利用Laplace轉換配合無因次化解析一維土壤入滲問題

本文共分為兩部份，第一部份推求於地表定量入滲時，表面未達飽和、具地下水位且均質土壤之含水量剖面，同時預測積水時間，並假設超滲降雨可及時排除不造成積水深度，計算積水後之土壤含水量剖面，此外並求解地表定量入滲時，表面未達飽和、半無限區域、均質土壤積水前之土壤含水量剖面解析解。第二部份則利用解析解探討不同性質土壤含水量剖面及積水時間特性。本文利用指數型水力傳導係數K_*＝K_se^(αφ)及保水曲線θ＝θ_γ＋（θ_s-θ_γ）e^(αφ)，推導線性一維入滲方程式並利用Laplace轉換配合無因次分析求得入滲解析解，並探討地下水水位及土壤臨前狀況對地表入滲之影響，本解析解假設之土壤特性雖不具一般性，但解析解之結果可供非飽和入滲數值模式之驗證。

關鍵字

定量入滲；解析解；土壤含水量剖面

並列摘要

There are two parts in this research. In the first part, water content profiles under constant surface infiltration rate toward the water table through homogeneous soil were derived before the ponding time. And the water content profiles after the ponding time were obtained under the presumption of no accumulation depth above the surface. Besides, the water content profiles of semi-infinite homogeneous soil were derived before the ponding time. In the second part, adapted the analytical solutions, the different characters of the water content profiles and the ponding time between different types of the soil were suggested. The Exponential functional forms of the hydraulic conductivity-pressure head K_*=K_se^(αφ) and the soil water retention curve θ=θ_r+(θ_s-θ_r)e^(αφ) were used to introduce the linearized one-dimension infiltration equation. The equation was solved by Laplace transform combined with dimensionless analysis and then the groundwater level and the ante moisture content influence on infiltration were discussed. Although these assumptions of the soil properties may be very restricted for any practical application, but the analytical solutions may serve as a means for verifying numerical models for the unsaturated flow.

並列關鍵字

Constant surface infiltration ； Analytical solution ； Water content profile

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