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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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

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	DENG Dongping
	XU Ruidong
	PENG Yihang

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DENG Dongping,XU Ruidong,PENG Yihang. Limit equilibrium variational method for stability analysis of fractured rock slopes under generalized H-B strength criterion[J]. , 2025, 44(4): 959-976.

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

[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))
[14]	SPENCER E. A method of analysis of the stability of embankments assuming parallel inter-slice forces[J]. Géotechnique，1967，17(1)：11-26.
[1]	ZHAO L H，YU C H，LI L，et al. Rock slope reliability analysis using Barton-Bandis failure criterion with modified pseudo-dynamic approach[J]. Soil Dynamics and Earthquake Engineering，2020，139(6)：106310.
[20]	周凤玺，朱顺望，梁玉旺，等. 变分极限平衡法对土质边坡稳定性的精确分析[J]. 岩土工程学报，2023，45(7)：1 341-1 346.(ZHOU Fengxi，ZHU Shunwang，LIANG Yuwang，et al. Exact analysis of soil slope stability by using variational limit equilibrium method[J]. Chinese Journal of Geotechnical Engineering，2023，45(7)：1 341- 1 346.(in Chinese))
[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))
[15]	MORGENSTERN N R，PRICE V. The analysis of the stability of general slip surface[J]. Geotechnique，1965，l5(1)：79-93.
[2]	HOEK E，CARRANZA-TORRES C，CORKUM B. Hoek-Brown failure criterion-2002 edition[C]// Proceedings of NARMS-TAC Conference. Toronto：[s. n.]，2002，1：267-273.
[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.
[16]	KOPASCY J. Three-dimensional stress distribution and slip surfaces in earth works at rupture[C]// Proceedings of the 4th International Conference on Soil Mechanics and Foundations Engineering. London：John Wiley，1957：339-342.
[3]	HOEK E，BROWN E T. Empirical strength criterion for rock masses[J]. Journal of the Geotechnical Engineering Division，1980，106(9)：1 013-1 035.
[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.
[17]	BAKER R，GARBER M. Discussion of “on slip surface and slope stability analysis.” by CHEN W F，SNITBHAN N[J]. Soil and Foundations，1977，17(1)：65-68.
[4]	HOEK E，BROWN E T. The Hoek-Brown failure criterion and GSI-2018 edition[J]. Journal of Rock Mechanics and Geotechnical Engineering，2019，11(3)：445-463.
[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))
[18]	BAKER R，GARBER M. Theoretical analysis of the stability of slopes[J]. Geotechnique，1978，26(4)：395-411.
[5]	DENG D P，ZHAO L H，LI L. Limit equilibrium slope stability analysis using the nonlinear strength failure criterion[J]. Canadian Geotechnical Journal，2015，52(5)：563-576.
[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))
[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))
[6]	SARKAR S，CHAKRABORTY M. Pseudostatic stability analysis of rock slopes using variational method[J]. Indian Geotechnical Journal，2021，51(5)：935-951.
[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))
[20]	周凤玺，朱顺望，梁玉旺，等. 变分极限平衡法对土质边坡稳定性的精确分析[J]. 岩土工程学报，2023，45(7)：1 341-1 346.(ZHOU Fengxi，ZHU Shunwang，LIANG Yuwang，et al. Exact analysis of soil slope stability by using variational limit equilibrium method[J]. Chinese Journal of Geotechnical Engineering，2023，45(7)：1 341- 1 346.(in Chinese))
[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))
[7]	DENG D P，ZHAO L，LI L. Limit equilibrium analysis for rock slope stability using basic Hoek-Brown strength criterion[J]. Journal of Central South University，2017，24(9)：2 154-2 163.
[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.
[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.
[8]	HOEK E. Estimating Mohr-Coulomb friction and cohesion values from the Hoek-Brown failure criterion[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1990，27(3)：227-229.
[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))
[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.
[9]	胡卫东，曹文贵，袁青松. 基于非线性破坏准则的临坡地基承载力上限分析[J]. 岩土力学，2017，38(6)：1 639-1 646.(HU Weidong，CAO Wengui，YUAN Qingsong. Upper bound solution for ultimate bearing capacity of ground adjacent to slope based on nonlinear failure criterion[J]. Rock and Soil Mechanics，2017，38(6)：1 639-1 646.(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.
[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))
[10]	AHMED Z，WANG S，JASIM O H，et al. Variability effect of strength and geometric parameters on the stability factor of failure surfaces of rock slope by numerical analysis[J]. Arabian Journal of Geosciences，2020，13(21)：1 112.
[30]	KUMAR P. Shear failure envelope of Hoek-Brown criterion for rockmass[J]. Tunnelling and Underground Space Technology，1998，13(4)：453-458.
[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))
[11]	FELLENIUS W. Calculation of the stability of earth dams[C]// Proceedings of 2nd Congress on Large Dams. Washington：[s. n.]，1936：445-462.
[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.
[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))
[12]	BISHOP A W. The use of the slip circle in the stability analysis of slopes[J]. Geotechnique，1955，5(1)：7-17.
[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))
[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.
[13]	JANBU N. Earth pressure and bearing capacity calculation by generalized procedure of slices[C]// The 4th International Conference on Soil Mechanics and Foundations Engineering. London：John Wiley，1957：47-86.
[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.
[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))
[14]	SPENCER E. A method of analysis of the stability of embankments assuming parallel inter-slice forces[J]. Géotechnique，1967，17(1)：11-26.
[34]	BOLZA O. Lectures on the calculus of variations[M]. New York：Chelsea Publishing Company，1973：4-15.
[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.
[15]	MORGENSTERN N R，PRICE V. The analysis of the stability of general slip surface[J]. Geotechnique，1965，l5(1)：79-93.
[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))
[30]	KUMAR P. Shear failure envelope of Hoek-Brown criterion for rockmass[J]. Tunnelling and Underground Space Technology，1998，13(4)：453-458.
[16]	KOPASCY J. Three-dimensional stress distribution and slip surfaces in earth works at rupture[C]// Proceedings of the 4th International Conference on Soil Mechanics and Foundations Engineering. London：John Wiley，1957：339-342.
[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))
[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.
[17]	BAKER R，GARBER M. Discussion of “on slip surface and slope stability analysis.” by CHEN W F，SNITBHAN N[J]. Soil and Foundations，1977，17(1)：65-68.
[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))
[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))
[18]	BAKER R，GARBER M. Theoretical analysis of the stability of slopes[J]. Geotechnique，1978，26(4)：395-411.
[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.
[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))
[34]	BOLZA O. Lectures on the calculus of variations[M]. New York：Chelsea Publishing Company，1973：4-15.
[20]	周凤玺，朱顺望，梁玉旺，等. 变分极限平衡法对土质边坡稳定性的精确分析[J]. 岩土工程学报，2023，45(7)：1 341-1 346.(ZHOU Fengxi，ZHU Shunwang，LIANG Yuwang，et al. Exact analysis of soil slope stability by using variational limit equilibrium method[J]. Chinese Journal of Geotechnical Engineering，2023，45(7)：1 341- 1 346.(in Chinese))
[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))
[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.
[34]	BOLZA O. Lectures on the calculus of variations[M]. New York：Chelsea Publishing Company，1973：4-15.
[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))
[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))
[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))
[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.