School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture
Institute of Deep Earth Sciences, Chinese Institute of Coal Science
Institute of Geotechnical Engineering, Huaqiao University
School of Mechanics and Civil Engineering, China University of Mining and Technology-Beijing

节理的剪切力学特性一直是岩石工程关注的重点，峰值剪胀角是描述节理抗剪能力的关键物理量，合理的峰值剪胀角模型应能充分反映节理的峰值抗剪强度。为预测节理峰值剪胀角，阐明节理峰值剪胀角与节理形貌的内在联系，首先明确了节理面上对剪切强度有贡献的微凸体分布范围，然后确定了实际接触节理中各部分微凸体对强度的贡献比例。在节理面上抵抗剪切的阻力是由面向剪切方向的所接触的微凸体产生的。提出了实际接触的最小视倾角$ {theta }_{text{cr1}}^{*} $和剪胀破坏过渡到剪断破坏的临界角度$ {theta }_{text{cr2}}^{*} $分别用于界定微凸体是否参与剪切过程，以及微凸体的破坏模式。对于有效视倾角${theta }^{*} $在$ {theta }_{text{cr1}}^{*} $～$ {theta }_{text{cr2}}^{*} $间的微凸体，其破坏模式为剪胀破坏，对剪切强度的贡献正比于${theta }^{*} $。对于${theta }^{*} $在$ {theta }_{text{cr2}}^{*} $～$ {theta }_{text{max}}^{*} $(其中，${theta }_{text{max}}^{*} $为最大有效视倾角)间的微凸体，其破坏模式为剪断破坏，对剪切强度的贡献正比于$ {theta }_{text{cr2}}^{*} $。进一步考虑实际接触节理微凸体对剪切强度不同贡献比例与微凸体面积比含量，推导出了等效实际接触节理平均角。将等效实际接触节理平均角等同于节理峰值剪胀角，提出了新的节理峰值剪胀角模型。新模型物理意义明确，现有相关所提粗糙度指标仅仅是等效实际接触节理平均角的一种特殊情况。采用89组试验数据对比分析了6种模型的计算精度，结果表明新模型的预测精度最佳(平均误差为10%)。新的峰值剪胀角模型中确定$ {theta }_{text{cr2}}^{*} $较为关键，不同材料节理对应的临界角度$ {theta }_{text{cr2}}^{*} $不同，考虑到模型形式的简化，取$ {theta }_{text{cr2}}^{*} $=32°来统一确定新的峰值剪胀角模型。简化后的节理峰值剪胀角新模型估算的相对平均误差为11%，预测精度高于本文列举的多个模型。讨论了$ {theta }_{text{cr2}}^{*} $对不同形貌节理的影响及其取值依据。结果显示，节理粗糙度较大时，新模型精度高于其他模型，通过89组试验数据拟合得到${theta }_{text{cr2}}^{*} $取值是合理的。

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. $ {theta }_{text{cr1}}^{*} $ and $ {theta }_{text{cr2}}^{*} $ are proposed to define whether asperities participate in the shear process and the failure mode of asperities, respectively. For the asperities of ${theta }^{*} $ at ($ {theta }_{text{cr1}}^{*} $, $ {theta }_{text{cr2}}^{*} $), the failure mode is shear dilation failure, and the contribution to shear strength is proportional to ${theta }^{*} $. For the asperities of ${theta }^{*} $ at ($ {theta }_{text{cr2}}^{*} $, $ {theta }_{text{max}}^{*} $), the failure mode is shear off failure, and the contribution to shear strength is proportional to $ {theta }_{text{cr2}}^{*} $. 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 $ {theta }_{text{cr2}}^{*} $ in the new peak dilation angle model. The angles $ {theta }_{text{cr2}}^{*} $ corresponding to the joints of different rock materials are different in the new model. Considering the simplification of the model form, $ {theta }_{text{cr2}}^{*} $ = 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 $ {theta }_{text{cr2}}^{*} $ on the rock joints with different morphologies, and the value basis of $ {theta }_{text{cr2}}^{*} $ 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 ${theta }_{text{cr2}}^{*} $, obtained by fitting 89 sets of experimental data, appears to be a reasonable estimate.

国家自然科学基金资助项目(52208328，52104090)；中国煤炭科工集团有限公司科技创新创业资金专项资助项目(2022-MS003)

班力壬，候宇航，杜伟升，等. 考虑实际接触节理微凸体对剪切强度不同贡献比例的峰值剪胀角模型[J]. 煤炭学报，2023，48(10)：3688−3699.

BAN Liren，HOU Yuhang，DU Weisheng，et al. A new peak dilation angle model for rock joints considering different contribution proportions of actual contact joint asperities to shear strength[J]. Journal of China Coal Society，2023，48(10)：3688−3699.