According to the Novak's plane strain theory and Biot's wave equation, this paper proposes an analytical model for horizontal vibration of partially embedded offshore piles under distribution effect of wave loads (DEWL) incorporating the diffraction effects of waves. Firstly, for the pile above the mudline, the wave force acting on the pile is obtained through the method of separation of variables. Secondly, for the embedded section of offshore piles, the governing equations of the seabed are decoupled by introducing potential functions, and then the boundary condition of the seabed and the continuity condition at the soil-pile contact surface are combined to obtain the frequency domain analysis of the soil reaction forces. Furthermore, by applying the continuity condition of displacement at mudline and using the matrix transfer method, the analytical solution for the horizontal vibration characteristics (HVC) is derived. Finally, a comparison analysis with existing theoretical solutions is conducted to validate the rationality and accuracy of the analytical solution proposed in this paper. Based on this, a parametric analysis is conducted to discuss the effects of the parameters of the soil, the pile and the wave on the HVC of partially embedded offshore piles.

To comprehensively investigate the effects of secondary ground waves (SGWs) induced by the vibration of receiver piles (RPs) in layered soils on the pile-pile horizontal vibration (PPHV), a simplified mechanical model for frequency-domain analysis of PPHV is proposed. This proposed model is based on layered Pasternak soils and elastic Euler-Bernoulli beam theory, incorporating the effects of axial loads and SGW. Firstly, the horizontal displacements (HDs) and the internal forces of the source pile (SP) are obtained using the differential transformation method combined with the continuity boundary conditions (BCs) at the pile-soil interface. Secondly, considering the influence of the vibration of the SP on the RP, a horizontal vibration analysis model for the RP is established, followed by the derivation of an analytical solution for the horizontal dynamic response (HDR). Furthermore, to consider the influence of SGWs induced by the vibration of the RP on the HDR of the SP, an improved analytical solution for the HDR of the RP is obtained. Finally, based on the definition of the dynamic interaction factor, the pile-pile horizontal dynamic interaction factor (PPHDIF) is derived and its rationality is validated by comparisons with existing solutions. Parametric analyses are performed to explore the effects of soil shear deformation, pile-soil modulus ratio, and axial loads on the PPHDIF. The results provide theoretical guidance and references for the dynamic design of pile groups in engineering practice.

Employing Biot's dynamic equations and Novak's thin-layer theory, an analytical model for the horizontal vibration of a single pile embedded in the radially heterogeneous saturated soil is established. Firstly, the frequency-domain response of surrounding soil is derived by means of the potential function, Laplace transformation and variable separation methods. Secondly, the analytical solution for the horizontal impedance of pile head is deduced by combining the conditions of the displacement continuity and stress equilibrium on the soil-pile interface. Finally, the obtained solution is degenerated to validate its accuracy via independent comparisons with different existing solutions. On this basis, the effect of soil radial heterogeneity on the horizontal vibration of an end bearing pile is further discussed by conducting an extensive parametric analysis.

A simplified model for a single pile is established based on the Pasternak foundation and Euler beam models considering the axial second-order effects of pile shaft. The corresponding analytical solutions are derived by utilizing the differential transformation methods and the double-shear theory as well as the pile-soil continuity conditions. Then, considering the dynamic displacement of receiver pile Ⅱ caused by the vibration of source pile Ⅰ, the control equation for horizontal vibration of receiver pile Ⅱ is established, and the analytical solutions for the response of receiver pile Ⅱ are obtained.According to the definition of dynamic interaction factor, the pile-pile horizontal dynamic interaction factor is further obtained.Finally, the superposition principle is used to solve the horizontal dynamic impedance of pile groups, and its rationality is verified by comparing with the existing analytical solutions. On this basis, the influences of soil shear coefficient, pile type, pile to diameter ratio and axial feature parameters on the horizontal impedance of pile groups are discussed through the parametric analysis, and the distribution of the reaction force at the top of the pile and the distribution of the internal force of the pile body are discussed. It may provide theoretical guidance and reference for the design of pile groups in practical engineering.

A rigorous analytical model for partially embedded large-diameter floating pile (PLFP) is devised based on a three-dimensional continuum pile and soil model. The analytical solutions to the dynamic response of PLFP are obtained using Fourier transformation and variable separation. Then, the accuracy of the obtained dynamic impedance and velocity is verified by comparing the derived values with existing solutions and the measured data of the experimental model. Finally, parameter analyses of dynamic impedance and velocity response are conducted. The results indicate the following. The use of a one-dimensional pile model to calculate the dynamic impedance of PLFP results in the overestimation of resonance amplitude and frequency. Defect detection is more difficult to implement in a partially embedded pile than in a fully embedded pile. In practice, the suitable position for a signal receiver installed on a pile head during low-strain pile integrity testing is 0.6r0.

为分析大直径浮承桩纵向振动特性,基于黏弹性连续介质理论同时考虑桩身和桩底土的三维波动效应,提出了一种三维虚土桩模型.首先,采用拉普拉斯变换和分离变量法求解得到桩身和桩底虚土桩的位移基本解;然后,结合桩-土及桩-虚土桩完全耦合条件,推导得出大直径桩桩顶动力阻抗解析解,并通过与已有解答对比分析验证了推导所得解析解的合理性和准确性;最后,利用数值算例分析了桩顶径向位置及三维虚土桩参数对大直径浮承桩桩顶动力阻抗的影响.计算结果表明:大直径桩顶动刚度和动阻尼呈现由桩中心向桩边缘减小的趋势,且桩长径比越小桩顶动力阻抗的这种径向不均匀性越明显;对于大直径桩忽略桩身径向波动效应会过高估计桩顶动力阻抗的振幅和频率,不利于桩基抗振防振设计;三维虚土桩模型不仅对于大直径浮承桩纵向振动问题具有更好的适用性,而且可以通过调整虚土桩参数将其应用于端承桩动力特性分析中.

According to the theories of wave propagation in visco-elastic continuum and Rayleigh-Love rod, a simplified model in axisymmetric conditions for the longitudinal vibration of large-diameter pipe pile (LDPP) in radially heterogeneous surrounding soil with viscous damping is presented. The relevant analytical solution for dynamic impedance at pile head is derived by using complex stiffness transfer method, which is also validated via independent comparisons with previous solutions. Besides, parametric analyses are carried out to reveal both the radial heterogeneity of surrounding soil and the lateral inertia effect of pile shaft on the dynamic impedance of LDPP. The obtained analytical solutions are suitable for the longitudinal vibration issues of floating LDPP in visco-elastic surrounding soil with radial heterogeneity, which can be conveniently degenerated to describe the longitudinal vibration of a floating solid pile in soil with radial heterogeneity as well as a floating LDPP or solid pile in radially homogenous soil.

Based on the dynamic Winkler model and fictitious soil pile model to consider the relative sliding at the pile-soil interface and the propagation effect of soil beneath the pile toe, respectively, a more rigorous analytical model for the vertical vibration problems of a floating pile is established. The general solution for the displacement of soil is derived by combining the Laplace transform and variable separation methods. Then, the vertical dynamic solution of the floating pile is obtained by introducing the pile-soil interface condition and transfer function recursion method. Furthermore, extensive parametric analyses are performed to investigate the effects of the stiffness coefficient for the dynamic Winkler model, the length of the fictitious soil pile, and the inhomogeneity of the soils and pile on the vertical vibration for the floating pile. This indicates that the proposed analytical model provides a wider range and more rigorous application for the vertical vibration problems of floating piles embedded in layered and limited thickness soils. Moreover, the reduced form of the obtained solution can also be applied to investigate the corresponding vibration problems of end-bearing piles.

基于Pasternak地基和桩体Timoshenko梁理论,考虑了轴向作用二阶效应,建立了大直径桩?成层土相互作用体系水平振动分析简化模型,采用微分变换方法和双剪切理论,结合桩土连续边界条件,进而推导出桩身位移、内力、转角解析解,并与已有相关解析解进行退化对比验证.在此基础上,探讨了桩身长径比、地基剪切系数、桩土模量比、桩身剪切变形系数及轴向荷载对桩基水平振动特性的影响规律.计算分析结果表明推导所得对应解析解,能综合考虑轴向压力二阶效应、桩周土和桩身剪切变形的影响,可为大直径桩基工程相关水平向振动分析和设计提供参考.

In this study, a novel analytical method combining a 3D continuum model, Biot propagation theory, a fictitious saturated soil pile (FSSP) model, and a heterogeneous pile model is proposed to analyze the dynamic response of a defective floating pile embedded in saturated soils. The vertical velocity of the defective pile in the frequency domain is obtained by introducing the complete coupling conditions of the pile and soil. With the most widely used half‐sine pulse as the excitation force in the low‐strain integrity testing of the pile, the solution is extended to the time domain using the inverse Fourier transform (IFT). The rationality and accuracy of the proposed approach are verified via comparison with previous methods and measured data from an engineering example. Parametric analyses are also conducted to investigate the quantitative relationship between the pile defect parameters and the dynamic response characteristics of a defective pile. It is indicated that the depth and length of a pile defect can be roughly evaluated using the proposed methodology when clear signals are reflected from pile defect interfaces in practical engineering.

基于三维连续黏性阻尼介质理论和径向多圈层复刚度传递模型,综合考虑桩周土径向非均质效应和纵向成层性,建立双向非均质土体中桩基扭转振动简化分析模型.采用拉普拉斯变换和复刚度传递法求解得出土体位移形式解,进而利用桩?土耦合条件将该形式解耦合进桩身动力平衡方程中,并通过扭转阻抗传递法推导得出桩顶扭转阻抗解析解答.将该解退化并分别与均质土及径向非均质土中的解答进行对比验证其合理性.在此基础上,通过参数化分析探讨了桩周土施工扰动程度和扰动范围、扩颈及缩颈缺陷对桩顶扭转阻抗的影响规律,可为具体工程实践提供理论指导和参考作用.

Based on the Rayleigh–Love rod model and Novak’s plane-strain theory, an analytical method for the longitudinal vibration of a large-diameter pipe pile in radially heterogeneous soil is proposed. Firstly, the governing equations of the pile-soil system are established by taking both the construction disturbance effect and transverse inertia effect into account. Secondly, the analytical solution of longitudinal dynamic impedance at the pile top can be achieved by using Laplace transform and complex stiffness transfer techniques. Thirdly, the present analytical solution for dynamic impedance can also be performed in contrast with the existing solution to examine the correctness of the analytical method in this work. Further, the effect of pile Poisson’s ratio, pile diameter ratio as well as soil disturbed degree on the dynamic impedance are investigated. The results demonstrate that the Rayleigh–Love rod is appropriate for simulating the vibration of a large-diameter pipe pile in heterogeneous soils.

Based on the three-dimensional axisymmetric model to consider the radial wave effect of the pile, a three-dimensional axisymmetric coupling system of pile-soil interaction for longitudinal vibration is established, in which the pile and surrounding soil are simplified as elastic and viscoelastic media respectively.Firstly, the fundamental solutions for displacements of the pile and surrounding soil are obtained by using the variables separation method.And then a frequency domain solution for the dynamic impedance at the pile head is derived by adopting the fully coupled conditions at the interface between the pile and surrounding soil.Furthermore, the obtained analytical solution for dynamic impedance at the pile head is also reduced to verify its validity by the comparison with existing solution.Finally, parametric analyses are conducted to investigate the effects of the stiffness coefficient of pile base support, the radial wave effect of pile and the pile length on the dynamic impedance at the pile head.The results show that when the pile slenderness ratio is small, the pile modeled with Rayleigh-Love rod may lead to nonnegligible inaccuracy to consider the three dimensional wave effect of pile shaft.Therefore, the obtained solution in this paper can provide reasonable result for a wider range of application.