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。     

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。     

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。     

饱和土半空间中地下圆形衬砌洞室对平面SV波的散射

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,通过对舍有衬砌洞室的局部场地进行波场分析,得到饱和土半空间中圆柱形衬砌洞室对平面SV波的散射问题的解析解。经验证,本文得到的解可以退化为半空间单相介质的情况。通过与已有的单相弹性介质半空间中圆柱形衬砌洞室对平面SV波散射问题的解析解的对比,验证了此解的正确性。在解析解的基础上,数值计算给出洞口动应力集中放大系数,分析了入射频率和孔洞埋深对柱面上的应力集中因子的影响。     

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。     

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.     

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．      

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（Ⅰ）——方法及验证

利用间接边界元法, 求解了弹性层状半空间中无限长洞室对斜入射平面SH波的三维散射问题. 通过与文献结果进行对比, 验证了本方法的正确性. 与工程中常用的二维模型比较表明, 工程中将三维散射问题简单地分解为平面内问题和平面外问题的做法存在较大误差. 文中并研究了斜入射角度对散射的影响, 表明斜入射角度对地表位移幅值有着重要影响.      

弹性地基中波阻板对入射Rayleigh波的远场被动隔振研究

针对被保护结构下埋置波阻板的远场被动隔振问题,采用频域弹性边界元法,推导得到了弹性地基中波阻板对入射Rayleigh波散射的边界元方程,在此基础上对波阻板的远场被动隔振效果进行了计算,并对影响波阻板隔振效果的因素进行了分析。研究结果表明:在地基一定深度设置波阻板能够有效降低波阻板上方及后方区域的地面振动;减小波阻板埋深以及增大波阻板厚度均能获得更好的隔振效果;而增加波阻板的剪切模量是提高波阻板被动隔振效果的最有效措施。     

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…     

A series solution for surface motion amplification due to underground twin tunnels: incident SV waves

A series solution of displacement response of the ground surface in the presence of underground twin tunnels subjectcd to excitation of incident plane SV waves is derived by using Fourier-Bessel series expansion method. The numerical parametric study shows that underground twin tunnels significantly amplify the nearby surface ground motion. It is suggested that the effect of subways on ground motion should be considered when the subways are planned and designed.     

Effects of underground cavities on Rayleigh waves—Field and numerical experiments

This paper presents the results of a multi-channel analysis of surface waves (MASW) test conducted over near-surface mine workings, with the objective of delineating the underlying. Numerical studies were carried out to explain and extend the results. The displacement time histories at the surface show amplitude changes in the region over the void, and the Fourier spectra show significant energy concentration on and in the vicinity of the cavity. Different numerical models are constructed and the responses at the surface of the medium and around voids of different sizes and embedment depths are monitored. The numerical results show that part of the incident energy is trapped within the void. The trapped energy bounces back and forth inside the void, until it is attenuated by radiation. The effect of the trapped energy is seen as a concentration of energy over the void region in the frequency domain. The amount of trapped energy is a function of the size and embedment of the void, as well as of the frequency content of the source. The void absorbs part of the energy and radiates it as body waves. Therefore, the recorded responses at the surface carry valuable information about the void. The characteristics of the void can be extracted from the surface responses by analyzing the responses in time, frequency, and spatial domains.     

Transverse response of underground cavities and pipes to incident SV waves

The transverse response of underground cylindrical cavities to incident SV waves is investigated. Analytical solutions are derived for unlined cavities embedded within an elastic half‐space using Fourier–Bessel series and a convex approximation of the half‐space free surface. The computed displacements at the half‐space free surface and the tangential stresses on the cavity are compared with the results of previous investigations. The analytical solutions are extended to formulate approximate solutions for assessing hoop stresses within cavity liners impinged by low‐frequency waves having wavelengths much longer than the cavity diameter. The approximate solutions are compared to existing numerical solutions, and used to evaluate the dynamic response of a flexible buried pipe shaken by the 1994 Northridge earthquake. The proposed approximate model for cavity liners is useful for the seismic analysis of underground pipes and small‐diameter tunnels. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

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.     

Apparent phase velocities and fundamental-mode phase velocities of Rayleigh waves

Rayleigh wave dispersion data usually appear in the form of multimodal spectra for a layered model structure. The number of dispersion modal curves depends on the number of layers in the model. The measured dispersion velocities from the frequency–wavenumber (F–K) space, however, may not represent the true phase velocities of the fundamental-mode dispersion curve, but apparent phase velocities. The present study discusses how multimode curves are generated in the multichannel analysis of surface waves (MASW) method and the cause of the apparent velocity produced by the F–K method. Results from a field trial demonstrate that apparent phase velocities fail to reveal thin layers with low velocities. A better agreement of the inverted model with the geotechnical record is obtained by using the data points extracted from the fundamental-mode curve of the MASW spectral image.