挡土墙地震主动土压力的库仑解
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摘要
传统的Mononobe-Okabe法在实际工程中有着广泛应用,但它仅适用于无黏性土的极限土压力计算,且不能给出土压力分布。基于极限平衡理论,视墙后填土为服从Mohr-Coulomb屈服准则的理想弹塑性材料,假定墙后塑性区的一簇滑移线为直线即平面滑裂面,考虑墙背倾角、地面倾角、土黏聚力和内摩擦角、墙土之间黏结力和外摩擦角、地面均布超载、塑性临界深度以及水平和竖向地震系数等因素的影响,建立较为完善的塑性滑楔分析模型,进而采用极限平衡法求解挡土墙地震主动土压力、滑裂面土反力及其分布,并且通过量纲一化的分析首次提出几何力学相似原理。研究结果表明,总地震主动土压力随水平地震系数代数值的增大而增大;但随竖向地震系数代数值的增大并非总是减小,当水平地震系数较大时,可能出现先减后增的情况。
Although the conventional Mononobe-Okabe method is widely used in practice,it is only applicable for calculating total limit earth pressure of non-cohesive soil,and not for solving earth pressure distribution.Based on the limit equilibrium theory in this paper,the backfill is treated as a perfectly elastoplastic material which follows the Mohr-Coulomb yield criterion,and a family of slip-lines in the plastic zone is assumed as straight lines,i.e.the plane slip surfaces.The influence factors including inclination of wall,slope angle of backfill,cohesion and internal friction angle of soil,adhesion and external friction angle between wall and soil,surface uniform surcharge,plastic critical depth,horizontal and vertical seismic coefficients are considered.And a more reasonable plastic slip wedge analysis model is established to solve the seismic active earth pressure on retaining wall,the reaction force on slip surface and their distributions by using limit equilibrium method.Furthermore,the geometric and mechanical similarity principle is first presented by means of dimensional analysis.The results show that the total seismic active earth pressure increases with the increasing algebraic value of the horizontal seismic coefficient;but it does not always decrease with the increase of the algebraic value of the vertical seismic coefficient;and it may decrease first and then increase when the horizontal seismic coefficient is rather large.
Although the conventional Mononobe-Okabe method is widely used in practice,it is only applicable for calculating total limit earth pressure of non-cohesive soil,and not for solving earth pressure distribution.Based on the limit equilibrium theory in this paper,the backfill is treated as a perfectly elastoplastic material which follows the Mohr-Coulomb yield criterion,and a family of slip-lines in the plastic zone is assumed as straight lines,i.e.the plane slip surfaces.The influence factors including inclination of wall,slope angle of backfill,cohesion and internal friction angle of soil,adhesion and external friction angle between wall and soil,surface uniform surcharge,plastic critical depth,horizontal and vertical seismic coefficients are considered.And a more reasonable plastic slip wedge analysis model is established to solve the seismic active earth pressure on retaining wall,the reaction force on slip surface and their distributions by using limit equilibrium method.Furthermore,the geometric and mechanical similarity principle is first presented by means of dimensional analysis.The results show that the total seismic active earth pressure increases with the increasing algebraic value of the horizontal seismic coefficient;but it does not always decrease with the increase of the algebraic value of the vertical seismic coefficient;and it may decrease first and then increase when the horizontal seismic coefficient is rather large.
引文
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[13]GRECO V R.Discussion of“Active earth pressure on retaining wallfor c-soil backfill under seismic loading condition”by S.K.Shukla,S.K.Gupta,and N.Sivakugan[J].Journal of Geotechnicaland Geoenvironmental Engineering,2010,136(11):1 583–1 585.
[14]KIM W C,PARK D,KIM B.Development of a generalised formulafor dynamic active earth pressure[J].Geotechnique,2010,60(9):723–727.
[15]SHUKLA S K.Dynamic active thrust from c-soil backfills[J].SoilDynamics and Earthquake Engineering,2011,31(3):526–529.
[16]KUMAR J.Seismic passive earth pressure coefficients for sands[J].Canadian Geotechnical Journal,2001,38(4):876–881.
[17]SUBBA RAO K S,CHOUDHURY D.Seismic passive earth pressuresin soils[J].Journal of Geotechnical and Geoenvironmental Engineering,2005,131(1):131–135.
[18]KUMAR J,CHITIKELA S.Seismic passive earth pressure coefficientsusing the method of characteristics[J].Canadian Geotechnical Journal,2002,39(2):463–471.
[19]CHENG Y M.Seismic lateral earth pressure coefficients for c-soilsby slip line method[J].Computers and Geotechnics,2003,30(8):661–670.
[20]SOUBRA A H.Static and seismic passive earth pressure coefficientson rigid retaining structures[J].Canadian Geotechnical Journal,2000,37(2):463–478.
[21]彭明祥.挡土墙被动土压力的库仑统一解[J].岩土工程学报,2008,30(12):1 783–1 788.(PENG Mingxiang.Coulomb s unifiedsolution of passive earth pressure on retaining wall[J].Chinese Journalof Geotechnical Engineering,2008,30(12):1 783–1 788.(inChinese))
[22]彭明祥.挡土墙主动土压力的库仑统一解[J].岩土力学,2009,30(2):379–386.(PENG Mingxiang.Coulomb s unified solution ofactive earth pressure on retaining wall[J].Rock and Soil Mechanics,2009,30(2):379–386.(in Chinese))
[23]彭明祥.挡土墙主动土压力塑性临界深度的解析解[J].岩土力学,2010,31(10):3 179–3 183.(PENG Mingxiang.Analytical solution ofplastic critical depth for active earth pressure on retaining wall[J].Rock and Soil Mechanics,2010,31(10):3 179–3 183.(in Chinese))
[24]陈仲颐,周景星,王洪谨.土力学[M].北京:清华大学出版社,2009:226–227.(CHEN Zhongyi,ZHOU Jingxing,WANG Hongjin.Soil mechanics[M].Beijing:Tsinghua University Press,2009:226–227.(in Chinese))
[2]CHOUDHURY D,NIMBALKAR S.Seismic passive resistance bypseudo-dynamic method[J].Géotechnique,2005,55(9):699–702.
[3]CHOUDHURY D,NIMBALKAR S S.Pseudo-dynamic approach ofseismic active earth pressure behind retaining wall[J].Geotechnicaland Geological Engineering,2006,24(5):1 103–1 113.
[4]GHOSH P.Seismic active earth pressure behind a non-verticalretaining wall using pseudo-dynamic analysis[J].Canadian GeotechnicalJournal,2008,45(1):117–123.
[5]AZAD A,YASROBI S S,PAK A.Seismic active pressure distributionhistory behind rigid retaining walls[J].Soil Dynamics and EarthquakeEngineering,2008,28(9):365–375.
[6]OKABE S.General theory of earth pressure[J].Journal of theJapanese Society of Civil Engineers,1926,12(1):123–134.
[7]MONONOBE N,MATSUO H.On the determination of earth pressureduring earthquakes[C]//Proceedings of the World EngineeringConference.Tokyo,Japan:[s.n.],1929:179–187.
[8]SARAN S,PRAKASH S.Dimensionless parameters for static anddynamic earth pressure for retaining walls[J].Indian GeotechnicalJournal,1968,7(3):259–310.
[9]SARAN S,GUPTA R P.Seismic earth pressures behind retainingwalls[J].Indian Geotechnical Journal,2003,33(3):195–213.
[10]DAS B M,PURI V K.Static and dynamic active earth pressure[J].Geotechnical and Geological Engineering,1996,14(4):353–366.
[11]王云球.黏性土地震土压力的计算方法[J].水运工程,1980,11(8):7–13.(WANG Yunqiu.Calculation method of cohesive soil earthquakeearth pressure[J].Port and Waterway Engineering,1980,11(8):7–13.(in Chinese))
[12]SHUKLA S K,GUPTA S K,SIVAKUGAN N.Active earth pressureon retaining wall for c-soil backfill under seismic loading condition[J].Journal of Geotechnical and Geoenvironmental Engineering,2009,135(5):690–696.
[13]GRECO V R.Discussion of“Active earth pressure on retaining wallfor c-soil backfill under seismic loading condition”by S.K.Shukla,S.K.Gupta,and N.Sivakugan[J].Journal of Geotechnicaland Geoenvironmental Engineering,2010,136(11):1 583–1 585.
[14]KIM W C,PARK D,KIM B.Development of a generalised formulafor dynamic active earth pressure[J].Geotechnique,2010,60(9):723–727.
[15]SHUKLA S K.Dynamic active thrust from c-soil backfills[J].SoilDynamics and Earthquake Engineering,2011,31(3):526–529.
[16]KUMAR J.Seismic passive earth pressure coefficients for sands[J].Canadian Geotechnical Journal,2001,38(4):876–881.
[17]SUBBA RAO K S,CHOUDHURY D.Seismic passive earth pressuresin soils[J].Journal of Geotechnical and Geoenvironmental Engineering,2005,131(1):131–135.
[18]KUMAR J,CHITIKELA S.Seismic passive earth pressure coefficientsusing the method of characteristics[J].Canadian Geotechnical Journal,2002,39(2):463–471.
[19]CHENG Y M.Seismic lateral earth pressure coefficients for c-soilsby slip line method[J].Computers and Geotechnics,2003,30(8):661–670.
[20]SOUBRA A H.Static and seismic passive earth pressure coefficientson rigid retaining structures[J].Canadian Geotechnical Journal,2000,37(2):463–478.
[21]彭明祥.挡土墙被动土压力的库仑统一解[J].岩土工程学报,2008,30(12):1 783–1 788.(PENG Mingxiang.Coulomb s unifiedsolution of passive earth pressure on retaining wall[J].Chinese Journalof Geotechnical Engineering,2008,30(12):1 783–1 788.(inChinese))
[22]彭明祥.挡土墙主动土压力的库仑统一解[J].岩土力学,2009,30(2):379–386.(PENG Mingxiang.Coulomb s unified solution ofactive earth pressure on retaining wall[J].Rock and Soil Mechanics,2009,30(2):379–386.(in Chinese))
[23]彭明祥.挡土墙主动土压力塑性临界深度的解析解[J].岩土力学,2010,31(10):3 179–3 183.(PENG Mingxiang.Analytical solution ofplastic critical depth for active earth pressure on retaining wall[J].Rock and Soil Mechanics,2010,31(10):3 179–3 183.(in Chinese))
[24]陈仲颐,周景星,王洪谨.土力学[M].北京:清华大学出版社,2009:226–227.(CHEN Zhongyi,ZHOU Jingxing,WANG Hongjin.Soil mechanics[M].Beijing:Tsinghua University Press,2009:226–227.(in Chinese))
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