(1. Key Laboratory of New Technology for Construction of Cities in Mountain Area,Ministry of Education,Chongqing University,Chongqing 400045,China;2. College of Civil and Transportation Engineering,Hohai University,
Nanjing,Jiangsu 210098,China)
Abstract:To investigate the horizontal vibrating characteristics of large-diameter pipe piles,a governing equation with Timoshenko model assumed for pipe piles was established. Methods of differential transformations and variable separation were adopted to decouple the three-dimensional equations of soil. The implicit analytical expressions of the soil displacements and horizontal impedances were deduced. Analytical solutions of the pile response were derived based on the assumption of perfect contacts between the pile and soil and thus the expression of the complicated impedances was obtained. On the basis of the analytical solutions,parametric analyses were carried out to find out the most significant factors influencing on the behavior of the horizontal vibrating pipe piles. The results show that the variation of horizontal complex impedances deduced according to the Euler-Bernoulli model agrees well with that deduced from the Timoshenko model,which validates the solution. The real parts of the complex impedances decrease with the increase of the pile length and vice versa for the imaginary parts. Both the real parts and imaginary parts show little variation when the pile length reaches the certain critical value. Although the complex impedances increase with the decrease of the inner radius,their influences on the complex impedances are marginal when the inner radii are less than 0.2 m. Both the average radius and wall thickness of the piles significantly influence the complex impedances when the cross sectional areas are approximately equal.
[1] NOVAK M. Dynamic stiffness and damping of piles[J]. Canadian Geotechnical Journal,1974,11(4):574–598.
[2] NOGAMI T,OTANI J,KONAGAI K,et al. Nonlinear soil-pile interaction model for dynamic lateral motion[J]. Journal of Geotechnical Engineering,1992,118(1):89–106.
[3] 胡安峰,谢康和,应宏伟,等. 黏弹性地基中考虑桩体剪切变形的单桩水平振动解析理论[J]. 岩石力学与工程学报,2004,23(9): 1 515–1 520.(HU Anfeng,XIE Kanghe,YING Hongwei,et al. Analytical theory of lateral vibration of single pile in visco-elastic considering shear deformation[J]. Chinese Journal of Rock Mechanics and Engineering,2004,23(9):1 515–1 520.(in Chinese))
[4] GEROLYMOS N,GAZETAS G. Winkler model for lateral response of rigid caisson foundations in linear soil[J]. Soil Dynamics and Earthquake Engineering,2006,26(5):347–361.
[5] BARANOV V A. On the calculation of excited vibrations of an embedded foundation[J]. Voprosy Dynamiki Prochnocti,1967,14:195–209.
[6] NOVAK M,ABOUL-ELLA F,NOGAMI T. Dynamic soil reactions for plane strain case[J]. Journal of the Engineering Mechanics Division,1978,104(4):953–959.
[7] 孔德森,栾茂田,杨 庆. 非均质土层中单桩水平动力阻抗计算及影响因素分析[J]. 大连理工大学学报,2004,44(4):560–565. (KONG Desen,LUAN Maotian,YANG Qing. The calculation and factor analysis of the pile horizontal impedance in heterogeneous soil[J]. Journal of Dalian University of Technology,2004,44(4):560–565.(in Chinese))
[8] NOGAMI T,NOVAK M. Resistance of soil to a horizontally vibrating pile[J]. Earthquake Engineering and Structure Dynamics,1977,5(3):249–261.
[9] NOVAK M,NOGAMI T. Soil‐pile interaction in horizontal vibration[J]. Earthquake Engineering and Structural Dynamics,1977,5(3):263–281.
[10] CHAU K T,YANG X. Nonlinear interaction of soil–pile in horizontal vibration[J]. Journal of Engineering Mechanics,2005,131(8):847–858.
[11] 余 俊,尚守平,李 忠,等. 饱和土中端承桩水平振动动力响应分析[J]. 岩土工程学报,2009,31(3):408–415.(YU Jun,SHANG Shouping,LI Zhong,et al. Dynamical characteristics of an end bearing pile embedded in saturated soil under horizontal vibration[J]. Chinese Journal of Geotechnical Engineering,2009,31(3):408–415.(in Chinese))
[12] 刘林超,闫启方. 分数导数模型描述的黏弹性土层中桩基水平振动研究[J]. 工程力学,2011,28(12):139–145.(LIU Linchao,YAN Qifang. Lateral vibration of single pile in viscoelastic soil described by fractional derivative model[J]. Engineering Mechanics,2011,28(12):139–145.(in Chinese))
[13] 姚 戈,杨 骁. Timoshenko模型桩水平振动的动力刚度[J]. 上海大学学报:自然科学版,2011,17(5):662–668.(YAO Ge,YANG Xiao. Dynamic stiffness of Timoshenko type pile in horizontal vibration[J]. Journal of Shanghai University:Natural Science,2011,17(5):662–668.(in Chinese))
[14] 丁选明,刘汉龙. 轴对称均匀黏弹性地基中现浇薄壁管桩竖向动力响应简化解析方法[J]. 岩土力学,2008,29(12):3 353–3 359. (DING Xuanming,LIU Hanlong. Simplified analytical method of vertical dynamic response of cast-in-situ concrete thin-wall pipe piles in axisymmetric homogeneous viscoelastic soil[J]. Rock and Soil Mechanics,2008,29(12):3 353–3 359.(in Chinese))
[15] DING X,LIU H,LIU J,et al. Wave propagation in a pipe pile for low-strain integrity testing[J]. Journal of Engineering Mechanics,2011,137(9):598–609.
[16] 郑长杰,丁选明,黄 旭,等. 滞回阻尼土中大直径管桩纵向振动响应解析解[J]. 岩石力学与工程学报,2014,33(增1):3 284–3 290. (ZHENG Changjie,DING Xuanming,HUANG Xu,et al. Analytical solution of vertical vibration response of large diameter pipe pile in hysteretic damping soil[J]. Chinese Journal of Rock Mechanics and Engineering,2014,33(Supp.1):3 284–3 290.(in Chinese))
[17] ZHENG C,LIU H,DING X,et al. Horizontal vibration of a large-diameter pipe pile in viscoelastic soil[J]. Mathematical Problems in Engineering,2013,(4):1–13.
[18] ZHENG C,LIU H,DING X. Lateral dynamic response of a pipe pile in saturated soil layer[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2015,40(2):159–184.