated points with a large apparent dip angle when processing test data. The shear mechanism of rough joints is further clarified in this study: the dilation is regarded as the average apparent dip angle of the asperities in contact at a certain stress level. This view is easy to understand and follow. It is as simple and beautiful as many natural principles.