三维极限平衡法研究与应用
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摘要
我国乃多山国家,山地约占国土面积的2/3;经济发展,开山填土,必然造就大量新的边坡。据国土资源部统计,2010年全国共发生滑坡灾害22329起,占总地质灾害发生数的72.8%。建立在Mohr-Coulomb屈服准则与静力平衡基础上的二维极限平衡法目前广泛应用于边坡稳定性分析,但二维极限平衡法将边坡近似地作为平面应变问题考虑,忽略滑裂面侧面的阻滑力作用,使得计算过于保守。而现实边坡本身就是三维问题,作为二维问题来分析,必然会有局限性及不完善性,因此将二维分析扩展为三维分析,计算结果才能更符合实际。根据实际研究需要,本文对三维极限平衡法进行了研究,并将本文模型应用到工程实例计算中,论文主要包括以下几个方面内容:
1)边坡稳定性分析的三维极限平衡法模型建立
在水科院三维极限平衡分析方法模型基础之上提出本文的边坡稳定性分析的三维极限平衡法模型,主要表现在建立本文的三维极限平衡法力学模型和几何模型,对条柱受力情况进行了局部改进,增加了条柱列界面上的剪切力R,并规定R的大小及方向。
2)建立力、力矩平衡方程并求解安全系数
分析条柱所受力情况,求解条柱底滑面法向力N i;建立S方向上的整体静力平衡方程,建立y方向上的整体静力平衡方程,以及建立绕y轴的整体力矩平衡方程。根据牛顿-勒普生法迭代求解安全系数F、行界面条间力E与x轴夹角为β、底滑面剪切力T与xoz平面的夹角为ρ。
3)建立边坡三维滑裂面搜索模型
建立以双二次曲面贝塞尔曲面为滑裂面的边坡三维滑裂面搜索模型,简化曲面的控制参数S = S ( w, h, v , d , x , y , z ,θ,φ),以便于利用遗传算法对最危险滑裂面进行搜索。
4)程序实现与算例测试
编程实现滑裂面的搜索以及边坡安全系数的计算,并通过Zhang Xing椭球滑裂面边坡算例检测分析本文模型的合理性以及程序的可靠性。
5)工程实例应用
以昆明小哨国际机场高填方路基边坡稳定性评价为工程分析实例,对其进行二维、三维稳定性评价,并提出相应的边坡防护意见。
In our country which is mountainous,more than two thirds of land area are mountains. With the development of economy,the mountain cutting and the soli filling,a large number of slops are being created. According to the statistics of Ministry of Land and Resources, 22,329 landslides occurred in our country in the year of 2010,72.8% of the total number of geological disasters. Based on the Mohr-Coulomb yield criterion and the static equilibrium, two-dimensional limit equilibrium slope stability analysis is widely used,but the two-dimensional limit equilibrium method approximately consideres the slope as a plane strain problem, ignoring the blocking sliding force of the sliding flank surface,so the calculation is too conservative. The slope itself is a real three-dimensional problem.If taking it as a two-dimensional problem,there must be limitations and imperfections,so the two-dimensional analysis should be extended to three-dimensional analysis to make the results of calculation more practical. Based on actual research needs ,three-dimensional limit equilibrium method has been studied in this thesis,and is applied to engineering calculations.The thesis includes the following aspects:
1) Build the model of the three-dimensional limit equilibrium of slope stability analysis
The model of the three-dimensional limit equilibrium in this thesis is based on the IWHR method,mainly embodying that mechanical model and geometric model of the three-dimensional limit equilibrium method are be established,the forces on the columns are be partly improved,shear force R is be added onto the row surface,and the size and direction of R are be provided.
2)Establish the forces and torque balance equation,and caculate the safety factor
Study the forces on the columns and calculate the normal force N i on the base sliding surface;establish the overall static equilibrium equation on the direction of S;establish the overall static equilibrium equation on the direction of Y;and establish the overall torque equilibrium equation around the y-axis. According to Newton-Raphson method,the safety factor,the angleβbetween the force E on the line surface and the x-axis,the angleρbetween the shear T on the base sliding surface and the plane xoz.
3) Establish the search model of three-dimensional slip surface
Establish the Bezier sliding surface search model of three-dimensional slip surface,simplifying the control parameters of Bezier S = S ( w, h, v , d , x , y , z ,θ,φ)for using the genetic algorithms to search the most dangerous slip surface.
4) Procedure implementation and example testing
Write programme to search the three-dimensional slip surface and calculate the safety factor,and then test the three-dimensional model in this thesis and the reliability of the programme.
5) Engineering example
This thesis takes the high fill embankment slope of the Kunming Xiaoshao International Airport as stability analysis engineering example to calculate its two-dimensional,three-dimensional safety factors and proposes advice of the slope protection.
1)边坡稳定性分析的三维极限平衡法模型建立
在水科院三维极限平衡分析方法模型基础之上提出本文的边坡稳定性分析的三维极限平衡法模型,主要表现在建立本文的三维极限平衡法力学模型和几何模型,对条柱受力情况进行了局部改进,增加了条柱列界面上的剪切力R,并规定R的大小及方向。
2)建立力、力矩平衡方程并求解安全系数
分析条柱所受力情况,求解条柱底滑面法向力N i;建立S方向上的整体静力平衡方程,建立y方向上的整体静力平衡方程,以及建立绕y轴的整体力矩平衡方程。根据牛顿-勒普生法迭代求解安全系数F、行界面条间力E与x轴夹角为β、底滑面剪切力T与xoz平面的夹角为ρ。
3)建立边坡三维滑裂面搜索模型
建立以双二次曲面贝塞尔曲面为滑裂面的边坡三维滑裂面搜索模型,简化曲面的控制参数S = S ( w, h, v , d , x , y , z ,θ,φ),以便于利用遗传算法对最危险滑裂面进行搜索。
4)程序实现与算例测试
编程实现滑裂面的搜索以及边坡安全系数的计算,并通过Zhang Xing椭球滑裂面边坡算例检测分析本文模型的合理性以及程序的可靠性。
5)工程实例应用
以昆明小哨国际机场高填方路基边坡稳定性评价为工程分析实例,对其进行二维、三维稳定性评价,并提出相应的边坡防护意见。
In our country which is mountainous,more than two thirds of land area are mountains. With the development of economy,the mountain cutting and the soli filling,a large number of slops are being created. According to the statistics of Ministry of Land and Resources, 22,329 landslides occurred in our country in the year of 2010,72.8% of the total number of geological disasters. Based on the Mohr-Coulomb yield criterion and the static equilibrium, two-dimensional limit equilibrium slope stability analysis is widely used,but the two-dimensional limit equilibrium method approximately consideres the slope as a plane strain problem, ignoring the blocking sliding force of the sliding flank surface,so the calculation is too conservative. The slope itself is a real three-dimensional problem.If taking it as a two-dimensional problem,there must be limitations and imperfections,so the two-dimensional analysis should be extended to three-dimensional analysis to make the results of calculation more practical. Based on actual research needs ,three-dimensional limit equilibrium method has been studied in this thesis,and is applied to engineering calculations.The thesis includes the following aspects:
1) Build the model of the three-dimensional limit equilibrium of slope stability analysis
The model of the three-dimensional limit equilibrium in this thesis is based on the IWHR method,mainly embodying that mechanical model and geometric model of the three-dimensional limit equilibrium method are be established,the forces on the columns are be partly improved,shear force R is be added onto the row surface,and the size and direction of R are be provided.
2)Establish the forces and torque balance equation,and caculate the safety factor
Study the forces on the columns and calculate the normal force N i on the base sliding surface;establish the overall static equilibrium equation on the direction of S;establish the overall static equilibrium equation on the direction of Y;and establish the overall torque equilibrium equation around the y-axis. According to Newton-Raphson method,the safety factor,the angleβbetween the force E on the line surface and the x-axis,the angleρbetween the shear T on the base sliding surface and the plane xoz.
3) Establish the search model of three-dimensional slip surface
Establish the Bezier sliding surface search model of three-dimensional slip surface,simplifying the control parameters of Bezier S = S ( w, h, v , d , x , y , z ,θ,φ)for using the genetic algorithms to search the most dangerous slip surface.
4) Procedure implementation and example testing
Write programme to search the three-dimensional slip surface and calculate the safety factor,and then test the three-dimensional model in this thesis and the reliability of the programme.
5) Engineering example
This thesis takes the high fill embankment slope of the Kunming Xiaoshao International Airport as stability analysis engineering example to calculate its two-dimensional,three-dimensional safety factors and proposes advice of the slope protection.
引文
Anthony TG.Genetic algorithm search for critical slip surface inmultiple-wedge stability analysis[J].Can.Geotech.J.,1999,Vol.36:382-391.
Baker, Garber. Variation approach to slope stability. Int. Conf. on Soil Mech. and Found. Engng. 1977, Vol.2, 9-12.
Bishop. The use of the slip circle in the stability analysis of slopes. Geotechnique. 1955, Vol.5.
Boutrup, Lovell. Search technical in slope stability analysis. Engineering Geotechnical. 1980, Vol.16, 51-61.
Chen Z.Y.,Shao C.Evaluation of minimum factor of safety in slope stability analysis. Canadian Geotechnical Journal,1988,25:735-748.
Chen,Z.,Wang J.,Wang Y.,Haberfield C.A three-dimensional slope stability analysis method using the upper bound theorem,PartⅡ:Numerical approaches,applications and extensions[J]. International Journal of Rock Mechanics and Mining Sciences.2001,(38):379-39.
Chen.R.H.and Chameau,J.L.Three-dimensional limit equilibrium analysis of slopes. Geotechnique,1982.33:31-40.
Cheng Y.M.Location of critical failure surface and some further studies on slope stability analysis.Computers and Geotechnics,2003,30:255-267.
Duncan,J.M, Byrne,P, Wong,K. Strength, stress-strain and bulk modulus parameters for finite element analyses of stresses and movements in soil masses, Report No. UCB/GT/80-01, University of California, Berkeley, California (1980)R.
Duncan,J.M.State of art:Limit equilibrium and finite element analysis of slopes.Journal of Geotechnical engineering,1996 July.122(7):577-596.
Guy Lefebvre, James M. Duncan, M.Asce,et al.Three-dimensional finite element analyses of dams. Journal of the Soil Mechanics and Foundations Division, Vol. 99, No. 7, July 1973, pp. 495-507.
Hutchinson,Sarma. Discussion on three-dimensional limit equilibrium of slopes. Geotechnique. 1985, Vol.35, 215-216.
Lam L ,Fredlund DG.A general limite quilibrium model fortliree-dimensional slope analysis[J].Canadian Geoteelmieal Joumal,1993,30(6):905 919.
Leshchisky D,Huang Ching-Chang. Generalized three dimensional slope stability analysis[J]. Journal of Geotechnical Engineering,1992,118(11):1748~1763.
Orang Farzaneh, Faradjollah Askari, Navid Ganjian. Three-Dimensional Stability Analysis of Convex Slopes in Plan View. Journal of Geotechnical and Geoenvironmental Engineering, (ASCE)1090-0241(2008)134: 8(1192).
Pham H.T.V.,Fredlund D.G.The application of dynamic programming to slope stability analysis.Canadian Geotechnical Journal,2003,40:830-847.
Yamagami T,Ueta Y.Search for noncircular slip surfaces by the Morgenstern-Preice method. Proc.of 6th Int.Conf.on Numerical Methods in Geomechanics[J]. Innsbruck, 1988.1335-1340.
包太,刘宝深.遗传算法在边坡稳定系数计算中的应用[J].重庆建筑大学学报.2007,l (29):49-5.
曹亚星.饱和一非饱和土坡稳定性的三维极限平衡分析[D].天津大学,天津,2006.
曹亚星.饱和一非饱和土坡稳定性的三维极限平衡分析[D].天津大学,天津,2006.
陈昌富,龚晓南,王贻荪.自适应蚁群算法及其在边坡工程中的应用[J].浙江大学学报(工学版).2003,5(37):566-569.
陈昌富.混沌扰动启发式蚁群算法及其在边坡非圆弧临界滑动面搜索中的应用[J].岩石力学与工程学报.2004,20(23):3450-3453.
陈锋.基于矢量和法的边坡三维极限平衡稳定分析法及应用.浙江大学硕士学位论文,2008.6.
陈惠发.极限分析与土体塑性.北京:人民交通出版社, 1995.
陈云敏,魏新江,李育超.边坡非圆弧临界滑面的粒子群优化算法[J].岩石力学与工程学报. 2006,7(25):1443-l449.
陈仲颐,周景星,王洪瑾.土力学.北京:清华大学出版社, 1994.4.
陈祖煜,弥宏亮,汪小刚.边坡稳定三维分析的极限平衡方法.岩土工程学报. 2001, Vol.23:525-529.
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[J].岩土工程学报, 1988,(4):1-13.
陈祖煜.边坡稳定分析—极限平衡法的改进和应用.清华大学博士论文, 1991.
陈祖煜.土质边坡稳定性分析—原理方法程序,2003.
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, Vol.33:9-12.
方建瑞.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.同济大学博士学位论文,2007.5.
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, Vol.21, 657-661.
龚晓南.土工计算机分析.北京:中国建筑工业出版社, 2000.
龚晓南.土工计算机分析.北京:中国建筑工业出版社, 2000.
顾晓强.边坡稳定分析方法及其应用研究[D].上海交通大学,上海,2007.
何则干,陈胜宏.遗传模拟退火算法在边坡稳定分析中的应用[J].岩土力学.2004,2(25): 316-319.
姜清辉,王笑海,丰定祥,冯树仁.三维边坡稳定性极限平衡分析系统软件SLOPE3D的设计及
应用.岩石力学与工程学报. 2003, Vol.22:1121-1125.
李亮,迟世春,林皋.基于蚁群算法的复合形法及其在边坡稳定分析中的应用[J].岩土工程学报.2004,5(26):691-696.
李亮,迟世春,林皋.禁忌模拟退火复合形法及其在边坡稳定性分析中的应用[J].岩石力学与工程学报.2005,18(24):3342-3349.
李亮,迟世春,郑榕明等.一种新型遗传算法及其在土坡任意滑动面确定中的应用[J].水利学报.2007,2(38):157-162.
卢萌盟,曾宪桃.边坡稳定的三维极限平衡分析法及工程应用.四川建筑. 2004, Vol.24: 77-78.
吕文杰,李晓军,朱合华.基于遗传算法的边坡稳定分析通用算法[J].岩土工程学报.2005, 5(27):595-599.
马忠政,祁红卫,侯学渊.边坡稳定验算中全面搜索的一种新方法.岩土力学. 2000, Vol.21, 256-259.
莫海鸿.应用模式搜索法寻找最危险滑动圆弧.岩土工程学报. 1999, Vol.22, 696-699. 全国地质灾害通报,中华人民共和国国土资源部, 2010.
时卫民,郑颖人,唐伯明.边坡稳定不平衡推力法的精度分析及其使用条件.岩土工程学报. 2004, 26(3):313～317.
孙君实.条分法的数值分析[J].岩土工程学报,1984,6(2):1-12.
孙平.基于非相关流动法则的三维边坡稳定极限分析[D].中国水利水电科学研究院,北京,2005.
万娜.滑坡的三维稳定分析方法研究.武汉大学硕士学位论文,2005.3.
王栋. Visual Basic程序设计使用教程.北京:清华大学出版社, 2000
吴余生,陈胜宏.并行组合模拟退火算法在边坡稳定分析中的应用[J].岩土力学.2006,9 (27):1554-1558.
谢漠文,蔡美峰.信息边坡工程学的理论与实践[M].北京:科学出版社,2005.
杨华.边坡稳定的三维极限平衡法.西北农林科技大学硕士论文,2005.6.
张常亮.边坡稳定性三维极限平衡法研究.长安大学博士论文,2008.6.
张常亮.边坡最危险滑动面的三维搜索方法研究[D].长安大学,西安,2005.
张发明,郭丙跃,庞正江等.基于模拟退火算法的边坡稳定分析方法[J].岩土力学,2006,4 (27) : 514-518.
张浩,王常明,马文东.边坡最危险滑动面全局搜索的模拟退火算法及改进[J].吉林大学学报(地球科学版).2007,l(37):129-133.
张新连.山区机场高填方边坡静力稳定分析.清华大学硕士论文,2010.6.
中国建筑西南勘察设计研究院.昆明新机场航站楼前区岩土工程详细勘察报告,2007.
中国民航机场建设集团公司.昆明新机场工程项目全场地基处理与土石方工程设计说明及施工技术要求, 2008.8.
祝志恒.三维边坡极限平衡分析软件开发技术研究.中南大学硕士学位论文,2008.5.
Baker, Garber. Variation approach to slope stability. Int. Conf. on Soil Mech. and Found. Engng. 1977, Vol.2, 9-12.
Bishop. The use of the slip circle in the stability analysis of slopes. Geotechnique. 1955, Vol.5.
Boutrup, Lovell. Search technical in slope stability analysis. Engineering Geotechnical. 1980, Vol.16, 51-61.
Chen Z.Y.,Shao C.Evaluation of minimum factor of safety in slope stability analysis. Canadian Geotechnical Journal,1988,25:735-748.
Chen,Z.,Wang J.,Wang Y.,Haberfield C.A three-dimensional slope stability analysis method using the upper bound theorem,PartⅡ:Numerical approaches,applications and extensions[J]. International Journal of Rock Mechanics and Mining Sciences.2001,(38):379-39.
Chen.R.H.and Chameau,J.L.Three-dimensional limit equilibrium analysis of slopes. Geotechnique,1982.33:31-40.
Cheng Y.M.Location of critical failure surface and some further studies on slope stability analysis.Computers and Geotechnics,2003,30:255-267.
Duncan,J.M, Byrne,P, Wong,K. Strength, stress-strain and bulk modulus parameters for finite element analyses of stresses and movements in soil masses, Report No. UCB/GT/80-01, University of California, Berkeley, California (1980)R.
Duncan,J.M.State of art:Limit equilibrium and finite element analysis of slopes.Journal of Geotechnical engineering,1996 July.122(7):577-596.
Guy Lefebvre, James M. Duncan, M.Asce,et al.Three-dimensional finite element analyses of dams. Journal of the Soil Mechanics and Foundations Division, Vol. 99, No. 7, July 1973, pp. 495-507.
Hutchinson,Sarma. Discussion on three-dimensional limit equilibrium of slopes. Geotechnique. 1985, Vol.35, 215-216.
Lam L ,Fredlund DG.A general limite quilibrium model fortliree-dimensional slope analysis[J].Canadian Geoteelmieal Joumal,1993,30(6):905 919.
Leshchisky D,Huang Ching-Chang. Generalized three dimensional slope stability analysis[J]. Journal of Geotechnical Engineering,1992,118(11):1748~1763.
Orang Farzaneh, Faradjollah Askari, Navid Ganjian. Three-Dimensional Stability Analysis of Convex Slopes in Plan View. Journal of Geotechnical and Geoenvironmental Engineering, (ASCE)1090-0241(2008)134: 8(1192).
Pham H.T.V.,Fredlund D.G.The application of dynamic programming to slope stability analysis.Canadian Geotechnical Journal,2003,40:830-847.
Yamagami T,Ueta Y.Search for noncircular slip surfaces by the Morgenstern-Preice method. Proc.of 6th Int.Conf.on Numerical Methods in Geomechanics[J]. Innsbruck, 1988.1335-1340.
包太,刘宝深.遗传算法在边坡稳定系数计算中的应用[J].重庆建筑大学学报.2007,l (29):49-5.
曹亚星.饱和一非饱和土坡稳定性的三维极限平衡分析[D].天津大学,天津,2006.
曹亚星.饱和一非饱和土坡稳定性的三维极限平衡分析[D].天津大学,天津,2006.
陈昌富,龚晓南,王贻荪.自适应蚁群算法及其在边坡工程中的应用[J].浙江大学学报(工学版).2003,5(37):566-569.
陈昌富.混沌扰动启发式蚁群算法及其在边坡非圆弧临界滑动面搜索中的应用[J].岩石力学与工程学报.2004,20(23):3450-3453.
陈锋.基于矢量和法的边坡三维极限平衡稳定分析法及应用.浙江大学硕士学位论文,2008.6.
陈惠发.极限分析与土体塑性.北京:人民交通出版社, 1995.
陈云敏,魏新江,李育超.边坡非圆弧临界滑面的粒子群优化算法[J].岩石力学与工程学报. 2006,7(25):1443-l449.
陈仲颐,周景星,王洪瑾.土力学.北京:清华大学出版社, 1994.4.
陈祖煜,弥宏亮,汪小刚.边坡稳定三维分析的极限平衡方法.岩土工程学报. 2001, Vol.23:525-529.
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[J].岩土工程学报, 1988,(4):1-13.
陈祖煜.边坡稳定分析—极限平衡法的改进和应用.清华大学博士论文, 1991.
陈祖煜.土质边坡稳定性分析—原理方法程序,2003.
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, Vol.33:9-12.
方建瑞.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.同济大学博士学位论文,2007.5.
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, Vol.21, 657-661.
龚晓南.土工计算机分析.北京:中国建筑工业出版社, 2000.
龚晓南.土工计算机分析.北京:中国建筑工业出版社, 2000.
顾晓强.边坡稳定分析方法及其应用研究[D].上海交通大学,上海,2007.
何则干,陈胜宏.遗传模拟退火算法在边坡稳定分析中的应用[J].岩土力学.2004,2(25): 316-319.
姜清辉,王笑海,丰定祥,冯树仁.三维边坡稳定性极限平衡分析系统软件SLOPE3D的设计及
应用.岩石力学与工程学报. 2003, Vol.22:1121-1125.
李亮,迟世春,林皋.基于蚁群算法的复合形法及其在边坡稳定分析中的应用[J].岩土工程学报.2004,5(26):691-696.
李亮,迟世春,林皋.禁忌模拟退火复合形法及其在边坡稳定性分析中的应用[J].岩石力学与工程学报.2005,18(24):3342-3349.
李亮,迟世春,郑榕明等.一种新型遗传算法及其在土坡任意滑动面确定中的应用[J].水利学报.2007,2(38):157-162.
卢萌盟,曾宪桃.边坡稳定的三维极限平衡分析法及工程应用.四川建筑. 2004, Vol.24: 77-78.
吕文杰,李晓军,朱合华.基于遗传算法的边坡稳定分析通用算法[J].岩土工程学报.2005, 5(27):595-599.
马忠政,祁红卫,侯学渊.边坡稳定验算中全面搜索的一种新方法.岩土力学. 2000, Vol.21, 256-259.
莫海鸿.应用模式搜索法寻找最危险滑动圆弧.岩土工程学报. 1999, Vol.22, 696-699. 全国地质灾害通报,中华人民共和国国土资源部, 2010.
时卫民,郑颖人,唐伯明.边坡稳定不平衡推力法的精度分析及其使用条件.岩土工程学报. 2004, 26(3):313～317.
孙君实.条分法的数值分析[J].岩土工程学报,1984,6(2):1-12.
孙平.基于非相关流动法则的三维边坡稳定极限分析[D].中国水利水电科学研究院,北京,2005.
万娜.滑坡的三维稳定分析方法研究.武汉大学硕士学位论文,2005.3.
王栋. Visual Basic程序设计使用教程.北京:清华大学出版社, 2000
吴余生,陈胜宏.并行组合模拟退火算法在边坡稳定分析中的应用[J].岩土力学.2006,9 (27):1554-1558.
谢漠文,蔡美峰.信息边坡工程学的理论与实践[M].北京:科学出版社,2005.
杨华.边坡稳定的三维极限平衡法.西北农林科技大学硕士论文,2005.6.
张常亮.边坡稳定性三维极限平衡法研究.长安大学博士论文,2008.6.
张常亮.边坡最危险滑动面的三维搜索方法研究[D].长安大学,西安,2005.
张发明,郭丙跃,庞正江等.基于模拟退火算法的边坡稳定分析方法[J].岩土力学,2006,4 (27) : 514-518.
张浩,王常明,马文东.边坡最危险滑动面全局搜索的模拟退火算法及改进[J].吉林大学学报(地球科学版).2007,l(37):129-133.
张新连.山区机场高填方边坡静力稳定分析.清华大学硕士论文,2010.6.
中国建筑西南勘察设计研究院.昆明新机场航站楼前区岩土工程详细勘察报告,2007.
中国民航机场建设集团公司.昆明新机场工程项目全场地基处理与土石方工程设计说明及施工技术要求, 2008.8.
祝志恒.三维边坡极限平衡分析软件开发技术研究.中南大学硕士学位论文,2008.5.