出平面波作用下地下复杂衬砌结构的地震动研究

采用复变函数、Green函数方法研究了SH波作用下,地下圆形衬砌与多个裂纹复合缺陷的地震动问题。求解关键是构造适合所需的Green函数,即含圆形衬砌的弹性半空间内任意一点承受时间谐和的出平面线源荷载的位移函数的基本解。再结合裂纹"切割"方法在任意位置上构造多个任意长度的裂纹,求得圆形衬砌和多个裂纹同时存在情况下的位移场与应力场。最后通过算例,进一步探讨不同参数对水平地表地震动的影响规律。     

圆形隧洞对地下地震动的影响:SH波入射

地下结构对地震波的散射改变了场地的动力特性,无论是地上建筑还是地下结构的安全评价和抗震设计中,目前均没有很好的考虑由于地下结构的存在对原场地地震动尤其是地下地震动的影响。基于弹性波动理论,运用波函数展开法和镜像原理,分析了弹性半空间中圆形隧洞对柱面SH波的散射问题,得到了含圆形隧洞的弹性半空间位移解析解。通过数值算例分析了圆形隧洞对原场地地震动的影响,重点考察了隧洞埋深、隧洞半径和围岩衬砌模量比等参数的影响规律。结果表明,地下结构对沿线场地的动力特性有着显著的影响,对其自身以及沿线工程结构的抗震设计提供一定参考价值。     

分离式双圆形隧道衬砌对平面SH波的散射

采用波函数展开法,将入射、散射和折射SH波的位移势函数展开成Fourier-Bessel函数的级数形式,根据Graf加法定理,得到了任一局部圆柱坐标系下的波场势函数的表达式.根据隧道衬砌与周围岩体都在界面处应力和位移连续及衬砌内边界完全自由的边界条件,得到了分离式双隧道衬砌对入射平面,SH波的多重散射问题的理论解.通过数值计算分析得出:入射频率、衬砌间距、衬砌与围岩的模量比及衬砌的厚度等是影响衬砌内侧的无量纲位移和动应力集中因子分布的重要因素,为双衬砌或多衬砌的地震评价提供了理论依据.     

SH波入射时等腰三角形与半圆形凸起地形的地震动

利用复变函数和移动坐标研究了等腰三角形凸起和半圆形凸起地形对SH波的散射.首先将求解区域分为三个部分,区域I为一个带有半圆形弧线的等腰三角形区域,区域II为含有两个半圆形凹陷的弹性半空间,区域III为包括半圆形凸起在内的圆形区域.在区域I中构造满足在腰三角形斜边上应力自由的驻波函数WA,在区域II中分别构造两个半圆形凹陷的散射波WB和WC,且两者均预先满足水平界面上应力为零的边界条件,在区域III构造一个上半部边界应力为零,而其余部分位移、应力任意的驻波函数.将所研究的问题转换成一个求解满足在"公共边界"上位移应力连续的问题.可利用坐标移动方法,通过傅立叶级数展开,建立该问题代数方程组,并采用截断有限项的方法对其进行求解.最后,给出了一个算例.     

地下夹塞断面形状随机性对平面SH波散射的影响

采用波函数展开法及边界离散的方法给出了任意断面形状的地下夹塞对平面SH波散射的半解析解; 利用蒙特卡罗方法随机模拟产生了30组夹塞断面样本, 通过对该样本在平面SH波入射下地表位移幅值的统计分析, 研究了夹塞断面形状随机性对平面SH波散射的影响. 结果表明, 夹塞断面形状随机性对平面SH波的散射具有重要影响. 以圆形夹塞为例, 当断面半径的变异系数为0.1时, 地表位移响应幅值变异系数可达0.71. 随着入射频率的升高, 变异系数逐渐增大; 随着夹塞刚度的降低, 变异系数逐渐增大; 随着夹塞埋深的增加, 变异系数逐渐减小.     

SH波入射时半圆形凸起地形附近浅埋圆形衬砌结构的动应力分析

本文给出了地下圆形衬砌结构与地面上的半圆形凸起地形对垂直于地面入射的SH波散射问题的解答。方法是将求解区域分割成两部分。其一为包含半圆形凸起地形在内的圆形区域Ⅰ，其二为带有一个半圆形凹陷和一个圆形衬砌结构的弹性半空间Ⅱ，半圆形凹陷部分为其公共边界，在区域Ⅰ和Ⅱ中分别构造其位移解，然后再通过移动坐标，使其满足“公共边界”上的条件和地下衬砌的边界条件，建立起求解该问题的无穷代数方程组。最后，本文给出了算例，并讨论了数值结果，给出了圆形衬砌结构周边上的动应力集中系数变化规律。     

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。     

半无限空间界面附近SH波对圆形衬砌的散射

建立了求解半无限空间中SH波对浅埋圆形衬砌结构的散射与动应力集中问题的解析方法。利用SH波散射的对称性和多极坐标的方法，在复平面上构造出了一个可以预先满足半空间自由表面上应力自由的边界条件的浅埋圆形衬砌对稳态SH波散射的波函数，并构造出衬砌内的散射波函数。然后根据衬砌周围的边界条件，将该问题转化为对一组无穷代数方程组的求解。最后给出了具体算例，并讨论了其数值结果。     

SH波在浅埋多个圆孔处的散射与地震动

研究了以任意方向入射的平面SH波在浅埋多个圆孔处的散射与地震动问题。利用SH散射的对称性和多极坐标方法构造了问题的位移解。当入射波的波长与圆孔的半径相比较小时,地震动将受到较大的影响。影响地震动有三个主要参数:(1)SH波的入射角α0;(2)入射波波数η,即圆形孔洞的半径与入射波半波长之比;(3)诸圆孔的埋置情况,诸孔的埋深hi/ai、孔心距Di/ai,即圆形孔洞至表面距离与圆半径之比和圆形孔洞中心的距离与半径之比。当η较大时,地震动幅值变化激烈,位移幅值可出现跳动和放大的现象。当诸圆孔的最小埋深量hi/ai和孔心距Di/ai超过10-12时,位移幅值恢复至半空间单一圆孔散射的情况,表明圆形孔洞的影响可被忽略。     

Surface motion of a semi-elliptical hill for incident plane SH waves

A closed-form analytical solution of surface motion of a semi-elliptical cylindrical hill for incident plane SH waves is presented. Although some previous analytical work had already dealt with hill topography of semi-circular and shallow circular, our work aims at calculating surface motion of very prolate hill for high incident frequency, and explaining the special vibrating properties of very prolate hill. Accuracy of the solution is checked by boundary conditions, numerical results for surface motion of oblate and prolate hills are calculated, and some conclusions are obtained.     

弹性层状半空间中沉积谷地对入射平面SH波的放大作用

对Wolf理论进行拓展,使之可解决沉积谷地对波的散射问题,进而利用间接边界元法,求解了弹性层状半空间中沉积谷地对入射平面SH波的放大作用问题。通过自由场反应分析,求得假想边界上各点的位移和各单元的应力反应。施加虚拟均布荷载,求得位移和应力的格林函数。根据应力和位移连续边界条件确定虚拟分布荷载,将自由场反应和虚拟分布荷载产生的反应叠加起来,即得到问题的解答。最后,以基岩上单一土层中沉积谷地对入射平面SH波的放大作用为例进行了数值计算分析,结果表明,层状半空间中沉积谷地和均匀半空间中沉积谷地对波的放大作用存在显著差别。文中分析了造成差别的原因,并讨论了覆盖层厚度和刚度对放大作用的影响。     

弹性层状半空间中凸起地形对入射平面SH波的放大作用

对Wolf理论进行拓展,使之可解决凸起地形对波的散射问题,进而利用间接边界元法,求解了弹性层状半空间中凸起地形对入射平面SH波的放大作用问题。本文模型的显著特点之一是考虑了层状半空间的动力特性以及层状半空间和凸起地形的阻尼;特点之二是计算精度高。文中以基岩上单一土层中半圆凸起地形对入射平面SH波的放大作用为例进行了数值计算分析。研究表明,基岩上单一土层中凸起地形对入射平面SH波放大作用和均匀半空间中凸起地形有着本质的差别;土层动力特性不仅影响凸起地形地表位移的幅值,还会影响地表位移的频谱;阻尼会显著降低凸起地形对高频波的放大作用。     

Scattering of plane SH waves by a circular- arc hill with a circular tunnel

IntroductionEarthquakedamageinvestigationsandtheoreticalanalysesshowthatahillamplifiesincidentwavestremendouslyduetomulti-reflectionofthewaveswithinthehill;notabledynamicstressconcentrationisobservedonwallofatunnel(Pao,Mow,1973;Lee,Trifunac,1979).Therefore,itmaybeassumedthattheexistenceofatunnelinahillmighthavegreateramplificationeffectonthegroundmotionnearby,andthedynamicstressconcentrationofthetunnelinthehillmightbemorenotable.Itiscommonthattherailwaysorhighwaysarethroughahilloramountainwi…     

2.5D scattering of incident plane SH waves by a canyon in layered half-space

This paper presents 2.5D scattering of incident plane SH waves by a canyon in layered half-space by the indirect boundary element method (IBEM). The free field response is carried out to give the displacements and stresses on the line which forms boundary of the canyon. The fictitious uniform moving loads are applied to the same line to calculate the Green’s functions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The displacements due to the free ...     

Surface motion of a cylindrical hill of circular-arc cross-section for incident plane SH waves

A closed-form solution of two-dimensional scattering of plane SH waves by a cylindrical hill of circular-arc cross-section in a half-space is presented using the wave functions expansion method. The solution is reduced to solving a set of infinite linear algebraic equations, using the auxiliary functions and the exterior region form of the Graf's addition theorem. Numerical solutions are obtained by truncation of the infinite equations and their accuracies are demonstrated by convergence of the numerical results and by the extent to which the numerical results fit the exact boundary conditions with increasing the truncation order. The numerical results for some typical cases are then presented for checking accuracies of various numerical methods. The effects of the height-to-width ratio of the hill on surface ground motion are finally illustrated.     

长应力波对于深部隧道衬砌的作用

应力波与隧道衬砌的相互作用问题为岩石力学的一个十分复杂的问题,到目前为止还没有得到圆满的解决。对于考虑介质与结构弹塑性性质的课题,解析解更难以求得。研究表明长波与深地下硐室的作用问题可以用拟静法解答。本文用拟静法研究了考虑岩体塑性性质时长纵波与地下硐室的相互作用问题。并获得了确定长应力波对于隧道支护作用的解析解。     

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.