Horizontal dynamic response of a large-diameter pipe pile considering the second-order effect of axial force

The second-order effect of axial force on horizontal vibrating characteristics of a large-diameter pipe pile is theoretically investigated. Governing equations of the pile-soil system are established based on elastodynamics. Three-dimensional wave equations of soil are decoupled through differential transformation and variable separation. Consequently, expressions of soil displacements and horizontal resistances can be obtained. An analytical solution of the pile is derived based on continuity conditions between the pile and soil, subsequently from which expressions of the complex impedances are deduced. Analyses are carried out to examine the second-order effect of axial force on the horizontal vibrating behavior of the pipe pile. Some conclusions can be summarized as follows: stiffness and damping factors are decreased with the application of axial force on the pile head; distributions of the pile horizontal displacement and rotation angle are regenerated due to the second-order effect of the applied axial force; and redistributions of the bending moment and shearing force occur due to the second-order effect of the applied axial force.     

瞬变电磁场时域格林函数解

近源时间域电磁场具有信号强、探测深度大、精度高等优点,但传统勘探电磁场理论中偶极子近似在近源会引起较大误差,导致这一优势的发挥受到了制约.开展直接时间域电磁场解析式研究,是解决这一问题的途径之一.本文提出在点电荷微元假设下,引入时域格林函数,求取瞬变电磁场时间域解析解.采用积分运算法,把电磁场阻尼波动方程的求解问题转化为求其格林函数积分形式解的问题;建立辅助路径解决奇点问题,利用复分析中的约当引理、留数定理和广义函数等理论和方法,推导计算出时间域格林函数的时空四重广义积分.得到达朗贝尔方程的直接时域格林函数精确解析式,与传统方法“比拟”出的公式具有相同的形式,验证了本文推导的时域格林函数解析公式的正确性;推导出扩散方程的直接时间域解析解.通过与时变点电荷源时间域的电磁响应近似表达式进行对比,得出本文所推导的公式计算精度较高的结论;建立了全空间回线源瞬变电磁场问题的直接时间域求解公式.为解决全场区瞬变电磁场精细探测直接时域解析问题提供了基础理论.     

Nonlinear analysis for dynamic lateral pile response

An analysis of pile lateral response to transient dynamic loading and to harmonic loading is presented allowing for nonlinear soil behavior, discontinuity conditions at the pile-soil interface and energy dissipation through different types of damping. Furthermore, the effect of neighbouring piles is taken into account for piles in a group. The validity of the approach was examined and a reasonable agreement with field tests and more rigorous solutions was found. Equivalent linear stiffness and damping parameters of single piles and interaction factors for approximate nonlinear analysis are presented.     

Time-domain dynamic constitutive model suitable for mucky soil site seismic response

Soil nonlinear behavior displays noticeable effects on the site seismic response. This study proposes a new functional expression of the skeleton curve to replace the hyperbolic skeleton curve. By integrating shear modulus and combining the dynamic skeleton curve and the damping degradation coefficient, the constitutive equation of the logarithmic dynamic skeleton can be obtained, which considers the damping effect in a soil dynamics problem. Based on the finite difference method and the multi-t...     

求解结构动力响应的小波分解法

本文用时程分析、振型迭加和小波变换3种方法,对一个10层建筑结构的地震动力响应进行了计算和比较,三者的结果完全一致,从而说明了线性时不变系统结构动力响应的唯一性定律是正确的。由于时程分析法可以用于非线性系统,而振型分解法只能用于线性系统,小波变换不但可以用于非线性,更可以用来进行多尺度分析的能谱计算,它能使抗震分析从传统的滞回耗能模型,提高到以结构损伤和延性评价的体系上来。     

液化土中桩基础动力反应试验研究

本文设计完成了包括三种密度饱和砂土和非液化干砂的多工况桩-土相互作用振动台动力试验,研究液化对土体和桩-承台动力反应的影响。通过试验和分析,得到了液化和非液化土层中土体水平加速度、侧向位移和桩-承台的水平加速度、侧向位移、桩身弯矩等指标的反应过程和模式,对比了液化和非液化条件对这些指标的影响方式,提出了各因素影响大小的分析结果。     

结构动力反应分析的三阶显式方法

本通过对传统动力反应分析方法的总结，阐明了建立隐式和显式方法的一般思路及数学本质，提出了使用系统位移反向向量三阶导数的隐工和实用显式积分方法－3阶显式方法，分析了该显式方法的精度和稳定性，并对建立更高阶隐式和显式方法以及方法的精度和稳定性作了初步讨论。最后，通过算例对本方法、献[1]方法和经典的常平均加速度法（隐式方法、视为精确解）的精度和稳定性进行了比较分析。结果表明，本方法具有明显的优点。     

欧拉梁动力反应初边值问题的微分求积解

动荷载作用下欧拉梁动响应的计算是一个初边值问题,通常很难得到解析解,传统数值方法一般是把空间和时间分别离散进行求解,计算相对复杂,效率也不高.针对分布动荷载作用下欧拉梁的振动偏微分方程,采用传统微分求积法,在空间和时间上同时进行离散;对于所有非0阶的初/边值条件,采用嵌入法在权系数计算中予以考虑.算例的数值结果与精确解的对比证明采用传统微分求积法处理此问题是可行的,而且是高效的.对于实际工程中的其他类似问题,该方法同样适用.     

半空间异质隆起的出平面动力响应:闭合级数解答

采用分区思想和辅助函数方法,利用波函数展开技术,提出了水平地表圆形非匀质隆起出平面动力响应的闭合级数解答。将解答归结为一组无穷代数方程组的求解,解答的数值结果可由无穷方程的截断计算得出。计算结果表明,给出的闭合解答在宽频带内能很快收敛。     

Torsional vibration of a pipe pile in transversely isotropic saturated soil

This study considers the torsional vibration of a pipe pile in a transversely isotropic saturated soil layer. Based on Biot’s poroelastic theory and the constitutive relations of the transversely isotropic medium, the dynamic governing equations of the outer and inner transversely isotropic saturated soil layers are derived. The Laplace transform is used to solve the governing equations of the outer and inner soil layers. The dynamic torsional response of the pipe pile in the frequency domain is derived utilizing 1D elastic theory and the continuous conditions at the interfaces between the pipe pile and the soils. The time domain solution is obtained by Fourier inverse transform. A parametric study is conducted to demonstrate the influence of the anisotropies of the outer and inner soil on the torsional dynamic response of the pipe pile.     

地震作用下液化场地变截面桩与等截面桩的动力响应对比分析

为研究液化场地变截面桩的动力响应,依托翔安大桥实体工程,采用有限元软件,建立变截面桩－土和等截面桩－土相互作用模型,模拟液化场地变截面桩及等截面桩在地震作用下的振动反应,分析在地震作用下变截面位置不同的变截面桩及等截面桩的动力响应特征。结果表明:地震作用下,液化土层不同深度处的孔压比变化规律基本相同,均从0逐渐增大最后趋于稳定;变截面桩的桩身加速度和桩身位移均大于等截面桩,且桩顶加速度峰值出现的时刻均滞后于桩底;在饱和砂土层处,桩身位移变化趋势均较陡;变截面桩的桩身弯矩峰值和桩身剪力峰值均大于等截面桩,且其峰值出现的位置较等截面桩深;地震作用下,变截面桩及等截面桩的弯矩与剪力均在安全范围之内;液化场地变截面梁桥桩基础抗震设计时,应着重分析液化土层与非液化土层分界面以下的抗弯能力设计及液化土层中抗剪能力设计。     

Experimental and numerical investigation on the dynamic response of pile group in liquefying ground

The response of pile foundation in liquefiable sand reinforced by densification techniques remains a very complex problem during strong earthquakes. A shake-table experiment was carried out to investigate the behavior of a reinforced concrete low-cap pile group embedded in this type of ground. In this study, a three-dimensional (3D) finite element (FE) analysis of the experiment was conducted. The computed response of the soil-pile system was in reasonable agreement with the experimental results, highlighting some key characteristics. Then, a parametric study was performed to explore the influence of pile spacing, pile stiffness (EI), superstructure mass, sand permeability, and shaking characteristics of input motion on the behavior of the pile. The investigation demonstrated a stiffening behavior appearing in the liquefied mediumdense sand, and the pile group effect seemed negligible. Furthermore, the kinematic effect was closely connected with both EI and sand permeability. Nevertheless, the inertial effect was strongly influenced by the superstructure mass. Meanwhile, high frequency and large amplitude of the input motion could produced greater the pile’s moments. It is estimated that this case study could further enhance the current understanding of the behavior of low-cap pile foundations in liquefied dense sand.     

Simple formulas for the dynamic stiffness of pile groups

Simple formulas are derived for the dynamic stiffness of pile group foundations subjected to horizontal and rocking dynamic loads. The formulations are based on the construction of a general model of impedance matrices as the condensation of matrices of mass, damping, and stiffness, and on the identification of the values of these matrices on an extensive database of numerical experiments computed using coupled finite element–boundary element models. The formulations obtained can be readily used for the design of both floating piles on homogeneous half‐space and end‐bearing piles and are applicable for a wide range of mechanical and geometrical parameters of the soil and piles, in particular for large pile groups. For the seismic design of a building, the use of the simple formulas rather than a full computational model is shown to induce little error on the evaluation of the response spectra and time histories. Copyright © 2009 John Wiley & Sons, Ltd.     

Static solution of a crack degenerated from dynamic solution of a propagating crack

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圆弧形凹陷在SH波入射下瞬态反应的解析解

针对现有地震波散射问题的解析解均在频域内给出,其适用的频带较窄,不能获取到可靠的瞬态反应解析解的问题,本文利用宽频带频域解析解进一步获取了不同空间点地震反应的宽频带频响函数,并基于傅里叶变换得出SH波入射下圆弧形凹陷地形瞬态动力响应的解析解.以上述为基础,研究了输入脉冲与实际地震动时凹陷的瞬态反应的基本特征,并重点分析...     

Torsional response of pile embedded in a poroelastic medium

The response of a cylindrical elastic pile embedded in a homogeneous poroelastic medium and subjected to torsional loading is studied for the first time. Based on the Muki's model, the pile-porous medium system is decomposed into a fictitious pile system and an extended porous medium system. The one-dimensional, vertical, elastic pile and the three-dimensional poroelastic medium are solved, respectively. Considering the mixed boundary-value conditions at the interface of pile and soil, a Fredholm's integral equation of the second kind for the bar-force is established. The force and the displacement of the pile are calculated by applying numerical quadrature.     

Analytical layer-element solution to axisymmetric dynamic response of transversely isotropic multilayered half-space

Starting with the governing equations of motion and the constitutive equations of transversely isotropic elastic body, and based on the corresponding algebraic operations and the Hankel transform, the analytical layer-elements of a finite layer and a half-space are obtained in the transformed domain. According to the continuity conditions between adjacent layers, the global stiffness matrix equation is obtained by assembling the analytical layer-element of each single layer. The solutions in the transformed domain are acquired by introducing the boundary conditions into the global stiffness matrix equation, and thus, the corresponding solutions in frequency domain are achieved by taking the inversion of Hankel transform. Finally, some numerical examples are given to illustrate the accuracy of the proposed method, and to study the influence of properties and the frequency of excitation on the dynamic response of the medium.     

Intensity measures for the seismic response of pile foundations

In this study the efficacy of various ground motion intensity measures for the seismic response of pile foundations embedded in liquefiable and non-liquefiable soils is investigated. A soil-pile-structure model consisting of a two-layer soil deposit with a single pile and a single degree-of-freedom superstructure is used in a parametric study to determine the salient features of the seismic response of the soil-pile-structure system. A suite of ground motion records scaled to various levels of intensity are used to investigate the full range of pile behaviour, from elastic response to failure. Various intensity measures are used to inspect their efficiency in predicting the seismic demand on the pile foundation for a given level of ground motion intensity. It is found that velocity-based intensity measures are the most efficient in predicting the pile response, which is measured in terms of maximum curvature or pile-head displacement. In particular, velocity spectrum intensity (VSI), which represents the integral of the pseudo-velocity spectrum over a wide period range, is found to be the most efficient intensity measure in predicting the seismic demands on the pile foundation. VSI is also found to be a sufficient intensity measure with respect to earthquake magnitude, source-to-site distance, and epsilon, and has a good predictability, thus making it a prime candidate for use in seismic response analysis of pile foundations.     

An analytical solution for predicting the transient seepage from a subsurface drainage system

Subsurface drainage systems have been widely used to deal with soil salinization and waterlogging problems around the world. In this paper, a mathematical model was introduced to quantify the transient behavior of the groundwater table and the seepage from a subsurface drainage system. Based on the assumption of a hydrostatic pressure distribution, the model considered the pore-water flow in both the phreatic and vadose soil zones. An approximate analytical solution for the model was derived to quantify the drainage of soils which were initially water-saturated. The analytical solution was validated against laboratory experiments and a 2-D Richards equation-based model, and found to predict well the transient water seepage from the subsurface drainage system. A saturated flow-based model was also tested and found to over-predict the time required for drainage and the total water seepage by nearly one order of magnitude, in comparison with the experimental results and the present analytical solution. During drainage, a vadose zone with a significant water storage capacity developed above the phreatic surface. A considerable amount of water still remained in the vadose zone at the steady state with the water table situated at the drain bottom. Sensitivity analyses demonstrated that effects of the vadose zone were intensified with an increased thickness of capillary fringe, capillary rise and/or burying depth of drains, in terms of the required drainage time and total water seepage. The analytical solution provides guidance for assessing the capillary effects on the effectiveness and efficiency of subsurface drainage systems for combating soil salinization and waterlogging problems.     

A numerical model for the dynamic analysis of inclined pile groups

The paper presents a numerical model for the dynamic analysis of pile groups with inclined piles in horizontally layered soil deposits. Piles are modelled with Euler–Bernoulli beams, while the soil is supposed to be constituted by independent infinite viscoelastic horizontal layers. The pile–soil–pile interaction as well as the hysteretic and geometric damping is taken into account by means of two‐dimensional elastodynamic Green's functions. Piles cap is considered by introducing a rigid constraint; the condensation of the problem permits a consistent derivation of both the dynamic impedance matrix of the soil–foundation system and the foundation input motion. These quantities are those used to perform inertial soil–structure interaction analyses in the framework of the substructure approach. Furthermore, the model allows evaluating the kinematic stress resultants in piles resulting from waves propagating in the soil deposit, taking into account the pile–soil–pile interactions. The model validation is carried out by performing accuracy analyses and comparing results in terms of dynamic impedance functions, kinematic response parameters and pile stress resultants, with those furnished by 3D refined finite element models. To this purpose, classical elastodynamic solutions are adopted to define the soil–pile interaction problem. The model results in low computational demands without significant loss of precision, compared with more rigorous approaches or refined finite element models. Copyright © 2015 John Wiley & Sons, Ltd.