Study on the SH-Waves Scattering from a Crescent Alluvial Valley

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Project title

Code/計畫編號

NSC97-2221-E019-060

Translated Name/計畫中文名

新月形沖積山谷SH波散射之研究

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=1718591

Year

2008

Start date/計畫起

01-08-2008

Expected Completion/計畫迄

01-07-2009

Bugetid/研究經費

428千元

ResearchField/研究領域

土木水利工程

"關於部分填滿之沖積山谷，過去的研究者大多採用數值方法來評估它的地動反應，而當場址之地形地質構造過於複雜或者是相關資料不足時，就會採用一些簡化模型來近似模擬。在現今電腦科技的幫助下，儘管各種五花八門的數值方法迅速發展，使得研究者能夠在個人電腦上輕易地處理龐大的運算量，可是，數值解的精度和可靠度還是得仰賴正確解析解來予以評估，尤其是在較高頻的情況下，正確解析解更是網格分割數量與計算效率之間取得平衡的標準。不過，令人感到遺憾的是，從西元1971 年迄今，只有極少數的簡單幾何形狀才有正確解析解，而最經典的就屬半圓形及半橢圓形這兩種形狀，這是因為它們的斷面與座標系統相符合，可直接使用分離變數法來求解偏微分控制方程式的緣故，所以成為後來眾多文章的比對標準。另外，有些地表地質構造的分佈形態會近似於一個新月的形狀，例如：希臘的Volvi 沈積盆地及法國的Ubaye 沖積山谷。因此，基於上述的理由，本研究計畫擬提出“新月形沖積山谷＂這種理想的簡化模型，然後使用領域媒親技巧搭配Graf 加法公式，推導出平面SH 波入射情況下的嚴密級數解，並探討沖積層之厚度、材質改變時，對頻率域及時間域之地動反應的影響。希望透過本計畫的理論分析結果，能夠讓我們更深入瞭解這種部分填滿之沖積山谷的反應特性。此外，我們所推導的嚴密級數解，不但填補了前述之正確解析解極為匱乏的缺憾，而且補充了現存解析資料庫的內容，同時，亦提供了另一種比對基準給其它數值方法做參考。最後，值得一提的是，不久前我們已經成功完成“半圓形部分填滿之沖積山谷＂的理論分析，所以，我們相信能夠順利完成此計畫。" "As to the partially-filled alluvial valley, previous researchers usually use numerical methods to estimate the ground motion response. When the topographic and geological conditions of the site are very complicated or the corresponding information is not accessible, they may use several simplified models to simulate these local configurations approximately. Nowadays, with the aid of computer technology, the miscellaneous numerical methods develop very fast, and the researcher can easily handle the enormous calculations via personal computer. However, the assessment of the accuracy and reliability of numerical solutions still rely on the exact analytical ones, which are also the balance between the number of mesh grids and computation efficiency, especially for higher frequency ranges. Nevertheless, it is much to be regretted that after 1971 exact analytical solutions are only available for a few simple geometric shapes. The representative cases are the semi-circular and semi-elliptical shapes, and which are also the benchmarks for numerous studies. This is because their surfaces coincide with the corresponding coordinate systems, so that the separation of variables can directly applied to solve the partial differential governing equation. Besides, the distribution pattern of some surface geological structures is close to the crescent shape such as the Volvi sedimentary basin in Greece and Ubaye alluvial valley in France. Therefore, for the above-stated reasons, this research project proposes an idealized, simplified model, that is, a “crescent alluvial valley”. By means of the region-matching technique and Graf’s addition formula, we intend to derive a rigorous series solution for the plane SH-waves incident case. Effects of the thickness and material of the alluvial layer on the frequency- and time-domain response of ground motion will be discussed. Through results of the theoretical analysis presented in this work, we hope we can deeply realize the response characteristic of this kind of partially-filled alluvial valley. In addition, the rigorous series solution derived herein not only replaces aforementioned regret for the lack of exact analytical solutions, but also enriches the content of the existing database for theoretical solutions. At the same time, it provides another criterion for other numerical solutionsFinally, it is worth to say that we have confidence in accomplishing this project since a few times ago we have successfully completed the theoretical analysis of “a partially-filled semi-circular alluvial valley”."

Keyword(s)

SH 波
散射
沖積山谷
場址效應
SH-waves
scattering
alluvial valley
site effect

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Study on the SH-Waves Scattering from a Crescent Alluvial Valley

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