A Numerical Study on Water Well Resonance Induced by Pre-earthquake signals

王俊翔(2006)以正規擾動法(regular perturbation method)與分離變數法(separation of variables method)證實了由地震所產生的微小之前兆壓力入射波，經由挶限含水層傳播進入水井，將產生自由水面之共振現象，且其共振頻率之影響因素只與水井半徑有關。本研究延伸王俊翔(2006)，擴充其解析解所不及之處，將水井濾管側壁設置一活動之通水孔，以三維線性邊界元素法求解通水孔開口大小對水井內、外部流況之影響，以提供建立地震預警觀測警系統設計之參考。 本研究之理論係以達西定律(Darcy’s law)及微小振幅波理論(small-amplitude water wave)分別探討經由挶限含水層傳遞之微小地震前兆壓力波及水井內部之波場。文中假設水井內部為非黏性、非旋性，以及不可壓縮之理想流體；而水井外部之波動媒介為多孔介質流體，固體則為剛性多孔介質結構。 本研究除了確實地找到地震前兆引發水井產生共振的機制外，亦發現了濾管通水孔大小與水井內部流速勢成一線性關係，是一很有趣的發現。另外，本研究探討當水井側壁濾管通水孔開口很小時，在水井外部流場是否會有繞射的情形產生，而由研究結果可得知水井外部流場並無繞射之情形。 由於此一數值模式的建立，僅需給定一已知的地震前兆入射波，即可求得觀測水井設置一活動開孔後之流場流況，本研究對於有關地震監測預警觀測井設計等工程應用，應能有所助益。Wang (2006) used regular perturbation method and separation of variables method to prove that the incident flow of the tiny pressure wave of the pre-earthquake signals passing through confined aquifer then penetrating into the well causes the occurrence of resonance at free surface. And only the radius of well can affect resonance frequency. This study tries to improve the shortcoming of analytic solution what Wang (2006) used. Setting a movable hole on the screen of well and applying three dimensional linear boundary element method (BEM) to solve problem of how the opening level of hole affects the flow inside and outside the well.arcy’s law and the small amplitude wave theory are adopted in this study to investigate the wave fields in the confined aquifer and in the water well respectively. In this study, it is assumed that the water in the well is incompressible, inviscid and irrotational, and the water outside the well is porous-media fluid with rigid structure.his study indeed finds the mechanism of resonant phenomenon of pre-earthquake signals, and also finds the relationship between the size of screen hole and the velocity potential on the screen hole to be linear. Besides, this study tries to find that when the screen hole of the well is very small whether diffraction happens outside the well or not. According to the result, diffraction doesn’t happen outside the well.fter setting this numerical model, we can get the flow field of well which has a movable hole through putting a known pre-earthquake signal incident wave. The study is be helpful in analyzing the well resonance and designing the observing water wells as the earthquake alert system.中文摘要 Ibstract II錄 IV目錄 VI目錄 VII號說明 X一章 導論 1.1 研究動機 1.2 文獻回顧 4.3 研究內容與方法 5.4 章節介紹 6二章 地震前兆引致水井水面共振數學模式之建立 8.1 地震前兆引致水井水面共振之邊界值問題 8.1.1控制方程式 8.1.2邊界條件 10.1.3邊界值問題之建立 13.2地震前兆引致水井水面共振問題之正規擾動法…..............15.2.1 擾動展開尺度函數之探討 16.2.2 正規擾動法展開之邊界值問題 20三章 數值方法 24.1 邊界積分式理論及推導 25.2 二維四邊形元素介紹與轉換建立 26.3 數值積分－高斯積分法 29.4 三維Laplace方程式之線性邊界元素法 30.5 水井外部邊界積分式之修正與處理－影射法 32.6 數值模式之驗證 34四章 數值模式之應用 37.1 地震前兆入射波 37.2 模式的計算 38.3 模式的應用 40五章 結論與建議 64.1 結論 64.2 建議 65考文獻 67錄A 三維線性邊界元素法奇異項處理 69錄B 王俊翔(2006)研究中之共振特徵頻率參考文獻 7