具有饱和土沉积层的充水河谷对平面波的散射

把波函数展开方法用于地震波散射问题的研究中,首次在频域内给出了具有饱和土沉积层的圆弧形充水河谷对平面P波和SV散射问题的解析解答. 其中半空间场地用单相介质弹性动力理论模拟,河谷中的饱和土沉积层用饱和多孔介质的Biot动力学理论模拟,河谷中的水用无黏性流体(理想流体)介质模拟. 文中还给出算例,计算了不同高宽比的河谷谷底的位移幅值,分析表明河谷地形的存在使得半空间介质表面的位移幅值随着观察点位置的变化变化较大.     

具有饱和土沉积层的充水河谷对平面瑞雷波的散射

针对具有饱和土沉积层的充水河谷对平面瑞雷波的散射问题,把半空间场地用单相弹性介质模拟,河谷中的饱和土沉积层用Biot饱和多孔介质动力理论模拟,河谷中的水假定为无黏性流体（理想流体）,利用波函数展开法在频域内给出了具有饱和土沉积层的圆弧形充水河谷对平面瑞雷波散射问题的解析解答.文中给出了算例,计算了不同输入频率和高宽比时河谷谷底的位移幅值.算例表明由于具有饱和土沉积层的充水河谷存在,使得河谷谷底的位移幅值放大4倍多,并且它的幅值随着河谷谷底位置的不同而产生较大的变化.     

圆弧形有水河谷场地对平面P波的散射

利用波函数展开法,在频域内给出了圆弧形充水河谷对平面P波散射问题的解析。并分析了入射波波长、入射角对充水河谷地形地面运动的影响。     

Scattering of plane P waves by circular-arc layered alluvial valleys: An analytical solution

IntroductionThe site effect of local inhomogeneity and irregularity on seismic wave propagation is one of the most attractive topics in seismology. The problem may be resolved by either analytical method or numerical method. Here, the analytical method is the wave function expansion method; numerical methods include the finite difference, finite element, boundary integration equation, and discrete wave number method, etc. Although these numerical methods can be applied for sites of arbitrary s…     

圆弧状多层沉积谷地在平面P波入射下稳态响应的解析解

利用波函数的FourierBessel级数展开法,给出了含任意多个圆弧状沉积层的谷地在平面P波入射下稳态动力响应的解析解.并以具有三个沉积层的谷地为例,在宽频范围内,利用稳态地面运动幅值的空间分布,讨论了谷地中沉积介质的成层性对地面运动的影响.     

饱和土中深埋圆柱形衬砌洞室对瞬态平面波的散射

基于Biot饱和多孔介质动力学理论,运用Laplace变换和波函数展开法,根据饱和土体与衬砌结构交界面的连续条件和衬砌结构内边界上的应力自由条件,得到饱和土中深埋圆柱形衬砌洞室对瞬态平面P波和SV波散射问题的解答,该解答可以退化成为饱和土中深埋圆柱形空穴或弹性夹塞物的情形,并很容易转换成为对稳态波散射的解.通过与已有的相关问题的解析解答进行对比,验证了该解答的正确性.同时利用Laplace逆变换的数值方法,给出了饱和土和衬砌中应力和位移场在时域内的数值解,通过算例,分析了衬砌厚度、刚度对衬砌内边界处应力集中因子的影响.     

Diffraction of plane P waves around an alluvial valley in poroelastic half-space

Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green’s functions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of fictitious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary...     

圆弧状多层沉积谷地在平面SV波入射下的动力响应

利用波函数的Fourier-Bessel级数展开法,推导出了含任意多个圆弧状沉积层的谷地在平面SV波入射下稳态动力响应的解析解,并分析了该级数形式的解析解随着截断项数的收敛问题.其结果表明,该级数解能够在一个非常宽的频带范围内收敛;通过在简化条件下与现有其他解析解的比较,验证了该解析解的正确性;并利用该解析解,以稳态地面运动的位移幅值和相位差为基本参数,在一个较宽的频带范围内讨论了谷地中沉积介质的成层性对地面运动的影响,其结果表明对于多层谷地而言,当入射波频率较高时,散射波之间的干涉显著并且出现了能量聚焦现象.     

饱和土沉积谷场地对平面SV波的散射问题的解析解

把波函数展开方法用于饱和多孔介质中波的传播的研究中,给出了不同土层界面条件（透水条件和不透水条件）下具有饱和土沉积层的圆弧形沉积河谷场地对平面SV波散射问题的解析解. 其中沉积谷软土场地用饱和多孔介质的Biot动力学理论模拟,半空间场地用单相介质弹性动力理论模拟. 对于入射角大于临界入射角时,产生的面波的波函数用有限Fourier级数展开,这种方法适用于较大的入射波频率范围,这是现存的数值方法所不能比拟的一大优点. 文中算例分析了入射波频率和入射角对地震地面运动的影响.     

Scattering of plane SV waves by cylindrical canyons in saturated porous medium

On the basis of Biot dynamic theory, an analytic solution of two-dimensional scattering and diffraction of plane SV waves by circular cylindrical canyons in a half space of saturated porous media is presented in this paper for the first time. The solution is obtained by employing the Fourier–Bessel series expansion technique. Parametric studies had been carried out, which includes: the angle of incidence, the frequency of the incident SV wave, the porosity of saturated porous medium and the stiffness and Poisson's ratio of the solid-skeleton. All the outcomes are useful for the seismic analysis of the surface topography conditions.     

半球形饱和土沉积谷场地对入射平面Rayleigh波的三维散射问题的解析解

用Biot饱和多孔介质动力学理论模拟半球形两相饱和土沉积谷,用单相介质弹性动力学理论模拟周围半空间场地.利用Fourier-Bessel 级数展开法,在频域内给出了半空间中半球形饱和土沉积谷场地在平面Rayleigh波入射下三维散射问题的解析解.利用这一解析解计算分析了入射波频率、场地特征（包括孔隙比）对地表位移幅值的影响,并与已有的三维半球形沉积谷场地在单相介质中的散射问题进行了对比分析.     

饱和土中浅圆弧状埋置基础对平面P波散射解答

在Biot饱和多孔介质动力学理论的基础上,利用Fourier—Bessel级数展开法,首次得到饱和土中浅圆弧状埋置基础对平面波散射问题的解答．并利用该解对有埋置基础的饱和土场地地面运动的幅值及其分布进行分析,研究了基础弹性对平面P波作用下饱和土地基与基础动力相互作用的影响。     

平面SV波在饱和半空间中沉积谷地周围的散射

采用一种特殊的间接边界积分方程法,求解了平面SV波在饱和半空间中任意形状沉积谷地周围的二维散射问题。结合饱和半空间中膨胀波源和剪切波源格林函数,由分布在沉积和半空间交界面附近两虚拟波源面上的波源分别构造沉积内外的散射波场,由交界面连续条件建立方程并求解确定虚拟波源密度,总波场反应即可由自由波场和散射波场叠加而得。然后通过边界条件验算、退化解答与现有结果的比较以及稳定性检验,验证了方法的计算精度。通过一组典型算例,研究了平面SV波在饱和半空间中沉积谷地周围散射的基本规律,详细给出了不同参数情况沉积谷地附近地表位移幅值和孔隙水压,着重分析了入射SV波频率和角度、边界渗透条件、沉积孔隙率等因素对场地反应的影响,得出了一些有益的结论。     

半空间饱和介质内圆形洞室对平面P1波的散射

考虑土颗粒和孔隙流体的压缩性以及孔隙流体与土骨架之间的粘性耦合作用,采用修正的Biot模型,假定半空间表面不透水,得到了平面P1波(快压缩波)在半空间表面的反射P1波、P2波(慢压缩波)和SV波(剪切波)的幅值.采用大圆弧假定将半空间内圆形洞室的散射问题转化为大圆弧和圆形洞室的多重散射问题,运用波函数展开法将入射波、反射波以及半空间表面和洞室的散射波的势函数展开成Fourier-Bessel函数的无穷级数形式,由Graf加法定理得到同一坐标系下的势函数的表达式,根据半空间表面和洞室完全自由的边界条件得到了待定复系数的理论解.通过数值计算,着重分析了平面P1波垂直向上入射时无量纲入射频率和洞室埋藏深度等对洞室的动应力集中因子和半空间表面的归一化水平和竖向位移的影响.     

平面P波在饱和半空间中洞室周围的散射(II):数值结果

本文通过数值计算研究了入射平面P波在饱和半空间中洞室周围散射问题,分析了入射波频率和角度、边界渗透条件、孔隙率、泊松比等参数对散射的影响。研究表明,平面P波入射情况下,饱和半空间和单相(干土)半空间中洞室附近地表位移幅值的差别很大,干土情况的水平位移幅值相对较大,饱和情况的竖向地表位移幅值相对较大;由于波在洞室附近的干涉,饱和情况与干土情况的地表位移出现相位漂移。随着孔隙率的增大,洞室附近水平地表位移幅值逐渐减小,竖向地表位移幅值则逐渐增大;当孔隙率较低时,边界渗透条件对地表位移幅值的影响很小,而当孔隙率较大时,边界渗透条件的影响则不可忽视,不透水情况下,水平和竖向地表位移幅值的峰值均相对较大;随着入射频率的增加,孔隙率的影响逐渐增大,而且不透水情况下孔隙率的影响相对较大。随着泊松比的增大,洞室附近水平地表位移幅值逐渐降低,竖向地表位移幅值则逐渐增大;泊松比较小时,边界渗透条件对位移幅值的影响较大,泊松比较大时,边界渗透条件对位移幅值的影响则较小;随着入射频率的增加,泊松比的影响逐渐增大。当孔隙率较小时,半空间地表和洞室表面孔隙水压幅值较小,但空间变化比较剧烈,随着孔隙率的增大,孔隙水压逐渐增大但空间变化逐渐平缓;随着入射频率的增加,孔隙水压幅值逐渐增大,且孔隙水压的空间变化逐渐变得复杂。     

平面P波在饱和半空间中洞室周围的散射(I):解析解

利用波函数展开法给出了入射平面P波在饱和半空间中圆形洞室周围散射问题的一个解析解。半空间假定为无粘性流体饱和介质,满足Biot理论。采用一种基于实验数据的孔隙率和模量之间的线性关系来确定Biot模型中的介质参数。解答考虑了透水边界和非透水边界两种情况。对边界条件进行了数值检验,结果表明,随着级数截断项数的增大,边界残量衰减很快。解答为进一步研究入射波频率和角度、边界渗透条件、孔隙率、泊松比等参数对散射的影响奠定了基础。     

Scattering of plane P waves by a semi-cylindrical hill： analytical solution

An analytical solution for scattering of plane P waves by a semi-cylindrical hill was derived by using the wave function expansion method, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and incident angle on the surface motion of the hill was discussed, and it was shown that a hill greatly amplifies incident plane P waves, and maximum horizontal displacement amplitudes appear mostly at the inclined incidence of waves, which are located at the half-space; and maximum vertical displacement amplitudes emerge mostly at the vertical incidence of waves, which are situated at the hill.     

Analysis of Rayleigh waves in saturated porous elastic media by finite element method

A numerical procedure for the analysis of Rayleigh waves in saturated porous elastic media is proposed by use of the finite element method. The layer stiffness matrix, the layer mass matrix and the layer damping matrix in a layered system are presented for the discretized form of the solid-fluid equilibrium equation proposed by Biot. In order to consider the influence of the permeability coefficient on the behavior of Rayleigh waves, attention is focused on the following states: ‘drained’ state, ‘undrained’ state and the states between two extremes of ‘drained’ and ‘undrained’ states. It is found from computed results that the permeability coefficient exerts a significant effect on dispersion curves and displacement distributions of Rayleigh waves in saturated porous media.     

Scattering and diffraction of earthquake motions in irregular,elastic layers,II: Rayleigh and body P and SV waves

We present our study of the wave propagation in an irregularly layered, elastic wave-guide excited by incoming Rayleigh surface waves and P and SV body waves. Our aim is to show examples of applying a method that will make it possible to analyze the distribution and amplification of displacements, rotations, curvatures, strains, and stresses on or below the ground surface during passage of strong earthquake ground motion. We employ the weighted-residuals method, which makes it possible to calculate the scattered and diffracted waves, and then we illustrate the amplification of motions in the vicinity of inhomogeneity.     

基于粘性-滑移界面接触模型半空间隧道衬砌对平面P波的散射

基于粘性-滑移模型模拟隧道衬砌和围岩之间的接触状态,采用间接边界积分方程法求解弹性半空间中隧道衬砌对平面P波的散射,着重考察了地表位移放大和衬砌动应力集中效应。结果表明:接触滑移边界的刚度系数和粘度系数对隧道衬砌的动应力分布影响较大,滑移刚度较小时,共振频率段动应力集中效果更加显著;随着粘度系数的增大,衬砌内部环向应力幅值逐渐减小。另外,界面刚度系数和粘度系数对隧道衬砌动力反应的影响程度也受控于入射频率和角度。