Slope stability analysis based on independent cover manifold method and vector sum method
LIU Gaoyang1,CAI Yongchang1,2
(1. College of Civil Engineering,Tongji University,Shanghai 200092,China;2. State Key Laboratory of Disaster Reduction
in Civil Engineering,Tongji University,Shanghai 200092,China)
Abstract:A method of slope stability analysis based on independent cover manifold method(ICMM) and vector sum method(VSM) was proposed in this paper. ICMM is employed to calculate the stress fields,particularly for slopes containing discontinuities(joint,faults etc.). This method avoids the complex pre-processing algorithm in the finite element and numerical manifold methods. To calculate the factor of safety,VSM is carried out with the real stress state and the vector sum algorithm. VSM possesses the merits of clear physical meaning and high efficiency without the time-consuming iterations involved in the strength reduction method. Besides,the simulated annealing genetic algorithm(SAGA) is used to determine the critical slip surface. With the above advantages,the factor of safety of complex slopes containing discontinuities could be calculated effectively and precisely by the proposed method. Four representative numerical examples and one engineering case validate the proposed method.
[1] SHI G H. Manifold method of material analysis[C]// Transaction of the 9th Army Conference on Applied Mathematics and Computing. [S.l.]:[s.n.],1991:57–76.
[2] CAI Y C,WU J. A robust algorithm for the generation of integration cells in numerical manifold method[J]. International Journal of Impact Engineering,2016,90:165–176.
[3] CHEN Y L,LI L X. An improved numerical manifold method and its application[J]. Engineering Analysis with Boundary Elements,2015,52:120–129.
[4] 苏海东,颉志强,龚亚琦,等. 基于独立覆盖的流形法的收敛性及覆盖网格特性[J]. 长江科学院院报,2016,33(2):131–136.(SU Haidong,XIE Zhiqiang,GONG Yaqi,et al. Characteristics of convergence and cover mesh in numerical manifold method based on independent covers[J]. Journal of Yangtze River Scientific Research Institute,2016,33(2):131–136.(in Chinese))
[5] 徐栋栋,郑 宏,夏开文,等. 高阶扩展数值流形法在裂纹扩展中的应用[J]. 岩石力学与工程学报,2014,33(7):1 375–1 387. (XU Dongdong,ZHENG Hong,XIA Kaiwen,et al. Application of higherorder enriched numerical manifold method to crack propagation[J]. Chinese Journal of Rock Mechanics and Engineering,2014,33(7):1 375–1 387.(in Chinese))
[6] 刘学伟,刘泉声,卢超波,等. 温度–应力耦合作用下岩体裂隙扩展的数值流形方法研究[J]. 岩石力学与工程学报,2014,33(7):1 432–1 441.(LIU Xuewei,LIU Quansheng,LU Chaobo,et al. A numerical manifold method for fracture propagation of rock mass considering Thermo-mechanical coupling[J]. Chinese Journal of Rock Mechanics and Engineering,2014,33(7):1 432-1 441.(in Chinese))
[7] 董志宏,邬爱清,丁秀丽. 基于数值流形元方法的地下洞室稳定性分析[J]. 岩石力学与工程学报,2004,23(增2):4 956–4 959.(DONG Zhihong,WU Aiqing,DING Xiuli. Stability study of underground cavern with numerical manifold method[J]. Chinese Journal of Rock Mechanics and Engineering,2004,23(Supp.2):4 956–4 959.(in Chinese))
[8] NING Y J,AN X M,MA G W. Footwall slope stability analysis with the numerical manifold method[J]. International Journal of Rock Mechanics and Mining Sciences,2011,48(6):964–975.
[9] MA G,AN X,HE L E I. The numerical manifold method:a review[J]. International Journal of Computational Methods,2010,7(1):1–32.
[10] 蔡永昌,刘高扬. 基于独立覆盖的高阶流形方法[J]. 同济大学学报:自然科学版,2015,43(12):1 794–1 800.(CAI Yongchang,LIU Gaoyang. High-order manifold method with independent covers[J]. Journal of Tongji University:Natural Science,2015,43(12):1 794–1 800.(in Chinese))
[11] CAI Y C,ZHU H H,ZHUANG X Y. A continuous/discontinuous deformation analysis(CDDA) method based on deformable blocks for fracture modeling[J]. Frontiers of Structural and Civil Engineering,2013,7(4):369–378.
[12] GE X R. Stability and deformation analysis of complex rock foundations of several large dams and hydropower stations in China[C]// Proceedings of International Workshop on Rock Foundation. Rotterdam:AA Balkema,1995:243–248.
[13] 葛修润. 用 PC 型微机对岩体工程课题进行有限元分析[C]// 第一届全国计算岩土力学研讨会论文集. 成都:西南交通大学出版社,1987:74–85.(GE Xiurun. The finite element analysis of rock mass and engineering with PC[C]// Proceedings of Symposium on the 1st National Computational Mechanics on Rock and Soil. Chengdu:Southwest Jiaotong University Press,1987:74–85.(in Chinese))
[14] 葛修润. 抗滑稳定分析新方法——矢量和分析法的基本原理及其应用[C]// 岩石力学与工程的创新和实践:第十一次全国岩石力学与工程学术大会. 武汉:湖北科学技术出版社,2010:26–44.(GE Xiurun. A new method for anti-sliding stability analysis—basic principle of vector sum analysis method and its application[C]// Proceedings of the 11th National Rock Mechanics and Engineering Conference. Wuhan:Hubei Science and Technology Press,2010:26–44.(in Chinese))
[15] 郭明伟,葛修润,李春光,等. 边坡和坝基抗滑稳定分析的三维矢量和法及其工程应用[J]. 岩石力学与工程学报,2010,29(1):8–20.(GUO Mingwei,GE Xiurun,LI Chunguang,et al. Threedimensional vector sum method employed in slope and dam foundation stability analyses and its applications to practical engineering[J]. Chinese Journal of Rock Mechanics and Engineering,2010,29(1):8–20.(in Chinese))
[16] GRECO V,GULLA G. Slip surface search in slope stability analysis[J]. Rivista Italiana di Geotecnica,1985,19(4):189–198.
[17] DE JOSSELIN DE JONG G. Application of the calculus of variations to the vertical cut off cohesive frictionless soil[J]. Geotechnique,1980,30(1):1–16.
[18] BAKER R. Determination of the critical slip surface in slope stability computations[J]. International Journal for Numerical and Analytical Methods in Geomechanics,1980,4(4):333–359.
[19] YAMAGAMI T,KOJIMA K,TAKI M. A search for the three-dimensional critical slip surface with random generation of surface[C]// Proceedings of the 36th Symposium on Slope Stability Analyses and Stabilizing Construction Methods. Tokyo,Japan:Japanese Geotechnical Society,1991:27–34.
[20] GAO W. Determination of the noncircular critical slip surface in slope stability analysis by meeting ant colony optimization[J]. Journal of Computing in Civil Engineering,2015,30(2):06015001.
[21] KAHATADENIYA K S,NANAKORN P,NEAUPANE K M. Determination of the critical failure surface for slope stability analysis using ant colony optimization[J]. Engineering Geology,2009,108(1/2):133–141.
[22] KALATEHJARI R,AREFNIA A,A RASHID A S,et al. Determination of three-dimensional shape of failure in soil slopes[J]. Canadian Geotechnical Journal,2015,52(9):1 283–1 301.
[23] 郭明伟,葛修润,王水林,等. 基于矢量和方法的边坡动力稳定性分析[J]. 岩石力学与工程学报,2011,30(3):572–579.(GUO Mingwei,GE Xiurun,WANG Shuilin,et al. Dynamic stability analysis of slope based on vector sum analysis method[J]. Chinese Journal of Rock Mechanics and Engineering,2011,30(3):572–579. (in Chinese))
[24] 王成华,夏绪勇,李广信. 基于应力场的土坡临界滑动面的遗传算法搜索[J]. 清华大学学报:自然科学版,2004,44(3):425–428.(WANG Chenghua,XIA Xuyong,LI Guangxin. Genetic algorithm for searching for critical slip surface in soil slopes based on stress field[J]. Journal of Tsinghua University:Science and Technology,2004,44(3):425–428.(in Chinese))
[25] 李南生,唐 博,谈风婕,等. 基于统一强度理论的土石坝边坡稳定分析遗传算法[J]. 岩土力学,2013,34(1):243–249.(LI Nansheng,TANG Bo,TAN Fengjie,et al. Slope stability analysis of earth-rock dams based on unified strength criterion by genetic algorithm[J]. Rock and Soil Mechanics,2013,34(1):243–249.(in Chinese))
[26] BOLTON H,HEYMANN G,GROENWOLD A. Global search for critical failure surface in slope stability analysis[J]. Engineering Optimization,2003,35(1):51–65.
[27] ZOLFAGHARI A R,HEATH A C,MCCOMBIE P F. Simple genetic algorithm search for critical non-circular failure surface in slope stability analysis[J]. Computers and Geotechnics,2005,32(3):139–152.
[28] CHENG Y M,LI L,CHI S C,et al. Particle swarm optimization algorithm for the location of the critical non-circular failure surface in two-dimensional slope stability analysis[J]. Computers and Geotechnics,2007,34(2):92–103.
[29] LI Y C,CHEN Y M,ZHAN T L,et al. An efficient approach for locating the critical slip surface in slope stability analyses using a real-coded genetic algorithm[J]. Canadian Geotechnical Journal,2010,47(7):806–820.
[30] MCCOMBIE P,WILKINSON P. The use of the simple genetic algorithm in finding the critical factor of safety in slope stability analysis[J]. Computers and Geotechnics,2002,29(8):699–714.
[31] SUN J P,LI J C,LIU Q Q. Search for critical slip surface in slope stability analysis by spline-based GA method[J]. Journal of Geotechnical and Geoenvironmental Engineering,2008,134(2):252–256.
[32] CHENG Y M. Location of critical failure surface and some further studies on slope stability analysis[J]. Computers and Geotechnics,2003,30(3):255–267.
[33] HOLLAND J H. Adaptation in natural and artificial systems:an introductory analysis with applications to biology,control,and artificial intelligence[M]. Michigan:U Michigan Press,1975:1–232.
[34] MaN K-F,TANG K-S,KWONG S. Genetic algorithms:concepts and applications[J]. IEEE transactions on Industrial Electronics,1996,43(5):519–534.
[35] BELEGUNDU A D,CHANDRUPATLA T R. Optimization concepts and applications in engineering[M]. Cambridge:Cambridge University Press,2011:1–432.
[36] 王银年,葛洪伟. 求解TSP问题的改进模拟退火遗传算法[J]. 计算机工程与应用,2010,46(5):44–47.(WANG Yinnian,GE Hongwei. Improved simulated annealing genetic algorithm for solving TSP problem[J]. Computer Engineering and Applications,2010,46(5):44–47.(in Chinese))
[37] 姚明海,王 娜,赵连朋. 改进的模拟退火和遗传算法求解TSP问题[J]. 计算机工程与应用,2013,49(14):60–65.(YAO Minghai,WANG Na,ZHAO Lianpeng. Improved simulated annealing algorithm and genetic algorithm for TSP[J]. Computer Engineering and Applications,2013,49(14):60–65.(in Chinese))
[38] 陈祖煜. 土质边坡稳定分析——原理•方法•程序[M]. 北京:中国水利水电出版社,2003:1–560.(CHEN Zuyu. Stability analysis of soil slope—principle and method,program[M]. Beijing:China Water Power Press,2003:1–560.(in Chinese))
[39] 李连崇,唐春安,邢 军,等. 节理岩质边坡变形破坏的RFPA模拟分析[J]. 东北大学学报,2006,27(5):559–562.(LI Lianchong,TANG Chun?an,XING Jun,et al. Numerical simulation and analysis of deformation and failure of jointed rock slopes by RFPA-slope[J]. Journal of Northeastern University,2006,27(5):559–562.(in Chinese))
[40] 郑文博,庄晓莹,李耀基,等. 基于流形方法和图论算法的岩/土质边坡稳定性分析[J]. 岩土工程学报,2013,35(11):2 045–2 052. (ZHENG Wenbo,ZHUANG Xiaoying,LI Yaoji,et al. The use of graph theory in rock/soil slope stability analysis based on numerical manifold method[J]. Chinese Journal of Geotechnical Engineering,2013,35(11):2 045–2 052.(in Chinese))
[41] 朱伯芳. 有限单元法原理与应用[M]. 北京:中国水利水电出版社,1998:1–607.(ZHU Bofang. The finite element method theory and applications[M]. Beijing:China Water Power Press,1998:1–607.(in Chinese))