刚性挡土墙平移模式的土拱形状与主动土压力分析
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摘要
与假定土拱形状与水平层分析相结合的土压力计算方法不同,本文不事先假设土拱形状,考虑条间剪切应力的影响,通过对滑动土体中二维微分单元的受力分析建立平衡微分方程,得到了滑动土体中任一点的应力解。同时求得作用在挡土墙上的土压力,并进一步推导出土拱曲线的解析表达式,讨论了内、外摩擦角等因素对土压力与土拱形状的影响,且与现有理论和试验结果进行了比较分析,在此基础上提出一个实用的土压力计算公式。计算结果表明:土压力计算公式得到的土压力分布与试验结果吻合较好,且当墙高增加时吻合程度更高。当外摩擦角较小时,土拱曲线表达式得到的土拱与圆弧拱较接近,随着外摩擦角的增大土拱越来越陡,但整体位于抛物线拱之下。该研究所提出的实用计算公式只与?/?有关,方便工程上应用。
Compared with the existing method combining soil arch shape and horizontal layer analysis, this study has no assumption of soil arch shape and shear stress is considered. The stress solution of any point in the sliding soil is obtained by solving equilibrium differential equations of the two-dimensional differential element, and the active earth pressure imposed on the rigid wall is further derived. Subsequently, based on the stress state of any point in the sliding soil, the analytic expression of the arch shape is established. Furthermore, the effects of internal friction angle, soil-wall friction angle on earth pressure and soil arching shape are discussed. Finally, the obtained results are compared with the results derived from existing theory and experimental results, and the conversion formula between the proposed active earth pressure coefficient and Coulomb theory is obtained. The results indicate that the proposed distribution of earth pressure is in good agreement with the experimental results, especially in the case of high wall. When the soil-wall friction angle is small, the calculated soil arch is similar to the arc, and the soil arch becomes steeper in terms of the increase of soil-wall friction angle, which is always under the parabolic arch. The practical formula is only related to ?/?, which is convenient to use in engineering.
Compared with the existing method combining soil arch shape and horizontal layer analysis, this study has no assumption of soil arch shape and shear stress is considered. The stress solution of any point in the sliding soil is obtained by solving equilibrium differential equations of the two-dimensional differential element, and the active earth pressure imposed on the rigid wall is further derived. Subsequently, based on the stress state of any point in the sliding soil, the analytic expression of the arch shape is established. Furthermore, the effects of internal friction angle, soil-wall friction angle on earth pressure and soil arching shape are discussed. Finally, the obtained results are compared with the results derived from existing theory and experimental results, and the conversion formula between the proposed active earth pressure coefficient and Coulomb theory is obtained. The results indicate that the proposed distribution of earth pressure is in good agreement with the experimental results, especially in the case of high wall. When the soil-wall friction angle is small, the calculated soil arch is similar to the arc, and the soil arch becomes steeper in terms of the increase of soil-wall friction angle, which is always under the parabolic arch. The practical formula is only related to ?/?, which is convenient to use in engineering.
引文
[1]TSAGARELI Z V.Experimental investigation of the pressure of a loose medium on retaining walls with a vertical back face and horizontal backfill surface[J].Soil Mechanics and Foundation Engineering,1965,2(4):197-200.
[2]SHERIF M A,FANG Y,SHERIF R I.aK and 0K behind rotating and non-yielding walls[J].Journal of Geotechnical Engineering,1984,110(1):41-56.
[3]FANG Y,ISHIBASHI I.Static earth pressures with various wall movements[J].Journal of Geotechnical Engineering,1994,120(8):317-333.
[4]CHANG M F.Lateral earth pressures behind rotating walls[J].Canadian Geotechnical Journal,1997,34(34):498-509.
[5]O’NEAL T S,HAGERTY D J.Earth pressures in confined cohesionless backfill against tall rigid wall:Acase history[J].Canadian Geotechnical Journal,2011,48(8):1188-1197.
[6]КАГАНМЕ.ОДавЛениинаподпорнуюстенкупринелинейномегораспределений[J].Строительнаямеханикаирасчетсооружений,1960,6:35-40.
[7]WANG Y Z.Distribution of earth pressure on a retaining wall[J].Geotechnique,2000,50(1):83-88.
[8]王元战,李新国,陈楠楠.挡土墙主动土压力分布与侧压力系数[J].岩土力学,2005,26(7):1019-1022.WANG Yuan-zhan,LI Xin-guo,CHEN Nan-nan.Active earth pressure on a retaining wall and lateral coefficient of earth pressure[J].Rock and Soil Mechanics,2005,26(7):1019-1022.
[9]HARROP-WILLIAMS K O.Geostatic wall pressures[J].Journal of Geotechnical Engineering,1989,115(9):1321-1325.
[10]林智勇,戴自航,苏美选.复杂条件下挡土墙主动土压力解析解[J].岩土工程学报,2008,30(4):555-559.LIN Zhi-yong,DAI Zi-hang,SU Mei-xuan.Analytical solution of active earth pressure acting on retaining walls under complicated conditions[J].Chinese Journal of Geotechnical Engineering,2008,30(4):555-559.
[11]林宇亮,杨果林,赵炼恒,等.地震动土压力水平层分析法[J].岩石力学与工程学报,2010,29(12):2581-2591.LIN Yu-liang,YANG Guo-lin,ZHAO Lian-heng,et al.Horizontal slices analysis method for seismic earth pressure calculation[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(12):2581-2591.
[12]TERZAGHI K.Theoretical soil mechanics[M].New York:[s.n.],1943.
[13]HANDY R L.The arch in soil arching[J].Journal of Geotechnical Engineering,2008,111(3):302-318.
[14]PAIK K H,SALGADO R.Estimation of active earth pressure against rigid retaining walls considering arching effects[J].Géotechnique,2003,53(7):643-653.
[15]GOEL S,PATRA N R.Effect of arching on active earth pressure for rigid retaining walls considering translation mode[J].International Journal of Geomechanics,2008,8(2):123-133.
[16]蒋波,应宏伟,谢康和.挡土墙后土体拱效应分析[J].浙江大学学报(工学版),2005,39(1):131-136.JIANG Bo,YING Hong-wei,XIE Kang-he.Analysis on soil arching behind retaining wall[J].Journal of Zhejiang University(Engineering Science),2005,39(1):131-136.
[17]杨贵,王阳阳,刘彦辰.基于曲线滑裂面的挡墙主动土压力分析[J].岩土力学,2017,38(8):2182-2188.YANG Gui,WANG Yang-yang,LIU Yan-chen.Analysis of active earth pressure on retaining walls based on curved sliding surface[J].Rock and Soil Mechanics,2017,38(8):2182-2188.
[18]彭述权,周健,樊玲,等.考虑土拱效应刚性挡墙土压力研究[J].岩土力学,2008,29(10):2701-2707.PENG Shu-quan,ZHOU Jian,FAN Ling,et al.Research on earth pressure of rigid retaining wall considering soil arching[J].Rock and Soil Mechanics,2008,29(10):2701-2707.
[19]章瑞文,徐日庆.土拱效应原理求解挡土墙土压力方法的改进[J].岩土力学,2008,29(4):1057-1060.ZHANG Rui-wen,XU Ri-qing.Solution of problem of earth pressure on retaining wall calculated by method of soil arching effect[J].Rock and Soil Mechanics,2008,29(4):1057-1060.
[20]侯键,夏唐代,孔祥冰,等.基于土拱效应原理求解挡土墙被动土压力[J].岩土力学,2012,33(10):2996-3000.HOU Jian,XIA Tang-dai,KONG Xiang-bing,et al.Passive earth pressure on retaining walls calculated by principle of soil arching effect[J].Rock and Soil Mechanics,2012,33(10):2996-3000.
[21]涂兵雄,贾金青.考虑土拱效应的黏性填土挡土墙主动土压力研究[J].岩石力学与工程学报,2012,31(5):1064-1070.TU Bing-xiong,JIA Jin-qing.Research on active earth pressure behind rigid retaining wall from clayey backfill considering soil arching effects[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(5):1064-1070.
[22]ZHOU Y T,CHEN Q S,CHEN F Q,et al.Active earth pressure on translating rigid retaining structures considering soil arching effect[J].European Journal of Environmental&Civil Engineering,2018,22(8):910-926.
[23]刘忠玉,陈捷,李东阳.考虑剪应力作用的刚性挡土墙主动土压力分析[J].岩土力学,2016,37(9):2443-2450.LIU Zhong-yu,CHEN Jie,LI Dong-yang.Calculation of active earth pressure against rigid retaining wall considering shear stress[J].Rock and Soil Mechanics,2016,37(9):2443-2450.
[24]周云东,杨德.基于土拱效应的挡墙后砂土主动土压力计算分析[J].河海大学学报(自然科学版),2016,44(2):149-153.ZHOU Yun-dong,YANG De.Calculation and analysis of active earth pressure on retaining walls considering soil arching effects[J].Journal of Hohai University(Natural Sciences),2016,44(2):149-153.
[25]茅以升.挡土墙土压力的两个经典理论中的基本问题[J].土木工程学报,1954,1(3):249-281.MAO Yi-sheng.Some apparent discrepancies in coulomb’s theory and unjustifiable questions about Rankine’s theory for earth pressure on retaining walls[J].China Civil Engineering Journal,1954,1(3):249-281.
[26]KRYNINE D P.Discussion of'Stability and stiffness of cellular cofferdams'by Karl Terzaghi[J].Transactions of the American Society of Civil Engineers,1945,110(1):1120-1186.
[27]WALKER D M.An approximate theory for pressures and arching in hoppers[J].Chemical Engineering Science,1966,21(11):975-997.
[28]LI M G,CHEN J J,WANG J H.Arching effect on lateral pressure of confined granular material:Numerical and theoretical analysis[J].Granular Matter,2017,19(2):20.
[2]SHERIF M A,FANG Y,SHERIF R I.aK and 0K behind rotating and non-yielding walls[J].Journal of Geotechnical Engineering,1984,110(1):41-56.
[3]FANG Y,ISHIBASHI I.Static earth pressures with various wall movements[J].Journal of Geotechnical Engineering,1994,120(8):317-333.
[4]CHANG M F.Lateral earth pressures behind rotating walls[J].Canadian Geotechnical Journal,1997,34(34):498-509.
[5]O’NEAL T S,HAGERTY D J.Earth pressures in confined cohesionless backfill against tall rigid wall:Acase history[J].Canadian Geotechnical Journal,2011,48(8):1188-1197.
[6]КАГАНМЕ.ОДавЛениинаподпорнуюстенкупринелинейномегораспределений[J].Строительнаямеханикаирасчетсооружений,1960,6:35-40.
[7]WANG Y Z.Distribution of earth pressure on a retaining wall[J].Geotechnique,2000,50(1):83-88.
[8]王元战,李新国,陈楠楠.挡土墙主动土压力分布与侧压力系数[J].岩土力学,2005,26(7):1019-1022.WANG Yuan-zhan,LI Xin-guo,CHEN Nan-nan.Active earth pressure on a retaining wall and lateral coefficient of earth pressure[J].Rock and Soil Mechanics,2005,26(7):1019-1022.
[9]HARROP-WILLIAMS K O.Geostatic wall pressures[J].Journal of Geotechnical Engineering,1989,115(9):1321-1325.
[10]林智勇,戴自航,苏美选.复杂条件下挡土墙主动土压力解析解[J].岩土工程学报,2008,30(4):555-559.LIN Zhi-yong,DAI Zi-hang,SU Mei-xuan.Analytical solution of active earth pressure acting on retaining walls under complicated conditions[J].Chinese Journal of Geotechnical Engineering,2008,30(4):555-559.
[11]林宇亮,杨果林,赵炼恒,等.地震动土压力水平层分析法[J].岩石力学与工程学报,2010,29(12):2581-2591.LIN Yu-liang,YANG Guo-lin,ZHAO Lian-heng,et al.Horizontal slices analysis method for seismic earth pressure calculation[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(12):2581-2591.
[12]TERZAGHI K.Theoretical soil mechanics[M].New York:[s.n.],1943.
[13]HANDY R L.The arch in soil arching[J].Journal of Geotechnical Engineering,2008,111(3):302-318.
[14]PAIK K H,SALGADO R.Estimation of active earth pressure against rigid retaining walls considering arching effects[J].Géotechnique,2003,53(7):643-653.
[15]GOEL S,PATRA N R.Effect of arching on active earth pressure for rigid retaining walls considering translation mode[J].International Journal of Geomechanics,2008,8(2):123-133.
[16]蒋波,应宏伟,谢康和.挡土墙后土体拱效应分析[J].浙江大学学报(工学版),2005,39(1):131-136.JIANG Bo,YING Hong-wei,XIE Kang-he.Analysis on soil arching behind retaining wall[J].Journal of Zhejiang University(Engineering Science),2005,39(1):131-136.
[17]杨贵,王阳阳,刘彦辰.基于曲线滑裂面的挡墙主动土压力分析[J].岩土力学,2017,38(8):2182-2188.YANG Gui,WANG Yang-yang,LIU Yan-chen.Analysis of active earth pressure on retaining walls based on curved sliding surface[J].Rock and Soil Mechanics,2017,38(8):2182-2188.
[18]彭述权,周健,樊玲,等.考虑土拱效应刚性挡墙土压力研究[J].岩土力学,2008,29(10):2701-2707.PENG Shu-quan,ZHOU Jian,FAN Ling,et al.Research on earth pressure of rigid retaining wall considering soil arching[J].Rock and Soil Mechanics,2008,29(10):2701-2707.
[19]章瑞文,徐日庆.土拱效应原理求解挡土墙土压力方法的改进[J].岩土力学,2008,29(4):1057-1060.ZHANG Rui-wen,XU Ri-qing.Solution of problem of earth pressure on retaining wall calculated by method of soil arching effect[J].Rock and Soil Mechanics,2008,29(4):1057-1060.
[20]侯键,夏唐代,孔祥冰,等.基于土拱效应原理求解挡土墙被动土压力[J].岩土力学,2012,33(10):2996-3000.HOU Jian,XIA Tang-dai,KONG Xiang-bing,et al.Passive earth pressure on retaining walls calculated by principle of soil arching effect[J].Rock and Soil Mechanics,2012,33(10):2996-3000.
[21]涂兵雄,贾金青.考虑土拱效应的黏性填土挡土墙主动土压力研究[J].岩石力学与工程学报,2012,31(5):1064-1070.TU Bing-xiong,JIA Jin-qing.Research on active earth pressure behind rigid retaining wall from clayey backfill considering soil arching effects[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(5):1064-1070.
[22]ZHOU Y T,CHEN Q S,CHEN F Q,et al.Active earth pressure on translating rigid retaining structures considering soil arching effect[J].European Journal of Environmental&Civil Engineering,2018,22(8):910-926.
[23]刘忠玉,陈捷,李东阳.考虑剪应力作用的刚性挡土墙主动土压力分析[J].岩土力学,2016,37(9):2443-2450.LIU Zhong-yu,CHEN Jie,LI Dong-yang.Calculation of active earth pressure against rigid retaining wall considering shear stress[J].Rock and Soil Mechanics,2016,37(9):2443-2450.
[24]周云东,杨德.基于土拱效应的挡墙后砂土主动土压力计算分析[J].河海大学学报(自然科学版),2016,44(2):149-153.ZHOU Yun-dong,YANG De.Calculation and analysis of active earth pressure on retaining walls considering soil arching effects[J].Journal of Hohai University(Natural Sciences),2016,44(2):149-153.
[25]茅以升.挡土墙土压力的两个经典理论中的基本问题[J].土木工程学报,1954,1(3):249-281.MAO Yi-sheng.Some apparent discrepancies in coulomb’s theory and unjustifiable questions about Rankine’s theory for earth pressure on retaining walls[J].China Civil Engineering Journal,1954,1(3):249-281.
[26]KRYNINE D P.Discussion of'Stability and stiffness of cellular cofferdams'by Karl Terzaghi[J].Transactions of the American Society of Civil Engineers,1945,110(1):1120-1186.
[27]WALKER D M.An approximate theory for pressures and arching in hoppers[J].Chemical Engineering Science,1966,21(11):975-997.
[28]LI M G,CHEN J J,WANG J H.Arching effect on lateral pressure of confined granular material:Numerical and theoretical analysis[J].Granular Matter,2017,19(2):20.
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