應用權重最小二乘局部近似法於土石流之數值模擬研究

Numerical Simulation of Debris Flows with Weighted Moving-least-square Local Approximation

莊哲凱(Che-Kai Chuang)

指導教授 ： 蔡丁貴

國立臺灣大學/工學院/土木工程學研究所/碩士(2015年)

https://doi.org/10.6342/NTU.2015.01884

摘要

台灣位於板塊交界帶，於板塊推擠作用下，使得台灣地質狀態相當脆弱，加上降雨集中、氣候變遷以及人為山坡地開發等影響，導致土石災害發生更加頻繁，每當土石災害發生，不僅造成下游地區人民之生命財產損失，災後的整治也造成社會資源上極大負擔。
本研究主要以無網格數值計算方法中權重最小二乘局部近似法，分析土石流於堆積段(即山坡地、河谷等)之運動情形，並以解析解及室內實驗結果來驗證本模式的精準度。試圖建立一套土石流數值模式，作為土石流防治工程及土石流預警之應用工具。本研究以淺水波方程式為基礎，結合O’Brien & Julien (1985)提出之土石流本構關係式，建構用以描述土石流之數學模型。
本模式之正確性，由黃 (2003)推導之解析解及洪 (2011)室內實驗，得到良好驗證。配合土石流潛勢溪流調查及航空攝影測量取得現場數值高程模型資料，無須網格建置，即能快速求得土石流動情形及其漫淹範圍，藉以提供土石流防治工程及土石流預警之參考依據。

關鍵字

淺水波方程式 ； 土石流 ； 本構關係 ； 局部多項式近似 ； 權重最小二乘法 ； 無網格數值方法

並列摘要

Taiwan is located in the convergence of tectonic plates. The plate-tectonic movement makes Taiwan’s geological status quite vulnerable. On top of that, the concentrated rainfall, climate change, hillside development, and other influences cause the land disasters to occur more frequently. In the land disaster, it not only causes the loss of life or property of the local resident, but the remediation also is a huge burden for the society.
In this research, the weighted moving-least-square local approximation method of the mesh-less method is used to analyze the debris flow in the movements of the deposition regions (mountain slopes, valleys, etc.). An analytical solution and laboratory experimental results are introduced to verify present model’s accuracy.
This research uses the shallow water equations as the bases, combining the constitutive relation model of debris flow proposed by O’Brien & Julien (1985) to construct the mathematical model to characterize debris flows. The model has a good verification performance comparing with the analytical solution derived by 黃 (2003) and the laboratory experiments conducted by 洪 (2011).
The established numerical model of debris flow can be used in debris flow prevention schemes and debris flow warning tools. Combining the data of potential debris flow stream and on-site DEM from authority, the debris flow movements and influence range can be rapidly obtained, without numerical grid construction. The model can efficiently provide information for the provision of debris flow hazard.

並列關鍵字

shallow water equations ； debris flow ； constitutive relation ； local polynomial approximation ； weighted moving-least-square method (WLS) ； mesh-less method

參考文獻

24. 洪啟耀，「以小尺度模型實驗模擬土石流形貌變化與流變參數之關係」，國立台灣大學土木工程學研究所碩士論文，2011。

25. 姜國正，「以修正有限配點法模擬水波港池共振問題」，國立台灣大學土木工程學研究所碩士論文，2012。

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