Meitan xuebao (Oct 2023)
A new peak dilation angle model for rock joints considering different contribution proportions of actual contact joint asperities to shear strength
Abstract
The shear properties of rock joints have always been the focus of rock engineering, and the peak dilation angle is a key physical quantity describing the shear behavior of joints. A reasonable peak dilation angle model should fully reflect the peak shear strength of rock joints. To predict the peak dilation angle of rock joints and clarify the intrinsic relationship between the peak dilation angle and the morphology of rock joints, the distribution range of asperities on the joint surface that contribute to the shear strength is defined at first, and then the contribution ratio of asperities to the strength in actual contact joints is determined. The resistance to shear on the joint surface is generated by the touched asperities facing the shear direction. \begin{document}$ {\theta }_{\text{cr1}}^{*} $\end{document} and \begin{document}$ {\theta }_{\text{cr2}}^{*} $\end{document} are proposed to define whether asperities participate in the shear process and the failure mode of asperities, respectively. For the asperities of \begin{document}${\theta }^{*} $\end{document} at (\begin{document}$ {\theta }_{\text{cr1}}^{*} $\end{document}, \begin{document}$ {\theta }_{\text{cr2}}^{*} $\end{document}), the failure mode is shear dilation failure, and the contribution to shear strength is proportional to \begin{document}${\theta }^{*} $\end{document}. For the asperities of \begin{document}${\theta }^{*} $\end{document} at (\begin{document}$ {\theta }_{\text{cr2}}^{*} $\end{document}, \begin{document}$ {\theta }_{\text{max}}^{*} $\end{document}), the failure mode is shear off failure, and the contribution to shear strength is proportional to \begin{document}$ {\theta }_{\text{cr2}}^{*} $\end{document}. Furthermore, the equivalent average angle of joints in contact is deduced considering the different contribution ratios of asperities in contact to shear strength and the area ratio of asperities. Equating the equivalent average angle of joints in contact with the peak dilation angle, a new model of peak dilation angle of joints is proposed. The physical meaning of the new model is clear, and the existing parameter of peak dilation angle is only a special case of equivalent average angle of actual contact joints. The calculation accuracy of six peak dilation angle models is compared through 89 sets of experimental results, which show that the prediction results of the new model are the best (the average error is 10%). It is critical to determine \begin{document}$ {\theta }_{\text{cr2}}^{*} $\end{document} in the new peak dilation angle model. The angles \begin{document}$ {\theta }_{\text{cr2}}^{*} $\end{document} corresponding to the joints of different rock materials are different in the new model. Considering the simplification of the model form, \begin{document}$ {\theta }_{\text{cr2}}^{*} $\end{document} = 32° fitted by tests is used to determine the new peak dilation angle model. The relative average error of the new simplified peak dilation angle model is 11%, and the prediction accuracy is higher than that of other models listed in this study. The influence of \begin{document}$ {\theta }_{\text{cr2}}^{*} $\end{document} on the rock joints with different morphologies, and the value basis of \begin{document}$ {\theta }_{\text{cr2}}^{*} $\end{document} are discussed. The findings reveal that in cases of pronounced joint roughness, the new model outperforms other models in terms of accuracy. Additionally, the derived value of \begin{document}${\theta }_{\text{cr2}}^{*} $\end{document}, obtained by fitting 89 sets of experimental data, appears to be a reasonable estimate.
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