本文選題：波函數(shù)展開法　切入點：圓形夾塞　出處：《中國地震局工程力學(xué)研究所》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：大量計算數(shù)據(jù)顯示,淺埋夾塞圓弧凸起地形對地面運動有著明顯放大作用。目前針對這類問題的解析解很少,僅給出了淺埋空腔任意圓弧凸起地形和淺埋夾塞半圓弧凸起地形的解析解。因此本文做了以下工作:(1)本文基于波函數(shù)展開法和Graf加法公式,首次給出了地下圓形夾塞及任意圓弧凸起地形對二維出平面SH波散射的封閉級數(shù)解答,結(jié)合邊界條件引入兩個恒為零的輔助函數(shù),通過對邊界處條件方程組進(jìn)行傅里葉展開最終使問題簡化為對一組無窮級數(shù)代數(shù)方程組的求解。本文給出的解析解可退化為單獨考慮地形或夾塞(空腔)的解。(2)通過對無窮方程組進(jìn)行有限項的截斷計算我們得到了淺埋夾塞的圓弧凸起地形的地表位移幅值的數(shù)值結(jié)果,同時為了與其退化模型(僅存在地形和僅存在淺埋夾塞的情況)作對比,本文同時計算了退化模型的地表位移幅值,結(jié)果表明,SH波垂直入射下,淺埋夾塞的圓弧凸起地形退化到無夾塞和無地形的兩個模型后,當(dāng)兩者地面運動放大區(qū)域重合時,原模型對應(yīng)區(qū)域的地表位移一般明顯放大。另外,當(dāng)夾塞退化為空腔時,圓弧凸起部分某些頻率的位移幅值很大,且這些頻率具有明顯周期性,頻率值可通過半空間介質(zhì)波速及空腔到水平地表的距離確定。(3)由于淺埋夾塞圓弧凸起地形與其退化模型之間的關(guān)系,本文對純夾塞(空腔)水平地形和純凸起地形分別進(jìn)行了研究。研究發(fā)現(xiàn),當(dāng)?shù)叵虏痪鶆驑?gòu)造埋深加大和圓弧凸起地形高寬比減小時,地表位移幅值逐漸接近自由半空間,通過加大埋深和減小凸起地形高寬比,本文得到了可忽略對地表運動影響的夾塞埋深和凸起高寬比。(4)最后本文忽略波的二次反射后利用波的疊加原理簡單計算了半空間淺埋空腔時地表產(chǎn)生較大位移幅值的位置和頻率,與利用波函數(shù)展開法解析解得到的數(shù)值結(jié)果進(jìn)行對比發(fā)現(xiàn),該方法能較準(zhǔn)確的預(yù)測地表出現(xiàn)較大位移幅值的位置和頻率。另外,對于分析得到的垂直入射下地表在空腔圓心正上方點處的運動規(guī)律與已有結(jié)論一致。
[Abstract]:A large number of calculated data show that the shallow buried plug arc uplift has a significant effect on the ground motion. At present, there are few analytical solutions to this kind of problems. Only the analytical solutions of arbitrary arc raised terrain and shallow buried plug semi-circular arc raised terrain are given. Therefore, the following work is done in this paper: this paper is based on the wave function expansion method and the Graf addition formula. For the first time, the closed series solution for scattering of 2-D plane SH waves by underground circular plug and arbitrary arc raised terrain is given. Two auxiliary functions with constant zero are introduced in combination with boundary conditions. The problem is simplified to a set of infinite series algebraic equations by Fourier expansion of the equations of conditions at the boundary. The analytical solution given in this paper can be reduced to a solution which considers only the terrain or the stopper (cavity). By truncating the finite term of the infinite equations, we obtain the numerical results of the surface displacement amplitude of the circular arc uplift terrain with shallow plug. In order to compare with the degradation model (only the terrain and the shallow plug), the amplitude of the surface displacement of the degradation model is also calculated. The results show that the SH-wave is incident vertically. After the arc uplift of shallow buried plug degenerates to two models without clamping and no topography, when the ground motion amplification region of the two models coincides with each other, the surface displacement of the corresponding area of the original model is obviously enlarged. In addition, when the clamping plug degenerates into an empty cavity, The displacement amplitudes of some frequencies in the arc protrusions are very large, and these frequencies have obvious periodicity. The frequency value can be determined by the wave velocity of the half-space medium and the distance between the cavity and the horizontal surface. In this paper, the horizontal topography of pure plug (cavity) and the terrain of pure uplift are studied. It is found that when the buried depth of non-uniform underground structure increases and the ratio of height to width decreases, the amplitude of surface displacement gradually approaches the free half-space. By increasing the depth of burying and reducing the aspect ratio of the raised terrain, In this paper, the plugged depth and the ratio of height to width are obtained. Finally, after ignoring the secondary reflection of the wave, the superposition principle of the wave is used to calculate the large displacement amplitude of the surface when the cavity is shallow buried in half space. The position and frequency of the. Compared with the numerical results obtained by using the analytical solution of the wave function expansion method, it is found that this method can accurately predict the position and frequency of large displacement amplitude on the surface of the earth's surface. The law of the surface motion at the point directly above the center of the cavity under vertical incidence is consistent with the existing conclusions.
【學(xué)位授予單位】：中國地震局工程力學(xué)研究所
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：P315.9

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