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研究生:許子建
研究生(外文):Hsu Tzu-Jian
論文名稱:有限差分法於雷利波波傳反算之應用
論文名稱(外文):Applying Finite Difference Method to Process Inversion of Rayleigh Wave Propagation
指導教授:左天雄
指導教授(外文):Tso Tien - Hsiung
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:土木工程學研究所
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:1999
畢業學年度:87
語文別:中文
論文頁數:127
中文關鍵詞:有限差分法雷利波雷利波速剪力波剪力波速反算頻散曲線表面波
外文關鍵詞:finite difference methodRayleigh waveRayleigh wave velocityshear waveshear wave velocityinversiondispersion curvesurface wave
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本研究主要應用連續表面波試驗(Continuous Surface Wave Test,簡稱CSWT)之現地震測試驗,求得現地之頻散曲線(dispersion curve)。從實驗中,我們可以輸入一固定頻率(f )之震波,將得到之震測資料經過處理,可得到波長(L )。利用Vr=f*L ,即可得到雷利波速。雷利波速和波長的關係圖,即是頻散曲線。為了方便進行反算,則將左右兩側震測資料,共同進行多項式二次或三次迴歸。
在反算的方法上,本研究採用有限差分法來進行數值運算。利用有限差分法的原理,將2-D波傳理論,在平面應變的條件下,改寫成有限差分方程式。在本研究中,所採用的格點為600x600,邊界為鉸接(hinge),以震源位置垂直自由表面之軸線為對稱軸,並且考慮初始條件為所有應力狀態皆為零。震源以正弦波輸入。格點距離範圍為0.25∼2m,時步大小範圍為0.0001∼0.0005sec。反算的流程,則是先利用簡化法,猜測初步評估之地盤剪力波速與地盤厚度,代入有限差分法中,建立正算模式,以求得有限差分頻散曲線;再將所得之有限差分頻散曲線跟現地迴歸之頻散曲線比較,進行試誤法,直到有限差分所得之頻散曲線與現地頻散曲線吻合,則猜測之地盤剪力波速與地盤厚度,即為反算結果。
利用有限差分法對雷利波波傳所進行的反算,針對台大校園、士林百齡橋、台北民族公園SCPT比較結果,大致都相當符合。對花蓮和平電廠之跨孔法,亦有良好的結果。將各場址反算結果與簡化法加以比較,則簡化法較易有高估的現象。
The objective of this research is to get dispersion curve by using in situ test of the Continuous Surface Wave Test. In the test, we can get some data by inputting seismic waves of a specific frequency(f ) and then get wavelength(L ) by analyzing the data. By using Vr=f*L , we get the Rayleigh Wave Velocity. The graphic relationship of the Rayleigh Wave Velocity and wavelength is dispersion curve. In order to process inversion, we use 2 or 3 orders polynomial to deal with the new data which are combined with the data from left and right side seismic test, and then make a fitting curve.
As to the inversion, this research applies Finite Difference Method(FDM) to process numerical calculation. Based on FDM theory and the plane strain condition, we rewrite the 2-D wave propagation theory into finite difference equations. In this research, the mesh is 600x600 grids, the boundary condition is hinge, and symmetry axis is a vertical line which goes through the seismic source. Moreover, the initial condition of the stress state is zero. This research assumes that the seismic source is inputted by sine waves. The range of the grid size is 0.25m to 2m and the time step is from 0.0001 to 0.0005 second. The first step of the process of inversion is applying simplify method to assume the data of the shear wave velocity and thickness of layers, and input the assumed data to the finite difference equations for accomplishing forward model to get finite difference dispersion curve. Applying the Try and Error Method to compare the results of FDM dispersion curve and in situ dispersion curve. If the FDM dispersion curve matches the in situ dispersion curve, the results of this study indicate that the ground shear wave velocity and thickness of the layers are the final output of the inversion.
This research compares the inversion results and SCPT data of the National Taiwan University campus, Pai-Ling Bridge in Shi-Ling, and Ming-Tsu Park in Taipei, and the results indicate that the inversion results meet the SCPT. Furthermore, the comparison of the inversion result and the crosshole method test in Ho-Ping Power Plant in Hua-Lien is satisfying. Comparing the inversion results of different locations to the simplify method, the latter is likely to be over-estimation.
第一章 導論1
1.1 前言1
1.2 研究動機與目的2
1.3 研究內容3
第二章 文獻回顧5
2.1 震波之相關背景5
2.2 雷利波與波傳反算相關研究5
2.3 有限差分法於波傳反算之相關研究7
第三章 波傳理論與有限差分法10
3.1 無限均質等向性線彈性介質中之波傳理論10
3.2 半無限空間均質線彈性之波傳理論14
3.3 波傳理論之有限差分分析法23
3.3.1 有限差分方程式23
3.3.2內部格點25
3.3.3 外力作用格點27
3.3.4 自由表面格點28
3.3.5 數值穩定條件29
3.3.6 數值震盪之分析29
第四章 連續表面波試驗(CSWT)設備與試驗方法35
4.1 試驗設備35
4.2 試驗方法36
第五章 試驗場址介紹39
5.1 台大校園39
5.2 五股工業區39
5.3 士林百齡橋39
5.4 台北市民族公園40
5.5 花蓮和平電廠40
5.6 蘆洲抽水站40
第六章 連續表面波分析方法47
6.1 試驗資料分析方法47
6.2 以簡化法初步反算土層動態參數48
第七章 速度-應力有限差分法之正反算模式61
7.1 正算模式61
7.2 反算模式62
第八章 分析結果與討論68
8.1 台大校園68
8.1.1 連續表面波試驗結果68
8.1.2 反算分析69
8.2 五股工業區70
8.2.1 連續表面波試驗結果70
8.2.1 反算分析70
8.3 士林百齡橋71
8.3.1 連續表面波試驗結果71
8.3.2 反算分析72
8.4 台北市民族公園72
8.4.1 連續表面波試驗結果72
8.4.2 反算分析73
8.5 花蓮和平電廠73
8.5.1 連續表面波試驗結果73
8.5.2 反算分析74
8.6 蘆洲抽水站75
8.6.1 連續表面波試驗結果75
8.6.2 反算分析75
8.7 綜合討論75
第九章 結論與建議106
9.1 結論106
9.2 建議107
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中文參考文獻
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