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.

中文翻译：

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考虑岩石节理实际接触面积的峰值膨胀角模型

基于Grasselli的视倾角分布函数研究了不同视倾角的凹凸体的面积比含量。根据接触理论，进一步得到了接触粗糙面最小倾角的近似表达式。对于规则接头，峰值膨胀角是接触部分所有凹凸的平均倾角。将上述思想推广到粗糙节理的峰胀角，根据实际接触粗糙的表观倾角分布推导出峰胀角模型。在推导过程中，直接得到任意应力状态下的峰胀角，而不是先求出初始胀角，然后再定义峰胀角与初始胀角的关系。更重要的创新是新模型中的所有参数都具有物理意义且易于获取；此外，它们不是通过拟合测试结果获得的。基于89组测试数据，将新模型的预测值与其他4个现有模型的预测值进行比较。结果表明，新模型的预测精度是最好的。此外，讨论了岩石节理的网格尺度，得到了三角形网格的尺寸范围。建议在处理试验数据时去除表观倾角较大的孤立点。本研究进一步阐明了粗糙接头的剪切机制：膨胀被视为在一定应力水平下接触的粗糙体的平均表观倾角。这种观点很容易理解和遵循。