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研究生:蔡義誌
研究生(外文):Yi-Zhih Tsai
論文名稱:不飽和土壤水力傳導度與介質孔隙分佈關係之研究
論文名稱(外文):Studies of Relationships between Unsaturated Soil Hydraulic Conductivity and Pore Size Distribution of Media
指導教授:林俐玲林俐玲引用關係
學位類別:博士
校院名稱:國立中興大學
系所名稱:水土保持學系所
學門:農業科學學門
學類:水土保持學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:中文
論文頁數:163
中文關鍵詞:水力傳導度孔隙半徑孔隙分佈粒徑分佈曲線水分特性曲線
外文關鍵詞:Hydraulic conductivityPore radiusPore-size distributionParticle size distribution curveWater characteristic curve
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  土壤內的水分移動與該介質的孔隙分佈情形,有著密不可分的關係。因此,本研究以Arya和Kosugi的理論為基礎,推導出兩個一維垂直流動的水力傳導度函數式,此兩函數式為孔隙半徑與水力傳導度的關係式,用以呈現孔隙半徑(r)對於不飽和水力傳導度(K)的影響。(公式略)式中K(θi)為第i個水分含量分段的水力傳導度(L T-1);ΔΨm為基質勢能(L);Δz為深度(L);rj為第j個粒徑分段之土壤顆粒平均半徑(L);wi為第j個分段之質量比例(M M-1);ψ是孔隙度(L3 L-3);c和x是參數。K為不飽和水力傳導度(L T-1);Ks為飽和水力傳導度(L T-1);Se為有效飽和度(L3 L-3);r為孔隙半徑(L);rg為幾何平均孔隙半徑(L);rmax為孔隙半徑最大值(L);σ為ln(r)的標準偏差。這兩個函數式的水力傳導度估算值與瞬間剖面法的實測值,以均方根誤差(RMSE)檢驗分別為RMSE = 0.508和RMSE = 0.553,均比van Genuchten的水力傳導度函數式(RMSE = 0.766)來得佳,代表能以物理模式及經驗參數合理地描述孔隙半徑與水力傳導度之關係。
  以四種質地不同的土樣進行實驗分析,分別為粘質壤土、壤土、砂質壤土及石英砂,求取所須參數及實測資料。由實驗取得的資料,包括基本理化性質、粒徑分佈、水分特性曲線及水力傳導度;經由模式或迴歸分析計算而得的資料,計有孔隙半徑(r)、孔隙半徑最大值(rmax)、幾何平均孔隙半徑(rg)及ln(r)標準偏差(σ),乃至於單一孔隙體積流量(qsi)的無維度參數x和c。以這些資料應用於上述的函數式之中,可得四種土樣的孔隙半徑與水力傳導度之關係。依此關係而言,較小的孔隙半徑有著較小的水力傳導度;反之,大的孔隙半徑具有較大的水力傳導度。
  再將土柱實驗以瞬間剖面法所求得的水力傳導度,代入上列兩函數式反求等效孔隙半徑(re),並由這些等效孔隙半徑的分佈情形,呈現出土壤剖面內的孔隙分佈。最後,並以兩個剖面深度5 cm (z5)和13 cm (z13)來展現不同深度之孔隙半徑分佈。
There is inseparable relation between moisture movement in soil and pore size distribution of porous media. Therefore, this study developed two one-dimensional vertical flow hydraulic conductivity functions which are based on Arya and Kosugi model. The functions were developed by applying pore radius to present the influence of pore radius (r) on unsaturated hydraulic conductivity (K). (公式略) Where K(θi) is the hydraulic conductivity (L T-1) corresponding with water content θi (L3 L-3); ΔΨm is matric potentials (L); Δz is depth (L); rj is the mean pore radius (L) for the jth pore fraction; wi is the mass ratio (M M-1) for the jth pore fraction from particle-size fraction; ψ is total porosity (L3 L-3); c and x are parameters. K is unsaturated hydraulic conductivity (L T-1); Ks is saturated hydraulic conductivity (L T-1); Se represents the effective saturation (L3 L-3); r is the pore radius (L); rg is the geometric mean pore radius (L); rmax is the maximal pore radius (L); andσis the standard deviation of ln(r). The calculated hydraulic conductivity from these two functions and observed hydraulic conductivity from instantaneous profile method are tested by root mean square error (RMSE). The RMSE of these two functions are 0.508 and 0.553 respectively, all are better than the RMSE of van Genuchten’s hydraulic conductivity function (RMSE = 0.766). The result showed that the relationship between pore radius and hydraulic conductivity can be expressed reasonably by physical function and their empirical parameters.
Four soil samples with different texture were collected and analyzed. The soil texture for four soil samples are clay loam, loam, sandy loam and quartz sand. The soil physical properties and required parameters for developing function were measured by the experiments. The measured data sets include basic properties, particle size distribution, water characteristic curve and hydraulic conductivity of soil samples. The parameters which computed from models or regression analysis have pore radius (r), maximal pore radius (rmax), geometric mean pore radius (rg), standard deviation (σ) of ln(r). Furthermore, the dimensionless parameters x and c of volumetric flow rate for a single pore (qsi) can be calculated. These data sets and parameters are applied to develop two functions that was mentioned before. The relevant functions expressed by pore radius and hydraulic conductivity of four soil samples were obtained. And that smaller pore radius has lower hydraulic conductivity, otherwise, larger pore radius has higher hydraulic conductivity.
The hydraulic conductivity data which observed by instantaneous profile method on sandbox experiment in the laboratory, were substituted into two functions. Equivalent pore radius (re) can be determined from hydraulic conductivity data according to two functions. The distribution of any amount of equivalent pore radius presented pore-size distribution in soil profile. Finally, pore radius distribution of different depth which at two soil profile depth 5 cm (z5) and 13 cm (z13) were displayed.
中文摘要 i
英文摘要 iii
目錄 v
表目錄 vii
圖目錄 viii
符號說明 xii

第一章 緒論 1
 第一節 前言 1
 第二節 研究目的與動機 3
   一、研究動機 3
   二、研究目的 3
第二章 前人研究 4
 第一節 水分移動模式及發展 4
 第二節 Arya理論與模式發展 8
   一、孔隙半徑 9
   二、水分含量 11
   三、水分特性與水力傳導度 12
 第三節 Kosugi理論與模式發展 13
   一、孔隙分佈 14
   二、水分含量 15
   三、水分特性與水力傳導度 16
 第四節 不飽和水力傳導度之經驗模式及量測方法 17
第三章 理論基礎 19
 第一節 土壤內之水分流動 19
 第二節 孔隙半徑與水力傳導度 24
   一、基於Arya model的函數式推導 24
   二、基於Kosugi model的函數式推導 26
第四章 研究材料與方法 29
 第一節 研究材料 29
 第二節 研究方法及流程 31
   一、研究方法 31
   二、研究流程 31
   三、實驗方法及步驟 35
第五章 結果與討論 48
 第一節 土壤理化性質 48
 第二節 粒徑分佈曲線 51
 第三節 水分特性曲線及參數α、n 54
 第四節 土柱排水實驗結果與水力傳導度 59
 第五節 推求孔隙半徑及其分佈 74
 第六節 單一孔隙體積流量qsi及參數c、x 79
 第七節 水力傳導度與孔隙半徑之關係 83
 第八節 土柱的等效孔隙半徑分佈估算 107
 第九節 不同深度之孔隙半徑分佈 129
第六章 結論 144
參考文獻 148
中文文獻
圖書
1.林俐玲 (1996),土壤物理學實習手冊,國立中興大學。
2.萬鑫森 譯 (1987),基礎土壤物理學,國立編譯館主編,茂昌圖書有限公司發行。
3.張舒婷 (2007),土壤水分特性曲線與不飽和水力傳導度之研究,國立中興大學水土保持學系碩士論文。


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