Abstract：Research purposes: As an extension of two － dimensional FEM limit equilibrium method，the three －dimensional FEM limit equilibrium method based on the concept of strength reduction and the unique sliding direction，is presented． The definition and physical meaning of factor of safety ( FOS) ，the relationship between FOS and unique sliding direction are clarified as well as the application in earth and rock slope． On the basis of mean value theorem of integrals，the FOS corresponding to sliding body of arbitrary shape is defined． The relationship between partial FOS and overall FOS can be demonstrated by the definition of factor of safety in this approach．
Research conclusions: ( 1) the factor of safety and critical sliding surface for soil and rock slopes calculated from the proposed approach are in good agreement with those from 3D rigid limit equilibrium method and 3D shear strength reduction method． ( 2) 3D problem shouldn＇t be modeled as a 2D one owing to obvious spatial effect when the axial length of slope is short，the factor of safety obtained by 2D method is conservative． However，the stability analysis for 3D problem can be approximated by a corresponding 2D problem when the axial length of slope reaches a certain value．
李红军,邵龙潭. 有限元极限平衡法在三维边坡中的应用研究[J]. 铁道工程学报, 2011, 28(5): 17-21.
LI Hong － jun，SHAO Long － tan. Application of Three － Dimensional Finite Element Method Limit Equilibrium Method for Slope Stability Analysis. 铁道工程学报, 2011, 28(5): 17-21.
Chen Zuyu，Mi Honglia，Wang Xiaogang． A Three － dimensional Limit Equilibrium Method for Slope Stability Analysis［J］． Chinese Journal of Geotechnical Engineering，2001( 5) : 525 － 529．
Zheng Hong． A Rigorous Three － dimensional Limit Equilibrium Method ［J］． Chinese Journal of Rock Mechanics and Engineering，2007( 8) : 1529 － 1537．
［3］ 王春雷，关凤琚，韩会勋． 桥基高边坡稳定的二维、三维有限元对比分析［J］． 铁道工程学报，2010( 2) : 49 －53． Wang Chunlei， Guan Fengju， Han Huixun．
Comparative Analysis of Stability of High － Steep Slope under Bridge Load with 2D and 3D Finite Element［J］． Journal of Railway Engineering Society，2010( 2) : 49 －53．
［4］ Duncan J M． State of the art : Limit Equilibrium and Finite Element Analysis of Slopes ［J］． Journal of Geotechnical Engineering，1996( 7) : 577 － 596．
［5］ 郑颖人，陈祖煜，王恭先，等． 边坡与滑坡工程治理［M］．北京: 人民交通出版社，2007．
Zheng Yingren， Chen Zuyu， Wang Gongxian etc． Engineering Treatment of Slope ＆Landslide ［M］． Beijing: China Communications Press，2007．
［6］ W． B． Wei， Y． M． Cheng， L． Li． Three － dimensional Slope Failure Analysis by the Strength Reduction and Limit Equilibrium Methods ［J ］． Computers and Geotechnics，2008( 1) : 70 － 80．
Feng Shuren，Feng Dingxiang，Ge Xiurun，etc． 3D Limit Equilibrium Method for Slope Stability and Its Application ［J］． Chinese Journal of Geotechnical Engineering，1999( 6) : 657 － 661．
［8］ Cheng Y M，Yip C． Three － dimensional Asymmetrical Slope Stability Analysis – Extension of Bishop ’s， Janbu’s and Morgenstern － Price’s techniques［J］． J Geotechnical Geoenvironmental Engineering， ASCE， 2007( 12) : 1544 － 1555．
Fang Jianrui． Slope Stability Analysis Using Direct Search Method Based on 3D Fem and Its Application in Tunnel Excavation［D］． Shanghai: Tongji university， 2007．
［10］ Zhang X． Three － dimensional Stability Analysis of Concave Slopes in Plane View ［J］． Journal． of Geotechnical Engineering，1988( 6) : 658 － 671．
2011, Vol. 28 
版权所有 © 2014 《铁道工程学报》编辑部