下卧基岩饱和地基中埋置刚性基础的竖向振动问题研究

基于Biot提出的饱和土波动方程,研究了埋置于单层饱和地基中的有质量的刚性圆柱基础的竖向振动问题。运用Hankel积分变换求解饱和土基本动力方程,并考虑基础与地基接触面的混合边值条件,求得了基础底面和基础侧面的动反力,结合基础振动的动力平衡方程,得到了基础竖向振动振幅和地基等效动力刚度的表达式。数值分析结果表明：下卧基岩饱和地基的等效动力刚度和基础振动振幅都呈现出明显的波动现象,土层厚度、基础埋深比、基础质量比对埋置基础的竖向振动有很大影响。     

层状饱和地基上刚性圆板的扭转振动及参数分析

用解析的方法首次研究了层状饱和地基上刚性圆板的扭转振动特性.运用Hankel变换求解饱和介质动力问题的控制方程,按混合边值条件建立了层状饱和地基上刚性圆板扭转振动的第二类Fredholm积分方程.数值算例给出了动力柔度系数和扭转角幅值随无量纲频率的变化曲线,与单相弹性及匀质饱和介质情况进行了对比分析,并进行了参数研究.     

上覆单相弹性层饱和地基上刚性条形基础竖向振动的混合边值问题

根据Biot动力控制方程,运用Fourier积分变换技术,并按照混合边值条件和连续条件建立了上覆单相弹性层饱和地基上刚性条形基础竖向振动的对偶积分方程,并将其退化到完全饱和地基的情形。通过引进正交多项式将对偶积分方程化为线性代数方程组,从而得到了上覆单相弹性层的饱和地基上刚性条形基础的竖向振动规律。通过算例分析得到,单相弹性层的厚度对动力柔度系数有着较大的影响,在单相弹性层厚度较小时（小于条形基础半宽的0.1）,动力柔度系数曲线与完全饱和的基本重合;完全饱和地基上刚性基础的竖向振动是上覆弹性层厚度Hn=0的特例。     

广义Gibson饱和地基中刚性圆板的扭转柔度系数

考虑到地基在竖直方向上的非均匀性,结合扭转振动的特点,建立了简谐扭转动荷载作用时剪切模量随深度增大的广义Gibson饱和地基的动力方程,通过积分变换求解了动力方程。考虑到半空间地基表面处应力自由、埋置圆板所在平面为混合边界和无穷深度处为波的辐射边界等条件,得到了广义Gibson饱和地基中刚性圆板扭转振动时的对偶积分方程,通过合适的变换转化成了一个第2类Fredholm积分方程,求解了相应的动力响应问题。对比静扭距作用时的荷载-位移关系,给出了动力柔度系数和扭转角位移幅值的表达式,并把所研究的问题进行退化且与前人成果进行了对比。数值研究表明：当基础的埋置深度小于5倍基础半径时,广义Gibson饱和地基中埋置基础的扭转振动存在明显的边界层现象,且埋置深度越小,边界层现象越明显。     

水运工程堆载预压处理地基动力测试应用研究

地基经过真空堆载预压处理后,其地基承载性状及动力参数特性都产生不同改变,这种变化会对动力基础设计产生较大影响。基于此,结合实际水运工程项目对真空堆载预压处理后旋喷桩复合地基及钻孔灌注桩基础分别进行地基动力测试,通过测试获得地基及桩基模型基础的抗压、抗剪及抗扭的刚度参数、竖向及水平转向的第一振型以及扭转向的阻尼比及参振总质量。依据各项实测数据计算出旋喷桩复合地基及钻孔灌注桩基础底面与静应力有关的振动换算系数,推算出两种不同类型基础的地基抗压、抗剪、抗扭刚度,扭转向阻尼比以及地基竖向和水平回转向第一振型的提高系数。各项实际参数测试计算结果显示,当把两种不同类型地基现场实际获得的地基动力参数用于动力机器基础振动和隔振设计时,应分别根据动力机器基础的实际使用工况换算成设计采用的地基动力参数,以免对基础设计造成偏差。     

饱和地基表面基础在Rayleigh波作用下的摇摆振动分析

考虑地基与基础的相互作用,运用Biot波动方程理论,研究了饱和地基表面有质量的刚性圆形基础在入射Rayleigh波作用下的摇摆振动问题。将饱和地基中的总波场分解为自由波场、刚体辐射波场及刚体散射波场,从而考虑基础对Rayleigh波的散射。采用Hankel变换求解土体控制方程,结合基础摇摆振动的混合边值条件以及Rayleigh波的动力作用获得基础摇摆振动振幅的表达式。计算结果分析了泊松比、基础质量、透水条件、土体渗透系数等对基础摇摆振动的影响。研究结果表明,与弹性介质相比,饱和地基中孔隙水的存在减弱了基础的摇摆振动,其作用效果与土体渗透系数及地基表面排水条件密切相关。     

均质弹性地基中单桩的扭转振动特性研究

利用积分方程的方法研究了均质弹性地基中单桩的扭转振动问题。在分析过程中,首先利用积分变换的方法得出均质弹性地基内作用一埋置扭矩时的基本解。基于基本解,根据变形协调条件建立了控制单桩扭转振动特性的第2类Fredholm积分方程。对所得积分方程进行数值求解得到单桩扭转振动时的扭矩和扭转角及动力柔度系数,并对其进行了参数分析。所得结论对桩基础设计与计算以及桩基低应变扭转波动测技术有一定的指导意义。     

下卧基岩黏弹性地基上刚性条形基础竖向振动响应研究

考虑地基土层厚度的影响,对黏弹性地基上刚性条形基础承受竖向荷载下的动力响应问题进行了理论研究。通过Fourier积分变换求解了地基土的动力控制方程,并结合基底和地基的混合边界条件及土层刚性基岩边界条件,得到了刚性条形基础的对偶积分方程。通过Jacobi正交多项式将其转化为线性方程组并进行数值求解。将所得解退化至弹性半空间,并与已有文献进行了对比,验证了解析解的合理性。分析结果表明：地基土层厚度是影响地基振动产生的表面波衰减以及条形基础动力柔度系数变化的重要因素。通过数值算例发现,只有在土层厚度超过基底宽度大约50倍的情况下,现有的将地基土视为无限半空间的理论解才是合理的。     

横观各向同性地基上刚性矩形基础分析

对横观各向同性地基上刚性矩形板进行了求解。首先,利用表面受矩形均布荷载作用下的层状横观各向同性地基的位移解答,获得地基的柔度矩阵;然后,通过刚性矩形基础与层状横观各向同性地基的协调条件,建立刚性矩形基础与横观各向同性地基共同作用的方程,进而求得基础的地基反力。通过编制相应的程序,确定了合理的网格划分值;最后,进行算例分析,分析了地基横观各向同性性质、矩形刚性基础的长宽比以及地基分层性对地基反力的影响。分析表明：以上3种因素对地基反力有重要影响。     

饱和地基上条形弹性基础的摇摆振动

基于Biot动力方程,研究了饱和均质弹性半空间上弹性条形基础的摇摆振动问题。通过Fourier积分变换求解了饱和土的动力控制方程,然后结合基础底部为混合边界的条件得到了弹性条形基础的摇摆振动对偶积分方程,利用正交多项式将对偶积分方程转化为求解一组线性代数方程组,同时利用复合Simpson法则,得到了动力柔度系数的表达式,通过算例得出了不同参数时地基动力柔度系数随无量纲频率的关系曲线。     

Vertical dynamic response of a rigid foundation embedded in a poroelastic soil layer

A simplified analytical method is presented for the vertical dynamic analysis of a rigid, massive, cylindrical foundation embedded in a poroelastic soil layer. The foundation is subjected to a time‐harmonic vertical loading and is perfectly bonded to the surrounding soil in the vertical direction. The soil underlying the foundation base is represented by a single‐layered poroelastic soil based on rigid bedrock while the soil at the side of the foundation is modeled as an independent poroelastic layer composed of a series of infinitesimally thin layers. The behavior of the soil is governed by Biot's poroelastodynamic theory and its governing equations are solved by the use of Hankel integral transform. The contact surface between the foundation base and the soil is smooth and fully permeable. The dynamic interaction problem is solved following standard numerical procedures. The accuracy of the present solution is verified by comparisons with the well‐known solutions obtained from other approaches for both the elastodynamic interaction problem and poroelastodynamic interaction problem. Numerical results for the vertical dynamic impedance and response factor of the foundation are presented to demonstrate the influence of nondimensional frequency of excitation, soil layer thickness, poroelastic material parameters, depth ratio and mass ratio on the dynamic response of a rigid foundation embedded in a poroelastic soil layer. Copyright © 2008 John Wiley & Sons, Ltd.     

Rocking vibrations of a rigid embedded foundation in a poroelastic half‐space

This paper presents an analysis of the rocking vibrations of a rigid cylindrical foundation embedded in poroelastic soil. The foundation is subjected to time‐harmonic rocking excitation and is perfectly bonded to the surrounding soil. The soil underlying the foundation base is represented by a homogeneous poroelastic half‐space, whereas the soil along the side of the foundation is modeled as an independent poroelastic stratum composed of a series of infinitesimally thin layers. The behavior of the soil is governed by Biot's poroelastodynamic theory. The contact surface between the foundation base and the poroelastic soil is assumed to be smooth and either fully permeable or impermeable. The dynamic interaction problem is solved by employing a simplified analytical method. Some numerical results for the nondimensional rocking dynamic impedance and nondimensional angular displacement amplitude of the foundation are presented to show the effect of nondimensional frequency of excitation, poroelastic material parameters, hydraulic boundary condition, depth ratio and mass ratio of the foundation. Copyright © 2009 John Wiley & Sons, Ltd.     

可液化地基上地铁车站结构地震反应特征有效应力分析

采用Byrne简化的Martin-Finn振动孔压增量模型描述土体的液化特性,采用Davidenkov黏弹性本构模型描述土体的非线性特性,建立了可液化地基-地铁车站结构非线性静、动力耦合相互作用的二维分析模型,采用动力有效应力分析方法对可液化地基上两层三跨岛式地铁车站结构的地震动反应进行了数值分析,并与动力总应力方法分析的结果进行对比,结果表明：地铁车站结构两侧及底部邻近位置的土体较易液化,地基土的液化对地下结构邻近地表的加速度反应有明显的影响,且在地基土液化的影响下地下结构有明显上浮的趋势,并呈现出中部上凸的变形特征,地下结构的破坏型式为上层顶板和底板两端的受拉破坏、下层底板边跨跨中的上拱弯曲破坏、中柱的受压破坏、侧墙底端的弯曲破坏。     

文克尔地基模型下液化土桩基水平振动响应分析

在桩基顶部承受竖向荷载作用的条件下,将完全液化后的上层土体视为流体,将桩基等效为欧拉-伯努利梁模型,探讨了桩底嵌固时桩基顶部的水平振动阻抗。运用流体动力方程模拟顶部液化土层的运动,运用文克尔地基模拟下部非液化分层土的运动。结合传递矩阵法,利用液化土与非液化分层土交界面处的位移、转角和内力连续条件,得到桩基顶部和底部的相关位移?内力表达关系式。根据桩基底部的嵌固条件,求得桩顶阻抗的表达式。与已有文献解进行对比,验证了分析过程的正确性。对阻抗影响条件进行参数分析,表明液化深度、轴力和流体密度大小对桩顶阻抗有不同的影响。     

Elastic lateral dynamic impedance functions for a rigid cylindrical shell type foundation

Elastic lateral dynamic impedance functions are defined as the ratio of the lateral dynamic force/moment to the corresponding lateral displacement/rotation at the top ending of a foundation at very small strains. Elastic lateral dynamic impedance functions have a defining influence on the natural frequencies of offshore wind turbines supported on cylindrical shell type foundations, such as suction caissons, bucket foundations, and monopiles. This paper considers the coupled horizontal and rocking vibration of a cylindrical shell type foundation embedded in a fully saturated poroelastic seabed in contact with a seawater half‐space. The formulation of the coupled seawater–shell–seabed vibration problem is simplified by treating the shell as a rigid one. The rigid shell vibration problem is approached by the integral equation method using ring‐load Green's functions for a layered seawater‐seabed half‐space. By considering the boundary conditions at the shell–soil interface, the shell vibration problem is reduced to Fredholm integral equations. Through an analysis of the corresponding Cauchy singular equations, the intrinsic singular characteristics of the problem are rendered explicit. With the singularities incorporated into the solution representation, an effective numerical method involving Gauss–Chebyshev method is developed for the governing Fredholm equations. Selected numerical results for the dynamic contact load distributions, displacements of the shell, and lateral dynamic impedance functions are examined for different shell length–radius ratio, poroelastic materials, and frequencies of excitation. Copyright © 2016 John Wiley & Sons, Ltd.     

Vertical vibration of a rigid strip footing on viscoelastic half-space

This paper presents an analytical method for modeling the dynamic response of a rigid strip footing subjected to vertical-only loads. The footing is assumed to rest on the surface of a viscoelastic half-space; therefore, effects of hysteretic soil damping on the impedance of the foundation and the generated ground vibrations are considered in the solution. To solve the mixed boundary value problem, we use the Fourier transform to cast a pair of dual integral equations providing contact stresses, which are solved by means of Jacobi orthogonal polynomials. The resulting soil and footing displacements and stresses are obtained by means of the Fourier inverse transform. The solution provides more realistic estimates of footing impedance, compared to existing solutions for elastic soil, as well as of the attenuation of ground vibrations with distance of the footing. The latter is important for the estimation of machine vibration effects on nearby structures and installations.