基于径向不变假定的现浇大直径管桩纵向振动响应频域解

假定各物理量沿径向不变化,建立了低应变瞬态集中荷载作用下现浇大直径管桩振动响应的计算模型和波动方程。采用Laplace变换法,求得了波动方程的频域解析解,采用Fourier逆变换求得了时域响应。将文中解计算结果与三维频域解析解进行了对比分析,文中解的入射峰-反射峰时间差与三维频域解差别很小,说明对于PCC桩这种大直径薄壁管桩,采用径向不变假定对计算结果几乎没有影响。因此,在PCC桩低应变检测波形分析时,采用基于径向不变假定的二维解是完全合理的。将文中二维频域解的计算结果与二维时域解的结果进行了对比分析,结果表明,2种解在入射波、第一个桩底反射波、第二个桩底反射波峰值大小和到达时间非常吻合,这说明考虑环向位移与否对计算结果没有太大的影响,研究PCC桩低应变动力响应的问题时忽略水平方向的位移是完全可以的。     

黏弹性地基中管桩水平动力特性分析

从土体三维波动方程出发,将管桩看作一维欧拉-伯努利梁,对黏弹性地基中管桩水平振动响应进行了理论研究。摒弃传统的设立势函数法,而采用微分变换直接对土体振动方程进行解耦,并结合分离变量法求得了桩周土和桩芯土位移和应力表达式,进而利用管桩与桩周土和桩芯土接触界面的耦合连续条件得到桩的位移解析解,给出了管桩桩顶水平动力复阻抗表达式。将所得解完全退化到实心桩解,并与现有文献进行对比,验证了所提方法的合理性。通过参数分析,研究了桩周土、桩芯土剪切模量和密度以及管桩桩长对管桩桩顶复阻抗的影响。     

基于虚土桩模型的三维饱和介质中浮承桩纵向振动特性分析

基于Biot波动理论提出了一种桩底饱和虚土桩模型,同时考虑桩周、桩底土体三维波动效应及饱和特性,建立了三维饱和黏弹性土、虚土桩和实体桩完全耦合振动定解问题。采用势函数求解得出饱和土体位移解,并利用饱和土-桩界面耦合条件,求解得出桩顶纵向振动动力阻抗解析解答。将所得解退化到已有解析解进行对比验证,并在此基础上对浮承桩纵向振动特性进行参数化分析,计算结果表明:桩底饱和土层厚度越大,桩顶动刚度和动阻尼曲线振幅及共振频率越小,且当桩底饱和土层厚度增大到一定程度后,振幅呈现大、小峰值交替现象;桩周饱和土体孔隙率仅对桩顶动力阻抗曲线振幅产生明显影响,而桩底饱和土体孔隙率对桩顶动力阻抗曲线共振幅值和共振频率均影响显著;随桩周、桩底饱和土体剪切模量的增加,桩顶动力阻抗曲线共振幅值水平均明显降低,且受桩周饱和土体剪切模量影响更为突出。     

考虑黏性的液化土中水平振动桩基桩顶阻抗研究

建立了三维黏性流体-桩-土体相互作用分析模型,对简谐激振水平动荷载作用下的液化土中桩基振动响应问题进行解析研究。将桩周液化土体视为黏性不可压缩流体,建立流体运动方程,利用亥姆霍兹分解和分离变量法并结合流体边界条件和桩-流体位移、速度连续条件及桩身边界条件,求得了黏性流体动压力及流体速度势解析表达式,从而得到桩身阻力表达式。用饱和多孔介质模型模拟饱和未液化土层,在已有饱和未液化土层振动响应解析解的基础上,推导得出上覆黏性液化流体,下层土体为饱和未液化土中水平振动桩基桩顶阻抗解析解。与已有的水中悬臂梁自由振动解析解对比,验证提出的模型解的正确性,最后分析了流体黏滞系数、桩长、桩土模量比对桩顶阻抗的影响。结果表明,忽略液化土体的黏性特征会高估桩基础桩顶的刚度阻抗,低估其阻尼阻抗。     

PCC桩低应变检测中的三维效应

分析了低应变检测对PCC大直径薄壁混凝土管桩的适用性。对低应变中受瞬间冲击荷载作用的完整和缺陷PCC桩的动力响应进行了一维及三维有限元模拟,详细研究了PCC桩低应变检测中的三维效应。研究结果表明：除了一维应力波理论中的纵向振动外,PCC桩顶所测的动力响应中还包含弯曲振动以及波在桩顶表面传播和内外边界上的反射的影响。在研究结果的基础上,对PCC桩低应变检测试验中激振点和测点的最佳位置和如何合理分析试验结果给出了建议。     

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

与实心桩相比,由于土塞与管桩内壁复杂的相互作用,开口管桩的桩-土动力相互作用问题更为复杂。因此,需深入研究考虑土塞效应时的管桩-土体动力相互作用问题。首先,考虑管桩的横向惯性效应及其黏性性质,采用Rayleigh-Love动力杆件模型和附加质量模型建立了桩侧土-管桩-土塞系统的纵向振动控制方程。进一步,采用积分变换和阻抗函数传递技术,分别得到了任意荷载形式下管桩桩顶速度频域响应的解析解以及半正弦脉冲激励作用下桩顶速度时域响应的半解析解。最后,通过与现有解及模型试验的对比研究验证了理论解的合理性,并研究了管桩设计参数对桩顶纵向振动特性的影响。结果表明,当管桩其他设计参数不变时,管桩截面尺寸越大或长度越小时,应力波传播过程中的弥散效应越明显。对于同样外半径的管桩,壁厚越大时,越容易检测到土塞顶部界面及桩尖传来的反射信号,就能对管桩的施工质量进行更为合理的评价。     

轴对称均匀黏弹性地基中现浇薄壁管桩竖向动力响应简化解析方法

考虑土体材料的黏性阻尼和桩-土纵向耦合振动,建立了轴对称均匀黏弹性地基中现浇薄壁管桩管桩纵向振动的定解问题,采用Laplace变换的方法求得了解析解。对一算例进行了分析,将计算结果与实测波形和有限元进行了对比,三者吻合较好。进一步分析了桩周土和桩芯土黏性阻尼系数对桩顶速度导纳和复动刚度的影响以及桩底土阻尼系数对桩顶速度导纳的影响,得到了各参数对桩纵向振动特性影响的规律     

现浇薄壁管桩低应变动力检测适应性探讨

现浇薄壁管桩是一种大直径的管桩,在低应变检测时必然存在平截面假定不满足以及桩头三维效应的问题。无桩帽管桩低应变检测时由于激发了非轴对称的弯曲模态,并不是达到一定的深度平截面假定就会满足,各截面不同的点会受到不同程度的高频干扰,桩顶90°点受到了较小的高频干扰,低应变检测时激振点与传感器夹角为90°时更容易得到清晰的反射波信号。解析解和有限元解的结果均表明,带帽桩在桩帽的动力响应信号能看到明显的桩底反射和缺陷反射时距离桩心不同点上所感受的高频干扰的频率一样,速度振幅不同,距桩心0.50 （ 为桩半径）的点受到最小的干扰。     

非均质土中桩端扩散虚土桩法的桩基纵向振动研究

根据桩端土应力扩散的规律,建立了桩端扩散虚土桩模型。基于该模型对非均质土中桩-土纵向耦合振动进行研究。利用复刚度传递多圈层平面应变模型,得到桩与虚土桩桩侧土的剪切复刚度。结合边界条件、初始条件和连续条件,对扩散虚土桩和实体桩动力方程从底层往顶层逐层进行求解,得到桩顶动力响应的频域解析解和时域半解析解。通过对桩端扩散虚土桩扩散角、扩散层厚度、桩侧土非均质性和桩长的影响进行计算分析,得到基于扩散虚土桩法桩-土纵向振动响应特性。研究结论可为桩基础动力设计和动态检测提供理论依据。     

黏弹性地基中PCC桩扭转振动响应解析方法研究

考虑土体材料的黏性阻尼和桩-土扭转耦合振动,把桩看作一维杆,将土体视作三维轴对称黏弹性介质,对黏弹性地基中现浇混凝土大直径管桩（简称PCC桩）扭转振动频域特性进行了理论研究,采用Laplace变换和分离变量的方法求得了桩顶扭转频域响应解析解。将所得解完全退化到实心桩的解,并与经典平面应变解进行对比,验证了解析解的合理性。分析了桩长以及土体黏性阻尼系数对桩顶速度导纳和复动刚度的影响,得到了各参数对桩扭转振动特性影响的规律。分析表明：桩周土黏性阻尼系数增大可以显著提高桩顶扭转复动刚度和减小速度导纳振荡幅值,而桩芯土黏性阻尼系数的影响不明显;桩长越长,桩顶复动刚度越大,速度导纳振荡幅值越小,但当桩长增大到一定程度时,再继续增加桩长,桩顶复动刚度基本没有改变。     

Lateral dynamic response of a pipe pile in saturated soil layer

This paper presents an analytical solution for the lateral dynamic response of a pipe pile in a saturated soil layer. The wave propagations in the saturated soil and the pipe pile are simulated by Biot's three‐dimensional poroelastic theory and one‐dimensional elastic theory, respectively. The governing equations of soil are solved directly without introducing potential functions. The displacement response and dynamic impedances of the pipe pile are obtained based on the continuous conditions between the pipe pile and both the outer and inner soil. A comparison with an existing solution is performed to verify the proposed solution. Selected numerical results for the lateral dynamic responses and impedances of the pipe pile are presented to reveal the lateral vibration characteristics of the pile‐soil system. Copyright © 2015 John Wiley & Sons, Ltd.     

A new analytical model to study the influence of weld on the vertical dynamic response of prestressed pipe pile

This investigation is concerned with the mathematical analysis of a viscoelastic prestressed pipe pile embedded in multilayered soil under vertical dynamic excitation. The pile surrounding soil is governed by the plane strain model, and the soil plug is assumed to be an additional mass connected to the pipe pile shaft by applying the distributed Voigt model. Meanwhile, the prestressed pipe pile is assumed to be a vertical, viscoelastic, and hollow cylinder governed by the one‐dimensional wave equation. Then, analytical solutions of the dynamic response of the pipe pile in the frequency domain are derived by means of the Laplace transform and impedance function transfer method. Subsequently, the corresponding quasi‐analytical solution in the time domain for the case of the prestressed pipe pile undergoing a vertical semi‐sinusoidal exciting force applied at the pile top is obtained by employing the inverse Fourier transform. Utilizing these solutions, selected results for the velocity admittance curve and the reflected wave curve are presented for different heights of the soil plug to examine the influence of weld properties on the vertical dynamic response of prestressed pipe pile. The reasonableness of the theoretical model is verified by comparing the calculated results based on the presented solutions with measured results. Copyright © 2017 John Wiley & Sons, Ltd.     

Time-domain analysis of velocity waves in a pipe pile due to a transient point load

The propagation of stress waves in a pipe pile subjected to a transient point load cannot be expressed using traditional one-dimensional (1D) wave theory. This paper presents an analytical solution used to investigate the wave propagation in a pipe pile under an axial point load. The soil resistance is simulated using the Winkler model, and the excitation force is simulated with a semi-sinusoidal impulse. A time-domain analytical solution for the three-dimensional wave equation is derived using the separation of variables and variation of constants methods. The solution is verified with a frequency domain analytical solution in which the time-domain response is calculated by numerical Fourier inverse transformation. Furthermore, the solution proposed in this paper is compared with the results of model testing and 3D FEM analysis. The comparisons show that the analytical solution proposed in this study agrees well with the results of previous studies. The proposed solution is subsequently applied in case studies. The vertical velocity responses in the circumferential and axial directions are analyzed to reveal the propagation characteristics of transient waves in the pipe pile. Moreover, the effects of the location and period of the excitation force, the side and tip resistances and high-order modes are studied in detail.     

横观各向同性层状地基动应力响应的求解与分析

动力响应问题的求解对于地基在外荷载作用下引起的弹性波动问题研究有重要的意义。本文提出了一种求解横观各向同性层状地基在施加时间简谐荷载作用下任意点的应力响应的算法。此算法利用傅里叶变换将广义平面应变问题频率-空间域的动力方程转化到频率-波数域内,结合对偶变量的引入,利用高精度的精细积分算法对状态方程进行求解,在得到频率-波数域内的位移响应的基础上,利用傅里叶逆变换得到任意点的动应力响应。简谐荷载不仅可以施加在地基表面,而且可以施加在地基内部。对比算例验证了本文算法的准确性,同时对地基各向异性特性、激励频率和阻尼比对动应力响应的影响进行了参数分析,为工程实际提供可靠的数值依据。     

周期分布桩体对平面SH波隔振效应的解析求解

将排桩对平面SH波的隔振简化为弹性波散射的二维平面问题,基于全空间中无限周期结构的周期特性,给出了一种求解无限周期分布桩体对平面SH波隔振效应的解析方法。该方法采用波函数展开法并结合Graf加法定理,利用全空间中相邻周期单元的散射波场在频域内相差一个相位的特性,仅选取一个周期单元,将入射波场和所有散射波场的贡献叠加后,根据边界条件求解待定系数,从而求得整个散射波场。该解析解能够精确求解无限周期分布桩体的散射问题,分析周期分布桩体数量较多时的隔振规律,弥补了以往理论分析中桩体个数较多时难以求解的不足。重点讨论了桩体个数、桩体刚度、桩体间距和桩体类型等因素对隔振效果的影响,结果表明：（1）该方法显著降低了求解大量桩体问题时的存储量和计算量,有限周期模型计算结果随桩体个数增多收敛于无限周期模型,反映了该方法的正确性;（2）整体上桩体刚度增大有利于提高隔振效果,但桩体刚度对隔振效果的提升有限,桩体剪切波速为土体5倍时已具有足够的隔振效果;（3）桩间距对隔振效果有着直接影响,间距越小则低频禁带宽度越大;（4）桩体类型对隔振效果有着显著影响,实心桩有着良好的隔振效果,而具有柔性内填充的管桩在低频段有着更佳的隔振效果。     

Torsional dynamic response of a large‐diameter pipe pile in viscoelastic saturated soil

An analytical solution is developed in this paper to investigate the dynamic response of a large‐diameter end‐bearing pipe pile subjected to torsional loading in viscoelastic saturated soil. The wave propagation in saturated soil and pile are simulated by Biot's two‐phased linear theory and one‐dimensional elastic theory, respectively. The dynamic equilibrium equations of the outer soil, inner soil, and pile are established. The solutions for the outer and inner soils in frequency domain are obtained by Laplace transform technique and the separation of variables method. Then, the dynamic response of the pile is obtained on the basis of the perfect contacts between the pile and the outer soil as well as the inner soil. The results in this paper are compared with that of a solid pile in elastic saturated soil to verify the validity of the solution. Furthermore, the solution in this paper is compared with the classic plane strain solution to verify the solution further and check the accuracy of the plane strain solution. Numerical results are presented to analyze the vibration characteristics and illustrate the effect of the soil parameters and the geometry size of the pile on the complex impedance and velocity admittance of the pile head. Finally, the displacement of the soil at different depth and frequency is analyzed. Copyright © 2014 John Wiley & Sons, Ltd.     

Vertical dynamic response of a pipe pile in saturated soil layer

An analytical solution is developed in this paper to investigate the vertical time-harmonic response of a pipe pile embedded in a viscoelastic saturated soil layer. The wave propagation in the saturated soil is simulated by Biot’s 3D poroelastic theory and that in the pipe pile is simulated by 1D elastodynamic theory. Potential functions are applied to decouple the governing equations of the soil. The analytical solutions of the outer and inner soil in frequency domain are obtained by the method of separation of variables. The vertical response of the pipe pile is then obtained based on the continuity assumption of the displacement and stress between the pipe pile and both the outer and inner soil. The solution is compared with existing solutions to verify the validity. Numerical examples are presented to analyze the vibration characteristics of the pile.