基于GIS的三维对称边坡滑面正应力分布逼近函数构造
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摘要
基于栅格柱体单元构造出对称边坡滑面正应力分布的逼近函数,为在GIS(地理信息系统)中建立基于滑面正应力假定的极限平衡法提供了理论计算基础。结合GIS的强大空间数据分析能力,建立出一个基于栅格柱体单元的三维边坡稳定性分析极限平衡模型,且在无任何力的假设条件下,推导出基于栅格单元的滑面正应力分布构成。结合算例分析表明:在滑体滑动方向上,滑面正应力的分布一部分由滑体自重和外力构成,且对滑面正应力的贡献所占比例很大,为已知函数,另一部分由柱间作用力构成,所占比例很小,为未知函数,因此,柱间作用力分布可选用三阶拉格朗日多项式来近似逼近拟合;在垂直于滑体滑动方向上,滑面正应力分布采用抛物线近似逼近拟合;进而构造出对称边坡的基于栅格单元的滑面正应力分布逼近函数。并通过算例对该逼近函数的合理性进行了验证。
The approximate function of normal stress distribution of symmetrical slope slip surface based on grid element is constructed, which provides a theoretical basis for establishing the limit equilibrium method based on the assumption of normal stress on slip surface in GIS(geographic information systems). Combining GIS's powerful spatial data analysis capabilities, a three-dimensional slope stability analysis model is established based on grid element. Under the assumption that there is no force, the distribution of normal stress on slip surface is deduced. With an analysis example, we can draw a conclusion: in the perspective of the sliding direction of the sliding body, the distribution of the normal stress on slip surface comprises several portions. The largest portion is the dead-weight of the sliding body and the external force, as a known function. The other portion that accounts for a small percentage is consisted of the force between the columns, as an unknown function. Therefore, the approximation function on the distribution of forces between the columns can be performed by a third-order Lagrange polynomials. In the direction perpendicular to the sliding body, the normal stress distribution on slip surface is approximated by parabolic approximation, and then we construct an approximation function of the normal stress distribution of slip surface based on grid element. This kind of approximation function is easily expressed in the GIS. In the end, the rationality of the approximation function is verified by an example.
The approximate function of normal stress distribution of symmetrical slope slip surface based on grid element is constructed, which provides a theoretical basis for establishing the limit equilibrium method based on the assumption of normal stress on slip surface in GIS(geographic information systems). Combining GIS's powerful spatial data analysis capabilities, a three-dimensional slope stability analysis model is established based on grid element. Under the assumption that there is no force, the distribution of normal stress on slip surface is deduced. With an analysis example, we can draw a conclusion: in the perspective of the sliding direction of the sliding body, the distribution of the normal stress on slip surface comprises several portions. The largest portion is the dead-weight of the sliding body and the external force, as a known function. The other portion that accounts for a small percentage is consisted of the force between the columns, as an unknown function. Therefore, the approximation function on the distribution of forces between the columns can be performed by a third-order Lagrange polynomials. In the direction perpendicular to the sliding body, the normal stress distribution on slip surface is approximated by parabolic approximation, and then we construct an approximation function of the normal stress distribution of slip surface based on grid element. This kind of approximation function is easily expressed in the GIS. In the end, the rationality of the approximation function is verified by an example.
引文
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[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 Jun-feng,WANG Si-ying,QI Tao.Three-dimensional Spencer method for slope stability analysis[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(19):3434-3439.
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[10]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.
[11]ZHENG H,THAM L G.Improved Bell’s method for the stability analysis of slopes[J].International Journal for Numerical and Analytical Methods in Geomechanics,2010,33(14):1673-1689.
[12]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.
[13]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.
[14]XIE M,ESAKI T,ZHOU G,et al.Geographic information systems-based three-dimensional critical slope stability analysis and landslide hazard assessment[J].Journal of Geotechnical and Geoenvironmental Engineering,2003,129(12):1109-1118.
[15]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):260-274.
[16]XIE M,ESAKI T,CAI M.GIS-based implementation of three-dimensional limit equilibrium approach of slope stability[J].Journal of Geotechnical and Geoenvironmental Engineering,2006,132(5):656-660.
[17]刘华丽,朱大勇,钱七虎,等.滑面正应力分布对边坡安全系数的影响[J].岩石力学与工程学报,2006,25(7):1323-1330.LIU Hua-li,ZHU Da-yong,QIAN Qi-hu,et al.Effect of normal stress distribution on factor of safety of a slope[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(7):1323-1330.
[18]LESHCHINSKY D.Slope stability analysis:generalized approach[J].Journal of Geotechnical Engineering,1990,116(5):851-867.
[19]余国,谢谟文,郑正勤,等.基于GIS的边坡稳定性计算方法研究[J].岩土力学,2019,40(4):1397-1404,1412.YU Guo,XIE Mo-wen,ZHENG Zheng-qin,et al.Research on slope stability calculation method based on GIS[J].Rock and Soil Mechanics,2019,40(4):1397-1404.
[20]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 Chang-fu,ZHU Jian-feng.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.
[21]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.
[22]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.
[23]卢坤林,朱大勇,杨扬.边坡滑面正应力构成及分布模式选择[J].岩土力学,2012,33(12):3741-3746.LU Kun-lin,ZHU Da-yong,YANG Yang.Selection of constitution and distribution model of normal stresses over slip surface of slope[J].Rock and Soil Mechanics,2012,33(12):3741-3746.
[24]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.
[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]张均锋,丁桦.边坡稳定性分析的三维极限平衡法及应用[J].岩石力学与工程学报,2005,24(3):365-370.ZHANG Jun-feng,DING Hua.Generalized 3D limit equilibrium method for slope stability analysis and its application[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(3):365-370.
[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 Jun-feng,WANG Si-ying,QI Tao.Three-dimensional Spencer method for slope stability analysis[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(19):3434-3439.
[6]BELL J M.General slope stability analysis[J].Journal of the Soil Mechanics and Foundations Division,1968,94(SM6):1253-1270.
[7]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.
[8]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.
[9]朱大勇,卢坤林,台佳佳,等.基于数值应力场的极限平衡法及其工程应用[J].岩石力学与工程学报,2009,28(10):1969-1975.ZHU Da-yong,LU Kun-lin,TAI Jia-jia,et al.Limit equilibrium method based on numerical stress field and its application to engineering[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(10):1969-1975.
[10]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.
[11]ZHENG H,THAM L G.Improved Bell’s method for the stability analysis of slopes[J].International Journal for Numerical and Analytical Methods in Geomechanics,2010,33(14):1673-1689.
[12]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.
[13]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.
[14]XIE M,ESAKI T,ZHOU G,et al.Geographic information systems-based three-dimensional critical slope stability analysis and landslide hazard assessment[J].Journal of Geotechnical and Geoenvironmental Engineering,2003,129(12):1109-1118.
[15]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):260-274.
[16]XIE M,ESAKI T,CAI M.GIS-based implementation of three-dimensional limit equilibrium approach of slope stability[J].Journal of Geotechnical and Geoenvironmental Engineering,2006,132(5):656-660.
[17]刘华丽,朱大勇,钱七虎,等.滑面正应力分布对边坡安全系数的影响[J].岩石力学与工程学报,2006,25(7):1323-1330.LIU Hua-li,ZHU Da-yong,QIAN Qi-hu,et al.Effect of normal stress distribution on factor of safety of a slope[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(7):1323-1330.
[18]LESHCHINSKY D.Slope stability analysis:generalized approach[J].Journal of Geotechnical Engineering,1990,116(5):851-867.
[19]余国,谢谟文,郑正勤,等.基于GIS的边坡稳定性计算方法研究[J].岩土力学,2019,40(4):1397-1404,1412.YU Guo,XIE Mo-wen,ZHENG Zheng-qin,et al.Research on slope stability calculation method based on GIS[J].Rock and Soil Mechanics,2019,40(4):1397-1404.
[20]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 Chang-fu,ZHU Jian-feng.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.
[21]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.
[22]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.
[23]卢坤林,朱大勇,杨扬.边坡滑面正应力构成及分布模式选择[J].岩土力学,2012,33(12):3741-3746.LU Kun-lin,ZHU Da-yong,YANG Yang.Selection of constitution and distribution model of normal stresses over slip surface of slope[J].Rock and Soil Mechanics,2012,33(12):3741-3746.
[24]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.