Modal analysis of circular flexible foundations under vertical vibration

A methodology using modal analysis is presented to evaluate dynamic displacements of a circular flexible foundation on soil media subjected to vertical vibration. The interaction effects between the foundation and the underlying soil are represented using modal soil impedance functions determined by an efficient procedure developed. The displacements of the foundation can then be easily solved by modal superposition. Comparing with existing solutions, the presented method is found to provide accurate results with less computational effort using only a few vibration modes. In addition, parametric studies for modal responses of the flexible foundation indicate that the response of the foundation are significantly influenced by relative stiffness between the foundation and the soil medium, load distributions, vibration frequency range, and the foundation mass. Besides, justification for flexible foundations to be considered as rigid are investigated.     

三维层状地基空沟主动隔振分析

基于薄层法在研究层状介质中波的传播问题的高效性、边界单元法处理无限域问题的精确性,结合二者的优点提出三维层状地基薄层法基本解答,建立了基于三维层状半空间薄层法位移基本解答的半解析动力边界元法。该方法可有效的分析多层场地的动力问题,解决土-结构动力相互作用问题。同时分别对粘弹性上软下硬地基及上硬下软地基的三维空沟主动隔振进行了详细的分析。结果表明,两种情况下采用空沟屏障隔振均可以取得一定的隔振效果;同时,地基分层参数对空沟隔振体系的隔振效果影响显著。     

Seismic response of tall building considering soil-pile-structure interaction

The seismic behavior of tall buildings can be greatly affected by non-linear soil-pile interaction during strong earthquakes. In this study a 20-storey building is examined as a typical structure supported on a pile foundation for different conditions: (1) rigid base, i.e. no deformation in the foundation: (2) linear soil-pile system; and (3) nonlinear soil-pile system. The effects of pile foundation displacements on the behavior of tall building are investigated, and compared with the behavior of buildings supported on shallow foundation. With a model of non-reflective boundary between the near field and far field, Novak’s method of soil-pile interaction is improved. The computation method for vibration of pile foundations and DYNAN computer program are introduced comprehensively. A series of dynamic experiments have been done on full-scale piles, including single pile and group, linear vibration and nonlinear vibration, to verify the validity of boundary zone model.     

北京市防震减灾中心结构地震反应观测及振动特性识别

以北京市防震减灾中心结构为例,进行了结构的地震反应观测及振动特性识别研究。基于半功率带宽法对结构脉动测试数据进行了分析,计算出了结构自振周期和振型以及相应的阻尼比。各振型都具有较大幅值的楼层分别位于3、6和8层,据此设计并建成了结构地震反应观测台阵。分析台阵地震记录识别出了结构的自振特性,同时功率谱曲线显示,井下数据存在高频特性,初步判定其来自钢套管振动。开展结构的数值模拟分析,利用观测楼层上地震记录的卓越频率不断修正结构数值模型,直至结构反应与地震记录的频率值相符,且与脉动测试数据基本一致,相对位移对比分析发现,在该模型基础上相对位移反应与相对位移记录基本吻合。结构地震反应观测和数值模拟分析较好地实现了结构地震反应观测台阵的观测目的。     

软土地基核电厂房动力响应振动台试验

为了分析软土地基－筏基础核电厂房结构地震反应规律和特征,利用地震模拟振动台开展了软土地基－筏基础－核电厂房动力相互作用问题的试验研究。分别进行了表面水平土体模型和表面凹陷土体模型的运动相互作用试验、地基土－筏基础－核电厂房振动台相互作用试验、核电厂房直接固定在振动台面上的刚性基底振动台试验。试验采用圆形叠层剪切模型箱,地基土模型为某工程场地的均匀粉质粘土,其剪切波速为213 m/s;核电厂房简化为3层框架剪力墙结构模型。试验输入波形为美国核电规范常用的RG1.60反应谱合成得到的人工地震动时程。振动台试验结果对比分析表明:土－结构体系中系统的振动周期和阻尼明显大于刚性基底下结构的振动周期和阻尼;相同地震作用下在土－结构动力相互作用体系中结构加速度明显小于刚性基底下的结构加速度反应;而位移明显大于刚性基底下结构的位移。本文的研究成果可为软土地基建立核岛厂房的适应研究提供参考。     

Dynamic response of flexible rectangular foundations on an elastic half-space

An approximate method for the analysis of the dynamic interaction between a flexible rectangular foundation and the soil with consideration of the out-of-plane deformation of the foundation is presented. The procedure is based on an extension of the subdivision method developed by Wong and Luco for rigid foundations. Numerical results describing the influence of the flexibility of the foundation on the vertical and rocking impedance functions and on the contact stresses between the foundation and the soil are presented. The possibility of representing a flexible foundation by an equivalent rigid foundation having the same force-displacement relationships is also discussed. The results obtained indicate that at low frequencies, the dynamic stiffness coefficients for flexible foundations are lower than those for a rigid foundation of the same area. At higher frequencies the opposite behaviour is observed. The radiation damping coefficients for flexible foundations are significantly lower than those for a rigid foundation of the same area.     

Response of circular flexible foundations subjected to horizontal and rocking motions

A methodology using modal analysis is developed to evaluate dynamic vertical displacements of a circular flexible foundation resting on soil media subjected to horizontal and rocking motions. The influence of the soil reaction forces on the foundation is considered by introducing modal impedance functions, which can be determined by an efficient procedure with ring elements. The displacements of the foundation can then be easily solved by modal superposition. Parametric studies for modal responses of the flexible foundation indicate that the coupled response of the foundation is significantly influenced by relative stiffness among the foundation and the soil medium, vibration frequency range, foundation mass, and boundary contact conditions. The welded boundary condition should be considered to predict the coupling response while the relaxed boundary condition may be used to predict approximately the vertical displacements. As a foundation with a relative stiffness ratio more than three, it is found that the foundation can be considered as rigid to calculate coupling displacements. For a slightly flexible foundation, considerations of three modes are sufficient enough to obtain accurate foundation responses. Moreover, at low frequencies, the coupling effect due to higher mode can be neglected.     

近断层脉冲型地震下建筑地桩基础沉降分析

传统基于碰撞回弹系数Stereo-mechanical方法在分析建筑地桩基础的沉降位移过程中未考虑地桩基础碰撞的能量损耗,造成分析结果存在准确性和可信度较低的问题。因此提出改进的Kelvin建筑地桩基础碰撞沉降分析方法,以解决基于碰撞回弹系数Stereo-mechanical法存在的问题。采用线性阻尼构建Kelvin模型,分析地桩基础碰撞靠近阶段和回弹阶段的阻尼做功,构建地桩基础碰撞转换单自由度体系振动模型,实现对地桩基础的相对沉降速度和相对沉降位移的有效运算,基于建筑地桩基础碰撞沉降发生初始和结束时刻的能量和动量守恒定理,得到建筑地桩基础的最大沉降位移,实现对建筑地桩基础沉降的有效分析。实验结果说明,所提方法能提高地桩基础沉降分析的准确性和可信度。     

Simplified analysis of dynamic response of rigid foundations with arbitrary geometries

A simple, efficient numerical procedure is presented for the analysis of the steady-state dynamic response of rigid foundations of arbitrary shape on a homogeneous, isotropic elastic half-space. The contact area of the foundation and soil medium is discretized into square subregions. The influence of the rigid square subregion is approximated by that of an equivalent rigid circular base with the same contact area. This approximation is a better representation of a rigid square subregion than a uniformly stressed subregion used in earlier approaches. Simple expressions are used to determine the influence of the subregion on itself and on the rest of the subregions, without the expense of numerical integration procedures. The present method is demonstrated to converge rapidly. The accuracy of this method is examined by comparison with available published theoretical and experimental results.     

Wave dispersion in high‐rise buildings due to soil–structure interaction

Nonparametric techniques for estimation of wave dispersion in buildings by seismic interferometry are applied to a simple model of a soil–structure interaction (SSI) system with coupled horizontal and rocking response. The system consists of a viscously damped shear beam, representing a building, on a rigid foundation embedded in a half‐space. The analysis shows that (i) wave propagation through the system is dispersive. The dispersion is characterized by lower phase velocity (softening) in the band containing the fundamental system mode of vibration, and little change in the higher frequency bands, relative to the building shear wave velocity. This mirrors its well‐known effect on the frequencies of vibration, i.e. reduction for the fundamental mode and no significant change for the higher modes of vibration, in agreement with the duality of the wave and vibrational nature of structural response. Nevertheless, the phase velocity identified from broader band impulse response functions is very close to the superstructure shear wave velocity, as found by an earlier study of the same model. The analysis reveals that (ii) the reason for this apparent paradox is that the latter estimates are biased towards the higher values, representative of the higher frequencies in the band, where the response is less affected by SSI. It is also discussed that (iii) bending flexibility and soil flexibility produce similar effects on the phase velocities and frequencies of vibration of a building. Copyright © 2014 John Wiley & Sons, Ltd.     

建筑结构中抗震分析模型的优化研究

大多数建筑结构由梁、柱、支撑、剪力墙、地基和楼板等主要结构组成。一般而言,楼板对建筑结构的抗震性能可以忽略不计,所以进行建筑结构分析的模型是无楼板的。因此,楼板被刚性隔板代替,以提高分析效率。本文提出的建筑结构抗震分析解析模型考虑了楼板抗弯刚度,该模型采用超级单元、刚性隔板和子结构技术来减少自由度。通过实例分析,验证了该模型在多层建筑结构抗震分析中的有效性和准确性。且此模型能够显著减少计算量,提高分析效率,振动周期和响应时间等分析结果的精度与精化模型的结果非常接近,说明该模型的提出是合理的。     

Vibrations of square and circular foundations with concentric openings on elastic half space

A study on the dynamic characteristics of rigid foundations with special geometries such as square or circular with concentric internal holes, is presented. The foundations are resting on a homogeneous, linear elastic halfspace and are subjected to external forces or seismic wave excitation. Both ‘relaxed’ and ‘non-relaxed’ boundary conditions at the interface between the foundation and the halfspace are considered, and several parametric studies are conducted to assess the influence of either type of boundary conditions upon each of the possible modes of vibration. Results for massive and massless foundations are presented in time and frequency domains for impulsive and harmonic excitations, respectively. A time domain boundary element method (BEM) developed by the authors for the solution of a class of 3-D soil-structure interaction (SSI) problems is used for all the analyses reported in this work. The accuracy and efficiency of the method and the BEM models developed in this work are assessed on the basis of comparison studies with published results.     

Earthquake analysis of gravity dams including hydrodynamic interaction

A general procedure for analysis of the response of gravity dams, including hydrodynamic interaction and compressibility of water, to the transverse horizontal and vertical components of earthquake ground motion is presented. The problem is reduced to one in two dimensions considering the transverse vibration of a monolith of a dam, and the material behaviour is assumed to be linearly elastic The complete system is considered as composed of two substructures—the dam, represented as a finite element system, and the reservoir, as a continuum of infinite length in the upstream direction governed by the wave equation. The structural displacements of the dam (including effects of water) are expressed as a linear combination of the modes of vibration of the dam with the reservoir empty. The effectiveness of this analytical formulation lies in its being able to produce excellent results by considering only the first few modes. The complex frequency response for the modal displacements are obtained first. The responses to arbitrary ground motion are subsequently obtained with the aid of the Fast Fourier Transform algorithm An example analysis is presented to illustrate results obtained from this method. It is concluded that the method is very effective and efficient and is capable of producing results to any desired degree of accuracy by including the necessary number of modes of vibration of the dam.     

Effect of soil-structure interaction on damping of structures

Damping of structures resting on flexible foundations is affected by soil-structure interaction in two ways: (1) the structure gains damping through energy dissipation in soil, and (2) the damping the structure would have on a rigid foundation is reduced. These effects are evaluated using two approaches: an energy consideration which is a simple but approximate approach, and the complex eigenvalue analysis which is mathematically accurate but uses damped, non-classical vibration modes. These two methods are compared and the accuracy of the more convenient energy approach is assessed. Examples of modal damping are given for rigid structures, buildings and towers.     

建筑施工中振动影响的测试分析

工程建设对房屋建筑的振动影响和破坏的测试鉴定是当今城市建设中一项迫切需要开展而又具有重要意义的工作。首次将地震学原理与工程抗震鉴定方法有机结合对大楼受桩基础施工振动的影响和损害进行测试和分析，其结果用震级和烈度的方式定量给出了振动影响的程度，继而对场地地基、基础和大楼进行了具体的抗震分析鉴定。     

Rocking vibrations of a rigid circular foundation on poroelastic half-space to elastic waves

A study is carefully conducted for the rocking response of a rigid circular foundation resting on a poroelastic half-space when subjected to seismic waves under the framework of Biot’s theory. The free-field waves, rigid-body scattering field waves and radiation scattering field waves are introduced to consider the complex behavior of the soil owing to the scattering phenomena caused by the existence of the foundation. The contact surface between the soil and the foundation is supposed to be perfectly bonded and fully permeable. Combining with the divided wave fields, two sets of dual integral equations elaborating the mixed boundary-value conditions are established, and then reduced to Fredholm integral equations. Therefore, with a semi-analytical method, the expressions of the rocking displacements are obtained. The numerical results of the rocking vibration of the foundation for incident P, SV and Rayleigh waves are presented. The influences of certain parameters, such as the permeability of the soil, the incident angle, Poisson’s ratio and the mass of the foundation, on the rocking vibration of the foundation are explored and studied. Different reactions are found when the foundation is excited by different waves.     

基础柔性对土-结构相互作用系统响应影响的一个解析解

采用波函数展开法,通过SH波入射均匀半空间中二维埋置半圆形刚柔复合基础-单质点模型,推导土-刚柔复合基础-上部结构动力相互作用的解析解,并验证解的正确性。研究表明:基础柔性对于系统响应峰值与系统频率有较大影响。考虑基础柔性后,上部结构相对响应峰值相比全刚性基础结果均有一定减小,且系统频率也会产生向低频偏移的现象。     

考虑地基土液化影响的桩基高层建筑体系地震反应分析

本文建立了土体－结构体系地震反应分析的混合有限元法，并研究了地基土液化对地震反应的影响。本方法把土体－结构体系简化为一个完整的体系，该体系由梁（柱）单元、剪切杆单元、刚体单元、平面四边形等参单元与三角形单元、界面单元的任意组合来模拟。桩与上部结构材料视为线弹性体，土介质视为非线性材料。土的静应力－应变关系之间的非线性用邓肯一张模型来描述；土的动应力－应变关系之间的非线性和振动孔隙水压力对土的软化效     

单索面混凝土矮塔斜拉桥的动力特性

以厦门银湖矮塔斜拉桥为例,通过引入拉索自振频率影响度的概念,分析了拉索的存在对矮塔斜拉桥自振特性的影响,探讨了矮塔斜拉桥的自振特性与相应连续梁桥(或刚构桥)的区别;在分析矮塔斜拉桥地震反应的基础上,通过引入振型贡献率的概念,分析了高阶振型对矮塔斜拉桥动力性能的影响;分析了矮塔斜拉桥的振型耦联效应。最后首次较全面地总结了单索面混凝土矮塔斜拉桥的动力特性,对进一步认识矮塔斜拉桥的动力性能有一定的参考意义。     

土-结构动力相互作用及基础形式对超大型冷却塔结构地震反应的影响分析

采用ABAQUS有限元分析软件,分别对基于刚性地基假定的环板基础、考虑土-结构动力相互作用的环板基础和桩基础超大型冷却塔模型进行了模态分析、弹性和弹塑性时程分析,研究了土-结构动力相互作用和基础形式对超大型冷却塔结构动力特性和地震反应的影响。结果表明:当考虑相同阶数的振型时,刚性地基模型的振型参与质量系数最小。地震作用下,刚性地基模型和桩基础模型的加速度响应、支柱内力、塔壳混凝土主应力等一般比考虑土-结构动力相互作用的环板基础模型偏大,但塔顶水平位移偏小。土-结构动力相互作用比基础形式对冷却塔动力特性以及地震反应的影响更大,且二者对冷却塔竖向振动的影响比水平向大。三种模型计算所获得的冷却塔薄弱部位均集中于支柱,且支柱最大侧移角相差不大。