Reviewing classical studies in soil physics. Analysis of the vertical downward flow of water through a two layered soil By S. Takagi.

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1 J. Jpn. Soc. Soil Phys. No. +*1, p.31+*0,**1 S. Takagi, * 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* (,) :32+*- (+30*) Jiro CHIKUSHI* * Biotron Institute, Kyushu University, Hakozaki 0+*+, Higashi-ku, Fukuoka 2+,2/2+, Japan Key words : layered soil, unsaturated water flow, pressure profile, open system, closed system + Takagi Takagi +30*, +3.* +3/*, + +, +a +b +3/2, +3/. Navier-Stokes * 2+,2/2+ 0+*+ :

2 98 +*1,**1 Fig. + +, Water pressure profiles in two-layered soil under steady flow of water in unsaturated condition in open system, (a) with and (b) without the constant pressure zone. Takagi Day and Luthin +3/-, Kisch +3/3 Takagi + Kisch Buckingham Narasimhan,**/ +2,, Buckingham Buckingham Buckingham

3 : S. Takagi, 99 Buckingham Buckingham Richards Richards, +3-+ Richards Buckingham +3/* Philip +3/1 Klute +3/, +30* Narasimhan,,**/ ; Raats and van Genuchten,,**0 Takagi Buckingham Richards Philip Klute Takagi, Dacry Kisch Takagi, H + H, H * H - +a +30* Takagi / vk (* (y v k y * * - Takagi * p rg y, +3/2 Takagi, Takagi k p Takagi Takagi Takagi + Kisch +3/3 p r g y* *H * * v k + yh * p rg v + k + yh* k + * v k, HH -yh p rg + v HH k, -yh - k, HH +H, yy B yy E p* v + k + ybh*

4 100 +*1,**1, Takagi Takagi, +30* Fig., Water flow system that Takagi analyzed in a two-layered soil (after Takagi, +30*). + v k, HH -y EH - pp*rgh* *h*y vk,h* k + k, k + k, dx dy v k + +x prgx dx vk +x+ yyb C xh* dx H*k+ H+ vk +x+ vk + v k +xdx k H*k+ H +,h*k +x k,h*k + dh dy v k +,h yy E h* dh +vk yey,h prgh D hh* dh +vk,h yeyd y D Gardner +3/2 Zaslavsky +301 Takagi + v k,h h*h a a+ y B y E Takagi, k,vk + + H* H + +,

5 : S. Takagi, 101. Takagi Takagi Behnke and Bianchi +30/ + Zaslavsky +30- Takagi H * h C + H *H + k, k + + hc k, k + H + H, + H * H *H + k, k + + hc h C* H * H *, Zaslavsky, +301 Srinilta et al Takagi +30* Kisch +3/3 Zaslavsky Srinilta et al. Takagi Kisch Srinilta et al., +b h* v h *+ H * H *h *+ y h k +hdh k+h*h*+ y k +hv vk + h *, H - H - h *, k,hdh k,h-h*, H+H, y k,hv k,v h Takagi x h yh + hh* h* v y h Srinilta et al. Takagi k, h Gardner k,h abbhh C a ; a, b, a *a+ Takagi Srinilta et al.,* Warrick and Yeh +33* Takagi, Zaslavsky, Srinilta et al. / +300, +a

6 102 +*1,**1 - Kisch, +3/3 ; /- +30* air binding Henry.. Fig.. +30* Emergence of air bubbles in the expanded zone during water flow through the glass pipe. Time elapses from I to IV. (after Yahata, +30*) - Fig. - Changes in water pressure profiles due to the elevation of outflow pressure in (a) open system and (b) closed system.

7 : S. Takagi, agitation Henry 0 Takagi Gardner +3/2 k Y Yprg +3/* k q q Childs and Collis- George +3/* Mualem +310 van Genuchten +32* / /a Y q /c +3/* /b Gardner, Brooks and Corey +30. van Genuchten Y q k k q k Y +300 Irmay +3/. SS * - kqk S +S * - k S S qn ; n S * q *n ; q * / Fig. / Unsaturated conditions contacting with tensiometer filter depending on the type of air : (a) atmospheric air, (b) atmospheric and entrapped air, and (c) entrapped air.

8 104 +*1,**1 Irmay Wycko# and Botset Wycko# and Botset 1 NaCl CO, 0 Fig. 0 Relative specific permeabilities of air and water depending on water saturation in sand (after Wyko# and Botman, +3-0) CO, CO, /c Dp Dp / 1 1 Wyko# and Botset +3-0 a CO, ;b ;c ;d b c ;e ;f ;g ;h Fig. 1 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)

9 : S. Takagi, 105 Takagi + Takagi Takagi Buckingham Takagi Takagi Behnke, J. J. and W.C. Bianchi (+30/) : Pressure distribution in layered sand columns during transient and steady-state flow. Wate Resour. Res., + (.) : //1/0,. Brooks, R.H. and A.T. Corey (+30.) : Hydraulic properties of porous media. In : Hydrology paper -. Fort Collins, CO : Corolado State Univ., pp., : -- : +-2. Childs, E.C. and N. Collis-George (+3/*) : The permeability of porous materials. Proc. Roy. Soc. London, Ser. A,*+ : -3,.*/. Day, P.R. and J.N. Luthin (+3/-) : Pressure distribution in layered soils during continuous water flow. Soil Sci. Soc. Am. Proc., +1 (,) :2,3+. +3/. :,+ 0 : 2+-. Gardner, W.R. (+3/2) : Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table. Soil Sci., 2/ :,,3,-,. Irmay, S. (+3/.) : On the hydraulic conductivity of unsaturated soils. Trans. Amer. Geophys. Union., -/ (-) : Kisch, K. (+3/3) : The theory of seepage from clayblanketed reservoir. Geotechnique. 3 : 3,+. Klute, A. (+3/,) : A numerical method for solving the flow equation for water in unsaturated materials. Soil Sci., 1- : +*/ :,, - :,,/-**. Mualem, Y. (+310) : A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res., +, (-) :/+-/,, : +. + : +*0. Narasimhan, T.N. (,**/) : Buckingham, +3*1 :Anappreciation. Vadoze Zone J.,. : Philip, J.R. (+3/1) : The theory of infiltration : +. The infiltration equation and its solution. Soil Sci., 2- : -./-/1. Raats, P.A.C. and M.Th. van Genuchten (,**0) : Milestones in soil physics. Soil Sci., +1+ (+) :S,+S,2. Richards, L.A. (+3-+) : Capillary conduction of liquids through porous mediums. Physics, + : Srinilta, S., D.R. Nielsen. and D. Kirkham (+303) : Steady flow of water through a two-layer soil. Water Resour. Res., / (/) :+*/-+*0-. +3/* : + : * : + : Takagi, S. (+30*) : Analysis of the vertical downward flow of water through a two layered soil. Soil. Sci., 3* (,) :32+* :,2, : +*/ /- :,,/ :,++. Van Genuchten, M.Th. (+32*) : A closed form equation for predicting the hydraulic conductivity of unsaturated soil. Soil Sci. Soc. Am. J.,.. : 23, 232. 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.

10 106 +*1,**1 Physics, 1 : -,/-./. +3/2 : 0 : +-*. +30* : +* : +-,. Zaslavsky. D. (+30-) : Theory of unsaturated flow into a non-uniform soil profile. Soil Sci., 31 (0) :.**.+*. Zaslavsky. D. (+301) : Saturation-unsaturation transition in infiltration to a non-uniform soil profile. Soil Sci., +*1 (-) :+0*+0/. +30* Takagi :,** :,**1 +*,

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