Sarma法在不同方位地震力下的计算研究
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摘要
Sarma法是计算边坡和堤坝稳定性分析广泛应用的方法,但在构建平衡方程时假设地震力方向为水平方向,未能考虑不同方位地震力对临界地震系数和边坡稳定系数的影响。为了研究临界地震系数和稳定系数在不同方位地震力下分布规律,本文在原Sarma的基础上,假设地震力非水平方向,在任意角度上尝试给出推导公式,并引入平均值对临界地震系数进行迭代求解。再求出临界地震系数对应的边坡稳定系数值后,可以得到地震力方向与临界地震系数和边坡稳定性系数的关系,临界地震系数最小值所代表的地震力方位作为用于边坡稳定性分析。经分析,临界地震系数极小值所代表的地震力方向不一定是指向坡外的水平方向;修正后临界地震系数极小值代表着边坡所能承受最小地震力的情况;同时求出的边坡稳定系数和原Sarma求出的边坡稳定系数相比误差不大,说明在假设地震力方位时,任意方位都可求解出准确的边坡稳定系数。
The Sarma method is widely used to calculate the slope and embankment stability analysis.But the method assumes the horizontal direction as seismic force direction.So it does not consider the impact of the different directions of seismic force.In order to study the critical seismic coefficient and stability factor in different directions under the distribution of seismic forces,this paper,based on the traditional Sarma,assumes that non-horizontal seis-mic force,at any given positions of seismic force,and try to derive the formula.And the mean value is introduced to iteration when deal with the result of critical seismic coefficient.Examples are used to show the relationship among the directions of seismic force and the slope stability factor.After solving the minimum critical seismic coefficient,the represent angle of the minimum critical seismic coefficient is the angle of the smallest seismic force.On this point of the smallest seismic force,the stability analysis is gained in two classical examples.The analyses of the two examples derive the minimum value at last.Through the analysis,on the one hand,the direction of seismic forces re-presented by the minimum value is not necessarily pointing the outside horizontal direction.On the other hand,the corrected minimum critical seismic coefficient represents the authentic status that the smallest seismic force can be withstood by slope.Last but not the least,there is no sharp contrast between the calculated slope stability factor and the original slope stability factor.That is to say,when assuming the direction of seismic force,there will be no inac-curacy of assuming any position of the seismic force to calculate the valid slope stability factor.
The Sarma method is widely used to calculate the slope and embankment stability analysis.But the method assumes the horizontal direction as seismic force direction.So it does not consider the impact of the different directions of seismic force.In order to study the critical seismic coefficient and stability factor in different directions under the distribution of seismic forces,this paper,based on the traditional Sarma,assumes that non-horizontal seis-mic force,at any given positions of seismic force,and try to derive the formula.And the mean value is introduced to iteration when deal with the result of critical seismic coefficient.Examples are used to show the relationship among the directions of seismic force and the slope stability factor.After solving the minimum critical seismic coefficient,the represent angle of the minimum critical seismic coefficient is the angle of the smallest seismic force.On this point of the smallest seismic force,the stability analysis is gained in two classical examples.The analyses of the two examples derive the minimum value at last.Through the analysis,on the one hand,the direction of seismic forces re-presented by the minimum value is not necessarily pointing the outside horizontal direction.On the other hand,the corrected minimum critical seismic coefficient represents the authentic status that the smallest seismic force can be withstood by slope.Last but not the least,there is no sharp contrast between the calculated slope stability factor and the original slope stability factor.That is to say,when assuming the direction of seismic force,there will be no inac-curacy of assuming any position of the seismic force to calculate the valid slope stability factor.
引文
[1]俞培基,刘小生,牛建新.萨尔马法在大广坝抗震稳定分析中的应用[J].水利水电技术,1994,(7):10～15.Yu Peixin,Liu Xiaosheng,Niu Jianxin.Seismic stability analysis ofdaguang earth dam by using Sarma method.Water Resources andHydropower Engineering,1994,(7):10～15.
[2]佴磊,徐燕,代树林.边坡工程[M].北京:科学出版社,2010,79.Er Lei,Xu Yan,Dai Shulin.Slope Engineering.Beijing:SciencePress,2010,79.
[3]李新利,陈力,任向宇.Sarma法分析动水压力对藤子沟水电站边坡稳定性的影响[J].岩土工程界,2006,9(12):58～60.Li Xinli,Chen Li,Ren Xiangyu.Sarma analysis of hydrodynamicpressure on slope stability Tengzigou hydropower impact.Geotech-nical Engineering World 2005,9(12):58～60.
[4]范鹏贤,郭志鹏,朱大勇.牛顿法计算Sarma法边坡稳定系数[J].减灾防灾工程学报,2006,26(3):274～278.Fan Pengxian,Guo Zhipeng,Zhu Dayong.The computation ofSafety factor of Sarma method by Newton method.Journal of Disas-ter Prevent and mitigation Engineering,2006,26(3):274～278.
[5]陈祖煜.土质边坡稳定分析——原理.方法.程序[M].北京:中国水利水电出版社,2003.Chen Zuyu.Soil Slope Stability Analysis—Theory,Methods andPrograms.Beijing:China WaterPower Press,2003.
[6]何满潮,姚爱军.边坡岩体水力学作用的研究[J].岩石力学与工程学报,1998,17(6):662～666.He Manchao,Yao Aijun.Research on hydraulic action for sloperockmass.Chinese Journal of Rock Mechanics and Engineering,1998,17(6):662～666.
[7]庄心善,胡其志,何世秀.锚杆加固岩体边坡设计法分析[J].岩石力学与工程学报,2002,21(7):1013～1015.Zhuang Xinshan,Hu Qizhi,He Shixiu.Design method analysis foranchored rockmass slope.Chinese Journal of Rock Mechanics andEngineering,2002,21(7):1013～1015.
[8]崔政权,李宁.边坡工程——理论与实践最新发展[M].北京:中国水利水电出版社,1999.Cui Zhengquan,Li Ning.Slope Engineering—Recent Advances inTheory and Practice.Beijing:China Water Power Press,1999.
[9]朱大勇,范鹏贤,郭志鹏.关于Sarma改进算法的补充[J].岩石力学与工程学报,2006,25(11):2343～2345.Zhu Dayong,Fan Penxian,Guo Zhipeng.Complementarities tomodified computation procedure of Sarma method.Chinese Journalof Rock Mechanics and Engineering,2006,25(11):2343～2345.
[10]张强勇,刘大文,蔡德文.Sarma法在加锚岩质高边坡安全稳定性评价分析中的应用[J].岩石力学与工程学报,2005,24(18):3365～3372.Zhang Qiangyong,Liu Dawen,Cai Dewen.Application of Sarmamethod to stability evaluation analysis of a large anchoredrockmass slope.Chinese Journal of Rock Mechanics and Engi-neering,2005,24(18):3365～3372.
[11]Zhu D,Lee CF.Explicit limit equilibrium solution for slope sta-bility.Int.J.Numer.Anal.Meth.Geomech.,2002,(26):1573～1590.
[12]Sarma SK.Stability analysis of embankments and slopes.Geotech-nique,1973,(23):423～433.
[2]佴磊,徐燕,代树林.边坡工程[M].北京:科学出版社,2010,79.Er Lei,Xu Yan,Dai Shulin.Slope Engineering.Beijing:SciencePress,2010,79.
[3]李新利,陈力,任向宇.Sarma法分析动水压力对藤子沟水电站边坡稳定性的影响[J].岩土工程界,2006,9(12):58～60.Li Xinli,Chen Li,Ren Xiangyu.Sarma analysis of hydrodynamicpressure on slope stability Tengzigou hydropower impact.Geotech-nical Engineering World 2005,9(12):58～60.
[4]范鹏贤,郭志鹏,朱大勇.牛顿法计算Sarma法边坡稳定系数[J].减灾防灾工程学报,2006,26(3):274～278.Fan Pengxian,Guo Zhipeng,Zhu Dayong.The computation ofSafety factor of Sarma method by Newton method.Journal of Disas-ter Prevent and mitigation Engineering,2006,26(3):274～278.
[5]陈祖煜.土质边坡稳定分析——原理.方法.程序[M].北京:中国水利水电出版社,2003.Chen Zuyu.Soil Slope Stability Analysis—Theory,Methods andPrograms.Beijing:China WaterPower Press,2003.
[6]何满潮,姚爱军.边坡岩体水力学作用的研究[J].岩石力学与工程学报,1998,17(6):662～666.He Manchao,Yao Aijun.Research on hydraulic action for sloperockmass.Chinese Journal of Rock Mechanics and Engineering,1998,17(6):662～666.
[7]庄心善,胡其志,何世秀.锚杆加固岩体边坡设计法分析[J].岩石力学与工程学报,2002,21(7):1013～1015.Zhuang Xinshan,Hu Qizhi,He Shixiu.Design method analysis foranchored rockmass slope.Chinese Journal of Rock Mechanics andEngineering,2002,21(7):1013～1015.
[8]崔政权,李宁.边坡工程——理论与实践最新发展[M].北京:中国水利水电出版社,1999.Cui Zhengquan,Li Ning.Slope Engineering—Recent Advances inTheory and Practice.Beijing:China Water Power Press,1999.
[9]朱大勇,范鹏贤,郭志鹏.关于Sarma改进算法的补充[J].岩石力学与工程学报,2006,25(11):2343～2345.Zhu Dayong,Fan Penxian,Guo Zhipeng.Complementarities tomodified computation procedure of Sarma method.Chinese Journalof Rock Mechanics and Engineering,2006,25(11):2343～2345.
[10]张强勇,刘大文,蔡德文.Sarma法在加锚岩质高边坡安全稳定性评价分析中的应用[J].岩石力学与工程学报,2005,24(18):3365～3372.Zhang Qiangyong,Liu Dawen,Cai Dewen.Application of Sarmamethod to stability evaluation analysis of a large anchoredrockmass slope.Chinese Journal of Rock Mechanics and Engi-neering,2005,24(18):3365～3372.
[11]Zhu D,Lee CF.Explicit limit equilibrium solution for slope sta-bility.Int.J.Numer.Anal.Meth.Geomech.,2002,(26):1573～1590.
[12]Sarma SK.Stability analysis of embankments and slopes.Geotech-nique,1973,(23):423～433.
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