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。     

地下衬砌洞室对Rayleigh波的放大作用

本文利用波函数展开法,给出了半空间中圆形衬砌洞室引起的Rayle igh波散射问题的一个级数解,并通过对求解技术的改进,获得了高频解答。论文通过入射波长、洞室直径、衬砌刚度和埋置深度等参数分析,研究了地下洞室对Rayle igh波的放大作用。数值结果表明,地下洞室情况下地表位移幅值可以达到无洞室情况的2.6倍以上;多数情况下,柔性衬砌洞室情况地表位移幅值最大,无衬砌洞室情况次之,刚性衬砌情况最小。     

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。     

大型岩体洞室采用柔性垫层减震的可行性研究

采用无限元作为岩体地下洞室静动力分析的边界条件,建立了岩体地下洞室的静动力有限元一无限元(FE-IE)计算模型,分析了柔性垫层对水电站厂房这类大型岩体洞室结构的减震效果.研究结果表明:柔性垫层虽未能从根本上改变岩体洞室结构的地震响应,但是设置一定厚度的柔性垫层后不仅能充分发挥岩体洞室围岩的自承能力,而且还能明显地减小混...     

地震作用下大型地下洞室群应力传播特征研究

选用攀枝花-会理地震波,通过基线校正和高频滤波,作为实际地震动输入,利用FLAC3D软件对某水电站大型地下洞室群进行了地震作用下应力传播特性的研究。数值分析结果表明,洞室群周围应力时程的变化趋势与输入加速度时程的变化趋势相似,但由于地震波的传播需要一定的时间,因此存在一定的滞后效应。洞室边墙出现了一定面积的拉应力区,随着输入加速度的增大,拉应力区的范围有所扩展,但是扩展的范围不大。所得结果对大型地下洞室群地震动传播特征问题的研究具有一定的参考意义。     

水工地下厂房岩体洞室地震反应问题分析

我国西南部地区新建和在建的一些大型水电站工程中地下发电厂房均形成主体为大型岩体的地下洞室群,合理估计地震作用下这些大型地下洞室群的反应是一个亟待解决的问题.为了对水工地下厂房岩体洞室结构地震反应数值分析问题进行探讨,回顾了该类工程在我国的发展现状,总结了该类工程的结构特点和震害特点,并基于一些典型的地下洞室地震反应数值分析结果,阐述了水工地下厂房岩体洞室地震反应数值分析中应当关注的问题和研究方向.     

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.     

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.     

节理岩体地下洞室群的地震动力响应分析

节理岩体开挖后经常形成楔形体，对大型地下洞室顶拱和边墙的稳定笥构成威胁。地震的动力作用将加剧块体的运动，进而影响洞室的整体稳定性，合理地评价高烈度地区大型地下洞室的稳定性具有现实意义。节理岩体中地下结构的动力响应与稳定性分析目前研究较少。本文采用了动力离散元法分析了大型地下洞室群的动力响应，认为地下结构并不能完全免于震害，高烈度地震对于节理岩体中的地下结构有明显影响。     

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(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.      

Diffraction of plane SV waves by a cavity in poroelastic half-space

This paper presents an indirect boundary integration equation method for diffraction of plane SV waves by a 2-D cavity in a poroelastic half-space.The Green’s functions of compressive and shear wave sources are derived based on Biot’s theory. The scattered waves are constructed using fi ctitious wave sources close to the boundary of the cavity, and their magnitudes are determined by the boundary conditions. Verifi cation of the accuracy is performed by: (1) checking the satisfaction extent of the boundary c...     

P波入射时含圆柱形空腔板弹性波散射与动应力集中

采用波函数展开法给出了板的横截面处孔洞在平面P波入射下动应力集中问题的解。本文使用大圆弧假定法来满足板中的自由表面的边界条件。数值结果表明,上表面和孔洞间的距离与下表面和孔洞间的距离都对结果有影响。如果孔洞半径相对板的厚度很小,解近似等于孔洞全空间解。所给出的解是半解析解。因此能被用来验证诸如BEM,FEM,FDM等数值法。     

Diffraction of obliquely incident waves by a cylindrical cavity embedded in a layered viscoelastic half-space

The three-dimensional harmonic response in the vicinity of an infinitely long, cylindrical cavity of circular cross-section buried in a layered, viscoelastic half-space is obtained when the half-space is subjected to homogeneous plane waves and surface waves impinging at an oblique angle with respect to the axis of the cavity. The solution is obtained by an indirect boundary integral method based on the use of moving Green's functions for the viscoelastic half-space. Numerical results describing the motion on the ground surface and the motion and stresses on the wall of the cavity are presented for obliquely incident P-, SV-, SH- and Rayleigh waves with different horizontal angles of incidence.     

The effect of an interface boundary layer on the resonance properties of a buried structure

This paper presents a model for the analysis of the diffraction of plane waves at a cavity in an infinite homogeneous linear elastic medium supported by a segmented lining. An elastic boundary layer is introduced between the cavity lining and the infinite medium. The boundary layer is simulated by ‘elastic boundary conditions’ in which the stress is proportional to the relative displacement of the lining and of the surrounding medium boundary. A closed‐form analytical solution of the problem was obtained using the Fourier–Bessel series, the convergence of which was proven. It was shown that the number of series terms required to obtain a desired level of accuracy can be determined in advance. Using amplitude–frequency response analysis it was shown that the boundary layer produces additional ‘pseudo‐resonance’ frequencies that depend on the layer properties. These frequencies are almost identical to the eigenvalues obtained from the simple analysis of a segmented elastically supported lining. Copyright © 2003 John Wiley & Sons, Ltd.     

Time-domain boundary element method in viscoelasticity with application to a spherical cavity

The weighted-residual technique, the indirect boundary element method, the truncated indirect boundary element method and the direct boundary element method can be used to analyse nonlinear soil-structure interaction in the time domain. They are illustrated and compared by using the one-dimensional dynamic problem of the spherical cavity in an infinite space. For realistic time steps, all formulations lead to accurate results, but the weighted-residual technique and the truncated indirect boundary element method are much more efficient than the direct boundary element method in the time domain. Hysteretic damping leads to noncausal behaviour, which can, however, be neglected from a practical point of view.     

Peak surface motion due to scattering of plane harmonic P,SV, or Rayleigh waves by a rough cavity embedded in an elastic half-space

Scattering of plane harmonic P, SV, or Rayleigh waves by a two-dimensional rough cavity completely embedded in an isotropic elastic half-space is investigated by using a direct boundary integral equation method. The cavity’s roughness is assumed to be in the form of periodic or random perturbations of arbitrary amplitude superimposed to a smooth elliptical shape. For the randomly corrugated cavities the normal or the uniform probability distribution functions are assumed. Based on multiple random cavity results, the corresponding average surface response is computed. These are compared with the corresponding periodically corrugated and smooth cavity responses. The surface response is evaluated for different cavity shapes and incident waves and for a range of frequencies. The surface motion results are used to determine the peak surface motion frequencies. They depend strongly upon the basic inclusion shape (the principal axes) and the nature of the incident wave. Strong similarity in the peak surface motion frequencies can be observed for the rough and smooth cavity models for both circular and elliptical shapes. In order to quantify the importance of the cavity corrugation upon the surface motion, a roughness influence factor is defined in terms of the rough and smooth cavity surface responses. This factor strongly depends upon the type of the incident wave, the nature of the cavity corrugation, the basic cavity shape, and the frequency. The factor clearly shows the effect of the cavity roughness upon the surface motion.     

Water exclusion from tunnel cavities in the saturated capillary fringe

The problem of water flow around a tunnel cavity located in the saturated capillary fringe on top of a very permeable, freely draining substratum is considered for the critical non-leakage condition when there is uniform vertical downward flow through the upper surface of the saturated region. In this critical condition the soil–water pressure is equal to zero everywhere on the cavity wall that is also a streamline. The conditions at the upper fringe boundary are that the soil–water pressure is equal to the air-entry value of the soil and the flux through this surface is the uniform infiltration rate. The cavity surface and the fringe boundary which is elevated above the cavity position, are found through conformal mapping and the use of integral representations of non-standard mixed boundary-value problems. They are calculated for a range of infiltration rates and compared with those obtained by assuming the upper fringe boundary to be horizontal. The exact analysis given here gives larger tunnel cavities than those given by the approximate treatment of the problem. The results have application in the design of underground repositories against entry of seepage water, the construction of protective capillary barriers and in the design of interceptor drainage systems.     

Transient response of finitely long cylindrical cavity with arbitrary cross-section

A semi-analytical boundary element method is developed for the efficient time-domain dynamic response analysis of a finitely long cylindrical cavity with an arbitrary cross-section geometry. High computational efficiency is achieved by mapping a complex shape of the cross-section into a circular shape. For this purpose a special coordinate transformation equation is presented. This mapping enables us to discretize the boundary element equation only along the longitudinal axis of the cavity. The versatility and accuracy of the method are amply demonstrated through a number of examples. The transient stresses and displacements are found to be considerably influenced by the slenderness ratio, length over diameter of the cavity and the incidence angle of the incident wave.     

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。