摘要
大型地下隧道结构对地震波的散射会影响隧道附近场地的地震动,进而会影响附近地面上的建筑物。因此,对此类问题的求解,不仅在理论上,而且在工程应用上都有着重要的意义。
本文采用一种特殊的边界积分方程法,研究了半空间内地下衬砌隧洞对弹性波P、SV、Rayleigh波的散射情况,介质内总波场由自由场和散射场叠加而得,根据单层位势理论,由虚拟源面上的分布线源构造散射波场,通过边界条件建立方程,求解得到虚拟波源密度,进而求得总的波场。
本文从边界条件的满足情况以及与现有解析解的对比两个方面来检验结果的正确性。研究了弹性入射P、SV波以及Rayleigh面波的不同入射波频率、入射角、衬砌材料的性质等因素对地下圆形衬砌隧洞附近场地的地表位移和衬砌隧洞洞周环向动应力集中因子的影响。数值结果表明,地下隧洞的存在对附近场地的地表位移以及洞室的动应力集中因子有很大的放大作用,柔性衬砌对中低频波的放大作用大一些,刚性衬砌对高频波的放大作用明显一些,刚性衬砌能够有效降低半空间介质中的应力。本文的研究对该领域的理论研究及工程应用都有重要的意义,为地下洞室群的抗震设计提供了科学依据。
Scattering and diffraction of earthquake waves by the large, underground tunnelstructures can affect the ground motion near the tunnels, still, it can also affect thebuildingsonthegroundnearby.Therefore,tosolvethiskindofproblemhasimportantmeaningonboththeoryandengineeringapplication.
In this paper, a special boundary integral equation method will be used to studythe scattering of elastic P、SV and Rayleigh waves by underground, circular linedtunnel. The total wave field is superposed by free field and scattered field. Based onthe theory of simple layer potential, scattered wave field is constructed by distributedlinesources onthe virtual source plane. The densityofthe virtual wavesource can begained by solving the equations which are derived by boundary conditions. Finally,thewholewavefieldcanbeachieved.
The accuracy of the numerical result is checked up by the analytic solution andresidual errors of boundary conditions. At the same time, the effects of some factorssuch as the frequencyof the incident waves, the incident angle, the lining’s propertieson the surface ground motion of the lined tunnels and the lining’s properties on thehoop stress amplitude on the wall of the lined tunnel are illustrated. The numericalresults show that, the underground tunnel will amplify the amplitude of the surfaceground motion and the dynamic stress concentration factor, the tunnel with soft linerhas great effect on the low frequency incident waves, while the tunnel with stiff linerhas great effect on the high frequency incident waves, and the tunnel with stiff linercan also decrease the stress in the half-space. And some useful conclusions arederived in this thesis, which have great significance both in theoryand in engineeringapplication and provide foundations for the anti-seismic design of undergroundcavities.
引文
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