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(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.     

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.      

柱面SH波在地下圆形衬砌洞室周围散射解析解

采用波函数展开法给出了半空间中柱面SH波在圆形衬砌洞室周围散射的解析解,并对解答的精度进行了分析。通过数值算例分析了入射频率、波源与洞室的距离、洞室埋深、衬砌刚度等对洞室衬砌动应力集中因子的影响。研究表明,柱面波在地下衬砌洞室周围的散射与平面波情况有着显著的差别,衬砌动应力集中因子和波源与洞室的距离密切相关;柱面波在全空间衬砌洞室周围的散射与半空间情况有着显著的差别,半空间地表对动应力集中因子有着重要影响。     

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。     

层状半空间中洞室对平面SH波的放大作用

利用间接边界元法,求解了弹性层状半空间中洞室对入射平面SH波的放大作用问题,并以基岩上单一土层中洞室对入射平面SH波的放大作用为例进行了数值计算分析。本文模型的特点之一是考虑了层状场地的动力特性,因而更接近于实际工程;特点之二是计算精度非常高。研究表明,层状半空间中洞室对波的放大作用与均匀半空间中情况有着本质的差别;层状半空间中洞室附近地表动力响应由土层动力特性和洞室对波的散射二者共同决定。土层动力特性不仅影响洞室附近地表位移的幅值,还会影响地表位移的频谱。在土层的前几阶共振频率附近,随着基岩与土层剪切波速比的增大,土层的影响随之增大,而随着土层厚度的增加,土层的影响随之减小,并逐渐趋于均匀半空间情况。     

地下圆形衬砌洞室在平面P波入射下的动应力集中:三维级数解

利用波函数展开法,研究了地下圆形衬砌洞室在入射平面P波作用下的动应力集中问题并给出了三维级数解。研究表明:(1)衬砌刚度对环向与轴向动应力集中系数都具有重要影响,刚性衬砌、无衬砌和柔性衬砌三种情况下的动应力集中系数在空间上的分布基本相同,但刚性衬砌情况的动应力集中系数最大,无衬砌情况次之,柔性衬砌情况最小,波阵面夹角入射时1δ=45°,环向与轴向动应力集中系数最大可分别达到16.62与8.53;(2)随着入射频率的增大,环向动应力集中系数在多数情况下逐渐减小;(3)波入射角度对动应力集中系数也有很大影响,随着入射波与y轴夹角2δ的增加,环向动应力集中系数总体上逐渐减小,而轴向动应力集中系数多数情况下逐渐增大。     

浅圆沉积谷地对瑞雷波的散射--高频解

利用波函数展开法给出了浅圆沉积谷地对瑞雷波散射的一个高频解析解,并分析了入射频率、沉积谷地宽度和深度等因素对波散射的影响. 数值结果表明,由于沉积谷地的影响, 在入射波的近端,地表位移分布变得相对复杂,但位移幅值并不大;而在入射波远端,地表位移分布相对简单,但位移幅值却相对较大,多数情况下高于沉积地表位移幅值.      

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.     

Scattering of plane P,SV or Rayleigh waves by a shallow lined tunnel in an elastic half space

Based on the plane complex variable theory and the image technique, an analytical solution is presented for scattering of plane harmonic P, SV or Rayleigh waves by a shallow lined circular tunnel in an elastic half space. The major contribution of this study is the treatment of the orthogonality of the boundary conditions along the half surface and the cavity wall. In terms of the image technique, the scattered waves by the half surface are simulated as transmitting from the image source of the origin of the tunnel. Using two different conformal mapping functions, we obtained the complex-valued stresses and displacements of the elastic medium and the liner in the image domain, respectively. The boundary value problem results in a set of infinite algebraic equations. The accuracy of the present approach is verified by comparing the present solution results with the available published data. Parametric study indicates that the embedment depth, the shear modulus and the thickness of the liner have significant influences on the dynamic response of the liner and the medium.     

地下洞室群对地面运动影响问题的级数解答-P波入射.

采用波函数展开法，给出了平面P波入射下半空间中洞室群对地面运动影响问题的一个级数解答. 数值结果表明，地下洞室群对附近地面运动具有显著的放大作用．建议地铁等地下工程在规划和设计时，考虑工程建设后对沿线地面运动的影响．      

Scattering of Rayleigh waves by a shallow circular alluvial valley： High-frequency solution

Introduction The effect of local site conditions on wave propagation is one of the most attractive topics in engineering seismology. It may be resolved by either a numerical method or an analytical method. Numerical methods include the finite difference, finite element, boundary element method, etc. The analytical method is the wave function expansion method. The advantage of these numerical methods is that they can be applied to local inhomogeneity of arbitrary shapes, but analytical method …     

A series solution for surface motion ampli-fication due to underground group cavities: Incident P waves

Introduction In recent years some big cities in China commonly build subways in central urban areas to improve crowded surface transportation, and the subways usually are large-scale group cavities composed by two parallel cavities. Construction of large-scale group cavities will certainly affect the design ground motion near the cavities, and further affect seismic safety of the existing build-ings nearby. So it is of significance to estimate this effect on seismic design of the buildings. H…     

Detecting underground cavities using microtremor data: physical modelling and field experiment

In this paper, we study the possibilities of the use of microtremor records in the detection and delineation of near‐surface underground cavities. Three‐dimensional physical modelling data showed that the averaging amplitude spectra of a large number of microtremor records makes it possible to evaluate the frequencies and amplitudes of compressional standing waves generated by microtremor in the space between the ground surface and underground cavities. We illustrate how these parameters can be used to estimate the shape of the underground cavity horizontal projection. If the compressional wave velocity in the enclosing rock is known, it is possible to evaluate the depth to the cavity top using the frequencies of the standing waves. The results of the field experiment confirmed the possibility of underground cavities detection using microtremor data.     

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。     

Dynamic analysis of large 3-D underground structures by the bem

An up to date literature survey on the dynamics of underground structures is presented briefly. The dynamic response of large three-dimensional underground structures to external or internal dynamic forces or to seismic waves is numerically determined by the frequency domain boundary element method. This method is used to model both the structure and the soil medium, which are assumed to behave as linear elastic or viscoelastic bodies. The full-space dynamic fundamental solution is employed in the formulation and this requires a free soil surface discretization, confined to a finite portion around the area of interest, in addition to soil—structure interface and free structural surface discretizations. The dynamic disturbances can have a harmonic or a transient time variation. The transient case is treated with the aid of numerical Laplace transforms with respect to time. Various numerical examples involving lined cavities and long lined tunnels buried in the full- or the half-space subjected to harmonic or transient external forces or seismic waves are presented to illustrate the method and demonstrate its advantages.     

Effect of underground cavities on surface earthquake ground motion under SH wave propagation

A theoretical approach is presented to study the antiplane seismic response of underground structures, subjected to the incidence of both plane and cylindrical waves. The structure is assumed to be a circular inclusion embedded in a homogenous, isotropic and linear visco‐elastic halfspace. The inclusion may consist either of a cavity, with or without a ring‐shaped boundary, or it may be filled in with a linear‐elastic material, without loss of generality. The analytical solution is obtained using expansions of wave functions in terms of Bessel and Hankel functions, relying on the technique of images and the use of Graf's addition theorem to enforce the boundary conditions. The effects of underground cavities on surface earthquake ground motion are studied as a function of the size of the cavity, its embedment depth, the frequency content of the excitation, the incidence angle and the distance from the axis of symmetry of the cavity itself. A simple application of Rayleigh's method allows us to verify that the ground surface response is dominated by the fundamental vibration mode of the portion of soil between the cavity and ground surface itself, in the frequency range of interest for engineering purposes. A simple relationship to estimate the fundamental natural frequency as a function of the embedment depth of the cavity is given. Finally, amplification factors on response spectra are obtained, to provide a practical insight into the effect of an underground cavity on surface ground motion during real earthquakes. Copyright © 2009 John Wiley & Sons, Ltd.     

两种不同势函数下半空间饱和多孔介质中Rayleigh波求解比较

分别对"考虑两种压缩波和幅值比例系数"和"考虑一种压缩波(P1或P2波)但不考虑幅值比例系数"两种不同势函数下的半空间饱和多孔介质中Rayleigh波求解进行详细推导,理论分析表明"考虑两种压缩波和幅值比例系数"下Rayleigh波求解推导更为严密,与饱和多孔介质中存在两种压缩波的事实相一致。在研究半空间饱和多孔介质中Rayleigh波时应采用"考虑两种压缩波和幅值比例系数"的势函数。