Rayleigh波在浅圆凹陷地形附近的散射:高频解答

利用波函数展开法给出了Rayleigh波在浅圆凹陷地形附近散射的一个高频解析解，并分析了入射频率、凹陷地形宽度和深度等因素对波散射的影响。数值结果表明，由于Rayleigh波幅值随深度而衰减，凹陷地形表面位移幅值整体上较小，且随着凹陷地形深度的增加而减小；由于Rayleigh波幅值还随频率而衰减，随着入射频率的升高，凹陷地形表面位移幅值逐渐减小；由于凹陷地形的屏障作用，在人射波的近端，地表位移分布变得相对复杂，地表位移峰值出现在左角点附近，而在入射波远端，地表位移分布相对简单，地表位移峰值出现在距凹陷地形较远的地方。     

圆弧形凹陷饱和土场地对平面P波散射问题的解析解

以Biot 饱和多孔介质动力学理论为基础，利用Fourier Bessel级数展开法, 得到饱和多孔介质半空间中圆弧形凹陷地形对平面P波的散射问题的解析解. 数值计算给出地表位移幅值，分析了入射波波长、入射角、圆弧高宽比对地表位移幅值的影响，并与现存的在单相介质情况下得到的结论进行对比.     

无破碎带断层场地对SH波的散射

在层状半空间精确动力刚度矩阵和斜线荷载动力格林函数的基础上建立间接边界元方法,在频域内求解无破碎带断层场地对入射平面SH波的散射。为方便求解,将总波场分解为自由波场和散射波场,自由波场由直接刚度法求得,断层两侧的散射波场通过在断层面上分别对两侧施加均布斜线荷载产生的动力响应来模拟,虚拟荷载的密度可通过引入断层表面的边界条件确定,最后叠加自由波场和散射波场求得总波场。以有落差断层和无落差断层模型为例进行数值计算,分析断层落差、断层倾角以及断层两侧介质的刚度比对散射效应的影响。研究表明,断层落差与波长相当时,断层对SH波的放大作用最大;地表位移幅值随着断层倾角的增大逐渐增大;若断层无落差且其两侧刚度不同时,一般刚度较小一侧地表位移幅值较大且振荡更为剧烈,波从刚度较小一侧入射时位移幅值放大尤为显著。     

弹性层状半空间中无限长洞室对斜入射 平面SH波的三维散射(Ⅱ) 数值结果与分析

以基岩上单一土层场地为例, 计算分析了在斜入射平面SH波作用下弹性层状半空间中无限长洞室附近的地表位移. 研究表明, 层状半空间中地下洞室对波的散射与均匀半空间情况存在显著差别. 层状场地由于考虑了场地自身的动力特性, 使得洞室附近地表位移幅值的空间变化更为复杂, 基岩与土层刚度比、 土层厚度对散射效应均有着重要影响. 随着基岩与土层刚度比的增大, 地表位移幅值整体上逐渐增大; 随着土层厚度的增大, 土层对地表位移幅值的影响逐渐减小. 在频域解答的基础上, 给出了层状半空间中洞室对斜入射SH波散射的时域解答, 并以Ricker波为例进行了数值计算.      

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。     

弹性层状半空间中无限长洞室对斜入射平面SH波的三维散射(Ⅱ)——数值结果与分析

以基岩上单-土层场地为例,计算分析了在斜入射平面SH波作用下弹性层状半空间中无限长洞室附近的地表位移.研究表明,层状半空间中地下洞室对波的散射与均匀半空间情况存在显著差别.层状场地由于考虑了场地自身的动力特性,使得洞室附近地表位移幅值的空间变化更为复杂,基岩与土层刚度比、土层厚度对散射效应均有着重要影响.随着基岩与土层刚度比的增大,地表位移幅值整体上逐渐增大;随着土层厚度的增大,土层对地表位移幅值的影响逐渐减小.在频域解答的基础上,给出了层状半空间中洞室对斜入射SH波散射的时域解答,并以Ricker波为例进行了数值计算.     

层状半空间中洞室对入射平面P波的放大作用

文中利用间接边界元法,在频域内求解了层状弹性半空间中洞室对入射平面P波的放大作用问题。通过自由场反应分析,求得假想洞室边界上各单元的应力响应。在洞室边界各个单元上施加虚拟分布荷载,求得位移和应力的格林函数。根据应力边界条件确定虚拟分布荷载,将自由场位移响应和虚拟分布荷载产生的位移响应叠加起来,即得到问题的解答。比较了层状半空间和均匀半空间中洞室对入射平面P波的放大作用,结果表明,层状半空间情况有可能导致较大的地表位移幅值,尤其是对于较低频率入射波。     

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。     

横观各向同性层状半空间中凹陷地形对平面SH波的散射

沉积风化作用下土体表现出明显的成层特性和横观各向同性(TI)特性。将更为符合实际的TI介质模型引入到局部地形对地震波的散射问题研究有着重要的理论意义和工程实用价值。本文在TI土层平面外动力刚度矩阵的基础上,推导了斜线均布荷载动力格林函数,进而以该格林函数为基本解建立间接边界元方法研究了TI层状半空间中凹陷地形对平面SH波的散射问题。文中验证了方法的正确性,并分别在频域和时域内进行了数值计算分析。研究表明,TI介质中凹陷地形对SH波的散射与各向同性介质情况存在较大差异,凹陷附近地表位移幅值依赖于SH波的入射角度、入射频率和竖向与水平剪切模量比值;另外土体竖向与水平剪切模量比值对基岩上单一土层场地动力特性有着显著影响,进而使得TI层状场地凹陷附近位移幅值与各向同性情况差异变得更为复杂。     

A new boundary element solution to evaluate the geometric effects of the canyon site on the displacement response spectrum

This paper presents a step-by-step procedure using the three-dimensional boundary element approach to study the behavior of semi-circular canyons under seismic shear waves. The boundary element code TDASC allows utilization for various canyon geometries, evaluation of concurrent seismic waves and calculation of the ground motions on canyons due to an excitation at any arbitrary point of the incident field. Considering the widening ratio of the canyon(including prismatic, semi-prismatic and non-prismatic canyons), wave characteristics(wavelength, dimensionless period, direction) and maximum amplification pattern, the solution was applied to carry out a series of parametric studies. It was shown that canyon form can significantly affect the displacement amplification, especially at the points located on its edges. By increasing the wave dimensionless frequency(η 1), the amplification pattern becomes more complex. On the basis of the results from a variety of considered cases, a new expression has been presented for the limiting wavelength beyond which the widening of the canyon will not have a major effect on the displacement amplification. To verify the reliability of the proposed approach, the obtained results, expressed in terms of displacement amplitude, were compared with those from the available published literature and a reasonably good agreement was observed.     

风化半圆形河谷对柱面SH波的散射解析解

风化河谷地震效应对建在此类场地上工程结构(如大坝、桥梁)的动力稳定性具有潜在的威胁,为揭示河谷风化层对地面运动的影响,利用波函数展开法推导风化半圆形河谷对线源柱面SH波散射问题的解析解。计算不同震源位置条件下风化半圆形河谷的地表位移反应和地面运动放大因子,分析地面运动的幅值和形态,发现随着震源距离的增大,在河谷附近地震动的放大和衰减的交替更频繁。     

Scattering of plane harmonic SH,SV, P and rayleigh waves by non-axisymmetric three-dimensional canyons: A wave function expansion approach

Scattering of elastic waves by three-dimensional canyons embedded within an elastic half-space is investigated by using a wave function expansion technique. The geometry of the canyon is assumed to be non-axisymmetric. The canyon is subjected to incident plane Rayleigh waves and oblique incident SH, SV and P waves. The unknown scattered wavefield is expressed in terms of spherical wave functions which satisfy the equations of motion and radiation conditions at infinity, but they do not satisfy stress-free boundary conditions at the half-space surface. The boundary conditions are imposed locally in the least-squares sense at several points on the surface of the canyon and the half-space. Through a comparative study the validity and limitations of two-dimensional approximations (antiplane strain and plane strain models) have been examined. It is shown that scattering of waves by three-dimensional canyons may cause substantial change in the surface displacement patterns in comparison to the two-dimensional models. These results emphasize the need for three-dimensional modelling of realistic problems of interest in strong ground motion seismology and earthquake engineering.     

Study of effects of focal depth on the characteristics of Rayleigh waves using finite difference method

This paper presents a relationship between the focal depth in terms of Rayleigh-wave wavelength and the dominant frequency of Rayleigh waves generated in a homogeneous half-space. Rayleigh waves were simulated using a (2, 4) staggered grid P-SV wave finite difference algorithm with VGR-stress imaging technique as a free surface boundary condition. VGR is an acronym for vertical grid-size reduction. The simulated seismic responses using P-wave and SV-wave sources at different focal depths revealed Rayleigh-wave generation up to certain focal depth only for the considered frequency bandwidth. A shift of normalized spectral shape of Rayleigh wave towards lower frequency with increasing focal depth was inferred. Largest spectral amplitude was obtained in the wavelength for which the ratio of focal depth to the wavelength of Rayleigh wave was around 0.17 in the case of P-wave source and 0.9 in the case of SV-wave source. An exponential decrease of spectral amplitude of Rayleigh wave with the departure of the ratio of focal depth to Rayleigh wave wavelength from the above mentioned values was obtained.     

三维椭球形盆地对球面波的散射

针对三维沉积盆地对球面波的散射问题,发展一种快速宽频间接边界元方法(IBEM)。利用ANSYS建立求解模型,基于Intel-Fortran编译器编译相应的计算程序,对基岩半空间三维半椭球形盆地对球面波的散射进行了数值分析,着重探讨入射波频率、波源埋深、波源与不规则地形(沉积盆地)距离等参数对地震动特性的影响规律,计算方法适用于求解任意复杂形状的局部场地,实现对沉积盆地三维地震响应的频域精细求解。研究结果表明:随着入射波频率增大,沉积盆地相对半空间的放大效应越显著,且干涉效应越强烈;高频波入射时,由于盆地底部透射的体波和盆地内部由体波转换为的面波以及从盆地边缘处透射的体波相互叠加,次方向位移出现一定的边缘效应。位移频谱分析表明,沉积盆地在较低频率时,地表不同点位的主方向位移幅值基本相同;在较高频率域内,地表不同点位的位移频谱特性差别很大;球面波入射与平面波入射相比之下,位移幅值均有所降低。整体来看,随着膨胀波源与盆地水平距离增大,地表主方向最大位移幅值降低,地表次方向位移聚焦区域增加且分布更分散。     

地震体波斜入射情形下台阶地形引起的波型转换

本文首次对地震体波斜入射情形下竖直、倾斜台阶地形引起的波型转换进行了数值模拟，结果表明：地震波的斜入射会使台阶上角点引起更强的转换面波；转换Rayleigh面波最大振幅可达弹性半空间表面自由场位移的1.1倍左右。     

Scattering of plane sh waves by a semi-cylindrical canyon

The two-dimensional scattering and diffraction of plane SH waves by a semi-cylindrical canyon is analysed for a general angle of wave incidence. The closed-form solution of the problem shows that the surface topography can have prominent effects on incident waves only when the wavelengths of incident motion are short compared to the radius of a canyon. The surface amplification of displacement amplitudes around and in the canyon changes rapidly from one point to another, but the amplification is always less than 2. The over-all trends of amplification pattern are determined by two principal parameters: (1) γ, the angle of incidence of plane SH waves, and (2) η, the ratio of radius of the canyon to one-half wave length of incident waves. The higher η leads to greater complexity of the pattern of surface displacement amplitudes characterized by more abrupt changes of amplification from one point to another, while γ mainly determines the over-all trends of displacement amplitudes. For grazing and nearly grazing incidences, for example, a strong shadow zone is developed behind the canyon. The qualitative analysis of the topographic effects on the Pacoima Dam accelerogram,¹ based on the semi-cylindrical canyon, suggests that this strong-motion record was not seriously affected by surface topography of the recording site.     

Anomalous Rayleigh-Wave Propagation Along Oceanic Trench

A clear later phase of amplitude larger than the direct surface wave packet was observed at stations in Hokkaido, Japan, for several events of the December 1991 off-Urup earthquake swarm in the Kuril Islands region. From its particle motion, this phase is likely to be a fundamental Rayleigh wave packet that arrived with an azimuth largely deviated from each great-circle direction. As its origin, Nakanishi (1992) proposed that the sea-trench topography in this area as deep as 10 km may produce a narrow zone of low velocity for Rayleigh waves of periods around 15 sec. Following this idea, we compute ray paths and estimate how Rayleigh waves would propagate if we assume that lateral velocity variations are caused only by seafloor topography. We confirm that thick sea water in the trench indeed produces the phase velocity of Rayleigh waves to be smaller than in a surrounding area by the degree over 100%. Such a low-velocity zone appears only in a period range from 12 to 20 sec. Although this strong low-velocity zone disturbs the direction of Rayleigh wave propagation from its great circle, the overall ray paths are not so affected as far as an epicentre is outside this low-velocity zone, that is, off the trench axis. In contrast, the majority of rays are severely distorted for an event within the low-velocity zone or, in other words, in the neighborhood of the trench axis. For such an event, a part of wave energy appears to be trapped in this zone and eventually propagates outwards due to the curvature or bend of trench geometry, resulting in very late arriving waves of large amplitude with an incident direction clearly different from great circles. This phenomenon is observed only at a very limited period range around 16 sec. These theoretical results are consistent with the above mentioned observation of Nakanishi (1992).     

Forward modeling of Rayleigh surface waves for analytical characterization of dominant dispersion trends

Forward modeling is of critical importance for inversion analysis of surface wave methods to obtain shear-wave velocity (V_S) profiles of soil sites. The dynamic stiffness matrix (DSM) method can provide forward modeling of Rayleigh surface waves to simulate complex wave propagation in layered soil sites. However, contamination from body waves and interference of multiple Rayleigh wave modes can reduce the accuracy of theoretical dispersion curves, especially at irregular soil sites with embedded low-velocity or high-velocity layers. An analytical method is developed herein to combine the techniques of the multichannel analysis of surface waves method with the DSM method to improve the accuracy of the theoretical dispersion analysis for soil sites. The proposed method implements multichannel analysis of the analytical displacement responses to capture dominant dispersion trends. Comparison of the results obtained with the new method against those from the transfer matrix method and the literature indicates that the new method can (1) effectively minimize the effects of contamination caused by body waves and interference from several Rayleigh wave modes, and (2) generate accurate dominant dispersion trends for soil sites with various stiffness profiles, especially for the high-frequency dispersion characteristics of the profiles with embedded low-velocity layers.