对空间曲面取矩的三维边坡稳定性分析方法研究
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摘要
三维边坡稳定分析解析解的推导是岩土工程领域的难点.基于空间一点应力分析,进行了空间曲面上一点的应力分析,得出了曲面上一点的法向应力、剪应力与应力分量、曲面一阶偏导数的关系;建立了曲面至边坡表面土柱上力的微分平衡方程、力的平衡方程、力矩平衡方程.和库仑屈服条件一起,构成了边坡稳定问题普遍适用的基本方程组;采用与二维问题的简化Bishop法类似假定,得出了一种三维边坡稳定性分析的计算方法.算例表明本文方法计算结果是合理的,对下一步的推导和应用具有指导意义.
The deducation of analytic solutions for 3D slope stability analysis is the difficult problem in the anea of geotechnical Engineering.Based on the stress analysis of a point in space,the stress analysis of a point on a surface is performed,and then the relationship among the normal stress,the shear stress,the stress component of a point on a surface and the first order partial derivative of the surface equation is deduced. Equilibrium equations of soil columns between the sliding surface and the top surface of the slope are established,which include differential equilibrium equation of force,equilibrium equation of force,and equilibrium equation of moment. These equilibrium equations and Coulomb yield condition can form the fundamental equations of three-dimensional slope stability analysis. Applying the supposition similar to that applied in the simplified Bishop method,a kind of three-dimensional slope analysis method can be obtained. An example is presented to show that the computation method is rea-sonable and applicable,which provides significance for the further deducation and application.
The deducation of analytic solutions for 3D slope stability analysis is the difficult problem in the anea of geotechnical Engineering.Based on the stress analysis of a point in space,the stress analysis of a point on a surface is performed,and then the relationship among the normal stress,the shear stress,the stress component of a point on a surface and the first order partial derivative of the surface equation is deduced. Equilibrium equations of soil columns between the sliding surface and the top surface of the slope are established,which include differential equilibrium equation of force,equilibrium equation of force,and equilibrium equation of moment. These equilibrium equations and Coulomb yield condition can form the fundamental equations of three-dimensional slope stability analysis. Applying the supposition similar to that applied in the simplified Bishop method,a kind of three-dimensional slope analysis method can be obtained. An example is presented to show that the computation method is rea-sonable and applicable,which provides significance for the further deducation and application.
引文
[1] HUNGRO,SALGADO F M,BRYNE P M.Evaluation of a threedimensional method of slope stability analysis[J].Canadian Geotechnical Journal,1989,26:679—686.
[2]冯树仁,丰定祥,葛修润,等.边坡稳定性的三维极限平衡分析方法及应用[J].岩土工程学报,1999,21(6):657—661.FENG S R,FENG D X,GE X R,et al.3D limit equilibrium method for slope stability and its application[J]. Chinese Journal of Geotechnical Engineering,1999,21(6):657—661.(In Chinese)
[3]张均锋.三维简化Janbu法分析边坡稳定性的扩展[J],岩石力学与工程学报,2004,23(17):2876-2881.ZHANG J F. Extension of three-dimensional simplified Janbu's method for slope stability analysis[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(17):2876—2881.(In Chinese)
[4]陈祖煜,弥宏亮,汪小刚.边坡稳定三维分析的极限平衡法[J].岩土工程学报,2001,23(5);525-529.CHEN Z Y,MI H L,WANG X G.A three-dimensional limit equilibrium method for slope stability analysis[J].Chinese Journal of Geotechnical Engineering,2001,23(5):525—529.(In Chinese)
[5]张均锋,王思莹,祈涛.边坡稳定分析的三维Spencer法[J],岩石力学与工程学报,2005,24(19):3434—3439.ZHANG J F,WANG S Y,QI T.Three dimensional Spencer method for slope stability analysis[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(19):3434—3439.(In Chinese)
[6]陈昌富,朱剑锋.基于Morgenstern-Price法边坡三维稳定性分析[J],岩石力学与工程学报,2010,29(7):1473—1480.CHEN C F,ZHU J F.A three-dimensional slope stability analysis procedure based on Morgenstern-Price method[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(7):1473—1480.(In Chinese)
[7]邓东平,李亮.一般形状边坡下准严格与非严格三维极限平衡法[J].岩土工程学报,2013,35(3):501—510.DENG D P,LI L.Quasi-rigorous and non-rigorous 3D limit equilibrium method for generalized-shaped slopes[J].Chinese Journal of Geotechnical Engineering,2013,35(3):501—510.(In Chinese)
[8]陈胜宏,万娜.边坡稳定分析的三维剩余推力法[J].武汉大学学报(工学版),2005,38(3):69-73.CHEN S H,WAN N.Study on three-dimensional residual thrust method for slope stability analysis[J].Engineering Journal of Wuhan University,2005,38(3):69—73.(In Chinese)
[9]朱大勇,丁秀丽,邓建辉.基于力平衡的三维边坡安全系数显式解及工程应用[J].岩土力学,2008,29(8):2011—2015.ZHU D Y,DING X L,DENG J H.Explicit solution to 3D safety factor of slope based on force equilibrium and its application to engineering[J].Rock and soil Mechnics,2008,29(8):2011—2015.(In Chinese)
[10]郑宏,谭国焕,刘德富.边坡稳定性分析的无条分法[J].岩土力学,2007,28(7):1285-1290.ZHENG H,TAN G H,LIU D F.A slice-free method for stability analysis of slopes[J].Rock and Soil Mechnics,2007,28(7):1285—1290.(In Chinese)
[11]BELL J M. General slope stability analysis[J]. Journal of the Soil Mechanics and Foundations Division,ASCE,1968,94(SM6):1253—1270.
[12]郑宏.严格三维极限平衡法[J].岩石力学与工程学报,2007,26(8):1529—1537.ZHENG H.A rigorous three-dimensional limit equilibrium method[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(8):1529—1537.(In Chinese)
[13]朱大勇,丁秀丽.三维边坡稳定准严格极限平衡解答[C]//三峡库区地质灾害与岩土环境学术研讨会论文集,重庆,2006:166-177.ZHU D Y,DING X L.Quasi-strict limit equilibrium solutions on three-dimensional slope stability[C]//Proceedings of the symposium about Three Gorges Reservoir Geological Disasters and Geotechnical Enviroment,Chongqing,2006:166-177.
[14]李树奇,黄传志,曹永华,等.三维边坡稳定问题的基本方程与分析方法[J].岩土工程学报,2010,32(12):1892—1897.LI S Q,HUANG C Z,CAO Y H,et al.Basic equation and analysis method of three dimensional slope stability[J].Chinese Journal of Geotechnical Engineering,2010,32(12):1892—1897.(In Chinese)
[15]李亮,迟世春,郑榕明,基于椭球滑动体假定和三维简化JANBU法的边坡稳定分析[J],岩土力学,2008,29(9):2439—2445.LI L,CHI S C,ZHENG R M.Three-dimensional slope stability analysis based on ellipsoidal sliding body and simplified JANBU method[J].Rock and Soil Mechnics,2008,29(9):2439—2445.(In Chinese)
[16] CHEN R H,CHAMEA J L. Three-dimensional limit equilibrium analysis of slopes[J]. Geomechanics,1982,33:31—40.
[17] DUNCAN J M. State of the art:limit equilibrium and finineelement analysis of slopes[J]. Journal Geotechnical Engineering,ASCE,1996,122(7):577—596.
[18] HUANG C C,TSAI C C. New method for 3D and asymmetrical slope stability analysis[J]. Journal of Geotechnical and Geoenvironmental Engineering,2000,126(10):917—927.
[19]ZHU D Y,LEE C F,JIANG H D. Generalised framework of limit equilibrium methods and numerical procedure for slope stability[J]. Geotechnique,2003,53(4):377—395.
[20] ZHU D Y,LEE C F,JIANG H D. Explicit limit equilibrium solution for slope stability[J].International Journal for Numerical and Mnalytical Methods in Geomechanics,2002,26:1573—1590.
[2]冯树仁,丰定祥,葛修润,等.边坡稳定性的三维极限平衡分析方法及应用[J].岩土工程学报,1999,21(6):657—661.FENG S R,FENG D X,GE X R,et al.3D limit equilibrium method for slope stability and its application[J]. Chinese Journal of Geotechnical Engineering,1999,21(6):657—661.(In Chinese)
[3]张均锋.三维简化Janbu法分析边坡稳定性的扩展[J],岩石力学与工程学报,2004,23(17):2876-2881.ZHANG J F. Extension of three-dimensional simplified Janbu's method for slope stability analysis[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(17):2876—2881.(In Chinese)
[4]陈祖煜,弥宏亮,汪小刚.边坡稳定三维分析的极限平衡法[J].岩土工程学报,2001,23(5);525-529.CHEN Z Y,MI H L,WANG X G.A three-dimensional limit equilibrium method for slope stability analysis[J].Chinese Journal of Geotechnical Engineering,2001,23(5):525—529.(In Chinese)
[5]张均锋,王思莹,祈涛.边坡稳定分析的三维Spencer法[J],岩石力学与工程学报,2005,24(19):3434—3439.ZHANG J F,WANG S Y,QI T.Three dimensional Spencer method for slope stability analysis[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(19):3434—3439.(In Chinese)
[6]陈昌富,朱剑锋.基于Morgenstern-Price法边坡三维稳定性分析[J],岩石力学与工程学报,2010,29(7):1473—1480.CHEN C F,ZHU J F.A three-dimensional slope stability analysis procedure based on Morgenstern-Price method[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(7):1473—1480.(In Chinese)
[7]邓东平,李亮.一般形状边坡下准严格与非严格三维极限平衡法[J].岩土工程学报,2013,35(3):501—510.DENG D P,LI L.Quasi-rigorous and non-rigorous 3D limit equilibrium method for generalized-shaped slopes[J].Chinese Journal of Geotechnical Engineering,2013,35(3):501—510.(In Chinese)
[8]陈胜宏,万娜.边坡稳定分析的三维剩余推力法[J].武汉大学学报(工学版),2005,38(3):69-73.CHEN S H,WAN N.Study on three-dimensional residual thrust method for slope stability analysis[J].Engineering Journal of Wuhan University,2005,38(3):69—73.(In Chinese)
[9]朱大勇,丁秀丽,邓建辉.基于力平衡的三维边坡安全系数显式解及工程应用[J].岩土力学,2008,29(8):2011—2015.ZHU D Y,DING X L,DENG J H.Explicit solution to 3D safety factor of slope based on force equilibrium and its application to engineering[J].Rock and soil Mechnics,2008,29(8):2011—2015.(In Chinese)
[10]郑宏,谭国焕,刘德富.边坡稳定性分析的无条分法[J].岩土力学,2007,28(7):1285-1290.ZHENG H,TAN G H,LIU D F.A slice-free method for stability analysis of slopes[J].Rock and Soil Mechnics,2007,28(7):1285—1290.(In Chinese)
[11]BELL J M. General slope stability analysis[J]. Journal of the Soil Mechanics and Foundations Division,ASCE,1968,94(SM6):1253—1270.
[12]郑宏.严格三维极限平衡法[J].岩石力学与工程学报,2007,26(8):1529—1537.ZHENG H.A rigorous three-dimensional limit equilibrium method[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(8):1529—1537.(In Chinese)
[13]朱大勇,丁秀丽.三维边坡稳定准严格极限平衡解答[C]//三峡库区地质灾害与岩土环境学术研讨会论文集,重庆,2006:166-177.ZHU D Y,DING X L.Quasi-strict limit equilibrium solutions on three-dimensional slope stability[C]//Proceedings of the symposium about Three Gorges Reservoir Geological Disasters and Geotechnical Enviroment,Chongqing,2006:166-177.
[14]李树奇,黄传志,曹永华,等.三维边坡稳定问题的基本方程与分析方法[J].岩土工程学报,2010,32(12):1892—1897.LI S Q,HUANG C Z,CAO Y H,et al.Basic equation and analysis method of three dimensional slope stability[J].Chinese Journal of Geotechnical Engineering,2010,32(12):1892—1897.(In Chinese)
[15]李亮,迟世春,郑榕明,基于椭球滑动体假定和三维简化JANBU法的边坡稳定分析[J],岩土力学,2008,29(9):2439—2445.LI L,CHI S C,ZHENG R M.Three-dimensional slope stability analysis based on ellipsoidal sliding body and simplified JANBU method[J].Rock and Soil Mechnics,2008,29(9):2439—2445.(In Chinese)
[16] CHEN R H,CHAMEA J L. Three-dimensional limit equilibrium analysis of slopes[J]. Geomechanics,1982,33:31—40.
[17] DUNCAN J M. State of the art:limit equilibrium and finineelement analysis of slopes[J]. Journal Geotechnical Engineering,ASCE,1996,122(7):577—596.
[18] HUANG C C,TSAI C C. New method for 3D and asymmetrical slope stability analysis[J]. Journal of Geotechnical and Geoenvironmental Engineering,2000,126(10):917—927.
[19]ZHU D Y,LEE C F,JIANG H D. Generalised framework of limit equilibrium methods and numerical procedure for slope stability[J]. Geotechnique,2003,53(4):377—395.
[20] ZHU D Y,LEE C F,JIANG H D. Explicit limit equilibrium solution for slope stability[J].International Journal for Numerical and Mnalytical Methods in Geomechanics,2002,26:1573—1590.