彈塑性本構關係式於土石流之研究

The Study of Debris Flow with Elastoplastic Constitutive Equation

許秘嘉(Mi-Chia Hsu)

指導教授 ： 劉格非

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.2015.02114

摘要

在台灣由於地狹人稠，隨著社會經濟的持續發展，平地開發趨於飽和的狀況下，造成以前沒有使用的山坡地區陸續的開發使用，破壞了原有集水區的水土保持，尤其在地震以及豪雨發生時間密集的台灣來說，土石流災害更是頻繁的發生；因此土石流的防治與預警將顯得更為重要。

對土石流的預警來說，往往需要以動力分析的方式推導出適合的土石流方程式，而在過程中土石流的本構關係式的研究將成為土石流在動力分析上的重要依據。本研究即是在Julien and Lan(1991)所提出的二次本構式以及降伏應力將土石流分成弱剪層、強剪層的分層概念下，描述強剪層的黏性與慣性剪應力行為之外；並在原有的弱剪層本構關係式上加上線彈性本構理論，多考慮了應力與應變之間的關係。並在二維卡氏座標的描述下以尺度分析的方式得到在長波理論下的土石流控制方程式以及邊界條件，求解土石流體從靜止到啟動前一刻的非穩態解析解，以及土石流體啟動後形成穩態均勻流之後的解析解，並試著描述整個土石流從靜止開始運動至啟動，再至穩態均勻流的整個過程。希冀提供後續土石流在啟動以及強剪層為應力與應變率，弱剪層為應力與應變本構式的研究問題上，作為基本分析或數值實驗的參考。

關鍵字

土石流 ； 彈塑性理論 ； 本構關係式 ； 廣義的虎克定律 ； 尺度分析

並列摘要

In Taiwan, the population is dense, especially in the city. As the development of social economics.it is nearly saturated about the urban development. As a result, the development of slope land is unavoidable. Then, it destroys the soil and water conservation of the original watershed. Especially in the high frequency of earthquake and heavy rain in Taiwan. Debris flow disasters is more frequent occurrence, therefore mudslide prevention and early warning will become more important.

For early warning of debris flow, it often using the dynamic analysis to derive the governing equation of debris flow. In that case, the constitutive equation of debris flow will becomes very important in the process of derivation. In this study, based on Julien and Lan(1991), the constitutive equation of debris flow is divided into shear layer part and plug layer part. In shear layer, we considered the relation of shear stress and shear strain rate. In shear layer, we applied the linear elasticity and considered the relation of shear stress and shear strain.

With the continuity equation and momentum equation in Cartesian coordinate system and long wave assumption. We derived the new debris flow governing equation and tried to solve steady and uniform state and unsteady state. Wish can provide a new debris flow analytical solutions to becomes a reference of fundamental analysis or reference of numerical experiments.

並列關鍵字

Debris Flow ； Elastoplastic theorem ； Constitutive equation ； Scale analysis

參考文獻

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