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Infiltration into Two-Layered Soil: The Green–Ampt and Averyanov Models Revisited

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Abstract

Infiltration into a two-layered soil (continuum scale) is studied by the Green–Ampt (GA) model where the rate of infiltration (wetting front propagation) is a non-monotonic and discontinuous function of time. Both a constant ponding depth and a ponding level falling due to evaporation and infiltration are studied theoretically and in column experiments. The triads of saturated conductivity, porosity and front pressure in the two zones, as well as gravity, control vertical infiltration. Another model on the scale of a straight cylindrical capillary uses the Averyanov regime of a film flow, modified to include a front which is a quarter of a torus, rather than a spherical cap in a standard Washburn–Lukas model. The rate of front propagation is controlled by the Newtonian viscosity, tube-film sizes, surface tension, contact angle and gravity. For both scales, Cauchy problems for ODEs with respect to the front position are solved by computer algebra integration. In the field, pedon description and textural analysis of sedimentation-controlled layering are done. Of particular note is the thick cake deposited from a flash flood water pulse, which has very low permeability and can greatly inhibit infiltration. The infiltration rates measured by tension infiltrometers fluctuate, which is attributed to the mosaic and layered special distribution of hydraulic and capillary properties of the accrued sediments. Falling ponding depth laboratory experiments were conducted in four columns with a coarse substratum (sand) subjacent to a layer of thoroughly homogenized repacked dam silt. Imbibition front stopped at the interface between two texturally contrasting strata and the “waiting time” of the capillary barrier breakthrough was measured, as well as further oscillations of the infiltrations rate.

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References

  • Ahuja, L.R., Nofziger, D.L., Swartzendruber, D., Ross, J.D.: Relationship between Green and Ampt parameters based on scaling concepts and field-measured hydraulic data. Water Resour. Res. 25(7), 1766–1770 (1989)

    Article  Google Scholar 

  • Ali, S., Ghosh, N.C., Singh, R., Sethy, B.K.: Generalized explicit models for estimation of wetting front length and potential recharge. Water Resour. Manag. 27, 2429–2445 (2013)

    Article  Google Scholar 

  • Al-Ismaily S., Al-Maktoumi, A.K., Kacimov, A., Al-Saqri, S., Al-Busaidi, H., Al-Haddabi, M.: A Hydropedological morphed block-crack capillary barrier: human influence and lessons from nature. Abstracts of 2012 International Annual Meetings of SSSA, Visions for a Sustainable Planet. Oct. 21–24, Cincinnati, USA (2012)

  • Al-Ismaily, S., Al-Maktoumi, A.K., Kacimov, A., Al-Saqri, S., Al-Busaidi, H., Al-Haddabi, M.: A morphed block-crack preferential sedimentation: a smart design and evolution in nature. Hydrol. Sci. J. 58(8), 1779–1788 (2013). doi:10.1080/02626667.2013.838002

    Article  Google Scholar 

  • Al-Ismaily, S., Al-Maktoumi, A.K., Kacimov, A., Al-Saqri, S., Al-Busaidi, H.: Impact of a recharge dam on the hydropedology of arid zone soils in Oman: anthropogenic formation factor. J. Hydrol. Eng. 20(4), 04014053 (2015). doi:10.1061/(ASCE)HE.1943-5584.0000886

    Article  Google Scholar 

  • Al-Turbak, A., Al-Muttair, F.F.: Evaluation of dams as a recharge method. Int. J. Water Resour. Dev. 5(2), 119–124 (1989). doi:10.1080/07900628908722423

    Article  Google Scholar 

  • Anderson, M.G., Burt, T.P.: Process Studies in Hillslope Hydrology: An Overview. Wiley, Chichester (1990)

    Google Scholar 

  • Angulo- Jaramillo, R., Vandervaere, J.P., Roulier, S., Thony, J.L., Gaudet, J.P., Vauclin, M.: Field measurement of soil surface hydraulic properties by disc and ring infiltrometers. A review and recent developments. Soil Tillage Res. 55, 1–29 (2000)

    Article  Google Scholar 

  • Assouline, S.: Infiltration into soils: conceptual approaches and solutions. Water Resour. Res. 49, 1–18 (2013). doi:10.1002/wrcr.2015

    Article  Google Scholar 

  • Averyanov, S.F.: The dependence of permeability of soils on their air content. Dokl. AN SSSR 69, 141–144 (1949)

    Google Scholar 

  • Avkhadiev, F.G., Kacimov, A.R.: Analytical solutions and estimates for micro-level flows. J. Porous Media 8(2), 125–148 (2005)

    Article  Google Scholar 

  • Bagarello, V., Iovino, M.: Field testing parameter sensitivity of the two-term infiltration equation using differentiated linearization. Vadose Zone J. 2, 358–367 (2003)

    Article  Google Scholar 

  • Chanson, H., James, D.P.: Siltation of Australian reservoirs: some observations and dam safety implications. Scientific report, The University of Queensland, Brisbane, Australia (1998)

  • Chua, X., Marino, M.A.: Determination of ponding condition and infiltration into layered soils under unsteady rainfall. Hydrology 313, 195–207 (2005)

    Article  Google Scholar 

  • Currell, M., Gleeson, T., Dahlhaus, P.: A new assessment framework for transience in hydrogeological systems. Groundwater (2015) (accepted)

  • Dullien, F.A.L.: Porous Media: Fluid Transport and Structure. Academic Press, San Diego (1992)

    Google Scholar 

  • El-Hames, A.S., Al-Wagdany, A.S.: Investigation of wetting front behavior due to rainfall and ponding head effects in arid region wadi alluvium. Arab. J. Geosci. (2011). doi:10.1007/s12517-011-0457-6

  • Green, W.H., Ampt, G.A.: Studies on soil physics: 1. Flow of air and water through soils. J. Agric. Sci. 4, 1–24 (1911)

    Article  Google Scholar 

  • Haimerl, G.: Groundwater Recharge in Wadi Channels Downstream of Dams Efficiency and Management Strategies. Institute of Hydraulic and Water Resources Engineering. Technische Universitat Munchen, Germany (2002)

    Google Scholar 

  • Hilpert, M., Glantz, R.: Exploring the parameter space of the Green–Ampt model. Adv. Water Resour. 53, 225–230 (2013)

    Article  Google Scholar 

  • Jacques, D., Mohanty, B.P., Feyen, J.: Comparison of alternative methods for deriving hydraulic properties and scaling factors from single-disc tension infiltrometer measurements. Water Resour. Res. 38(7), 1120 (2002). doi:10.1029/2001WR000595

    Article  Google Scholar 

  • Joseph, O.F.F.: Siltation of Reservoirs. Eildon Surveys Analysed. AQUA, pp. 19–23 (1953)

  • Kacimov, A., Brown, G.: A transient phreatic surface mound, evidenced by a strip of vegetation in an earth dam shoulder: the Lembke–Youngs reductionist model revisited. Hydrol. Sci. J. 60(2), 361–378 (2015). doi:10.1080/02626667.913793

    Article  Google Scholar 

  • Kacimov, A.R., Obnosov, Y.V.: Pseudo-hysteretic double-front hiatus-stage soil water parcels supplying a plant-root continuum: the Green–Ampt–Youngs model revisited. Hydrol. Sci. J 58(1), 237–248 (2013). doi:10.1080/02626667.2013.743028

    Article  Google Scholar 

  • Kacimov, A.R., Kayumov, I.R.: Viscous flow through straight pore channels. J. Porous Media 5(3), 199–208 (2002)

    Google Scholar 

  • Kacimov, A.R., AI-Ismaily, S., AI-Maktoumi, A.: Green–Ampt one-dimensional infiltration from a ponded surface into a heterogeneous soil. J. Irrigation Drain. Eng. 136(1), 68–72 (2010)

    Article  Google Scholar 

  • Kale, R., Sahoo, B.: Green–Ampt infiltration models for varied field conditions: a revisit. Water Resour. Manag. 25, 3505–3536 (2011). doi:10.1007/s11269-011-9868-0v

    Article  Google Scholar 

  • Lehmann, P., Or, D.: Evaporation and capillary coupling across vertical textural contrasts in porous media. Phys. Rev. E 80(4), 046318 (2009)

    Article  Google Scholar 

  • Logsdon, S.D.: Transient variation in the infiltration rate during measurement with tension infiltrometers. Soil Sci. 162(4), 233–241 (1997)

    Article  Google Scholar 

  • Lunati, I., Or, D.: Gravity-driven slug motion in capillary tubes. Phys. Fluids 21(5), 052003 (2009)

    Article  Google Scholar 

  • Masoodi, R., Languri, E., Ostadhossein, A.: Dynamics of liquid rise in a vertical capillary tube. J. Colloid Interface Sci. 389, 268–272 (2013)

    Article  Google Scholar 

  • Morel-Seytoux, H.J.: The capillary barrier effect ut the interface of two soil layers with some contrast in properties. Hydrowar Reports Division, No 92.4, Hydrology Days Publications, Atherton, CA (1992)

  • Neuman, S.P.: Wetting front pressure head in the infiltration model of Green and Ampt. Water Resour. Res. 12, 564–566 (1976)

    Article  Google Scholar 

  • Polubarinova-Kochina, P.Y.: Theory of ground-water movement, First edn. Nauka, Moscow, 1952 (in Russian), translated from the Russian by J.M. Roger de Weist (1962), Princeton University Press, Princeton. Second Russian edition (1977)

  • Rawls, W., Brakensiek, D., Miller, N.: Green–Ampt infiltration parameters from soils data. J. Hydraul. Eng. 109(1), 62–70 (1983)

    Article  Google Scholar 

  • Reynolds, W.D., Elrick, D.E.: Determination of hydraulic conductivity using a tension infiltrometer. Soil Sci. Soc. Am. J. 55, 633–639 (1991)

    Article  Google Scholar 

  • Siemens, G.A., Peters, S.B., Take, W.A.: Comparison of confined and unconfined infiltration in transparent porous media. Water Resour. Res. 49, 851–863 (2013). doi:10.1002/wrcr.20101

    Article  Google Scholar 

  • Simpson, M.J., Jazaei, F., Clement, T.P.: How long does it take for aquifer recharge or aquifer discharge processes to reach steady state? J. Hydrol. 501, 241–248 (2013)

    Article  Google Scholar 

  • Stanly Consultants, Feasibility Report Summary: The Wadi Al-Khoud Aquifer Recharge Project. Ministry of Agriculture and Fisheries, Sultanate of Oman (1981)

  • Szekely, J., Neumann, A.W., Chuang, Y.K.: The rate of capillary and the applicability of the Washburn equation. J. Colloid Interface Sci. 35(2), 273–278 (1971)

    Article  Google Scholar 

  • Valiantzas, J.D.: New linearized two-parameter infiltration equation for direct determination of conductivity and sorptivity. J. Hydrol. 384, 1–13 (2010)

    Article  Google Scholar 

  • Van den Putte, A., Govers, G., Leys, A., Langhans, C., Clymans, W., Diels, J.: Estimating the parameters of the Green–Ampt infiltration equation from rainfall simulation data: Why simpler is better. Hydrology 476, 332–344 (2013)

    Article  Google Scholar 

  • Vandervaere, J.-P., Vauclin, M., Elrick, D.E.: Transient flow from tension infiltrometers: the two-parameter equation. Soil Sci. Soc. Am. J. 64, 1263–1272 (2000)

    Article  Google Scholar 

  • Ventrella, D., Losavio, N., Vonella, A.V., Leij, F.J.: Estimating hydraulic conductivity of a fine-textured soil using tension infiltrometry. Geoderma 124, 267–277 (2005)

    Article  Google Scholar 

  • Whisler, F.D., Bouwer, H.: Comparison of methods for calculating vertical drainage and infiltration for soils. J. Hydrol. 10(1), 1–19 (1970)

    Article  Google Scholar 

  • Wolfram, S.: Mathematica: A System for Doing Mathematics by Computer. Addison-Wesley, Redwood City (1991)

    Google Scholar 

  • Wooding, R.A.: Steady infiltration from a shallow circular pond. Water Resour. Res. 4, 1259–1273 (1968)

    Article  Google Scholar 

Download references

Acknowledgments

The authors acknowledge the financial support through the IG/AGR/SWAE/10/02 from the Sultan Qaboos University, Oman. Valuable comments of two anonymous referees are highly appreciated.

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Authors and Affiliations

  1. Department of Soils, Water and Agricultural Engineering, Sultan Qaboos University, PO Box 34, Al-Khoud, 123, Sultanate of Oman

    Ali Al-Maktoumi, Anvar Kacimov, Said Al-Ismaily, Hamed Al-Busaidi & Said Al-Saqri

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  1. Ali Al-Maktoumi
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  2. Anvar Kacimov
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  3. Said Al-Ismaily
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  4. Hamed Al-Busaidi
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  5. Said Al-Saqri
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Correspondence to Ali Al-Maktoumi.

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Al-Maktoumi, A., Kacimov, A., Al-Ismaily, S. et al. Infiltration into Two-Layered Soil: The Green–Ampt and Averyanov Models Revisited. Transp Porous Med 109, 169–193 (2015). https://doi.org/10.1007/s11242-015-0507-8

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