路堑式坡残积土质边坡变形与稳定性的研究
摘要
边坡工程是岩土工程三大问题之一；路堑式土边坡是边坡工程中的重要类型之一；迅速发展的山区和丘陵地区的公路、铁路等交通工程建设，必然会遭遇路堑式坡残积土边坡的变形与稳定性问题。而这将是目前乃至今后相当长一段时间内需要解决的重要技术问题之一。因此，本文结合福建省交通厅科研课题《深挖路堑高填路堤的变形与稳定性的研究》以永—漳公路(永安段)K15+183工点残坡积土边坡工程实例为背景，采用非线性理论、现代监测技术和数值仿真模拟技术，从理论计算分析和现场监测分析与评价二大方面，全面系统综合地研究了路堑坡残积土质高边坡的稳定性和变形问题，主要的研究工作和工作成果概述如下：
(1)通过了解边坡变形与稳定性研究的国内外动态和发展历程，进行了系统分类和总结，并从影响土质边坡变形与稳定性的因素入手，分析了路堑边坡的地质模式与破坏形式，为路堑边坡的变形与稳定性评价提供指导和依据；(2)通过工程地质建模和数学力学建模，拟订了较为完整的路堑坡残积土质边坡变形与稳定性评价思路，并运用极限平衡法(解析法与简化毕肖普法)与数值法(非线性有限元与Ansys)相结合的复合分析法对永漳公路永安段K15+183工点路堑坡残积土质边坡的变形与稳定性进行了计算分析评价；(3)通过现场位移跟踪监测，了解并掌握了该路堑高边坡随边坡开挖过程中内部位移情况。并分析了其坡体内部土体位移发展规律；(4)基于本文的研究和前人的成果，编制相应的计算程序，进行了计算、分析与比较。并通过K15+183工点路堑土质边坡的各类位移变形的监测成果验证了该程序的正确性及适用性；(5)通过应用大型有限元软件Ansys模拟分析，不仅分析了其随着开挖时间步的应力应变关系，并模拟了与实际测斜管相匹配的测斜路径，通过对各开挖时间步的模拟计算分析，得到了与实测数据较符合的结果；(6)综合监测分析成果和极限平衡理论计算分析成果，对K15+183工点路堑边坡的原设计坡率和几何形态进行了优化计算分析，取得了较为满意的结果。
通过计算分析表明：
1、该路堑边坡自然稳定性较高，其稳定安全系数为1.47~1.59。
2、该路堑边坡开挖后侧向位移最大值为4.70cm(NLFEP)~5.38cm(Ansys)，与实测值3.5cm~5.5cm基本接近。同时边坡开挖后期坡顶会出现回弹现象。
3、数值计算成果表明，随着开挖阶数的增加，大小主应力在边坡内也进行不断的调整。边坡开挖后坡脚处大小主应力值NLFEP程序结果与Ansys计算结果较为相似，两者吻合性较好。
The slope project is one of the three big problems of geotechnical engineering; Cut soil slope is one of the important types of slope projects; Engineering construction of the traffic, such as highway, railway in the mountain area and hills area etc. is developing rapidly, which will inevitably encounter the deformation and stability of cutting cliff debris and residual soil slopes. And this will be one of the important technological problems to be solved in a quite long time at present and even in the future. Combining with the research task Researching on the deformation and stability of deep excavated cuts and high filled embankment of the Traffic Department in Fujian Province, based on the residual soil slope project on the project site at K15 +183 of Yong- Zhang highway (Yong'an section), adopting non-linear theory, modern monitoring technology and numerical simulation technology, the deformation and stability of cutting cliff debris and residual soil slopes have been studied systemically and synthetically in the thesis. At the same time theory analysis, the analysis and estimate of field monitoring are taken into account in this course. Main research work and working achievement are summed up as follows:
(1)With the acquaintance of the trends and development about the deformation and stability of slopes at home and abroad, slopes are classified and summarized systemically. In order to offer the guidance to the deformation and stability of cut slopes, the geological mode and the mode of failure of cut slopes have been analysed, considering the influence of the deformation and stability of soil slopes. (2)By building geological models and mathe-mechanical models, this context has created a clear valuation approach in research, It concluded the deformation and stability of cutting cliff debris and residual soil slopes. Using the balanced method of the utmost limits analytic method (analytic method and simplified Bishop method) and numerical analysis method (non-linear finite element Ansys). And combining with compound analysis, this thesis has calculated and estimated the deformation and stability of slopes of the cliff debris and residual soil slope project on the project site at K15 +183 of Yong'an section of Yong- Zhang highway; (3)In the course of the cut slope excavation Inner displacement has been in control of real time field monitoring. It has analysed the development of inner soil mass displacement, and also analysed the rule
of development of displacement of inner soil body of the slope. (4)Based on current research fruits, corresponding calculated procedure was programmed, which was calculated, analysed and compared. Its validity and applicability is validated by the different displacements of the slope of the project site at K15 +183 of Yong'an section of Yong-Zhang highway. (5)By the simulation and analysis of large-scale non-linear finite element soft Ansys, Not only the real tine stress- strain relation with each excavation time step is analysed, but also corresponding with the routes of the actual clinometers are simulated. The result is similar to the facts, which is approved by the simulated calculation and analysis to the each excavation time step. (6)It also uses synthetically monitoring method and utmost limits analytic theory. Through the optimized calculation and analysis of primary designed rate of slope and geometry shape at K15 +183 of Yong'an section of Yong- Zhang highway, the satisfactory achievement is obtained.
The calculating and analysis results are shown as follows:
1.The cut slope natural stability is higher and its stability safety factor is 1.47~1.59
2.The maximum lateral displacement is 4.70 cm (NLFEP)~5.38 cm (Ansys) after the excavation of the slope, it's more close with actual values, at the same time the resilience phenomenon will appear at the top of slope in the later excavation of the slope
3.The number value results indicate: with the excavation step number increasing, the major and minor principal stress values of the slope are adjusted constantly,
(1)通过了解边坡变形与稳定性研究的国内外动态和发展历程，进行了系统分类和总结，并从影响土质边坡变形与稳定性的因素入手，分析了路堑边坡的地质模式与破坏形式，为路堑边坡的变形与稳定性评价提供指导和依据；(2)通过工程地质建模和数学力学建模，拟订了较为完整的路堑坡残积土质边坡变形与稳定性评价思路，并运用极限平衡法(解析法与简化毕肖普法)与数值法(非线性有限元与Ansys)相结合的复合分析法对永漳公路永安段K15+183工点路堑坡残积土质边坡的变形与稳定性进行了计算分析评价；(3)通过现场位移跟踪监测，了解并掌握了该路堑高边坡随边坡开挖过程中内部位移情况。并分析了其坡体内部土体位移发展规律；(4)基于本文的研究和前人的成果，编制相应的计算程序，进行了计算、分析与比较。并通过K15+183工点路堑土质边坡的各类位移变形的监测成果验证了该程序的正确性及适用性；(5)通过应用大型有限元软件Ansys模拟分析，不仅分析了其随着开挖时间步的应力应变关系，并模拟了与实际测斜管相匹配的测斜路径，通过对各开挖时间步的模拟计算分析，得到了与实测数据较符合的结果；(6)综合监测分析成果和极限平衡理论计算分析成果，对K15+183工点路堑边坡的原设计坡率和几何形态进行了优化计算分析，取得了较为满意的结果。
通过计算分析表明：
1、该路堑边坡自然稳定性较高，其稳定安全系数为1.47~1.59。
2、该路堑边坡开挖后侧向位移最大值为4.70cm(NLFEP)~5.38cm(Ansys)，与实测值3.5cm~5.5cm基本接近。同时边坡开挖后期坡顶会出现回弹现象。
3、数值计算成果表明，随着开挖阶数的增加，大小主应力在边坡内也进行不断的调整。边坡开挖后坡脚处大小主应力值NLFEP程序结果与Ansys计算结果较为相似，两者吻合性较好。
The slope project is one of the three big problems of geotechnical engineering; Cut soil slope is one of the important types of slope projects; Engineering construction of the traffic, such as highway, railway in the mountain area and hills area etc. is developing rapidly, which will inevitably encounter the deformation and stability of cutting cliff debris and residual soil slopes. And this will be one of the important technological problems to be solved in a quite long time at present and even in the future. Combining with the research task Researching on the deformation and stability of deep excavated cuts and high filled embankment of the Traffic Department in Fujian Province, based on the residual soil slope project on the project site at K15 +183 of Yong- Zhang highway (Yong'an section), adopting non-linear theory, modern monitoring technology and numerical simulation technology, the deformation and stability of cutting cliff debris and residual soil slopes have been studied systemically and synthetically in the thesis. At the same time theory analysis, the analysis and estimate of field monitoring are taken into account in this course. Main research work and working achievement are summed up as follows:
(1)With the acquaintance of the trends and development about the deformation and stability of slopes at home and abroad, slopes are classified and summarized systemically. In order to offer the guidance to the deformation and stability of cut slopes, the geological mode and the mode of failure of cut slopes have been analysed, considering the influence of the deformation and stability of soil slopes. (2)By building geological models and mathe-mechanical models, this context has created a clear valuation approach in research, It concluded the deformation and stability of cutting cliff debris and residual soil slopes. Using the balanced method of the utmost limits analytic method (analytic method and simplified Bishop method) and numerical analysis method (non-linear finite element Ansys). And combining with compound analysis, this thesis has calculated and estimated the deformation and stability of slopes of the cliff debris and residual soil slope project on the project site at K15 +183 of Yong'an section of Yong- Zhang highway; (3)In the course of the cut slope excavation Inner displacement has been in control of real time field monitoring. It has analysed the development of inner soil mass displacement, and also analysed the rule
of development of displacement of inner soil body of the slope. (4)Based on current research fruits, corresponding calculated procedure was programmed, which was calculated, analysed and compared. Its validity and applicability is validated by the different displacements of the slope of the project site at K15 +183 of Yong'an section of Yong-Zhang highway. (5)By the simulation and analysis of large-scale non-linear finite element soft Ansys, Not only the real tine stress- strain relation with each excavation time step is analysed, but also corresponding with the routes of the actual clinometers are simulated. The result is similar to the facts, which is approved by the simulated calculation and analysis to the each excavation time step. (6)It also uses synthetically monitoring method and utmost limits analytic theory. Through the optimized calculation and analysis of primary designed rate of slope and geometry shape at K15 +183 of Yong'an section of Yong- Zhang highway, the satisfactory achievement is obtained.
The calculating and analysis results are shown as follows:
1.The cut slope natural stability is higher and its stability safety factor is 1.47~1.59
2.The maximum lateral displacement is 4.70 cm (NLFEP)~5.38 cm (Ansys) after the excavation of the slope, it's more close with actual values, at the same time the resilience phenomenon will appear at the top of slope in the later excavation of the slope
3.The number value results indicate: with the excavation step number increasing, the major and minor principal stress values of the slope are adjusted constantly,
引文
[1]王玮,冯治安,高建立,等.高等级公路边坡综合防护系统探讨.河南交通,1999,6
[2]杨航宇,颜志平,朱赞凌,等.公路边坡防护与冶理.北京:人民交通出版社,2002,3~7
[3]陈大勇.对高填深挖路基设计的一些看法．广西交通科技,Vol.24,No.4,1999
[4] Janbu N. Slope Stability Computations, Embankment-Dam ngineering,1973
[5] Bishop A.W. The Use of the Slip Circle in the Stability Analysis of Slopes, Geotechnique,Vol.5,No.1,1955：457～468。
[6]潘家铮．建筑物的抗滑稳定和滑坡分析．北京:水利出版社,1980
[7]张天宝.土坡稳定分析和土工建筑物的边坡设计.成都:成都科技大学出版社，1987
[8]孙君实.条分法的提法及其数值计算的最优化方法.水力发电学报,1983.1
[9]孙君实.条分法的数值分析.岩土工程学报,Vol.6,No.2,1984
[10] Chen Z. and Morgenstern N. R. Extensions to the Generalized for Earth Slopes, Geotechnique, Vol.20. No.1,1983。
[11]陈祖煜.土坡稳定分析通用条分法及其改进.岩土工程学报Vol.5, No.4,1983
[12]李守义,吕生龙,张长喜.某工程边坡蠕滑机理与监测资料分析.岩石力学与工程学报,1998.17(2)
[13]马崇武.边坡稳定性与滑坡预测预报的力学研究:[博士论文],兰州:兰州大学，1999
[14]李靖,周欣华,党进谦.黄土边坡稳定性图解法.岩土工程学报,1998.7
[15]陈新民,罗国煜.基于经验的边坡稳定性灰色系统分析与评价.岩土工程学报，1999.9
[16]辛鸿博,王余庆.岩土边坡地震崩滑及其初判准则.岩土工程学报,1999,9
[17]卢才金,胡厚田,徐建平,罗斌.改进的BP网络在岩质边坡的稳定性评判中的应用.岩石力学与工程学报,1999,6
[18]刘瑞伶,谭国焕,李启光,徐铖,等.岩石边坡稳定性和Fuzzy综合评判法.岩石力学与工程学报,1999,4
[19]廖小平.福建省公路学会第一届岩土工程学术交流会专家专题论文,2003.3
[20]邓卫东，吴光勇，唐树名.路堑边坡破坏机理的试验与计算分析.中国公路学报，Vol.14, No.3,2001
[21]王庚荪.边坡的渐近破坏及稳定性分析.岩石力学及工程学报，2000,19(1)
[22]杨明,王波,胡厚田.类土质边坡特征的初步探讨.水土保持学报, Vol.16, No.6，2002
[23]曲永新，吴宏伟，尚彦军.华南花岗岩残积土红土化程度的地带性与香港该类土不发育的原因.工程地质学报,2000, 8 (1):16～20.
[24]胡中雄.土力学与环境土工学.上海：同济大学出版社，1997
[25]黄昌乾，丁恩保.边坡工程常用稳定性分析方法.水电站设计,Vol.15, No.1 1999
[26] Whitman R. V. and Bailey, W. A. Use of Computers for Slope Stability of General Slip Surfaces, Geotechnique, Vol.15, No.1, 1965：1102～1113。
[27] Spencer. E. A Method of Analysis of the Stability of Embankments Assuming Parallel Iater-Slice Forces,Geotechnique,Vol.17,1967：1521～1534。
[28] Morgenstern N. R. and Price V. E. The Analysis of the Stability of General SlipSurfaces,Geotechnique,Vol.15,No.1,1965：93～102。
[29]交通部第二公路勘察设计院.公路路基设计规范.人民交通出版社,1996
[30] Sarma S. K. Stability Analysis of Embankments and Slopes, Geotechnique, Vol.23, No.3,1973
[31]张兴彦.京沪高速公路金山路堑边坡稳定性研究:[硕士论文].成都:西南交通大学，2000
[32]Wilson blake. Finite element model study of slope modification at the kimbley pit, Transaction of the society of mining engineering of aime, vol.24. 1996.10.4
[33] S. H. Boshkov. Determination of the stresses and Displacement in Slopes by the Finite Element Method.
[34] Zienkiewicz D. C and Chen Y. K. Application of the Finite Element Method to problem of Rockmechanice, Pro.lstcenger.intnl.Soc Rock Mechn, Vol.1996.661~666
[35] R. E. Goodman. Method of Geolegical Engineering in Discontinus Rocks, West publishion Co.1976.320~327
[36] H. D. Hibbitt, P. V. Marcal and J. R. Rice. A finite element formulation for problems of large strain and large displacement，int. J. solids structures，1970
[37] J. C. Chai. And D. T. Bergado. The analysis of grid reinforced embankment on soft clay. Computer and geotechnics，1995
[38]施斌,吴智深,李琦,村上预.边坡大变形弹塑性有限元分析.水文地质工程地质，No.2,1999
[39]魏瑛莺.复杂土坡稳定问题的非线性有限元分析:[硕士论文].福州:福州大学.2002
[40] I. B. Donald. Australian-china landslide seminar, 1993
[41] James Michael Duncan. State of the art: limit equilibrium and finite element analysis of slopes. Journal of Geotechnical Engineering, 1996,122(7): 577-596.
[42] Ugai K. A method of calculation of total factor of safety of slope by elaso-plastic FEM，Soils and Foundations，1989,29(2):190～195
[43] Matsui T. and San K C. Finite element slope stability analysis by shear strength reduction technique，Soils and Foundations，1989,32(1):59～70
[44]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，Vol.21, No.5
2001
[45]连镇营,韩国城,孔宪京.强度折减有限元法研究开挖边坡的稳定性.岩土工程学报,Vol.23, No.4,2001
[46]郑颖人,赵尚毅,时卫民,林丽.边坡稳定分析的一些进展.地下空间,Vol.21,No.4 1999
[47]江见鲸.土建工程常用微机程序汇编，北京:水利电力出版社,1987
[48]张鲁渝,时卫民,郑颖人.平面应变条件下土坡稳定有限元分析.岩土工程学报，Vol.24, No.4,2002
[49]易大义,沈云宝,李有法.计算方法.杭州:浙江大学出版社,2002
[50]杨大地,谈骏渝.实用数值分析，成都:重庆大学出版社,2000
[51]刘国明.非线性有限元分析.福州:福州大学（内部讲义）2002
[52]钱家欢,殷宗泽.土工数值分析.北京:中国铁道出版社,1991
[53]彭国伦.Fortran95程序设计.北京:中国电力出版社,2002
[54]美国Ansys公司.Ansys高级技术分析指南,1998
[55]张季如.边坡开挖的有限元模拟与稳定性评价.岩石力学与工程学报,Vo21,No,6 2001
[56]徐干成,郑颖人.岩土工程中屈服准则应用的研究.岩土工程学报,1990,12(2):
93～99
[57]戴自航,沈蒲生.莫尔—库仑等面积屈服准则的简化形式及应用.福州大学学报(自然科学版),Vol.31, No.4, 2001
[58]龚晓南.土工计算机分析.北京:中国建筑工业出版社,2000.
[59] Jiang G L and Magnan J P. Stability analysis of embankments: comparison of limit analysis with methods of slices. Geotechnique, 1997,47(4):857-872.
[60] Griffith D V and Lane P A . Slope stability analysis by finite elements,Geotechnique, 1999,49(3):387-403。
[61] Dawson E .M, Roth W H, Drescher A. Slope stability analysis by strength reduction. Geotechnique, 1999, 49(6):835-840
[62]杨英华.土力学.北京:地质出版社,1986
[63]张喜发.岩土工程勘察与评价.长春:吉林科学技术出版社.1995
[64]岩土工程手册编写委员会,岩土工程手册.北京:中国建筑工业出版社，1994
[65]朱伯芳.有限单元法原理与应用.北京:水利电力出版社，1979
[66]殷宗泽.土坝非线性有限元计算程序.南京:河海大学出版社，1992
[67]黄文熙.土的工程性质.北京:水利电力出版社,1983
[68]杨熙章.土工试验与原理.南京:同济大学出版社,1993
[69]工程地质手册(第二版).北京:中国建筑工业出版社，1987
[70]美国ANSYS公司北京办事处.APDL使用指南,1998
[71]朱益军.高速公路路堑边坡稳定性研究[硕士论文].浙江:浙江大学,2002
[2]杨航宇,颜志平,朱赞凌,等.公路边坡防护与冶理.北京:人民交通出版社,2002,3~7
[3]陈大勇.对高填深挖路基设计的一些看法．广西交通科技,Vol.24,No.4,1999
[4] Janbu N. Slope Stability Computations, Embankment-Dam ngineering,1973
[5] Bishop A.W. The Use of the Slip Circle in the Stability Analysis of Slopes, Geotechnique,Vol.5,No.1,1955：457～468。
[6]潘家铮．建筑物的抗滑稳定和滑坡分析．北京:水利出版社,1980
[7]张天宝.土坡稳定分析和土工建筑物的边坡设计.成都:成都科技大学出版社，1987
[8]孙君实.条分法的提法及其数值计算的最优化方法.水力发电学报,1983.1
[9]孙君实.条分法的数值分析.岩土工程学报,Vol.6,No.2,1984
[10] Chen Z. and Morgenstern N. R. Extensions to the Generalized for Earth Slopes, Geotechnique, Vol.20. No.1,1983。
[11]陈祖煜.土坡稳定分析通用条分法及其改进.岩土工程学报Vol.5, No.4,1983
[12]李守义,吕生龙,张长喜.某工程边坡蠕滑机理与监测资料分析.岩石力学与工程学报,1998.17(2)
[13]马崇武.边坡稳定性与滑坡预测预报的力学研究:[博士论文],兰州:兰州大学，1999
[14]李靖,周欣华,党进谦.黄土边坡稳定性图解法.岩土工程学报,1998.7
[15]陈新民,罗国煜.基于经验的边坡稳定性灰色系统分析与评价.岩土工程学报，1999.9
[16]辛鸿博,王余庆.岩土边坡地震崩滑及其初判准则.岩土工程学报,1999,9
[17]卢才金,胡厚田,徐建平,罗斌.改进的BP网络在岩质边坡的稳定性评判中的应用.岩石力学与工程学报,1999,6
[18]刘瑞伶,谭国焕,李启光,徐铖,等.岩石边坡稳定性和Fuzzy综合评判法.岩石力学与工程学报,1999,4
[19]廖小平.福建省公路学会第一届岩土工程学术交流会专家专题论文,2003.3
[20]邓卫东，吴光勇，唐树名.路堑边坡破坏机理的试验与计算分析.中国公路学报，Vol.14, No.3,2001
[21]王庚荪.边坡的渐近破坏及稳定性分析.岩石力学及工程学报，2000,19(1)
[22]杨明,王波,胡厚田.类土质边坡特征的初步探讨.水土保持学报, Vol.16, No.6，2002
[23]曲永新，吴宏伟，尚彦军.华南花岗岩残积土红土化程度的地带性与香港该类土不发育的原因.工程地质学报,2000, 8 (1):16～20.
[24]胡中雄.土力学与环境土工学.上海：同济大学出版社，1997
[25]黄昌乾，丁恩保.边坡工程常用稳定性分析方法.水电站设计,Vol.15, No.1 1999
[26] Whitman R. V. and Bailey, W. A. Use of Computers for Slope Stability of General Slip Surfaces, Geotechnique, Vol.15, No.1, 1965：1102～1113。
[27] Spencer. E. A Method of Analysis of the Stability of Embankments Assuming Parallel Iater-Slice Forces,Geotechnique,Vol.17,1967：1521～1534。
[28] Morgenstern N. R. and Price V. E. The Analysis of the Stability of General SlipSurfaces,Geotechnique,Vol.15,No.1,1965：93～102。
[29]交通部第二公路勘察设计院.公路路基设计规范.人民交通出版社,1996
[30] Sarma S. K. Stability Analysis of Embankments and Slopes, Geotechnique, Vol.23, No.3,1973
[31]张兴彦.京沪高速公路金山路堑边坡稳定性研究:[硕士论文].成都:西南交通大学，2000
[32]Wilson blake. Finite element model study of slope modification at the kimbley pit, Transaction of the society of mining engineering of aime, vol.24. 1996.10.4
[33] S. H. Boshkov. Determination of the stresses and Displacement in Slopes by the Finite Element Method.
[34] Zienkiewicz D. C and Chen Y. K. Application of the Finite Element Method to problem of Rockmechanice, Pro.lstcenger.intnl.Soc Rock Mechn, Vol.1996.661~666
[35] R. E. Goodman. Method of Geolegical Engineering in Discontinus Rocks, West publishion Co.1976.320~327
[36] H. D. Hibbitt, P. V. Marcal and J. R. Rice. A finite element formulation for problems of large strain and large displacement，int. J. solids structures，1970
[37] J. C. Chai. And D. T. Bergado. The analysis of grid reinforced embankment on soft clay. Computer and geotechnics，1995
[38]施斌,吴智深,李琦,村上预.边坡大变形弹塑性有限元分析.水文地质工程地质，No.2,1999
[39]魏瑛莺.复杂土坡稳定问题的非线性有限元分析:[硕士论文].福州:福州大学.2002
[40] I. B. Donald. Australian-china landslide seminar, 1993
[41] James Michael Duncan. State of the art: limit equilibrium and finite element analysis of slopes. Journal of Geotechnical Engineering, 1996,122(7): 577-596.
[42] Ugai K. A method of calculation of total factor of safety of slope by elaso-plastic FEM，Soils and Foundations，1989,29(2):190～195
[43] Matsui T. and San K C. Finite element slope stability analysis by shear strength reduction technique，Soils and Foundations，1989,32(1):59～70
[44]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，Vol.21, No.5
2001
[45]连镇营,韩国城,孔宪京.强度折减有限元法研究开挖边坡的稳定性.岩土工程学报,Vol.23, No.4,2001
[46]郑颖人,赵尚毅,时卫民,林丽.边坡稳定分析的一些进展.地下空间,Vol.21,No.4 1999
[47]江见鲸.土建工程常用微机程序汇编，北京:水利电力出版社,1987
[48]张鲁渝,时卫民,郑颖人.平面应变条件下土坡稳定有限元分析.岩土工程学报，Vol.24, No.4,2002
[49]易大义,沈云宝,李有法.计算方法.杭州:浙江大学出版社,2002
[50]杨大地,谈骏渝.实用数值分析，成都:重庆大学出版社,2000
[51]刘国明.非线性有限元分析.福州:福州大学（内部讲义）2002
[52]钱家欢,殷宗泽.土工数值分析.北京:中国铁道出版社,1991
[53]彭国伦.Fortran95程序设计.北京:中国电力出版社,2002
[54]美国Ansys公司.Ansys高级技术分析指南,1998
[55]张季如.边坡开挖的有限元模拟与稳定性评价.岩石力学与工程学报,Vo21,No,6 2001
[56]徐干成,郑颖人.岩土工程中屈服准则应用的研究.岩土工程学报,1990,12(2):
93～99
[57]戴自航,沈蒲生.莫尔—库仑等面积屈服准则的简化形式及应用.福州大学学报(自然科学版),Vol.31, No.4, 2001
[58]龚晓南.土工计算机分析.北京:中国建筑工业出版社,2000.
[59] Jiang G L and Magnan J P. Stability analysis of embankments: comparison of limit analysis with methods of slices. Geotechnique, 1997,47(4):857-872.
[60] Griffith D V and Lane P A . Slope stability analysis by finite elements,Geotechnique, 1999,49(3):387-403。
[61] Dawson E .M, Roth W H, Drescher A. Slope stability analysis by strength reduction. Geotechnique, 1999, 49(6):835-840
[62]杨英华.土力学.北京:地质出版社,1986
[63]张喜发.岩土工程勘察与评价.长春:吉林科学技术出版社.1995
[64]岩土工程手册编写委员会,岩土工程手册.北京:中国建筑工业出版社，1994
[65]朱伯芳.有限单元法原理与应用.北京:水利电力出版社，1979
[66]殷宗泽.土坝非线性有限元计算程序.南京:河海大学出版社，1992
[67]黄文熙.土的工程性质.北京:水利电力出版社,1983
[68]杨熙章.土工试验与原理.南京:同济大学出版社,1993
[69]工程地质手册(第二版).北京:中国建筑工业出版社，1987
[70]美国ANSYS公司北京办事处.APDL使用指南,1998
[71]朱益军.高速公路路堑边坡稳定性研究[硕士论文].浙江:浙江大学,2002