Study on the SH-Waves Scattering from a Partially Filled Semi-Elliptical Alluvial Valley

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Project title

Code/計畫編號

NSC99-2221-E019-017

Translated Name/計畫中文名

半橢圓形部分填滿沖積山谷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=2109185

Year

2010

Start date/計畫起

01-08-2010

Expected Completion/計畫迄

31-07-2011

Bugetid/研究經費

446千元

ResearchField/研究領域

土木水利工程

"雖然過去已有很多研究者採用不同的方法，研究過SH 波入射時沖積山谷的地表反應，不過絕大多數是研究完全填滿的沖積山谷，就實際上而言，部分填滿比完全填滿是更符合實際沖積山谷的情況，所以我們曾經研究過“半圓形部分填滿沖積山谷＂的SH 波散射問題 (Tsaur & Chang, 2008, GJI, 173 (1), 157-167)；然而半橢圓形比半圓形能模擬更多實際的山谷地形，因此，SH 波入射情況下的“半橢圓形部分填滿沖積山谷＂的反應特性，對地震工程的研究會更具有參考價值，而且它比眾所周知的“半橢圓形空谷＂(Wong & Trifunac, 1974, EESD, 3, 157–169) 及“半橢圓形完全填滿沖積山谷＂ (Wong & Trifunac 1974, BSSA, 64, 1389–1408) 等種兩情形更具一般性。本計畫即擬針對 “半橢圓形部分填滿沖積山谷的SH 波散射問題＂進行研究，希望透過理論解析的方式來求解這個問題，首先，以半橢圓山谷的邊界將整個求解領域分割成一個內領域(部分半橢圓領域)和一個外領域(半無限領域)，然後各領域的位移場以Mathieu 函數展開來表示，接著應用Mathieu 函數的加法定理，或以適當的座標轉換把內領域的座標轉換至與外領域的座標一致，再以半橢圓邊界上應滿足的條件來建立聯立方程式，即可求出兩領域的各未知係數，得到此問題的級數解，然後以計算例探討不同半橢圓山谷形狀、沖積層厚度、地質參數等情況下，這種半橢圓部分填滿沖積山谷的地動反應特性及影響。另外，本研究的結果，亦可提供給其他數值方法作比對參考。" "The responses of ground motion of alluvial valley have been investigated by a lot of researchers adopting different methods in the past, but the studied alluvial valley that is fully-filled with overwhelming majority. In fact, the real situation of alluvial valley is partially-filled more than fully-filled. So we had studied SH-wave scattering problem that “the partially-filled semi-circular alluvial valley” (Tsaur & Chang, 2008, GJI, 173 (1), 157-167). However, the semi-elliptical shape than semi-circular fits more actual alluvial valley and topography. Such that, the response characteristic of the semi-elliptical partially -filled alluvial valley under SH-wave incidence is worth to research and consult for earthquake engineering. The results will be general than the well known two cases, “the semi-elliptical empty valley” (Wong & Trifunac, 1974, EESD, 3, 157-169) and “the semi-elliptical fully-filled alluvial valley” (Wong & Trifunac 1974, BSSA, 64, 1389-1408). This plan plans to carry on studying theoretically to “SH-wave scattering problem of the semi-elliptical partially -filled alluvial valley”. First of all, the analysis region is divided into an interior (partially semi-elliptical) and an outer (semi-infinite) region by the semi-elliptical cavity boundary. The displacement field of each sub-region is expressed in terms of an infinite series of Mathieu function. Then use the addition theorem of Mathieu function or the proper coordinate transformation to change the coordinate of the interior region to keeping the same with coordinate of the outer region. After imposing the traction-free condition on the partially semi-elliptical cavity surface and the matching conditions on the interface of the two regions, the unknown coefficients are obtained. Effects of valley shape, the thickness and material of the alluvial layer on the response of ground motion will be discussed with some numerical examples. In addition, the result of this research can also offer another criterion for other numerical solutions."

Keyword(s)

SH 波
散射
沖積山谷
馬修函數
SH waves
scattering
alluvial valley
Mathieu function

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Study on the SH-Waves Scattering from a Partially Filled Semi-Elliptical Alluvial Valley

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