基于薄环层元法的层状地基中摩擦桩竖向受荷计算
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摘要
基于薄环层元法和虚土桩假设,提出了层状地基中竖向受荷摩擦桩计算模型。将桩身正下方至基岩间的土层视为虚土桩,并将桩土体系划分为多个薄层单元;随后利用虚位移原理求得薄环单元和桩单元的单元矩阵方程,并根据单元间平衡关系建立整体矩阵方程;最后通过桩与桩周土的协调关系,计算出层状地基中桩土体系位移。计算结果与已有方法结果吻合良好,验证了本文的正确性与可靠性。参数分析表明,计算单元厚度越小,精度越高;三层地基中的摩擦桩,中间夹层模量越大,其分担的荷载越多。桩端下卧土层厚度越小,桩端刚度越大。当桩端土厚度小于0.3倍地基厚度时,桩端刚度显著增大。当桩端以下土体分层时,桩端刚度与持力层厚度和强度密切相关。
Based on the thin annulus element method and the hypothesis of fictitious soil pile, a model for the settlement of an axially-loaded single floating pile in the layered soils is proposed. The soil column beneath the floating pile is regarded as the fictitious pile shaft. The soil-pile system is then divided into the separate thin-layer elements. The stiffness matrices for the soil element and pile element are deduced using the principle of virtual displacements. The global matrices are constructed by considering the continuity and equilibrium conditions between the elements. The vertical displacement of the soil-pile system can be obtained by solving the matrix equation. The comparisons of the results between the proposed model and the available solutions indicate the accuracy of the proposed model. Parametric study shows that the accuracy of the proposed solution depends greatly on the thickness of the thin annulus element and the choice of the displacement function. For the floating pile in the three-layer soil, the bearing capacity of the middle layer around the shaft increases with the increase of its elastic modulus.The tip stiffness of the floating pile increases with the decrease of the layer thickness between the pile tip and bedrock. When this thickness is less than 0.3 times the soil thickness, the pile tip stiffness will increase significantly. The pile tip stiffness is also dependent greatly on the properties of the underlying soil below the tip of the floating pile.
Based on the thin annulus element method and the hypothesis of fictitious soil pile, a model for the settlement of an axially-loaded single floating pile in the layered soils is proposed. The soil column beneath the floating pile is regarded as the fictitious pile shaft. The soil-pile system is then divided into the separate thin-layer elements. The stiffness matrices for the soil element and pile element are deduced using the principle of virtual displacements. The global matrices are constructed by considering the continuity and equilibrium conditions between the elements. The vertical displacement of the soil-pile system can be obtained by solving the matrix equation. The comparisons of the results between the proposed model and the available solutions indicate the accuracy of the proposed model. Parametric study shows that the accuracy of the proposed solution depends greatly on the thickness of the thin annulus element and the choice of the displacement function. For the floating pile in the three-layer soil, the bearing capacity of the middle layer around the shaft increases with the increase of its elastic modulus.The tip stiffness of the floating pile increases with the decrease of the layer thickness between the pile tip and bedrock. When this thickness is less than 0.3 times the soil thickness, the pile tip stiffness will increase significantly. The pile tip stiffness is also dependent greatly on the properties of the underlying soil below the tip of the floating pile.
引文
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[2]KOG Y C.Axially loaded piles in consolidating layered soil[J].International Journal of Geomechanics,2016,16(1):0415039.
[3]DIAS T,BEZUIJEN A.Load-transfer method for piles under axial loading and unloading[J].Journal of Geotechnical and Geoenvironmental Engineering,2018,144(1):04017096.
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[5]POULOS H G,DAVIS E H.The settlement behavior of single axially loaded incompressible piles and piers[J].Géotechnique,1968,18(3):351-371.
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[8]TEHRANI F S,SALGADO R,PREZZI M.Analysis of axial loading of pile groups in multilayered elastic soil[J].International Journal of Geomechanics,2016,16(2):04015063.
[9]WU W B,NAGGER M H E I,ADBLRAHEM M,et al.A new interaction model for the vertical dynamic response of pipe piles considering soil plug effect[J].Canadian Geotechnical Journal,2017,54(7):987-1001.
[10]RANDOLPH M F,WROTH C P.Analysis of deformation of vertically loaded piles[J].Journal of Geotechnical Engineering Division,ASCE,1978,104(12):1465-1488.
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[13]OTTAVIANI M.Three-dimensional finite element analysis of vertically loaded pile groups[J].Géotechnique,1975,25(2):159-174.
[14]陈斌,卓家寿,吴天寿.嵌岩桩承载性状的有限元分析[J].岩土工程学报,2002,24(1):51-55.(CHEN Bin,ZHUO Jia-shou,WU Tian-shou.Vertical bearing capacity of rock-socketed piles[J].Chinese Journal of Geotechnical Engineering,2002,24(1):51-55.(in Chinese))
[15]AI Z Y,HAN J.Boundary element analysis of axially loaded piles embedded in a multi-layered soil[J].Computers and Geotechnics,2009,36(3):427-434.
[16]AI Z Y,CHENG Y C.Analysis of vertically loaded piles in multilayered transversely isotropic soils by BEM[J].Engineering Analysis with Boundary Elements,2013,37(2):327-335.
[17]桩基工程手册编写委员会.桩基工程手册[M].北京:中国建筑工业出版社,1995.(Compile Committee of Pile Foundation.Pile foundation[M].Beijing:China Architecture and Building Press,1995.(in Chinese))
[18]王奎华,王宁,刘凯,等.三维轴对称条件下基于虚土桩法的单桩纵向振动分析[J].岩土工程学报,2012,34(5):885-892.(WANG Kui-hua,WANG Ning,LIU Kai,et al.Longitudinal vibration of piles in 3D axisymmetric soil based on fictitious soil pile method[J].Chinese Journal of Geotechnical Engineering,2012,34(5):885-892.(in Chinese))
[19]王宁,王奎华.桩底土的成层性对桩体纵向刚度的影响[J].岩石力学与工程学报,2013,32(5):1042-1048.(WANG Ning,WANG Kui-hua.Influence of layering of stratum under pile tip on pile longitudinal stiffness[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(5):1042-1048.(in Chinese))
[20]WU W B,LIU H,NAGGER M H E I,et al.Torsional dynamic response of a pile embedded in layered soil based on the fictitious soil pile model[J].Computers and Geotechnics,2016,80:190-198.
[21]徐芝纶.弹性力学[M].北京:高等教育出版社,2006.(XUZhi-lun.Elasticity[M].Beijing:Higher Education Press,2006.(in Chinese))
[22]VLAZOV V Z,LEONTIEV U N.Beams,plates and shells on elastic foundations[M].Jerusalem:Israel Program for Scientific Translations,1966.
[23]ANOYATIS G,MYLONAKIS G.Novel Tajimi models for static and dynamic soil-pile interaction[C]//Proceedings of the 8th International Conference on Structural Dynamics,EURODYN 2011.Leuven,2011.
[24]RUSSO G.Full-scale load tests on instrumented micropiles[J].Geotechnical Engineering,2004,157(3):127-135.
[2]KOG Y C.Axially loaded piles in consolidating layered soil[J].International Journal of Geomechanics,2016,16(1):0415039.
[3]DIAS T,BEZUIJEN A.Load-transfer method for piles under axial loading and unloading[J].Journal of Geotechnical and Geoenvironmental Engineering,2018,144(1):04017096.
[4]木林隆,康兴宇,李婉.砂土地基中V-H-M组合荷载下单桩分析方法研究[J].岩土工程学报,2017,39(增刊2):153-156.(MU Lin-long,KANG Xing-yu,LI Wan.Analytical method for single pile under V-H-M combined loads in sand[J].Chinese Journal of Geotechnical Engineering,2017,39(S2):153-156.(in Chinese))
[5]POULOS H G,DAVIS E H.The settlement behavior of single axially loaded incompressible piles and piers[J].Géotechnique,1968,18(3):351-371.
[6]RAJAPAKSE R K N D.Response of an axially loaded elastic pile in a Gibson soil[J].Géotechnique,1990,40(2):237-249.
[7]ZHENG C J,DING X M,LI P,et al.Vertical impedance of an end-bearing pile in viscoelastic soil[J].International Journal for Numerical and Analytical Methods in Geomechanics,2015,39(6):676-684.
[8]TEHRANI F S,SALGADO R,PREZZI M.Analysis of axial loading of pile groups in multilayered elastic soil[J].International Journal of Geomechanics,2016,16(2):04015063.
[9]WU W B,NAGGER M H E I,ADBLRAHEM M,et al.A new interaction model for the vertical dynamic response of pipe piles considering soil plug effect[J].Canadian Geotechnical Journal,2017,54(7):987-1001.
[10]RANDOLPH M F,WROTH C P.Analysis of deformation of vertically loaded piles[J].Journal of Geotechnical Engineering Division,ASCE,1978,104(12):1465-1488.
[11]LEE C Y.Discrete layer analysis of axially loaded piles and pile groups[J].Computers and Geotechnics,1991,11(4):295-313.
[12]周立朵,孔纲强.彭怀风,等.倾斜荷载下群桩承载特性理论分析[J].岩土力学,2017,38(9):2647-2654.(ZHOULi-duo,KONG Gang-qiang,PENG Huai-feng,et al.Theoretical analysis of bearing capacities of pile group under oblique load[J].Rock and Soil Mechanics,2017,38(9):2647-2654.(in Chinese))
[13]OTTAVIANI M.Three-dimensional finite element analysis of vertically loaded pile groups[J].Géotechnique,1975,25(2):159-174.
[14]陈斌,卓家寿,吴天寿.嵌岩桩承载性状的有限元分析[J].岩土工程学报,2002,24(1):51-55.(CHEN Bin,ZHUO Jia-shou,WU Tian-shou.Vertical bearing capacity of rock-socketed piles[J].Chinese Journal of Geotechnical Engineering,2002,24(1):51-55.(in Chinese))
[15]AI Z Y,HAN J.Boundary element analysis of axially loaded piles embedded in a multi-layered soil[J].Computers and Geotechnics,2009,36(3):427-434.
[16]AI Z Y,CHENG Y C.Analysis of vertically loaded piles in multilayered transversely isotropic soils by BEM[J].Engineering Analysis with Boundary Elements,2013,37(2):327-335.
[17]桩基工程手册编写委员会.桩基工程手册[M].北京:中国建筑工业出版社,1995.(Compile Committee of Pile Foundation.Pile foundation[M].Beijing:China Architecture and Building Press,1995.(in Chinese))
[18]王奎华,王宁,刘凯,等.三维轴对称条件下基于虚土桩法的单桩纵向振动分析[J].岩土工程学报,2012,34(5):885-892.(WANG Kui-hua,WANG Ning,LIU Kai,et al.Longitudinal vibration of piles in 3D axisymmetric soil based on fictitious soil pile method[J].Chinese Journal of Geotechnical Engineering,2012,34(5):885-892.(in Chinese))
[19]王宁,王奎华.桩底土的成层性对桩体纵向刚度的影响[J].岩石力学与工程学报,2013,32(5):1042-1048.(WANG Ning,WANG Kui-hua.Influence of layering of stratum under pile tip on pile longitudinal stiffness[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(5):1042-1048.(in Chinese))
[20]WU W B,LIU H,NAGGER M H E I,et al.Torsional dynamic response of a pile embedded in layered soil based on the fictitious soil pile model[J].Computers and Geotechnics,2016,80:190-198.
[21]徐芝纶.弹性力学[M].北京:高等教育出版社,2006.(XUZhi-lun.Elasticity[M].Beijing:Higher Education Press,2006.(in Chinese))
[22]VLAZOV V Z,LEONTIEV U N.Beams,plates and shells on elastic foundations[M].Jerusalem:Israel Program for Scientific Translations,1966.
[23]ANOYATIS G,MYLONAKIS G.Novel Tajimi models for static and dynamic soil-pile interaction[C]//Proceedings of the 8th International Conference on Structural Dynamics,EURODYN 2011.Leuven,2011.
[24]RUSSO G.Full-scale load tests on instrumented micropiles[J].Geotechnical Engineering,2004,157(3):127-135.
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