广义H-B强度准则下破碎岩质边坡稳定分析极限平衡变分法

doi:10.3724/1000-6915.jrme.2024.0571

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摘要由于岩体剪切失效行为往往呈现为复杂的非线性特征，使得现有理论方法在开展破碎岩质边坡稳定性分析方面存在一定的挑战。在此，提出岩质边坡稳定性极限平衡变分法，其利用变分法构建滑面与滑面应力微分控制方程，并应用极限平衡原理建立边坡安全系数和滑面应力未知变量计算公式。进一步，针对广义Hoek-Brown强度准则下滑面形状–滑面正应力–滑面瞬时剪切强度参数的相互嵌套关系，实施离散计算方式与耦合关联求解策略，破解非线性强度准则直接引入的难题。基于此，将边坡全局变分极值问题视为众多确定边界变分极值问题。随后，以滑面参数为优化变量，并以最小边坡安全系数和变分极值条件为优化目标，引入多目标优化遗传算法，实现可动边界横截条件解除与变分控制条件严格满足下边坡临界滑面精准快速搜索。通过算例对比分析，本文方法的可行性与实用性得以验证。现有研究将有助于边坡稳定性极限平衡理论发展和完善，并为复杂条件下破碎岩质边坡稳定性分析提供一种行之有效的计算思路。

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	邓东平
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	彭一航

关键词 ：边坡工程, 破碎岩质边坡, 广义H-B强度准则, 稳定性分析, 极限平衡变分法, 多目标遗传算法

Abstract：Due to the complex nonlinear characteristics often exhibited in the shear failure behavior of rock mass， existing theoretical methods face challenges in analyzing the stability of fractured rock slopes. In this study，a limit equilibrium(LE) variational method for assessing the stability of rock slopes is proposed. This method utilizes the variational method to derive the differential control functions for the slip surface and its associated stress. Additionally, the LE principle is employed to establish the calculation formulas for the factor of safety (FOS) of the slope and the unknown variable related to the slip surface stress. Furthermore，to address the interdependent relationship among the shape of the slip surface，the normal stress on the slip surface，and the instantaneous shear strength parameters under the generalized Hoek-Brown(H-B) strength criterion，a discrete calculation approach coupled with a correlational solving strategy is applied to overcome the challenges posed by the direct incorporation of the nonlinear strength criterion. Building on this foundation，the global vraiational extremum problems of the slope are considered as multiple deterministic boundary variational extremum problems. Subsequently，the slip surface parameters are treated as optimization variables, with the objective of minimizing the slope FOS while satisfying the variational extreme conditions. A multi-objective optimization genetic algorithm is introduced to achieve a precise and rapid search for the critical slip surface of the slope，ensuring the removal of movable boundary cross-sectional conditions and strict adherence to the variational control conditions. The feasibility and practicability of the proposed method are verified through comparisons with several examples. This research contributes to the advancement and refinement of the LE theory for slope stability and provides an effective computational framework for the stability analysis of fractured rock slopes under complex conditions.

Key words： slope engineering fractured rock slope generalized H-B strength criterion stability analysis limit equilibrium(LE) variational method multi-objective genetic algorithm

引用本文:

邓东平，徐润冬，彭一航. 广义H-B强度准则下破碎岩质边坡稳定分析极限平衡变分法[J]. 岩石力学与工程学报, 2025, 44(4): 959-976.
DENG Dongping，XU Ruidong，PENG Yihang. Limit equilibrium variational method for stability analysis of fractured rock slopes under generalized H-B strength criterion. , 2025, 44(4): 959-976.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.3724/1000-6915.jrme.2024.0571 或 https://rockmech.whrsm.ac.cn/CN/Y2025/V44/I4/959

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[33]	DENG D P，LI L，ZHAO L H. Stability analysis of a layered slope with failure mechanism of a composite slip surface[J]. International Journal of Geomechanics，2019，19(6)：04019050.
[19]	陈建功，李会，贺自勇. 基于变分法的均质土坡稳定性分析[J]. 岩土力学，2019，40(8)：2 931-2 937.(CHEN Jiangong，LI Hui，HE Ziyong. Homogeneous soil slope stability analysis based on variation method[J]. Rock and Soil Mechanics，2019，40(8)：2 931- 2 937.(in Chinese))
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[21]	邓东平，彭一航，陈浩宇，等. 局部安全系数引入下岩质边坡稳定性分析极限平衡滑面应力法[J]. 岩石力学与工程学报，2024，43(4)：964-985.(DENG Dongping，PENG Yihang，CHEN Haoyu，et al. Limit equilibrium method based on stresses of slip surface for stability analysis of rock slope with introduction of local factor of safety[J]. Chinese Journal of Rock Mechanics and Engineering，2024，43(4)：964-985.(in Chinese))
[35]	邓东平，李亮. 两种滑动面型式下边坡稳定性计算方法的研究[J]. 岩土力学，2013，34(2)：372-380.(DENG Dongping，LI Liang. Research on calculation methods of slope stability under two types of sliding surface[J]. Rock and Soil Mechanics，2013，34(2)：372-380. (in Chinese))
[22]	HU S H，LI L，ZHAO L H，et al. Strength reduction strategy for rock slope stability using the variation principle based on the Hoek-Brown failure criterion[J]. Bulletin of Engineering Geology and the Environment，2023，82(8)：297.
[36]	沈银斌，朱大勇，姚华彦. 基于广义 Hoek-Brown 破坏准则的边坡临界滑动场[J]. 岩石力学与工程学报，2011，30(11)：2 267- 2 275.(SHEN Yinbin，ZHU Dayong，YAO Huayan. Critical slip field of slope based on generalized Hoek-Brown criterion[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(11)：2 267- 2 275.(in Chinese))
[23]	BELANDRIA N，ÚCAR R，LEÓN F M，et al. Stability analysis of slopes with planar failure using variational calculus and numerical methods[J]. Frontiers of Structural and Civil Engineering，2020，14(5)：1 262-1 273.
[37]	匡波，付宏渊，付传飞，等. 基于广义 Hoek-Brown准则的节理岩质边坡可靠性分析[J]. 中外公路，2009，29(6)：58-61.(KUANG Bo，FU Hongyuan，FU Chuanfei，et al. Reliability analysis of jointed rocky slopes based on generalised Hoek-Brown failure criterion[J]. Journal of China and Foreign Highway，2009，29(6)：58-61.(in Chinese))
[24]	陈祖煜，汪小刚，杨健，等. 岩质边坡稳定性分析——原理•方法•程序[M]. 北京：中国水利水电出版社，2005：206-240.(CHEN Zuyu，WANG Xiaogang，YANG Jian，et al. Rock slope stability analysis——Theory，methods and programs[M]. Beijing：China Water Power Press，2005：206-240.(in Chinese))
[38]	DENG D P，LIU G C，WANG Y M，et al. A novel limit-equilibrium method based on increments of interslice forces for stability analysis of slopes with weak interlayers[J]. International Journal of Geomechanics，2023，23(9)：04023159.
[25]	贺续文. 基于离散单元法的节理岩体边坡稳定性分析[硕士学位论文][D]. 湖南：湘潭大学，2010.(HE Xuwen. Numerical analysis of the stability of jointed rock slopes based on DEM[M. S. Thesis][D]. Hunan：Xiangtan University，2010.(in Chinese))
[26]	郑楠. 岩质边坡稳定性的数值分析及其应用[硕士学位论文][D].大连：大连理工大学，2013.(ZHENG Nan. The numerical analysis of rock slope stability and application[M. S. Thesis][D]. Dalian：Dalian University of Technology，2013.(in Chinese))
[27]	MICHALOWSKI R L，PARK D. Stability assessment of slopes in rock governed by the Hoek-Brown strength criterion[J]. International Journal of Rock Mechanics and Mining Sciences，2020，127(3)：104217.
[28]	刘立鹏，姚磊华，陈洁，等. 基于 Hoek-Brown 准则的岩质边坡稳定性分析[J]. 岩石力学与工程学报，2010，29(增1)：2 879-2 886. (LIU Lipeng，YAO Leihua，CHEN Jie，et al. Rock slope stability analysis based on Hoek-Brown failure criterion[J]. Chinese Journal of Rock Mechanics and Engineering，2010，29(Supp.1)：2 879-2 886.(in Chinese))
[29]	LI A J，MERIFIELD R S，LYAMIN A V. Stability charts for rock slopes based on the Hoek-Brown failure criterion[J]. International Journal of Rock Mechanics and Mining Sciences，2008，45(5)：689-700.
[30]	KUMAR P. Shear failure envelope of Hoek-Brown criterion for rockmass[J]. Tunnelling and Underground Space Technology，1998，13(4)：453-458.
[31]	BAKER R，GARBER M. Variational analysis of the stability of slopes[C]// Proceedings of the 9th International Conference on Soil Mechanics and Foundations Engineering. Tokyo：[s. n.]，1977：9-12.
[32]	钱伟长. 变分法及有限元-上册[M]. 北京：科学出版社，1980：1-37.(QIAN Weichang. Variational method and finite element method-Volume I[M]. Beijing：Science Press，1980：1-37.(in Chinese))
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