Theory of infiltration: infiltration into swelling soils in a material coordinate

Su, Ninghu (2010) Theory of infiltration: infiltration into swelling soils in a material coordinate. Journal of Hydrology, 395 (1-2). pp. 103-108.

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Abstract

The majority of infiltration equations in use today were developed for infiltration into rigid porous media based either on the classic diffusion equation or empirical formulation. In this paper, we present new equations of infiltration into swelling soils derived from the fractional Fokker–Planck equation (fFPE) of flow in swelling porous media formulated in a material coordinate. The cumulative infiltration we derived is I(t) = At + Stβ/2, where S is the fractional sorptivity, A the final infiltration rate, and β the order of fractional derivative in the fFPE. Using the data published in the literature on cumulative infiltration against time, β, S and A are determined. The determined value of β = 0.2385 for this reported soil is much less than 1.0 which implies that infiltration into this specific swelling soil belongs to the category of sub-diffusion. We show that the new cumulative infiltration equation not only fits the reported data exceptionally better than Philip’s two-term infiltration equation, more importantly, it provides fresh explanation and understanding of infiltration into swelling media. The new infiltration equation deviates from the majority of infiltration equations which were developed for rigid soils and ignore the realistic swelling and shrinking properties of the soils.

Item ID: 15229
Item Type: Article (Refereed Research - C1)
Keywords: infiltration, swelling porous media, super-diffusion, sub-diffusion, fractional Fokker–Planck equation, anomalous diffusion
ISSN: 0022-1694
Funders: Xiangtan University; James Cook University
Date Deposited: 18 Jan 2011 02:33
FoR Codes: 04 EARTH SCIENCES > 0404 Geophysics > 040403 Geophysical Fluid Dynamics @ 30%
01 MATHEMATICAL SCIENCES > 0105 Mathematical Physics > 010599 Mathematical Physics not elsewhere classified @ 30%
05 ENVIRONMENTAL SCIENCES > 0503 Soil Sciences > 050305 Soil Physics @ 40%
SEO Codes: 96 ENVIRONMENT > 9614 Soils > 961402 Farmland, Arable Cropland and Permanent Cropland Soils @ 50%
96 ENVIRONMENT > 9611 Physical and Chemical Conditions of Water > 961103 Physical and Chemical Conditions of Water in Fresh, Ground and Surface Water Environments (excl. Urban and @ 50%
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