成层广义Gibson地基中桩的水平动力响应

doi:10.16183/j.cnki.jsjtu.2020.382

摘要/Abstract

摘要：

为直接求解桩周土切变模量随深度线性变化情形下的单桩水平动力响应问题,基于成层广义Gibson地基,引入Adomian分解法,提出了一种求解非均质地基中桩水平动力响应的方法.相较于初参数法和传递矩阵法,该方法无需对非均质地基进行离散化处理.与数值方法相比,具有计算成本低、精度高和收敛速度快等优点.通过将本文方法和分层方法、均质地基解析方法、数值方法的计算结果进行对比,验证了本文方法的正确性和合理性.分析了桩底边界条件、地基土参数及桩身长细比对桩水平动力响应的影响.结果表明:在非均质地基中,桩土刚度比是影响桩水平动力响应的重要因素,随着地基土切变模量的增大,桩身水平位移幅值减小且分布趋于平缓.此外,相比于其他参数,土层泊松比和阻尼比对桩的水平动力响应影响较小.

关键词: 成层广义Gibson地基, 非均质地基, Adomian分解法, Novak薄层单元法, 水平动力响应

Abstract:

In order to directly solve the horizontal dynamic response of a single pile under the condition that the shear modulus of the soil around the pile varies linearly with the depth, a method for solving the horizontal dynamic response of piles in nonhomogenous foundation is proposed based on the layered generalized Gibson foundation and the Adomian decomposition method. Compared with the initial parameter method and the transfer matrix method, the proposed method does not need to discretize the nonhomogeneous foundation. Compared with the numerical method, it has the advantages of low computational cost, high accuracy, and fast convergence speed. The correctness and rationality of this method are verified by comparing it with the calculation results of the layered method, the analytical method of homogeneous foundation, and the numerical method. The influence of boundary conditions on the pile bottom, soil parameters, and pile slenderness on the horizontal dynamic response of the pile is investigated. The result show that in nonhomogeneous foundation, the pile-soil elastic modulus ratio is an important factor affecting the horizontal dynamic response of pile. As the shear modulus of soil increases, the amplitude of horizontal displacement of the pile decreases, and the distribution tends to be gentle. In addition, compared with other parameters, Poisson’s ratio and damping ratio of soil have less influence on the horizontal dynamic response of pile.

Key words: layered generalized Gibson foundation, nonhomogeneous foundation, Adomian decomposition method, Novak’s thin layer method, horizontal dynamic response

中图分类号:

TU435

邱杰凯, 丁肇伟, 宋春雨, 陈龙珠. 成层广义Gibson地基中桩的水平动力响应[J]. 上海交通大学学报, 2022, 56(4): 431-442.

QIU Jiekai, DING Zhaowei, SONG Chunyu, CHEN Longzhu. Horizontal Dynamic Response of Pile Based on Layered Generalized Gibson Foundation[J]. Journal of Shanghai Jiao Tong University, 2022, 56(4): 431-442.

图/表 13

图1

表1

桩端水平动力位移幅值与 N的关系

N	$U - 1 (0)$	$U - 1 (l 1)$
2	0.819792340	2.708522741
3	0.575465393	0.438747062
4	0.588914776	0.094956192
5	0.589908739	0.103157714
6	0.589898262	0.103125582
7	0.589898281	0.103125562
8	0.589898281	0.103125562
9	0.589898281	0.103125562
10	0.589898281	0.103125562
11	0.589898281	0.103125562
12	0.589898281	0.103125562

表1

图2

图3

图4

图5

图6

图7

图8

图9

图10

图11

图12

参考文献 27

[1]	ANOYATIS G, LAORA R D, LEMNITZER A. Dynamic pile impedances for fixed-tip piles[J]. Soil Dynamics and Earthquake Engineering, 2017, 97: 454-467. doi: 10.1016/j.soildyn.2017.03.025 URL
[2]	ANOYATIS G, LEMNITZER A. Dynamic pile impedances for laterally-loaded piles using improved Tajimi and Winkler formulations[J]. Soil Dynamics and Earthquake Engineering, 2017, 92: 279-297. doi: 10.1016/j.soildyn.2016.09.020 URL
[3]	KE W H, ZHANG C. A closed-form solution for kinematic bending of end-bearing piles[J]. Soil Dynamics and Earthquake Engineering, 2017, 103: 15-20. doi: 10.1016/j.soildyn.2017.09.004 URL
[4]	陈昌富, 汤宇, 梁冠亭. 剪切模量随深度呈指数函数增大地基中锚杆弹塑性分析[J]. 中南大学学报(自然科学版), 2016, 47(3): 905-912.
	CHEN Changfu, TANG Yu, LIANG Guanting. Elastic-plastic analysis for bolts in ground with shear modulus increasing following an exponential function with depth[J]. Journal of Central South University (Science and Technology), 2016, 47(3): 905-912.
[5]	LI Y, AI Z Y. Transient analysis of a fixed-head pile group in multi-layered transversely isotropic media due to horizontal loadings[J]. Computers and Geotechnics, 2020, 127: 103772. doi: 10.1016/j.compgeo.2020.103772 URL
[6]	AI Z Y, ZHAO Y Z, YE Z. A coupling rational finite element-boundary element method for a laterally loaded pile in transversely isotropic poroelastic soils[J]. Computers and Geotechnics, 2020, 117: 103227. doi: 10.1016/j.compgeo.2019.103227 URL
[7]	AI Z Y, ZHAO Y Z, CHENG Y C. Time-dependent response of laterally loaded piles and pile groups embedded in transversely isotropic saturated viscoelastic soils[J]. Computers and Geotechnics, 2020, 128: 103815. doi: 10.1016/j.compgeo.2020.103815 URL
[8]	熊辉, 江雅丰, 禹荣霞. 层状地基中基于Laplace变换的桩基横向振动阻抗计算[J]. 岩土力学, 2018, 39(5): 1901-1907.
	XIONG Hui, JIANG Yafeng, YU Rongxia. Lateral vibration impedance of piles embedded in layered soil based on Laplace transform[J]. Rock and Soil Mechanics, 2018, 39(5): 1901-1907.
[9]	陈云敏, 边学成. 高速铁路路基动力学研究进展[J]. 土木工程学报, 2018, 51(6): 1-13.
	CHEN Yunmin, BIAN Xuecheng. The review of high-speed railway track foundation dynamics[J]. China Civil Engineering Journal, 2018, 51(6): 1-13.
[10]	王路君, 朱斌, 文凯, 等. 层状路基路面体系温度应力和变形问题的位移函数解法[J]. 岩石力学与工程学报, 2018, 37(7): 1691-1699.
	WANG Lujun, ZHU Bin, WEN Kai, et al. Displacement function method on thermal stress and thermal deformation problems for layered pavement structure[J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(7): 1691-1699.
[11]	DENG D P, LI L, ZHAO L H. Stability analysis of a layered slope with failure mechanism of a composite slip surface[J]. International Journal of Geomechanics, 2019, 19(6): 04019050. doi: 10.1061/(ASCE)GM.1943-5622.0001417 URL
[12]	SARKAR R, MAHESHWARI B K. Effects of separation on the behavior of soil-pile interaction in liquefiable soils[J]. International Journal of Geomechanics, 2012, 12(1): 1-13. doi: 10.1061/(ASCE)GM.1943-5622.0000074 URL
[13]	DI LAORA R, ROVITHIS E. Kinematic bending of fixed-head piles in nonhomogeneous soil[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2015, 141(4): 04014126. doi: 10.1061/(ASCE)GT.1943-5606.0001270 URL
[14]	WANG J, ZHOU D, LIU W Q. Horizontal impedance of pile groups considering shear behavior of multilayered soils[J]. Soils and Foundations, 2014, 54(5): 927-937. doi: 10.1016/j.sandf.2014.09.001 URL
[15]	AWOJOBI A O. Estimation of the dynamic surface modulus of a generalized Gibson soil from the rocking frequency of rectangular foundations[J]. Géotechnique, 1973, 23(1): 23-31. doi: 10.1680/geot.1973.23.1.23 URL
[16]	靳建明, 梁仕华. 成层Gibson地基中单桩沉降的非线性分析[J]. 岩土力学, 2012, 33(6): 1857-1863.
	JIN Jianming, LIANG Shihua. Nonlinear analysis of settlement of axially loaded single pile in Gibson soil[J]. Rock and Soil Mechanics, 2012, 33(6): 1857-1863.
[17]	邹新军, 夏尉桓, 王亚雄. 非均质地基中V-T联合受荷桩承载力分析[J]. 中南大学学报(自然科学版), 2018, 49(10): 2553-2560.
	ZOU Xinjun, XIA Weihuan, WANG Yaxiong. Bearing capacity analysis of a single pile under combined V-T Loads in non-homogeneous subsoil[J]. Journal of Central South University (Science and Technology), 2018, 49(10): 2553-2560.
[18]	ZOU X J, ZHAO L J, ZHOU M, et al. Investigation of the torsional behaviour of circular piles in double-layered nonhomogeneous soil[J]. Applied Ocean Research, 2020, 98: 102110. doi: 10.1016/j.apor.2020.102110 URL
[19]	KALIYAPPAN M, GRACE G H. Solving nonlinear integral equations and nonlinear integro-differential equations using laplace adomian decomposition method through sagemath[J]. International Journal of Advanced Research in Engineering and Technology, 2020, 11(6): 298-306.
[20]	TURKYILMAZOGLU M. Accelerating the convergence of Adomian decomposition method (ADM)[J]. Journal of Computational Science, 2019, 31: 54-59. doi: 10.1016/j.jocs.2018.12.014 URL
[21]	CHEN W, LU Z. An algorithm for Adomian decomposition method[J]. Applied Mathematics and Computation, 2004, 159(1): 221-235. doi: 10.1016/j.amc.2003.10.037 URL
[22]	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. doi: 10.1061/JMCEA3.0002392 URL
[23]	丁肇伟, 宋春雨, 陈龙珠. 基于Pasternak地基模型和Adomian分解方法的扩底桩水平动力响应分析[J]. 地震工程学报, 2019, 41(6): 1587-1596.
	DING Zhaowei, SONG Chunyu, CHEN Longzhu. Horizontal dynamic response of a belled pile based on the Pasternak foundation model and the Adomian decomposition method[J]. China Earthquake Engineering Journal, 2019, 41(6): 1587-1596.
[24]	胡安峰, 谢康和, 肖志荣. 水平荷载下单桩动力反应分析[J]. 浙江大学学报(工学版), 2003, 37(4): 420-425.
	HU Anfeng, XIE Kanghe, XIAO Zhirong. Dynamic response analysis for a single pile subjected to lateral load ing[J]. Journal of Zhejiang University (Engineering Science), 2003, 37(4): 420-425.
[25]	刘林超, 闫启方. 饱和土-管桩-刚性承台水平振动研究[J]. 振动与冲击, 2019, 38(12): 126-132.
	LIU Linchao, YAN Qifang. A study on the lateral vibration of saturated soil-pipe pile-rigid platform[J]. Journal of Vibration and Shock, 2019, 38(12): 126-132.
[26]	MAHESHWARI B K, WATANABE H. Nonlinear dynamic behavior of pile foundations: Effects of separation at the soil-pile interface[J]. Soils and Foundations, 2006, 46(4): 437-448. doi: 10.3208/sandf.46.437 URL
[27]	杜秦文, 王金昌, 朱向荣, 等. 双层广义Gibson地基轴对称问题求解[J]. 岩土力学, 2007, 28(5): 933-938.
	DU Qinwen, WANG Jinchang, ZHU Xiangrong, et al. Solutions for axisymmetric problems of double layers generalized Gibson subgrade[J]. Rock and Soil Mechanics, 2007, 28(5): 933-938.