Soil Water Hydraulic Functions for a Sandy Soil and an Aggregated Soil

Transcript

1 J. Jpn. Soc. Soil Phys. No. +*1, p.0-11,**1 ** Soil Water Hydraulic Functions for a Sandy Soil and an Aggregated Soil Masaru SAKAI* and Nobuo TORIDE* Abstract The Fayer and Durner models, which modified the water retention curve of the van Genuchten (VG) model, combined with the statistical pore-size distribution model of Mualem were used to predict unsaturated hydraulic conductivity functions of Tottori dune sand and aggregated Kumamoto Andisol. Parameters of the Fayer and Durner models, as well as the VG model, were inversely estimated with the evaporation method. The Fayer model well described unsaturated hydraulic conductivity for the dune sand reflecting pore water retention for higher water contents and absorbed water retention on the surface of soil particles for lower water contents. The Durner model was suitable to the Andisol whose hydraulic properties were strongly a#ected with the distinct the aggregated structure. The Mualem model can predict unsaturated hydraulic conductivity for a wide range of soil water pressure when an appropriate model is used for the water retention curve and the pore-connectivity coe$cient, l is estimated. Furthermore, it was also suggested that we need to use an appropriate soil water retention function to predict unsaturated hydraulic conductivity for much smaller pressure heads than the minimum pressure head observed during the evaporation experiment. Key words : soil water hydraulic function, Mualem model, Fayer model, Durner model, evaporation method + q h q h soil water hydraulic function Jury and Horton,,**0 Brooks and Corey +30. van Genuchten +32* S Kosugi +330 Childs and Collis-George, +3/* ; Burdine, +3/- ; Mualem, +310 ; Jury and Horton,,**0 * /+.2/*1 +/11 : Mualem Fayer Durner

2 64 +*1,**1,**1 Eching and Hopmans, +33- ;SÀimůnek et al., +332 ;,**1 Mualem +310,**1 van Genuchten +32* Mualem closed-form van Genuchten VG,**1 VG VG q r q r q r VG q r Tuller and Or,,**+ ;,**1 q r VG Fayer and Simmons +33/ q r +* 1 cm * VG q r S VG,,**/ Durner +33. VG Fayer and Simmons Durner Mualem Fayer Durner Fayer Durner Fayer Durner Fayer Durner,+, Mualem Mualem +310 KS ek sk r K ss l e, + + hs e dse hs e dse K LT + K s LT + K r K s S e l pore-connectivity coefficient h L Mualem +310./ l*./ Mualem h S e K h S e,,,,+ van Genuchten Mualem van Genuchten +32* van Genuchten VG VG qq r S e+ah n m q sq r q L - L - q r L - L - q s L - L - a L + n m ++n

3 : 65 Mualem KS ek ss l e++s +m e m,,,, Fayer VG q r Tuller and Or,,**+ ;,**1 Fayer and Simmons +33/ Campbell and Shiozawa, +33, * VG q r qq ss e+chq aq s +ah n m chq aq s q a ch+lnhlnh m h m q* Rossi and Nimmo */++* /* h m+* 1 cm h m+* 0 cm.. + qq ss e+ah n m ++ah n m chq aq s + a + +, + q r* VG, h.* cm h S e + VG Fayer and Simmons Mualem KS ek ss l eg shg max, G s h G max + Fayer,,- Durner VG S, Durner +33. VG,, VG + Fig. + a Fayer b Durner, : +,, Two di#erent regions for water retention of (a) the Fayer model (eq. (.)) and (b) the Durner model (eq. (1)) : dashed and chain lines indicate the first and second terms of the right-hand side of the equations, respectively, and solid lines indicate the sum of the two terms (left-hand side).

4 66 +*1,**1 + Table + K s Mualem +310 l Soil water hydraulic parameters of the VG, Fayer, and Durner models fit to the observed soil water retention curves, the observed saturated hydraulic conductivity K s, and the poreconnectivity coe$cient l presented by Mualem (+310). Tottori dune sand q r q a q s a cm + n w, a, cm + n, K s cm d + l VG model Fayer model Durner model *4*-* *4**, *4*2/ *4-.+ *4--0 *4--1 *4*-/ *4*-0 *4*-0 /4,* 14* *4*, 3430+*. +4/ //* //* //* *4/ *4/ *4/ Andisol VG model Fayer model Durner model * * *41/. *4103 *41,. *41.. *4+3, *4*.* *4* ,,4.. *4/3 +4*++*. +4.1,**,**,** *4/ *4/ *4/ qq r q sq r S e w ++ah n m w,+a,h n, m, Durner - w w +w,+ + b + + a Fayer +, + h+,*** cm, h+,*** cm Fayer Durner,,,, Durner Fayer Durner Mualem Priesack and Durner,,**0 KS ek sw +S e+w,s e, l w+a++s+m e+ m w,a,++s +m w +aw,a,,,, e, m, -+,,* h/* cm h/* cm h +,*** cm +33/ h +,*** cm +32., h+/* cm r b+.0, gcm - r b*..2 gcm cm 2 cm, 1.2 cm +2.0 cm - *./ +, - / cm, /./ +*./ +/./ cm Campbell CR+***

5 : 67, a b : Fayer Durner VG Fig., Water retention curves for (a) Tottori dune sand and (b) Kumamoto Andisol : open circles are the observed data, and solid, dashed, and chain lines describe the fitted curves described with the Fayer, Durner, and VG model, respectively. q ave -, -,+ L + (q (t ( (z Kh (h (z + t T z L * Philip and de Vries, +3/1 ;,**0 (q (t ( (z Kh (h (z + (h Kvh (z K vh LT +, h i z hz*h iz Kh (h (z + (h K vh zl (z * zl L L, * Rassam et al.,,**. ;,**0 Kh (h (z + (h K vh z* (z Et z* h*th A h*th A, * h * t h A L E LT + h * t h A h * th A E E h A h A+* 0 cm h*th A E t

6 68 +*1,**1 -,, F q ave 0- *.*03 cm - cm -,*2 *..0 cm - cm - E cum t i, F v pjw pp* j t ip jt i, w qq* aveq ave, v Ew EE* cumt ie cumt i, v qhw qhqh*qh, * p j t i j t i m n j j E cum t i t i w p, w q, w E,w qh,,**1, *./ cm / cm, /./ cm +/./ cm q ave q SÀimůnek et al., +332 h * t h A E t E cum t i w p + w qh, w q,w E +* v *./ cm * h1** cm *q*.-/ v s, n v + ns, - v E s E, n E v E+n Es E,, Levenberg-Marquardt Marquardt, +30- F Fayer q a, q s, a, n,k s,l Durner q r, q s, a, n,w,, a,, n,, K s, l q s,**1.. + F h-* cm K s l VG q r, q s, a, n,k s, l Rassam et al.,,** K s K s//* cm d + K s,** cm d + l Mualem +310 l*./ E t HYDRUS-+D SÀimůnek et al.,,**/..+, a, b Fayer Durner VG

7 : 69,, Durner q r*, a,+* -, w,* + Fayer q h Durner Fayer h,** cm h,** cm Durner VG q r *.*- 2*h+*,*** cm h+*,*** cm +., - *./ cm.* h 1** cm / cm h0* cm.,+ - Fayer Durner VG., Fayer -. a h VG Fayer h2* cm. b Mualem S e q r VG h m +* 0 cm q* Fayer S e VG VG - : Fayer Durner VG Fig. - Pressure heads change during the evaporation process for Tottori dune sand : plots are the observed data, and solid, dashed, and chain lines indicate predicted pressure head changes using the Fayer, Durner, and VG model, respectively.

8 70 +*1,**1. Fig.. a b : Fayer Durner van Genuchten (a) Water retention curve and (b) unsaturated hydraulic conductivity as a function of the pressure head for Tottori dune sand estimated with the evaporation method : open circles are the observed retention data, and solid, dashed, and chain lines are those predicted with the Fayer, Durner, and VG model, respectively. Table,, Soil water hydraulic parameters for Tottori dune sand and Kumamoto Andisol obtained inversely with the evaporation method. Tottori dune sand q r q a q s a cm + n w, a, cm + n, K s cm d + l VG model Fayer model Durner model Fayer (with vapor) Fayer (with K data) *4*,3* * *4*23 *4*23 *4*23 *4--* *4-+1 *4--- *4-+3 *4-+- *4*-. *4*-/ *4*-/ *4*-/ *4*-/.41, , * * *. +4., /4,. +** ,4/3+* -,42-+*. -4-*+* - *4+/ +4+2 Andisol VG model Durner model *4***. *4*+*2 *4020 *4012 *4*20 *4*-* +4+.,4,3 * *. +4., / *4*3, *421 Tuller and Or,,**+ Fayer Mualem - Fayer l Durner -. a Durner, Fayer. b Durner, VG Fayer

9 : 71. Fayer VG VG *./ cm 0* 1* cm - VG.,, / Fayer h,* cm K +** cm d +,*h1* cm *.*+ cm d +, q a, q s, a, n - l l,.2-+*. l*.+/ l h0* cm 0 0- *., cm K uh *,**0 *./ cm / Fig. / : Fayer Impacts of accounting for vapor flow and the observed unsaturated hydraulic conductivity data for higher water content on the estimation of hydraulic conductivity of Tottori dune sand : open circles are the observed hydraulic conductivity data, and dashed, gray, and black solid lines describe predicted hydraulic conductivity using the Fayer model without neither vapor flow nor the observed data, with vapor flow, and with the observed data, respectively..,- / cm - h,, cm

10 72 +*1,**1 0 Fig. 0 : Calculated water content profiles near the soil surface with (solid line) and without (dashed line) considering vapor flow. K s K s, SÀimůnek et al., +332 ;,**1 K s K s//* cm d + Fayer K s cm d + +33/ h,1.1 cm K +/,.+0 cm d + h-/./ cm K2.,- cm d + Fayer w+* /, K s2.-.0 cm d + h.* cm.- 1 /./ cm, +/./ cm +1* +1* /./ cm.** cm +/./ cm +/* cm 1 Durner VG 2, Fayer Fayer, Durner 1 2 a Durner h,** cm h+** cm h +** cm Durner VG /./ cm +1* 1

11 : 73 2 VG 1 Fig. 1 : Durner VG Pressure heads change during the evaporation process for Kumamoto Andisol : plots are the observed data, and solid and chain lines indicate predicted pressure head changes using the Durner and VG models, respectively... Mualem Mualem, Fayer Durner Mualem l Mualem./ l*./ Mualem, +310 l Fayer Durner l Mualem 2 Fig. 2 a b : Durner VG (a) Water retention curve and (b) unsaturated hydraulic conductivity as a function of the pressure head for Kumamoto Andisol estimated with the evaporation method : open circles are the observed retention data, and solid and chain lines indicate those predicted with the Durner and VG model, respectively.

12 74 +*1,**1 h1** cm SÀimůnek et al., +332 Mualem Fayer Durner Mualem l Mualem VG Fayer Durner / VG q r Fayer, VG, Durner Malem Fayer Durner Fayer h2* cm h m+* 0 cm q * Fayer S e q r VG, Durner Fayer Fayer Durner Durner h,** cm, Durner Fayer Durner l Mualem Fayer Durner VG

13 : 75 Fayer Durner Brooks, R.H. and Corey, A.T. (+30.) : Properties of porous media a#ecting fluid flow. J. Irrig. Drainage Div., ASCE Proc. 1, (IR,) :0+22. Burdine, N.T. (+3/-) : Relative permeability calculations from pore-size distribution data. Trans. Am. Inst. Min. Metall. Pet. Eng., +32 : Campbell, G.S. and Shiozawa, S. (+33,) : Prediction of hydraulic properties of soils using particle size distribution and bulk density data, in International workshop on indirect methods for estimating the hydraulic properties of unsaturated soils, University of California Press, Berkeley, +33,. Childs, E.C. and Collis-George, N. (+3/*) : The permeability of porous materials. Proc. Roy. Soc. London, Ser. A,,*+ : -3,.*/. Durner, W. (+33.) : Hydraulic conductivity estimation for soils with heterogeneous pore structure. Water Resour. Res., -* :,++,,-. Eching, S.O. and Hopmans, J.W. (+33-) : Optimization of hydraulic functions from transient outflow and soil water pressure data. Soil Sci. Soc. Am. J., /1 : /. Fayer, M.H. and Simmons, C.S. (+33/) : Modified soil water retention functions for all matric suctions. Water Resour. Res., -+ : +,--+, : ++, :.-/-. Jury, W.A. and Horton, R.,**0 : : pp *1+*2 Kosugi, K. (+330) : Lognormal distribution model for unsaturated soil hydraulic properties. Water Resour. Res., -, :,031,1*-.,**1 : : Y. Mualem M. Th. van Genuchten +*0 : +*/++,. Marquardt, D.W. (+30-) : An algorithm for leastsquares estimation of nonlinear parameters. SIAM J. Appl. Math., ++ : Millington, R. J. and Quirk, J.M. (+30+) : Permeability of porous solids. Trans. Faraday Soc., /1 : +,** +,*1. Mualem, Y. (+310) : A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res., +, : /+-/,,. +33/ : pp. ++/+-0 Philip, J.R. and de Vries, D.A. (+3/1) : Moisture movement in porous media under temperature gradients. Eos Trans. AGU, -2 (,) :,,,,-,. Priesack, E. and Durner, W. (,**0) : Closed-form expression for the multi-modal unsaturated conductivity function. Vadose zone J., / : 23,232. Rassam, D., SÀimůnek, J. and van Genuchten, M.Th.,**. : HYDRUS-,D HYDRUS Rossi, C. and Nimmo, J.R. (+33.) : Modeling of soil water retention from saturation to oven dryness. Water Resour. Res., -* : 1*+1*2. Jiri SÀimůnek,**0 : +*. : 0-1-.,**0 : : J.R. Philip and D.A. de Vries +*- : +*/ ++,.,**1 : +*0 : SÀimůnek, J., van Genuchten, M.Th. and SÀejna, M. (,**/) : The HYDRUS-+D software package for simulating the movement of water, heat, and multiple solutes in variably saturated media. Version -.*. HYDRUS Software Series +, Dep. of Environmental Sciences, Univ. of California Riverside, Riverside, CA.

14 76 +*1,**1 SÀimůnek, J., Wendroth, O. and van Genuchten, M.Th. (+332) : Parameter estimation analysis of the evaporation method for determining soil hydraulic properties. Soil Sci. Soc. Am. J., 0, : 23. 3*/.,**/ : +2. :.*+.+*. Tuller, M. and Or, D. (,**+) : Hydraulic conductivity of variably saturted porous media. Water Resour. Res., -1 : +,/1+,10. van Genuchten, M.Th. (+32*) : A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Soc. Am. J.,.. : 23, G s h G max Fayer and Simmons, +33/ S exgs a+xgs a+ah n m A+ S aq aq s,x+lnahlnh m gln alnh m Mualem G shi +wa+gs as a asa I-w I,hw lnh m n A, w+ah n + I + w I, h, w I - w I +w+w m m +w m I + +,hw ah + h m A- +w m m+ +w m+ A. I -wi -awi -bw * ww * A/ I -wi -bw ww * w m h m w w * +* +* A/ I -a w I -b w I -aw+w * m ln +w * + w * m +wm ln +w w + G+wG+w* A0 m I -bwmmw mw m lnw mwlnw A1 A0 G w GwG sw *H+W *H+w ww * GwG sw ww * A2 W **.3 H w G s w Hwlnwmwmm+ w,. mm+m, w- +2 G sww w k m+ m+k A3 A+* Mualem G maxg sh *G *c A++ h * A, *.*,/a G *c h G *ca +gsasa S a nlnh m ah * n+ ah c n+ A+, asa lnh m ah*n+ lnah* + n+ ah c n+ lnahc + n+ h c A, + +* 1 cm, K vh K D Mg vh r vs H r B+ r w RT ads D L, T + r w ML * 0 T., -.13+* 2 T. - kg m - T K,,* r vs ML - T + +* - exp *+..13T + 1.3,+* - T kg m - M Mmol + *.*+2*+/ kg mol + g LT, 3.2+ ms, R ML, T, mol + K Jmol + K + T abs K H r D

15 : 77 Dt aq aird a B, q air L - L - D a L, T +,.+,+* / T abs,1-.+/, m, s + t a Millington and Quirk, +30+ t a qair1q, s B- Philip and de Vries, +3/1 H hmg rexp B. RT abs van Genuchten VG Fayer Durner Fayer Durner, VG Mualem l :,**1 2,, :,**1 +* +0