考虑横向惯性效应时非均质土中大直径桩纵向振动特性及其应用
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摘要
基于Rayleigh-Love杆模型,研究考虑横向惯性效应时非均质土中大直径桩纵向振动特性。首先,采用虚土桩模型模拟桩底土对桩的支承作用,通过径向圈层间的剪切复刚度传递,考虑施工扰动造成的桩周土的径向非均质性;然后,将桩与虚土桩假设为Rayleigh-Love杆,建立其纵向振动控制方程,通过Laplace变换和阻抗函数递推方法,得到桩顶频域响应解析解,并通过Fourier逆变换得到桩顶时域响应半解析解;在此基础上,通过参数分析的方法,研究横向惯性效应对大直径桩纵向振动特性的影响以及与桩–土参数之间的关系;最后,将理论计算结果与现场实测曲线进行对比,验证了本文解的合理性。
Based on the Rayleigh-Love rod model,the vertical vibration of a large diameter pile embedded in inhomogeneous soil is investigated considering the transverse inertia effect. First,the reaction of the soil on the pile tip is simulated by virtual soil pile model,and the radial inhomogeneity of the surrounding soil caused by the construction disturbance effect is considered by using the vertical shear complex stiffness transfer model. Then,the pile and virtual soil pile are assumed to be Rayleigh-Love rod,and the vertical vibration equation is built. The analytical solution for dynamic response at the pile head is obtained in the frequency domain by virtue of Laplace transform and impedance function transfer method,and the semi-analytical solution in the time domain is derived by inverse Fourier transform. Based on the present solutions,the influence of the transverse inertia effect on the dynamic response at the pile head and its relationship to the pile-soil parameters are discussed. Finally,the calculated curves are compared with the measured results to demonstrate the rationality of the present solution.
Based on the Rayleigh-Love rod model,the vertical vibration of a large diameter pile embedded in inhomogeneous soil is investigated considering the transverse inertia effect. First,the reaction of the soil on the pile tip is simulated by virtual soil pile model,and the radial inhomogeneity of the surrounding soil caused by the construction disturbance effect is considered by using the vertical shear complex stiffness transfer model. Then,the pile and virtual soil pile are assumed to be Rayleigh-Love rod,and the vertical vibration equation is built. The analytical solution for dynamic response at the pile head is obtained in the frequency domain by virtue of Laplace transform and impedance function transfer method,and the semi-analytical solution in the time domain is derived by inverse Fourier transform. Based on the present solutions,the influence of the transverse inertia effect on the dynamic response at the pile head and its relationship to the pile-soil parameters are discussed. Finally,the calculated curves are compared with the measured results to demonstrate the rationality of the present solution.
引文
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[3]赵春风,鲁嘉,孙其超,等.大直径深长钻孔灌注桩分层荷载传递特性试验研究[J].岩石力学与工程学报,2009,28(5):1 020–1 026.(ZHAO Chunfeng,LU Jia,SUN Qichao,et al.Experimental study of load transmission property of large-diameter bored cast-in-situ deep and long pile in different soil layers[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(5):1 020–1 026.(in Chinese))
[4]李玲玲,王立忠,邢月龙.大直径钻孔灌注桩负摩阻力试验研究[J].岩石力学与工程学报,2009,28(3):583–590.(LI Lingling,WANG Lizhong,XING Yuelong.Experimental research on negative skin friction of large-diameter bored piles[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(3):583–590.(in Chinese))
[5]王卫东,李永辉,吴江斌.上海中心大厦大直径超长灌注桩现场试验研究[J].岩土工程学报,2011,33(12):1 817–1 826.(WANG Weidong,LI Yonghui,WU Jiangbin.Filed loading tests on large-diameter and super-long bored piles of Shanghai Center Tower[J].Chinese Journal of Geotechnical Engineering,2011,33(12):1 817–1 826.(in Chinese))
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[7]CHAI H Y,PHOON K K,ZHANG D J.Effects of the source on wave propagation in pile integrity testing[J].Journal of Geotechnical and Geoenvironmental Engineering,2010,136(9):1 200–1 208.
[8]KRAWCZUK M,GRABOWSKA J,PALACZ M.Longitudinal wave propagation.Part I-comparison of rod theories[J].Journal of Sound and Vibration,2006,295(3):461–478.
[9]STEPHEN N G,LAI K F,YONG K,CHAN K T.Longitudinal vibrations in circular rods:a systematic approach[J].Journal of Sound and Vibration,2012,331(1):107–116.
[10]李强,王奎华,谢康和.饱和土中大直径嵌岩桩纵向振动特性研究[J].振动工程学报,2005,18(4):500–505.(LI Qiang,WANG Kuihua,XIE Kanghe.Dynamic response for vertical vibration of large diameter pile in saturated soil[J].Journal of Vibration Engineering,2005,18(4):500–505.(in Chinese))
[11]杨骁,蔡雪琼.考虑横向效应饱和粘弹性土层中桩的纵向振动[J].岩土力学,2011,32(6):1 857–1 863.(YANG Xiao,CAI Xueqiong.Vertical vibration of pile in saturated viscoelastic soil layer considering transversal effects[J].Rock and Soil Mechanics,2011,32(6):1 857–1 863.(in Chinese))
[12]杨骁,唐洁.成层饱和土中考虑横向惯性的单桩纵向振动[J].岩土力学,2013,34(6):1 560–1 566.(YANG Xiao,TANG Jie.Vertical vibration of single pile with transversal inertia effect in saturated soil[J].Rock and Soil Mechanics,2013,34(6):1 560–1 566.(in Chinese))
[13]YU J,CAI Y Y,WU W B.Effect of sediment on vertical dynamic impedance of rock-socketed pile with large diameter[J].Journal of Central South University,2013,20(10):2 856–2 862.
[14]LüS H,WANG K H,WU W B,et al.Longitudinal vibration of a pile embedded in layered soil considering the transverse inertia effect of pile[J].Computers and Geotechnics,2014,62:90–99.
[15]刘福天,赵春风,吴杰,等.常州地区大直径钻孔灌注桩承载性状及尺寸效应试验研究[J].岩石力学与工程学报,2010,29(4):858–864.(LIU Futian,ZHAO Chunfeng,WU Jie,et al.Experimental research on bearing behavior and size effect of large diameter bored cast-in-situ piles in Changzhou area[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(4):858–864.(in Chinese))
[16]龚成中,何春林,龚伟明,等.基于自平衡试桩法大直径嵌岩桩尺寸效应分析[J].岩土力学,2012,33(8):2 403–2 407.(GONG Chengzhong,HE Chunlin,GONG Weiming,et al.Analysis of size effect on large diameter rock-socketed pile based on self-balance method[J].Rock and Soil Mechanics,2012,33(8):2 403–2 407.(in Chinese))
[17]KODIKARA J K,MOORE I D.Axial response of tapered piles in cohesive frictional ground[J].Journal of Geotechnical Engineering,1993,119(4):675–693.
[18]El NAGGAR M H,WEI J Q.Uplift behavior of tapered piles established from model tests[J].Canadian Geotechnical Journal,2000,37(1):56–74.
[19]NOVAK M,SHETA M.Approximate approach to contact problems of piles[C]//Proceedings of the Geotechnical Engineering Division,ASCE National Convention.Florida:[s.n.],1980:53–79.
[20]EL NAGGAR M H.Vertical and torsional soil reactions for radially inhomogeneous soil layer[J].Structural Engineering and Mechanics,2000,20(4):299–312.
[21]WANG K H,YANG D Y,ZHANG Z Q,et al.A new approach for vertical impedance in radially inhomogeneous soil layer[J].International Journal for Numerical and Analytical Methods in Geomechanics,2012,36(6):697–707.
[22]TIAN X J,HU W T,GONG X N.Longitudinal dynamic response of pile foundation in a nonuniform initial strain field[J].KSCE Journal of Civil Engineering,2015,19(6):1 656–1 666.
[23]WU W B,WANG K H,MA S J,et al.Longitudinal dynamic response of pile in layered soil based on virtual soil pile model[J].Journal of South University,2012,19(7):1 999–2 007.
[24]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):1 042–1 048.(WANG Ning,WANG Kuihua.Influence of layering of stratum under pile tip on pile longitudinal stiffness[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(5):1 042–1 048.(in Chinese))
[25]NOVAK M,NOGAMI T,ABOUL-ELLA F.Dynamic soil reactions for plane strain case[J].Journal of Engineering Mechanics Division,ASCE,1978,104(4):953–959.
[26]WANG N,WANG K H,WU W B.Analytical model of vertical vibrations in piles for different tip boundary conditions:parametric study and applications[J].Journal of Zhejiang University:Science A,2013,14(2):79–93.
[2]高盟,高广运,顾宝和,等.一种大直径扩底桩的沉降计算实用方法[J].岩土工程学报,2012,34(8):1 448–1 452.(GAO Meng,GAO Guangyun,GU Baohe,et al.Practical method for settlement calculation of large-diameter belled piles[J].Chinese Journal of Geotechnical Engineering,2012,34(8):1 448–1 452.(in Chinese))
[3]赵春风,鲁嘉,孙其超,等.大直径深长钻孔灌注桩分层荷载传递特性试验研究[J].岩石力学与工程学报,2009,28(5):1 020–1 026.(ZHAO Chunfeng,LU Jia,SUN Qichao,et al.Experimental study of load transmission property of large-diameter bored cast-in-situ deep and long pile in different soil layers[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(5):1 020–1 026.(in Chinese))
[4]李玲玲,王立忠,邢月龙.大直径钻孔灌注桩负摩阻力试验研究[J].岩石力学与工程学报,2009,28(3):583–590.(LI Lingling,WANG Lizhong,XING Yuelong.Experimental research on negative skin friction of large-diameter bored piles[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(3):583–590.(in Chinese))
[5]王卫东,李永辉,吴江斌.上海中心大厦大直径超长灌注桩现场试验研究[J].岩土工程学报,2011,33(12):1 817–1 826.(WANG Weidong,LI Yonghui,WU Jiangbin.Filed loading tests on large-diameter and super-long bored piles of Shanghai Center Tower[J].Chinese Journal of Geotechnical Engineering,2011,33(12):1 817–1 826.(in Chinese))
[6]黎正根,龚育龄.波在大直径桩中传播的三维效应现象[J].岩石力学与工程学报,1998,17(4):434–439.(LI Zhenggen,GONG Yuling.Discussion on three dimensional effect of wave propagating in the pile with large diameter[J].Chinese Journal of Rock Mechanics and Engineering,1998,17(4):434–439.(in Chinese))
[7]CHAI H Y,PHOON K K,ZHANG D J.Effects of the source on wave propagation in pile integrity testing[J].Journal of Geotechnical and Geoenvironmental Engineering,2010,136(9):1 200–1 208.
[8]KRAWCZUK M,GRABOWSKA J,PALACZ M.Longitudinal wave propagation.Part I-comparison of rod theories[J].Journal of Sound and Vibration,2006,295(3):461–478.
[9]STEPHEN N G,LAI K F,YONG K,CHAN K T.Longitudinal vibrations in circular rods:a systematic approach[J].Journal of Sound and Vibration,2012,331(1):107–116.
[10]李强,王奎华,谢康和.饱和土中大直径嵌岩桩纵向振动特性研究[J].振动工程学报,2005,18(4):500–505.(LI Qiang,WANG Kuihua,XIE Kanghe.Dynamic response for vertical vibration of large diameter pile in saturated soil[J].Journal of Vibration Engineering,2005,18(4):500–505.(in Chinese))
[11]杨骁,蔡雪琼.考虑横向效应饱和粘弹性土层中桩的纵向振动[J].岩土力学,2011,32(6):1 857–1 863.(YANG Xiao,CAI Xueqiong.Vertical vibration of pile in saturated viscoelastic soil layer considering transversal effects[J].Rock and Soil Mechanics,2011,32(6):1 857–1 863.(in Chinese))
[12]杨骁,唐洁.成层饱和土中考虑横向惯性的单桩纵向振动[J].岩土力学,2013,34(6):1 560–1 566.(YANG Xiao,TANG Jie.Vertical vibration of single pile with transversal inertia effect in saturated soil[J].Rock and Soil Mechanics,2013,34(6):1 560–1 566.(in Chinese))
[13]YU J,CAI Y Y,WU W B.Effect of sediment on vertical dynamic impedance of rock-socketed pile with large diameter[J].Journal of Central South University,2013,20(10):2 856–2 862.
[14]LüS H,WANG K H,WU W B,et al.Longitudinal vibration of a pile embedded in layered soil considering the transverse inertia effect of pile[J].Computers and Geotechnics,2014,62:90–99.
[15]刘福天,赵春风,吴杰,等.常州地区大直径钻孔灌注桩承载性状及尺寸效应试验研究[J].岩石力学与工程学报,2010,29(4):858–864.(LIU Futian,ZHAO Chunfeng,WU Jie,et al.Experimental research on bearing behavior and size effect of large diameter bored cast-in-situ piles in Changzhou area[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(4):858–864.(in Chinese))
[16]龚成中,何春林,龚伟明,等.基于自平衡试桩法大直径嵌岩桩尺寸效应分析[J].岩土力学,2012,33(8):2 403–2 407.(GONG Chengzhong,HE Chunlin,GONG Weiming,et al.Analysis of size effect on large diameter rock-socketed pile based on self-balance method[J].Rock and Soil Mechanics,2012,33(8):2 403–2 407.(in Chinese))
[17]KODIKARA J K,MOORE I D.Axial response of tapered piles in cohesive frictional ground[J].Journal of Geotechnical Engineering,1993,119(4):675–693.
[18]El NAGGAR M H,WEI J Q.Uplift behavior of tapered piles established from model tests[J].Canadian Geotechnical Journal,2000,37(1):56–74.
[19]NOVAK M,SHETA M.Approximate approach to contact problems of piles[C]//Proceedings of the Geotechnical Engineering Division,ASCE National Convention.Florida:[s.n.],1980:53–79.
[20]EL NAGGAR M H.Vertical and torsional soil reactions for radially inhomogeneous soil layer[J].Structural Engineering and Mechanics,2000,20(4):299–312.
[21]WANG K H,YANG D Y,ZHANG Z Q,et al.A new approach for vertical impedance in radially inhomogeneous soil layer[J].International Journal for Numerical and Analytical Methods in Geomechanics,2012,36(6):697–707.
[22]TIAN X J,HU W T,GONG X N.Longitudinal dynamic response of pile foundation in a nonuniform initial strain field[J].KSCE Journal of Civil Engineering,2015,19(6):1 656–1 666.
[23]WU W B,WANG K H,MA S J,et al.Longitudinal dynamic response of pile in layered soil based on virtual soil pile model[J].Journal of South University,2012,19(7):1 999–2 007.
[24]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):1 042–1 048.(WANG Ning,WANG Kuihua.Influence of layering of stratum under pile tip on pile longitudinal stiffness[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(5):1 042–1 048.(in Chinese))
[25]NOVAK M,NOGAMI T,ABOUL-ELLA F.Dynamic soil reactions for plane strain case[J].Journal of Engineering Mechanics Division,ASCE,1978,104(4):953–959.
[26]WANG N,WANG K H,WU W B.Analytical model of vertical vibrations in piles for different tip boundary conditions:parametric study and applications[J].Journal of Zhejiang University:Science A,2013,14(2):79–93.