Analytical solution of lateral dynamic response of a large diameter pipe pile considering influence of axial load
LUAN Lu-bao, DING Xuan-ming, LIU Han-long, ZHENG Chang-jie
1. Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education,Chongqing 400045, China; 2. College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China
Abstract：The horizontal vibration model for a large diameter pipe pile subjected to axial load in viscoelastic soil is established. The potential functions are adopted to decouple the governing equations of the soil. Analytical solution of the impedance of the pipe pile is obtained based on the assumption of perfect contact between the pile and the soil. This analytical solution can be perfectly simplified to the horizontal vibration solution of pipe pile without axial load, which demonstrates the validity of the solution deduced in this study. Numerical examples are presented to analyze the influences of axial load, excitation frequencies, and pile lengths on the complex impedances, displacements and internal forces. The results show that the complex impedance resonates at the inherent frequency of the pile-soil system. The vertical loads cause the redistribution of the displacements and internal forces of the pipe pile. The maximum displacement, bending moment and shear stress are located at the upper part of the pile shaft when the vertical load is 0, however, they move to the pile bottom gradually with the increase of the vertical load. The horizontal displacement of the pipe pile varies with the frequency. The changes of rotation angle, bending moment and shear force are obvious at the lower part of the pile shaft. The influences of pile length on displacement and internal force at the middle and bottom parts of the pile are more significant than those in the other parts. The displacements located at the upper part of the pile shaft without inner soil are larger than those with inner soil.
栾鲁宝，丁选明，刘汉龙，郑长杰. 考虑竖向荷载影响的大直径管桩水平振动响应解析解[J]. 岩土工程学报, 2016, 38(10): 1859-1868.
LUAN Lu-bao, DING Xuan-ming, LIU Han-long, ZHENG Chang-jie. Analytical solution of lateral dynamic response of a large diameter pipe pile considering influence of axial load. Chinese J. Geot. Eng., 2016, 38(10): 1859-1868.
[1] NOVAK M. Dynamic stiffness and damping of piles[J]. Canadian Geotechnical Journal, 1974, 11(4): 574-598. [2] NOVAK M, ABOUL-ELLA F. Impedance functions of piles in layered media[J]. Journal of the Engineering Mechanics Division, 1978, 104(3): 643-661. [3] NOVAK M, NOGAMI T. Soil‐pile interaction in horizontal vibration[J]. Earthquake Engineering & Structural Dynamics, 1977, 5(3): 263-281. [4] NOGAMI T, NOVAK M. Resistance of soil to a horizontally vibrating pile[J]. Earthquake Engineering & Structural Dynamics, 1977, 5(3): 249-261. [5] DOYLE P F, PAVLOVIC M N. Vibration of beams on partial elastic foundations[J]. Earthquake Engineering & Structural Dynamics, 1982, 10(5): 663-674. [6] EISENBERGER M, YANKELEVSKY D Z, ADIN M A. Vibrations of beams fully or partially supported on elastic foundations[J]. Earthquake Engineering & Structural Dynamics, 1985, 13(5): 651-660. [7] GAZETAS G, DOBRY R. Horizontal response of piles in layered soils[J]. Journal of Geotechnical Engineering, ASCE, 1984, 110(1): 20-40. [8] 杨 军, 宋二祥, 陈肇元. 桩在饱和土中水平振动的辐射阻尼简化算法[J]. 岩土力学, 2002(2): 179-183. (YANG Jun, SONG Er-xiang, CHEN Zhao-yuan. Simple radiation damping model for horizontally vibrating pile in saturated soil[J]. Rock and Soil Mechanics, 2002(2): 179-183. (in Chinese)) [9] 尚守平, 余 俊, 王海东, 等. 饱和土中桩水平振动分析[J]. 岩土工程学报, 2007, 29(11): 1696-1702. (SHANG Shou-ping, YU Jun, WANG Hai-dong, et al. Horizontal vibration of piles in saturated soil[J]. Chinese Journal of Geotechnical Engineering, 2007, 29(11): 1696-1702. (in Chinese)) [10] 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 Shou-ping, 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)) [11] HALABE U B, JAIN S K. Lateral free vibration of a single pile with or without an axial load[J]. Journal of Sound and Vibration, 1996, 195(3): 531-544. [12] 周绪红, 蒋建国, 邹银生. 黏弹性介质中考虑轴力作用时桩的动力分析[J]. 土木工程学报, 2005, 38(2): 87-91. (ZHOU Xu-hong, JIANG Jian-guo, ZOU Yin-sheng. Dynamic analysis of piles under axial loading and lateral dynamic force in visco-elastic media[J]. Chinese Civil Engineering Journal, 2005, 38(2): 87-91. (in Chinese)) [13] CATAL H H. Free vibration of partially supported piles with the effects of bending moment, axial and shear force[J]. Engineering Structures, 2002, 24(12): 1615-1622. [14] CATAL H H. Free vibration of semi-rigid connected and partially embedded piles with the effects of the bending moment, axial and shear force[J]. Engineering Structures, 2006, 28(14): 1911-1918. [15] LU J F, ZHANG X, WAN J W, et al. The influence of a fixed axial top load on the dynamic response of a single pile[J]. Computers and Geotechnics, 2012, 39: 54-65. [16] LIU H L, CHU J, DENG A. Use of large-diameter, cast-in situ concrete pipe piles for embankment over soft clay[J]. Canadian Geotechnical Journal, 2009, 46(8): 915-927. [17] LIU H L, NG C W W, FEI K. Performance of a geogrid-reinforced and pile-supported highway embankment over soft clay: case study[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2007, 133(12): 1483-1493. [18] XU X T, LIU H L, LEHANE B M. Pipe pile installation effects in soft clay[J]. Geotechnical Engineering, 2006, 159(4): 285-296. [19] DING X M, LIU H L, LIU J Y, et al. Wave propagation in a pipe pile for low-strain integrity testing[J]. Journal of Engineering Mechanics, ASCE, 2011, 117(9): 598-609. [20] ZHENG C, DING X, LI P, et al. Vertical impedance of an end‐bearing pile in viscoelastic soil[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2014, 39(6): 676-684. [21] 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(3): 1-13.
