有限无黏性填土刚性挡土墙主动土压力计算
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摘要
针对经典的Rankine或Coulomb土压力理论不适用于山区挡土墙或邻近既有地下室基坑工程中常常遇到的墙后为有限宽度填土的情况,以墙背和稳定岩质坡面间为有限无黏性填土的刚性挡土墙为研究对象,假定在平面应变条件下,墙体平移使得墙后土体在极限平衡状态时出现通过墙踵的直线形或折线形滑裂面,且其中形成圆弧形土拱,考虑滑动土楔内水平土层间存在的平均剪应力,引入水平层分析法,得到非线性分布的主动土压力表达式。通过与文献中离心机模型试验结果的对比,验证所提方法的合理性,并在此基础上,以三角形和矩形断面有限填土挡土墙为例,探讨墙背倾角、岩质坡面倾角、墙土摩擦角、岩土摩擦角、填土内摩擦角或填土宽度等参数对主动土压力的影响。计算结果表明:该方法合理可行;有限填土时主动土压力沿墙高一般为非线性分布,且其合力作用点的位置一般不在墙高的1/3处;当填土宽度较大时,主动土压力合力大小有可能大于Coulomb土压力理论计算值,而且对于矩形断面有限填土的挡土墙,滑裂面的倾角都小于Coulomb土压力理论值。
The classical Rankine or Coulomb earth pressure theories were established on the basis of the infinite soil behind the retaining walls,so they are inappropriate in estimating the active earth pressure on retaining walls with limited backfill space built in mountainous regions or retaining structures for foundation pit built close to the existing basement.Taking a rigid retaining wall with the granular backfill built adjacent to a stable rock face as a research object,it was assumed that the outward horizontal translation of the wall made the backfill in the limit equilibrium state,the slip surface with the linear type or the mansard appeared through the wall heel.And the soil arch in the backfill took the form of a circle under the plane strain condition.Considering the mean shear stress between level soil layers in the failure wedge,the differential level layer method was introduced to obtain a new formulation for estimating the active earth pressure.In order to verify the accuracy and rationality of the proposed formulation,the predictions from the equation were compared with the centrifuge model test results in the literature.On this basis,taking these retaining walls with triangular-section or rectangular-section backfill as examples,the influences of the inclination angle of wall back,the slope angle,the interface friction angle between the wall and the backfill,the interface friction angle between the rock face and the backfill,the internal friction angle of backfill and the width of backfill on the active earth pressure distribution were investigated.The results show that:for the wall with limited backfill space,the distribution of active earth pressure along the depth is generally nonlinear,and the location of its resultant is possibly higher or lower than one third of the wall height.For the wall with wide backfill,the value of the resultant of active earth pressure is possibly greater than the solution based on the Coulomb theory.In addition,the inclination angle of the slip surface is less than that based on the Coulomb theory for the wall with rectangularsection backfill space.
The classical Rankine or Coulomb earth pressure theories were established on the basis of the infinite soil behind the retaining walls,so they are inappropriate in estimating the active earth pressure on retaining walls with limited backfill space built in mountainous regions or retaining structures for foundation pit built close to the existing basement.Taking a rigid retaining wall with the granular backfill built adjacent to a stable rock face as a research object,it was assumed that the outward horizontal translation of the wall made the backfill in the limit equilibrium state,the slip surface with the linear type or the mansard appeared through the wall heel.And the soil arch in the backfill took the form of a circle under the plane strain condition.Considering the mean shear stress between level soil layers in the failure wedge,the differential level layer method was introduced to obtain a new formulation for estimating the active earth pressure.In order to verify the accuracy and rationality of the proposed formulation,the predictions from the equation were compared with the centrifuge model test results in the literature.On this basis,taking these retaining walls with triangular-section or rectangular-section backfill as examples,the influences of the inclination angle of wall back,the slope angle,the interface friction angle between the wall and the backfill,the interface friction angle between the rock face and the backfill,the internal friction angle of backfill and the width of backfill on the active earth pressure distribution were investigated.The results show that:for the wall with limited backfill space,the distribution of active earth pressure along the depth is generally nonlinear,and the location of its resultant is possibly higher or lower than one third of the wall height.For the wall with wide backfill,the value of the resultant of active earth pressure is possibly greater than the solution based on the Coulomb theory.In addition,the inclination angle of the slip surface is less than that based on the Coulomb theory for the wall with rectangularsection backfill space.
引文
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[2]FRYDMAN S,KEISSAR I.Earth Pressure on Retaining Walls Near Rock Faces[J].Journal of Geotechnical Engineering,1987,113(6):586-599.
[3]TAKE W A,VALSANGKAR A J.Earth Pressures on Unyielding Retaining Walls of Narrow Backfill Width[J].Revue Canadiene De Géotechnical,2001,38(6):1220-1230.
[4]高印立.极限分析法计算有限范围土体土压力[J].建筑结构,2001,31(8):66-68.GAO Yin-li.Calculation of Finite Earth Pressure by Limit Analysis[J].Building Structures,2001,31(8):66-68.
[5]李峰,郭院成.基坑工程有限土体主动土压力计算分析研究[J].建筑科学,2008,24(1):15-18.LI Feng,GUO Yuan-cheng.Analytical Study on Active Soil Pressure from Finite Soil Body in Construction Pit[J].Building Science,2008,24(1):15-18.
[6]马平,秦四清,钱海涛.有限土体主动土压力计算[J].岩石力学与工程学报,2008,27(增1):3070-3074.MA Ping,QIN Si-qing,QIAN Hai-tao.Calculation of Active Earth Pressure for Limited Soils[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(S1):3070-3074.
[7]应宏伟,黄东.临近既有地下室平动模式挡土墙主动土压力研究[J].固体力学学报,2011,32(10):356-360.YING Hong-wei,HUANG Dong.Study on Active Earth Pressures on Translation Retaining Wall Adjacent to Existing Basements[J].Chinese Journal of Solid Mechanics,2011,32(10):356-360.
[8]王洪亮,宋二祥,宋福渊.紧邻既有建筑基坑有限土体主动土压力计算方法[J].工程力学,2014,31(4):76-81.WANG Hong-liang,SONG Er-xiang,SONG Fuyuan.Calculation of Active Earth Pressure for Limited Soil Between Existing Building and Excavation[J].Engineering Mechanics,2014,31(4):76-81.
[9]应宏伟,黄东,谢新宇.考虑邻近地下室外墙侧压力影响的平动模式挡土墙主动土压力研究[J].岩石力学与工程学报,2011,30(增1):2970-2978.YING Hong-wei,HUANG Dong,XIE Xin-yu.Study of Active Earth Pressure on Retaining Wall Subject to Translation Mode Considering Lateral Pressure on Adjacent Existing Basement Exterior Wall[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(S1):2970-2978.
[10]杨明辉,汪罗成,赵明华.有限土体主动土压力计算的土拱效应分析[J].建筑结构,2013,43(2):72-75.YANG Ming-hui,WANG Luo-cheng,ZHAO Minghua.Calculation of Active Earth Pressure for Finite Soils Based on the Soil Arching Theory[J].Building Structure,2013,43(2):72-75.
[11]赵琦,朱建明.临近地下室外墙影响下的考虑土拱效应的挡土墙主动土压力研究[J].岩土力学,2014,35(3):723-728.ZHAO Qi,ZHU Jian-ming.Research on Active Earth Pressure Behind Retaining Wall Adjacent to Existing Basements Exterior Wall Considering Soil Arching Effects[J].Rock and Soil Mechanics,2014,35(3):723-728.
[12]岳树桥,左人宇,陆钊.相邻基坑有限宽度土条主动土压力的计算[J].岩土力学,2016,37(7):2063-2069.YUE Shu-qiao,ZUO Ren-yu,LU Zhao.A Method for Calculating Active Earth Pressure of Soil Piece with a Finite Width Between Adjacent Foundation Pits[J].Rock and Soil Mechanics,2016,37(7):2063-2069.
[13]金亚兵,刘吉波.相邻基坑土条土压力计算方法探讨[J].岩土力学,2009,30(12):3759-3764.JIN Ya-bing,LIU Ji-bo.Discussion on Calculation Method of Earth Pressure of Earth-strip Between Neighbouring Excavations[J].Rock and Soil Mechanics,2009,30(12):3759-3764.
[14]周含川.有限土体主动土压力计算及探讨[J].重庆建筑,2009,12(8):35-37.ZHOU Han-chuan.Analytical Study and Discussion on Active Soil Pressure from Finite Soil Body[J].Chongqing Architecture,2009,12(8):35-37.
[15]FAN C C,FANG Y S.Numerical Solution of Active Earth Pressures on Rigid Retaining Walls Built Near Rock Faces[J].Computers and Geotechnics,2010,37(7/8):1023-1029.
[16]张孝彬,乐金朝,马清文.分层有限填土路基挡土墙主动土压力计算[J].中外公路,2014,34(6):16-20.ZHANG Xiao-bin,YUE Jin-chao,MA Qing-wen.Calculation of Active Earth Pressure on Retaining Wall from Layed Limited Backfills Subgrade[J].Journal of China&Foreign Highway,2014,34(6):16-20.
[17]杨明辉,戴夏斌,赵明华,等.曲线滑裂面下有限宽度填土主动土压力计算[J].岩土力学,2017,38(7):2029-2035.YANG Ming-hui,DAI Xia-bin,ZHAO Ming-hua,et al.Calculation of Active Earth Pressure for Limited Soils with Curved Sliding Surface[J].Rock and Soil Mechanics,2017,38(7):2029-2035.
[18]朱伟.考虑有限土体及挡墙变位影响的土压力试验及理论研究[D].杭州:浙江大学,2014.ZHU Wei.Experimental and Theoretical Study on Earth Pressures Considering Limited Soils and Retaining Wall Deformation[D].Hangzhou:Zhejiang University,2014.
[19]HANDY R L.The Arch in Soil Arching[J].Journal of Geotechnical Engineering,2008,111(3):302-318.
[20]HARROP-WILLIAMS K.Arch in Soil Arching[J].Journal of Geotechnical Engineering,1989,115(3):415-419.
[21]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.
[22]李东阳.基于土拱效应和剪应力作用的挡土墙主动土压力分析[D].郑州:郑州大学,2015.LI Dong-yang.Study on Active Earth Pressure on Retaining Wall Based on Soil Arch Effect and Shear Stress[D].Zhengzhou:Zhengzhou University,2015.
[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]刘忠玉,陈捷.平动模式下考虑剪应力作用的刚性挡土墙主动土压力计算[J].岩土工程学报,2016,38(12):2254-2261.LIU Zhong-yu,CHEN Jie.Active Earth Pressure Against Rigid Retaining Wall Considering Shear Stress Under Translation Mode[J].Chinese Journal of Geotechnical Engineering,2016,38(12):2254-2261.
[25]朱建明,赵琦.考虑土拱效应的挡土墙主动土压力与被动土压力统一解[J].岩土力学,2014,35(9):2501-2505.ZHU Jian-ming,ZHAO Qi.Unified Solution to Active Earth Pressure and Passive Earth Pressure on Retaining Wall Considering Soil Arching Effects[J].Rock and Soil Mechanics,2014,35(9):2501-2505.
[2]FRYDMAN S,KEISSAR I.Earth Pressure on Retaining Walls Near Rock Faces[J].Journal of Geotechnical Engineering,1987,113(6):586-599.
[3]TAKE W A,VALSANGKAR A J.Earth Pressures on Unyielding Retaining Walls of Narrow Backfill Width[J].Revue Canadiene De Géotechnical,2001,38(6):1220-1230.
[4]高印立.极限分析法计算有限范围土体土压力[J].建筑结构,2001,31(8):66-68.GAO Yin-li.Calculation of Finite Earth Pressure by Limit Analysis[J].Building Structures,2001,31(8):66-68.
[5]李峰,郭院成.基坑工程有限土体主动土压力计算分析研究[J].建筑科学,2008,24(1):15-18.LI Feng,GUO Yuan-cheng.Analytical Study on Active Soil Pressure from Finite Soil Body in Construction Pit[J].Building Science,2008,24(1):15-18.
[6]马平,秦四清,钱海涛.有限土体主动土压力计算[J].岩石力学与工程学报,2008,27(增1):3070-3074.MA Ping,QIN Si-qing,QIAN Hai-tao.Calculation of Active Earth Pressure for Limited Soils[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(S1):3070-3074.
[7]应宏伟,黄东.临近既有地下室平动模式挡土墙主动土压力研究[J].固体力学学报,2011,32(10):356-360.YING Hong-wei,HUANG Dong.Study on Active Earth Pressures on Translation Retaining Wall Adjacent to Existing Basements[J].Chinese Journal of Solid Mechanics,2011,32(10):356-360.
[8]王洪亮,宋二祥,宋福渊.紧邻既有建筑基坑有限土体主动土压力计算方法[J].工程力学,2014,31(4):76-81.WANG Hong-liang,SONG Er-xiang,SONG Fuyuan.Calculation of Active Earth Pressure for Limited Soil Between Existing Building and Excavation[J].Engineering Mechanics,2014,31(4):76-81.
[9]应宏伟,黄东,谢新宇.考虑邻近地下室外墙侧压力影响的平动模式挡土墙主动土压力研究[J].岩石力学与工程学报,2011,30(增1):2970-2978.YING Hong-wei,HUANG Dong,XIE Xin-yu.Study of Active Earth Pressure on Retaining Wall Subject to Translation Mode Considering Lateral Pressure on Adjacent Existing Basement Exterior Wall[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(S1):2970-2978.
[10]杨明辉,汪罗成,赵明华.有限土体主动土压力计算的土拱效应分析[J].建筑结构,2013,43(2):72-75.YANG Ming-hui,WANG Luo-cheng,ZHAO Minghua.Calculation of Active Earth Pressure for Finite Soils Based on the Soil Arching Theory[J].Building Structure,2013,43(2):72-75.
[11]赵琦,朱建明.临近地下室外墙影响下的考虑土拱效应的挡土墙主动土压力研究[J].岩土力学,2014,35(3):723-728.ZHAO Qi,ZHU Jian-ming.Research on Active Earth Pressure Behind Retaining Wall Adjacent to Existing Basements Exterior Wall Considering Soil Arching Effects[J].Rock and Soil Mechanics,2014,35(3):723-728.
[12]岳树桥,左人宇,陆钊.相邻基坑有限宽度土条主动土压力的计算[J].岩土力学,2016,37(7):2063-2069.YUE Shu-qiao,ZUO Ren-yu,LU Zhao.A Method for Calculating Active Earth Pressure of Soil Piece with a Finite Width Between Adjacent Foundation Pits[J].Rock and Soil Mechanics,2016,37(7):2063-2069.
[13]金亚兵,刘吉波.相邻基坑土条土压力计算方法探讨[J].岩土力学,2009,30(12):3759-3764.JIN Ya-bing,LIU Ji-bo.Discussion on Calculation Method of Earth Pressure of Earth-strip Between Neighbouring Excavations[J].Rock and Soil Mechanics,2009,30(12):3759-3764.
[14]周含川.有限土体主动土压力计算及探讨[J].重庆建筑,2009,12(8):35-37.ZHOU Han-chuan.Analytical Study and Discussion on Active Soil Pressure from Finite Soil Body[J].Chongqing Architecture,2009,12(8):35-37.
[15]FAN C C,FANG Y S.Numerical Solution of Active Earth Pressures on Rigid Retaining Walls Built Near Rock Faces[J].Computers and Geotechnics,2010,37(7/8):1023-1029.
[16]张孝彬,乐金朝,马清文.分层有限填土路基挡土墙主动土压力计算[J].中外公路,2014,34(6):16-20.ZHANG Xiao-bin,YUE Jin-chao,MA Qing-wen.Calculation of Active Earth Pressure on Retaining Wall from Layed Limited Backfills Subgrade[J].Journal of China&Foreign Highway,2014,34(6):16-20.
[17]杨明辉,戴夏斌,赵明华,等.曲线滑裂面下有限宽度填土主动土压力计算[J].岩土力学,2017,38(7):2029-2035.YANG Ming-hui,DAI Xia-bin,ZHAO Ming-hua,et al.Calculation of Active Earth Pressure for Limited Soils with Curved Sliding Surface[J].Rock and Soil Mechanics,2017,38(7):2029-2035.
[18]朱伟.考虑有限土体及挡墙变位影响的土压力试验及理论研究[D].杭州:浙江大学,2014.ZHU Wei.Experimental and Theoretical Study on Earth Pressures Considering Limited Soils and Retaining Wall Deformation[D].Hangzhou:Zhejiang University,2014.
[19]HANDY R L.The Arch in Soil Arching[J].Journal of Geotechnical Engineering,2008,111(3):302-318.
[20]HARROP-WILLIAMS K.Arch in Soil Arching[J].Journal of Geotechnical Engineering,1989,115(3):415-419.
[21]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.
[22]李东阳.基于土拱效应和剪应力作用的挡土墙主动土压力分析[D].郑州:郑州大学,2015.LI Dong-yang.Study on Active Earth Pressure on Retaining Wall Based on Soil Arch Effect and Shear Stress[D].Zhengzhou:Zhengzhou University,2015.
[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]刘忠玉,陈捷.平动模式下考虑剪应力作用的刚性挡土墙主动土压力计算[J].岩土工程学报,2016,38(12):2254-2261.LIU Zhong-yu,CHEN Jie.Active Earth Pressure Against Rigid Retaining Wall Considering Shear Stress Under Translation Mode[J].Chinese Journal of Geotechnical Engineering,2016,38(12):2254-2261.
[25]朱建明,赵琦.考虑土拱效应的挡土墙主动土压力与被动土压力统一解[J].岩土力学,2014,35(9):2501-2505.ZHU Jian-ming,ZHAO Qi.Unified Solution to Active Earth Pressure and Passive Earth Pressure on Retaining Wall Considering Soil Arching Effects[J].Rock and Soil Mechanics,2014,35(9):2501-2505.