Discrete mechanism for upper bound analysis of nonhomogeneous slopes
SUN Zhibin1，PAN Qiujing2，YANG Xiaoli3，HOU Chaoqun1，SHANG Manting1
(1. School of Automotive and Transportation Engineering，Hefei University of Technology，Hefei，Anhui 230009，China；
2. Laboratory 3SR，Grenoble Alpes University，Grenoble F–38000，France；3. School of Civil Engineering，Central South University，Changsha，Hunan 410075，China)
Abstract：A new mechanism of two-dimensional failure was proposed for the upper bound analysis of nonhomogeneous slopes with the friction angle varying spatially. This failure mechanism obeys the associated flow rule and geometry uniform condition and was established based on the idea of discretized slip surface. The velocity discontinuity surface was generated point by point. The rate of external work and the internal energy dissipation were derived. The critical height of the slope was derived through the methods of sequential quadratic programming(SQP) and bisection searching. The effectiveness of the presented method was verified in homogeneous，anisotropic and nonhomogeneous conditions respectively. Finally，the critical height of the nonhomogeneous slope was analyzed using the failure mechanism with the friction angle increases linearly with the depth. The results show that the nonhomogeneous coefficient of friction angle has the significant effect on the critical height.
[1] 肖锐铧，王思敬，贺小黑，等. 非均质边坡多级稳定性分析方法[J]. 岩土工程学报，2013，35(6)：1 062–1 068.(XIAO Ruihua，WANG Sijing，HE Xiaohei，et al. Multi-level stability analysis of inhomogeneous slopes[J]. Chinese Journal of Geotechnical Engineering，2013，35(6)：1 062–1 068.(in Chinese))
[2] 薛 雷，孙 强，秦四清，等. 非均质边坡强度折减法折减范围研究[J]. 岩土工程学报，2011，33(2)：275–280.(XUE Lei，SUN Qiang，
QIN Siqing，et al. Scope of strength reduction for inhomogeneous slopes[J]. Chinese Journal of Geotechnical Engineering，2011，33(2)：275–280.(in Chinese))
[3] 范明桥，盛金保. 土强度指标 ， 的互相关性[J]. 岩土工程学报，1997，19(4)：100–104.(FAN Mingqiao，SHENG Jinbao. Cross- correlation between the indexes of soil strength ， [J]. Chinese Journal of Geotechnical Engineering，1997，19(4)：100–104.(in Chinese))
[4] 张文杰，邱清文，邱战洪. 垃圾填埋场边坡稳定可靠度分析[J]. 岩石力学与工程学报，2010，29(增1)：2 958–2 963.(ZHANG Wenjie，QIU Qingwen，QIU Zhanhong. Reliability analysis of stability of a municipal solid waste landfill[J]. Chinese Journal of Rock Mechanics and Engineering，2010，29(Supp.1)：2 958–2 963.(in Chinese))
[5] FARZANEH O，ASKARI F. Three-dimensional analysis of nonhomogeneous slopes[J]. Journal of Geotechnical and Geoenvironmental Engineering，2003，129(2)：137–145.
[6] MICHALOWSKI R L. Slope stability analysis：a kinematical approach[J]. Géotechnique，1995，45(2)：283–293.
[7] 陈祖煜. 土力学经典问题的极限分析上、下限解[J]. 岩土工程学报，2002，24(1)：1–11.(CHEN Zuyu. Limit analysis for the classic problems of soil mechanics[J]. Chinese Journal of Geotechnical Engineering，2002，24(1)：1–11.(in Chinese))
[8] 王根龙，伍法权，祁生文，等. 加锚岩质边坡稳定性评价的极限分析上限法研究[J]. 岩石力学与工程学报，2007，26(12)：2 556– 2 563.(WANG Genlong，WU Faquan，QI Shengwen，et al. Research on limit analysis upper bound method for stability evaluation of anchored rock slope[J]. Chinese Journal of Rock Mechanics and Engineering，2007，26(12)：2 556–2 563.(in Chinese))
[9] 唐高朋，李 亮，赵炼恒，等. 非线性破坏准则下边坡稳定性极限分析斜条分法[J]. 岩土力学，2015，36(7)：2 063–2 072.(TANG Gaopeng，LI Liang，ZHAO Lianheng，et al. Inclined slices method for limit analysis of slope stability with nonlinear failure criterion[J]. Rock and Soil Mechanics，2015，36(7)：2 063–2 072.(in Chinese))
[10] CHEN W F. Limit analysis and soil plasticity[M]. New York：Elsevier Scientific Publishing Co.，1975：403–436.
[11] KUMAR J，SAMUI P. Stability determination for layered soil slopes using the upper bound limit analysis[J]. Geotechnical and Geological Engineering，2006，24(6)：1 803–1 819.
[12] 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.
[13] AL-KARNI A A，AL-SHAMRANI M A. Study of the effect of soil anisotropy on slope stability using method of slices[J]. Computers and Geotechnics，2000，26(2)：83–103.
[14] LO K Y. Stability of slopes in anisotropic soils[J]. Journal of Soil Mechanics and Foundations Division，1966，91(SM)：85–106.
[15] 周 勇，苏 倩. 考虑不同位置单根锚杆破坏对框架预应力锚杆柔性边坡支护结构的影响分析[J]. 工程勘察，2013，41(4)：13–18. (ZHOU Yong，SU Qian. Analysis on the influence of single anchor failure at different positions for grillage flexible supporting structure with prestressed anchors[J]. Geotechnical Investigation and Surveying，2013，41(4)：13–18.(in Chinese))
[16] PAN Q J，DIAS D. Upper-bound analysis on the face stability of a non-circular tunnel[J]. Tunnelling and Underground Space Technology，2017，62(1)：96–102.
[17] PAN Q J，DIAS D. Safety factor assessment of a tunnel face reinforced by horizontal dowels[J]. Engineering Structures，2017，142(1)：56–66.
2017, Vol. 36 
