多层加筋垫层刚性桩网复合地基的承载特性
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摘要
为研究多层加筋垫层刚性桩网复合地基的承载特性,将设置有多层土工格栅的加筋垫层视为大挠度薄板进行分析,运用层合板理论,模拟多层土工格栅与碎石垫层之间的相互作用,建立加筋垫层抗弯刚度矩阵的计算方法。考虑刚性桩网复合地基的三维应力和位移边界条件,根据静力平衡条件,建立加筋垫层应力函数和挠度微分控制方程,并利用伽辽金方法进行求解。在此基础上,利用Winkler地基梁理论和大挠度薄板理论对桩土应力比和格栅拉力进行计算。最后,运用实际工程对计算方法进行验证,并综合分析格栅总层数、铺设间隔和位置等因素对桩土应力比及格栅拉力的影响。研究结果表明:理论计算结果与实测结果较为吻合;随着格栅总层数的增大,桩土应力比增大而格栅拉力降低,铺设2～3层格栅效率最高;随着铺设格栅间隔和底层格栅距桩帽距离的增大,桩土应力比降低,而格栅拉力增大。
This study aims to explore the bearing characteristics of rigid pile-net composite foundation with multi-layer reinforced cushion.Firstly,the reinforced cushion layer with multi-layer geogrids is regarded as a large deflection plate for simplification.The interaction characteristics between multi-layer geogrids and gravel cushions were analyzed based on laminating theory.The stiffness matrix of reinforced cushion was then derived.Considering the actual three-dimensional stress and displacement boundary of the rigid pilenet composite foundation,the stress function and the deflection differential control equations were deduced through the static equilibrium.Subsequently,Galerkin method was used to solve the equations.Based on the deformation of the reinforced cushion layer,the pile-soil stress ratio of rigid pile-net composite foundation was calculated through Winkler foundation beam method and the tension force of geogrids was derived via large deflection plate theory.Finally,the calculation method was validated by practical engineering.The factors that affect pile-soil stress ratio and tension force,such as total number of geogrids,geogrids spacing and location of the geogrids,were systematically analyzed.It is shown that the analytical solutions agree well with the measured data.With increase of the total number of geogrid layers,the pile-soil stress ratio increases and the geogrid tensile force decreases.The most efficient number of geogrid layers is 2 or 3.With the increase of vertical spacing between geogrids and the spacing from the bottom geogrid to pile cap,pile-soil stress ratio decreases and tension force increases.More importantly,these findings may provide guidance on optimal design of geogrid in engineering practice.
This study aims to explore the bearing characteristics of rigid pile-net composite foundation with multi-layer reinforced cushion.Firstly,the reinforced cushion layer with multi-layer geogrids is regarded as a large deflection plate for simplification.The interaction characteristics between multi-layer geogrids and gravel cushions were analyzed based on laminating theory.The stiffness matrix of reinforced cushion was then derived.Considering the actual three-dimensional stress and displacement boundary of the rigid pilenet composite foundation,the stress function and the deflection differential control equations were deduced through the static equilibrium.Subsequently,Galerkin method was used to solve the equations.Based on the deformation of the reinforced cushion layer,the pile-soil stress ratio of rigid pile-net composite foundation was calculated through Winkler foundation beam method and the tension force of geogrids was derived via large deflection plate theory.Finally,the calculation method was validated by practical engineering.The factors that affect pile-soil stress ratio and tension force,such as total number of geogrids,geogrids spacing and location of the geogrids,were systematically analyzed.It is shown that the analytical solutions agree well with the measured data.With increase of the total number of geogrid layers,the pile-soil stress ratio increases and the geogrid tensile force decreases.The most efficient number of geogrid layers is 2 or 3.With the increase of vertical spacing between geogrids and the spacing from the bottom geogrid to pile cap,pile-soil stress ratio decreases and tension force increases.More importantly,these findings may provide guidance on optimal design of geogrid in engineering practice.
引文
[1]SUN L,ZHENG J J,ZHANG J,et al.Mechanical performance of geosynthetic-reinforced pile-supported embankments[J]. Advanced Materials Research,2010,156/157:1696-1701.
[2]LU W H,MIAO L C.A simplified 2-D evaluation method of the arching effect for geosynthetic-reinforced and pile-supported embankments[J].Computers and Geotechnics,2015,65:97-103.
[3]钱劲松,白墨,罗鑫,等.桩承式加筋路堤桩体荷载分担比计算[J].岩石力学与工程学报,2017,19(6):3587-3595.QIAN J S,BAI M,LUO X,et al.,Pile efficacy calculation of geosynthetics reinforced pile supported embankment[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(Sup):3587-3595.(in Chinese)
[4]闫澍旺,郎瑞卿,孙立强,等.基于薄板理论的刚性桩网复合地基桩土应力比计算[J].岩石力学与工程学报,2017,36(8):2051-2060.YAN S W,LANG R Q,SUN L Q,et al.,Calculation of pile-soil stress ratio in composite foundation with rigid pile-net based on plate theory[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(8):2051-2060.(in Chinese)
[5]ARIYARATHNE P,LIYANAPATHIRANA D S,LEO C J.Comparison of different two-dimensional idealizations for a geosynthetic-reinforced pilesupported embankment[J].International Journal of Geomechanics,2013,13(6):754-768.
[6]ROWE R K,LIU K W.Three-dimensional finite element modelling of a full-scale geosyntheticreinforced,pile-supported embankment[J].Canadian Geotechnical Journal,2015,52(12):2041-2054.
[7]曹文昭,郑俊杰,严勇,桩承式变刚度加筋垫层复合地基数值模拟[J].岩土工程学报,2017(Sup2):83-86.CAO W Z, ZHENG J J, YAN Y. Numerical simulation of composite foundation using pile-supported and geosynthetics-reinforced cushion with variable stiffness[J]. Chinese Journal of Geotechnical Engineering,2017(Sup2):83-86.(in Chinese)
[8]XING H F,ZHANG Z,LIU H B,et al.Large-scale tests of pile-supported earth platform with and without geogrid[J].Geotextiles and Geomembranes,2014,42(6):586-598.
[9]CAO W Z,ZHENG J J,ZHANG J,et al.Field test of a geogrid-reinforced and floating pile-supported embankment[J].Geosynthetics International,2016,23(5):348-361.
[10]ARIYARATHNE P,LIYANAPATHIRANA D S,LEO C J.Effect of geosynthetic creep on reinforced pile-supported embankment systems[J].Geosynthetics International,2013,20(6):421-435.
[11]British Standards Institution.Code of practice for strengthened reinforced soils and other fills:BS8006[S].London,UK,1995.
[12]FUR D G.Recommendations for Design and Analysis of Earth Structures using Geosynthetic ReinforcementsEBGEO,Second Edition[M].Ernst &Sohn,2011.
[13]Nordic Handbook.Reinforced soils and fill[M].Stockholm:Nordic Geotechnical Society,2002.
[14]The design and construction handbook of mixing piled foundation(machine mixing)[M].Tokyo:Railway Technology Research Institute,2001.
[15]VAN EEKELEN S J M,BEZUIJEN A,VAN TOL A F.Analysis and modification of the British Standard BS8006 for the design of piled embankments[J].eotextiles and Geomembranes,2011,29(3):345-359.
[16]BLANC M, THOREL L, GIROUT R,et al.Geosynthetic reinforcement of a granular load transfer platform above rigid inclusions:comparison between centrifuge testing and analytical modeling[J].Geosynthetics International,2014,21(1):37-52.
[17]魏平,魏静,杨松林,等.动载作用下桩网结构低路基双层土工格栅力学特性[J].铁道工程学报,2017,34(7):30-35.WEI P,WEI J,YANG S L,et al.Research on the mechanical characteristics of double-deck geogrids of pile net structure of low embankment under dynamic load[J].Journal of Railway Engineering Society,2017,34(7):30-35.(in Chinese)
[18]HALVORDSON K A,PLAUT R H,FILZ G M.Analysis of geosynthetic reinforcement in pilesupported embankments.Part II:3Dcable-net model[J].Geosynthetics International,2010,17(2):68-76.
[19]PLAUT R H,FILZ G M.Analysis of geosynthetic reinforcement in pile-supported embankments.Part III:Axisymmetric model[J].Geosynthetics International,2010,17(2):77-85.
[20]徐超,林潇,沈盼盼.桩承式加筋路堤张力膜效应模型试验研究[J].岩土力学,2016,37(7):1825-1831.XU C,LIN X,SHEN P P.Model tests of tensile membrane effect of geosynthetic-reinforced piled embankments[J].Rock and Soil Mechanics,2016,37(7):1825-1831.(in Chinese)
[21]陈仁朋,汪焱卫,陈金苗.桩网结构路基格栅加筋作用及其拉力特性研究[J].西南交通大学学报,2016,51(6):1080-1086.CHEN R P,WANG Y W,CHEN J M.Reinforcing mechanism and tension behaviors of geogrid in pilesupported reinforced embankment[J].Journal of Southwest Jiaotong University,2016,51(6):1080-1086.(in Chinese)
[22]郑俊杰,曹文昭,周燕君,等.三向土工格栅筋土界面特性拉拔试验研究[J].岩土力学,2017,38(2):317-324.ZHENG J J,CAO W Z,ZHOU Y J,et al.Pull-out test study of interface behavior between triaxial geogrid and soil[J].Rock and Soil Mechanics,2017,38(2):317-324.(in Chinese)
[23]杨明辉,邓岳保,赵明华.基于叠梁试验的土工格室垫层刚度确定方法研究[J].土木工程学报,2011,44(11):87-92.YANG M H,DENG Y B,ZHAO M H.Study of stiffness test method of geocell cushion based on superposed beam theory[J].China Civil Engineering Journal,2011,44(11):87-92.(in Chinese)
[24]TAN H M,GAO Z B,HUANG Y L.Calculation method of pile-supported geogrid-reinforced embankment based on elastic large deflection theory[C]//International Conference on Electric Technology and Civil Engineering,IEEE,2011:2974-2978.
[25]ZHANG J,ZHENG J J,MA Q.Mechanical analysis of fixed geosynthetic technique of GRPS embankment[J].Journal of Central South University,2013,20(5):1368-1375.
[26]ARIYARATHNE P,LIYANAPATHIRANA D S.Review of existing design methods for geosyntheticreinforced pile-supported embankments[J].Soils and Foundations,2015,55(1):17-34.
[27]FROIO D,RIZZI E.Analytical solution for the elastic bending of beams lying on a variable Winkler support[J].Acta Mechanica,2016,227(4):1157-1179.
[28]蔡德钩.加筋网垫在桩网结构路基中的计算方法研究[D].北京:中国铁道科学研究院,2011.CAI D G.Calculating method of reinforced bedding in the geosynthetics reinforced and pile supported embankment[D].Beijing:China Academy of Railway Sciences,2011.(in Chinese)
[2]LU W H,MIAO L C.A simplified 2-D evaluation method of the arching effect for geosynthetic-reinforced and pile-supported embankments[J].Computers and Geotechnics,2015,65:97-103.
[3]钱劲松,白墨,罗鑫,等.桩承式加筋路堤桩体荷载分担比计算[J].岩石力学与工程学报,2017,19(6):3587-3595.QIAN J S,BAI M,LUO X,et al.,Pile efficacy calculation of geosynthetics reinforced pile supported embankment[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(Sup):3587-3595.(in Chinese)
[4]闫澍旺,郎瑞卿,孙立强,等.基于薄板理论的刚性桩网复合地基桩土应力比计算[J].岩石力学与工程学报,2017,36(8):2051-2060.YAN S W,LANG R Q,SUN L Q,et al.,Calculation of pile-soil stress ratio in composite foundation with rigid pile-net based on plate theory[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(8):2051-2060.(in Chinese)
[5]ARIYARATHNE P,LIYANAPATHIRANA D S,LEO C J.Comparison of different two-dimensional idealizations for a geosynthetic-reinforced pilesupported embankment[J].International Journal of Geomechanics,2013,13(6):754-768.
[6]ROWE R K,LIU K W.Three-dimensional finite element modelling of a full-scale geosyntheticreinforced,pile-supported embankment[J].Canadian Geotechnical Journal,2015,52(12):2041-2054.
[7]曹文昭,郑俊杰,严勇,桩承式变刚度加筋垫层复合地基数值模拟[J].岩土工程学报,2017(Sup2):83-86.CAO W Z, ZHENG J J, YAN Y. Numerical simulation of composite foundation using pile-supported and geosynthetics-reinforced cushion with variable stiffness[J]. Chinese Journal of Geotechnical Engineering,2017(Sup2):83-86.(in Chinese)
[8]XING H F,ZHANG Z,LIU H B,et al.Large-scale tests of pile-supported earth platform with and without geogrid[J].Geotextiles and Geomembranes,2014,42(6):586-598.
[9]CAO W Z,ZHENG J J,ZHANG J,et al.Field test of a geogrid-reinforced and floating pile-supported embankment[J].Geosynthetics International,2016,23(5):348-361.
[10]ARIYARATHNE P,LIYANAPATHIRANA D S,LEO C J.Effect of geosynthetic creep on reinforced pile-supported embankment systems[J].Geosynthetics International,2013,20(6):421-435.
[11]British Standards Institution.Code of practice for strengthened reinforced soils and other fills:BS8006[S].London,UK,1995.
[12]FUR D G.Recommendations for Design and Analysis of Earth Structures using Geosynthetic ReinforcementsEBGEO,Second Edition[M].Ernst &Sohn,2011.
[13]Nordic Handbook.Reinforced soils and fill[M].Stockholm:Nordic Geotechnical Society,2002.
[14]The design and construction handbook of mixing piled foundation(machine mixing)[M].Tokyo:Railway Technology Research Institute,2001.
[15]VAN EEKELEN S J M,BEZUIJEN A,VAN TOL A F.Analysis and modification of the British Standard BS8006 for the design of piled embankments[J].eotextiles and Geomembranes,2011,29(3):345-359.
[16]BLANC M, THOREL L, GIROUT R,et al.Geosynthetic reinforcement of a granular load transfer platform above rigid inclusions:comparison between centrifuge testing and analytical modeling[J].Geosynthetics International,2014,21(1):37-52.
[17]魏平,魏静,杨松林,等.动载作用下桩网结构低路基双层土工格栅力学特性[J].铁道工程学报,2017,34(7):30-35.WEI P,WEI J,YANG S L,et al.Research on the mechanical characteristics of double-deck geogrids of pile net structure of low embankment under dynamic load[J].Journal of Railway Engineering Society,2017,34(7):30-35.(in Chinese)
[18]HALVORDSON K A,PLAUT R H,FILZ G M.Analysis of geosynthetic reinforcement in pilesupported embankments.Part II:3Dcable-net model[J].Geosynthetics International,2010,17(2):68-76.
[19]PLAUT R H,FILZ G M.Analysis of geosynthetic reinforcement in pile-supported embankments.Part III:Axisymmetric model[J].Geosynthetics International,2010,17(2):77-85.
[20]徐超,林潇,沈盼盼.桩承式加筋路堤张力膜效应模型试验研究[J].岩土力学,2016,37(7):1825-1831.XU C,LIN X,SHEN P P.Model tests of tensile membrane effect of geosynthetic-reinforced piled embankments[J].Rock and Soil Mechanics,2016,37(7):1825-1831.(in Chinese)
[21]陈仁朋,汪焱卫,陈金苗.桩网结构路基格栅加筋作用及其拉力特性研究[J].西南交通大学学报,2016,51(6):1080-1086.CHEN R P,WANG Y W,CHEN J M.Reinforcing mechanism and tension behaviors of geogrid in pilesupported reinforced embankment[J].Journal of Southwest Jiaotong University,2016,51(6):1080-1086.(in Chinese)
[22]郑俊杰,曹文昭,周燕君,等.三向土工格栅筋土界面特性拉拔试验研究[J].岩土力学,2017,38(2):317-324.ZHENG J J,CAO W Z,ZHOU Y J,et al.Pull-out test study of interface behavior between triaxial geogrid and soil[J].Rock and Soil Mechanics,2017,38(2):317-324.(in Chinese)
[23]杨明辉,邓岳保,赵明华.基于叠梁试验的土工格室垫层刚度确定方法研究[J].土木工程学报,2011,44(11):87-92.YANG M H,DENG Y B,ZHAO M H.Study of stiffness test method of geocell cushion based on superposed beam theory[J].China Civil Engineering Journal,2011,44(11):87-92.(in Chinese)
[24]TAN H M,GAO Z B,HUANG Y L.Calculation method of pile-supported geogrid-reinforced embankment based on elastic large deflection theory[C]//International Conference on Electric Technology and Civil Engineering,IEEE,2011:2974-2978.
[25]ZHANG J,ZHENG J J,MA Q.Mechanical analysis of fixed geosynthetic technique of GRPS embankment[J].Journal of Central South University,2013,20(5):1368-1375.
[26]ARIYARATHNE P,LIYANAPATHIRANA D S.Review of existing design methods for geosyntheticreinforced pile-supported embankments[J].Soils and Foundations,2015,55(1):17-34.
[27]FROIO D,RIZZI E.Analytical solution for the elastic bending of beams lying on a variable Winkler support[J].Acta Mechanica,2016,227(4):1157-1179.
[28]蔡德钩.加筋网垫在桩网结构路基中的计算方法研究[D].北京:中国铁道科学研究院,2011.CAI D G.Calculating method of reinforced bedding in the geosynthetics reinforced and pile supported embankment[D].Beijing:China Academy of Railway Sciences,2011.(in Chinese)