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題名 | 應用等通量原則與土壤水力特性函數參數化等價未飽和水力傳導係數=Equivalent Hydraulic Conductivity Parameterization Based on Constant-Flux Principle and Soil Moisture Characteristic Functions |
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作者 | 李天浩; 馮智勇; Lee, Tim Hau; Feng, Chih-Yung; |
期刊 | 中國土木水利工程學刊 |
出版日期 | 20070600 |
卷期 | 19:2 2007.06[民96.06] |
頁次 | 頁199-211 |
分類號 | 441.12 |
語文 | chi |
關鍵詞 | 廣義達西定律; 未飽和土壤; 等價水力傳導係數; 理查氏方程式; 參數化; 有限差分; 等通量; 土壤水分特徵函數; 數值模擬; Generalized Darcy's law; Unsaturated soil; Equivalent hydraulic conductivity; Richards' equation; Parameterization; Finite difference; Constant flux; Soil moisture characteristic function; Numerical simulation; |
中文摘要 | 本研究利用廣義達西定律通量為定值的原理,以有限差分網格為單元,將水力傳導係數函數對壓力水頭積分;令此積分等於等價水力傳導係數乘以網格兩端節點壓力水頭差值的方式,決定等價水力傳導係數。由於符合土壤水力特性曲線型態,若為穩態狀況,此等通量等價水力傳導係數為廣義達西定律的解析解,在各種壓力水頭梯度和空間間距下,都可獲得完全正確的估計值。使用砂土與黏土的Brooks and Corey形式土壤特徵函數為例,藉由改變有限差分網格濕潤相飽和度與壓力水頭梯度的方式,以等通量等價水力傳導係數為參考,比較與算術平均、幾何平均、調和平均等三種權重水力傳導係數估計值,發現當有限差分網格兩端的壓力水頭差異愈大時,三種權重方法估計等價水力傳導係數的誤差也愈大。 利用具備局部質量守恆特性的未飽和數值模式,模擬文獻砂柱試驗數據,在定流量邊界條件下,由於進入土壤的水量已知,使用算術平均、幾何平均以及等通量等價水力傳導係數等三種參數化方法的模擬結果均能正確掌握濕鋒的位置;在定水頭邊界條件下,採用等通量等價水力傳導係數,在不同數值網格大小下,均能正確估計進出控制體積的流量,相對而言,使用幾何平均權重估計模擬結果的誤差相對較大。誤差除了與網格大小有關外,也和土壤水力特性函數相關。 |
英文摘要 | Based on the constant-flux principle of the Generalized Darcy's Law, this study assumes constant-flux and integrates hydraulic conductivity along the flow path with respect to pressure head within a finite difference block (FDB). The constant-flux equivalent hydraulic conductivity (CF EHC) is defined as the integral divided by the pressure head difference across the FDB. For the integral comprises soil moisture characteristic functions, the CF EHC is the analytical solution of Generalized Darcy's Law under steady condition. Therefore, it is free of error in flux estimate despite the pressure heads, gradients and grid size. The CF EHC flux estimates applying Brooks-Corey sol moisture characteristic functions are used to evaluate the arithmetic-mean (AM), geometric-mean (GM), and harmonic-mean (HM) of hydraulic conductivities at 2 ends of FDB. Since the Brooks-Corey soil moisture curves are monotonic functions, comparison results reveal that flux estimates of the weighting techniques all lend to be more biased as the saturation gradient increases. Different EHCs are applied with a local mass-conserved scheme to simulate 1-D infiltration. The results are compared to experiment data for performance evaluation. When the surface boundary condition is Neumann type, i.e. given flux, simulation results with all 4 EHC techniques are close to infiltration experiment data. However, for Dirichlet boundary condition, simulation results using the CF EHC is closer to the experiments' compared to those using AM and GM weighted EHC. The magnitude of error depends not only on gird size but also on soil moisture characteristic functions. |
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