边坡稳定三维有限元直接搜索法及其在隧道施工中的应用
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摘要
对边坡稳定直接采用三维方法进行分析具有重要的理论和现实意义，本文对边坡稳定三维分析的基本方法做了比较系统的总结，并指出各种方法存在的问题，同时提出一种基于三维有限元应力场计算边坡安全系数与直接搜索临界滑裂面的新方法。该方法克服了三维极限平衡分析方法在理论上引入较多假设条件，且搜索临界滑裂面困难的问题；它直接采用三维有限元应力场，不同于三维有限元强度折减法基于虚拟荷载上得出的实用价值；同时异于沿用极限平衡理论的有限元法仍需要进行条柱划分，并事先假设滑裂面形状及位置的缺点。在这种方法中，临界滑裂面上的应力分布直接使用三维有限元计算的应力结果，并且直接利用三维有限元的单元体网格面作为滑移面搜索网格面，鉴于有限元单元体网格和图的直观相似性，可以把网格抽象成图，通过引用动态规划中最优化思想搜索临界滑裂面。本文方法不需要假定三维滑裂面的形状与位置，只需通过构筑滑动模式，搜索出来的临界滑裂面是由单元体的网格面以边相互连接而成的一个空间曲面。
本文通过对三维有限元直接搜索法的研究，并将其应用于隧道边坡的稳定性分析中，主要的研究内容有：
1、研究了动态规划原理及其在三维边坡稳定性分析中的应用，引入图论概念，构筑出一种边坡三维滑裂面的滑动模式，借助一个包含安全系数的辅助函数并通过动态搜索求得临界滑裂面与最小安全系数；
2、采用C++程序设计语言，编制出边坡三维稳定性分析以及直接搜索法的程序，通过一些算例的对比分析，验证本文方法的适用性，并讨论了三维分析中的一些影响因素。
3、结合隧道边坡的不同实际情况，考虑施工开挖过程、衬砌结构及降雨渗流等方面的因素，利用本文方法研究对其稳定性的影响和规律，并提出处理措施。
It is very important academic and practical significance to use 3D method directly in the slope stability analysis. Systemic summary to the essential method of 3D slope stability analysis and their problems are presented in this paper. Simultaneously a new method to calculate the safety factor and search critical slip surface based on 3D FEM's stress result is given in this paper too. This method overcome the problems of many supposition conditions in theory and difficulty in searching critical slip surface in 3D limiting equilibrium analysis; It uses the 3D FEM's stress field directly, differs from the practical value of 3D FEM strength reduction method used hypothesized load, and differs from the characteristic of the FEM with limiting equilibrium theory still to need to divide the columniation, and suppose the critical slip surface in advance. In this method, stresses acting along the critical slip surface are computed using 3D FEM analysis, moreover the 3D FEM mesh is used directly as the searching grid. In view of the fact that it is intuitionistic similarity between a FEM mesh and a graph, the mesh may be abstract to a graph, and the optimized thought in dynamic programming may be used to search. This method does not need to suppose the shape and position of 3D critical slip surface, only through the construction of glide pattern, and the searched critical slip surface is a space surface which connects mutually by the grid surface.
Through the research of direct search method based on 3D FEM, and its application for the tunnel slope stability analysis, the objectives of this work in this paper are as follows:
1. The dynamic programming as well as its application for 3D side slope stability analysis is studied. With the introduction of graph theory concept, one kind of glide pattern of 3D slope is constructed, and the critical slip surface with smallest safety factor is searched with the aid of one auxiliary function including safety factor;
2. Using the C++ programming language, the 3D slope stability analysis and the direct search procedure is established, and this method is testified applicably by some contrast analysis, also some influence factor in analysis is discussed;
3. Integrated with the different actual situation in tunnel slope, considered its excavation, timbering and rain infiltration, its stability influence and rule is researched used this method, also some processing measure is proposed.
本文通过对三维有限元直接搜索法的研究，并将其应用于隧道边坡的稳定性分析中，主要的研究内容有：
1、研究了动态规划原理及其在三维边坡稳定性分析中的应用，引入图论概念，构筑出一种边坡三维滑裂面的滑动模式，借助一个包含安全系数的辅助函数并通过动态搜索求得临界滑裂面与最小安全系数；
2、采用C++程序设计语言，编制出边坡三维稳定性分析以及直接搜索法的程序，通过一些算例的对比分析，验证本文方法的适用性，并讨论了三维分析中的一些影响因素。
3、结合隧道边坡的不同实际情况，考虑施工开挖过程、衬砌结构及降雨渗流等方面的因素，利用本文方法研究对其稳定性的影响和规律，并提出处理措施。
It is very important academic and practical significance to use 3D method directly in the slope stability analysis. Systemic summary to the essential method of 3D slope stability analysis and their problems are presented in this paper. Simultaneously a new method to calculate the safety factor and search critical slip surface based on 3D FEM's stress result is given in this paper too. This method overcome the problems of many supposition conditions in theory and difficulty in searching critical slip surface in 3D limiting equilibrium analysis; It uses the 3D FEM's stress field directly, differs from the practical value of 3D FEM strength reduction method used hypothesized load, and differs from the characteristic of the FEM with limiting equilibrium theory still to need to divide the columniation, and suppose the critical slip surface in advance. In this method, stresses acting along the critical slip surface are computed using 3D FEM analysis, moreover the 3D FEM mesh is used directly as the searching grid. In view of the fact that it is intuitionistic similarity between a FEM mesh and a graph, the mesh may be abstract to a graph, and the optimized thought in dynamic programming may be used to search. This method does not need to suppose the shape and position of 3D critical slip surface, only through the construction of glide pattern, and the searched critical slip surface is a space surface which connects mutually by the grid surface.
Through the research of direct search method based on 3D FEM, and its application for the tunnel slope stability analysis, the objectives of this work in this paper are as follows:
1. The dynamic programming as well as its application for 3D side slope stability analysis is studied. With the introduction of graph theory concept, one kind of glide pattern of 3D slope is constructed, and the critical slip surface with smallest safety factor is searched with the aid of one auxiliary function including safety factor;
2. Using the C++ programming language, the 3D slope stability analysis and the direct search procedure is established, and this method is testified applicably by some contrast analysis, also some influence factor in analysis is discussed;
3. Integrated with the different actual situation in tunnel slope, considered its excavation, timbering and rain infiltration, its stability influence and rule is researched used this method, also some processing measure is proposed.
引文
[1] Abdallah, I.H., Waleed, F.H., Sarada, K.S. Global search method for locating general slip surface using Monte Carlo Techniques [J]. J.of Geotech. and Geoenviro. Engng., ASCE, 2001,127: 688-698.
[2] Ahmed, M.H., Thomas, F. Wolff. Search algorithm for minimum reliability index of earth slopes. Journal of Geotechnical and Geoenvironmental Engineering 1999, 125(4):301-308.
[3] 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.
[4] Anthony, T.G. Genetic algorithm search for critical slip surface in multiple-wedge stability analysis [J]. Can. Geotech. J, 1999,36:382-391.
[5] Baker, R. Determination of Critical Slip Surface in Slope Stability Computation [J]. Int. J. for Numer. and Analytical Meth. In Geomech., 1980,4: 333-359.
[6] Baker, R., Garber, M. Variation approach to slope stability [J].Proc.9th Int. Conf. on Soil Mech. and Found. Engng. [C]. 1977,2:9-12.
[7] Bathe, K.J. Finite element procedures in engineering analysis. Prentice-Hall. 1982.
[8] Bellman, R. Dynamic programming. Princeton University press, Princeton, New Jersey, USA. 1957.
[9] Belytschko, T., Liu, Y. and Gu, L. Element Free Galerkin Methods. International Journal of Numerical Methods in Engineering, 1994, 37: 229-256.
[10] Bishop, A.W. The Use of the Slip Circle in Stability Analysis of Slopes. Geotechnique, 1955, 5(1): 7-17.
[11] Chen, R.H., Chameau, J.L. Three-dimensional limit equilibrium analysis of slopes[J]. Geotechnique, 1982, 32 (1): 31-40.
[12] Chen, Z.Y., et al. A three-Dimensional Slope Stability Analysis Method Using the Upper Bound Theorem. Part I: Theory and Methods [J]. International Journal of Rock Mechanics and Mining Sciences, 2001, 38: 369-378.
[13] Chen, Z.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: 379-397.
[14] Chen, Z.Y. and Morgenstern, N.R. Extensions to the Generalized Method of Slices for Stability Analysis, Canadian Geotechnical Journal, 1983,20(1): 104-119.
[15] Chen, Z.Y. and Shao, C. Evaluation of minimum factor of safety in slope stability analysis [J]. Canadian Geotechnical Journal, 1988, 25: 735-748.
[16] Chen, Z.Y. Random trials used in determining global minimum factors of safety of slopes. Canadian Geotechnical Journal, 1992.29(2):225-233.
[17] Chen, W.F. Limit Analysis and Soil Plasticity. Elsevier Amsterdam, 1975.
[18] Chen, W.E, Mizuno, E. Nonlinear Analysis in Soil Mechanics:Theory and Implementation. Netherlands: Elsevire Science Publishers B.V. 1990.
[19] Cheng, Y.M. Location of critical failure surface and some further studies on slope stability analysis [J]. Computers and Geotechnics, 2003, 30: 255-267.
[20] Chugh, A.K.S. STAB2 - Slope Stability Analysis Program, U.S. Bureau of Reclamation, Denver, Colo. 1992.
[21] Celestino, T.B. and Duncan, J.M. Simplified search for non-circular slip surfaces. In Proceedings of the International Conference on Soil Mechanics and Foundation Engineering, Stockholm, 1981.3: 391-394.
[22] COLBYC.SWAN, YOUNG-KYOSEO. Limit state analysis of earthen slopes using dual CONTINUUM/FEM approaches. Int.J.Numer.Anal.Meth.Geomech. 1999, 23:1359-1371.
[23] Consortium for mathematics and its applications(COMAP). 数学的原理与实践. 北京: 高等教育出版社. 1998.
[24] Cundall, P.A. and Hut, R.D. Numerical Modeling of Discontinuous Proceedings of 1st U. S. Conference on Discrete Element Methods (DEM). CSM Press, 1989.
[25] Dawson, E.M., Roth, W.H., Drescher, A. Slope stability analysis by strength reduction[J]. Geotechnique, 1999, 49(6): 835-840.
[26] Da-Yong Zhu. A method for locating critical slip surfaces in slope stability.2001.
[27] De Josselin, De Jong G. Application of the calculus of variation to vertical cut off in cohesive frictionless soil [J]. Geotechnique,1980, 30(1):1-16.
[28] De Natale, J.S. Raped identification of critical slip surface: structure[J]. J. Geotech. Engng., ASCE,1991, 177(10):1,568-58.
[29] Donald, I.B., Tan, C.P. And Goh, T.C.A. Stability ofgeomechanical structures assessed by finite element method. Proc. 2nd Int. Conf. In Civil Engr. Hangzhou, Science Press. Beijing. 1985.845-856.
[30] Donald, I.B. Finite element assessment of slope stability. Australian-China Landslide Seminiar,1993,3-18, July, 1-42.D1-D8.
[31] Donald, I., Chen, Z.Y. Slope stability analysis by the upper bound approach: fundamentals and methods [J]. Canadian Geotechnical Journal,1997,34(6): 853-862.
[32] Duncan, J.M. State of the Art: Limit Equilibrium and Finite Element Analysis of Slopes. Journal of Geotechnical engineering, 1996.122(7):577-596.
[33] Enoki, M., Yagi, N., Yatabe, R. Generalized slice method for slope stability [J].Soil and Foundation, JSSMFE,1990,30(2).
[34] Farias, M.M., Naylor, D.J. Safety analysis using finite elements [J]. Computers and Geotechnics, 1998,22(2): 165-181.
[35] Fredlund, D.G. and Rahardjo, H. Soil mechanics for unsaturated soils. John Wiley & Sons, Inc. 1993.
[36] Fredlund, D.G. and Scoular, R.E.G. Using limit equilibrium in finite element slope stability analysis. Slope Stability Engineering, Rotterdam, 1999:31-47.
[37] Fredlund, D.G. Analytical methods for slope stability analysis [A].Proc. of the Fourth Int. Symposium on Landslides[C]. 1984,229-250.
[38] Giam, S.K. and Donald, I.B. Determination of Critical Slip Surfaces for Slopes Via Stress-Strain Calculations 5th A.N.Z.Conf.Geomechanics, Sydney. 1988.461-464.
[39] Goh, A.T.C. Genetic algorithm search for critical slip surface in multiple-wedge stability analysis [J]. Canadian. Geotechnical Journal, 1999,36:382-391.
[40] Greco, V.R. Numerical methods for locating the critical slip surface in slope-stability analysis. In Proceedings of the International Conference on Numerical Methods in Geomechanics, Innsbruck, 1988:1219-1223.
[41] Greco, V.R. Efficient Monte Carlo technique for locating critical slip surface [J].J - Geotech. Engng., ASCE, 1996,122(7):517-525.
[42] Griffiths, D.V., Gordon, A. Fenton. Probabilistic Slope Stability Analysis by Finite Elements. Journal of Geotechnical and Geoenvironmental Engineering.2004, 130(5):507-518.
[43] Griffiths, D.V., Lane, P. A. Slope stability analysis by finite elements. Geotechnique. 1999.49(3): 387-403.
[44] Hovland, H.J. Three dimensional slope stability analysis method[J].J Geotech Engng Div, ASCE, 1997, 103(9):971-986.
[45] Hungr, O. An extension of Bishop's simplified method of slope stability analysis to three dimensions[J]. Geotechnique, 1987,37(1):113-117.
[46] Hungr, O., Salgado, F.M., Byr, P.M. Evaluation of a three dimensional method of slope stability analysis [J]. CanGenotech 1989.26:679-686.
[47] Huang, C.C., Ysai, C.C. New method for 3D and asymmetrical slope stability analysis [J]. Geotech and Geoenv Engng, 2000, 126(10):917-927.
[48] Huang, Y.H. Stability analysis of earths lopes [M].Van Nostrand Reinhold Company, New York, 1983.
[49] Hutchinson, J.N., Sarma, S.K. Discussion on three dimensional limit equilibrium analysis of slope[J]. Geotechnique, 1985,35:215-216.
[50] Itasca. FLAC - Fast Lagrangian Analysis of Continua. Itasca Consulting Group, Minneapolis, Minn. 1995.
[51] I．M．Smith，D．VGrimth．有限单元法编程．北京：电子工业出版社．2003．
[52] Janbu, N. Stability analysis of slopes with dimensionless parameters. Harvard Soil Mechanics Series,1954,46:811-815.
[53] J.B.Lechman, D.V.Griffiths. Analysis of the Progression of Failure of Earth Slopes by Finite Elements.2000.
[54] J.P.Carter, C.S.Desai, D.M.Potts, H.ESchweiger, S.W.Sloan. Computing and computer modeling in geotechnical engineering, at Lancaster.2000.
[55] John Krahn. The limits of limit equilibrim analysis.2001.
[56] K.J.Bath. Finite Element Procedures. New Jersey: Prentice Hall. 1996.
[57] Krahn, J. The limits of limit equilibrium analysis. An Earth Odyssey, Calgary, Canada.2001.
[58] Kulhawy, F.H. Finite element analysis of the behavior of embankments. Ph.D. thesis, University of California, Berkley, CL, USA. 1969.
[59] Lam, L, Fredlund, D.G. A general limit equilibrium method for three-dimensional slope stability analysis[J].Can Geotech J, 1993,30:905-919.
[60] Leshchinsky, D., Baker, R.,Silver, M.L. Three-dimensional analysis of slope stability [J]. International Journal for Numerical and Analytical Method in Geomechanics,1985,9: 199-223.
[61] Leshchinsky, D., Huang, C.C. Generalized three-dimensional slope stability analysis[J]. Geotech Engng,ASCE,1992,118(11):1748-1764.
[62] Lefebvre, G. STABR user's manual [M]. Dept.of Civil Engineering, The Univ. of California at Berkeley, 1971.
[63] Li, K.S. and White, W. Rapid evaluation of the critical slip surface in slope stability problems. International Journal for Numerical and Analytical Methods in Geomechanics, 1987,11:449-473.
[64] Luceno, A., Castillo, E. Evaluation of variational methods in slope Analysis [A]. Proc. 1st Int. Symp on Landslides[C]. Meerut: Sarita Prakashan, New Delhi, 1980:255-258
[65] Lysmer, J. Limit Analysis of Plane Problems in Soil Mechanics. Journal of the Soil Mechanics and Foundations Division, ASCE, 1970,96 (4): 1311-1333.
[66] Maikawi, A.I.H., Hassan. W.F, Sarma, S.K. Global search method for locating general slip surface using Monte Carlo Techniques[J]. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 2001,127(8):688-698.
[67] Matsui, T., San, K.C. Finite element slope stability analysis by shear strength reduction technique[J]. Soils and Foundations, 1992, 32(1):59-70.
[68] M.A.Crisfield. Non-Linear Finite Element Analysis of Solids and Structures. John Wiley & Sons; New Ed edition. 1996.
[69] Majid, T, Manzari Mohamed, A. Nour. Significance of soil dilatancy in slope stability analysis. Journal of Geotechnical and Geoenvironmental Engineering. 2000,126(1):75-80.
[70] Manzari, M.T., Nour, M.A. Significance of soil dilatancy in slope stability analysis [J]. Journal of Geotechnical and Geoenvironmental Engineering ASCE 2000 126(1): 75-80.
[71] Morgenstern, N.R. and Price, V.E. The Analysis of the Stability of General Slip Surfaces. Geotechnique, 1965,15(1): 79-93.
[72] Nguyen, V.U. Determination of critical slope failure surfaces. Journal of Geotechnical Engineering, ASCE,1985,111(2):238-250.
[73] Nguyen, T.M.T. Solution of saturated/unsaturated seepage problems using a general partial differential equation solver. M.Sc. thesis, University of Saskatchewan, Saskatoon, Canada. 1999.
[74] Owen, D.R.J., Hinton, E. Finite Element in Plasticity: Theory and Practice. Swansea: Pineridge Press Limited analysis. Can.Geotech.J. 1980,38:328-337.
[75] Pham, Ha.T.V. Dynamic Programming. Method In Slope Stability. Computations.2003.
[76] Pham, Ha.T.V., Fredlund, D.G. The application of dynamic programming to slope stability analysis [J]. Canadian Geotechnical Journal,2003,40:830-847.
[77] Pham, Ha.T.V. Slope stability analysis using dynamic programming method combined with a finite element stress analysis. M.Sc. thesis, University of Saskatchewan, Saskatoon, SK, Canada. 2002.
[78] Ramamurthy, T., Narayan, C.G.P., Bhatkar, V.P. Variational method for slope stability analysis[A]. Proc. 9th Int. Conf. on Soil Mech.and Found. Engng.[C].1977(3): 139-142.
[79] Rao, S.S. Optimization: Theory and application[M]. New Delhi: Wiley Eastern Ltd,1984.
[80] Revilla, J.,Castillo, E. The calculus of variations applied to stability of slopes[J]. Geotechniaue. 1977.27(1): 1-11.
[81] Richard，A．Brualdi．组合数学．北京：机械工业出版社．2002．
[82] Robert Sedgewick. Algorithms in C-Graph algorithms. 北京: 中国电力出版社. 2003.
[83] Rocscience Inc. Application of the Finite Element Method to Slope Stability.
[84] Rocscience Inc. Critical Slip Surface Search Methods in Slide.
[85] Spencer, E. A Method for Analysis of the Stability of Embankments Assuming Parallel Interslice Forces. Geotechnique, 1967, 17(1):11-26.
[86] Spencer, E. The thrust-line criterion in embankment stability analysis [J]. Geotechnique, 1973, 3: 85-101.
[87] Sarma, S.K. Stability Analysis of Embankments and Slopes. Gertechnique, 1973, 23 (3): 423-433.
[88] Sloan, S.W. Lower Bound Limit Analysis Using Finite Elements and Linear Programming. International Joarnal for Numerical and Analytical Methods in Geomechanics, 1988,12(1): 61-67.
[89] Sloan, S.W. Upper Bound Limit Analysis Using Finite Elements and Linear Programming. International Journal for Numerical and Analytical Methods in Garmmhanies. 1988, 13(3): 263-282.
[90] Shi, G.H. Discontinuous Deformation Analysis: A New Numerical Model for the Statics and Dynamics of Block Systems. Ph. D Dissertation, University of California, Berkeley, 1988.
[91] Shi, G.H. Manifold Method. Proceedings of the First International Forum on Discontinuous Deformation Analysis(DDA) and Simulation of Discontinuous Media (Edited by Salami M R and Banks D), Berkeley, California, 1996, 52-204.
[92] Siegel, R.A. Computer analysis of general slope stability problems [M]. Res. Report No. JHRP-75-8, Engineering Experiment Station,Purdue University, West Lafayette, Ind., 1975.
[93] Siegel, R.A., Kovacs, W.D., Lovell, C.W. Random surface generation in stability analysis [J].J. Geotech. Engng., ASCE, 1981, 107(7):996-1002.
[94] Stark, T.D. and Eid, H.T. Performance of three-dimensional slope stability analysis method in Practice. ASCE Journal of Geotechnical Engineering.1998.124:1049-1060.
[95] Swamy，M．N．S．，Thulasiraman，K．图，网络与算法．北京：高等教育出版社．1988．
[96] Tamotsu Matsui, Ka-Ching San. Finite element slope stability analysis by shear strength reducation technique. Soils and Foundations. 1992, 32(1):59-70.
[97] Thomas, H.C., Charles, E. Leiserson Donald L. Rivest Clifford Stein. Introduction to Algorithms. 2001.
[98] Ugai, K. A method of calculation of total factor of safety of slopes by elaso-plastic FEM[J]. Soils and Foundations, 1989, 29(2): 190-195.
[99] William, P. Soil Mechanics Concepts and Applications[M].London Weinheim. 1977, 302-303.
[100] Xiao-Li Yang, Jian-Hua Yin. Slope Stability Analysis with Nonlinear Failure Criterion. Journal of Engineering Mechanics. 2004, 130(3):267-273.
[101] Yamagami, T. and Ueta ,Y. Search for critical slip lines in finite element stress field by dynamic programming. In Proceedings of the International Conference on Numerical Methods in Geomechanics, Innsbruck,1988,1347-1352.
[102] Yamagami, T., Ueta ,Y. Search for noncircular slip surfaces by the Morgenstern-Price method. Proc. of 6th Int. Conf. on Numerical Methods in Geomechanics [J]. Innsbruck, 1988. 1335-1340.
[103] Yamagami, T., Jiang, J.C. A search for the critical slip surface in three-dimensional slope stability analysis[J].Soils and Foundations, 1997,37(3): 1-16.
[104] Zhang, X. Three-dimensional stability analysis of concave slopes in plan view. ASCE Journal of Geotechnical Engineering, 1988, 114: 658-671.
[105] Zienkiewicz, O.C., Zhu, J.Z. The superconvergent patch recovery (SPR) and adaptive finite element refinement[J].Computer Methods in Applied Mechanics and Engineering, 1992,101: 207-224.
[106] Zienkiewicz, O.C., Taylor, R.L. The Finite Element Method. Butterworth-Heinemann. 2000.
[107] Zou, J.Z., Williams, D.J. and Xiong, W.L. Search for critical slip surfaces based on finite element method. Canadian Geotechnical Journal. 1995, 32: 233-246.
[108] 曹文贵，颜荣贵．边坡非圆临界滑动面确定之动态规划法研究[J]．岩石力学与工程学报，1995，(4)：320-328．
[109] 成岩等．C++语言与应用基础．北京．科学出版社．2002．
[110] 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．
[111] 陈祖煜．岩质边坡稳定分析----原理·方法·程序[M]，北京：中国水利水电出版社．2005．
[112] 陈祖煜，张宏亮，汪小刚．边坡稳定三维分析的极限平衡法．岩土工程学报，2001，23(5)：525-529．
[113] 陈祖煜，邵长明．最优化方法在确定边坡最小安全系数方面的应用．岩土工程学报，1998，10(4)：1-13．
[114] 陈惠发．极限分析与土体塑性．北京：人民交通出版社，1995．
[115] 冯树仁，丰定祥，葛修润，谷先荣．边坡稳定性的三维极限平衡分析方法及应用．岩土工程学报，1999．21(6)：657-661．
[116] 杜建成，黄大寿，胡定．边坡稳定的三维极限平衡分析法．四川大学学报(工程科学版)2001，33(4)：9-12．
[117] 方建瑞，李志高，朱合华．弧长法在边坡稳定非线性有限元分析中的应用．水利学报，2006，37(9)：1142-1146．
[118] 丰定祥，吴家秀，葛修润．边坡稳定性分析中几个问题的探讨．岩土工程学报，1990，12(3)：1-9．
[119] 龚晓南．土工计算机分析．北京：中国建筑工业出版社．2000．
[120] 龚晓南．高等土力学．杭州：浙江大学出版社．1996．
[121] 龚晓南．土塑性力学．杭州：浙江大学出版社．1997．
[122] 高大钊．土力学与基础工程．北京：中国建筑工业出版社．1998．
[123] 黄俊，王晓形，刘学增，丁文其．边坡影响下的连拱隧道施工方案优化分析[J]．地下空间与工程学报，2007，3(2)：272-276．
[124] 江见鲸．土建工程常见程序选编[M]．北京：水利电力出版社，1987．
[125] 李国英，沈珠江．下限原理有限单元法及其在土工问题的应用．岩土工程学报，1997，19(5)：84-89．
[126] 李京山等．C++语言基础与编程技术．北京-航宇出版社．1994．
[127] 李新星，朱合华，蔡永昌，丁文其．连拱隧道施工方法对边坡稳定性的影响分析[J]．地下空间与工程学报，2007，3(3)：483-487．
[128] 栾茂田，林皋，郭莹．土体稳定分析的改进滑楔模型及其应用[J]．岩土工程学报，1995(4)．
[129] 栾茂田，黎勇，杨庆．非连续变形计算力学模型在岩体边坡稳定性分析中的应用．岩石力学与工程学报，2000，19(3)：289-294．
[130] 栾茂田，武亚军，年廷凯．强度折减有限元法中边坡失稳的塑性区判据及其应用闭．防灾减灾工程学报，2003，23(3)：1-8．
[131] 莫海鸿，唐超宏，刘少跃．应用模式搜索法寻找最危险滑动圆弧[J]．岩土工程学报，1999，21(6)：696-699．
[132] 倪恒，刘佑荣，龙治国．正交设计在滑坡敏感性分析中的应用．岩石力学与工程学报，2002，21(7)：989-992．
[133] 钱家欢，殷宗泽．土工原理与计算．北京：中国水利水电出版社．1996．
[134] 邵龙潭，唐洪祥，韩国城．有限元边坡稳定分析方法及其应用．计算力学学报，2001，18(1)：81-87．
[135] 宋二祥．土工结构安全系数的有限元计算[J]．岩土工程学报，1997，19(2)：1-7．
[136] 史恒通，王成华．土坡有限元稳定分析若干问题的探讨[J]．岩土力学，2000，21(2)：152-155．
[137] 孙君实．条分法的数值分析[J]．岩土工程学报，1984，6(2)：1-12．
[138] 唐焕文．实用最优化方法[M]．大连理工出版杜，2000．
[139] 田荣．连续与非连续变形分析的有限覆盖无单元方法及其应用研究．大连理工大学博士学位论文，2000．12．
[140] 王恭先．面向21世纪我国滑坡灾害防治的思考．兰州滑坡泥石流学术研讨会文集．兰州大学出版社，文集编委会主编．1998，1-8．
[141] 王成华，夏绪勇．边坡稳定分析中的临界滑动面搜索方法述评．四川建筑科学研究，2002，28(3)：34-39．
[142] 王勖成，邵敏．有限单元法基本原理和数值方法．北京：清华大学出版社．1997．
[143] 王立成，李俊杰．边坡三维稳定分析的数学规划法．西部探矿工程，2003，10：38-40．
[144] 王建秀．连拱隧道边坡变形的三维监测分析．岩石力学与工程学报，2006，25(11)：2226-2232．
[145] 吴家龙．弹性力学．高等教育出版社，2002．
[146] 谢康和，周建．岩土工程有限元分析理论与应用．北京：科学出版社．2002．
[147] 阎中华．均质土坝与非均质土坝稳定安全系数极值分布规律及电算程序简介[J]．水利 水电技术，1983，(7)．
[148] 张国祥，刘宝深．边坡滑动面三维空间有限元分析．中国公路学报,2003．16(4)：25-29．
[149] 张国祥．三维边坡滑动面及稳定性的非线性弹塑性有限元分析[n]．长沙：长沙铁道学院，1999．
[150] 张鲁渝，郑颖人，赵尚毅，时卫民．有限元强度折减系数法计算土坡稳定安全系数的精度研究[J]．水利学报，2003，1(1)：21-27．
[151] 张孟喜，陈炽照．土坡稳定分析的有限元追踪法[J]．岩土工程学报，1991(6)：35-41．
[152] 张延军．边坡渗流耦合变形分析方法的研究及其应用[J]．吉林大学学报(地球科学版)，2006，36(1)：103-107．
[153] 章根德．土的本构模型及其工程应用．北京：科学出版社．1995．
[154] 赵尚毅．用有限元强度折减法求边坡稳定安全系数．岩土工程学报，2002，24(3)：343-346．
[155] 赵尚毅，时卫民，郑颖人．边坡稳定性分析的有限元法．地下空间，2001，21(5)：450-454．
[156] 赵尚毅．有限元强度折减法及其在土坡与岩坡中的应用．后勤工程学院，2004．
[157] 郑颖人，赵尚毅，时卫民．边坡稳定分析的一些进展．地下空间，2001，21(4)：262-271．
[158] 郑颖人，赵尚毅，张鲁渝．用有限元强度折减法进行边坡稳定分析[J]．中国工程科学，2002，4(10)：57-61．
[159] 郑颖人，龚晓南．岩土塑性力学基础[M]．北京：中国建筑工业出版社，1989．
[160] 郑颖人，沈珠江，龚晓南．岩土塑性力学原理．北京：中国建筑工业出版社．2002．
[161] 周文通．最优化方法在土坝稳定分析中的应用[J]．土石坝工程，1984,(2)．
[162] 朱伯芳．有限单元法原理与应用．北京：中国水利水电出版社．1998．
[163] 朱大勇．边坡临界滑动场及其数值模拟．岩土工程学报，1997，19(1)：63-68．
[164] 朱大勇，周早生．边坡全局临界滑动场(GCSF)理论及工程应用[J]，土木工程学报，1999，32(3)：66-72．
[165] 朱合华，李新星，蔡永昌，丁文其．隧道施工中洞口边仰坡稳定性三维有限元分析[J]．公路交通科技，2005，22(6)：119-122．
[2] Ahmed, M.H., Thomas, F. Wolff. Search algorithm for minimum reliability index of earth slopes. Journal of Geotechnical and Geoenvironmental Engineering 1999, 125(4):301-308.
[3] 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.
[4] Anthony, T.G. Genetic algorithm search for critical slip surface in multiple-wedge stability analysis [J]. Can. Geotech. J, 1999,36:382-391.
[5] Baker, R. Determination of Critical Slip Surface in Slope Stability Computation [J]. Int. J. for Numer. and Analytical Meth. In Geomech., 1980,4: 333-359.
[6] Baker, R., Garber, M. Variation approach to slope stability [J].Proc.9th Int. Conf. on Soil Mech. and Found. Engng. [C]. 1977,2:9-12.
[7] Bathe, K.J. Finite element procedures in engineering analysis. Prentice-Hall. 1982.
[8] Bellman, R. Dynamic programming. Princeton University press, Princeton, New Jersey, USA. 1957.
[9] Belytschko, T., Liu, Y. and Gu, L. Element Free Galerkin Methods. International Journal of Numerical Methods in Engineering, 1994, 37: 229-256.
[10] Bishop, A.W. The Use of the Slip Circle in Stability Analysis of Slopes. Geotechnique, 1955, 5(1): 7-17.
[11] Chen, R.H., Chameau, J.L. Three-dimensional limit equilibrium analysis of slopes[J]. Geotechnique, 1982, 32 (1): 31-40.
[12] Chen, Z.Y., et al. A three-Dimensional Slope Stability Analysis Method Using the Upper Bound Theorem. Part I: Theory and Methods [J]. International Journal of Rock Mechanics and Mining Sciences, 2001, 38: 369-378.
[13] Chen, Z.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: 379-397.
[14] Chen, Z.Y. and Morgenstern, N.R. Extensions to the Generalized Method of Slices for Stability Analysis, Canadian Geotechnical Journal, 1983,20(1): 104-119.
[15] Chen, Z.Y. and Shao, C. Evaluation of minimum factor of safety in slope stability analysis [J]. Canadian Geotechnical Journal, 1988, 25: 735-748.
[16] Chen, Z.Y. Random trials used in determining global minimum factors of safety of slopes. Canadian Geotechnical Journal, 1992.29(2):225-233.
[17] Chen, W.F. Limit Analysis and Soil Plasticity. Elsevier Amsterdam, 1975.
[18] Chen, W.E, Mizuno, E. Nonlinear Analysis in Soil Mechanics:Theory and Implementation. Netherlands: Elsevire Science Publishers B.V. 1990.
[19] Cheng, Y.M. Location of critical failure surface and some further studies on slope stability analysis [J]. Computers and Geotechnics, 2003, 30: 255-267.
[20] Chugh, A.K.S. STAB2 - Slope Stability Analysis Program, U.S. Bureau of Reclamation, Denver, Colo. 1992.
[21] Celestino, T.B. and Duncan, J.M. Simplified search for non-circular slip surfaces. In Proceedings of the International Conference on Soil Mechanics and Foundation Engineering, Stockholm, 1981.3: 391-394.
[22] COLBYC.SWAN, YOUNG-KYOSEO. Limit state analysis of earthen slopes using dual CONTINUUM/FEM approaches. Int.J.Numer.Anal.Meth.Geomech. 1999, 23:1359-1371.
[23] Consortium for mathematics and its applications(COMAP). 数学的原理与实践. 北京: 高等教育出版社. 1998.
[24] Cundall, P.A. and Hut, R.D. Numerical Modeling of Discontinuous Proceedings of 1st U. S. Conference on Discrete Element Methods (DEM). CSM Press, 1989.
[25] Dawson, E.M., Roth, W.H., Drescher, A. Slope stability analysis by strength reduction[J]. Geotechnique, 1999, 49(6): 835-840.
[26] Da-Yong Zhu. A method for locating critical slip surfaces in slope stability.2001.
[27] De Josselin, De Jong G. Application of the calculus of variation to vertical cut off in cohesive frictionless soil [J]. Geotechnique,1980, 30(1):1-16.
[28] De Natale, J.S. Raped identification of critical slip surface: structure[J]. J. Geotech. Engng., ASCE,1991, 177(10):1,568-58.
[29] Donald, I.B., Tan, C.P. And Goh, T.C.A. Stability ofgeomechanical structures assessed by finite element method. Proc. 2nd Int. Conf. In Civil Engr. Hangzhou, Science Press. Beijing. 1985.845-856.
[30] Donald, I.B. Finite element assessment of slope stability. Australian-China Landslide Seminiar,1993,3-18, July, 1-42.D1-D8.
[31] Donald, I., Chen, Z.Y. Slope stability analysis by the upper bound approach: fundamentals and methods [J]. Canadian Geotechnical Journal,1997,34(6): 853-862.
[32] Duncan, J.M. State of the Art: Limit Equilibrium and Finite Element Analysis of Slopes. Journal of Geotechnical engineering, 1996.122(7):577-596.
[33] Enoki, M., Yagi, N., Yatabe, R. Generalized slice method for slope stability [J].Soil and Foundation, JSSMFE,1990,30(2).
[34] Farias, M.M., Naylor, D.J. Safety analysis using finite elements [J]. Computers and Geotechnics, 1998,22(2): 165-181.
[35] Fredlund, D.G. and Rahardjo, H. Soil mechanics for unsaturated soils. John Wiley & Sons, Inc. 1993.
[36] Fredlund, D.G. and Scoular, R.E.G. Using limit equilibrium in finite element slope stability analysis. Slope Stability Engineering, Rotterdam, 1999:31-47.
[37] Fredlund, D.G. Analytical methods for slope stability analysis [A].Proc. of the Fourth Int. Symposium on Landslides[C]. 1984,229-250.
[38] Giam, S.K. and Donald, I.B. Determination of Critical Slip Surfaces for Slopes Via Stress-Strain Calculations 5th A.N.Z.Conf.Geomechanics, Sydney. 1988.461-464.
[39] Goh, A.T.C. Genetic algorithm search for critical slip surface in multiple-wedge stability analysis [J]. Canadian. Geotechnical Journal, 1999,36:382-391.
[40] Greco, V.R. Numerical methods for locating the critical slip surface in slope-stability analysis. In Proceedings of the International Conference on Numerical Methods in Geomechanics, Innsbruck, 1988:1219-1223.
[41] Greco, V.R. Efficient Monte Carlo technique for locating critical slip surface [J].J - Geotech. Engng., ASCE, 1996,122(7):517-525.
[42] Griffiths, D.V., Gordon, A. Fenton. Probabilistic Slope Stability Analysis by Finite Elements. Journal of Geotechnical and Geoenvironmental Engineering.2004, 130(5):507-518.
[43] Griffiths, D.V., Lane, P. A. Slope stability analysis by finite elements. Geotechnique. 1999.49(3): 387-403.
[44] Hovland, H.J. Three dimensional slope stability analysis method[J].J Geotech Engng Div, ASCE, 1997, 103(9):971-986.
[45] Hungr, O. An extension of Bishop's simplified method of slope stability analysis to three dimensions[J]. Geotechnique, 1987,37(1):113-117.
[46] Hungr, O., Salgado, F.M., Byr, P.M. Evaluation of a three dimensional method of slope stability analysis [J]. CanGenotech 1989.26:679-686.
[47] Huang, C.C., Ysai, C.C. New method for 3D and asymmetrical slope stability analysis [J]. Geotech and Geoenv Engng, 2000, 126(10):917-927.
[48] Huang, Y.H. Stability analysis of earths lopes [M].Van Nostrand Reinhold Company, New York, 1983.
[49] Hutchinson, J.N., Sarma, S.K. Discussion on three dimensional limit equilibrium analysis of slope[J]. Geotechnique, 1985,35:215-216.
[50] Itasca. FLAC - Fast Lagrangian Analysis of Continua. Itasca Consulting Group, Minneapolis, Minn. 1995.
[51] I．M．Smith，D．VGrimth．有限单元法编程．北京：电子工业出版社．2003．
[52] Janbu, N. Stability analysis of slopes with dimensionless parameters. Harvard Soil Mechanics Series,1954,46:811-815.
[53] J.B.Lechman, D.V.Griffiths. Analysis of the Progression of Failure of Earth Slopes by Finite Elements.2000.
[54] J.P.Carter, C.S.Desai, D.M.Potts, H.ESchweiger, S.W.Sloan. Computing and computer modeling in geotechnical engineering, at Lancaster.2000.
[55] John Krahn. The limits of limit equilibrim analysis.2001.
[56] K.J.Bath. Finite Element Procedures. New Jersey: Prentice Hall. 1996.
[57] Krahn, J. The limits of limit equilibrium analysis. An Earth Odyssey, Calgary, Canada.2001.
[58] Kulhawy, F.H. Finite element analysis of the behavior of embankments. Ph.D. thesis, University of California, Berkley, CL, USA. 1969.
[59] Lam, L, Fredlund, D.G. A general limit equilibrium method for three-dimensional slope stability analysis[J].Can Geotech J, 1993,30:905-919.
[60] Leshchinsky, D., Baker, R.,Silver, M.L. Three-dimensional analysis of slope stability [J]. International Journal for Numerical and Analytical Method in Geomechanics,1985,9: 199-223.
[61] Leshchinsky, D., Huang, C.C. Generalized three-dimensional slope stability analysis[J]. Geotech Engng,ASCE,1992,118(11):1748-1764.
[62] Lefebvre, G. STABR user's manual [M]. Dept.of Civil Engineering, The Univ. of California at Berkeley, 1971.
[63] Li, K.S. and White, W. Rapid evaluation of the critical slip surface in slope stability problems. International Journal for Numerical and Analytical Methods in Geomechanics, 1987,11:449-473.
[64] Luceno, A., Castillo, E. Evaluation of variational methods in slope Analysis [A]. Proc. 1st Int. Symp on Landslides[C]. Meerut: Sarita Prakashan, New Delhi, 1980:255-258
[65] Lysmer, J. Limit Analysis of Plane Problems in Soil Mechanics. Journal of the Soil Mechanics and Foundations Division, ASCE, 1970,96 (4): 1311-1333.
[66] Maikawi, A.I.H., Hassan. W.F, Sarma, S.K. Global search method for locating general slip surface using Monte Carlo Techniques[J]. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 2001,127(8):688-698.
[67] Matsui, T., San, K.C. Finite element slope stability analysis by shear strength reduction technique[J]. Soils and Foundations, 1992, 32(1):59-70.
[68] M.A.Crisfield. Non-Linear Finite Element Analysis of Solids and Structures. John Wiley & Sons; New Ed edition. 1996.
[69] Majid, T, Manzari Mohamed, A. Nour. Significance of soil dilatancy in slope stability analysis. Journal of Geotechnical and Geoenvironmental Engineering. 2000,126(1):75-80.
[70] Manzari, M.T., Nour, M.A. Significance of soil dilatancy in slope stability analysis [J]. Journal of Geotechnical and Geoenvironmental Engineering ASCE 2000 126(1): 75-80.
[71] Morgenstern, N.R. and Price, V.E. The Analysis of the Stability of General Slip Surfaces. Geotechnique, 1965,15(1): 79-93.
[72] Nguyen, V.U. Determination of critical slope failure surfaces. Journal of Geotechnical Engineering, ASCE,1985,111(2):238-250.
[73] Nguyen, T.M.T. Solution of saturated/unsaturated seepage problems using a general partial differential equation solver. M.Sc. thesis, University of Saskatchewan, Saskatoon, Canada. 1999.
[74] Owen, D.R.J., Hinton, E. Finite Element in Plasticity: Theory and Practice. Swansea: Pineridge Press Limited analysis. Can.Geotech.J. 1980,38:328-337.
[75] Pham, Ha.T.V. Dynamic Programming. Method In Slope Stability. Computations.2003.
[76] Pham, Ha.T.V., Fredlund, D.G. The application of dynamic programming to slope stability analysis [J]. Canadian Geotechnical Journal,2003,40:830-847.
[77] Pham, Ha.T.V. Slope stability analysis using dynamic programming method combined with a finite element stress analysis. M.Sc. thesis, University of Saskatchewan, Saskatoon, SK, Canada. 2002.
[78] Ramamurthy, T., Narayan, C.G.P., Bhatkar, V.P. Variational method for slope stability analysis[A]. Proc. 9th Int. Conf. on Soil Mech.and Found. Engng.[C].1977(3): 139-142.
[79] Rao, S.S. Optimization: Theory and application[M]. New Delhi: Wiley Eastern Ltd,1984.
[80] Revilla, J.,Castillo, E. The calculus of variations applied to stability of slopes[J]. Geotechniaue. 1977.27(1): 1-11.
[81] Richard，A．Brualdi．组合数学．北京：机械工业出版社．2002．
[82] Robert Sedgewick. Algorithms in C-Graph algorithms. 北京: 中国电力出版社. 2003.
[83] Rocscience Inc. Application of the Finite Element Method to Slope Stability.
[84] Rocscience Inc. Critical Slip Surface Search Methods in Slide.
[85] Spencer, E. A Method for Analysis of the Stability of Embankments Assuming Parallel Interslice Forces. Geotechnique, 1967, 17(1):11-26.
[86] Spencer, E. The thrust-line criterion in embankment stability analysis [J]. Geotechnique, 1973, 3: 85-101.
[87] Sarma, S.K. Stability Analysis of Embankments and Slopes. Gertechnique, 1973, 23 (3): 423-433.
[88] Sloan, S.W. Lower Bound Limit Analysis Using Finite Elements and Linear Programming. International Joarnal for Numerical and Analytical Methods in Geomechanics, 1988,12(1): 61-67.
[89] Sloan, S.W. Upper Bound Limit Analysis Using Finite Elements and Linear Programming. International Journal for Numerical and Analytical Methods in Garmmhanies. 1988, 13(3): 263-282.
[90] Shi, G.H. Discontinuous Deformation Analysis: A New Numerical Model for the Statics and Dynamics of Block Systems. Ph. D Dissertation, University of California, Berkeley, 1988.
[91] Shi, G.H. Manifold Method. Proceedings of the First International Forum on Discontinuous Deformation Analysis(DDA) and Simulation of Discontinuous Media (Edited by Salami M R and Banks D), Berkeley, California, 1996, 52-204.
[92] Siegel, R.A. Computer analysis of general slope stability problems [M]. Res. Report No. JHRP-75-8, Engineering Experiment Station,Purdue University, West Lafayette, Ind., 1975.
[93] Siegel, R.A., Kovacs, W.D., Lovell, C.W. Random surface generation in stability analysis [J].J. Geotech. Engng., ASCE, 1981, 107(7):996-1002.
[94] Stark, T.D. and Eid, H.T. Performance of three-dimensional slope stability analysis method in Practice. ASCE Journal of Geotechnical Engineering.1998.124:1049-1060.
[95] Swamy，M．N．S．，Thulasiraman，K．图，网络与算法．北京：高等教育出版社．1988．
[96] Tamotsu Matsui, Ka-Ching San. Finite element slope stability analysis by shear strength reducation technique. Soils and Foundations. 1992, 32(1):59-70.
[97] Thomas, H.C., Charles, E. Leiserson Donald L. Rivest Clifford Stein. Introduction to Algorithms. 2001.
[98] Ugai, K. A method of calculation of total factor of safety of slopes by elaso-plastic FEM[J]. Soils and Foundations, 1989, 29(2): 190-195.
[99] William, P. Soil Mechanics Concepts and Applications[M].London Weinheim. 1977, 302-303.
[100] Xiao-Li Yang, Jian-Hua Yin. Slope Stability Analysis with Nonlinear Failure Criterion. Journal of Engineering Mechanics. 2004, 130(3):267-273.
[101] Yamagami, T. and Ueta ,Y. Search for critical slip lines in finite element stress field by dynamic programming. In Proceedings of the International Conference on Numerical Methods in Geomechanics, Innsbruck,1988,1347-1352.
[102] Yamagami, T., Ueta ,Y. Search for noncircular slip surfaces by the Morgenstern-Price method. Proc. of 6th Int. Conf. on Numerical Methods in Geomechanics [J]. Innsbruck, 1988. 1335-1340.
[103] Yamagami, T., Jiang, J.C. A search for the critical slip surface in three-dimensional slope stability analysis[J].Soils and Foundations, 1997,37(3): 1-16.
[104] Zhang, X. Three-dimensional stability analysis of concave slopes in plan view. ASCE Journal of Geotechnical Engineering, 1988, 114: 658-671.
[105] Zienkiewicz, O.C., Zhu, J.Z. The superconvergent patch recovery (SPR) and adaptive finite element refinement[J].Computer Methods in Applied Mechanics and Engineering, 1992,101: 207-224.
[106] Zienkiewicz, O.C., Taylor, R.L. The Finite Element Method. Butterworth-Heinemann. 2000.
[107] Zou, J.Z., Williams, D.J. and Xiong, W.L. Search for critical slip surfaces based on finite element method. Canadian Geotechnical Journal. 1995, 32: 233-246.
[108] 曹文贵，颜荣贵．边坡非圆临界滑动面确定之动态规划法研究[J]．岩石力学与工程学报，1995，(4)：320-328．
[109] 成岩等．C++语言与应用基础．北京．科学出版社．2002．
[110] 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．
[111] 陈祖煜．岩质边坡稳定分析----原理·方法·程序[M]，北京：中国水利水电出版社．2005．
[112] 陈祖煜，张宏亮，汪小刚．边坡稳定三维分析的极限平衡法．岩土工程学报，2001，23(5)：525-529．
[113] 陈祖煜，邵长明．最优化方法在确定边坡最小安全系数方面的应用．岩土工程学报，1998，10(4)：1-13．
[114] 陈惠发．极限分析与土体塑性．北京：人民交通出版社，1995．
[115] 冯树仁，丰定祥，葛修润，谷先荣．边坡稳定性的三维极限平衡分析方法及应用．岩土工程学报，1999．21(6)：657-661．
[116] 杜建成，黄大寿，胡定．边坡稳定的三维极限平衡分析法．四川大学学报(工程科学版)2001，33(4)：9-12．
[117] 方建瑞，李志高，朱合华．弧长法在边坡稳定非线性有限元分析中的应用．水利学报，2006，37(9)：1142-1146．
[118] 丰定祥，吴家秀，葛修润．边坡稳定性分析中几个问题的探讨．岩土工程学报，1990，12(3)：1-9．
[119] 龚晓南．土工计算机分析．北京：中国建筑工业出版社．2000．
[120] 龚晓南．高等土力学．杭州：浙江大学出版社．1996．
[121] 龚晓南．土塑性力学．杭州：浙江大学出版社．1997．
[122] 高大钊．土力学与基础工程．北京：中国建筑工业出版社．1998．
[123] 黄俊，王晓形，刘学增，丁文其．边坡影响下的连拱隧道施工方案优化分析[J]．地下空间与工程学报，2007，3(2)：272-276．
[124] 江见鲸．土建工程常见程序选编[M]．北京：水利电力出版社，1987．
[125] 李国英，沈珠江．下限原理有限单元法及其在土工问题的应用．岩土工程学报，1997，19(5)：84-89．
[126] 李京山等．C++语言基础与编程技术．北京-航宇出版社．1994．
[127] 李新星，朱合华，蔡永昌，丁文其．连拱隧道施工方法对边坡稳定性的影响分析[J]．地下空间与工程学报，2007，3(3)：483-487．
[128] 栾茂田，林皋，郭莹．土体稳定分析的改进滑楔模型及其应用[J]．岩土工程学报，1995(4)．
[129] 栾茂田，黎勇，杨庆．非连续变形计算力学模型在岩体边坡稳定性分析中的应用．岩石力学与工程学报，2000，19(3)：289-294．
[130] 栾茂田，武亚军，年廷凯．强度折减有限元法中边坡失稳的塑性区判据及其应用闭．防灾减灾工程学报，2003，23(3)：1-8．
[131] 莫海鸿，唐超宏，刘少跃．应用模式搜索法寻找最危险滑动圆弧[J]．岩土工程学报，1999，21(6)：696-699．
[132] 倪恒，刘佑荣，龙治国．正交设计在滑坡敏感性分析中的应用．岩石力学与工程学报，2002，21(7)：989-992．
[133] 钱家欢，殷宗泽．土工原理与计算．北京：中国水利水电出版社．1996．
[134] 邵龙潭，唐洪祥，韩国城．有限元边坡稳定分析方法及其应用．计算力学学报，2001，18(1)：81-87．
[135] 宋二祥．土工结构安全系数的有限元计算[J]．岩土工程学报，1997，19(2)：1-7．
[136] 史恒通，王成华．土坡有限元稳定分析若干问题的探讨[J]．岩土力学，2000，21(2)：152-155．
[137] 孙君实．条分法的数值分析[J]．岩土工程学报，1984，6(2)：1-12．
[138] 唐焕文．实用最优化方法[M]．大连理工出版杜，2000．
[139] 田荣．连续与非连续变形分析的有限覆盖无单元方法及其应用研究．大连理工大学博士学位论文，2000．12．
[140] 王恭先．面向21世纪我国滑坡灾害防治的思考．兰州滑坡泥石流学术研讨会文集．兰州大学出版社，文集编委会主编．1998，1-8．
[141] 王成华，夏绪勇．边坡稳定分析中的临界滑动面搜索方法述评．四川建筑科学研究，2002，28(3)：34-39．
[142] 王勖成，邵敏．有限单元法基本原理和数值方法．北京：清华大学出版社．1997．
[143] 王立成，李俊杰．边坡三维稳定分析的数学规划法．西部探矿工程，2003，10：38-40．
[144] 王建秀．连拱隧道边坡变形的三维监测分析．岩石力学与工程学报，2006，25(11)：2226-2232．
[145] 吴家龙．弹性力学．高等教育出版社，2002．
[146] 谢康和，周建．岩土工程有限元分析理论与应用．北京：科学出版社．2002．
[147] 阎中华．均质土坝与非均质土坝稳定安全系数极值分布规律及电算程序简介[J]．水利 水电技术，1983，(7)．
[148] 张国祥，刘宝深．边坡滑动面三维空间有限元分析．中国公路学报,2003．16(4)：25-29．
[149] 张国祥．三维边坡滑动面及稳定性的非线性弹塑性有限元分析[n]．长沙：长沙铁道学院，1999．
[150] 张鲁渝，郑颖人，赵尚毅，时卫民．有限元强度折减系数法计算土坡稳定安全系数的精度研究[J]．水利学报，2003，1(1)：21-27．
[151] 张孟喜，陈炽照．土坡稳定分析的有限元追踪法[J]．岩土工程学报，1991(6)：35-41．
[152] 张延军．边坡渗流耦合变形分析方法的研究及其应用[J]．吉林大学学报(地球科学版)，2006，36(1)：103-107．
[153] 章根德．土的本构模型及其工程应用．北京：科学出版社．1995．
[154] 赵尚毅．用有限元强度折减法求边坡稳定安全系数．岩土工程学报，2002，24(3)：343-346．
[155] 赵尚毅，时卫民，郑颖人．边坡稳定性分析的有限元法．地下空间，2001，21(5)：450-454．
[156] 赵尚毅．有限元强度折减法及其在土坡与岩坡中的应用．后勤工程学院，2004．
[157] 郑颖人，赵尚毅，时卫民．边坡稳定分析的一些进展．地下空间，2001，21(4)：262-271．
[158] 郑颖人，赵尚毅，张鲁渝．用有限元强度折减法进行边坡稳定分析[J]．中国工程科学，2002，4(10)：57-61．
[159] 郑颖人，龚晓南．岩土塑性力学基础[M]．北京：中国建筑工业出版社，1989．
[160] 郑颖人，沈珠江，龚晓南．岩土塑性力学原理．北京：中国建筑工业出版社．2002．
[161] 周文通．最优化方法在土坝稳定分析中的应用[J]．土石坝工程，1984,(2)．
[162] 朱伯芳．有限单元法原理与应用．北京：中国水利水电出版社．1998．
[163] 朱大勇．边坡临界滑动场及其数值模拟．岩土工程学报，1997，19(1)：63-68．
[164] 朱大勇，周早生．边坡全局临界滑动场(GCSF)理论及工程应用[J]，土木工程学报，1999，32(3)：66-72．
[165] 朱合华，李新星，蔡永昌，丁文其．隧道施工中洞口边仰坡稳定性三维有限元分析[J]．公路交通科技，2005，22(6)：119-122．