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Reviewing classical studies in soil physics“Analysis of the vertical downward ﬂow of water through a two layered soil”
By S. Takagi
Soil Sci., 3* (,) : 32ῌ+*- (+30*)
Jiro CHIKUSHI** Biotron Institute, Kyushu University, Hakozaki 0ῌ+*ῌ+, Higashi-ku, Fukuoka 2+,ῌ2/2+, Japan
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Unsaturated conditions contacting with tensiometer ﬁlter depending on
the type of air : (a) atmospheric air, (b) atmospheric and entrapped air,and (c) entrapped air.

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ῑῌ0Fig. 0¹Kº»a*4<4<sRelative speciﬁc permeabilities of air andwater depending on water saturation insand (after Wyko# and Botman, +3-0))* v<$ IjQL$ _ g3gy ?
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Apparatus used by Wyko# and Botset (+3-0)’s experiment. a. CO, gas cylinder ;b. mercury manometer ; c. electric resistance meter ; d. soil column plus ring,
including ¸ pressure tap, connected with b, and wire screen, connected with c)e. gas and liquid supply regulator ; f. gas and liquid separator ; g. gas meter ; h.
graduated cylinder. (with alphabetical marks to the original ﬁgure)¸¹ : S. Takagi º »,  ¦-(-23¼ 
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105

blanketed reservoir. Geotechnique. 3 : 3῎,+.

  !

Klute, A. (+3/,) : A numerical method for solving the"!"#$%& '( )*ﬂow equation for water in unsaturated materi- +,-&./0( Takagi  
- 1-2345 6 +
-

78

als. Soil Sci., 1- : +*/῎++0.

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FGD(;H 8  Takagi Mualem, Y. (+310) : A new model for predicting the23I-JK=>-L

hydraulic conductivity of unsaturated porous me-8 M-N O!
Takagi 

dia. Water Resour. Res., +, (-) : /+-῎/,,.

PQ-R=>STUV u+303v : -&YZ! -E=>yWX! 88 YZC[PQE\] ^! Buckingham -_-

2`8a]H5b=>c-

'| ( +. u+v : +*0.
Narasimhan, T.N. (,**/) : Buckingham, +3*1 : An ap-

d8

preciation. Vadoze Zone J., . : .-.῎..+.

 Takagi eD( D fg g -Philip, J.R. (+3/1) : The theory of inﬁltration : +. The

R-hH=>cijklmno9inﬁltration equation and its solution. Soil Sci., '-pqc Takagi  e2- : -./῎-/1.

H

Raats, P.A.C. and M.Th. van Genuchten (,**0) : Milestones in soil physics. Soil Sci., +1+ (+) : S,+῎S,2.

ῌ ῏ ῎ ῍Richards, L.A. (+3-+) : Capillary conduction of liquids

Behnke, J. J. and W.C. Bianchi (+30/) : Pressure distri-through porous mediums. Physics, + : -+2῎---.

bution in layered sand columns during transient

Srinilta, S., D.R. Nielsen. and D. Kirkham (+303) : Steadyand steady-state ﬂow. Wate Resour. Res., + (.) :ﬂow of water through a two-layer soil. Water Resour. Res., / (/) : +*/-῎+*0-.

//1῎/0,.
Brooks, R.H. and A.T. Corey (+30.) : Hydraulic pro-)* u+3/*v : +YZ! y - + :perties of porous media. In : Hydrology paper -.
Fort Collins, CO : Corolado State Univ., pp. ,1.

3῎+0.

)* u+30*v : Y'(YZ῍y ¡¢£+-w5¤¥¦ §¨ y=~rst u+32+v : w5YZx=>y z{|R R!=>"} -- ~ : +῎-2.

u+v : +-῎+3.

Childs, E.C. and N. Collis-George (+3/*) : The permea-

Takagi, S. (+30*) : Analysis of the vertical downward

bility of porous materials. Proc. Roy. Soc. Lon-ﬂow of water through a two layered soil. Soil.

don, Ser. A ,*+ : -3,῎.*/.

Sci., 3* (,) : 32῎+*-.

Day, P.R. and J.N. Luthin (+3/-) : Pressure distribu-

,- ῌ  ῌ |©./ ῌ ª«0 ῌ |¬­

tion in layered soils during continuous water

u+31.v : ¦®-YZ¦x§¨E=>yﬂow. Soil Sci. Soc. Am. Proc., +1 (,) : 2,῎3+.

| n ,2 u,v : +*/῎++-.

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u+3/.v : -&x=> uῌvYZw5+W$=> ,+ u0v :

2῎+-.

¯

° u+3/-v : ±"²³w5´-12!
y ¦µ¶·ny ,,/ : ,῎++.

Van Genuchten, M.Th. (+32*) : A closed form equa-Gardner, W.R. (+3/2) : Some steady-state solutions oftion for predicting the hydraulic conductivity of

the unsaturated moisture ﬂow equation with ap-

unsaturated soil. Soil Sci. Soc. Am. J., .. : 23,῎plication to evaporation from a water table. Soil

232.

Sci., 2/ : ,,3῎,-,.
Irmay, S. (+3/.) : On the hydraulic conductivity ofunsaturated soils. Trans. Amer. Geophys. Union.,-/ (-) : .0-῎.01.
Kisch, K. (+3/3) : The theory of seepage from clay-

Warrick, A.W. and T.C. J. Yeh (+33+) : One-dimensional,
steady vertical ﬂow in a layered soil proﬁle. Adv.
Water Resour., +- : ,*1῎,+*.
Wycko#, R.R. and H.G. Botset (+3-0) : The ﬂow of gasliquid mixtures through unconsolidated sands.

2  +*1  ,**1

106

Physics, 1 : -,/ῌ-./.

 +3/2 : 

Zaslavsky. D. (+30-) : Theory of unsaturated ﬂow into

   !" 0 : +ῌ-*.

a non-uniform soil proﬁle. Soil Sci., 31 (0) : .**ῌ.+*.

#$%& +30* : '()ῌ*+,-.,/0

Zaslavsky. D. (+301) : Saturation-unsaturation transi-

12 3456   tion in inﬁltration to a non-uniform soil proﬁle.

!" +* : +ῌ-,.

Soil Sci., +*1 (-) : +0*ῌ+0/.

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