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
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摘要
基于滑动面法向应力的简单计算模式及Mohr-Coulomb强度准则,多个计算参数被使用对滑动面应力进行合理假设,并依据三维滑动体所满足的静力平衡条件,推导三维边坡稳定性极限平衡解答。同时,在三维边坡稳定性分析中,以往研究成果被采用对滑动面剪应力方向进行假定,且基于所采用极限平衡方程数目的不同,由此实现三维边坡极限平衡非严格法、准严格法和严格法。经与经典算例对比,验证了方法的可行性,并分析了三维非对称滑动体时非严格法、准严格法和严格法之间所得结果的差异。研究表明:非严格法所得计算结果偏小,其分析得到的边坡稳定性较为保守;准严格法与严格法计算所得结果接近,故采用不完全满足滑动体所有静力平衡条件的准严格法同样能得到较为可靠的安全系数。此外,所提方法构建了合理的滑动面应力假设,且求解过程简单,无需迭代计算,便于编程,从而利于工程应用。
Through simple calculation of the normal stress on slip surface and the Mohr-Coulomb strength criterion, various calculation parameters are introduced and the stresses on slip surface are properly assumed, from which the limit equilibrium solution for three-dimensional slope stability is derived based on the static equilibrium conditions that three-dimensional sliding body satisfies Meanwhile, in stability analysis of three-dimensional slope, the direction of shear stress on slip surface is also assumed based on the previous research results, and the nonstrict method, quasi-strict method and strict method are adopted for three-dimensional slope stability analysis. By comparing with the classical results, the proposed method is validated, and the differences among various methods are analyzed. It is shown that the nonstrict method yields the smallest factor of safety, i.e., a conservative result; the quasi-strict method is similar to the strict method, yielding reliable results in calculating the safety factor of slope. In the proposed method, reasonable assumptions are made for the stresses on slip surface, and the simple solution process can be easily implemented into a computer code.
Through simple calculation of the normal stress on slip surface and the Mohr-Coulomb strength criterion, various calculation parameters are introduced and the stresses on slip surface are properly assumed, from which the limit equilibrium solution for three-dimensional slope stability is derived based on the static equilibrium conditions that three-dimensional sliding body satisfies Meanwhile, in stability analysis of three-dimensional slope, the direction of shear stress on slip surface is also assumed based on the previous research results, and the nonstrict method, quasi-strict method and strict method are adopted for three-dimensional slope stability analysis. By comparing with the classical results, the proposed method is validated, and the differences among various methods are analyzed. It is shown that the nonstrict method yields the smallest factor of safety, i.e., a conservative result; the quasi-strict method is similar to the strict method, yielding reliable results in calculating the safety factor of slope. In the proposed method, reasonable assumptions are made for the stresses on slip surface, and the simple solution process can be easily implemented into a computer code.
引文
[1]陈祖煜,弥宏亮,汪小刚.边坡稳定三维分析的极限平衡方法[J].岩土工程学报,1999,23(5):525-529.CHEN Zu-yu,MI Hong-liang,WANG Xiao-gang.Athree-dimensional limit equilibrium method for slope stability analysis[J].Chinese Journal of Geotechnical Engineering,1999,23(5):525-529.
[2]袁维,胡叶江,李小春,等.一种基于位移场分析的临界滑动面确定方法研究[J].岩土力学,2016,37(6):1791-1798.YUAN Wei,HU Ye-jiang,LI Xiao-chun,et al.An approach to determining critical slip surface based on displacement field analysis[J].Rock and Soil Mechanics,2016,37(6):1791-1798.
[3]沈华章,王水林,郭明伟,等.应变软化边坡渐进破坏及其稳定性初步研究[J].岩土力学,2016,37(1):175-184.SHEN Hua-zhang,WANG Shui-lin,GUO Ming-wei,et al.A preliminary study of the progressive failure and stability of slope with strain-softening behaviour[J].Rock and Soil Mechanics,2016,37(1):175-184.
[4]袁恒,罗先启,张振华.边坡稳定分析三维极限平衡条柱间力的讨论[J].岩土力学,2011,32(8):2453-2011.YUAN Heng,LUO Xian-qi,ZHANG Zhen-hua.Discussion on force between columns of threedimensional limit equilibrium for slope stability analysis[J].Rock and Soil Mechanics,2011,32(8):2453-2011.
[5]HUNGR O.An extension of Bishop’s simplified method of slope stability analysis to three dimensions[J].Geotechnique,1987,37(1):113-117.
[6]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 Shu-ren,FENG Ding-xiang,GE Xiu-run,et al.3Dlimit equilibrium method for slope stability and its application[J].Chinese Journal of Geotechnical Engineering,1999,21(6):657-661.
[7]张均锋,丁桦.边坡稳定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.
[8]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 Jun-feng.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.
[9]ZHANG X.Three-dimensional stability analysis of concave slopes in plan view[J].Journal of Geotechnical Engineering,ASCE,1988,114(6):658-671.
[10]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.
[11]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):501-511.DENG Dong-ping,LI Liang.Quasi-rigorous and non-rigorous 3D limit equilibrium methods for generalized-shaped slopes[J].Chinese Journal of Geotechnical Engineering,2013,35(3):501-511.
[12]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 Sheng-hong,WAN Na.Study on threedimensional residual thrust method for slope stability analysis[J].Engineering Journal of Wuhan University,2005,38(3):69-73.
[13]李同录,王艳霞,邓宏科.一种改进的三维边坡稳定性分析方法[J].岩土工程学报,2003,25(5):611-614.LI Tong-lu,WANG Yan-xia,DENG Hong-ke.An improved method for three-dimensional slope stability analysis[J].Chinese Journal of Geotechnical Engineering,2003,25(5):611-614.
[14]朱大勇,钱七虎.三维边坡严格与准严格极限平衡解答及工程应用[J].岩石力学与工程学报,2007,26(8):1513-1528.ZHU Da-yong,QIAN Qi-hu.Rigorous and quasi-rigorous limit equilibrium solutions of 3D stability and application to engineering[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(8):1513-1528.
[15]朱大勇,丁秀丽,钱七虎.一般形状边坡三维极限平衡解答[J].岩土工程学报,2007,29(10):1460-1464.ZHU Da-yong,DING Xiu-li,QIAN Qi-hu.Threedimensional limit equilibrium solution to generalizedshaped slope stability[J].Chinese Journal of Geotechnical Engineering,2007,29(10):1460-1464.
[16]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 Da-yong,JING Xiu-li,DENG Jian-hui.Explicit solution to 3D safety factor of slope based on force equilibrium and its application to engineering[J].Rock and Soil Mechanics,2008,29(8):2011-2015.
[17]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.
[18]卢坤林,朱大勇,甘文宁,等.一种边坡稳定性分析的三维极限平衡法及应用[J].岩土工程学报,2013,35(12):2276-2282.LU Kun-lin,ZHU Da-yong,GAN Wen-ning,et al.A 3Dlimit equilibrium method for slope stability analysis and its application[J].Chinese Journal of Geotechnical Engineering,2013,35(12):2276-2282.
[19]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 Hong.A rigorous three-dimensional limit equilibrium method[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(8):1529-1537.
[20]BELL J M.General slope stability analysis[J].Journal of the Soil Mechanics and Foundations,ASCE,1968,94(6):1253-1270.
[21]HOVLAND H J.Three-dimensional slope stability analysis method[J].Journal of Geotechnical Engineering Division,1997,103(9):971-986.
[22]HUNGR O,SALGADO F M,BYRNE P M.Evaluation of a three-dimensional method of slope stability analysis[J].Canadian Geotechnical Journal,1989,26(4):679-686.
[23]邓东平,李亮,赵炼恒.一种三维均质土坡滑动面搜索的新方法[J].岩石力学与工程学报,2010,29(增刊2):3719-3727.DENG Dong-ping,LI Liang,ZHAO Lian-heng.A new method for searching sliding surface of three-dimensional homogeneous soil slope[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(Supp.2):3719-3727.
[24]李亮,邓东平,赵炼恒.任意滑动面搜索新方法应用于三维复杂土坡稳定性分析[J].岩土工程学报,2011,33(4):544-553.LI Liang,DENG Dong-ping,ZHAO Lian-heng.Application of new method of arbitrary sliding surface search to stability analysis of complex three-dimensional slopes[J].Chinese Journal of Geotechnical Engineering,2011,33(4):544-553.
[2]袁维,胡叶江,李小春,等.一种基于位移场分析的临界滑动面确定方法研究[J].岩土力学,2016,37(6):1791-1798.YUAN Wei,HU Ye-jiang,LI Xiao-chun,et al.An approach to determining critical slip surface based on displacement field analysis[J].Rock and Soil Mechanics,2016,37(6):1791-1798.
[3]沈华章,王水林,郭明伟,等.应变软化边坡渐进破坏及其稳定性初步研究[J].岩土力学,2016,37(1):175-184.SHEN Hua-zhang,WANG Shui-lin,GUO Ming-wei,et al.A preliminary study of the progressive failure and stability of slope with strain-softening behaviour[J].Rock and Soil Mechanics,2016,37(1):175-184.
[4]袁恒,罗先启,张振华.边坡稳定分析三维极限平衡条柱间力的讨论[J].岩土力学,2011,32(8):2453-2011.YUAN Heng,LUO Xian-qi,ZHANG Zhen-hua.Discussion on force between columns of threedimensional limit equilibrium for slope stability analysis[J].Rock and Soil Mechanics,2011,32(8):2453-2011.
[5]HUNGR O.An extension of Bishop’s simplified method of slope stability analysis to three dimensions[J].Geotechnique,1987,37(1):113-117.
[6]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 Shu-ren,FENG Ding-xiang,GE Xiu-run,et al.3Dlimit equilibrium method for slope stability and its application[J].Chinese Journal of Geotechnical Engineering,1999,21(6):657-661.
[7]张均锋,丁桦.边坡稳定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.
[8]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 Jun-feng.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.
[9]ZHANG X.Three-dimensional stability analysis of concave slopes in plan view[J].Journal of Geotechnical Engineering,ASCE,1988,114(6):658-671.
[10]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.
[11]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):501-511.DENG Dong-ping,LI Liang.Quasi-rigorous and non-rigorous 3D limit equilibrium methods for generalized-shaped slopes[J].Chinese Journal of Geotechnical Engineering,2013,35(3):501-511.
[12]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 Sheng-hong,WAN Na.Study on threedimensional residual thrust method for slope stability analysis[J].Engineering Journal of Wuhan University,2005,38(3):69-73.
[13]李同录,王艳霞,邓宏科.一种改进的三维边坡稳定性分析方法[J].岩土工程学报,2003,25(5):611-614.LI Tong-lu,WANG Yan-xia,DENG Hong-ke.An improved method for three-dimensional slope stability analysis[J].Chinese Journal of Geotechnical Engineering,2003,25(5):611-614.
[14]朱大勇,钱七虎.三维边坡严格与准严格极限平衡解答及工程应用[J].岩石力学与工程学报,2007,26(8):1513-1528.ZHU Da-yong,QIAN Qi-hu.Rigorous and quasi-rigorous limit equilibrium solutions of 3D stability and application to engineering[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(8):1513-1528.
[15]朱大勇,丁秀丽,钱七虎.一般形状边坡三维极限平衡解答[J].岩土工程学报,2007,29(10):1460-1464.ZHU Da-yong,DING Xiu-li,QIAN Qi-hu.Threedimensional limit equilibrium solution to generalizedshaped slope stability[J].Chinese Journal of Geotechnical Engineering,2007,29(10):1460-1464.
[16]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 Da-yong,JING Xiu-li,DENG Jian-hui.Explicit solution to 3D safety factor of slope based on force equilibrium and its application to engineering[J].Rock and Soil Mechanics,2008,29(8):2011-2015.
[17]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.
[18]卢坤林,朱大勇,甘文宁,等.一种边坡稳定性分析的三维极限平衡法及应用[J].岩土工程学报,2013,35(12):2276-2282.LU Kun-lin,ZHU Da-yong,GAN Wen-ning,et al.A 3Dlimit equilibrium method for slope stability analysis and its application[J].Chinese Journal of Geotechnical Engineering,2013,35(12):2276-2282.
[19]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 Hong.A rigorous three-dimensional limit equilibrium method[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(8):1529-1537.
[20]BELL J M.General slope stability analysis[J].Journal of the Soil Mechanics and Foundations,ASCE,1968,94(6):1253-1270.
[21]HOVLAND H J.Three-dimensional slope stability analysis method[J].Journal of Geotechnical Engineering Division,1997,103(9):971-986.
[22]HUNGR O,SALGADO F M,BYRNE P M.Evaluation of a three-dimensional method of slope stability analysis[J].Canadian Geotechnical Journal,1989,26(4):679-686.
[23]邓东平,李亮,赵炼恒.一种三维均质土坡滑动面搜索的新方法[J].岩石力学与工程学报,2010,29(增刊2):3719-3727.DENG Dong-ping,LI Liang,ZHAO Lian-heng.A new method for searching sliding surface of three-dimensional homogeneous soil slope[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(Supp.2):3719-3727.
[24]李亮,邓东平,赵炼恒.任意滑动面搜索新方法应用于三维复杂土坡稳定性分析[J].岩土工程学报,2011,33(4):544-553.LI Liang,DENG Dong-ping,ZHAO Lian-heng.Application of new method of arbitrary sliding surface search to stability analysis of complex three-dimensional slopes[J].Chinese Journal of Geotechnical Engineering,2011,33(4):544-553.