An analytical solution for wave propagation in a square pile due to transient point load

This paper presents an analytical solution for wave propagation in a square pile due to transient point load. The differential equation of dynamic equilibrium is established considering propagation of waves in both vertical and transverse directions. The soil resistance is simulated by Voigt model. The three-dimensional analytical solution is deduced by using Fourier transform and the separation of variable method. The arithmetical results of the proposed solution show that the velocity responses along the radial direction at the pile top are highly non-uniform. In addition, Young’s modulus and the pile side length exert undisputable influences on the velocity responses.     

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.     

Source signature and elastic waves in a half‐space under a momentary shear line impulse

The transient deformation of an elastic half‐space under a line‐concentrated impulsive vector shear load applied momentarily is disclosed in this paper. While in an earlier work, the author gave an analytical–numerical method for the solution to this transient boundary‐value problem, here, the resultant response of the half‐space is presented and interpreted. In particular, a probe is set up for the kinematics of the source signature and wave fronts, both explicitly revealed in the strained half‐space by the solution method. The source signature is the imprint of the spatiotemporal configuration of the excitation source in the resultant response. Fourteen wave fronts exist behind the precursor shear wave S: four concentric cylindrical, eight plane, and two relativistic cylindrical initiated at propagating centres that are located on the stationary boundaries of the solution domain. A snapshot of the stressed half‐space reveals that none of the 14 wave fronts fully extend laterally. Instead, each is enclosed within point bounds. These wave arresting points and the two propagating centres of the relativistic waves constitute the source signature. The obtained 14 wave fronts are further combined into 11 disparate wave fronts that are grouped into four categories: an axis of symmetry wave—so named here by reason of being a wave front that is contiguous to the axis of symmetry, three body waves, five surface waves and two inhibitor waves—so named here by reason that beyond them the material motion dies out. Of the three body waves, the first is an unloading shear wave, the second is a diffracted wave and the third is a reflected longitudinal two‐branch wave. Of the two inhibitor waves, the first is a two‐joint relativistic wave, while the second is a two‐branch wave. The wave system, however, is not the same for all the dependent variables; a wave front that appears in the behaviour of one dependent variable may not exist in the behaviour of another. It is evident from this work that Saint–Venant's principle for wave propagation problems cannot be formulated. Therefore, the above results are valid for the particular proposed model for the momentary line‐concentrated shear load. The formulation of the source signature, the wave system, and their role in the half‐space transient deformation are presented here. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

竖向力与水平向力同时作用下管桩的性状研究

用解析方法研究了管桩在轴向力和水平向力（倾斜力）联合作用下的受力及变形性状。在高层建筑、桥梁工程、海洋工程、新型海堤护岸等工程中桩基自由长度上作用土压力、风荷载、波浪荷载等荷载型式,基桩经常在竖向、水平向荷载同时作用下工作。国内外学者通过大量试验和理论研究得出了计算竖向、水平向荷载下基桩内力和挠度的半经验公式以及张氏法公式。为了分析竖向、水平向荷载同时作用下自由荷载的作用,在现行m法假设的基础上,从弹性桩的挠曲微分方程出发,导出了任意自由荷载作用下桩任意截面的水平变位、倾角、弯矩、剪力和地基反力计算表达式。桩的挠曲微分方程是分段函数,包括地上部分和地下部分桩,相应的内力和变位求解也分为两段。最后通过一个算例分析了桩顶竖向荷载、桩顶水平力和自由荷载对桩身的受力性状各参数的影响。计算结果表明, 桩顶水平力对桩身最大弯矩和桩顶水平变位的影响最大,而桩周内外摩阻力及桩身自重对桩身受力性状影响较小。     

低应变下变阻抗薄壁管桩动力响应频域解析解

管桩低应变完整性检测时,桩顶一点受到瞬态集中荷载的作用,其动力响应问题是一个三维波动问题。基于三维波动理论,建立了任意段变阻抗薄壁管桩动力响应的计算模型和波动方程,结合初边值条件,采用Laplace变换法求得了该波动方程的频域解析解,采用Fourier逆变换求得了时域响应。将计算结果与三维有限元结果进行了对比分析,解析解的计算结果和三维有限元结果较为接近,两者在入射波峰、缺陷反射峰和桩底反射峰处都较为吻合,两种方法位移响应曲线基本相同。给出了桩顶不同点的动力响应,并探讨了高频干扰问题。对变截面桩和变模量桩的动力响应特性进行了分析。     

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.     

带帽刚性桩复合地基荷载传递机理研究

为了研究带帽刚性桩复合地基荷载传递机理,基于弹性理论和合理假定,采用荷载传递函数法,建立了带帽刚性桩复合地基中桩体沉降及其轴向应力、桩帽下土体竖向位移及其竖向应力、桩帽间土体竖向位移及其竖向应力、桩身侧摩阻力、桩帽边缘土体之间的侧摩阻力与荷载水平、深度之间的控制微分方程。采用微分方程的近似解法,推导出相应地解析表达式。利用桩体荷载沉降关系作为已知条件进行求解,计算结果能够反映带帽刚性桩复合地基荷载传递的一般力学性状规律。     

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。     

Study on low‐strain integrity testing of pipe‐pile using the elastodynamic finite integration technique

This study focuses on the three‐dimensional (3‐D) characteristics of wave propagation in pipe‐pile using elastodynamic finite integration technique. First, a real 3‐D pile‐soil model in cylindrical coordinate system is presented. Then, the governing equations are established. With the boundary and initial conditions, the numerical solution is obtained. The accuracy and feasibility of the self‐written code are further verified via comparing with the measured data. Velocity histories at different angles of pile top and pile tip are illustrated, and the snapshots reflecting the 3‐D characteristics of wave propagation are given. It shows that the interferences of Rayleigh waves can confuse the result interpretation for pile integrity testing. The increase of hammer contact time can effectively mitigate the interferences, and the interferences of Rayleigh waves are weakest at an angle of 90° from where hammer hits. Besides, surrounding soil can partly mitigate the wave interferences. Copyright © 2012 John Wiley & Sons, Ltd.     

大直径钢管桩承载力的非线性分析

推导了砂土地基中闭口管桩的沉桩影响半径以及刚性桩的横向承载力（矩）。通过使用MATLAB程序对单桩轴向刚度的分析,得出了其与桩周单位深度土的等效刚度系数、桩端土的等效刚度系数、钢管桩的壁厚、桩径、桩长、桩身弹性模量等参数之间的一些关系,从而为此类桩的优化设计提供了理论依据。在此基础上通过桩身荷载传递的双曲线函数模型以及相关参数,在已知（假定）桩身压缩量的情况下求出相应的桩顶轴力。     

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.     

负摩阻力作用下锥形异型桩承载力研究

研制异型桩是降低负摩阻力的重要措施之一,对目前能降低负摩阻力的异型桩的种类和特征进行了系统分析与总结,并介绍了作者已授权的一项国家发明专利——一种端部螺纹X形变截面预制管桩及其施工方法。通过FLAC3D软件分别模拟了圆形等截面桩和锥形异型桩在相同地面堆载的情况下桩身轴力的分布情况,结果表明锥形纵截面的设置可以有效降低负摩阻力的影响。阐述了端部螺纹X形变截面预制管桩能更显著降低负摩阻力的机制,研究成果可为端部螺纹X形变截面预制管桩的设计和推广应用提供一定的理论基础。      

完全非线性聚焦波浪的数值模拟

利用高阶边界元方法求解拉普拉斯方程,建立了模拟完全非线性聚焦波的时域数值模型,其中追踪流体自由表面的方法为满足完全非线性自由水面条件的半混合欧拉-拉格朗日方法,运用四阶Runga-Kutta方法计算每一时间步新的波面高度和速度势,同时通过入射边界给定速度的二阶Stokes解析解产生波浪,并应用镜像格林函数消除水槽两个侧面和底面上的积分。对不同波陡的聚焦波群在水槽中开展了物理模型实验,并把试验结果和数值结果进行了对比,两者吻合得很好,然后对非线性条件下聚焦波的特点进行了研究。     

Simulation of axis-symmetric seismic waves in fluid-filled boreholes in the presence of a drill string

A numerical algorithm for simulation of 2-D (axis-symmetric) wave propagation using a multidomain approach is proposed. The method uses a cylindrical coordinate system, Chebyshev and Fourier differential operators to calculate the spatial derivatives along the radial and vertical direction, respectively, and a Runge–Kutta time-integration scheme. The numerical technique is based on the solution of the equations of momentum conservation combined with the stress–strain relations of the fluid (drilling mud) and isotropic elastic media (drill string and formation). Wave modes and radiated waves are simulated in the borehole-formation system. The algorithm satisfies the reciprocity condition and the results agree with an analytical solution and low-frequency simulation of wave-propagation modes reported in the literature. Examples illustrating the propagation of waves are presented for hard and soft formations. Moreover, the presence of casing, cement, and formation heterogeneity have been considered. Since the algorithm is based on a direct (grid) method, the geometry and the properties defining the media at each grid point, can be general, i.e., there are no limitations such as planar interfaces or uniform (homogeneous) properties for each medium.      

Vertical vibration of a large-diameter pipe pile considering the radial inhomogeneity of soil caused by the construction disturbance effect

This paper presents an analytical solution for the vertical vibration of a large-diameter pipe pile considering the radial inhomogeneity of both the outer and inner soil caused by the construction disturbance effect. The radial inhomogeneity of the soil is simulated by gradually varying the soil parameters in the radial direction. The complex impedance at the pile head is obtained by introducing the variable separation method and impedance function transfer method. The proposed solution is compared with existing solutions to verify its reliability. Parametric studies are conducted to investigate the vertical vibration characteristics of the pile.     

软黏土中超长预应力高强度混凝土 管桩竖向承载特性试验研究

港口码头工程建设将向外海开敞式发展,由于工程地质条件日趋复杂,在超厚软黏土地基上建设高桩码头面临重大难题。因持力层埋深较深,预应力高强度混凝土（PHC）管桩成为设计首选的超长桩基础型式。针对某军用码头85 m设计桩长的试桩进行了试验和数值计算,分析了超长PHC管桩承载力机制与传递规律,基于传递函数法提出改进的双曲函数计算模型,并对垂直静载试桩进行计算。结果表明：桩身轴力和桩顶位移的计算值与实测值吻合较好,证明提出的双曲线模型能够反映轴向承载PHC管桩桩-土相互作用实际情况,能够为软黏土中超长PHC管桩基桩设计提供依据。     

顶管推进对邻近桩基的影响分析

研究了顶管正面附加推力、掘进机和后续管道与土体之间的摩擦力在邻近桩基上引起的总的附加荷载的分布规律。研究结果表明,附加荷载的变化规律与桩基和掘进机的相对位置密切相关,是一个三维问题;在顶进方向和垂直于管壁方向,随着掘进机开挖面通过前后,附加荷载由压力变为拉力,顶进方向的附加荷载值和影响范围较垂直于管壁方向大;竖直方向的附加荷载较小,靠近管道轴线附近的桩基部位受到的附加荷载方向与两端相反,曲线呈“弓”型分布;随着桩基与管道距离的减小,附加荷载急剧增大。     

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。     

预应力管桩抗震性能试验研究

为研究预应力管桩的抗震性能,采用振动台通过对管桩-土-上部结构模型在不同地震波作用下的试验,分析研究管桩桩身产生的应力、应变、弯矩及位移沿桩身的分布、最大弯矩产生的位置、桩与承台的受力及破坏特征,得出地震作用下管桩桩身弯矩最大值的产生位置为距离桩顶5～6倍桩径处, 在El-centro波、LWD波和正弦波工况下,桩-上部结构体系的加速度反应在高度上呈现“K”型分布等反应规律及特征。