基于GIS的边坡稳定性计算方法研究
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摘要
结合GIS(地理信息系统)的空间分析能力和滑动面正应力分布假定模型,建立了基于栅格单元的三维边坡极限平衡模型,提出了基于GIS的边坡稳定性计算方法。该方法首先建立了基于栅格柱体单元的三维边坡稳定性分析模型,给出了模型参数在GIS中的空间表达式;其次,在极限平衡条件下,推导出滑体在GIS中的3个力平衡方程式和1个力矩平衡方程式,形成了用于求解三维安全系数的方程组;最后,基于摩尔-库仑强度准则,以及滑动面正应力分布的假定,求解三维安全系数。同时利用COM(组件对象模型)技术开发出一个基于GIS的三维边坡稳定性分析扩展模块,该模块可实现复杂的算法计算以及多种组合荷载下的稳定性计算,并通过算例验证了该模块的正确性和便利性。
Combined with the assumption of normal stress distribution on sliding surface and the spatial analysis capability of Geographic Information Systems(GIS), a three-dimensional(3 D) slope equilibrium model based on grid cells is established, and a GIS-based slope stability calculation method is proposed. In this method, a 3 D slope stability analysis model based on grid cylinder elements is firstly established, and the spatial computational expression of each parameter in GIS is clearly articulated. Secondly,under the condition of limit equilibrium, a set of stability analysis equations, including three force equilibrium equations and one moment equilibrium equation of the sliding body, are derived for solving the three-dimensional safety factor. Finally, following the Mohr-Coulomb strength criterion and the assumption of normal stress distribution on the sliding surface, the three-dimensional safety factor is solved. Moreover, the component object model(COM) technology is used to develop a GIS-based 3 D slope stability analysis module, which can be implemented for the complex algorithms and the calculation of multiple stratigraphic slopes and multiple combinations of factors in 3 D slope stability analyses. The correctness and feasibility of the module are verified by three typical cases.
Combined with the assumption of normal stress distribution on sliding surface and the spatial analysis capability of Geographic Information Systems(GIS), a three-dimensional(3 D) slope equilibrium model based on grid cells is established, and a GIS-based slope stability calculation method is proposed. In this method, a 3 D slope stability analysis model based on grid cylinder elements is firstly established, and the spatial computational expression of each parameter in GIS is clearly articulated. Secondly,under the condition of limit equilibrium, a set of stability analysis equations, including three force equilibrium equations and one moment equilibrium equation of the sliding body, are derived for solving the three-dimensional safety factor. Finally, following the Mohr-Coulomb strength criterion and the assumption of normal stress distribution on the sliding surface, the three-dimensional safety factor is solved. Moreover, the component object model(COM) technology is used to develop a GIS-based 3 D slope stability analysis module, which can be implemented for the complex algorithms and the calculation of multiple stratigraphic slopes and multiple combinations of factors in 3 D slope stability analyses. The correctness and feasibility of the module are verified by three typical cases.
引文
[1]DUNCAN J M.State of the art:limit equilibrium and finite-element analysis of slopes[J].Journal of Geotechnical Engineering,1996,123(9):577-596.
[2]HOVLAND H J.Three-dimensional slope stability analysis method[J].Journal of Geotechnical and Geoenvironmental Engineering,1979,105(GT5):693-695.
[3]HUNGR O.An extension of Bishop's simplified method of slope stability analysis to three dimensions[J].Geotechnique,1987,37(1):113-117.
[4]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 Liang,CHI Shi-chun,ZHENG Yung-ming.Three-dimensional slope stability analysis based on ellipsoidal sliding body and simplified Janbu method[J].Rock and Soil Mechanics,2008,29(9):2439-2445.
[5]朱大勇,李焯芬,姜弘道,等.基于滑面正应力修正的边坡安全系数解答[J].岩石力学与工程学报,2004,23(16):2788-2791.ZHU Da-yong,LEE C F,JIANG Hong-dao,et al.Solution of slope safety factor by modifying normal stresses over slip surface[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(16):2788-2791.
[6]邓东平,李亮.基于滑动面应力假设下的三维边坡稳定性极限平衡法研究[J].岩土力学,2017,38(1):189-196.DENG Dong-ping,LI Liang.Three-dimensional limit equilibrium method for slope stability based on assumption of stress on slip surface[J].Rock and Soil Mechanics,2017,38(1):189-196.
[7]杨明成.一般条分法的安全系数显示解[J].岩土力学,2004,25(增刊2):568-573.YANG Ming-cheng.Explicit solution to safety factor for general slice method[J].Rock and Soil Mechanics,2004,25(Suppl.2):568-573.
[8]BELL J M.General slope stability analysis[J].Journal of the Soil Mechanics and Foundations Division,1968,94(SM6):1253-1270.
[9]XIE M,ESAKI T,ZHOU G,et al.GIS-based 3D critical slope stability analysis and landslide hazard assessment[J].Journal of Geotechnical and Geoenvironmental Engineering,2003,129(12):1109-1118.
[10]XIE M,ESAKI T,QIU C,et al.Geographical information system-based computational implementation and application of spatial three dimensional slope stability analysis[J].Computers and Geotechnics,2006,33(4-5):260-274.
[11]谢谟文,江崎哲郎,周国云.基于边坡单元的三维滑坡灾害评价的GIS方法[J].岩石力学与工程学报,2003,22(6):969-976.XIE Mo-wen,TETSURO ESAKI,ZHOU Guo-yun.GISmethod for slope-unit-based 3D landslide hazard Evaluation[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(6):969-976.
[12]谢谟文,周国云.基于GIS空间数据库的三维边坡稳定性分析[J].岩石力学与工程学报,2002,21(10):1494-1499.XIE Mo-wen,ZHOU Guo-yun.Stability analysis of 3Dslope based on GIS spatial database[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(10):1494-1499.
[13]邱骋,谢谟文,江崎哲郎,等.基于GIS的住宅区周边危险边坡三维稳定性评价[J].中国地质灾害与防治学报,2007,18(2):89-93.QIU Cheng,XIE Mo-wen,ESAKI TETSURO,et al.GIS-based three-dimensional analysis of slope stability around residence area[J].The Chinese Journal of Geological Hazard and Control,2007,18(2):89-93.
[14]王旭春,何满潮,蒋宇静,等.在GIS中实现基于力学原理的滑坡稳定性计算[J].岩石力学与工程学报,2003,22(6):977-980.WANG Xu-chun,HE Man-chao,JIANG Yu-jing,et al.Stability analysis of landslide based on mechanics principle in GIS[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(6):977-980.
[15]赵春宏,崔大勇,刘振波,等.GIS数据用于复杂边坡三维极限平衡稳定分析[J].岩土力学,2009,30(3):707-711.ZHAO Chun-hong,CUI Da-yong,LIU Zhen-bo,et al.GIS data used for stability analysis of 3D limit equilibrium of complex slope[J].Rock and Soil Mechanics,2009,30(3):707-711.
[16]刘振平,杨波,刘建,等.基于GRASS GIS与TIN滑动面的边坡三维极限平衡方法研究[J].岩土力学,2017,38(1):221-228.LIU Zhen-ping,YANG Bo,LIU Jian,et al.Three-dimensional limit equilibrium method based on GRASS GIS and TIN sliding surface[J].Rock and Soil Mechanics,2017,38(1):221-228.
[17]ZHU D Y,LEE C F.Explicit limit equilibrium solution for slope stability[J].International Journal for Numerical and Analytical Methods in Geomechanics,2002,26(15):1573-1590.
[18]LESHCHINSKY D.Slope stability analysis:generalized approach[J].Journal of Geotechnical Engineering,1990,116(5):851-867.
[19]SRIDEVI B,DEEP K.Application of global optimization technique to slope stability analysis[C]//Proceedings of6th International Symposium on Landslides.Norway:Trondheim,1992.
[20]谢谟文,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.XIE Mo-wen,CAI Mei-feng.Theory and practice of information slope engineering[M].Beijing:Science Press,2005.
[2]HOVLAND H J.Three-dimensional slope stability analysis method[J].Journal of Geotechnical and Geoenvironmental Engineering,1979,105(GT5):693-695.
[3]HUNGR O.An extension of Bishop's simplified method of slope stability analysis to three dimensions[J].Geotechnique,1987,37(1):113-117.
[4]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 Liang,CHI Shi-chun,ZHENG Yung-ming.Three-dimensional slope stability analysis based on ellipsoidal sliding body and simplified Janbu method[J].Rock and Soil Mechanics,2008,29(9):2439-2445.
[5]朱大勇,李焯芬,姜弘道,等.基于滑面正应力修正的边坡安全系数解答[J].岩石力学与工程学报,2004,23(16):2788-2791.ZHU Da-yong,LEE C F,JIANG Hong-dao,et al.Solution of slope safety factor by modifying normal stresses over slip surface[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(16):2788-2791.
[6]邓东平,李亮.基于滑动面应力假设下的三维边坡稳定性极限平衡法研究[J].岩土力学,2017,38(1):189-196.DENG Dong-ping,LI Liang.Three-dimensional limit equilibrium method for slope stability based on assumption of stress on slip surface[J].Rock and Soil Mechanics,2017,38(1):189-196.
[7]杨明成.一般条分法的安全系数显示解[J].岩土力学,2004,25(增刊2):568-573.YANG Ming-cheng.Explicit solution to safety factor for general slice method[J].Rock and Soil Mechanics,2004,25(Suppl.2):568-573.
[8]BELL J M.General slope stability analysis[J].Journal of the Soil Mechanics and Foundations Division,1968,94(SM6):1253-1270.
[9]XIE M,ESAKI T,ZHOU G,et al.GIS-based 3D critical slope stability analysis and landslide hazard assessment[J].Journal of Geotechnical and Geoenvironmental Engineering,2003,129(12):1109-1118.
[10]XIE M,ESAKI T,QIU C,et al.Geographical information system-based computational implementation and application of spatial three dimensional slope stability analysis[J].Computers and Geotechnics,2006,33(4-5):260-274.
[11]谢谟文,江崎哲郎,周国云.基于边坡单元的三维滑坡灾害评价的GIS方法[J].岩石力学与工程学报,2003,22(6):969-976.XIE Mo-wen,TETSURO ESAKI,ZHOU Guo-yun.GISmethod for slope-unit-based 3D landslide hazard Evaluation[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(6):969-976.
[12]谢谟文,周国云.基于GIS空间数据库的三维边坡稳定性分析[J].岩石力学与工程学报,2002,21(10):1494-1499.XIE Mo-wen,ZHOU Guo-yun.Stability analysis of 3Dslope based on GIS spatial database[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(10):1494-1499.
[13]邱骋,谢谟文,江崎哲郎,等.基于GIS的住宅区周边危险边坡三维稳定性评价[J].中国地质灾害与防治学报,2007,18(2):89-93.QIU Cheng,XIE Mo-wen,ESAKI TETSURO,et al.GIS-based three-dimensional analysis of slope stability around residence area[J].The Chinese Journal of Geological Hazard and Control,2007,18(2):89-93.
[14]王旭春,何满潮,蒋宇静,等.在GIS中实现基于力学原理的滑坡稳定性计算[J].岩石力学与工程学报,2003,22(6):977-980.WANG Xu-chun,HE Man-chao,JIANG Yu-jing,et al.Stability analysis of landslide based on mechanics principle in GIS[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(6):977-980.
[15]赵春宏,崔大勇,刘振波,等.GIS数据用于复杂边坡三维极限平衡稳定分析[J].岩土力学,2009,30(3):707-711.ZHAO Chun-hong,CUI Da-yong,LIU Zhen-bo,et al.GIS data used for stability analysis of 3D limit equilibrium of complex slope[J].Rock and Soil Mechanics,2009,30(3):707-711.
[16]刘振平,杨波,刘建,等.基于GRASS GIS与TIN滑动面的边坡三维极限平衡方法研究[J].岩土力学,2017,38(1):221-228.LIU Zhen-ping,YANG Bo,LIU Jian,et al.Three-dimensional limit equilibrium method based on GRASS GIS and TIN sliding surface[J].Rock and Soil Mechanics,2017,38(1):221-228.
[17]ZHU D Y,LEE C F.Explicit limit equilibrium solution for slope stability[J].International Journal for Numerical and Analytical Methods in Geomechanics,2002,26(15):1573-1590.
[18]LESHCHINSKY D.Slope stability analysis:generalized approach[J].Journal of Geotechnical Engineering,1990,116(5):851-867.
[19]SRIDEVI B,DEEP K.Application of global optimization technique to slope stability analysis[C]//Proceedings of6th International Symposium on Landslides.Norway:Trondheim,1992.
[20]谢谟文,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.XIE Mo-wen,CAI Mei-feng.Theory and practice of information slope engineering[M].Beijing:Science Press,2005.
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