Vertical dynamic response of a static drill rooted nodular pile
WANG Kuihua1,2, XIAO Si1,2, GAO Liu1,2, WU Juntao1,2
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：Based on the planar strain model for radial heterogeneity of soil around a pile, the vertical dynamic response of a static drill rooted nodular pile was investigated.At first, by utilizing the shear complex stiffness transfer method, the shear complex stiffness at the pile side was gained.Then, considering the special structure of the pile, the pile-soil system was divided into finite micro-elements in longitudinal direction, and the pile bottom soil reaction exerted on the pile end was simulated with the fictitious soil pile model.Afterward, using Laplace transformation and the impedance function recursive method, considering the transverse inertia effect of the pile, the semi-analytical solution to the velocity response at the pile top under action of transient excitation was obtained by using the convolution theorem and Fourier transformation.Furthermore, the rationality of the obtained solution was verified, and it was compared with the degenerate solution and the measured curve.Finally, effects of pile pitch radius and spacing, and cement soil around pile’s parameters on the dynamic response at the pile top were analyzed to raise relevant issues paid attention to in low-strain integrity tests of static drill rooted nodular piles.
[1] Zhou J J, Gong X N, Wang K H, et al. A model test on the behavior of a static drill rooted nodular pile under compression[J]. Marine Georesources & Geotechnology, 2016, 34(3): 293-301.
[2] 周佳锦, 龚晓南, 王奎华,等. 静钻根植竹节桩荷载传递机理模型试验[J]. 浙江大学学报:工学版, 2015, 49(3):531-537.(Zhou ZHOU Jia-jin J, Gong GONG Xiao-nan N, Wang WANG Kui-hua H, et al. Model test on load transfer mechanism of a static drill rooted nodular pile[J]. Zhejiang Daxue Xuebao (Gongxue Ban)/Journal of Zhejiang University (Engineering Science Edition, 2015, 49(3):531-537 and 546.(in Chinese))
[3] Zhou J J, Wang K H, Gong X N, et al. Bearing capacity and load transfer mechanism of a static drill rooted nodular pile in soft soil areas[J]. Journal of Zhejiang University-SCIENCE A, 2013, 14(10):705-719.
[4] 周佳锦, 王奎华, 龚晓南,等. 静钻根植竹节桩承载力及荷载传递机制研究[J]. 岩土力学, 2014(5):1367-1376.( Zhou ZHOU Jia-jin J, Wang WANG Kui-hua H, Gong GONG Xiao-nan N, et al. Bearing capacity and load transfer mechanism of static drill rooted nodular piles[J]. Yantu Lixue/rock & Soil Mechanics, 2014, 35(5):1367-1376.(in Chinese))
[5] 周佳锦, 龚晓南, 王奎华,等. 静钻根植竹节桩抗拔承载性能试验研究[J]. 岩土工程学报, 2015, 37(3):570-576.( Zhou ZHOU Jia-jin J, Gong GONG Xiao-nan N, Wang WANG Kui-hua H, et al. Behavior of the static drill rooted nodular piles under tension[J]. Yantu Gongcheng Xuebao/chinese Journal of Geotechnical Engineering, 2015, 37(3):570-577.(in Chinese))
[6] 周佳锦, 龚晓南, 王奎华,等. 静钻根植竹节桩桩端承载性能数值模拟研究[J]. 岩土力学, 2015(s1):651-656.( Zhou J J, Gong X N, Wang K H, et al. Numerical simulation of tip bearing capacity of static drill rooted nodular pile[J]. Yantu Lixue/rock & Soil Mechanics, 2015, 36:651-656. (in Chinese))
[7] 王奎华, 李振亚, 吕述晖,等. 静钻根植竹节桩纵向振动特性及应用研究[J]. 浙江大学学报(工学版), 2015, 49(3):522-530.(Wang WANG Kui-hua H, Li LI Zhen-ya Y, Lv LV Shu-hui H, et al. Vertical vibration characteristics of static drill rooted nodular pile and its applications[J]. Zhejiang Daxue Xuebao (Gongxue Ban)/Journal of Zhejiang University (Engineering Science Edition, 2015, 49(3):522-530. (in Chinese))
[8] 李振亚, 王奎华, 高柳. 考虑土体竖向波动效应的静钻根植竹节桩纵向振动阻抗研究[J]. 岩石力学与工程学报, 2017, 36(7):1791-1802.( LI Zhen-ya, WANG Kui-hua, GAO Liu. Longitudinal dynamic impedance of static drill rooted nodular pile considering vertical wave effect of soil[J]. Yanshilixue Yu Gongcheng Xuebao/chinese Journal of Rock Mechanics\s&\sengineering, 2017, 36(7):1791-1802. (in Chinese))
[7][9] Li Z Y, Wang K H, Wu W B, et al. Longitudinal dynamic impedance of a static drill rooted nodular pile embedded in layered soil[J]. Marine Georesources & Geotechnology, 2016(1).
[8][10] Zheng C J郑长杰,Liu H L 刘汉龙, Ding X M丁选明, et al. Vertical vibration of a large diameter pipe pile considering transverse inertia effect of pile[J]. Journal of Central South University(中南大学学报(英文版)), 2016, 23(4):891-897.
[9][11] 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(s2):3618-3625.( Wu WU Wen-bing B, Wang WANG Kui-hua H, Wu WU Deng-hui H, et al. Study of dynamic longitudinal impedance of tapered pile considering lateral inertial effect[J]. Yanshilixue Yu Gongcheng Xuebao/chinese Journal of Rock Mechanics & Engineering, 2011, 30(2):3618-3625. (in Chinese))
[10][12] 吴文兵, 王奎华, 窦斌. 任意层地基中粘弹性楔形桩纵向振动响应研究[J]. 振动与冲击, 2013, 32(8):120-127. (Wen-Bing W U Wen-bing, Wang WANG Kui-hua H, Dou DOU Bin. Vertical dynamic response of a viscoelastic tapered pile embedded in layered foundation[J]. Journal of Vibration & Shock, 2013, 32(8):120-127. (in Chinese) )
[11][13] Wu W B, Jiang G S, Dou B, et al. Vertical dynamic impedance of tapered pile considering compacting effect[J]. Mathematical Problems in Engineering, 2013, 2013(2):1-9.
[12][14] 王奎华, 高柳, 肖偲,等. 考虑桩周土竖向作用大直径楔形桩纵向振动特性[J]. 岩土力学, 2016(S2):223-231.(Gao GAO Liu, Wang WANG Kui-hua, Xiao XIAO Si, et al. Vertical Impedance of Tapered Piles Considering the Vertical Reaction of Surrounding Soil and Construction Disturbance[J]. Yantu Lixue/rock & Soil Mechanics, 2016(S2):223-231. (in Chinese))
[13][15] Gao L, Wang K H, Wu J T, et al. Analytical solution for the dynamic response of a pile with a variable-section interface in low-strain integrity testing[J]. Journal of Sound & Vibration, 2017, 395:328-340.
[14][16] Novak M, Aboul-Ella F. Impedance functions of piles in layered media[J]. Journal of the Engineering Mechanics Division, 1978, 104(3):643-661.
[15] 王奎华, 杨冬英, 张智卿. 基于复刚度传递多圈层平面应变模型的桩动力响应研究[J]. 岩石力学与工程学报, 2008, 27(4):825-831. (WANG Kui-hua, YANG Dong-ying, ZHANG Zhi-qing. Study on dynamic response of pile based on complex stiffness transfer model of radial multizone plane strain[J]. Chinese Journal of Rock Mechanics & Engineering, 2008, 27(4):825-831. (in Chinese))Novak M, Nogami T, Aboul-Ella F. Dynamic soil reactions for plane strain case. Res. Rep. BLWT-I-77, Fac. of Engrg. Sci[J]. Journal of the Engineering Mechanics Division, 1978, 104(4):953-959.
[16] 王奎华, 杨冬英, 张智卿. 基于复刚度传递多圈层平面应变模型的桩动力响应研究[J]. 岩石力学与工程学报, 2008, 27(4):825-831.( Wang K H, Yang D Y, Zhang Z Q. Study on dynamic response of pile based on complex stiffness transfer model of radial multizone plane strain[J]. Yanshilixue Yu Gongcheng Xuebao/chinese Journal of Rock Mechanics & Engineering, 2008, 27(4):825-831. (in Chinese))
[17] 杨冬英, 王奎华. 径向非均质土中平面应变模型的精度及适用性研究[J]. 土木工程学报, 2009(7):98-105.( YANG Dong-ying, WANG Kui-hua. Study on the accuracy and applicability of plane-strain model in radial-heterogeneous soil layers[J]. China Civil Engineering Journal, 2009, 42(7):98-105. (in Chinese))
[17][18] 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 & Analytical Methods in Geomechanics, 2012, 36(6):697-707.
[18][19] 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.( Wen-Bing W U Wen-bing, Wang WANG Kui-hua H, Yang YANG Dong-ying Y, et al. Longitudinal dynamic response to the pile embedded in layered soil based on fictitious soil pile model[J]. China Journal of Highway & Transport, 2012, 25(2):72-80. (in Chinese))
[19][20] 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):434-434.( Li LI Zheng-gen, GONG Yu-ling. Discussion on three dimensional effect of wave propagating in the pile with large diameter[J]. Chinese Journal of Rock Mechanics & Engineering, 1998. 17(4):434-434.(in Chinese))
[20] 何伟杰, 杨冬英, 张言,等. 基于扩散虚土桩法的大直径桩纵向振动研究[J]. 地震工程与工程振动, 2016, 01(3):025-32.( He W J, Yang D Y, Zhang Y, et al. Study on vertical vibration of large-diameter pile based on fictitious soil pile with diffusion angle[J]. Earthquake Engineering and Engineering Dynamics, 2016, 01(3):025-32. (in Chinese))
[21] 周佳锦. 静钻根植竹节桩承载及沉降性能试验研究与有限元模拟[D]. 浙江大学, 2016.
