A Peak Dilation Angle Model Considering the Real Contact Area for Rock Joints
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ORIGINAL PAPER
A Peak Dilation Angle Model Considering the Real Contact Area for Rock Joints Liren Ban1 · Weisheng Du2 · Chengzhi Qi1 Received: 31 October 2019 / Accepted: 6 July 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract 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. Keywords Peak dilation angle · Real contact area · Rock joints · Roughness distribution · Asperities Abbreviations JRC Joint roughness coefficient JCS Joint wall compressive strength (MPa) JMC Joint matching coefficient 3D Three-dimensional Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00603-020-02193-1) contains supplementary material, which is available to authorized users. * Weisheng Du [email protected] * Chengzhi Qi [email protected] Liren Ban [email protected] 1
School of Civil and Transportation Engineering, Beijing Advanced Innovation Center for Future Urban Design, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China
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Max Maximum value θ Dip angle (°) θ* Apparent dip angle (°) t Shear direction n External vector of the triangle element n1 Projection vector of n α Azimuth n0 External vector of the shear plane ∗ 𝜃max Maximum apparent dip angle (°) A0 Maximum possib
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