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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.

A consecutive joint shear strength model for soft rock joints is proposed in this paper, which takes into account the degradation law of the actual contact three-dimensional (3D) roughness. The essence of the degradation of the maximum possible dilation angle is the degradation of the 3D average equivalent dip angle of the actual contact joint asperities. Firstly, models for calculating the maximum possible dilation angle at the initial and residual shear stress stages are proposed by analyzing the 3D joint morphology characteristics of the corresponding shear stages. Secondly, the variation law of the maximum possible dilation angle is quantified by studying the degradation law of the joint micro convex body. Based on the variation law of the maximum possible dilation angle, the maximum possible shear strength model is proposed. Furthermore, a method to calculate the shear stiffness degradation in the plastic stage is proposed. According to the maximum possible shear strength of rock joints, the shear stress-shear displacement prediction model of rock joints is obtained. The new model reveals that there is a close relationship between joint shear strength and actual contact joint roughness, and the degradation of shear strength after the peak is due to the degradation of actual contact joint roughness.

To explain the effect of joint roughness on joint peak shear strength (JPSS) and investigate the effect of different contact states of joint surface on JPSS, we try to clarify the physical mechanism of the effect of joint cavity percentage (JCP) on JPSS from the perspective of the three-dimensional (3D) distribution characteristics of the actual contact joint surface, and propose a JPSS model considering the JCP. Shear tests for red sandstone joints with three different surface morphologies and three different JCPs were performed under constant normal load condition. Based on test fitting results, the reduction effect of the JCP on JPSS is investigated, and a JPSS model for cavity-containing joints is obtained. However, the above model only considers the influence of JCP by fitting test data, and does not reveal the physical mechanism of JCP affecting the JPSS. Based on the peak dilation angle model for consideration of the actual contact joint morphology, and the influence of JCP on the roughness of the actual contact joint surface, a theoretical model of the JPSS considering the JCP is proposed. The derivation process does not depend on the test fitting, but is entirely based on the joint mechanical law, and its physical significance is clear. It is proposed that the essence of the influence of the JCP on JPSS is that the JCP first affects the normal stress of the actual contact joints, further affects the roughness of actual contact joints, and then affects the shear strength.