Study on the Scattering Problem of SH Waves by an Isosceles Triangular Hill

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簡歷

基本資料

Project title

Code/計畫編號

MOST103-2221-E019-009

Translated Name/計畫中文名

等腰三角形山峰引致SH波散射問題之研究

Project Coordinator/計畫主持人

Deng-How Tsaur

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Harbor and River Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=8360260

Year

2014

Start date/計畫起

01-08-2014

Expected Completion/計畫迄

31-07-2015

Bugetid/研究經費

423千元

ResearchField/研究領域

土木水利工程

由於一些實際山峰地形的斷面形狀趨近於三角形，因此，在以往凸起地形與地震波互制的研究中，不論是數值或理論方法相關，等腰三角形的簡化模型皆很常被拿來演示。Hayir 等人[Soil Dyn. Earthq. Eng. 21, 603-613 (2001)]曾應用波函數展開法探究等腰三角形山峰承受 SH波作用的反應，然而，Qiu與 Liu [Earthq. Eng. Eng. Vib. 4, 37-46 (2005)]認為他們針對山峰區域所構建的波函數並不滿足Helmholtz方程式，而這個錯誤導致他們的計算結果與 Sánchez-Sesma等人[Bull. seism. Soc. Am. 72, 473–490 (1982)]利用邊界法所得的結果差異頗大。因此，Qiu 與 Liu 企圖以複變函數法來修正 Hayir等人的錯誤，但可惜的是，Qiu與 Liu得到的結果仍與 Sánchez-Sesma等人的結果有所出入。於是，我們就利用邊界元素法檢驗 Qiu與 Liu所給出的計算例，發現他們的計算結果確實無法與邊界元素解相符合。因此，本年度(103 年)計畫，擬以《等腰三角形山峰引致 SH 波散射問題之研究》為主軸，期能透過「領域媒親技巧」的使用，搭配較妥當的「領域分割」策略及合適的「波函數」表示式，來求解這樣一個問題。預計將針對不同物理參數改變時，對山峰附近地動反應的影響做一系列分析與探討。本計畫成果將可提供給其他數值方法作為驗證比對之用，亦可作為地震工程或地球物理相關領域的研究做參考。 "Since some real mountain topographies are similar to triangles in cross-section, the simplified models with isosceles triangular shape are adopted frequently in numerical/theoretical studies pertaining to the interaction between convex topographies and seismic waves. Hayir et al. [Soil Dyn. Earthq. Eng. 21, 603-613 (2001)] applied the method of wavefunction expansions to analyze the response of isosceles triangular hills subjected to incident SH waves. However, Qiu & Liu [Earthq. Eng. Eng. Vib. 4, 37-46 (2005)] pointed out that the wavefunctions in the hill region do not satisfy the Helmholtz equation. Such a mistake leads to apparent disagreement between the results of Hayir et al. (2001) and those computed by Sánchez-Sesma et al. [Bull. seism. Soc. Am. 72, 473–490 (1982)] using the boundary method. Hence, Qiu & Liu (2005) attempted to utilize the complex-function method to correct the errors in Hayir et al. (2001). Unfortunately, the results of Qiu & Liu (2005) were still not consistent with those obtained by Sánchez-Sesma et al. (1982). In view of this point, we exploit the boundary-element method to check all the cases shown in Qiu & Liu (2005), and consequently find that the results of Qiu & Liu (2005) cannot be validated by our boundary-element solutions. Thus, this project is mainly aimed at exploring the problem of SH-wave scattering induced by an isosceles triangular hill. The region-matching technique, together with a suitable strategy of domain decomposition and the appropriate wavefuncions, is adopted to deal with this issue. Effects of various physical parameters on ground motions within the mountain area and neighboring regions are evaluated and discussed. The results obtained from this project will provide helpful validation data for other numerical methods and serve as a useful reference to pertinent investigations in earthquake engineering or geophysics."

Keyword(s)

SH波
散射
山峰
波函數
SH wave
scattering
hill
wavefunction

DSpace CRIS

Study on the Scattering Problem of SH Waves by an Isosceles Triangular Hill

基本資料

Description