水平条分法下边坡稳定性分析与计算方法研究
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摘要
极限平衡水平条分法较适用于成层岩土边坡,但较竖直条分法尚有不足之处。通过研究水平条分与竖直条分中条间力的关系,建立起水平与竖直条分法相对应的条间力假设条件;并针对水平条分法遇到滑动面存在弓形体时,采取水平条分和斜条分相结合的模式进行处理。在此基础上,推导出了瑞典法、简化Bishop法、简化Janbu法和Morgenster-Price(M-P)法在水平条分时的安全系数计算公式,其中,根据满足条件不同,得到了瑞典法的两种不同安全系数计算公式,并根据以往研究成果将一般简化Janbu法进行改进。当使用任意曲线和圆弧滑动面两种型式时,通过算例对比分析,验证了对水平条分法所做研究的可行性。同时,也表明了两种瑞典法得到的结果是一致的,改进的简化Janbu法在边坡稳定性分析上较一般简化Janbu法更优。
Limit equilibrium method with horizontal slice method is more suitable for layered soil slopes;but there are some deficiencies than vertical slice method.By studying the relationship of interaction forces between horizontal slice and vertical slice methods,corresponding assumptions of inter-slice forces between horizontal slice and vertical slice methods are established.And a combination model of horizontal slice and oblique slice is adopted when horizontal slice method encounters the sliding surface with toxoplasma.On this basis,the formulas of Sweden method,simplified Bishop method,simplified Janbu method,and Morgenster-Price(M-P) method for calculating factor of safety(FOS) are derived.Among those,two different FOS calculated formulas of Sweden method are obtained according to different satisfied conditions;and the general simplified Janbu method is improved based on previous studies.By using two types of sliding surfaces,arbitrary curve and arc,through analyzing some examples,the treatment of horizontal slice method taken in this article is verified feasible.At the same time,it also shows the results got by two Swedish methods are consistent;and the improved simplified Janbu method is better in analyzing stability of slope than general simplified Janbu method.
Limit equilibrium method with horizontal slice method is more suitable for layered soil slopes;but there are some deficiencies than vertical slice method.By studying the relationship of interaction forces between horizontal slice and vertical slice methods,corresponding assumptions of inter-slice forces between horizontal slice and vertical slice methods are established.And a combination model of horizontal slice and oblique slice is adopted when horizontal slice method encounters the sliding surface with toxoplasma.On this basis,the formulas of Sweden method,simplified Bishop method,simplified Janbu method,and Morgenster-Price(M-P) method for calculating factor of safety(FOS) are derived.Among those,two different FOS calculated formulas of Sweden method are obtained according to different satisfied conditions;and the general simplified Janbu method is improved based on previous studies.By using two types of sliding surfaces,arbitrary curve and arc,through analyzing some examples,the treatment of horizontal slice method taken in this article is verified feasible.At the same time,it also shows the results got by two Swedish methods are consistent;and the improved simplified Janbu method is better in analyzing stability of slope than general simplified Janbu method.
引文
[1]陈昌富,杨宇.边坡稳定性分析水平条分法及其进化计算[J].湖南大学学报(自然科学版),2004,31(3):72-75.CHEN Chang-fu,YANG Yu.Horizontal slice method ofslope stability analysis based on evolutionary algorithm[J].Journal of Hunan University(Natural Sciences),2004,31(3):72-75.
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[3]朱大勇,李焯芬,黄茂松,等.对3种著名边坡稳定性计算方法的改进[J].岩石力学与工程学报,2005,24(2):183-194.ZHU Da-yong,LEE C F,HUANG Mao-song,et al.Modifications to three well-known methods of slopestability analysis[J].Chinese Journal of RockMechanics and Engineering,2005,24(2):183-194.
[4]邹广电.边坡稳定分析条分法的一个全局优化算法[J].岩土工程学报,2002,24(3):309-312.ZOU Guang-dian.A global optimization method of theslice method for slope stability analysis[J].ChineseJournal of Geotechnical Engineering,2002,24(3):309-312.
[5]万文,曹平,冯涛,等.基于加速混合遗传算法搜索复杂边坡的最危险滑动面[J].岩土工程学报,2006,28(4):475-479.WAN Wen,CAO Ping,FENG Tao,et al.Searching forthe most dangerous failure surface of complex slopebased on accelerating hybrid genetic algorithm[J].Chinese Journal of Geotechnical Engineering,2006,28(4):475-479.
[6]陈祖煜.土坡稳定分析通用条分法及其改进[J].岩土工程学报,1983,5(4):11-27.CHEN Zu-yu.The generalized method of slices for slopestability analysis and its modifications[J].ChineseJournal of Geotechnical Engineering,1983,5(4):11-27.
[7]方玉树.边坡稳定性分析条分法最小解研究[J].岩土工程学报,2008,30(3):331-335.FANG Yu-shu.The lowest solution of slice method forslope stability analysis[J].Chinese Journal ofGeotechnical Engineering,2008,30(3):331-335.
[8]吴振君,葛修润.求解边坡矢量和安全系数的条分法[J].岩土力学,2009,30(8):2337-2342.WU Zhen-jun,GE Xiu-run.Solving vector sum factor ofsafety of slope by method of slices[J].Rock and SoilMechanics,2009,30(8):2337-2342.
[9]童志怡,陈从新,徐健,等.边坡稳定性分析的条块稳定系数法[J].岩土力学,2009,30(5):1393-1398.TONG Zhi-yi,CHEN Cong-xin,XU Jian,et al.Aslice-stability method for stability analysis of slopes[J].Rock and Soil Mechanics,2009,30(5):1393-1398.
[10]高玉峰,范昭平.多点、多向地震作用下非圆弧滑面边坡稳定分析通用条分法[J].岩土力学,2010,31(12):3816-3822.GAO Yu-feng,FAN Zhao-ping.Generalized slice methodfor stability analysis of slope with non-circular slide faceunder multipoint and multidirection seismic groundmotions[J].Rock and Soil Mechanics,2010,31(12):3816-3822.
[11]殷宗泽.土工原理[M].北京:中国水利水电出版社,2007.
[12]BISHOP A W.The use of slip circle for the stabilityanalysis of slopes[J].Geotechnique,1955,5(1):7-17.
[13]MORGENSTERN N R,PRICE V E.The analysis of thestability of general slip surfaces[J].Geotechnique,1965,15(l):79-93.
[14]SPENCER E.A method of analysis of the stability ofembankments assuming parallel inter-slice forces[J].Geotechnique,1967,17(1):11-26.
[15]陈昌富,杨宇,龚晓南.基于遗传算法地震荷载作用下边坡稳定性分析水平条分法[J].岩石力学与工程学报,2003,22(11):1919-1923.CHEN Chang-fu,YANG Yu,GONG Xiao-nan.Horizontal slice method of slope stability analysis underseismic load based on genetic algorithm[J].ChineseJournal of Rock Mechanics and Engineering,2003,22(11):1919-1923.
[16]杨明成.基于力平衡求解安全系数的一般条分法[J].岩石力学与工程学报,2005,24(7):1216-1221.YANG Ming-cheng.A general slice method fordetermination of factors of safety based on forceequilibrium[J].Chinese Journal of Rock Mechanicsand Engineering,2005,24(7):1216-1221.
[17]SHAHGHOLI M,FAKHER A,JONES C J F P.Horizontal slice method of analysis[J].Géotechnique,2001,51(10):881-885.
[18]NOURI H,FAKHER A,JONES C J F P.Development ofhorizontal slice method for seismic stability analysis ofreinforced slopes and walls[J].Geotextiles andGeomembranes,2006,24(3):175-187.
[19]NOURI H,FAKHER A,JONES C J F P.Evaluating theeffects of the magnitude and amplification ofpseudo-static acceleration on reinforced soil slopes andwalls using the limit equilibrium horizontal slicesmethod[J].Geotextiles and Geomembranes,2008,26(3):263-278.
[20]魏作安,朱彬,万玲,等.边坡锚固工程分析中的水平条分法[J].土木建筑与环境工程,2010,32(3):53-56.WEI Zuo-an,ZHU Bin,WAN Lin,et al.Horizontal slicemethod for the stability analysis of reinforced slopes[J].Journal of Civil Architectural and EnvironmentalEngineering,2010,32(3):53-56.
[21]邓东平,李亮,赵炼恒.基于Janbu法的边坡整体稳定性滑动面搜索新方法[J].岩土力学,2011,32(3):891-898.DENG Dong-ping,LI Liang,ZHAO Lian-heng.A newmethod of sliding surface searching for general stabilityof slope based on Janbu method[J].Rock and SoilMechanics,2011,32(3):891-898.
[22]邓东平,李亮,赵炼恒.稳定渗流条件下土坡稳定性分析的一种新方法[J].工程地质学报,2011,19(1):29-36.DENG Dong-ping,LI Liang,ZHAO Lian-heng.A newmethod of stability analysis of slope under the conditionof steady seepage[J].Journal of Engineering Geology,2011,19(1):29-36.
[23]Rocscience Inc.Slide verification manual[R].Toronto:Rocscience Inc.,2003.
[24]王根龙,伍法权,张军慧.非均质土坡稳定性分析评价的刚体单元上限法[J].岩石力学与工程学报,2008,28(增刊2):3425-3430.WANG Gen-long,WU Fa-quan,ZHANG Jun-hui.Upperbound approach of rigid elements for inhomogeneous soilslope stability analysis[J].Chinese Journal of RockMechanics and Engineering,2008,28(Supp.2):3425-3430.
[25]KUMAR J,SAMUI P.Stability determination for layeredsoil slopes using the upper bound limit analysis[J].Geotechnical and Geological Engineering,2006,24(6):1803-1819.
[2]朱大勇,邓建辉,台佳佳.简化Bishop法严格性的论证[J].岩石力学与工程学报,2007,26(3):455-458.ZHU Da-yong,DENG Jian-hui,TAI Jia-jia.Theoreticalverification of rigorous nature of simplified Bishopmethod[J].Chinese Journal of Rock Mechanics andEngineering,2007,26(3):455-458.
[3]朱大勇,李焯芬,黄茂松,等.对3种著名边坡稳定性计算方法的改进[J].岩石力学与工程学报,2005,24(2):183-194.ZHU Da-yong,LEE C F,HUANG Mao-song,et al.Modifications to three well-known methods of slopestability analysis[J].Chinese Journal of RockMechanics and Engineering,2005,24(2):183-194.
[4]邹广电.边坡稳定分析条分法的一个全局优化算法[J].岩土工程学报,2002,24(3):309-312.ZOU Guang-dian.A global optimization method of theslice method for slope stability analysis[J].ChineseJournal of Geotechnical Engineering,2002,24(3):309-312.
[5]万文,曹平,冯涛,等.基于加速混合遗传算法搜索复杂边坡的最危险滑动面[J].岩土工程学报,2006,28(4):475-479.WAN Wen,CAO Ping,FENG Tao,et al.Searching forthe most dangerous failure surface of complex slopebased on accelerating hybrid genetic algorithm[J].Chinese Journal of Geotechnical Engineering,2006,28(4):475-479.
[6]陈祖煜.土坡稳定分析通用条分法及其改进[J].岩土工程学报,1983,5(4):11-27.CHEN Zu-yu.The generalized method of slices for slopestability analysis and its modifications[J].ChineseJournal of Geotechnical Engineering,1983,5(4):11-27.
[7]方玉树.边坡稳定性分析条分法最小解研究[J].岩土工程学报,2008,30(3):331-335.FANG Yu-shu.The lowest solution of slice method forslope stability analysis[J].Chinese Journal ofGeotechnical Engineering,2008,30(3):331-335.
[8]吴振君,葛修润.求解边坡矢量和安全系数的条分法[J].岩土力学,2009,30(8):2337-2342.WU Zhen-jun,GE Xiu-run.Solving vector sum factor ofsafety of slope by method of slices[J].Rock and SoilMechanics,2009,30(8):2337-2342.
[9]童志怡,陈从新,徐健,等.边坡稳定性分析的条块稳定系数法[J].岩土力学,2009,30(5):1393-1398.TONG Zhi-yi,CHEN Cong-xin,XU Jian,et al.Aslice-stability method for stability analysis of slopes[J].Rock and Soil Mechanics,2009,30(5):1393-1398.
[10]高玉峰,范昭平.多点、多向地震作用下非圆弧滑面边坡稳定分析通用条分法[J].岩土力学,2010,31(12):3816-3822.GAO Yu-feng,FAN Zhao-ping.Generalized slice methodfor stability analysis of slope with non-circular slide faceunder multipoint and multidirection seismic groundmotions[J].Rock and Soil Mechanics,2010,31(12):3816-3822.
[11]殷宗泽.土工原理[M].北京:中国水利水电出版社,2007.
[12]BISHOP A W.The use of slip circle for the stabilityanalysis of slopes[J].Geotechnique,1955,5(1):7-17.
[13]MORGENSTERN N R,PRICE V E.The analysis of thestability of general slip surfaces[J].Geotechnique,1965,15(l):79-93.
[14]SPENCER E.A method of analysis of the stability ofembankments assuming parallel inter-slice forces[J].Geotechnique,1967,17(1):11-26.
[15]陈昌富,杨宇,龚晓南.基于遗传算法地震荷载作用下边坡稳定性分析水平条分法[J].岩石力学与工程学报,2003,22(11):1919-1923.CHEN Chang-fu,YANG Yu,GONG Xiao-nan.Horizontal slice method of slope stability analysis underseismic load based on genetic algorithm[J].ChineseJournal of Rock Mechanics and Engineering,2003,22(11):1919-1923.
[16]杨明成.基于力平衡求解安全系数的一般条分法[J].岩石力学与工程学报,2005,24(7):1216-1221.YANG Ming-cheng.A general slice method fordetermination of factors of safety based on forceequilibrium[J].Chinese Journal of Rock Mechanicsand Engineering,2005,24(7):1216-1221.
[17]SHAHGHOLI M,FAKHER A,JONES C J F P.Horizontal slice method of analysis[J].Géotechnique,2001,51(10):881-885.
[18]NOURI H,FAKHER A,JONES C J F P.Development ofhorizontal slice method for seismic stability analysis ofreinforced slopes and walls[J].Geotextiles andGeomembranes,2006,24(3):175-187.
[19]NOURI H,FAKHER A,JONES C J F P.Evaluating theeffects of the magnitude and amplification ofpseudo-static acceleration on reinforced soil slopes andwalls using the limit equilibrium horizontal slicesmethod[J].Geotextiles and Geomembranes,2008,26(3):263-278.
[20]魏作安,朱彬,万玲,等.边坡锚固工程分析中的水平条分法[J].土木建筑与环境工程,2010,32(3):53-56.WEI Zuo-an,ZHU Bin,WAN Lin,et al.Horizontal slicemethod for the stability analysis of reinforced slopes[J].Journal of Civil Architectural and EnvironmentalEngineering,2010,32(3):53-56.
[21]邓东平,李亮,赵炼恒.基于Janbu法的边坡整体稳定性滑动面搜索新方法[J].岩土力学,2011,32(3):891-898.DENG Dong-ping,LI Liang,ZHAO Lian-heng.A newmethod of sliding surface searching for general stabilityof slope based on Janbu method[J].Rock and SoilMechanics,2011,32(3):891-898.
[22]邓东平,李亮,赵炼恒.稳定渗流条件下土坡稳定性分析的一种新方法[J].工程地质学报,2011,19(1):29-36.DENG Dong-ping,LI Liang,ZHAO Lian-heng.A newmethod of stability analysis of slope under the conditionof steady seepage[J].Journal of Engineering Geology,2011,19(1):29-36.
[23]Rocscience Inc.Slide verification manual[R].Toronto:Rocscience Inc.,2003.
[24]王根龙,伍法权,张军慧.非均质土坡稳定性分析评价的刚体单元上限法[J].岩石力学与工程学报,2008,28(增刊2):3425-3430.WANG Gen-long,WU Fa-quan,ZHANG Jun-hui.Upperbound approach of rigid elements for inhomogeneous soilslope stability analysis[J].Chinese Journal of RockMechanics and Engineering,2008,28(Supp.2):3425-3430.
[25]KUMAR J,SAMUI P.Stability determination for layeredsoil slopes using the upper bound limit analysis[J].Geotechnical and Geological Engineering,2006,24(6):1803-1819.
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