Solution of a Green's function for a saturated porous medium in a half-space subjected to a torsional force

Based on the solutions of the Green＇s function for a saturated porous medium obtained by the authors, and using transformation of axisymmetric coordinates, Sommerfeld integrals and superposition of the influence field on a free surface, the authors have obtained displacement solutions of a saturated porous medium subjected to a torsional force in a half-space. The relationship curves of the displacement solutions and various parameters （permeability, frequency, etc.） under action of a unit of torque are also given in this paper. The results are consistent with previous Reissner＇s solutions, where a two-phase medium decays to a single-phase medium. The solution is useful in solving relevant dynamic problems of a two- phase saturated medium in engineering.

Green's function of multi-layered poroelastic half-space for models of ground vibration due to railway traffic

This study proposes a Green＇s function, an essential representation of water-saturated ground under moving excitation, to simulate ground borne vibration from trains. First, general solutions to the governing equations of poroelastic medium are derived by means of integral transform. Secondly, the transmission and reflection matrix approach is used to formulate the relationship between displacement and stress of the stratified ground, which results in the matrix of the Green＇s function. Then the Green＇s function is combined into a train-track-ground model, and is verified by typical examples and a field test. Additional simulations show that the computed ground vibration attenuates faster in the immediate vicinity of the track than in the surrounding area. The wavelength of wheel-rail unevenness has a notable effect on computed displacement and pore pressure. The variation of vibration intensity with the depth of ground is significantly influenced by the layering of the strata soil. When the train speed is equal to the velocity of the Rayleigh wave, the Mach cone appears in the simulated wave field. The proposed Green＇s function is an appropriate representation for a layered ground with shallow ground water table, and will be helpful to understand the dynamic responses of the ground to complicated moving excitation.

In-plane dynamic Green's functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic half-space

The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic（TI）half-space.The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces,which are then applied to the total system with the opposite sign.By adding solutions restricted in the loaded layer to solutions from the reaction forces,the global solutions in the wavenumber domain are obtained,and the dynamic Green’s functions in the space domain are recovered by the inverse Fourier transform.The presented formulations can be reduced to the isotropic case developed by Wolf（1985）,and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI halfspace subjected to horizontally distributed loads which are special cases of the more general problem addressed.The deduced Green’s functions,in conjunction with boundary element methods,will lead to significant advances in the investigation of a variety of wave scattering,wave radiation and soil-structure interaction problems in a layered TI site.Selected numerical results are given to investigate the influence of material anisotropy,frequency of excitation,inclination angle and layered on the responses of displacement and stress,and some conclusions are drawn.

THERMAL CONSOLIDATION OF LAYERED POROUS HALF-SPACE TO VARIABLE THERMAL LOADING

An analytical method was derived for the thermal consolidation of layered, saturated porous half-space to variable thermal loading with time. In the coupled governing equations of linear thermoelastic media, the influences of thermo-osmosis effect and thermal filtration effect were introduced. Solutions in Laplace transform space were first obtained and then numerically inverted. The responses of a double-layered porous space subjected to exponential decaying thermal loading were studied. The influences of the differences between the properties of the two layers （e.g., the coefficient of thermal consolidation, elastic modulus） on thermal consolidation were discussed. The studies show that the coupling effects of displacement and stress fields on temperature field can be completely neglected, however, the the thermal responses. effect has an obvious influence on

Analytical solutions for dynamic pressures of coupling fluid-solid-porous medium due to P wave incidence

Wave reflection and refraction in layered media is a topic closely related to seismology,acoustics,geophysics and earthquake engineering.Analytical solutions for wave reflection and refraction coefficients in multi-layered media subjected to P wave incidence from the elastic half-space are derived in terms of displacement potentials.The system is composed of ideal fluid,porous medium,and underlying elastic solid.By numerical examples,the effects of porous medium and the incident wave angle on the dynamic pressures of ideal fluid are analyzed.The results show that the existence of the porous medium,especially in the partially saturated case,may significantly affect the dynamic pressures of the overlying fluid.

基于空间三维非均匀SISO阵列雷达的介质目标快速成像算法

近年来,随着高精度定位系统的迅猛发展,基于手持式毫米波雷达的阵列成像技术在无损检测和医疗成像等涉及介质内部结构成像的领域中引起了广泛关注.与常见的二维(Two-Dimensional,2D)平面单发单收(SingleInput-Single-Output,SISO)阵列不同的是,基于手持式毫米波雷达的阵列,其阵元通常非均匀分布于三维(Three-Dimensional,3D)空间中,导致现有的基于平面SISO阵列的对介质目标内部结构进行快速成像重构的算法无法适用.为此,本文提出了一种适用于空间3D非均匀SISO阵列雷达的半空间介质目标快速成像算法.该算法将空间3D非均匀SISO阵列的每一个阵元扩展为一个的虚拟阵列,然后将所有虚拟阵列的回波数据变换至波数域后进行相干累加,最后通过3D逆傅里叶变换(Inverse Fourie Transform,IFT)实现快速成像.数值仿真和实验测量表明,与同样适用于该场景的改进后向投影(Improved Backward Projection,IBP)算法相比,在本文给定的成像参数条件下,所提算法可以在保证成像质量的同时,将成像时间缩短94%以上.

两相饱和介质半无限空间位错位移场

弹性位错理论是研究地震震源正演和反演的重要工具之一 .单相介质位错理论求得的地面变形场是稳定的、不变的 ,而实际地震后的地面变形场是变化的 .本文利用集中力作用下无限空间中两相饱和介质Green函数的柱函数表达式 ,通过弹性运动方程积分解的Helmholtz方程的Hansen矢量变换 ,再叠加自由表面影响场的方法求得两相饱和介质半无限空间位错位移场 .本文结果结合Nur的DD模式 ,在进水排水的假说下能解释地震后地面变形场的变化 .

横观各向同性饱和地基的三维动力响应

首先引入位移函数,将直角坐标系下横观各向同性饱和土Biot波动方程转化为2个解耦的六阶和二阶控制方程;然后基于双重Fourier变换,求解了Biot波动方程,得到以土骨架位移和孔隙水压力为基本未知量的积分形式的一般解,并用一般解给出了饱和土总应力分量的表达式.在此基础上系统研究了横观各向同性饱和半空间体的稳态动力响应问题,考虑表面排水和不排水两种情况,得到了半空间体在任意分布的表面谐振荷载作用下,表面位移的稳态动力响应,文末给出了算例.

轨道附近地面振动模型中的饱和地层动力格林函数

列车引起场地振动的建模需要能够表达地层的动力格林函数.本文兼顾饱和土的流固两相耦合性、场地土的分层性和波动的三维传播性,构建了半解析的场地动力格林函数.首先,基于Biot方程,在傅里叶变换域求解固体骨架和流体的位移和应力.然后采用传递矩阵方法建立地表位移和应力间的关系,得到格林函数矩阵.进而讨论矩阵的一些固有特征,提出改善竖向位移计算效率的措施.最后利用推导的格林函数计算了几个典型算例.数值结果与文献中其他方法得到的结果十分接近,与场地振动的现场观测试验基本符合.软土场地振动的计算结果高于饱和砂土场地,高速列车场地振动强度高于低速列车.当车速接近场地瑞利波速,模拟结果中显示出马赫锥.数值结果还显示,即使车速略低于瑞利波速,马赫锥也可能出现.本文推导的格林函数将有助于深入理解列车等移动激励作用下层状饱和土场地的振动特征.

饱和黏弹性半空间中摩擦桩的竖向振动

为深入了解饱和黏弹性半空间地基中摩擦桩的竖向振动特性,基于Boer多孔介质理论,考虑激振频率对摩擦桩桩底土体动刚度的影响,采用平面应变模型并结合桩土接触面的混合边值条件,推导求解得出了饱和黏弹性半空间地基中摩擦桩的竖向动力阻抗模型公式和桩顶速度时域响应解并验证了其合理性。进一步通过参数化对比分析探讨了桩基埋深比和土体渗透系数对所得竖向动力阻抗和桩顶速度时域响应的影响规律。解析推导得出的对应竖向动力阻抗模型公式和桩顶速度时域响应解,丰富了桩基动力学的理论,可为相关工程实践提供参考和理论支持。

基于外场场强测量的短波天线辐射效率监测

针对短波天线辐射效率难以现场监测的问题,研究一种基于外场场强测量的短波天线辐射效率监测方法。该方法结合天线仿真与测量技术,通过域变换法解析介质半空间位型并矢格林函数,采用RWG矩量法(RWG-MoM)离散平面分层介质C类混合位电场积分方程(MPIE),得到天线辐射功率的相对分布。测量天线外场场强,得到场点电磁功率面密度作为样本估计天线辐射功率,由辐射功率与输入功率的比值计算得到天线辐射效率。以短波双极天线为例,基于现有的飞艇场强测量平台,进行室外远场场强的测量,实验得到的归一化场强方向图与仿真结果吻合较好,通过该方法计算得到的天线辐射效率与公开文献一致性较好,实现了短波天线辐射效率的监测。

变温度荷载作用下半无限成层饱和介质的热固结分析

对半无限成层饱和多孔介质作用随时间变化的温度荷载的热固结问题进行解析求解.其中,热_水_力耦合线性弹性控制方程考虑了热渗效应和等温热流效应的影响.先采用Laplace变换求其在变换域上的解,然后用数值方法求逆变换.对半无限体表面作用呈指数衰减热荷载的双层体系进行研究,分析了两层介质热固结系数、弹性模量等的差异性对热固结特征的影响.研究表明:位移场和应力场对温度场的耦合作用可以忽略,而热渗效应对温度和孔压有显著影响.

层合介质中平面SH波的传播

研究了平面SH波通过多层弹性层状介质时的传播特性,求得了透射波和反射波振幅的解析解表达式,并把本文表达式的特例与现有文献结果作了对比,结论一致,同时进行了含单一夹层时SH波的室内砂池模拟试验,试验结果与理论结果基本吻合。

移动荷载作用下TI饱和半空间动力响应分析

列车运行产生的周围地基振动对列车运行安全以及周边环境振动有着重要的影响,其实质是移动荷载产生的应力波在地基中的传播问题。基于Biot流体饱和多孔介质模型,给出了移动荷载作用下横观各向同性(transversely isotropic,简称TI)饱和半空间动力响应的求解方法。首先,将Biot方程转换到频率-波数域中,通过坐标变换将方程解耦为平面内部分和出平面部分;其次,通过势函数方法求解平面内和平面外波动方程;最后,将移动荷载代入,其解可表示为对频率和单一波数的双重Fourier积分。与已有文献的结果进行了比较,验证了方法的正确性。开展了数值计算分析,讨论了荷载移动速度和TI介质参数等对半空间动力响应的影响,研究结论为列车荷载诱发复杂场地的振动控制技术提供了一定的理论依据。

半空间饱和土内置点载荷作用下的热弹性波动

基于Biot波动理论及热弹性动力理论,利用已建立的饱和多孔弹性介质热流固耦合控制方程,研究半无限地基在内置点热力源作用下的动力响应问题.求解过程引用Hankel变换技术,得到了热力源作用下土体中温度增量、应力、位移和孔隙水压力的积分形式解答.利用Hankel数值逆变换得到计算结果,分析了热流固耦合条件下激振频率对竖向位移和孔隙水压力响应的影响.对热流固耦合、热弹性和多孔弹性模型计算结果进行了比较.

双极化位相法测量半空间介质介电常数

在实验中试用了一种空间波测量无限大半空间介质复介电常数的方法:用一个喇叭同时发射垂直极化波和平行极化波,另一个喇叭交替接收两个极化波的前向散射的振幅和相位。实验在X波段进行,目标介电常数可在任意范围,结果与金属板定标法符合较好。该方法在微波遥感中将有较大实用价值。

层状TI饱和半空间均布斜线荷载及孔隙水压动力格林函数

基于Biot流体饱和多孔介质模型,采用动力刚度矩阵方法结合傅里叶变换,给出了层状横观各向同性(TI)饱和半空间中均布斜线荷载及孔隙水压的动力格林函数。方法首先将荷载作用层固定,在波数域内求得层内响应和固端反力,进而由刚度矩阵方法求得反加固端反力于整个层状半空间而产生的响应,最后叠加层内解和固端反力解经由傅里叶逆变换求得空间域内解。所给出的层状TI饱和半空间格林函数为建立相应边界元方法进而求解层状TI饱和介质相关波动问题提供了一组完备基本解。通过与已发表的各向同性饱和结果和TI弹性结果进行对比,验证了方法的正确性。进而给出了数值计算结果并进行了参数分析。结果表明:TI饱和介质与各向同性饱和介质对应的动力响应差异显著,且介质的各向异性参数对动力响应有着重要影响。此外,荷载埋深越小,地表位移和孔压波动更剧烈;介质渗透系数起到类似阻尼的作用,减小渗透系数可降低动力响应;随着频率的增大,位移、应力和孔压的波动也更为剧烈。

弹性地基上无限大板的统一解

利用汉克尔变换法,推演得到了文克勒地基、双参数地基、弹性半空间体地基上无限大薄板,赖斯纳、汉盖、克罗姆等中厚板,在任意竖向荷载作用下的统一解;并给出了竖向轴对称荷载条件下的无限大板挠度、弯矩、剪力系数、地基反力系数的计算公式;最后,对圆形均布荷载作用下的不同地基和板模型的板挠度和弯矩进行了对比分析。结果表明：半空间体地基板与文克勒地基板的荷载圆中点的弯矩参数十分相近,但其荷载圆中点挠度系数较后者大1/3~1/2;中厚板理论对地基板挠度有更好地拟合和解析,但对板弯矩等内力的计算精度无改善。

两媒质半空间电磁散射

从各向同性,均匀无源区域电磁场的矢量波函数展开式出发,利用标准与非标准球矢量波函数之间的转换关系、场型分析、广义索末菲积分得到了两媒质半空间散射场表达式。并讨论了平面波照射下埋入球的散射。与单距法结合就可求解任意形状不均匀结构埋入体的散射问题。

平面分层媒质中浅层埋入体的脉冲电磁散射

应用稳定的双共轭梯度快速傅立叶变换(BCGSFFT)方法,分析了两媒质半空间和三分层媒质中浅层埋入体的脉冲电磁散射。由于FFT及快速迭代算法的运用,相对于传统的矩量法而言大大降低了计算时间和内存需求,使得算法能够用于解决平面分层背景下大尺度电磁散射问题。数值验算的结果反映了媒质的构造特征及目标的相对位置,显示出算法的有效性,为浅层埋入目标相控阵探地雷达的实现奠定了一定的理论基础。