一种边坡稳定性分析新方法——小变形理论解

doi:0.3724/1000-6915.jrme.2025.0303

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摘要在对边坡边界条件分析的基础上，提出12种边坡边界条件。基于小变形理论特点，提出一种计算边坡稳定性分析新方法（小变形理论解法），针对滑坡体：（1）在满足应力平衡微分方程、协调方程、宏观力平衡、力矩平衡和力边界条件下，获得滑坡体每个单元每点的应力分布理论解，在单元与单元交界面之间满足应力连续条件；为了与有限单元法计算结果进行比较，应用线弹性虎克本构方程，获得坡体的应变解；（2）提出滑坡点破坏判定准则，以判定每点的应力状态。以湖北省恩施州稻池乡滑坡为例，将有限单元法计算结果与本文方法加以对比，其偏差较小，表明该方法是可行的。本文方法能为现行计算结果提供一种比较依据，获得的理论解能用Excel形式表示，清晰、可查。

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	卢应发1
	杨昊1
	卢里尔2
	陈卫忠2
	王今1

关键词 ：边坡工程, 边界条件, 有限单元法, 理论解, 比较分析

Abstract：Based on a detailed analysis of boundary conditions, twelve types of boundary conditions for slope stability analysis were proposed. A novel method for evaluating slope stability, utilizing the fundamental theories of small deformation, was introduced. The theoretical solutions for stress distributions within the sliding body can be derived when the stress balance differential equation, coordination equation, macroscopic force balance, torque balance, and force boundary conditions for each element are satisfied. Additionally, the stress continuity conditions between elements can also be met. To facilitate comparisons between the proposed theoretical results and those obtained using the finite element method (FEM), the linear elastic Hooke’s law was employed to derive the strain solutions for the sliding body. A point failure criterion was suggested to calibrate the stress state of the sliding body at each point. Using the Daochi Township landslide in Enshizhou, Hubei Province, as a case study, comparisons were made between the results obtained through FEM and those derived from the proposed theoretical method, demonstrating the feasibility of the latter. This proposed method establishes a comparative foundation for current computational results. The theoretical solutions obtained can be presented in Excel format, ensuring clarity and traceability.

Key words： slope engineering boundary condition FEM theoretical solution comparative analysis

引用本文:

卢应发1，杨昊1，卢里尔2，陈卫忠2，王今1. 一种边坡稳定性分析新方法——小变形理论解[J]. 岩石力学与工程学报, 2025, 44(12): 3212-3221.
LU Yingfa1, YANG Hao1, LU Lier2, CHEN Weizhong2, WANG Jin1. A new method of stability analysis of slope—theoretical solutions based on small deformation. , 2025, 44(12): 3212-3221.

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https://rockmech.whrsm.ac.cn/CN/0.3724/1000-6915.jrme.2025.0303 或 https://rockmech.whrsm.ac.cn/CN/Y2025/V44/I12/3212

[1] FELLENIUS W. Calculation of the stability of earth dams[C]// Transaction of the 2nd Congress Large Dams (ICOLD). [S. l.]：[s. n.]，1936：445–463.
[2] BISHOP A W. The use of the slip circle in the stability analysis of slopes[J]. Géotechnique，1955，5(1)：7–17.
[3] SPENCER E. A method of analysis of the stability of embankments assuming parallel inter-slice forces[J]. Géotechnique，1967，17(1)：11–26.
[4] JANBU N. Slope stability computations：In Embankment-dam Engineering. Textbook. Eds. R.C. Hirschfeld and S.J. Poulos. JOHN WILEY AND SONS INC. PUB. NY，1973，40[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1975，12(4)：67. DOI：10.1016/0148–9062(75)90139–4.
[5] SARMA S K，TAN D. Determination of critical slip surface in slope analysis[J]. Géotechnique，2006，56(8)：539–550.
[6] KELESOGLU M K. The evaluation of three-dimensional effects on slope stability by the strength reduction method[J]. KSCE Journal of Civil Engineering，2016，20(1)：1–14.
[7] NIAN T K，HUANG R Q，WAN S S，et al. Three-dimensional strength-reduction finite element analysis of slopes：geometric effects[J]. Canadian Geotechnical Journal，2012，49(5)：574–588.
[8] ZHU D，LEE C. Explicit limit equilibrium solution for slope stability[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2002，26(15)：1 573–1 590.
[9] GHARTI H N，KOMATITSCH D，OYE V，et al. Application of an elastoplastic spectral-element method to 3D slope stability analysis[J]. International Journal for Numerical Methods in Engineering，2012，91(1)：1–26.
[10] TIWARI R C，BHANDARY N P，YATABE R. 3D SEM Approach to evaluate the stability of large-scale landslides in Nepal Himalaya[J]. Geotechnical and Geological Engineering，2015，33(4)：773–793.
[11] WEI W B，CHENG Y M，LI L. Three-dimensional slope failure analysis by the strength reduction and limit equilibrium methods[J]. Computers and Geotechnics，2009，36(1)：70–80.
[12] BAKER R. Nonlinear Mohr envelopes based on triaxial data[J]. Journal of Geotechnical and Geoenvironmental Engineering，2004，130(5)：498–506.
[13] MATTHEWS C，FAROOK Z，HELM P. Slope stability analysis-limit equilibrium or the finite element method[J]. Ground Engineering，2014，48 (5)：22–28.
[14] FARAMARZI L，ZARE M，AZHARI A，et al. Assessment of rock slope stability at Cham-Shir Dam Power Plant pit using the limit equilibrium method and numerical modeling[J]. Bulletin of Engineering Geology and the Environment，2016，32(3)：1–12.
[15] 卢应发，杨丽平，华国辉. 一种新的节理本构模型及几种新的滑坡稳定系数计算方法[J]. 岩石力学与工程学报，2013，22(12)：433–454.(LU Yingfa，YANG Liping，HUA Guohui. A new joint constitutive model and a few new methods of stability coefficient calculation of landslides[J]. Chinese Journal of Rock Mechanics and Engineering，2013，22(12)：433–454.(in Chinese))
[16] 卢应发，黄学斌，刘德富. 边坡力的分布特征和稳定性分析[J]. 岩土工程学报，2017，39(7)：1 322–1 330.(LU Yingfa，HUANG Xuebin，LIU Defu，Distribution characteristics of force and stability analysis of slope[J]. Chinese Journal of Geotechnical Engineering，2017，39(7)：1 322–1 330.(in Chinese))
[17] LU Y F. Deformation and failure mechanism of slope in three dimensions[J]. Journal of Rock Mechanics and Geotechnical Engineering，2015，7(2)：109–119.
[18] HRENNIKOFF A. Solution of problems of elasticity by the framework method[J]. Journal of Applied Mechanics，1941，8(4)：169–175.
[19] ODEN J T，DUARTE C A M，ZIENKIEWICZ O C. A new cloud-based HP finite element method[J]. Computer Methods in Applied Mechanics and Engineering，1998，153(1/2)：117–126.
[20] WILSON Z A，BORDEN M J，LANDIS C M. A phase-field model for fracture in piezoelectric ceramics[J]. International Journal of Fracture，2013，183(2)：135–153.
[21] MOHAMMADI S. Extended finite element method：XFEM Fracture analysis of composites[M]. [S. l.]：John Wiley and Sons，2008：145–261.
[22] PLANAS J，ELICES M，GUINEA G V，et al. Generalizations and specializations of cohesive crack models[J]. Engineering Fracture Mechanics，2003，70(14)：1 759–1 776.
[23] ZHANG Y F，LU Y F，ZHONG Y，et al. Stability analysis of landfills，contained by retaining walls using continuous stress method[J]. Computer Modelling in Engineering and Sciences，2023，134(1)：357–381.
[24] LU Y F，SUN W Q，YANG H，et al，A new calculation method of force and displacement of retaining wall and slope[J]. Applied Sciences，2023，13：1–25.
[25] ZHANG S Q，LU Y F，LU L E. a new method for evaluating the stability of retaining walls[J]. Buildings，2025，15：1 732.