Vertical seismic responses of floating hollow pipe piles in layered soils
ZHANG Shiping1, 2, 3, ZHU Mingyue1, 2, 3
(1. School of Transportation, Changsha University of Science and Technology, Changsha, Hunan 410114, China; 2. National Engineering Research Center of Highway Maintenance Technology, Changsha, Hunan 410114, China; 3. International Innovation Cooperation Base of Advanced Highway Construction and Maintenance Technology in Hunan Province, Changsha, Hunan 410114, China)
Abstract:Soil typically exhibits a layered distribution due to long-term sedimentation and geological tectonic activities. The seismic response characteristics of pipe piles embedded in such stratified soil are highly complex, particularly regarding the vertical seismic response of friction-type hollow pipe piles, which warrants further investigation. This paper presents a semi-analytical solution for the dynamic responses of a floating tubular pile in layered soil subjected to time-harmonic seismic P-waves. The solution accounts for the dynamic interactions among the soil surrounding the pile, the pipe pile itself, and the soil beneath the pile, as well as the effects of soil stratification properties. The pile is modeled as an elastic hollow pipe structure, with the soil within its vertical projection area treated as a soil column, while the surrounding soil and the soil column are modeled as a multilayered continuum. Utilizing Hamilton?s variational principle, the equations of motion for the pile and the soil column, along with the pile-soil continuity conditions, are derived. The separation of variables technique and an iterative method are employed to solve these equations of motion for the pile-soil system, incorporating the pile-soil boundary and continuity conditions. This results in a frequency-domain semi-analytical solution for the kinematic responses of the pile-soil system to seismic P-waves. The proposed solution is validated through comparison with existing solutions. Additionally, numerical analyses are conducted to investigate the seismic pile-soil interaction effects across various material and geometric parameters. The results indicate that the layered nature of the soil surrounding the pile and the supporting conditions at the pile base significantly influence the seismic response of the pile to P-waves. Notably, the seismic response of friction-type piles in layered soils under P-waves differs substantially from that of end-bearing piles in homogeneous soils. Furthermore, existing solutions for homogeneous soil or end-bearing piles can be derived through parameter degradation of the developed solution. Additionally, when the inner diameter of the pipe pile exceeds 0.2 m, variations in its size significantly impact the seismic response of the pile-soil system under P-waves; conversely, when the inner diameter is 0.2 m or less, tubular piles exhibit seismic response characteristics comparable to those of solid piles with the same outer radius.
刘 林,肖 立,李翔宇,等. 水平荷载作用下大直径嵌岩桩力学特性研究[J]. 土木工程学报,2023,56(增2):44-49.(LIU Lin,XIAO Li,LI Xiangyu,et al. Mechanical behaviours of large-diameter rock-socketed piles under horizontal loads[J]. China Civil Engineering Journal,2023,56(Supp.2):44-49.(in Chinese))
[2]
邹新军,杨紫健,吴文兵. 非饱和土地基中端承桩对SH波的水平地震响应[J]. 岩土工程学报,2024,46(1):72-80.(ZOU Xinjun,YANG Zijian,WU Wenbing. Horizontal seismic response of end-bearing piles in unsaturated soil foundation under SH waves[J]. Chinese Journal of Geotechnical Engineering,2024,46(1):72-80.(in Chinese))
[3]
闫启方,刘林超. 考虑波动效应的SH简谐地震波作用下单桩水平振动研究[J]. 岩土工程学报,2012,34(8):1 483-1 487.(YAN Qifang,LIU Linchao. Lateral vibration of a single pile under SH harmonic seismic waves considering three-dimensional wave effect[J]. Chinese Journal of Geotechnical Engineering,2012,34(8):1 483-1 487.(in Chinese))
[4]
PAPAZOGLOU A J,ELNASHAI A S. Analytical and field evidence of the damaging effect of vertical earthquake ground motion[J]. Earthquake Engineering and Structural Dynamics,1996,25(10):1 109-1 137.
[5]
ANOYATIS G,DI LAORA R,MYLONAKIS G. Axial kinematic response of end-bearing piles to P waves[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2013,37(17):2 877-2 896.
[6]
WU,W B,WANG K H,ZHANG Z Q,et al. Soil-pile interaction in the pile vertical vibration considering true three-dimensional wave effect of soil[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2013,37(17):2 860-2 876.
[7]
ZHANG S P,CUI C Y,YANG G. Coupled vibration of an interaction system including saturated soils,pile group and superstructure under the vertical motion of bedrocks[J]. Soil Dynamics and Earthquake Engineering,2019,123:425-434.
[8]
DAI D H,EL NAGGAR M H,ZHANG N,et al. Vertical vibration of a pile embedded in radially disturbed viscoelastic soil considering the three-dimensional nature of soil[J]. Computers and Geotechnics,2019,111:172-180.
[9]
DAI D H,EL NAGGAR M H,ZHANG N,et al. Kinematic response of an end-bearing pile subjected to vertical P-wave considering the three-dimensional wave scattering[J]. Computers and Geotechnics,2020,120:103368.
[10]
HE R,KAYNIA A M,ZHANG J. Lateral free-field responses and kinematic interaction of monopiles to obliquely incident seismic waves in offshore engineering[J]. Computers and Geotechnics,2021,132:103956.
[11]
FAN K,GAZETAS G,KAYNIA A,et al. Kinematic seismic response of single piles and piles groups[J]. Journal of Geotechnical Engineering,1991,117(12):1 860-1 879.
[12]
MYLONAKIS G,GAZETAS G. Kinematic pile response to vertical P-wave seismic excitation[J]. Journal of Geotechnical and Geoenvironmental Engineering,2002,128(10):860-867.
[13]
LIU Q J,DENG F J,HE Y B. Kinematic response of single piles to vertically incident P-waves[J]. Earthquake Engineering and Structural Dynamics,2014,43(6):871-887.
[14]
KE W H,ZHANG C,DENG P. Kinematic response of single piles to vertical P-waves in multilayered soil[J]. Journal of Earthquake and Tsunami,2015,9(2):1550004.
[15]
DAI D H,EL NAGGAR M H,ZHANG N,et al. Rigorous solution for kinematic response of floating piles subjected to vertical P-wave[J]. Applied Mathematical Modelling,2022,106:114-125.
[16]
冯世进,陈云敏,刘明振. 成层土中黏弹性桩纵向振动分析及工程应用[J]. 中国公路学报,2004,17(2):59-63.(FENG Shijin,CHEN Yunmin,LIU Mingzhen. Analysis and application in engineering on vertical vibration of viscoelasticity piles in layered soil[J]. China Journal of Highway and Transport,2004,17(2):59-63.(in Chinese))
[17]
YAO A J,ZHANG J T,ZHOU Y J. Study on the dynamic response of the steel pipe pile foundation during construction of neighborhood deep excavation[J]. Procedia Engineering,2016,165:58-68.
[18]
黄福云,钱海敏,付 毳,等. 基于位移的PHC管桩-土相互作用计算方法[J]. 中国公路学报,2018,31(3):68-79.(HANG Fuyun,QIAN Haimin,FU Cui,et al. Displacement-based simplified calculation on soil-pile interaction of PHC pipe-piles[J]. China Journal of Highway and Transport,2018,31(3):68-79.(in Chinese))
[19]
ZHANG H Q,WANG F,LYU Z D,et al. Shake-table test on dynamic response of prestressed high-strength concrete pipe piles under soil-structure interaction[J]. Soil Dynamics and Earthquake Engineering,2023,174:108159.
[20]
胡贺松,唐孟雄,刘春林,等. 大直径随钻跟管桩竖向抗压承载性能试验研究[J]. 土木工程学报,2022,55(2):92-99.(HU Hesong,TANG Mengxiong,LIU Cunlin,et al. Vertical bearing capacity characteristics of large-diameter DPC pipe piles based on field tests[J]. China Civil Engineering Journal,2022,55(2):92-99.(in Chinese))
[21]
ZHENG C J,DING X M,SUN Y F. Vertical vibration of a pipe pile in viscoelastic soil considering the three-dimensional wave effect of soil[J]. International Journal of Geomechanics,2016,16:1-10.
[22]
RANDOLPH M F,MAY M,LEONG E C,et al. Soil plug response in open-ended pipe piles[J]. Journal of Geotechnical Engineering,1992,118:743-759.
[23]
刘林超,闫启方. 饱和土中管桩的纵向振动特性[J]. 水利学报,2011,42(3):366-372.(LIU Linchao,YAN Qifang. Vertical vibration characteristics of pipe pile in saturated soil[J]. Journal of Hydraulic Engineering,2011,42(3):366-372.(in Chinese))
[24]
郑长杰,丁选明,刘汉龙,等. 考虑土体三维波动效应的现浇大直径管桩纵向振动[J]. 岩土工程学报,2013,35(12):2 247-2 254. (ZHENG Changjie,DING Xuanming,LIU Hanlong,et al. Analytical solution to vertical vibration of cast-in-place concrete large-diameter pipe piles by considering 3D wave effect of soils[J]. Chinese Journal of Geotechnical Engineering,2013,35(12):2 247-2 254.(in Chinese))
[25]
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 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))
[26]
吴文兵,蒋国盛,王奎华,等. 土塞效应对管桩纵向动力特性的影响研究[J]. 岩土工程学报,2014,36(6):1 129-1 141.(WU Wenbing,JIANG Guosheng,WANG Kuihua,et al. Influence of soil plug effect on vertical dynamic response of pipe piles[J]. Chinese Journal of Geotechnical Engineering,2014,36(6):1 129-1 141.(in Chinese))
[27]
LIU H,JIANG G S,EL NAGGAR M H,et al. Influence of soil plug effect on the torsional dynamic response of a pipe pile[J]. Journal of Sound and Vibration,2017,410:231-248.
[28]
LI Z Y,GAO Y F. Effects of inner soil on the vertical dynamic response of a pipe pile embedded in inhomogeneous soil[J]. Journal of Sound and Vibration,2019,439:129-143.
[29]
吴君涛,王奎华,刘 鑫,等. 考虑桩身三维效应下的大直径薄壁管桩-桩端土塞耦合振动模型及其解析解[J]. 岩石力学与工程学报,2019,38(5):1 064-1 072.(WU Juntao,WANG Kuihua,LIU Xin,et al. A coupled dynamic model of large diameter thin-wall pipe pile and soil plug considering pile three-dimensional effect and its analytical solution[J]. Chinese Journal of Rock Mechanics and Engineering,2019,38(5):1 064-1 072.(in Chinese))
[30]
栾鲁宝,丁选明,刘汉龙,等. 考虑剪切变形的PCC桩水平振动响应解析解[J]. 岩石力学与工程学报,2016,35(11):2 345-2 358. (LUAN Lubao,DING Xuanming,LIU Hanlong,et al. Analytical solutions to lateral dynamic response of PCC piles considering shear deformation[J]. Chinese Journal of Rock Mechanics and Engineering,2016,35(11):2 345-2 358.(in Chinese))
[31]
ZHENG C J,KOURETZIS G,LUAN L B,et al. Kinematic response of pipe piles subjected to vertically propagating seismic P-waves[J]. Acta Geotechnica,2020,16(3):895-909.
[32]
LIU H B,DAI G L,ZHOU F X,et al. Vertical kinematic response of an end-bearing pipe pile in fractional viscoelastic unsaturated soil under vertically-incident P-waves[J]. Applied Mathematical Modelling,2023,120:686-710.
[33]
ZHANG S P,XU Z,DENG C. Kinematic responses of a pipe pile embedded in a poroelastic soil to seismic P waves[J]. Acta Geotechnica,2022,17(12):5 533-5 556.
[34]
吴文兵,王奎华,杨冬英,等. 成层土中基于虚土桩模型的桩基纵向振动响应[J]. 中国公路学报,2012,25(2):72-80.(WU Wenbing,WANG Kuihua,YANG Dongying,et al. Longitudinal dynamic response to the pile embedded in layered soil based on fictitious soil pile model[J]. China Journal of Highway and Transport,2012,25(2):72-80.(in Chinese))
[35]
SEO H,PREZZI M. Analytical solutions for a vertically loaded pile in multilayered soil[J]. Geomechanics and Geoengineering,2007,2(1):51-60.