UILU-WRC-83-0177
Research Report 177
UNDISTURBED CORE METHOD FOR DETERMINING
AND EVALUATING THE HYDRAULIC CONDUCTIVITY
OF UNSATURATED SEDIMENTS
A t e f E l zeftawy and Keros C a r t w r i g h t
Hydrogeol ogy and Geophysics Section
I 1 1 i n o i s S t a t e Geological Survey, Champaign
A p r i l 1983
P r o j e c t A-097-ILL
Matching Grant Agreement No. 14-34-0001-0115
F'inal Technical Completion Report
to
U.S. Department o f t h e I n t e r i o r
Washington, D.C.
20240
CONTENTS
......
Keywords . . . . .
Acknowledgments . .
Introduction . . . .
........................ 1
........................ 1
........................ 1
........................ 1
S o i l water p o t e n t i a l
........................ 2
S o i l water c h a r a c t e r i s t i c f u n c t i o n . . . . . . . . . . . . . . . . . . . 7
Hydraulic conductivity function . . . . . . . . . . . . . . . . . . . . 8
U n i t s f o r s o i l water p o t e n t i a l . . . . . . . . . . . . . . . . . . . . . 12
M a t e r i a l s and methods . . . . . . . . . . . . . . . . . . . . . . . . . 13
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
L i s t o f p u b l i c a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Abstract
.
.
.
.
.
.
.
.
.
.
TABLES
.
. . . . . . . . 13
. . . . . . . . . . . . . . . . . . 14
1
P o t e n t i a l expressed i n t h e major measurement systems
.
3.
Conversions f o r p o t e n t i a l u n i t s
2
Location. type and p a r t i c l e s i z e data o f undisturbed samples used
i n study
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4 . P r o p e r t i e s o f undisturbed core samples . . . . . . . . . . . . . . . 16
5
.
Bulk d e n s i t y and saturated hydraul i c c o n d u c t i v i t y o f Lakeland f i n e
sand
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
6 . Selected physical p r o p e r t i e s o f s o i l s used a t i n d i c a t e d depths . . . 21
FIGURES
1.
2.
3.
4.
C a p i l l a r y tubes showing c o n f i g u r a t i o n o f t h e a i r w a t e r i n t e r f a c e s
a t d i f f e r e n t h e i g h t s ( a f t e r Dempsey and E l z e f t a w y [231)
5
V a r i a t i o n i n pressure above and below water t a b l e ( a f t e r Dempsey
and E l zeftawy [22] )
.
.
.
6
R e l a t i v e s o i l - w a t e r c h a r a c t e r i s t i c curves f o r a c l a y e y s o i l and
.
.
.
sandy s o i l
7
......
........ ..... ..... ...
.. ........... .... .........
Tensiometer system ( a f t e r Dempsey and E l z e f t a w y [ 2 2 ] ) . . . . . . .
9
5.
H y s t e r e s i s e f f e c t s o f d r y i n g and w e t t i n g c o n d i t i o n s on m a t r i c
suction .
..
.
6.
Tempe pressure c e l l s set-up i n t h e
7.
D e t a i l e d c r o s s s e c t i o n o f tempe c e l l ( a f t e r S o i l m o i s t u r e
.
Equipment Corp 1231 )
18
8.
Permeameter used f o r
18
9.
Experimental and c a l c u l a t e d hydraul i c c o n d u c t i v i t y o f Lake1and
.
. .
f i n e sand
10.
Soi 1 m o i s t u r e - s u c t i o n r e l a t i o n s h i p s o f Lakeland f i n e sand and
.
Drummer s o i l
11.
Experimental and c a l c u l a t e d h y d r a u l i c c o n d u c t i v i t y o f D r u ~ m e rs o i l
12.
Experimental and c a l c u l a t e d hydraul i c c o n d u c t i v i t i e s of Ottawa
sand
13.
Experimental and c a l c u l a t e d hydraul i c c o n d u c t i v i t i e s o f F a y e t t e
C horizon
.
14.
Experimental and c a l c u l a t e d
...............
.... ....... 9
l a b o r a t o r y . . . . . . . . . . . 17
..... ..................
determining saturated hydraulic c o n d u c t i v i t y .
. . . . . . . . . . . . . . . . . . . 20
. ......
. . . . . . . . . . . . . . . . . . . . . . . . . . . 23
. 24
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
..........
. . . . . . . . . . . . . . . . . . 26
h y d r a u l i c c o n d u c t i v i t i e s o f Dana s o i l . 27
ABSTRACT
This paper describes a new method developed to predict the transport
of moisture and contaminants in soils. Study results indicate that this
method could help simplify evaluation of municipal and industrial waste
disposal s i t e s for their potential environmental impact. Saturated and
unsaturated hydraulic conductivities of several Illinois soils, calculated
on the basis of pore size distribution, were shown to predict reliably the
experimentally measured laboratory valhes. For coarse-textured soil materi a l s a n d materials with a relatively narrow range of pore size, only one
matching factor was required to calculate the hydraulic conductivity-water
content re1 ation accurately enough for many purposes; however, for finetextured soil materials with a wide range of pore size distribution, two
or more matching factors a t a water content in the 0.3 to 0.4 bar range
may be needed to obtain a useful evaluation for the unsaturated hydraulic
conductivity.
KEY WORDS
unsaturated hydraulic conductivity, soil water, matching factor, permeability,
groundwater, soil water potential, water retention
ACKNOWLEDGMENTS
W
e are grateful t o staff members of the Hydrogeology a n d Geophysics
Section a t the Illinois State Geological Survey for their advice and assistance during the course of the study; to Julie Engelhart, former research
assistant, for helping with the laboratory work; and to Glenn E. Stout,
Director of the Water Resources Center, University of Illinois, for his
cooperation and assistance. Partial funding for thi s study was provided
by the U.S. Department of Interior, Office of Water Research and Development.
INTRODUCTION
A t 1east two basic parameters of geologic sediments-hydraul ic conductivi ty and soi 1 water characteristic functi ons-must be eval uated before
predictive analyses can be made of the transport of moisture and contaminants
in the unsaturated-saturated zone of a s o i l . These parameters must be
measured a c c u r a t e l y b e f o r e d e t e r m i n a t i o n s can be made o f t h e p o t e n t i a l
environmental impact o f m u n i c i p a l and i n d u s t r i a l waste d i s p o s a l s i t e s .
R e l i a b l e measurement o f these parameters i s a l s o e s s e n t i a l t o p l a n n i n g
and managing e f f i c i e n t schernes f o r i r r i g a t i o n water.
T h i s r e s e a r c h p r o j e c t was undertaken t o determine t h e s o i l w a t e r parameters o f sorne nonindurated g e o l o g i c sediments i n I l l i n o i s .
Our s p e c i f i c
o b j e c t i v e s were:
. t o determine t h e s o i l water c h a r a c t e r i s t i c f u n c t i o n s i n t h e
l a b o r a t o r y , u s i n g u n d i s t u r b e d and d i s t u r b e d samples.
- t o determine t h e s a t u r a t e d - u n s a t u r a t e d h y d r a u l i c c o n d u c t i v i t y
f u n c t i o n s u s i n g t h e same u n d i s t u r b e d samples.
0,
t o e v a l u a t e t h e hydraul i c c o n d u c t i v i t y f u n c t i o n s of a1 1 samples,
u s i n g t h e c a p i l l a r y model and t h e pore s i z e d i s t r i b u t i o n data.
Before d i s c u s s i n g t h e methodology and r e s u l t s o f o u r s t u d y we w i l l
d e f i n e s e v e r a l i m p o r t a n t s o i l water concepts t h a t a r e c r i t i c a l t o unders t a n d i n g and p r e d i c t i n g s o i l water movement:
s o i l water p o t e n t i a l , s o i l
w a t e r c h a r a c t e r i s t i c f u n c t i o n , h y d r a u l i c c o n d u c t i v i t y f u n c t i o n , and u n i t s
f o r s o i l water p o t e n t i a l .
Soi 1 Water P o t e n t i a l
S o i l water c o n t a i n s energy i n d i f f e r e n t forms and q u a n t i t i e s .
The
two p r i n c i p l e forms of energy a r e k i n e t i c energy, a f u n c t i o n o f v e l o c i t y
and p o t e n t i a l energy t h a t i s a f u n c t i o n o f p o s i t i o n o f i n t e r n a l c o n d i t i o n
of t h e system.
Since water moves v e r y s l o w l y i n s o i l , k i n e t i c energy can
g e n e r a l l y be i g n o r e d i n t h e s t u d y o f s o i l w a t e r systems; however, p o t e n t i a l
energy i s o f p r i m a r y importance i n d e t e r m i n i n g t h e s t a t e and t h e movement
o f water i n s o i l .
The spontaneous and u n i v e r s a l tendency o f a1 1 m a t t e r i n n a t u r e i s t o
move from a p o i n t o f h i g h p o t e n t i a l energy t o a p o i n t o f l o w p o t e n t i a l
energy u n t i l an e q u i l i b r i u m c o n d i t i o n i s reached.
S o i l water systems obey
t h e same u n i v e r s a l p u r s u i t o f e q u i l i b r i u m .
A s o i l water system i s s u b j e c t e d t o a number o f f o r c e f i e l d s , which
causes i t s . p o t e n t i a l t o d i f f e r from t h a t o f f r e e water.
commonly considered a r e g r a v i t a t i o n a l p o t e n t i a l , $I
g'
The f o r c e f i e l d s
pressure p o t e n t i a l ,
, osmotic p o t e n t i a l , m0, and gas p o t e n t i a l , ma. The t o t a l p o t e n t i a l ,
P
o f t h e s o i l water system can be considered as t h e sum o f t h e i n d i v i d u a l
potentials:
mT
=
mg
+
"
+
m0
+
ma
mT,
(1)
and pressure p o t e n t i a l , 4 , a r e t h e
g'
P
p r i m a r y f o r c e f i e l d s i n s o i l water systems. The osmotic p o t e n t i a l , m0, i s
The g r a v i t a t i o n a l p o t e n t i a l , 4
dependent upon t h e presence o f a s o l u t e i n t h e s o i l water system.
ma,
potential,
The gas
i s dependent upon e x t e r n a l o r i n t e r n a l gas pressure i n t h e
I f the osmotic p o t e n t i a l and gas p o t e n t i a l a r e considered t o have
system.
minor i n f l u e n c e on t h e t o t a l p o t e n t i a l , then Equation 1 can be s i m p l i f i e d
as f o l 1ows :
.
mT
.
=
mg
+
mp
(2)
A t a h e i g h t z above an a r b i t r a r y r e f e r e n c e l e v e l , t h e g r a v i t a t i o n a l
energy of water i n s o i l , E, can b e s t a t e d as follows:
E =. Mgz = y
I n equation 3,
yw
W
gzv
(3)
i s t h e d e n s i t y o f water, g i s t h e a c c e l e r a t i o n o f g r a v i t y
and V i s t h e volume o f t h e mass, M.
p o t e n t i a l energy, 9
g'
From Equation 3, t h e g r a v i t a t i o n a l
can be expressed as f o l l o w s :
= gz ( p e r . u n i t mass, M)
(4
= y , gz ( p e r u n i t volume, V )
(5)
g
= z ( p e r u n i t weight, W )
(6
9
depends o n l y on z and i s d e f i n e d as t h e g r a v i t a t i o n a l head
@
I n Equation 6,
@
9
i n s o i 1 water systems.
i s n e g a t i v e f o r unsaturated s o i l water systems
P'
and p o s i t i v e f o r s a t u r a t e d s o i l water systems. I t can be shown t h a t t h e
Pressure p o t e n t i a l ,
@
pressure p o t e n t i a l concept a l l o w s f o r t h e c o n s i d e r a t i o n o f t h e e n t i r e
m o i s t u r e p r o f i l e i n t h e f i e l d i n terms o f a s i n g l e continuous p o t e n t i a l
extending from t h e s a t u r a t e d r e g i o n t o t h e unsaturated region, below and
above t h e water t a b l e .
The p o s i t i v e pressure p o t e n t i a l f o r a s a t u r a t e d s o i l water system i s
f a i r l y w e l l understood.
The n e g a t i v e pressure-less
w e l l understood-has
o f t e n been termed c a p i l l a r y p o t e n t i a l , s o i 1 s u c t i o n , o r (more a c c u r a t e l y )
matrix potential.
This p o t e n t i a l r e s u l t s from the c a p i l l a r y and a b s o r p t i v e
forces.developed i n t h e s o i l m a t r i x .
I n d i s c u s s i n g pressure p o t e n t i a l f o r unsaturated s o i l water systems,
t h e c a p i l l a r y tube analogy i s useful
.
S o i l can be assumed t o be a porous
medium composed o f c a p i l l a r y tubes o f d i f f e r e n t s i z e s .
I n f i g u r e 1 the a i r
water i n t e r f a c e s throughout t h e s o i l c o n s i s t s of menisci i n which t h e curvat u r e o r r a d i i i n d i c a t e t h e s t a t e o f t e n s i o n i n t h e s o i l water (much as a
c a p i l l a r y tube does).
As the m o i s t u r e c o n t e n t o f t h e s o i l i s reduced, t h e
a i r water i n t e r f a c e s recede i n t o t h e s m a l l e r pores, t h e r a d i i o f c u r v a t u r e
decrease, and t h e m o i s t u r e t e n s i o n increases.
I n t h e c a p i l l a r y tube shown i n f i g u r e 2 t h e water above t h e water t a b l e
w i l l be i n e q u i l i b r i u m when t h e upward component o f t h e s u r f a c e t e n s i o n
f o r c e i s equal t o t h e g r a v i t a t i o n a l f o r c e a c t i n g on t h e suspended water.
The height, h, t o which t h e water w i l l r i s e i n t h e c a p i l l a r y tube i s r e l a t e d
m a i n l y t o t h e s u r f a c e tension, a, and radius, r, o f t h e meniscus by t h e
f o l l o w i n g equation:
h =
2 a cos
Yw 9 r
e
I n f i g u r e 2 atmospheric pressure e x i s t s a t p o i n t s 1, 2, and 3.
However,
a t p o i n t 4, j u s t below t h e meniscus, t h e pressure i s l e s s than atmospheric
pressure by an amount equal t o hywg.
Assuming t h a t c o s i n e e I 1 f o r water
i n s o i l , and t h a t t h e c u r v a t u r e o f t h e water i n t h e s o i l m a t r i x i s s i m i l a r
t o t h a t i n a c a p i l l a r y tube o f t h e same s i z e ( f i g u r e 2 ) , t h e pressure potent i a l p e r u n i t mass can be expressed from Equation 7 as f o l l o w s :
The n e g a t i v e s i g n i s used i n Equation 8 because t h e pressure p o t e n t i a l
i n an unsaturated s o i l water system i s l e s s than atmospheric pressure and
because h would have a n e g a t i v e value i n an unsaturated system.
From Equations 2, 4, and 8 t h e t o t a l p o t e n t i a l p e r u n i t mass, excludi n g t h e osmotic p o t e n t i a l and gas p o t e n t i a l , can be s t a t e d as f o l l o w s :
On a u n i t weight basis, n o r m a l l y used i n s o i l water s t u d i e s , Equation 9 can
be shown i n t h e f o l l o w i n g form:
r
--.--
--
M ~ g n iled
f roil
--.(/ particles
Pressure change across meniscus
(= roil rnolsture s u c l ~ o n t = 8 6 Iblsq in
p F 2.78
- -- ------
-
R a d ~ u sof tncnlscub
0.0001 In.
Pressure change across menlscus
Redtus of rnentrcuc
Figure 1. Capillary tubes showing configuration of the air water interfaces at
different heights (after Dernpsey and Elzeftawy [22]).
Figure 2. Variation in pressure above and below water table
(after Dempsey and Elzeftawy [221 ).
H = z + h
(10)
I n Equation 10, H i s t h e t o t a l s o i l water head, z i s t h e g r a v i t a t i o n a l
head, and h i s t h e pressure head.
The pressure head i s negative ( s u c t i o n )
i n unsaturated s o i l water systems and p o s i t i v e f o r s a t u r a t e d s o i l water
systems.
To summarize, t h e c r i t e r i o n f o r t h e e q u i l i b r i u m i n s o i l water systems i s
t h a t t h e t o t a l water p o t e n t i a l be equal throughout t h e system.
To f a c i l i t a t e
t h e a n a l y s i s o f p a r t i c u l a r systems, t h e t o t a l water p o t e n t i a l i s p a r t i t i o n e d
i n t o various components t h a t can be measured.
Typically, the g r a v i t a t i o n a l
p o t e n t i a l i s determined by use o f a measuring tape, t h e pressure p o t e n t i a l
by a pietometer f o r saturated systems and a tensiometer f o r unsaturated
systems, and t h e gas p o t e n t i a l by a pressure gauge.
Soil Water Characteristic Function
The relationship expressed in a soil water characteristic function i s
a soil property of fundamental importance in the analysis of water equilibrium and flow behavior in s o i l . Figure 3 shows relative soil water charact e r i s t i c curves for two different s o i l s . Physically, the curve t e l l s ( a t
any given moisture content) how much energy (per unit quantity of water
removed) i s required to remove a small quantity of water from the s o i l .
I t indicates how tightly water i s held in the s o i l . Hillel ( I ) , Taylor
and Ashcroft (2), Kirkham and Powers ( 3 ) , and Rose ( 4 ) have presented detailed
explanations of how water i s held in s o i l . Childs ( 5 ) has considered the
mechanisms of water held in both swelling and non-swell ing s o i l s in great
detail.
Crorney, Coleman, and Bridge ( 6 ) have described the methods used to
determine the soil water characteristic curve-those used most frequently
are the tensiometer, direct suction, pressure plate, and centrifuge methods.
Because no single method can cover the entire moisture tension range,
several measurement methods are generally used in determining these curves.
Water content
Figure 3. Relative soil-water characterisitic curves for a clayey soil and sandy soil.
Figure 4 shows a simple type of tensiometer system t h a t can be used
f o r t h e low moisture-tension range ( < 100 kN/m
2
, or
< 1 bar).
The apparatus
shown i n f i g u r e 4 c o n s i s t s o f a porous p l a t e w i t h i t s pores f i l l e d w i t h
water.
The chamber beneath t h e porous p l a t e i s f i l l e d w i t h water and
connected t o a f l e x i b l e tube t h a t i s a l s o f i l l e d w i t h water.
The negative
head i s equal t o t h e distance, h, between t h e s o i l sample and t h e o u t f l o w
end o f t h e f l e x i b l e tube i n f i g u r e 4.
The s o i l water c h a r a c t e r i s t i c curve
i s determined frorn t h e r e l a t i o n s h i p between t h e water content o f t h e s o i l
sample and t h e magnitude of t h e negative pressure head o f t h e water.
Hysteresis e f f e c t s ( f i g u r e 5 ) w i 11 o f t e n occur between s o i 1 water
c h a r a c t e r i s t i c curves f o r d r y i n g and w e t t i n g .
The h y s t e r e s i s f o r t h e
d r y i n g and w e t t i n g c o n d i t i o n s a r i s e s frorn the i n f l u e n c e o f pore s i z e
d i s t r i b u t i o n on water h e l d i n t h e s o i l .
A complete moisture c h a r a c t e r i s -
t i c curve should c o n s i s t of a d r y i n g (desorption) curve and a w e t t i n g
( s o r p t i o n ) curve.
The d r y i n g curve should s t a r t a t s a t u r a t e d water content
a t c l o s e t o zero s u c t i o n and continue t o a low water content a t a h i g h
l e v e l o f suction.
The w e t t i n g curve should s t a r t a t t h e h i g h l e v e l o f
s u c t i o n and low water content and proceed t o s a t u r a t i o n .
This would
c h a r a c t e r i z e an envelope f o r water content and s u c t i o n values i n t h e given
range.
The i n f l u e n c e o f small moisture content changes on s o i l s u c t i o n i s
shown by t h e smaller h y s t e r e t i c curves i n s i d e t h e desorption and s o r p t i o n
curves i n f i g u r e 5.
A useful simp1 i f i c a t i o n occurs when t h e s o i l s u c t i o n i s given i n u n i t s
o f water head.
A s u c t i o n of 20 cm w i l l l i f t a column o f water 20 cm above
a f r e e water surface. Therefore, t h e s u c t i o n on t h e m o i s t u r e c h a r a c t e r i s t i c s
curve can be equated t o the distance above a water t a b l e f o r e q u i l i b r i u m
conditions.
Also, by use of the s o i l water c h a r a c t e r i s t i c curve i t i s
p o s s i b l e t o estimate t h e e q u i l i b i r u m water content a t v a r i o u s p o s i t i o n s
above the water t a b l e .
Hydraul i c C o n d u c t i v i t y Function
The f l o w of water through s o i l s i s o f t e n unsteady and unsaturated.
Examples o f such flows are t h e i n f i l t r a t i o n o f water from t h e ground surface,
t h e f l o w through t h e c a p i l l a r y f r i n g e of an unconfined aquifer, t h e d r a i n i n g
o f s o i l s , t h e evaporation from an a q u i f e r c l o s e t o t h e ground surface, t h e
'( [ZZ] A ~ e y a z l gpue Aasdwaa l a y e ) UIaJsAs JaIalrro!sual ' p a l n 6 ! j
f l u c t u a t i o n s o f groundwater l e v e l , t h e i n f l o w of water from i r r i g a t i o n
channels, and t h e l a n d disposal o f 1 i q u i d wastes.
The general nonl i n e a r p a r t i a l d i f f e r e n t i a l
equation t h a t describes t h e
t r a n s p o r t o f groundwater can be w r i t t e n as f o l l ows :
where e i s t h e v o l u m e t r i c water c o n t e n t d e f i n e d as t h e r a t i o o f t h e volume
o f water, V
operator.
t o t h e t o t a l volume of s o i l , V, v i s t h e v e c t o r d i f f e r e n t i a l
K i s t h e h y d r a u l i c c o n d u c t i v i t y , and $ i s t h e t o t a l p o t e n t i a l .
For a complete d e r i v a t i o n o f Equation 11 ( 5 o r 6 ) . An equation o f t h i s
t y p e a p p l i e s t o any nonreactive l i q u i d i n t h e porous medium; s i n c e we l i m i t
ourselves i n t h i s study t o water, i t i s convenient t o t a k e t h e l e n g t h of
water column as t h e u n i t o f p o t e n t i a l .
P o t e n t i a l g r a d i e n t s a r e then
dimensionless, and i f t h e time, t, i s expressed i n hours, t h e u n i t o f
h y d r a u l i c c o n d u c t i v i t y i s centimeters per hour.
When t h e t o t a l p o t e n t i a l i s composed o f o n l y g r a v i t a t i o n a l and n e g a t i v e
pressure ( c a p i l l a r y ) components, Equation 11 may be w r i t t e n :
where h i s t h e s u c t i o n ( n e g a t i v e pressure) p o t e n t i a l , and z i s t h e v e r t i c a l
o r d i n a t e , p o s i t i v e upward.
When h and K a r e s i n g l e - v a l u e d f u n c t i o n s o f 9, Equation 12 becomes
where
C h i l d s and Collis-George ( 7 ) c a l l e d D t h e d i f f u s i v i t y o f s o i l water
a r ~ dfound i t t o be a f u n c t i o n o f 9.
Rogers and K l u t e ( 8 ) have shown t h a t
h y d r a u l i c c o n d u c t i v i t y , K, i s u n i q u e l y r e l a t e d t o s o i l m o i s t u r e content, e.
Two p h y s i c a l p r o p e r t i e s of t h e s o i l t h a t e n t e r i n t o a saturated-unsaturated
f l o w problem a r e hydraul i c c o n d u c t i v i t y , K(e), and s o i 1 moi s t u r e r e t e n t i o n
h ( e ) ; these p r o p e r t i e s must be known i f a s o l u t i o n o f Equation 13 i s t o be
obtained.
C h i l d s and C o l l is-George (7), M i l 1i n g t o n and Q u i r k ( 9 ) , Green and
Corey ( l o ) , and o t h e r s have explored t h e p o s s i b i l i t y of p r e d i c t i n g t h e
h y d r a u l i c c o n d u c t i v i t y o f s o i l s and o t h e r porous m a t e r i a l s on t h e b a s i s o f
pore s i z e d i s t r i b u t i o n .
Such p r e d i c t i o n s a r e of i n t e r e s t because t h e
h y d r a u l i c c o n d u c t i v i t y f u n c t i o n , K(e), i s r e l a t i v e l y d i f f i c u l t t o measure,
whereas pore s i z e d i s t r i b u t i o n i s e a s i l y o b t a i n a b l e by t h e standard
measurement o f moisture content versus s u c t i o n ( n e g a t i v e pressure).
The h y d r a u l i c c o n d u c t i v i t y i s obtained by d i v i d i n g t h e r e l a t i o n of
m o i s t u r e content and suction, h(e), i n t o n equal water c o n t e n t increments,
o b t a i n i n g t h e s u c t i o n , h, a t t h e m i d p o i n t o f each increment, and c a l c u l a t i n g t h e c o n d u c t i v i t y by using t h e f o l l o w i n g equation (see r e f . 7 f o r more
details):
where
K(e)i = c a l c u l a t e d c o n d u c t i v i t y f o r a s p e c i f i e d m o i s t u r e c o n t e n t c o r responding t o t h e i t h increment, crn/min;
e
3
3
= m o i s t u r e content, cm /cm ;
y =
s u r f a c e t e n s i o n o f water, N/cm;
p =
d e n s i t y o f water, g/cm3;
g = g r a v i t a t i o n a l constant, cm/s2;
I-I
s
E
= kinematic v i s c o s i t y o f water, cm2/s;
= s a t u r a t e d moisture 'content, cm3/cm 3.,
3
= water-saturated p o r o s i t y (cm /cm
p =
3
), t h a t i s ,
E
= e
-
s,
constant whose value depends on t h e method o f c a l c u l a t i o n 6,
i s equal t o 2 i n these c a l c u l a t i o n s ;
'0
= lowest moisture c o n t e n t on t h e experimental h ( e ) curve;
n = t o t a l number of pore classes between e =
(eS
-
e and
0
9,
n = mBS/
go);
i = l a s t moisture-content increment on t h e wet end ( f o r example,
i
-
1 i d e n t i f i e s t h e pore c l a s s corresponding t o eo);
h. = suction (negative pressure) for a given class o f moistureJ
f i l l e d pores ( c e n t i m e t e r s o f water head); and
30 = t h e composite o f t h e c o n s t a n t 1/8 from P o i s e u i l l e ' s equation,
4 f r o m t h e square of r = 2y/h, where r i s t h e pore r a d i u s and
60 c o n v e r t s from seconds t o minutes.
Green and Corey (10) c o n ~ l u d e dt h a t Equation 15 y i e l d s reasonable
values o f t h e h y d r a u l i c c o n d u c t i v i t i e s f o r a range o f s o i l types i f a
matching f a c t o r i s used.
E l z e f t a w y and Mansell (11) and E l z e f t a w y and
Dempsey (12) s t a t e d t h a t a matching f a c t o r a t water s a t u r a t i o n ( t h e r a t i o
of t h e measured t o t h e c a l c u l a t e d , s a t u r a t e d h y d r a u l i c c o n d u c t i v i t y ) has a
d l s t i n c t advantage o v e r match p o i n t s because i n a c c u r a c i e s i n c a l c u l a t e d
and experimental l y e v a l u a t e d K(e) can be more e a s i l y t o 1 e r a t e d a t 1ower
moisture content.
f a c t o r KS/KSc,
Equation 15 can t h e n be w r i t t e n by u s i n g t h e matching
i n t h e f o l l o w i n g form:
m
c [(2j
j=i
~ ( 0 =) ~
+
1 - 2i)h;]
(16
where Ks i s t h e measured s a t u r a t e d h y d r a u l i c c o n d u c t i v i t y , and KSc i s t h e
calculated saturated conductivity.
U n i t s f o r S o i l Water P o t e n t i a l
The normal methods o f e x p r e s s i n g p o t e n t i a l i n s o i l water systems a r e
shown i n t a b l e 1 f o r t h e v a r i o u s measurement systems.
t h e measurement systems a r e shown i n t a b l e 2.
Relationships f o r
For p o t e n t i a l s expressed
on a p e r u n i t w e i g h t b a s i s o r on a p e r u n i t volume b a s i s , t h e dimensions
a r e those o f l e n g t h ( c e n t i m e t e r , meter, o r f o o t ) o r o f pressure (dyne/
square c e n t i m e t e r , newton/square meter, o r pound/square f o o t ) , r e p e c t i v e l y .
Equations f o r c o n v e r t i n g between t h e t h r e e forms o f p o t e n t i a l a r e s t a t e d
as f o l l o w s :
energy -mass
energy
weight
energy volume - Y~
energy
mass
energy -v o l urne
"w
energy
weight
(19)
Table 1.
Potential
P o t e n t i a l expressed i n t h e m a j o r measurement systems.
cgs system
mks system
English
sys tem
energy
mass
dyne cm -- erg
gm
Qm
Newton meter -- -J o u l e
kg
kg
energy
weight
dyne = crcm
Newton meter
Newton
- meter
-ft- 1b - ft
%%
dyne cm
3
cm
- dyne
Newton meter
3
meter
- Newton
-ft- -1b - 1b
dyne
-
2
cm
meter2
ft 1b
slug
1b
ft3
ft2
1 bar
14.5 p s i
33.4 ft w a t e r
1020 cm w a t e r
I n making analyses of s o i l w a t e r systems, i t i s convenient t o use one
of t h e s e methods c o n s i s t e n t l y f o r e x p r e s s i n g p o t e n t i a l r a t h e r than t o use
more t h a n one method i n t h e same analyses.
O f t h e t h r e e methods, p o t e n t i a l s
expressed as energy per u n i t w e i g h t appear t o be u t i l i z e d most i n t h e 1 i t e r a t u r e and a r e used i n t h i s paper.
MATERIALS AND METHODS
Determinations o f s o i l w a t e r c h a r a c t e r i s t i c and hydraul i c c o n d u c t i v i t y
functi.ons were made o f t r i p 1 i c a t e u n d i s t u r b e d and d i s t u r b e d s o i l samples.
The u n d i s t u r b e d c o r e samples (5.4 cm i n diameter and 3 cm i n h e i g h t ) were
c o l l e c t e d from s i t e s i n I l l i n o i s .
The s o i l cores used i n t h i s s t u d y were
o b t a i n e d d u r i n g p r e v i o u s s t u d i e s and taken from storage.
A l l t h e samples
htad been a l l o w e d t o dry, b u t o t h e r w i s e were undisturbed.
The l o c a t i o n s
and some p h y s i c a l p r o p e r t i e s o f t h e u n d i s t u r b e d c o r e samples a r e shown i n
t a b l e 3.
The d i s t u r b e d s o i l samples ( t a b l e 4 ) were passed through a 2-mm
seive, oven d r i e d , and hand packed i n t h e "Tempe" t e s t c e l l s .
A1 1 samples were placed i n "Tempe" pressure c e l l s and s a t u r a t e d w i t h
water.
The Tempe" pressure c e l l operates under t h e same p h y s i c a l p r i n c i -
p l e s as does t h e porous p l a t e apparatus o f t h e ASTM T e s t f o r C a p i l l a r y ,
w
r
r
0
N
O
r
0
W
*
.
.
P
O
w
w
9
P
r
o
.
O
O
r
" ON
9
w
w
P
r
N
.
O
O
W
p
m
l-
O
o
m
UY
W
W
W
W
g
N
S
0
o
W
W
m
r
r
0
u
U
Y
o
W
W
r
r
1
ON
m
O
~
m
r
0
r
0
0
W
W
.
O
O
0
r
o
o
03
'
W
5
.
N
rt
-h
03
N
W
IC
03
U Y O U Y
0
0
0
3
0
0
0
YE
Y " .
w
0
w
UY
o
w
w
0
r
r
.
o
S
W
0
0
O
0
N
w
0
0
03
03
r
r
o
O
O
O
W
o
o
r
UY
m
o
~
a
0
O
O
W
r
. .
0
w
w
ZNF
$IH
N3
N
N
?
.
Y
O
N
o
z mZ
W
03
a
.
r
n
w
0
o
w
o
W
W
r
a
W
UY
N
l-
u
w
0
W
N
W
o
W
W
m
r
0
0
.
C'
0
r
W
0
w
S
l-
.
o
S
00
o
-
3
0
S
N
. . . . .
.
5 8 8 S w " o8
m
O
O
0
o
0
0
0
0
r
u
UY
w
0
03
O
r
0
0
r
o
o
o
o
o
N
UY
0
-
.
w
N
O
w
~
0
N
. . . . . .
.
g Z 8P °O
o 0o 0o r o o ow o
O
w
N
O
m
%
l-
r
S 8
W
0
O
r
r
z s . . . .
0
P
W
r
0
O
m
K
O
0
W
0
r
0
r
0
r
W
o
ZO % w
0
N
r
N
o
g r
g
P
0
0
I
O
U
P
0
N
0
UY
r
ID
0
w
UY
. . . . . . . . .
r
0
r
0
W
0
o
0
o
o
o
0
0
l
0
-
0
0
0
z
g
o0 w
Z W
0
0
0
8 G Z Zg
0
0
U
Y
o
r
UY
l-
W
O
W
2 %
u
8::
,
0
. . . . . . . . . .
w
w
o Oo o o o ~
S
u
o
g
$o 8 8
- o
0
W
S
~
~
w
~
~
2
w
~!
ii8 ~
g
5
W
T)
g
ID
1
03
u
2
Cahokia
(a1 luvium
overbank o r /
backwater)
a l l Alexander County l o c a t i o n s
a l l C l a r k County l o c a t i o n s
A1 exander
A1 exander
A1 exander
A1 exander
A1 exander
A1 exander
A1 exander
Alexander
Alexander
' ~ c ~ a y ,e t a l . [25]:
' ~ o l l m e r [241:
1
2
3
4
5
6
7
8
9
no.
no.
no.
no.
no.
no.
no.
no.
no.
Parkland
(eolian
sand
and
silt)
13
14
15
16
17
19
20
no.
no.
no.
no.
no.
no.
no.
Ogle
Ogle
Ogle
Ogle
Ogle
Ogle
Ggl e
Vandal i a T i 1 1
Berry Clay
B e r r y Clay
Peoria Loess
Berry Clay
B e r r y Clay
Peoria Loess
Roxana S i l t
Roxana S i l t
Roxana S i l t
~l
ark1
Clark
Clark
Clark
Clark
Clark
Clark
Clark
Clark
Clark
11
12
21
22
25
26
27
28
29
30
no.
no.
no.
no.
no.
no.
no.
no.
no.
no.
Material
Peoria Loess
Peoria Loess
Peoria Loess(?)
R.
Piatt
Piatt
Piatt
Twp.
0-12" P i a t t
12-36" P i a t t
30-60" P i a t t
Sec.
E q u a l i t y Fm.
E q u a l i t y Fm.
County
Depth(cm)
Soi 1
Horizon
Location, type and p a r t i c l e s i z e data o f undisturbed s a m ~ l e sused i n study.
Champaign
Adams
Sampl e
No.
Table 3.
P a r t i c l e Size (%)
Sand
Silt
Clay
Table 4.
P r o p e r t i e s of d i s t u r b e d samples.
p a r t i c l e size (%)
s o i l sample
sand
silt
clay
Fine Ottawa Sand
100
-
Coarse Ottawa Sand
100
-
Ground Ottawa Sand
100
-
-
4
86
10
11
61
28
R i c h l a n d Loess
Roxana S i l t
M o i s t u r e R e l a t i o n s h i p s f o r Coarse and Medium-Textured S o i l s by PorousP l a t e Apparatus D 2325-68 ( 1 9 7 4 ) ~ w i t h maximum 1 atm pressure. Figures
6 and 7 show t h e l a b o r a t o r y setup and a schematic o f t h e pressure c e l l .
A
constant temperature was maintained a t a l l times i n t h e l a b o r a t o r y .
The s a t u r a t e d h y d r a u l i c c o n d u c t i v i t i e s o f a l l samples were determined
u t i l i z i n g an apparatus ( f i g u r e 8 ) s i m i l a r t o t h a t used i n t h e ASTM Test
f o r Permeabil it y o f Granular S o i l s (Constant Head) D 2434-68 (1974).
The
samples were then subjected t o a i r pressure.
A f t e r t h e i r s a t u r a t e d h y d r a u l i c c o n d u c t i v i t y was determined, t h e samples
were allowed t o d r a i n f o l l o w i n g sequential s u b j e c t i o n t o a i r pressures of
100, 200, 300, 500, 800, and 1000 cm o f water.
They were then placed i n a
15-bar porous-plate apparatus t o determine t h e e q u i l i b r i u m m o i s t u r e c o n t e n t
r e t a i n e d i n t h e s o i l sarr~plesf o r a i r pressures o f 1, 3, 5, and 15 atm ( u s i n g procedures s i m i l a r t o ASTM D 2325-68 o r ASTM Test f o r C a p i l l a r y - M o i s t u r e
R e l a t i o n s h i p s f o r Fine-Textured S o i l s by Pressure-Membrane Apparatus
D 3152-72 I1977)).
The water c o n t e n t (by volume) was determined from t h e
weight o f t h e pressure c e l l corresponding t o each s t a t e e q u i l ibrium pressure
and t h e oven-dry weight of t h e s o i l samples.
The measured hydraul i c c o n d u c t i v i t y f u n c t i o n , K(e) , o f a1 1 samples was
evaluated by t h e instantaneous p r o f i l e method suggested by Watson (13) and
described by Rogers and K l u t e ( 8 ) . Another method, described by Elzeftawy
and Mansell ( l l ) , was a l s o used t o determine K(e) o f each sample. This
method i s based on t h e u t i l i z a t i o n o f a u n i t h y d r a u l i c g r a d i e n t t o p r o v i d e
a steady-state, downward, unsaturated flow o f water across t h e s o i l core.
The computer program developed by Elzeftawy and Dempsey (12) was used t o
clamping wing nut
enlarged soil partical
in sample
soil core sample held
in retaining cylinder
"0"ring
cylinder seal
porous ceramic
plate
"0"ring porous
plate seal
pore in porous
plate
Figure 7. Detailed cross section of Tempe cell (after Soilmoisture Equipment Corp. 1231 ).
fl
-
to
40 psi air
pressure source
d e - a ~ r e dwater
inflow isolat~on
valve
J
lLk
beaker
Figure 8. Permeameter used for determining saturated hydraulic conductivity.
c a l c u l a t e t h e h y d r a u l i c c o n d u c t i v i t i e s , u s i n g Equation 16 and t h e s o i l
w a t e r - r e t e n t i o n curves.
The Lakeland f i n e sand samples were taken a t t h r e e depth i n t e r v a l s
from t h e A g r i c u l t u r a l Experiment S t a t i o n farm o f t h e U n i v e r s i t y of F l o r i d a
a t Quincy, F l o r i d a (Elzeftawy and Manse1 1 (11)).
RESULTS
Amerman (14) and P h i l i p (15) have pointed o u t t h e importance o f i n c l u d i n g i n f o r m a t i o n about t h e unsaturated s o i l p r o p e r t i e s i n l a r g e - s c a l e
hydrogeol o g i c i n v e s t i g a t i o n s .
For example, t o i n c o r p o r a t e p r i n c i p l e s of
s o i l physics i n t o a r a i n f a l l - r u n o f f model, i t i s p o s s i b l e t o use e i t h e r a
n u n ~ e r i c a ls o l u t i o n o f t h e unsaturated f l o w equation o r a simple i n f i l t r a t i o n
equation such as t h a t given by Green and Ampt (16) o r d e r i v e d by P h i l i p (17).
I n t h e f i r s t approach, t h e s o i 1 water c h a r a c t e r i s t i c ( t h e re1a t i o n s h i p
between s o i l s u c t i o n head, h, and v o l u m e t r i c water content, e ) and t h e
c o n d u c t i v i t y f u n c t i o n ( t h e re1a t i o n s h i p between t h e unsaturated hydraul ic
c o n d u c t i v i t y K and e ) must be known.
I n t h e second approach, composite
h y d r a u l i c parameters, s p e c i f i c a l l y t h e Green-Ampt (16) w e t t i n g f r o n t s u c t i o n ,
hf, and P h i l i p (17) s o r p t i v i t y , S, must be estimated o r computed d i r e c t l y
from s p e c i f i e d f u n c t i o n s of h, K, and e.
The need t o s p e c i f y r e l a t i o n s h i p s among h, K, and e presents a s i g n i f i c a n t problem i n hydrology because o f t h e d i f f i c u l t y o f o b t a i n i n g measurements o f these parameters and o f p r e s e n t i n g t h e c o l l e c t e d data.
Gardner,
e t a1 . (18), Campbell (19), and Clapp and Hornberger (20) have attempted
t o use power curves t o describe t h e s o i l moisture c h a r a c t e r i s t i c of s o i l s
and have had o n l y l i m i t e d success i n e s t i m a t i n g t h e h y d r a u l i c c o n d u c t i v i t i e s
from these power curves; however, Elzeftawy and Manse1 1 (11) have shown
t h a t t h e c a l c u l a t e d hydraul i c c o n d u c t i v i t y using Equation 16 provided a
good e s t i m a t i o n of t h e K(e) function o f Lakeland f i n e sand.
The measured and c a l c u l a t e d values of h y d r a u l i c c o n d u c t i v i t y o f Lakel a n d f i n e sand a r e presented i n Figure 9 f o r t h r e e d i f f e r e n t p r o f i l e depths.
The measured h y d r a u l i c c o n d u c t i v i t y values a t water s a t u r a t i o n , KS, were
used as t h e o n l y matching f a c t o r t o determine t h e c a l c u l a t e d curves o f t h e
K(e) f u n c t i o n .
I t i s w e l l known t h a t i t i s q u i c k e r and s i m p l e r t o determine
Ks e x p e r i m e n t a l l y then i t i s t o measure unsaturated h y d r a u l i c c o n d u c t i v i t i e s
Lakeland Fine Sand
: ,
'I
jt
0
0.10
c
0-15
30-45
0.20
K
Measured
a
0.30
K
Calculated
---
0.40
0.50
0.60
0.70
ISGS
Soil Moisture Content, 0 , cm3/cm3
Figure 9. Experimental and calculated hydraulic conductivity of Lakeland fine sand.
a t any m o i s t u r e c o n t e n t below t h e s a t u r a t i o n value.
But t h e pronounced
d e v i a t i o n between t h e c a l c u l a t e d and measured K ( e ) values f o r v o l u m e t r i c
water contents l e s s than 10 percent suggests t h a t a second matching p o i n t
somewhat w i t h i n t h e " f i e l d c a p a c i t y " range o f water c o n t e n t may be needed.
The average d e n s i t i e s and water-saturated h y d r a u l i c c o n d u c t i v i t i e s o f
t h e undisturbed samples of Lakeland sand a r e shown i n t a b l e 5.
The v a r i a -
t i o n o f b u l k d e n s i t y w i t h depth of t h e s o i l p r o f i l e i s almost n e g l i g i b l e ;
however, t h e h y d r a u l i c c o n d u c t i v i t y o f t h e bottom l a y e r (60 t o 90 cm) i s
much h i g h e r than t h a t f o r t h e s u r f a c e l a y e r ( 0 t o 15 cm).
Selected p h y s i c a l p r o p e r t i e s o f t h e undisturbed (Drummer and Dana) and
d i s t u r b e d (Ottawa sand and Fayette C h o r i z o n ) samples used a r e presented i n
t a b l e 6.
The s a t u r a t e d h y d r a u l i c c o n d u c t i v i t i e s o f t h e F a y e t t e C and Dana
s o i l s a r e l a r g e r than expected, which might be a t t r i b u t a b l e t o t h e low bul k
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c a p i l l a r y e f f e c t and t h e pore s i z e d i s t r i b u t i o n and t h e r e f o r e i s s t r o n g l y
a f f e c t e d by t h e s o i l s t r u c t u r e .
On t h e o t h e r hand, water r e t e n t i o n i n t h e
h i g h e r s u c t i o n range i s due i n c r e a s i n g l y t o a d s o r p t i o r ~and i s thus i n f l u e n c e d
l e s s by t h e s t r u c t u r e and more by t h e t e x t u r e and s p e c i f i c s u r f a c e o f t h e
s o i l material.
F i g u r e 10 i n d i c a t e s t h a t , i n general, t h e g r e a t e r t h e c l a y
content, t h e g r e a t e r t h e water content, a t any p a r t i c u l a r s u c t i o n (compare
Lakeland sand and Drummer s i l t y loam) and t h e more gradual t h e slope o f t h e
curve.
The e f f e c t of compaction upon a s o i l i s t o decrease i t s t o t a l p o r o s i t y ,
and e s p e c i a l l y t o decrease t h e volume of t h e l a r g e i n t e r a g g r e g a t e pores;
t h i s means t h a t water content a t s a t u r a t i o n and t h e i n i t i a l decrease o f
water c o n t e n t w i t h t h e a p p l i c a t i o n of low s u c t i o n a r e reduced.
The data
presented i n t a b l e 6 and f i g u r e 10 f o r t h e 30 t o 75-cm and 75 t o 90-cm depth
o f Drummer samples support t h e previous statement:
note the s i m i l a r i t y i n
t h e i r p a r t i c l e - s i z e a n a l y s i s and t h e d i f f e r e n c e s i n t h e i r b u l k d e n s i t i e s
and t h e s a t u r a t e d water contents.
The c a l c u l a t e d and experimental h y d r a u l i c c o n d u c t i v i t i e s o f t h r e e l a y e r s o f Drummer s o i l p r o f i l e s a r e shown i n f i g u r e 11.
The experimental data
were obtained by t h e u n i t g r a d i e n t method as published by Elzeftawy and
Mansell (12).
The h y d r a u l i c c o n d u c t i v i t y o f t h i s s o i l a t s a t u r a t i o n i s
g e n e r a l l y about 4 orders o f magnitude l a r g e r than a t 50 percent o f saturation.
The c a l c u l a t e d r e s u l t s were c o n s i s t e n t w i t h t h e experimental data;
3
3
however, t h e c a l c u l a t e d numerical values below 0.32 cm /cm water c o n t e n t
were l e s s than t h e e x p e r i m e n t a l l y hydraul i c c o n d u c t i v i t i e s obtained ( n o t
shown i n f i g u r e 11).
H y d r a u l i c c o n d u c t i v i t i e s as a f u n c t i o n o f m o i s t u r e c o n t e n t o f Ottawa
sand and Fayette C h o r i z o n a r e shown i n f i g u r e s 12 and 13.
The 1 i n e s repre-
sent t h e c a l c u l a t e d values of K(0) obtained by Equation 16 and t h e s o i l m o i s t u r e r e t e n t i o n curve.
The c i r c l e s a r e t h e experimental data p o i n t s .
These s o i l m a t e r i a l s represent a wide range o f pore s i z e d i s t r i b u t i o n s over
which t h e c a l c u l a t i o n s o f h y d r a u l i c c o n d u c t i v i t i e s a r e based. F i g u r e 13
3
3
shows t h a t a change i n water content o f Fayette s o i l from 0.47 t o 0.30 cm /cm
has reduced t h e h y d r a u l i c c o n d u c t i v i t y from 2.2 X 10-'cm/h t o 4.0 X 1 0 ' ~
crr~/h, r e s p e c t i v e l y .
Drummer
5
10
15
20
25.
30
35
Moisture Content, Gravimetric - w (%)
40
ISGS
Figure 10. Soil moisture-suction relationships of Lakeland fine sand and Drummer soil.
Green and Corey (10) and others have s t a t e d t h a t using a matching
f a c t o r a t water s a t u r a t i o n has a d i s t i n c t advantage, since inaccuracies i n
c a l c u l a t e d values o f K ( e ) can be more e a s i l y t o l e r a t e d a t lower water cont e n t s ; however, i n studying phenomena such as evaporation, t h e e a r l y stages
o f water i n f i l t r a t i o n , and t h e movement o f s o l u t e s such as contaminants i n
t h e unsaturated zone, more accurate methods a r e needed t o determine t h e
unsaturated h y d r a u l i c c o n d u c t i v i t i e s of s o i l s a t lower values o f water content.
Bruce (21) suggested t h a t matching f a c t o r s somewhat below t h e bubbling
pressure a r e s u f f i c i e n t l y accurate f o r c a l c u l a t i n g t h e unsaturated h y d r a u l i c
c o n d u c t i v i t i e s o f coarse-grained s o i l s ; however, he a l s o s t a t e d t h a t t h e
i n d i s c r i m i n a t e use o f such methods f o r c a l c u l a t i n g t h e h y d r a u l i c c o n d u c t i v i t i e s o f f i n e - g r a i n e d s o i l s i s inadvisable.
I n our study good r e s u l t s have
Drummer.Soil
P
Depth - 0-30 cm
K, = 0.02 cm/hr
Depth - 75-90 cm
Depth - 30-75 cm
1
0.20
I
I
I
0.30
I
I
0.40
I
0.50
,,,,
Soil Moisture Content, 0 , cm3/cm3
Figure 11. Experimental and calculated hydraulic conductivity of Drummer soil.
been obtained f o r t h e f i n e - g r a i n e d s o i l s (Drumrner and Fayette) u s i n g s a t u r ated h y d r a u l i c c o n d u c t i v i t y as the o n l y matching f a c t o r .
However, we n o t i c e d
t h a t t h e c a l c u l a t e d values deviated from t h e experimental r e s u l t s , e s p e c i a l l y
3
3
w i t h i n the range of low water content ( l e s s than 0.35 cm /cm moisture
content).
For t h i s reason, t h e Dana loam samples were chosen t o i n v e s t i g a t e
the p o s s i b i l i t y o f u s i n g two o r more matching f a c t o r s t o c a l c u l a t e t h e
function.
K(e)
Some of t h e physical p r o p e r t i e s o f Dana s o i l a r e presented i n
t a b l e 6.
DISCUSSION
A method of p r e d i c t i n g t h e saturated-unsaturated h y d r a u l i c c o n d u c t i v i t i e s o f some I l l i n o i s s o i l s u t i l i z e t h e s o i l moisture content-suction head
I
..
L
Ottawa Sand
6, = 0.382
K ,= 13.40 cmlh r
L
E,
10'z
- Calculated
2
Experimental
Y
>:
.->
.4d
4d
0
u
C
S 10":
.-0
3
m
L
u
>.
I
-
lo-'
I
0
0.10
I
0.20
I
I
0.30
Soil Moisture Content, 6, cm3/cm3
0.40
ISGS
Figure 12. Experimental and calculated hydraulic conductivities of Ottawa sand.
r e l a t i o n , h(e), t o calculate the unsaturated hydraulic conductivity of s o i l .
The value of the hydraul i c conductivity a t saturation, Ks (the s o i l permea b i l i t y ) , was used as a matching f a c t o r during the calculations. The h(e)
re1 ations and the saturated conductivities, KS, of soi 1 s were determined
i n the laboratory using the commercially available "Tempe" c e l l . Undisturbed
samples of Drummer and Dana s o i l s and disturbed samples of Fayette C s o i l ,
Ottawa sand, and other s o i l s were used i n t h i s study. Published data on
some agricultural s o i l s were a l s o used t o validate r e s u l t s of our investigations. On the basis of our study r e s u l t s , the following conclusions can
be made:
1. The model successfully predicts the hydraulic conductivity
of a wide range of s o i l s .
2. The proposed simp1 i f i e d laboratory procedure i s re1 iable and
can be used t o determine e a s i l y the soil moisture-suction
relationships of disturbed or undisturbed s o i l samples.
3.
Evaluation of the unsaturated hydraulic conductivities of
s o i l s using the proposed "Tempe" c e l l method i s quick and
economi cal
.
'"
1
lo-'-
Fayette C horizon
0, = 0.47
K ,= 0.22 cmlhr
-Calculated
• Experimental
r.
E
L
O
.
m,
Y
.-w>:
.-w>0
3
-0
6
U
10-3-
.-
0
3
I
>.
I
-0
1o --~
I o-'
0
I
I
I
I
0.20
0.30
0.40
0.50
ISGS
Soil Moisture Content, 0, cm3/cm3
Figure 13. Experimental and calculated hydraulic conductivities of Fayette C horizon.
The experimental and c a l c u l a t e d h y d r a u l i c c o n d u c t i v i t i e s o f t h e Dana
sample a r e shown i n f i g u r e 14; t h e c i r c l e s represent t h e experimental data
and t h e 1 i n e s represent t h e c a l c u l a t e d values.
The c a l c u l a t e d h y d r a u l i c
c o n d u c t i v i t y f u n c t i o n u s i n g Ks as t h e o n l y matching p o i n t i s shown i n t h e
f i g u r e by t h e sol i d 1 ine; n o t e t h e d e v i a t i o n between the c a l c u l a t e d and
3
3
Better results
experimental data below a water content o f 0.45 cm /cm
.
were obtained when two matching f a c t o r s were used, p a r t i c u l a r l y when t h e
s a t u r a t e d h y d r a u l i c c o n d u c t i v i t y , Ks, and another experimental value somewhat below the bubbling pressure o f t h e s o i l were used.
1.01 X
(The value K(8) =
3
3
cm/min was a r b i t r a r i l y chosen where 8 = 0.40 cm /cm .) I n t h i s
case, t h e dashed l i n e represents t h e K(e) f u n c t i o n c a l c u l a t e d w i t h two
matching f a c t o r s i n Equation 16.
Using two matching f a c t o r s i n t h e calcu-
-.-U
I L'
3
o
L
u
>
I
Dana Loam
0, = 0.50
K = 0.32 cmlmin.
a Experimental
Calculated with
-one Matching Factor
- - two Matching Factors
,
16"
'0-:.k5
0.30
I
I
0.40
0.50
I
0.60
ISGS
Soil Moisture Content, 0, cm3/cm3
Figure 14. Experimental and calculated hydraulic conductivities of Dana soil.
l a t i o n s o f K ( e ) functions of many fine-grained s o i l s has reduced t h e e r r o r
i n p r e d i c t i n g t h e hydraul i c c o n d u c t i v i t y values a t low s o i l water content.
Results o f o u r study presented i n g r a p h i c a l form i n Appendix B, i n d i c a t e
t h a t t h e method described i n t h i s r e p o r t f o r c a l c u l a t i n g t h e h y d r a u l i c
c o n d u c t i v i t y o f s o i l m a t e r i a l s can be used w i t h confidence f o r many p r a c t i c a l
a p p l i c a t i o n s d e s c r i b i n g t h e pore t r a n s p o r t system.
REFERENCES
H i l l e l , D., S o i l and Water, Physical P r i n c i p l e s and Processes, Academic
Press, New York, 1973.
Taylor, S. A. and G. L. Ashcroft, Physical Edaphology, The Physics o f
I r r i g a t e d and N o n i r r i g a t e d S o i l s , W. H. Freeman and Company, San
Francisco, Cal i f o r n i a , 1972.
Kirkham, D. and W. L. Powers, Advanced S o i l Physics, John Wiley and
Sons, Inc., New York, 1972.
Rose, C. W.,
A g r i c u l t u r e Physics, Pergamon Press, New York, 1966.
Childs, E. C., An I h t r o d u c t i o n t o t h e Physical Basis o f S o i l Water
Phenomena, John Wiley and Sons, Inc., New York, 1969.
Cromey, D., J. E. Coleman, and P. M. Bridge, Road Research Laboratory,
Crowthorne, England, 1951.
Childs, E. C. and N. Coll4s-George, Proceed4ngs o f t h e Royal S o c i e t y
of London, Vol. A, No. 2-1, 1950, pp. 392-405.
Rogers, J. S. and A. Klute, S o i l Science S o c i e t y o f America, Proceedings, Vol. 35, 1971, pp. 695-700.
M i l l i n g t o n , R. J. and J. R. Q u i r k , Transactions of t h e Faraday Society,
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Green, R. E. and J. C. Corey, Science S o c i e t y of America, Proceedings,
Vol. 35, 1971, pp. 3-8.
Elzeftawy, A. a r ~ dR. S. Mansell, S o i l Scier~ceS o c i e t y o f Arnerica,
Proceedings, Vol. 39, 1975, pp. 599-603.
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642, pp. 30-35.
Watson, K. K.,
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Water Resources Research, Vol. 2, 1966, pp. 509-517.
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Wisconsin, 1973.
i n P r e d i c t i o n i n Catchment Hydrology, C. H. M. van Bauel,
P h i l i p , J.
Ed., A u s t r a l i a n Acadew o f Science, 1975, pp. 23-30.
R
a
y
Green, W. Heber and G. A. Ampt, Journal o f A g r i c u l t u r a l Science, Vol.
4, 1911, pp. 1-24.
P h i l i p , J. R.,
S o i l Science, Vol. 84, 1957, pp. 257-264.
Gardner, W. R., D. H i l l e l , and Y. Benyamini, Water Resources Research,
Vol. 6, 1970, pp. 851-861.
19.
Campbell, G. S., S o i l Science, Vol. 117, 1974, pp. 311-314.
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Clapp, R. B. and G. M. Hornberger, Water Resources Research, Vol.
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Bruce, R. R., S o i l Science S o c i e t y o f America, Proceedings, Vol. 36,
1972, pp. 555-561.
22.
Dempsey, B. S. and A. Elzeftawy, M o i s t u r e Movement and M o i s t u r e
Movement Equi 1ib r i um i n Pavement Systems Univ. o f I 11 in o i s
Engineering Experimental S t a t i o n , Urbana, I 11 i n o i s , 'UILU-ENG76-2012, 1976, 147 p.
23.
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LIST OF PUBLICATIONS
1.
Elzeftawy, A t e f .
1979.
Modeling t h e Transport o f Heat, Water and
S o l u t e i n Unsaturated S o i l and Earth M a t e r i a l s .
ASAE Proceed-
ings o f "Hydro1 o g i c Transport Model ing Symposi um. " American
S o c i e t y o f A g r i c u l t u r a l Engineers, St. Joseph, Michigan, 49085.
2.
Elzeftawy, A t e f .
Soil.
1979.
Waste Disposal and Transport Phenomena i n
Proceedings o f t h e 2nd Annual Conference o f Applied
Research and P r a c t i c e on Municipal and I n d u s t r i a l Waste.
Madison, Wisconsin.
3.
P. 583-595.
Elzeftawy, A t e f and Keros C a r t w r i g h t .
1981.
E v a l u a t i n g t h e Saturated
and Unsaturated H y d r a u l i c C o n d u c t i v i t y o f S o i l s .
ASTM Special
Technical Pub1 i c a t i o n (STP) 746, P. 168-181, Phi 1adel phia,
Pennsylvania.
10,000
\
10.OM)
Fine Ottawa Sand
Coarse Ottawa Sand
G.
Soil moisture content 8 (%)
Soil moisture content 6 (%)
8
Richland Loess
t
%.
1000-
8
s
-E
L
C
..-2
4-
8
100-
8
..
.
10
0
Soil moisture content 6
(%I
Ib
d0
30
do
Soil moisture content 6
*
do
(%I
$0
70
P
1%) 0 iuaiuoa alnis!ou l!os
00
SC
OC
v
..-I3
1%)
1%) 0 iuaiuoa aJnis!ou IPS
@@.=I
OOO'OL
iuaiuoa alnis!ou I!OS
(%) 0 iuaiuo:, a~nis!ow(!oS
(%) 0 iuaiuo:, a~nis!owI!OS
z aldwes
...
= OOO'OL
Appendix B
The hydraul i c c o n d u c t i v i t y s o i 1-moisture r e l a t i o n s h i p s f o r
samples used i n t h i s study. Note, t h e r e w e t t i n g of d r y samples
may have increased t h e s a t u r a t e d h y d r a u l i c c o n d u c t i v i t y i n
some samples.
10'
1 o1
Fine Ottawa Sand
Coarse Ottawa Sand
1 o0-
Soil moisture content 0
1o0
(%I
Soil moisture content 0
lo1
Ground Ottawa Sand
(%I
Richland Loess
id4Ks = 1 .81 x 10' cm/hr
0, = 0.420 cm3/cm3
p = 1.50 gm/cm3
,
15
20
15
do
3'5
I
40
Soil moisture content 0 (46)
d5
Soil mqisturg content 0
(%I
1oO
,
'
Sample 21
Soil moisture content B (%)
Soil moisture content B
(%I
Sample 25
0.
Soil moisture content B
(%I
Soil moisture content B (%)
lo0
Soil moisture content 0 (%)
Soil moisture content 0
1o0
Sample 28
Sample 29
Soil moisture content 0
(%I
Soil moi~ture~content
0 (%)
(%) 8 iuaiuoa a~nis!owI!OS
10'
Sample 19
Sample 17
.-
i1
$
lo-?
Soil moisture content 0
Soil moisture content 0 (%)
Sample 1
I
Sample 2 0
(96)
1
°
1
I
10-51
-
4
Soil moisture content 0
(%I
0
1
Soil moisture content O (%)
I