入滲是水分自地表進入到土壤的過程，其重要性包括灌溉策略的制訂發展、
估計地下水補注的時間與數量，以及化學物質在土壤中的傳輸過程。在水文研究
的應用上，有很多估計入滲量的方法曾被提出，例如Green-Ampt model (GAM)
(Green and Ampt, 1911)、Richards方程(Richards, 1931)等。在傳統達西尺度中，毛
細壓力常常被假設為定值，稱為平衡毛細壓力，但相關研究顯示，流速較快時，
實際毛細壓力與平衡毛細壓力不相等。此非平衡的毛細壓力稱為動態毛細壓力。
本研究以沙柱實驗，觀測不同暫水深條件下，入滲過程中溼潤面的移動速度。並
搭配GAM與修正型GAM的模式比較，探討在不同材質與粒徑中，流速的變化與
動態毛細壓力的關係，沙粒特性對動態毛細壓力以及入滲現象的影響。

Infiltration happens when water on the ground surface enters the soil.
Understanding the infiltration process is important to draw up the irrigating strategies,
estimate the time and quantity of the groundwater recharge, and understand the
transport of the chemicals in the soil. Mathematical models had been presented to
simulate the infiltration process, such as Green-Ampt Model (GAM) (Green and
Ampt, 1911) and Richards’ equation (Richards, 1931). In the traditional Darcy-scale
model, the capillary pressure is usually assumed as a constant, that is equilibrium
capillary pressure. However, studies show that the difference between the capillary
pressure and the equilibrium capillary pressure is significant in high flow velocity.
This non-equilibrium capillary pressure is called dynamic capillary pressure. In this
study, we performed a series of infiltration experiments in sand columns with different
types of sands and under different boundary conditions. To show the effects of
dynamic capillary pressure, we compared the results of the experiments with the
simulations from the GAM and the modified GAM which takes the dynamic capillary
pressure into account. We found that the dynamic effects are more significant during
the infiltrations in sands with large grain size than the ones with small grain size.

1. Brooks, R.H. and Corey, A.T. ,Properties of porous media affesting fluid
flow‖, J. Irrig. Drain. Div. Am.Soc.Civ. Eng, Vol 92(IR2), pp. 61-88, 1964.
2. Brakensiek, D. L., 1977, Estimating the effective capillary pressure in the
Green and Ampt Infiltration Equation. Water Resources Research, 13(3):
680-682, doi: 10.1029/WR013i003p00680.
3. Chow, V. T., Maidment, D. R. and Mays, L. W., Applied hydrology,
Singapore: McGraw-Hill, pp. 99-126, 1988.
4. Cox, R. G., 1986, The dynamics of the spreading of liquids on a solid
surface. Part 1. Viscous flow.Journal of Fluid Mechanics, 168: 169-194.
5. de Gennes, P. G., 1985, Wetting: Statics and dynamics. Reviews of Modern
Physics, 57: 827-863.
6. Diamantopoulos, E., Iden, S. C. and Durner, W., 2012, Inverse modeling of
dynamic nonequilibrium in water flow with an effective approach. Water
Resources Research, 48(3), doi: 10.1029/2011WR010717.
7. Elzeftawy,A., and R.S. Mansel. 1975. Hydraulic conductivity calculations
for unsaturated steady-state and transient-state flow in sand.Soil Sci. Soc.
Am.Proc. 39:599-603. doi:10.2136/sssaj1975.03615995003900040013x
8. Hassanizadeh, S.M., M.A. Celia, and H.K. Dahle.2002.Dynamic effects in
capillary pressure-saturation relationships and its impact on unsaturated
flow. Vadose Zone J. 1:38-57.
9. S.-Y Hsu, M. Hilpert*. Incorporation of Dynamic Capillary Pressure into
the Green-Ampt Model for Infiltration. (2011, May), Vadose Zone Journal,
Vol. 10, no. 2, 642-532. (SCI, IF 1.67).
10. Hoffman, R. L., 1975, A study of the advancing interface. Journal of
Colloid and Interface Science,50(2): 228-241, doi: A study of the advancing
interface.
11. Green, W.H. and G.A. Ampt, 1911, Studies on soil physics Part I – The flow
of air and water through soils. Journal of Agricultural Science, 4(Part
1):1–24.
12. Geiger, S.L. and D.S. Durnford, 2000, Infiltration in homogeneous sands
and a mechanistic model of unstable flow. Soil Science Society of America
Journal, 64(2):460–469.
13. Morel-Seytoux, H. J. and Khanji, J., 1974, Derivation of an equation of
infiltration. Water Resources Research, 10(4): 795-800, doi:
10.1029/WR010i004p00795.
14. Mualem, Y., 1976, A new model for predicting the hydraulic conductivity
of unsaturated porous media.Water Resources Research, 12(3): 513-522,
doi: 10.1029/WR012i003p00513.
15. Joos, P., van Remoortere, P. and Bracke, M., 1990,The kinetics of wetting
in a capillary. Journal of Colloid and Interface Science, 136(1): 189.
16. Philip J R. 1957. The theory of infiltration: 1.The infiltration equation and
its solution [J]. Soil Sci, 1957, 83(5):345-357.
17. Pellichero, E., R. Glantz, M. Burns, D. Mallick, S.-Y. Hsu, and M. Hilpert
(2012), Dynamic capillary pressure during water infiltration: Experiments
and Green-Ampt modeling, Water Resour. Res., 48, W06515,
doi:10.1029/2011WR011541.
18. Poulovassilis, A. 1974. The uniqueness of the moisture characteristics. Soil
Sci. 25:27-33. doi:10.1111/j.1365-2389.1974.tb01099.x
19. Rose, W. and R. W. Heins, 1962, Moving interfaces and contact angle rate-dependency. Journal of Colloid Science, 17(1):39–48.
20. Richards, L.A. 1931. Capillary conduction of liquids through porous media.
Physics 1:318-333. doi:10.1063/1.1745010.
21. Schultze, B., O. Ippisch, B. Huwe, and W. Durner . 1999. Dynamic
nonequilibrium in unsaturated water flow. In:M.Th. van Genuchten et al.,
editors, Proceedings of an International Workshop on Characterization and
Measurement of the Hydraulic Properties of Unsaturated Porous Media,
Riverside, CA.22-24 Oct. 1997. Univ of California, Riverside. p.877-892.
22. Selker, J.S., J.F. Duan, and J.Y. Parlange, 1999, Green and Ampt infiltration
into soils of variable poresize with depth. Water Resources Research,
35:1685–1688.
23. Stauffer, F., 1978, Time dependence of the relations between capillary pressure,
water content and conductivity during drainage of porous media. p.
3.35–3.52. In IAHR Symp. on Scale Effects in Porous Media, Thessaloniki,
Greece. 28 Aug.−1 Sept. 1978. Int. Assoc. Hydro-Environ. Eng. Res.,
Madrid.
24. Tabuchi, T., 1971, Infiltration and capillarity in the particle packing [in
Japanese]. Rec. Land Reclam.Res., 19:1–121.
25. Topp, G.C., A. Klute, and D.B. Peters. 1967. Comparison of water
content-pressure head data obtained by equilibrium, steady-state, and
unsteady-state methods. Soil Sci. Soc. Am. Proc. 31:312-314.
doi:10.2136/sssaj1967.03615995003100030009x
26. van Genuchten, M.Th. and Nielsen, D.R. ,On describing and predicting the
hydraulic properties of unsaturated soils‖, Ann. Geophysica,., Vol 3, pp.
615–628, 1985.
27. van Genuchten, M.Th. ,A closed-form equation for predicting the hydraulic conductivity of unsaturated soils‖, Soil Sci. Soc. Am. J., Vol 44, pp.
892–898, 1980.
28. Weller, U., O. Ippisch, J.M. Kohne, and H.J. Vogel. 2011. Drect
measurement of unsaturated hydraulic conductivity including
nonequilibrium and hysteresis. Vadose Zone J. 10:654-661.
doi:10.2136/vzj2010.0074
29. Weitz, D. A., J. P. Stokes, R. C. Ball, and A. P. Kushnick, 1987, Dynamic
capillary pressure in porous media: Origin of the viscous-fingering length
scale. Physical Review Letters,59(26):2967–2970.
30. 林志欣，圓型沙柱探討入滲效應之研究，碩士論文，國立中央大學，2005
31. 王宗原，穩態與非穩態入滲效應之研究，碩士論文，中國科技大學，2006