Slip surface tracking based on displacement gradient field at limit state
DAI Lixian1，2，LI Chunguang1，2，ZHOU Lei1，2
(1. State Key Laboratory of Geotechnical Mechanics and Engineering，Institute of Rock and Soil Mechanics，Chinese Academy of Sciences，Wuhan，Hubei 430071，China；2. University of Chinese Academy of Sciences，Beijing 100049，China)
Abstract：The finite element strength reduction method is a commonly used method for slope stability analysis，but it cannot directly obtain the sliding surface. Based on the assumption that the shear direction is perpendicular to the displacement gradient when shear failure occurs on the slope，this paper proposes a sliding surface tracking method based on the displacement gradient field. After obtaining the displacement modulus gradient field of the slope at limit state，the maximum displacement modulus gradient point is taken as the starting point，and the slip surface is tracked along the shear direction by the Euler?s method. The maximum value of the gradient of the displacement modulus is obtained on the slip surface，and the position of the slip surface is corrected to accurately determine the position of the entire slip surface. Finally，the reliability of the method is verified by the calculation examples of homogeneous slope，horizontal weak intercalated slope，and inclined weak intercalated slope.
[1] 朱以文，吴春秋，蔡元奇. 基于滑移线场理论的边坡滑裂面确定方法[J]. 岩石力学与工程学报，2005，24(15)：2 609–2 616.(ZHU Yiwen，WU Chunqiu，CAI Yuanqi. Method for determining the sliding surface of slope based on slip line field theory[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(15)：2 609–2 616.(in Chinese))
[2] 王 娇，林 姗，罗 柳，等. 张拉–剪切破坏模式下边坡三维临界滑面的Cauchy问题[J]. 岩土力学，2022，43(9)：2 634–2 642.(WANG Jiao，LIN Shan，LUO Liu，et al. Cauchy problem of three-dimensional critical sliding surface of slope under tension shear failure mode[J]. Rock and Soil Mechanics，2022，43(9)：2634–2 642.(in Chinese))
[3] 郑 宏，李春光，李焯芬，等. 求解安全系数的有限元法[J]. 岩土工程学报，2002，24(5)：626–628.(ZHENG Hong，LI Chunguang，LEE C F，et al. Finite Element Method for Solving Safety Factors[J]. Chinese Journal of Geotechnical Engineering，2002，24(5)：626–628.(in Chinese))
[4] ZIENKIEWICZ O C，HUMPHESON C，LEWIS R. Associated and non-associated visco-plasticity and plasticity in soil mechanics[J]. Geotechnique，1975，25(4)：671–689.
[5] GRIFFITHS D V，LANE P A. Slope stability analysis by finite elements[J]. Geotechnique，1999，49(3)：387–403.
[6] 赵尚毅，郑颖人，时卫民，等. 用有限元强度折减法求边坡稳定安全系数[J]. 岩土工程学报，2002，24(3)：343–346.(ZHAO Shangyi，ZHENG Yingren，SHI Weimin，et al. Using finite element strength reduction method to calculate the safety factor of slope stability[J]. Chinese Journal of Geotechnical Engineering，2002，24(3)：343–346.(in Chinese))
[7] ZHENG H，SUN G，LIU D. A practical procedure for searching critical slip surfaces of slopes based on the strength reduction technique[J]. Computers and Geotechnics，2009，36(1/2)：1–5.
[8] 孙冠华，郑 宏，李春光. 基于等效塑性应变的边坡滑面搜索[J]. 岩土力学，2008，29(5)：1 159–1 163.(SUN Guanhua，ZHENG Hong，LI Chunguang. Slope slip surface search based on equivalent plastic strain[J]. Rock and Soil Mechanics，2008，29(5)：1 159–1 163. (in Chinese))
[9] 聂治豹，郑 宏，张 谭. 基于强度折减法确定边坡临界滑面的小波变换法[J]. 岩土力学，2017，38(6)：1 827–1 831.(NIE Zhibao，ZHENG Hong，ZHANG Tan. Wavelet transform method for determining the critical sliding surface of slope based on strength reduction method[J]. Rock and Soil Mechanics，2017，38(6)：1 827–1 831. (in Chinese))
[10] 孙冠华，郑 宏，李春光. 基于等效塑性应变的三维边坡滑面搜索[J]. 岩土力学，2010，31(2)：627–632.(SUN Guanhua，ZHENG Hong，LI Chunguang. Three dimensional slope sliding surface search based on equivalent plastic strain[J]. Rock and Soil Mechanics，2010，31(2)：627–632.(in Chinese))
[11] 丁秀美，刘光士，黄润秋，等. 剪应变增量在堆积体边坡稳定性研究中的应用[J]. 地球科学进展，2004，19(增1)：318–323.(DING Xiumei，LIU Guangshi，HUANG Runqiu，et al. Application of shear strain increment in stability study of accumulated slope[J]. Progress in Earth Science，2004，19(Supp.1)：318–323.(in Chinese))
[12] 李 剑，陈善雄，余 飞. 基于最大剪应变增量的边坡潜在滑动面搜索[J]. 岩土力学，2013，34(增1)：371–378.(LI Jian，CHEN Shanxiong，YU Fei. Potential sliding surface search of slope based on maximum shear strain increment[J]. Rock and Soil Mechanics，2013，34(Supp.1)：371–378.(in Chinese))
[13] ZHENG H，SUN G H，LI C G. Cauchy problem of three-dimensional critical slip surfaces of slopes[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2011，35(4)：519–527.
[14] DAVIS E. Theories of plasticity and the failure of soil masses，soil mechanics[M]. London：Butterworth，1969：32–34.
[15] 郭明伟，李春光，王水林. 基于有限元应力的三维边坡稳定性分析[J]. 岩石力学与工程学报，2012，31(12)：2 494–2 500.(GUO Mingwei，LI Chunguang，WANG Shuilin. Three dimensional slope stability analysis based on finite element stress[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(12)：2 494–2 500.(in Chinese))
[16] 张 科，曹 平. 基于变形分析的3维边坡滑动面搜索新方法[J]. 四川大学学报：工程科学版，2012，44(6)：55–60.(ZHANG Ke，CAO Ping A new method for searching the sliding surface of 3D slopes based on deformation analysis[J]. Journal of Sichuan University：Engineering Science，2012，44(6)：55–60.(in Chinese))
[17] 赵建平，张 建. 基于位移变形分析的边坡滑移面分布规律[J]. 北京工业大学学报，2014，40(9)：1 347–1 353.(ZHAO Jianping，ZHANG Jian. Distribution law of slope slip surface based on displacement deformation analysis[J]. Journal of Beijing Institute of Technology，2014，40(9)：1 347–1 353.(in Chinese))
[18] 张新启，龚爱民，徐兴倩，等. 基于临界位移等值线的多阶边坡多级滑动面搜索方法[J]. 水电能源科学，2021，39(9)：160–164.(ZHANG Xinqi，GONG Aimin，XU Xingqian，et al. A search method for multi-stage sliding surfaces of multi-stage slopes based on critical displacement contour lines[J]. Hydroelectric Energy Science，2021，39(9)：160–164.(in Chinese))
[19] 朱以文，李 伟，蔡元奇. 基于解析性质的等参有限元逆变换高效算法[J]. 武汉大学学报：工学版，2002，35(2)：62–65.(ZHU Yiwen，LI Wei，CAI Yuanqi. Efficient algorithm for isoparameter finite element inverse transform based on analytical properties[J]. Journal of Wuhan University：Engineering，2002，35(2)：62–65.(in Chinese))
[20] 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，2003：49–52.(CHEN Zuyu. Principles，methods，and programs of soil slope stability analysis[M]. Beijing：China Water Resources and Hydropower Press，2003：49–52.(in Chinese))
[21] 戴自航，刘志伟，刘成禹，等. 考虑张拉与剪切破坏的土坡稳定数值分析[J]. 岩石力学与工程学报，2008，27(2)：375–382.(DAI Zihang，LIU Zhiwei，LIU Chengyu，et al. Numerical analysis of soil slope stability considering tension and shear failure[J]. Chinese Journal of Rock Mechanics and Engineering，2008，27(2)：375–382.(in Chinese))
[22] GRECO V R. Efficient Monte Carlo technique for locating critical slip surface[J]. Journal of Geotechnical Engineering，1996，122(7)：517–525.
[23] ARAI K，TAGYO K. Determination of noncircular slip surface giving the minimum factor of safety in slope stability analysis[J]. Soils and Foundations，1985，25(1)：43–51.
[24] SRIDEVI B. Application of globaloptimization technique to slope-stability analysis[J]. Procintsympon Landslides，1992，12(1)：26–29.
[25] 孙 聪，李春光，郑 宏，等. 同时考虑张拉及剪切破坏的边坡上限原理有限元法[J]. 岩石力学与工程学报，2015，34(增1)：2 783–2 791. (SUN Cong，LI Chunguang，ZHENG Hong，et al. Finite element method based on the upper limit principle of slope considering both tensile and shear failure[J]. Chinese Journal of Rock Mechanics and Engineering，2015，34(Supp.1)：2 783–2 791.(in Chinese))
2024, Vol. 43 
