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| Three-dimensional upper bound analysis mechanism for slopes based on sliding surface discretization |
| SUN Zhibin1，2，HAO Zhuang1，TAN Xiaohui3，YANG Xiaoli4，JI Jian2 |
| (1. School of Automotive and Transportation Engineering，Hefei University of Technology，Hefei，Anhui 230009，China；
2. School of Civil Engineering and Transportation，Hohai University，Nanjing，Jiangsu 210029，China；3. School of Resource and Environmental Engineering，Hefei University of Technology，Hefei，Anhui 230009，China；4. School of Civil Engineering，Central South University，Changsha，Hunan 410075，China)
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Abstract The traditional log-spiral mechanism cannot be used for three-dimensional (3D) slope kinematic analysis with spatially varying friction angle. To address this problem，a 3D mechanism based on sliding surface discretization is proposed. This mechanism，with a sliding surface consisting of several triangular elements，uses the point-to-point technique in generation process and strictly satisfies the associated flow rule. The boundary conditions and construction process of this mechanism are described，and the equations of the gravity work power and the internal energy dissipation are derived. Further，the safety factor calculation process based on the dichotomous strategy is proposed，and the sensitivity analysis of the model parameters is carried out. The reliability of this mechanism under various conditions is verified by comparative analysis. Finally，the safety factor of a 3D slope with spatial variation of soil strength is calculated using the present mechanism. The results show that the variation coefficient of soil strength has a large influence on the mean value of the safety factor.
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| [1] VIRATJANDR C，MICHALOWSKI R L. Limit analysis of submerged slopes subjected to water drawdown[J]. Canadian Geotechnical Journal，2006，43(8)：802–814.
[2] HOU C Q，ZHANG T T，SUN Z B，et al. Seismic analysis of nonhomogeneous slopes with cracks using a discretization kinematic approach[J]. International Journal of Geomechanics，2019，19(9)：04019104.1‐04019104.14.
[3] 黄茂松，王浩然，刘怡林. 基于转动–平动组合破坏机构的含软弱夹层土坡降雨入渗稳定上限分析[J]. 岩土工程学报，2012，34(9)：1 561–1 567.(HUANG Maosong，WANG Haoran，LIU Yilin. Rotation-translation combined mechanism for stability analysis of slopes with weak interlayer under rainfall condition[J]. Chinese Journal of Geotechnical Engineering，2012，34(9)：1 561–1 567.(in Chinese))
[4] NIAN T K，CHEN G Q，LUAN M T，et al. Limit analysis of the stability of slopes reinforced with piles against landslide in nonhomogeneous and anisotropic soils[J]. Canadian Geotechnical Journal，2008，45(8)：1 092–1 103.
[5] GAO Y，YANG S，ZHANG F，et al. Three-dimensional reinforced slopes：Evaluation of required reinforcement strength and embedment length using limit analysis[J]. Geotextiles and Geomembranes，2016，44(2)：133–142.
[6] 夏元友，陈春舒. 考虑土体多参数非均质性及各向异性锚固边坡抗震稳定性极限分析[J]. 岩石力学与工程学报，2018，37(4)：829–837.(XIA Yuanyou，CHEN Chunshu. Seismic stability limit analysis of reinforced soil slopes with prestressed cables considering inhomogeneity and anisotropy of multiple parameters[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(4)：829–837.(in Chinese))
[7] 侯超群，邓 欣，孙志彬，等. 非线性准则下三维加筋边坡稳定性的上限分析[J]. 中国公路学报，2018，31(2)：124–132.(HOU Chaoqun，DENG Xin，SUN Zhibin，et al. Upper bound analysis of the stability of three-dimensional reinforced slopes based on nonlinear failure criterion[J]. China Journal of Highway and Transport，2018，31(2)：124–132.(in Chinese))
[8] YANG X L，CHEN J H. Factor of safety of geosynthetic-reinforced slope in unsaturated soils[J]. International Journal of Geomechanics，2019，19(6)：04019041.
[9] MICHALOWSKI R L. Stability of intact slopes with tensile strength cut-off[J]. Géotechnique，2017，67(8)：720–727.
[10] MICHALOWSKI R L. Stability of uniformly reinforced slopes[J]. Journal of Geotechnical and Geoenvironmental Engineering，1997，123(6)：546–556.
[11] JI J，ZHANG C S，GAO Y F，et al. Effect of 2D spatial variability on slope reliability：A simplified FORM analysis[J]. Geoscience Frontiers，2018，9(6)：1 631–1 638.
[12] JI J，WANG C W，GAO Y，et al. Probabilistic investigation of the seismic displacement of earth slopes under stochastic ground motion：A rotational sliding block analysis[J]. Canadian Geotechnical Journal，2021，58(7)：952–968.
[13] MOLLON G，PHOON K K，DIAS D，et al. Validation of a new 2D failure mechanism for the stability analysis of a pressurized tunnel face in a spatially varying sand[J]. Journal of Engineering Mechanics，2010，137(1)：8–21.
[14] 孙志彬，潘秋景，杨小礼，等. 非均质边坡上限分析的离散机构及应用[J]. 岩石力学与工程学报，2017，36(7)：1 680–1 688. (SUN Zhibin，PAN Qiujing，YANG Xiaoli，et al. Discrete mechanism for upper bound analysis of nonhomogeneous slopes[J]. Chinese Journal of Rock Mechanics and Engineering，2017，36(7)：1 680–1 688.(in Chinese))
[15] SUN Z，LI J，PAN Q，et al. Discrete kinematic mechanism for nonhomogeneous slopes and its application[J]. International Journal of Geomechanics，2018，18(12)：04018171.
[16] 卢坤林. 基于极限平衡理论的土质边坡空间效应研究及应用[博士学位论文][D]. 合肥：合肥工业大学，2013.(LU Kunlin. The 3D effect of homogeneous slope stability analysis based on the limit equilibrium method and its application to engineering[Ph. D. Thesis][D] Hefei：Hefei University of Technology，2013.(in Chinese))
[17] DE BUHAN P，GARNIER D. Three dimensional bearing capacity analysis of a foundation near a slope[J]. Soils and Foundations，1998，38(3)：153–163.
[18] MICHALOWSKI R L，DRESCHER A. Three-dimensional stability of slopes and excavations[J]. Géotechnique，2009，59(10)：839–850.
[19] YANG X L，ZHANG S. Stability analysis of 3D cracked slope reinforced with piles[J]. Computers and Geotechnics，2020，122：103544.
[20] GAO Y F，ZHANG F，LEI G H，et al. An extended limit analysis of three-dimensional slope stability[J]. Géotechnique，2013，63(6)：518–524.
[21] 李见飞，苏 杨，孙志彬，等. 基于Newmark滑块原理的抗滑桩加固三维土坡的地震位移分析方法[J]. 岩土力学，2020，41(8)： 2 785–2 795.(LI Jianfei, SU Yang，SUN Zhibin，et al. 3D seismic displacement analysis method of stepped slopes reinforced with piles based on Newmark principle[J]. Rock and Soil Mechanics，2020，41(8)：2 785–2 795.(in Chinese))
[22] ZHANG X. Three-dimensional stability analysis of concave slopes in plan view[J]. Journal of Geotechnical Engineering，1988，114(6)：658–671.
[23] 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.
[24] CHEN Z，WANG J，WANG Y，et al. A three-dimensional slope stability analysis method using the upper bound theorem. Part II：numerical approaches，applications and extensions[J]. International Journal of Rock Mechanics and Mining Sciences，2001，38(3)：379–397.
[25] GRIFFITHS D V，MARQUEZ R M. Three-dimensional slope stability analysis by elasto-plastic finite elements[J]. Geotechnique，2007，57(6)：537–546.
[26] 范明桥，盛金保. 土强度指标φ，c的互相关性[J]. 岩土工程学报，1997，19(4)：100–104.(FAN Mingqiao，SHENG Jinbao. Correlation of soil strength index φ，c[J]. Chinese Journal of Geotechnical Engineering，1997，19(4)：100–104.(in Chinese))
[27] 孙志豪，谭晓慧，孙志彬，等. 基于上限分析的空间变异土质边坡可靠度[J]. 岩土力学，2021，42(12)：3 397–3 406.(SUN Zhihao，TAN Xiaohui，SUN Zhibin，et al. Reliability of spatially variable earth slopes based on the upper bound analysis[J]. Rock and Soil Mechanics，2021，42(12)：3 397–3 406.(in Chinese))
[28] 谭晓慧，董小乐，费锁柱，等. 基于KL展开的可靠度分析方法及其应用[J]. 岩土工程学报，2020，42(5)：808–816.(TAN Xiaohui，DONG Xiaole，FEI Suozhu，et al. Reliability analysis method based on KL expansion and its application[J].Chinese Journal of Geotechnical Engineering，2020，42(5) ：808–816.(in Chinese))
[29] 姬 建，王乐沛，廖文旺，等. 基于WUS概率密度权重法的边坡稳定系统可靠度分析[J]. 岩土工程学报，2021，43(8)：1 492–1 501. (JI Jian，WANG Lepei，LIAO Wenwang，et al. System reliability analysis of slopes based on weighted uniform simulation method[J]. Chinese Journal of Geotechnical Engineering，2021，43(8)：1 492–1 501.(in Chinese)) |
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2022, Vol. 41 
