A coupled dynamic model of large diameter thin-wall pipe pile and soil plug considering pile three-dimensional effect and its analytical solution
WU Juntao1，2，WANG Kuihua1，2，LIU Xin1，2，SUN Fan1，2
(1. Research Center of Coastal and Urban Geotechnical Engineering，Zhejiang University，Hangzhou，Zhejiang 310058，China；2. Key Laboratory of Soft Soils and Geoenvironmental Engineering of Ministry of Education，Zhejiang University，Hangzhou，Zhejiang 310058，China)
Abstract：For large diameter thin-wall pipe piles，the soil plug at the pile toe and the pile three-dimensional effect should be taken into account during low-strain testing. A coupled dynamic model of large diameter thin-wall pipe and pile-soil plug considering the pile three-dimensional effect was presented，and an analytical solution in Laplace domain and a semi-analytical solution in time domain were subsequently deduced subjected to the longitudinal vibration. Comparisons between the solution and the existing solution based on Rayleigh-Love rod model were carried out. It is indicated that the two solutions are identical，which verifies the reliability of the one-dimensional rod model considering the lateral inertia effect in solving the dynamic problems of a pipe pile with soil plug. The influence of the combinations of the outer radius and the wall thickness of the pipe pile and the height of the soil plug on the low-strain testing results adopting the presented solution. The study can provide theoretical support and practical guidance for the engineering test on site.
[1] 王奎华，谢康和，曾国熙. 有限长桩受迫振动问题解析解及其应用[J]. 岩土工程学报，1997，19(6)：27–35.(WANG Kuihua，XIE Kanghe，ZENG Guoxi. Analytical solution to vibration of finite length pile under exciting force and its application[J]. Chinese Journal of Geotechnical Engineering，1997，19(6)：27–35.(in Chinese))
[2] 王奎华，谢康和，曾国熙. 变截面阻抗桩受迫振动问题解析解及应用[J]. 土木工程学报，1998，31(6)：56–67.(WANG Kuihua，XIE Kanghe，ZENG Guoxi. An analytical solution to force vibration of foundation pile under exciting force and its application[J]. China Civil Engineering Journal，1998，31(6)：56–67.(in Chinese))
[3] 吴君涛，王奎华，高 柳，等. 考虑桩身材料阻尼的桩基纵向振动积分变换解及其应用[J]. 岩石力学与工程学报，2017，36(9)：2 305–2 312.(WU Juntao，WANG Kuihua，GAO Liu，et al. Study on longitudinal vibration of a viscoelastic pile by integral transformation and its application[J]. Chinese Journal of Rock Mechanics and Engineering，2017，36(9)：2 305–2 312.(in Chinese))
[4] 吴文兵，王奎华，武登辉，等. 考虑横向惯性效应时楔形桩纵向振动阻抗研究[J]. 岩石力学与工程学报，2011，30(增2)：3 618–3 625. (WU Wenbing，WANG Kuihua，WU Denghui，et al. Study of dynamic longitudinal impedance of tapered pile considering inertial effect[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(Supp.2)：3 618–3 625.(in Chinese))
[5] 吕述晖，王奎华，吴文兵. 考虑横向惯性效应时黏弹性支承桩纵向振动特性研究[J]. 振动工程学报，2016，(4)：679–686.(LV Shuhui，WANG Kuihua，WU Wenbing. Logitudinal vibration of viscoelastic bearing piles considering transverse inertia effect[J]. Journal of Vibration Engineering，2016，(4)：679–686.(in Chinese))
[6] ZHENG C，KOURETZIS G P，DING X，et al. Three-dimensional effects in low-strain integrity testing of piles：analytical solution[J]. Canadian Geotechnical Journal，2015，53(2)：225–235.
[7] 吴君涛，王奎华，肖 偲，等. 静钻根植工法下变截面管桩纵向振动特性分析[J]. 岩石力学与工程学报，2018：37(4)：1 030–1 040. (WU Juntao，WANG Kuihua，XIAO Si，et al. Longitudinal vibration characteristics of static drill rooted tubular piles with variable section[J]. Chinese Journal of Rock Mechanics and Engineering，2018：37(4)：1 030–1 040.(in Chinese))
[8] ZHENG C，LIU H，DING X，et al. Three-dimensional effects in low-strain integrity testing of large diameter pipe piles[J]. Journal of Engineering Mechanics，2016，142(9)：04016064.
[9] 费 康，刘汉龙，张 霆. PCC桩低应变检测中的三维效应[J]. 岩土力学，2007，28(6)：1 095–1 102.(FEI Kang，LIU Hanlong，ZHANG Ting. Three-dimensional effects in low strain integrity test of PCC pile[J]. Rock and Soil Mechanics，2007，28(6)：1 095–1 102.(in Chinese))
[10] 刘汉龙，丁选明. 现浇薄壁管桩在低应变瞬态集中荷载作用下的动力响应解析解[J]. 岩土工程学报，2007，29(11)：1 611–1 617.(LIU Hanlong，DING Xuanming. Analytical solution of dynamic response of cast-in-situ concrete thin-wall pipe piles under transient concentrated load with low strain[J]. Chinese Journal of Geotechnical Engineering，2007，29(11)：1 611–1 617.(in Chinese))
[11] 丁选明，陈育民，孔纲强. PCC 桩低应变反射波法检测时速度波形成机制探讨[J]. 岩土力学，2012，33(1)：154–161.(DING Xuanming，CHEN Yumin，KONG Gangqiang. Formation mechanism of velocity waves in low strain integrity testing of PCC pile[J]. Rock and Soil Mechanics，2012，33(1)：154–161.(in Chinese))
[12] 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响应解析解[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))
[13] CHOI Y，O'NEILL M W. Soil plugging and relaxation in pipe pile during earthquake motion[J]. Journal of Geotechnical and Geoenvironmental Engineering，1997，123(10)：975–982.
[14] 石振明，陈建峰，祝龙根. PHC 管桩动力特性试验研究[J]. 岩土力学，2004，25(10)：1 622–1 626.(SHI Zhenming，CHEN Jianfeng，ZHU Longgen. Test study on dynamic properties of PHC pile[J]. Rock and Soil Mechanics，2004，25(10)：1 622–1 626.(in Chinese))
[15] 张振拴，杨树标，张 涛，等. 预应力管桩抗震性能试验研究[J]. 岩土力学，2012，33(增1)：79–84.(ZHANG Zhenshuan，YANG Shubiao，ZHANG Tao，et al. Experimental study of seismic behavior of prestressed pipe pile[J]. Rock and Soil Mechanics，2012，33(Supp.1)：79–84.(in Chinese))
[16] 陈 凡. FEIPWAPC特征线桩基波动分析程序[J]. 岩土工程学报，1990，12(5)：65–75.(CHEN Fan. Wave analysis program of pile based on FEIWAPC feature line[J]. Chinese Journal of Geotechnical Engineering，1990，12(5)：65–75.(in Chinese))
[17] 陈 波，闫澍旺，李家钢. 动力沉桩中土塞作用数值分析[J]. 天津大学学报：自然科学与工程技术版，2001，34(5)：636–640.(CHEN Bo，YAN Shuwang，LI Jiagang. Numerical analysis of soil plug effect on pile driving[J]. Journal of Tianjin University：Science and Technology，2001，34(5)：636–640.(in Chinese))
[18] 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]. Journal of Geotechnical Engineering，2014，36(6)：1 129–1 141.(in Chinese))
[19] 吴文兵，邓国栋，张家生，等. 考虑横向惯性效应时桩侧土–管桩–土塞纵向耦合振动特性研究[J]. 岩土力学，2017，38(4)：993–1 002.(WU Wenbing，DENG Guodong，ZHANG Jiasheng，et al. Vertical dynamic response of soil surrounding pile-pipe pile-soil plug by considering lateral inertial effect[J]. Rock and Soil Mechanics，2017，38(4)：993–1 002.(in Chinese))
[20] 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.
[21] RANDOLPH M F. Dynamic and static soil models for axial pile response[C]// Proceedings of the 4th International Conference on Application of Stress-wave Theory to Piles. [S. l.]：[s. n.]，1992：3–14.
2019, Vol. 38 
