简谐SH波作用下管桩的振动特性

刘林超，肖琪聃，闫启方，刘滕

(信阳师范学院 土木工程学院，河南 信阳 464000)



简谐SH波作用下管桩的振动特性

刘林超，肖琪聃，闫启方，刘滕

(信阳师范学院 土木工程学院，河南 信阳 464000)

管桩；SH波；振动特性；动力放大因子

桩基作为一种重要的基础形式通常要承受地震激励、海洋荷载、动力机器荷载等动态激励的作用，有关桩基振动特性的研究近几十年来受到了足够的重视并取得了一定的研究成果[1-7]，以往这些研究都是考察实芯桩的振动特性。管桩作为近年来才出现的一种桩基形式，由于具有抗弯抗拉性能好、强度和承载力高、耐久性好且造价较低等诸多优点而被广泛应用到众多工程领域。为了给桩基设计、施工、检测等提供理论依据，近几年来，针对管桩的振动特性的研究越来越受到关注，丁选明等[8]给出了瞬态集中荷载作用下大直径管桩的时域解析解，郑长杰等[9-10]针对粘弹性地基中现浇大直径管桩的纵向振动及扭转振动进行了研究，吴文兵等[11]考虑土塞效应运用附加质量法对成层地基中管桩的纵向振动进行了研究，刘林超等[12]针对饱和土中管桩的水平振动运用多孔介质理论进行了研究。

1 简谐SH波作用下桩周土和桩芯土的水平位移

考察图1所示的管桩在沿y方向简谐水平剪切波(SH波)作用下的振动问题，且简谐SH波满足

(1)

图1 管桩土相互作用模型Fig. 1 The interaction model of pipe pile-

桩周土

(2)

(3)

桩芯土

(4)

(5)

(6)

(7)

(8)

(9)

考虑边界条件式(7)和式(9)，设式(6)和式(8)的解分别为

(10)

(11)

(12)

(13)

进而可以得到简谐SH波作用下引起的桩周土和桩芯土体的水平位移分别为

(14)

(15)

2 水平简谐荷载作用下桩周土和桩芯土振动求解

桩周土

(ωOzeiωt)+

(16)

(17)

桩芯土

(ωIzeiωt)+

(18)

(19)

令

(20)

对式(16)～(19)进行无量纲运算并整理可得

φO=0

(21)

(22)

(23)

(24)

(25)

(26)

(27)

(28)

(29)

(30)

考虑式(14)、式(15)和式(27)～式(30)可以得到简谐SH波和桩顶水平集中荷载共同作用下产生的桩周土和桩芯土的水平位移分别为

(31)

(32)

(33)

(34)

考虑管桩与桩周土和桩芯土接触面处的位移连续条件，可有如下连续性边界条件

(35)

(36)

BOk=COkAOk，AIk=DkAOk，BIk=CIkDkAOk

(37)

3 简谐SH波和水平集中荷载作用下管桩振动求解

由桩周土和桩芯土径向位移和环向位移，可以求得桩周土和桩芯土无量纲化的径向应力和环向应力σOr、τOrθ、σIr、τIrθ，进而可以得到桩周土和桩芯土对管桩的水平作用力。单位厚度桩周土对管桩的无量纲化水平作用力幅值为

θ=

(38)

单位厚度桩芯土对管桩的无量纲化水平作用力幅值为

θ=

(39)

由式(37)知桩周土和桩芯土对管桩的共同作用力为

(40)

由于管桩同样作简谐振动，以单位桩长为研究对象，考虑式(40)可以建立无量纲化的管桩的水平振动方程为

(41)

(42)

Ap1、Ap2、Ap3、Ap4为待定系数。由于管桩桩底为基岩，可建立管桩桩顶和桩底的边界条件为

(43)

P0为无量纲化的桩顶简谐水平集中荷载幅值。由管桩桩顶和桩底的边界条件可以确定待定系数

(44)

由式(31)可知，

(45)

考虑管桩与桩周土的连续性条件可得

(46)

对式(46)两端运用三角函数的正交性可得

(47)

式(47)中

(48)

由此可得SH简谐地震波和桩基水平集中荷载作用下管桩的水平位移为

(49)

up(1)=SgUg

(50)

式(50)中，

λp+cosλp-tghλpsinhλp+

(51)

这里，Sg即为简谐SH波作用下管桩桩顶的动力放大因子。

4 数值算例与分析

图2 动力放大因子随频率变化曲线Fig. 2 Curves of dynamic amplification factor versus frequency

图3 管桩壁厚不同时放大因子随频率变化曲线Fig. 3 Curves of dynamic amplification factor versus frequency for different pipe pile wall thickness

图4 桩土模量比不同时放大因子随频率变化曲线Fig. 4 Curves of dynamic amplification factor versus frequency for different pile-soil modulus ratio

图5 桩芯土和桩周土模量比不同时放大因子随频率变化曲线Fig. 5 Curves of dynamic amplification factor versus frequency for different modulus ratio of

5 结论

以简谐SH波和水平集中荷载作用下管桩的振动特性为研究对象，运用波的传播理论、桩基动力学、数学物理方法等得到了管桩桩顶的动力放大因子，以数值算例的形式通过分析管桩壁厚、桩土模量比和桩芯土与桩周土模量比对管桩动力放大因子的影响，研究了管桩的振动特性。

1)管桩桩顶动力放大因子随频率变化曲线存在较明显的峰值，系统存在有共振现象。

2)当管桩壁厚过薄时动力放大因子随频率变化曲线将会出现急剧增大，桩基此时宜发生稳定性破坏，所以管桩不能过薄。

3)由于桩基在施工中通常会造成桩周土刚度的弱化，所以采用管桩的抗震性能有时要比实芯桩好。

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(编辑 胡玲)

Dynamic properties of pipe pile under harmonic SH waves

LiuLinchao，XiaoQidan，YanQifang，LiuTeng

(School of Civil Engineering, Xinyang Normal University, Xinyang, 464000 Henan, P.R.China)

The displacements of soil around pile and pile core soil under harmonic SH waves are obtained based on one-dimensional wave motion model. Under the three-dimensional axial symmetry case, the vibrations of soil around pile and pile core soil caused by horizontal harmonic concentrated load and SH waves are solved by potential functions and variable separation method, and the radial and ring displacements of soil around pile and pile core soil are also obtained. The vibration of pipe pile under harmonic concentrated load and SH waves is investigated by considering pipe pile-soil dynamic interaction and continuous conditions. And the dynamic magnification factor at pipe pile has got. The results of numeral example indicate that pipe pile has resonance phenomenon under harmonic SH waves, the pipe pilecould lead to instability if the pipe pile wall too thin, and seismic performance of pipe pile is better than solid core pile under the same outside diameter.

pipe pile; SH waves; dynamic properties; dynamic magnification factor

2016-03-09

国家自然科学基金(U1504505)；河南省科技发展计划(142102210063)；河南省高等学校重点科研项目(15A560036)；河南省高等学校青年骨干教师资助计划(2013GGJS-121)；信阳师范学院重大课题预研项目(2013ZDYY19)。

刘林超(1979-)，副教授，博士，主要从事多孔介质理论、粘弹性性理论、桩基动力学的研究，(E-mail)llc109@126.com。

Foundation item：National Natural Science Foundation of China (No.U1504505); Development of Science and Technology Plan Project of Henan Province(No.142102210063); Key Scientific Research Project of Henan Province(No.15A560036); Youth Backbone Teacher Plan Project of Colleges and Universities in Henan Province(No.2013GGJS-121); Major Beforehand Research Project of Xinyang Normal University(No.2013ZDYY19).

10.11835/j.issn.1674-4764.2016.06.006

TU435

A

1674-4764(2016)06-0038-08

Received:2016-03-09

Author brief：Liu Linchao(1979-),associate professor,PhD, main research interests: theory of porous medium,viscoelastic theory and pile dynamics, (E-mail) llc109@126.com.