裂縫入滲及Hele-Shaw模擬土體之滲流特性分析

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姓名

李伯亨(Bo-Heng Lee) 查詢紙本館藏

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土木工程學系

論文名稱

裂縫入滲及Hele-Shaw模擬土體之滲流特性分析
(The Effects of Crack Infiltration and Hele-Shaw Modeling the Seepage Flow)

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摘要(中)

本文重點在於探討未碰觸底床(不透水層或岩盤)之裂縫暫態入滲特性，並討論以裂縫內水深為坡體上游，沿著底床穩態滲流形成之自由滲流液面(簡稱滲流表面線)與坡體下游邊界之滲出點高程。本文實驗主軸以Hele-Shaw模型實驗，觀測裂縫暫態入滲濕鋒範圍、流量等特性，分析以Green-Ampt (G-A) 假設所推導之一維及擬二維裂縫暫態入滲公式的適用範圍，再根據一維G-A裂縫入滲理論，建立隨裂縫入滲濕鋒範圍變化之孔隙水壓模式。進而，裂縫內持續供水造成下游滲出點及坡體內滲流表面線，此範圍內之滲流對土體產生負面效應。本文利用鋁粉加入Hele-Shaw模型兩板內，以流線分析討論滲流於水平及傾斜底床之滲出點與滲流表面線特性。
本研究將裂縫入滲濕鋒由外而內分為目視乾濕界面、G-A 濕鋒及飽和濕鋒等三種，以G-A 濕鋒理論推導配合砂箱及Hele-Shaw 模型進行分析與比較。一維G-A理論解適用於土壤性質為飽和水力傳導係數小、毛細效應較大及裂縫水深較大之條件，適用時間較長，孔隙水壓公式適用於此條件；反之，類比於粗顆粒土壤之Hele-Shaw結果，飽和水力傳導係數大、毛細效應較小，需要較大之裂縫水深或極小之兩板間距，方可克服重力效應，因此適用時間較短。當無因次入滲時間進入重力效應顯著階段，本文以有效寬度入滲概念，推導以等值寬度入滲之擬二維G-A理論式，並利用入滲濕鋒為A1及A2上、下兩個無因次曲線組成，可推求濕鋒形態、範圍與流量。
於穩態滲流部分，先以加入鋁粉之Hele-Shaw實驗分析流線，再以理論解析探討水平底床之滲流表面及滲出點特性，並建立隨底床角度變化之無因次滲出點高程與無因次滲流表面線公式。於水平底床滲流理論解加入隨堆積土體厚與上游水深比值呈冪次增加之B參數，所得之無因次公式較Kashef模式及Dupuit模式符合實驗流況。實驗利用兩板間距、流體密度、上游定水頭高度與堆積土體厚比值等參數控制滲流表面及滲出點有無受毛細高度及出口阻力之影響。實驗結果顯示靜壓水頭符合由表面向下遞減之拋物線假設。本理論解之滲流表面及滲出點高度與實驗結果頗相近。當上下游水深度比值大於0.9、上游水深與堆積土體厚比值小於0.1時，Dupuit假設與水平底床滲流理論解相近。於傾斜底床滲流部分，分為傾斜入出流條件與垂直入出流條件，利用流線分析資料，建立與水平底床滲流有關之無因次滲流表面線與無因次滲出點高程，用以預測不同坡度與上游水位高所造成之滲出點高程。本研究之水流成果有助於了解現場堆積顆粒或邊坡破壞機制。

摘要(英)

This study explores the 2-D transient seepage flow and steady flow from cracks into different porous media, including both coarse material and fine material. The Crack Apparatus of Hele-Shaw Model is chosen to analyze the configuration of wetting front in the coarse material. Due to the effect of gravity on the flow condition, the wetting front in the coarse material is more elongated than that of the fine material. The limited width of wetting front is approaching a constant value in the coarse material. On the other hand, the effect of capillary causes the wetting front in the fine sand expands continuously as time increases. In this paper, a Green-Ampt type of conceptual model is proposed to describe the propagating process of the wetting front in different materials. The time-dependent wetting front and the corresponding wetted area are obtained in this study, which are beneficial for examining the leaky contaminant transport from cracks into different porous media or for the analysis of the slope stability problems.
The second topic of this study is development and validation of an analytical solution for the flow through horizontal and sloping bed. The parameter, B, shown in the analytical solution of horizontal bed increases with the increasing ratio of width to upstream level. The Hele–Shaw model is employed to examine the phreatic surface and exit point of seepage flow by adjusting gap width and fluids density. Aluminum powders were used to as tracking particles inside the gap and the flow visualization was performed. Both horizontal and sloping bed, the phreatic (free) surfaces and exit points are in good agreement between experimental data and the analytical solution. The assumption of a parabolic piezometric head was verified by experimental data. In the horizontal bed, the ratio of down-upstream water depth is large than 0.9 and the ratio of upstream depth -width is less than 0.1, the solution based on Dupuit model is close to the analytical solution.

關鍵字(中)

★ Green-Ampt
★ 裂縫
★ Hele-Shaw 模型
★ 濕鋒
★ 滲流表面線
★ 滲出點高程

關鍵字(英)

★ Green-Ampt
★ crack
★ Hele-Shaw
★ wetting front
★ phreatic surface
★ exit point.

論文目次

摘要 i
Absract iii
誌謝 iv
目錄 v
表目錄 viii
圖目錄 ix
符號表 xv
第一章序論 1
1-1 研就動機 1
1-2 研究方法與目的 1
1-3 論文架構 2
第二章二維裂縫暫態入滲過程 4
2-1 非飽和邊坡存在裂縫之降雨入滲模式 4
2-1-1 坡面開始積水時間 5
2-1-2 坡面垂直入滲量求算 6
2-1-3 裂縫上游逕流水進入裂縫之產生條件 6
2-1-4 裂縫入滲量之求算 6
2-1-5 裂縫內部積水時間 8
2-1-6 整體坡面逕流產生 9
2-2 隨入滲濕鋒變化之孔隙水壓 9
2-2-1 土層表面入滲之孔隙水壓分析 9
2-2-2 裂縫入滲孔隙水壓分析 10
2-3 裂縫入滲之實驗配置與步驟 10
2-4 裂縫對非飽和邊坡穩定之影響 16
2-4-1 模式流程分析 16
2-4-2 裂縫邊坡基本資料 17
2-4-3 非飽和裂縫邊坡入滲結果與討論 18
2-5 裂縫G-A理論式(式(2.5)、(2.7)、(2.8))之適用性探討 21
2-5-1 裂縫砂箱入滲濕鋒之特性 21
2-5-2 Hele-Shaw模型裂縫入滲濕鋒之特性 26
2-6 重力效應顯著後之暫態入滲特性 32
第三章邊坡內滲流表面及滲出點之特性分析 38
3-1 水平底床滲流之滲流表面線及滲出點高程 39
3-1-1 水平底床滲流理論解析 39
3-1-2 以Hele-Shaw模擬水平底床滲流之配置與步驟 44
3-1-3 水平底床滲流之靜壓水頭驗證 46
3-1-4 值隨x些微變化之討論 48
3-1-5 水平底床滲流之滲出點高程討論 50
3-1-6 水平底床滲流之滲流表面線比較 52
3-1-7 水平底床滲流之Dupuit適用範圍 56
3-2 傾斜入流條件於傾斜底床之滲流表面線及滲出點高程 57
3-2-1 傾斜入流(Inclined inflow)條件時之基本假設 57
3-2-2 傾斜底床滲流之靜壓水頭討論 58
3-2-3 傾斜入流於傾斜底床之滲出點高程討論 61
3-2-4 傾斜入流於傾斜底床之滲流表面線討論 63
3-3 垂直入流條件於傾斜底床之滲流表面線及滲出點高程 72
3-3-1 垂直入流(Vertical inflow)條件時之滲流表面線 72
3-3-2 垂直入流條件時之滲出點高程討論 87
第四章結論與建議 90
4-1 結論 90
4-2 建議 93
參考文獻 94

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指導教授

周憲德(Hsien-Ter Chou)

審核日期

2008-11-17

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