臺灣博碩士論文加值系統

地下水從岩盤出滲會升高其上層土體的孔隙水壓及降低土體的抗剪阻力，甚至引發崩塌，因此岩盤滲水是引發崩塌的重要因子之一。本研究探討岩盤滲水引發土體崩塌及崩塌後的運動特性。參照Iverson(2005)的做法，以牛頓第二運動定律建立無限邊坡崩塌土體之運動控制方程式，並以擴散方程式描述孔隙水壓的傳遞行為。有別於Iverson(2005)使用有限差分法求解前述方程式，本研究以柴比雪夫配置法將土體運動之控制方程式及孔隙水壓擴散方程式轉化為一階常微分方程，並搭配使用四階Runge-Kutta方法求解此一階常微分方程。
Iverson(2005)只討論均勻岩盤滲水對土體崩塌及崩塌運動的影響，本研究分析三種非均勻岩盤滲水率對土體崩塌及崩塌運動特性之影響。岩盤滲水率分布包括前峰型、中峰型及後峰型等三種非均勻分佈。計算結果顯示岩盤滲水率分佈的差異會影響土體崩塌時間點及崩塌後運動特性。運動控制方程式的抗剪阻力項受到孔隙水壓影響，因此崩塌運動的起始時間及特性都受到孔隙水壓的影響。對於前峰型岩盤滲水率分佈者，因為岩盤滲水前期出滲速率快，孔隙水壓力累積也快，因此崩塌的時間點較早；崩塌發生後的運動特性同樣受制於孔隙水壓，對於後峰型岩盤滲水率分佈者，岩盤滲水在前期出滲速率較低，雖然前期孔隙水壓累積較慢，但後期土體崩塌開始之後，岩盤滲水率較大，滑動阻力較小，崩塌土體移動速度較快。本研究分析比較前峰型、中峰型及後峰型等三種岩盤滲水率分佈對崩塌發生時間及滑動速度的影響。

A mathematical model clarifies how diverse styles and rates of landslide motion can result from regulation of Coulomb friction by dilation of watersaturated basal shear zones. Evolution of orbits in the phase plane of landslide velocity and basal dilatancy-induced pore pressure with impact of bedrock groundwater exfiltration was studied in the framework of the models of Iverson and Schaeffer(2008) and Iverson(2005).In these models, the velocity of block of soil sliding down an inclined plane is governed by Newton’s equation of motion, while the excess pore pressure, induced by dilatation of basal shear zone, is described by diffusion equation and coupled with the landslide velocity through a basal boundary condition that is expressed in the form of Darcy’s law. In this study, those governing equations are transformed to a system of first-order time ordinary differential equations by using the Chebyshev collocation method. Then a fourth-order Runge-Kutta scheme was employed to solve this initial-value problem to obtain the evolution of the phase orbits. we follow D’Odorico’s method (2005) to build three distribution type of nonuniform exfiltration rates to simulation how influence is the dependence on the hyetograph structure. Numerical simulations result show different case of distribution type of bedrock exfiltration rates that can produce difference trigger time and style of landslide motion. Case of ahead peak exfiltration distribution type can faster trigger landslide than another case, and postponed peak distribution type of bedrock exfiltration rates trigger time of landslide is later, but it can faster arrived at the same specified sidtance.

中文摘要 I
Abstract II
誌謝 V
目錄 VII
圖目錄 IX
表目錄 XI
符號說明 XII
第一章 緒論 1
1.1 研究動機與目的 1
1.2 本文架構 2
第二章 文獻回顧 3
2.1 崩塌的定義 3
2.2 水流滲透誘發的崩塌 4
第三章 控制方程式 15
3.1 基礎理論 15
3.2 運動控制方程式 21
3.3 擴散控制方程式 24
3.3.1 滲透孔隙水壓擴散方程式 24
3.3.2 超額孔隙水壓擴散方程式 25
3.4 無因次化控制方程式 28
第四章 數值計算方法 31
4.1 數值計算流程 31
4.2 滲透孔隙水壓擴散方程式的解 32
4.3 超額孔隙水壓擴散方程式數值解 34
4.3.1 配置法(Collocation Method) 34
4.3.2 柴比雪夫多項式 35
4.4 耦合控制方程式之系統矩陣 38
第五章 地下水出滲分析 50
5.1 穩定之岩盤出滲速率 50
5.2 非穩定之岩盤出滲速率 56
5.2.1 岩盤滲水出滲速率分佈型態建立 56
5.2.2 岩盤滲水出滲速率之時間間距 60
5.2.3 地下水出滲速率分佈型態差異 69
第六章 結論與建議 73
6.1 結論 73
6.2 建議 74
參考文獻 75

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