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ISGS CONTRACT/GRANT REPORT: 1983-5 UILU-WRC-83-0177^^^^^^^^^^^^^ Research Report 177
557.09773
IL6cr 1 983-5
Undisturbed Core Method for Determining
and Evaluating the Hydraulic Conductivity
of Unsaturated Sediments
ATEF ELZEFTAWYKEROSCARTWRIGHTState Geological Survey Division
April 1983
University of Illinois
WATER RESOURCES CENTERUrbana-Champaign, Illinois
Illinois Department of Energy and Natural Resources
STATE GEOLOGICAL SURVEY DIVISIONChampaign, Illinois
UILU-WRC-83-0177 UNDISTURBED CORE METHOD FOR DETERMINING
Rp<;p , rrh Ronnr+ 177 AND EVALUATING THE HYDRAULIC CONDUCTIVITYResearch Report 1770F UNSATURATED SEDIMENTS
By
Atef Elzeftawy and Keros CartwrightHydrogeology and Geophysics SectionIllinois State Geological Survey, Champaign
April 1983
Project A-097-ILLMatching Grant Agreement No. 14-34-0001-0115
Final Technical Completion Reportto
U.S. Department of the InteriorWashington, D.C. 20240
Digitized by the Internet Archive
in 2012 with funding from
University of Illinois Urbana-Champaign
http://archive.org/details/undisturbedcorem19835elze
CONTENTS
Abstract 1
Key words 1
Acknowledgments 1
Introduction 1
Soil water potential 2
Soil water characteristic function 7
Hydraulic conductivity function 8
Units for soil water potential 12
Materials and methods 13
Results 19
Discussion 24
References 28
List of publications 29
Appendix A 30
Appendix B 40
TABLES
1. Potential expressed in the major measurement systems 13
2. Conversions for potential units 14
3. Location, type and particle size data of undisturbed samples usedin study 15
4. Properties of undisturbed core samples 16
5. Bulk density and saturated hydraulic conductivity of Lakeland finesand 21
6. Selected physical properties of soils used at indicated depths ... 21
FIGURES
1. Capillary tubes showing configuration of the air water interfacesat different heights (after Dempsey and Elzeftawy [23]) 5
2. Variation in pressure above and below water table (after Dempseyand Elzeftawy [22]) 6
3. Relative soil-water characteristic curves for a clayey soil andsandy soil 7
4. Tensiometer system (after Dempsey and Elzeftawy [22]) 9
5. Hysteresis effects of drying and wetting conditions on matricsuction 9
6. Tempe pressure cells set-up in the laboratory 17
7. Detailed cross section of tempe cell (after SoilmoistureEquipment Corp [23]) 18
8. Permeameter used for determining saturated hydraulic conductivity . 18
9. Experimental and calculated hydraulic conductivity of Lakelandfine sand 20
10. Soil moisture-suction relationships of Lakeland fine sand andDrummer soil 23
11. Experimental and calculated hydraulic conductivity of Drummer soil . 24
12. Experimental and calculated hydraulic conductivities of Ottawasand 25
13. Experimental and calculated hydraulic conductivities of FayetteC horizon 26
14. Experimental and calculated hydraulic conductivities of Dana soil . 27
- 1 -
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 sites 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 values. For coarse-textured soil mater-
ials and materials with a relatively narrow range of pore size, only one
matching factor was required to calculate the hydraulic conductivity-water
content relation accurately enough for many purposes; however, for fine-
textured soil materials with a wide range of pore size distribution, two
or more matching factors at 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
We are grateful to staff members of the Hydrogeology and Geophysics
Section at the Illinois State Geological Survey for their advice and assis-
tance 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 this study was provided
by the U.S. Department of Interior, Office of Water Research and Develop-
ment.
INTRODUCTION
At least two basic parameters of geologic sediments— hydraulic conduc-
tivity and soil water characteristic functions—must be evaluated before
predictive analyses can be made of the transport of moisture and contaminants
in the unsaturated-saturated zone of a soil. These parameters must be
- 2
measured accurately before determinations can be made of the potential
environmental impact of municipal and industrial waste disposal sites.
Reliable measurement of these parameters is also essential to planning
and managing efficient schemes for irrigation water.
This research project was undertaken to determine the soil water para-
meters of some nonindurated geologic sediments in Illinois. Our specific
objectives were:
<to determine the soil water characteristic functions in the
laboratory, using undisturbed and disturbed samples.
•to determine the saturated-unsaturated hydraulic conductivity
functions using the same undisturbed samples.
•to evaluate the hydraulic conductivity functions of all samples,
using the capillary model and the pore size distribution data.
Before discussing the methodology and results of our study we will
define several important soil water concepts that are critical to under-
standing and predicting soil water movement: soil water potential, soil
water characteristic function, hydraulic conductivity function, and units
for soil water potential.
Soil Water Potential
Soil water contains energy in different forms and quantities. The
two principle forms of energy are kinetic energy, a function of velocity
and potential energy that is a function of position of internal condition
of the system. Since water moves very slowly in soil, kinetic energy can
generally be ignored in the study of soil water systems; however, potential
energy is of primary importance in determining the state and the movement
of water in soil
.
The spontaneous and universal tendency of all matter in nature is to
move from a point of high potential energy to a point of low potential
energy until an equilibrium condition is reached. Soil water systems obey
the same universal pursuit of equilibrium.
A soil water system is subjected to a number of force fields, which
causes its potential to differ from that of free water. The force fields
commonly considered are gravitational potential, <|> , pressure potential,
- 3 -
a , osmotic potential, a and gas potential, a . The total potential, a,,
of the soil water system can be considered as the sum of the individual
potentials:
a_=a+a+a+a (1)M yg
Tp
vo
ya
v '
The gravitational potential, a , and pressure potential, a , are they r
primary force fields in soil water systems. The osmotic potential, a , is
dependent upon the presence of a solute in the soil water system. The gas
potential, a , is dependent upon external or internal gas pressure in the
system. If the osmotic potential and gas potential are considered to have
minor influence on the total potential, then Equation 1 can be simplified
as follows:
* T = *g
+ *p
(2)
At a height z above an arbitrary reference level, the gravitational
energy of water in soil, E, can be stated as follows:
E = Mgz = y wgzv (3)
In equation 3, ywis the density of water, g is the acceleration of gravity
and V is the volume of the mass, M. From Equation 3, the gravitational
potential energy, a , can be expressed as follows:
* = gz (per unit mass, M) (4)
*n=
Yii 9Z (Per unit volume, V) (5)y w
a = z (per unit weight, W) (6)
In Equation 6, a depends only on z and is defined as the gravitational head
in soil water systems.
Pressure potential, a , is negative for unsaturated soil water systemsr
and positive for saturated soil water systems. It can be shown that the
pressure potential concept allows for the consideration of the entire
moisture profile in the field in terms of a single continuous potential
extending from the saturated region to the unsaturated region, below and
above the water table.
The positive pressure potential for a saturated soil water system is
fairly well understood. The negative pressure— less well understood— has
often been termed capillary potential, soil suction, or (more accurately)
matrix potential. This potential results from the capillary and absorptive
forces developed in the soil matrix.
In discussing pressure potential for unsaturated soil water systems,
the capillary tube analogy is useful. Soil can be assumed to be a porous
medium composed of capillary tubes of different sizes. In figure 1 the air
water interfaces throughout the soil consists of menisci in which the curva-
ture or radii indicate the state of tension in the soil water (much as a
capillary tube does). As the moisture content of the soil is reduced, the
air water interfaces recede into the smaller pores, the radii of curvature
decrease, and the moisture tension increases.
In the capillary tube shown in figure 2 the water above the water table
will be in equilibrium when the upward component of the surface tension
force is equal to the gravitational force acting on the suspended water.
The height, h, to which the water will rise in the capillary tube is related
mainly to the surface tension, a, and radius, r, of the meniscus by the
following equation:
2 a cos 6 ,-, xh =
y gr (7). 'w y
In figure 2 atmospheric pressure exists at points 1, 2, and 3. However,
at point 4, just below the meniscus, the pressure is less than atmospheric
pressure by an amount equal to hy g. Assuming that cosine e ; 1 for water
in soil, and that the curvature of the water in the soil matrix is similar
to that in a capillary tube of the same size (figure 2), the pressure poten-
tial per unit mass can be expressed from Equation 7 as follows:
<J>= - ^-2- = gh (8)
The negative sign is used in Equation 8 because the pressure potential
in an unsaturated soil water system is less than atmospheric pressure and
because h would have a negative value in an unsaturated system.
From Equations 2, 4, and 8 the total potential per unit mass, exclud-
ing the osmotic potential and gas potential, can be stated as follows:
<j>
T= gz + gh (9)
On a unit weight basis, normally used in soil water studies, Equation 9 can
be shown in the following form:
- 5 -
Magnified toil
particles
Pressure change across meniscut
(* soil moisture suction) 8 6 Ib/sq in
» pF 2.78
Radius ol meniscus •
0001 in.
Pressure change across meniscus
« 4.3 Ib/sq in
- pF 2 48
Radius o( memscut'0002 in.
Pressure change across
meniscus
2.13 Ib/sq in
-pF 2 18
idius ot jfsmscus /
Radi
meniscus
0004 in.
*IT r*
Pressure change
across meniscus- 0.43 Ib/tq in
- pF 1 48
Radius of
meniscus
0.002 in
a^^^*i<
pir>
pb
o
iJtspKt^*--^ -**^ "**•-j>.-:
ih'iifia*! mi ti
Figure 1 . Capillary tubes showing configuration of the air water interfaces at
different heights (after Dempsey and Elzeftawy [22] ).
+ hrm,9
"Pressure AboveAtmospheric
Figure 2. Variation in pressure above and below water table
(after Dempsey and Elzeftawy [22] ).
H = z + h (10)
In Equation 10, H is the total soil water head, z is the gravitational
head, and h is the pressure head. The pressure head is negative (suction)
in unsaturated soil water systems and positive for saturated soil water
systems.
To summarize, the criterion for the equilibrium in soil water systems is
that the total water potential be equal throughout the system. To facilitate
the analysis of particular systems, the total water potential is partitioned
into various components that can be measured. Typically, the gravitational
potential is determined by use of a measuring tape, the pressure potential
by a piezometer for saturated systems and a tensiometer for unsaturated
systems, and the gas potential by a pressure gauge.
- 7 -
Soil Water Characteristic Function
The relationship expressed in a soil water characteristic function is
a soil property of fundamental importance in the analysis of water equilib-
rium and flow behavior in soil. Figure 3 shows relative soil water charac-
teristic curves for two different soils. Physically, the curve tells (at
any given moisture content) how much energy (per unit quantity of water
removed) is required to remove a small quantity of water from the soil.
It indicates how tightly water is held in the soil. Hillel (1), Taylor
and Ashcroft (2), Kirkham and Powers (3), and Rose (4) have presented detailed
explanations of how water is held in soil. Childs (5) has considered the
mechanisms of water held in both swelling and non-swelling soils in great
detail
.
Cromey, 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.
3
ISGS
Water content
Figure 3. Relative soil -water characterisitic curves for a clayey soil and sandy soi
- 8 -
Figure 4 shows a simple type of tensiometer system that can be used2
for the low moisture- tension range (< 100 kN/m , or < 1 bar). The apparatus
shown in figure 4 consists of a porous plate with its pores filled with
water. The chamber beneath the porous plate is filled with water and
connected to a flexible tube that is also filled with water. The negative
head is equal to the distance, h, between the soil sample and the outflow
end of the flexible tube in figure 4. The soil water characteristic curve
is determined from the relationship between the water content of the soil
sample and the magnitude of the negative pressure head of the water.
Hysteresis effects (figure 5) will often occur between soil water
characteristic curves for drying and wetting. The hysteresis for the
drying and wetting conditions arises from the influence of pore size
distribution on water held in the soil. A complete moisture characteris-
tic curve should consist of a drying (desorption) curve and a wetting
(sorption) curve. The drying curve should start at saturated water content
at close to zero suction and continue to a low water content at a high
level of suction. The wetting curve should start at the high level of
suction and low water content and proceed to saturation. This would
characterize an envelope for water content and suction values in the given
range. The influence of small moisture content changes on soil suction is
shown by the smaller hysteretic curves inside the desorption and sorption
curves in figure 5.
A useful simplification occurs when the soil suction is given in units
of water head. A suction of 20 cm will lift a column of water 20 cm above
a free water surface. Therefore, the suction on the moisture characteristics
curve can be equated to the distance above a water table for equilibrium
conditions. Also, by use of the soil water characteristic curve it is
possible to estimate the equilibirum water content at various positions
above the water table.
Hydraulic Conductivity Function
The flow of water through soils is often unsteady and unsaturated.
Examples of such flows are the infiltration of water from the ground surface,
the flow through the capillary fringe of an unconfined aquifer, the draining
of soils, the evaporation from an aquifer close to the ground surface, the
9 -
sample
izrcira en
porous
plate
ezreznd
m
Figure 4. Tensiometer system (after Dempsey and Elzeftawy [22] ).
Water content
Figure 5. Hysteresis effects of drying and wetting conditions on matric suction.
10
fluctuations of groundwater level, the inflow of water from irrigation
channels, and the land disposal of liquid wastes.
The general nonlinear partial differential equation that describes the
transport of groundwater can be written as follows:
|f= V- (K v<f>) (11)
where e is the volumetric water content defined as the ratio of the volume
of water, V , to the total volume of soil, V, v is the vector differentialw
operator. K is the hydraulic conductivity, and<f>
is the total potential.
For a complete derivation of Equation 11 (5 or 6). An equation of this
type applies to any nonreactive liquid in the porous medium; since we limit
ourselves in this study to water, it is convenient to take the length of
water column as the unit of potential. Potential gradients are then
dimensionless, and if the time, t, is expressed in hours, the unit of
hydraulic conductivity is centimeters per hour.
When the total potential is composed of only gravitational and negative
pressure (capillary) components, Equation 11 may be written:
|| = V (K Vh) +§| (12)
where h is the suction (negative pressure) potential, and z is the vertical
ordinate, positive upward.
When h and K are single-valued functions of e, Equation 12 becomes
|f-v. (0ve) + f (13)
where
D(e) = K(e)|£ (14)
Childs and Collis-George (7) called D the diffusivity of soil water
and found it to be a function of e. Rogers and Klute (8) have shown that
hydraulic conductivity, K, is uniquely related to soil moisture content, e.
Two physical properties of the soil that enter into a saturated-unsaturated
flow problem are hydraulic conductivity, K(e), and soil moisture retention
h(e); these properties must be known if a solution of Equation 13 is to be
obtained.
- 11
Chi 1 ds and Coll is-George (7), Millington and Quirk (9), Green and
Corey (10), and others have explored the possibility of predicting the
hydraulic conductivity of soils and other porous materials on the basis of
pore size distribution. Such predictions are of interest because the
hydraulic conductivity function, K(e), is relatively difficult to measure,
whereas pore size distribution is easily obtainable by the standard
measurement of moisture content versus suction (negative pressure).
The hydraulic conductivity is obtained by dividing the relation of
moisture content and suction, h(e), into n equal water content increments,
obtaining the suction, h, at the midpoint of each increment, and calculat-
ing the conductivity by using the following equation (see ref. 7 for more
details):m
J
where
K(e). = (30Y/pgn)(eP/n
2)£[(2J + l - 2i)h
2
](15)
j = il JJ
K(e). = calculated conductivity for a specified moisture content cor-
responding to the -th increment, cm/mi n;
3 3e = moisture content, cm /cm ;
y = surface tension of water, N/cm;
3p = density of water, g/cm ;
2g = gravitational constant, cm/s ;
n = kinematic viscosity of water, cm/s;
3 3e = saturated moisture content, cm /cm ;
3 3e = water- saturated porosity (cm /cm ), that is, e = ;
p = constant whose value depends on the method of calculation 6,
is equal to 2 in these calculations;
o = lowest moisture content on the experimental h (e) curve;
n = total number of pore classes between e = e and e n = me /oss(e
s- e );
i = last moisture-content increment on the wet end (for example,
i - 1 identifies the pore class corresponding to e );
- 12
h- = suction (negative pressure) for a given class of moisture-
filled pores (centimeters of water head); and
30 = the composite of the constant 1/8 from Poiseuille's equation,
4 from the square of r = 2y/h, where r is the pore radius and
60 converts from seconds to minutes.
Green and Corey (10) concluded that Equation 15 yields reasonable
values of the hydraulic conductivities for a range of soil types if a
matching factor is used. Elzeftawy and Mansell (11) and Elzeftawy and
Dempsey (12) stated that a matching factor at water saturation (the ratio
of the measured to the calculated, saturated hydraulic conductivity) has a
distinct advantage over match points because inaccuracies in calculated
and experimentally evaluated K(e) can be more easily tolerated at lower
moisture content. Equation 15 can then be written by using the matching
factor K /K , in the following form:
K(e)i
= (Ks/K
sc)(30/7 Pgn)(ee/n
2) £ [(2j + 1 - 2i)h?] (16)
where K is the measured saturated hydraulic conductivity, and K is the
calculated saturated conductivity.
Units for Soil Water Potential
The normal methods of expressing potential in soil water systems are
shown in table 1 for the various measurement systems. Relationships for
the measurement systems are shown in table 2. For potentials expressed
on a per unit weight basis or on a per unit volume basis, the dimensions
are those of length (centimeter, meter, or foot) or of pressure (dyne/
square centimeter, newton/square meter, or pound/square foot), repectively.
Equations for converting between the three forms of potential are stated
as follows:
energy = energy , .
mass a weight Vi/;
ener9y = Yenergy , .
volume w mass K'
energy = energy , .
volume 3, w weight v '
- 13 -
Table 1. Potential expressed in the major measurement systems.
Potential cgs system mks systemEnglishsystem
energymass
energyweight
energyvol ume
dyne cmgm
dyne cmdyne i
dyne cm
cm
erggm
= cm
dyne2
cm
Newton meter Joulekg
Newton meterNewton
Newton meter
meter
kg
meter
Newton
meter
100 kM/ni =
1 bar14.5 psi
29.5 in Hg
75.1 cm Hg
33.4 ft water1020 cm water
ft lb
slug
ft lb
lb
ft lb
ft3
ft
j_b_
f?
In making analyses of soil water systems, it is convenient to use one
of these methods consistently for expressing potential rather than to use
more than one method in the same analyses. Of the three methods, potentials
expressed as energy per unit weight appear to be utilized most in the lit-
erature and are used in this paper.
MATERIALS AND METHODS
Determinations of soil water characteristic and hydraulic conductivity
functions were made of triplicate undisturbed and disturbed soil samples.
The undisturbed core samples (5.4 cm in diameter and 3 cm in height) were
collected from sites in Illinois. The soil cores used in this study were
obtained during previous studies and taken from storage. All the samples
had been allowed to dry, but otherwise were undisturbed. The locations
and some physical properties of the undisturbed core samples are shown in
table 3. The disturbed soil samples (table 4) were passed through a 2-mm
seive, oven dried, and hand packed in the "Tempe" test cells.
All samples were placed in "Tempe" pressure cells and saturated with
water. The Tempe" pressure cell operates under the same physical princi-
ples as does the porous plate apparatus of the ASTM Test for Capillary-
- 14 -
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- 16 -
Table 4. Properties of disturbed samples.
particle size (%)
soil sample sand silt clay
Fine Ottawa Sand 100 — —Coarse Ottawa Sand 100 — —Ground Ottawa Sand 100 — —Richland Loess 4 86 10
Roxana Silt 11 61 28
Moisture Relationships for Coarse and Medium-Textured Soils by Porous-
Plate Apparatus D 2325-68 (1974), with maximum 1 atm pressure. Figures
6 and 7 show the laboratory setup and a schematic of the pressure cell. A
constant temperature was maintained at all times in the laboratory.
The saturated hydraulic conductivities of all samples were determined
utilizing an apparatus (figure 8) similar to that used in the ASTM Test
for Permeability of Granular Soils (Constant Head) D 2434-68 (1974). The
samples were then subjected to air pressure.
After their saturated hydraulic conductivity was determined, the samples
were allowed to drain following sequential subjection to air pressures of
100, 200, 300, 500, 800, and 1000 cm of water. They were then placed in a
15-bar porous-plate apparatus to determine the equilibrium moisture content
retained in the soil samples for air pressures of 1, 3, 5, and 15 atm (us-
ing procedures similar to ASTM D 2325-68 or ASTM Test for Capillary-Moisture
Relationships for Fine-Textured Soils by Pressure-Membrane Apparatus
D 3152-72 {1977}). The water content (by volume) was determined from the
weight of the pressure cell corresponding to each state equilibrium pressure
and the oven-dry weight of the soil samples.
The measured hydraulic conductivity function, K(e), of all samples was
evaluated by the instantaneous profile method suggested by Watson (13) and
described by Rogers and Klute (8). Another method, described by Elzeftawy
and Mansell (11), was also used to determine K(e) of each sample. This
method is based on the utilization of a unit hydraulic gradient to provide
a steady-state, downward, unsaturated flow of water across the soil core.
The computer program developed by Elzeftawy and Dempsey (12) was used to
- 18 -
air pressure
inlet tube
enlarged soil partical
in sample
porous ceramic
plate
pore in porous
platewater outlet
drain tube
clamping wing nut
soil core sample held
n retaining cylinder
"0" ring
cylinder seal
"O" ring porousplate seal
Figure 7. Detailed cross section of Tempe cell (after Soilmoisture Equipment Corp. [23] ).
y- to ~ 40 psi air
r pressure source
outflow isolation r m 'cro-adjust
valve / valve
beaker
Figure 8. Permeameter used for determining saturated hydraulic conductivity.
- 19
calculate the hydraulic conductivities, using Equation 16 and the soil
water-retention curves.
The Lakeland fine sand samples were taken at three depth intervals
from the Agricultural Experiment Station farm of the University of Florida
at Quincy, Florida (Elzeftawy and Mansell {11}).
RESULTS
Amerman (14) and Philip (15) have pointed out the importance of includ-
ing information about the unsaturated soil properties in large-scale
hydrogeologic investigations. For example, to incorporate principles of
soil physics into a rainfall-runoff model, it is possible to use either a
numerical solution of the unsaturated flow equation or a simple infiltration
equation such as that given by Green and Ampt (16) or derived by Philip (17).
In the first approach, the soil water characteristic (the relationship
between soil suction head, h, and volumetric water content, e) and the
conductivity function (the relationship between the unsaturated hydraulic
conductivity K and e) must be known. In the second approach, composite
hydraulic parameters, specifically the Green-Ampt (16) wetting front suction,
h., and Philip (17) sorptivity, S, must be estimated or computed directly
from specified functions of h, K, and e.
The need to specify relationships among h, K, and e presents a signif-
icant problem in hydrology because of the difficulty of obtaining measure-
ments of these parameters and of presenting the collected data. Gardner,
et al. (18), Campbell (19), and Clapp and Hornberger (20) have attempted
to use power curves to describe the soil moisture characteristic of soils
and have had only limited success in estimating the hydraulic conductivities
from these power curves; however, Elzeftawy and Mansell (11) have shown
that the calculated hydraulic conductivity using Equation 16 provided a
good estimation of the K(e) function of Lakeland fine sand.
The measured and calculated values of hydraulic conductivity of Lake-
land fine sand are presented in Figure 9 for three different profile depths.
The measured hydraulic conductivity values at water saturation, K , were
used as the only matching factor to determine the calculated curves of the
K(e) function. It is well known that it is quicker and simpler to determine
Ksexperimentally then it is to measure unsaturated hydraulic conductivities
20 -
10 2-i
10' -
10"
10
* 10 2
% 10coO
£ 10
>I
10s
-
10~* -
10"
Lakeland Fine Sand
KCalculated K
scm/hr
14.80
13.00
17.10
1—
0.10
T 1
0.60 0.70ISGS
0.20 0.30 0.40 0.50
Soil Moisture Content, 6, cm 3 /cm 3
Figure 9. Experimental and calculated hydraulic conductivity of Lakeland fine sand.
at any moisture content below the saturation value. But the pronounced
deviation between the calculated and measured K(e) values for volumetric
water contents less than 10 percent suggests that a second matching point
somewhat within the "field capacity" range of water content may be needed.
The average densities and water-saturated hydraulic conductivities of
the undisturbed samples of Lakeland sand are shown in table 5. The varia-
tion of bulk density with depth of the soil profile is almost negligible;
however, the hydraulic conductivity of the bottom layer (60 to 90 cm) is
much higher than that for the surface layer (0 to 15 cm).
Selected physical properties of the undisturbed (Drummer and Dana) and
disturbed (Ottawa sand and Fayette C horizon) samples used are presented in
table 6. The saturated hydraulic conductivities of the Fayette C and Dana
soils are larger than expected, which might be attributable to the low bulk
- 21
Table 5. Bulk density and saturated hydraulic conductivityof Lakeland fine sand.
saturated hydraulicbulk density, p , conductivity K ,
soil depth, cm , . a „/„„,3 v , . a „m/uKps
+ t, g/cm Ks
+ t, cm/h
to 15 1.56 + 0.06 14.80 + 1.12
30 to 45 1.57+0.03 13.00+0.93
60 to 90 1.57+0.05 17.10+1.09
at-distribution at 95 percent confidence level.
Table 6. Selected physical properties of soils used at indicated depths.
DrummerDana
to 10 cmOttawa sand
0.85 to 2 mm
FayetteC horizon120 to 150 cmproperty to 30 cm 30 to 75 cm 75 to 90 cm
sand, % 6.00 6.00 6.00 6.1 100.00 7.00
silt, % 77.20 80.50 82.60 74.9 0.00 75.00
clay, % 16.80 13.20 10.50 19.00 0.00 18.003
bulk density, g/cm 1.52 1.30 1.43 1.22 1.65a
1.25a
saturated hydraulicconductivity, K ,
cm/h 2,.11 X 10" 23.6 X 10" 2
2.5 X 10" 21.92 X 10"° 1.34 X 10
+12.15 X 10" 1
hand packed.
densities and, in the Dana soil, the high organic matter content. The
grain size distribution of the natural soils material (Drummer, Dana, and
Fayette) is similar; however, these soils differ widely in their bulk
densities and hydraulic conductivities. For instance, the bulk densities
of the Drummer surface layer (0 to 30 cm) and Fayette C horizon are 1.523
and 1.25 gm/cm , respectively; the difference between their corresponding
Ks
values is 1 order of magnitude. The Dana and Fayette soils material are
similar in grain size analysis and bulk density; however, their saturated
hydraulic conductivities are 1 order of magnitude apart, which probably
indicates the effect of different natural soil structures.
Soil moisture content suction characteristic curves obtained by se-
quential drainage are shown in figure 10 for the three profile depths of
Drummer soil and the surface layer (0 to 15 cm) of Lakeland fine sand. It
is significant that the amount of water retained at relatively low values
of suction (for example, between and 1000 cm of suction) depends upon the
- 22 -
capillary effect and the pore size distribution and therefore is strongly
affected by the soil structure. On the other hand, water retention in the
higher suction range is due increasingly to adsorption and is thus influenced
less by the structure and more by the texture and specific surface of the
soil material. Figure 10 indicates that, in general, the greater the clay
content, the greater the water content, at any particular suction (compare
Lakeland sand and Drummer silty loam) and the more gradual the slope of the
curve.
The effect of compaction upon a soil is to decrease its total porosity,
and especially to decrease the volume of the large interaggregate pores;
this means that water content at saturation and the initial decrease of
water content with the application of low suction are reduced. The data
presented in table 6 and figure 10 for the 30 to 75-cm and 75 to 90-cm depth
of Drummer samples support the previous statement: note the similarity in
their particle-size analysis and the differences in their bulk densities
and the saturated water contents.
The calculated and experimental hydraulic conductivities of three lay-
ers of Drummer soil profiles are shown in figure 11. The experimental data
were obtained by the unit gradient method as published by Elzeftawy and
Mansell (12). The hydraulic conductivity of this soil at saturation is
generally about 4 orders of magnitude larger than at 50 percent of satura-
tion. The calculated results were consistent with the experimental data;3 3
however, the calculated numerical values below 0.32 cm /cm water content
were less than the experimentally hydraulic conductivities obtained (not
shown in figure 11).
Hydraulic conductivities as a function of moisture content of Ottawa
sand and Fayette C horizon are shown in figures 12 and 13. The lines repre-
sent the calculated values of K(e) obtained by Equation 16 and the soil-
moisture retention curve. The circles are the experimental data points.
These soil materials represent a wide range of pore size distributions over
which the calculations of hydraulic conductivities are based. Figure 13
3'
shows that a change in water content of Fayette soil from 0.47 to 0.30 cm /cm"
has reduced the hydraulic conductivity from 2.2 X 10_1
cm/h to 4.0 X 10" 3
cm/h, respectively.
- 23
10,000^1
1000
co'^u300
'5
00
100-
10
Lakeland Fine Sand
0- 15 cm
Drummer
75 - 90 cm
30 - 75 cm
30*r
5 10 15 20 25 30 35 40
Moisture Content, Gravimetric - w (%)
Figure 10. Soil moisture-suction relationships of Lakeland fine sand and Drummer soil.
Green and Corey (10) and others have stated that using a matching
factor at water saturation has a distinct advantage, since inaccuracies in
calculated values of K(e) can be more easily tolerated at lower water con-
tents; however, in studying phenomena such as evaporation, the early stages
of water infiltration, and the movement of solutes such as contaminants in
the unsaturated zone, more accurate methods are needed to determine the
unsaturated hydraulic conductivities of soils at lower values of water con-
tent. Bruce (21) suggested that matching factors somewhat below the bubbling
pressure are sufficiently accurate for calculating the unsaturated hydraulic
conductivities of coarse-grained soils; however, he also stated that the
indiscriminate use of such methods for calculating the hydraulic conductivi-
ties of fine-grained soils is inadvisable. In our study good results have
- 24 -
10"
Eu
o3acoo
a>X
10"
10
10"
10-5 _
10"6-
0.20
Drummer, Soil
Depth • 0-30 cm
S= O.43 ^^£
Ks= 0.02 cm/hr ^
/
/
/
/
A/Depth - 75-90 cm / /
S= O.49
K = 0.03 cm/hr
Depth - 30-75 cm
,=0.51
Ks= 0.04 cm/hr
—I
—
0.30 0.500.40
Soil Moisture Content, 6, cm 3 /cm 3
Figure 11. Experimental and calculated hydraulic conductivity of Drummer soil
been obtained for the fine-grained soils (Drummer and Fayette) using satur-
ated hydraulic conductivity as the only matching factor. However, we noticed
that the calculated values deviated from the experimental results, especially3 3
within the range of low water content (less than 0.35 cm /cm moisture
content). For this reason, the Dana loam samples were chosen to investigate
the possibility of using two or more matching factors to calculate the K(e)
function. Some of the physical properties of Dana soil are presented in
table 6.
DISCUSSION
A method of predicting the saturated-unsaturated hydraulic conductivi-
ties of some Illinois soils utilize the soil moisture content-suction head
- 25
102
E" 10'2.
3gcoo
a>I
10°
10"
Ottawa Sand
0^=0.382K
b= 13.40 cm/hr
Calculated
• Experimental
0.40ISGS
0.10 0.20 0.30
Soil Moisture Content, 6, cm 3 /cm 3
Figure 12. Experimental and calculated hydraulic conductivities of Ottawa sand.
relation, h(e), to calculate the unsaturated hydraulic conductivity of soil.
The value of the hydraulic conductivity at saturation, K (the soil perme-
ability), was used as a matching factor during the calculations. The h(e)
relations and the saturated conductivities, K , of soils were determined
in the laboratory using the commercially available "Tempe" cell. Undisturbed
samples of Drummer and Dana soils and disturbed samples of Fayette C soil,
Ottawa sand, and other soils were used in this study. Published data on
some agricultural soils were also used to validate results of our investi-
gations. On the basis of our study results, the following conclusions can
be made:
1. The model successfully predicts the hydraulic conductivity
of a wide range of soils.
2. The proposed simplified laboratory procedure is reliable and
can be used to determine easily the soil moisture-suction
relationships of disturbed or undisturbed soil samples.
3. Evaluation of the unsaturated hydraulic conductivities of
soils using the proposed "Tempe" cell method is quick and
economical
.
- 26 -
10Pl
10
E-10"
3XI
| 10
a>I
3_
104 _
10"
Fayette C horizon
S=O.47
Ks=0.22cm/hr
Calculated
• Experimental
0.50ISGS
0.20 0.30 0.40
Soil Moisture Content, 8, cm 3 /cm 3
Figure 13. Experimental and calculated hydraulic conductivities of Fayette C horizon.
The experimental and calculated hydraulic conductivities of the Dana
sample are shown in figure 14; the circles represent the experimental data
and the lines represent the calculated values. The calculated hydraulic
conductivity function using K as the only matching point is shown in the
figure by the solid line; note the deviation between the calculated and3 3
experimental data below a water content of 0.45 cm /cm . Better results
were obtained when two matching factors were used, particularly when the
saturated hydraulic conductivity, K , and another experimental value some-
what below the bubbling pressure of the soil were used. (The value K(6) =
-3 3 31.01 X 10 cm/min was arbitrarily chosen where = 0.40 cm /cm .) In this
case, the dashed line represents the K(e) function calculated with two
matching factors in Equation 16. Using two matching factors in the calcu-
27 -
10i _,
I
"2-10
Eu
S 103
10
DO i n'4O
10s
-.
10-6
K = 1.01 x 10
Dana Loam
ds= 0.50
Ks= 0.32 cm/min.
• Experimental
Calculated with
one Matching Factor
two Matching Factors
0.25 0.60ISGS
0.30 0.40 0.50
Soil Moisture Content, 6, cm 3 /cm 3
Figure 14. Experimental and calculated hydraulic conductivities of Dana soi
lations of K(e) functions of many fine-grained soils has reduced the error
in predicting the hydraulic conductivity values at low soil water content.
Results of our study presented in graphical form in Appendix B, indicate
that the method described in this report for calculating the hydraulic
conductivity of soil materials can be used with confidence for many practical
applications describing the pore transport system.
- 28 -
REFERENCES
1. Hi 1 lei , D. , Soil and Water, Physical Principles and Processes, AcademicPress, New York, 1973.
2. Taylor, S. A. and G. L. Ashcroft, Physical Edaphology, The Physics of
Irrigated and Nonirrigated Soils, W. H. Freeman and Company, San
Francisco, California, 1972.
3. Kirkham, D. and W. L. Powers, Advanced Soil Physics, John Wiley and
Sons, Inc., New York, 1972.
4. Rose, C. W., Agriculture Physics, Pergamon Press, New York, 1966.
5. Childs, E. C. , An Introduction to the Physical Basis of Soil WaterPhenomena, John Wiley and Sons, Inc., New York, 1969.
6. Cromey, D. , J. E. Coleman, and P. M. Bridge, Road Research Laboratory,Crowthorne, England, 1951.
7. Childs, E. C. and N. Collis-George, Proceedings of the Royal Societyof London, Vol. A, No. 2-1, 1950, pp. 392-405.
8. Rogers, J. S. and A. Klute, Soil Science Society of America, Proceed-ings, Vol. 35, 1971, pp. 695-700.
9. Millington, R. J. and J. R. Quirk, Transactions of the Faraday Society,Vol. 57, 1961, pp. 1200-1207.
10. Green, R. E. and J. C. Corey, Science Society of America, Proceedings,Vol. 35, 1971, pp. 3-8.
11. Elzeftawy, A. and R. S. Mansell, Soil Science Society of America,Proceedings, Vol. 39, 1975, pp. 599-603.
12. Elzeftawy, A. and B. J. Dempsey, Transportation Research Record, Vol.
642, pp. 30-35.
13. Watson, K. K. , Water Resources Research, Vol. 2, 1966, pp. 509-517.
14. Amerman, C. R. , Hydrology and Oil Science, SSSA Special PublicationsSeries, No. 5, Soil Science Society of America, Madison,Wisconsin, 1973.
15. Philip, J. R. , in Prediction in Catchment Hydrology, C. H. M. van Bauel
,
Ed., Australian Academy of Science, 1975, pp. 23-30.
16. Green, W. Heber and G. A. Ampt, Journal of Agricultural Science, Vol.
4, 1911, pp. 1-24.
17. Philip, J. R., Soil Science, Vol. 84, 1957, pp. 257-264.
18. Gardner, W. R. , D. Hi 1 1 el , and Y. Benyamini, Water Resources Research,Vol. 6, 1970, pp. 851-861.
- 29 -
19. Campbell, G. S., Soil Science, Vol. 117, 1974, pp. 311-314.
20. Clapp, R. B. and G. M. Hornberger, Water Resources Research, Vol.
14, 1978, pp. 601-614.
21. Bruce, R. R. , Soil Science Society of America, Proceedings, Vol. 36,
1972, pp. 555-561.
22. Dempsey, B. S. and A. Elzeftawy, Moisture Movement and MoistureMovement Equilibrium in Pavement Systems Univ. of IllinoisEngineering Experimental Station, Urbana, Illinois, UILU-ENG-76-2012, 1976, 147 p.
23. Soil Moisture Equipment Corp., Tempe Pressure Cell, CatalogNo. 1400, 8 p.
24. Follmer, L. R. , 1982, in Thorn, C. E. [ed.] Space and Time in
Geomorphology: The "Binghampton" Symposium in Geomorphology:International Series, no. 12, London: George Allen and Unwin,
p. 117-146.
25. McKay, E. D. , A. Elzeftawy and K. Cartwright, 1979, IllinoisGeological Survey, EGN No. 85, 32 p.
LIST OF PUBLICATIONS
1. Elzeftawy, Atef. 1979. Modeling the Transport of Heat, Water and
Solute in Unsaturated Soil and Earth Materials. ASAE Proceed-
ings of "Hydrologic Transport Modeling Symposium." American
Society of Agricultural Engineers, St. Joseph, Michigan, 49085.
P. 234-245.
2. Elzeftawy, Atef. 1979. Waste Disposal and Transport Phenomena in
Soil. Proceedings of the 2nd Annual Conference of Applied
Research and Practice on Municipal and Industrial Waste.
Madison, Wisconsin. P. 583-595.
3. Elzeftawy, Atef and Keros Cartwright. 1981. Evaluating the Saturated
and Unsaturated Hydraulic Conductivity of Soils. ASTM Special
Technical Publication (STP) 746, P. 168-181, Philadelphia,
Pennsylvania.
- 31 -
10,000-
1000-
100-
10-
Fine Ottawa Sand
10 15 20 25
Soil moisture content 6 (%)
To" 35
10.000-
1000-
100-
1010
Coarse Ottawa Sand
~l
—
15—
r
-
20-r—30 35 40 45
Soil moisture content 6 (%)
10,000
1000-
10.000-
20 40 45 50
Soil moisture content 8 (%)
1000-
100-
10
"1"Richland Loess
10r20 30 60 70
Soil moisture content 6 (%)
- 32 -
lO.OOO-i
\Roxana Silt
100-
20 30 40 50
Soil moisture content ft (%)
10,000
Soil moisture content 8 (%)
10.000
1000- 1000-
30 35
Soil moisture content ft (%)
50155
Soil moisture content ft (%)
- 33 -
10.000
1000-
10.000-
1000-
100- 100
30-60 in. Piatt
20 25 30 35-1
—
40-•-I-
50 55
Soil moisture content 8 (%) Soil moisture content 6 (%)
10.000
1000
10.000
100-
1000-
Sample 12
-r—20
#.
-1
—
50
Soil moisture content (%)
30 40
Soil moisture content (%)
-1
—
70 HO
34 -
10.000
1000-
10,000-
30 35 40 45
Soil moisture content (%)
50 55
Sample 22
25-
T
-45
Soil moisture content 8 (%)
Sample 25
15 25T35
10.000
Soil moisture content f) (%)
20 30 40
Soil moisture content 6 (%)
- 35 -
Sample 27
1000-
100-
10-
25 30 35 40
—r~45 50
-1
—
55
10.000
1000-
60
100-
Soil moisture content 6 (%)
30 35 40
Soil moisture content (%)
10,000
1000-
10.000-
100-
1000-
100
10
Soil moisture content 8 (%)
20 30 40 5(
Soil moisture content 6 (%)
60
- 36 -
Sample 13
1000-
100-
10 20 30 40 5(
Soil moisture content 8 (%)
ra
Sample 14
"~i
—
20 30 40 50 60 70
Soil moisture content 8 (%)
lO.OOOn
1000-
10-
Sample 15
20 30—I
—
40 50
Soil moisture content II (%)
« Sample 16
in 20 40 60 70
Soil moisture content 8 {%)
- 37
10.000
1000-
10.000
100-
1000
100
20 25 30 35
Soil moisture content (%) Soil moisture content 6 (%)
10.000
1000-
10.000
100-
40 50
Soil moisture content (%)
60 70
100-
45 55
Soil moisture content 6 (%)
65
- 38 -
1000-
10.000-
1000-
10-
%
Sample 3
10 30—1
—
50 60 80
Soil moisture content 8 (%) Soil moisture content 8 (%)
10.000-,
Sample 4
1000-
20 4030 40 50
Soil moisture content 8 (%)
70
10.000
1000
80
100-
35 45 55
Soil moisture content 8 (%)
;•,
39 -
10.000-
1000-
100-
Sample 6
20~1
—
30~
r
-
40—I
—
50 60-1
—
70 80
Soil moisture content 8 (%)
1000-
i nn-
10
Sample 7
10 20 30 60 70
Soil moisture content 8 (%)
10.000
100-
10
10.000-
25 30 35 40
Soil moisture content (%)
1000-
100
111
Sample 9
10 15 20 25 30
Soil moisture content 8 (%)
35
40 -
Appendix B
The hydraulic conductivity soil -moisture relationships forsamples used in this study. Note, the rewetting of dry samplesmay have increased the saturated hydraulic conductivity in
some samples.
- 41 -
10"
E3 m-M
10
10'
Fine Ottawa Sand
K = 1.03 x 10' cm/hr
= 0.363 cm 3 /cm 3
p = 1.70gm/cm3
10 15 20 25 30
Soil moisture content (%)
35 40
10°
e-^ io-
io"--
10
10
Coarse Ottawa Sand
••
••
••
•
•
•
•
•
•
•
•
•
•
•K$= 1.34x10' cm/hr
•
••
S= 0.382 cm 3 /cm 3
p = 1.65 gm/cm 3
•1 ~ - T "
T-
1
20 25 30 35
Soil moisture content 8 {%)
10
E
10
Ground Ottawa Sand
K = 1.81 x 10° cm/hrS= 0.420 cm 3 /cm 3
p = 1.50 gm/cm 3
20 25 30 35 40
Soil moisture content 6 (%)
50
10'
E£ io-
10
10
Richland Loess
K =5.05x 10° cm/hr
d = 0.520 cm 3 /cm 3
p = 1.30 gm/cm 3
I 25 30 35 40
Soil moisture content 6 (%)
42
10°-
Roxana Silt •
•
•
•tcrL •
•
•
.c•
conductivity
(cm
o•
•
•
•
y
| io"3-
I
•
•
•
•
•
10"4-
•
• Ks= 8.76x 10"' cm/hr
# 8S= 0.49 cm 3 /cm3
p = 1.19gm/cm 3
10"S-
•i i i i i ii i i
10"
10 25 30 35 40 50
E2 io-M
10
10"
RU-43
25
Ks
= 2.87x10"' cm/hr
d%= 0.480 cm 3 /cm 3
p = 1 .23 gm/cm 3
Soil moisture content 8 (%)
30 35 40
Soil moisture content 8 (%)
to"
10
E^ 10"
10"
10"
10
EL-53
K$= 1.37 x 10° cm/hr
0,. = 4.80 cm 3 /cm 3
p = 1.21 gm/cm 3
25 30 35 40
Soil moisture content 8 (%)
10"
E£ io-
lO"
10"
0-12 in. Piatt
Ks
= 2.11 x 10" 2 cm/hr
8 =0.432 cm 3 /cm 3
p = 1.52 gm/cm 3
30 35
Soil moisture content 8 {%)
- 43 -
10
E5 ,0-3.
10
10
10"20
12-30 in. Piatt
K$= 3.6x10"' cm/hr
S= 0.512 cm 3 /cm 3
p = 1.30gm/cm 3
25 40 45 lo~ 55
Soil moisture content 6 (%)
10
10"
E-2 io-
10"
10H
10
30-60 in. Piatt
Ks= 2.5x 10" J cm/hr
S= 0.488 cm 3 /cm 3
/> = 1.43gm/cm 3
20 25 30 35 40 45
Soil moisture content 6 {%)
10'-
Ea 10
-3.
10
-a>I
10
10
Sample 11
Ks
-= 1.15 x 10° cm/hr
S= 0.700 cm 3
/cm 3
p= 1.32gm/cm 3
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
Soil moisture content 6 (%)
10°nSample 12
•
•10"'-
•
•
.c
£-H io"
2-
>>
•
•
•
•t>3TJcOU •
•
o
| 10" 3-
•o>I
•
•
•
10"4-
•
•
K =7.04x 10"' cm/hrS= 0.740 cm 3 /cm 3
p = 1.15 gm/cm 3
,„-s.101 5 20 25 3'0 35 40 45 50 55 6'0 65 70 75 80
Soil moisture content 8 (%)
- 44 -
10"
E
10-
Sample 21
K =2.61 x 10"' cm/hr
6 = 0.450 cm 3 /cm 3
p= 1.34gm/cm 3
30 35 40
Soil moisture content 6 (%)
45
10"
ES. io-
10
10'
1025
Sample 22
Ks= 1.04 x10"2 cm/hr
8i= 0.480 cm 3 /cm 3
p = 1 .33 gm/cm 3
35 40
Soil moisture content 6 (%)
iou-
Sample 25
•
••
10"L
•
jr
•
Hydraulic
conductivity
(cm
O
°i
•
•
•
••
•
•
•
10-"-
•
•
•
Ks= 4.18x10-' cm/hr
S= 0.500 cm 3
/cm3
p = 1 .34 gm/cm 3
,n-S-
10"
20 25 30 35 40 45
Soil moisture content 6 (%)
50
E2 10"'
10-
1025
Sample 26
Ks= 3.70x 10"' cm/hr
= 0.580 cm 3 /cm 3
p = 1.31 gm/cm3
35 40 45 50
Soil moisture content 6 (%)
60
- 45 -
10
10
E2 io-
10"
10"
1025
Sample 27
K$= 1.24 x 10~2 cm/hr
6 =0.570 cm 3 /cm3
p = 1.20gm/cm3
30 35 50 55 60
10 -
Sample 28
•
•
io-'-
•
X•
Hydraulic
conductivity
(err
•
•
•
•
•
•
10"4- •
•
•
Ks= 4.19x 10"' cm/hr
S= 0.540 cm 3 /cm3
p = 1.21 gm/cm 3
•
,r»-S_ A
Soil moisture content (%)
25 30 35 40 45 50
Soil moisture content d (%)
1U~Sample 29
•
•
•
10"'- •
•
•
conductivity
(cm/hr)
o
•
•
•
•
•
•u
= in"J-ro 1U
•a>I
•
•
•
•
•
10"4 -
•
•
•
K = 1.13 x 10° cm/hr
$= 0.480 cm 3 /cm 3
p = 1.35 gm/cm 3
m-5. •
io"'-Sample 30
i
<
10" 2-
•
.c•
conductivity
(cm
•
•
o
| 10'4-
TJ>
•
•
•
•
•
•
10~ 5-
•
•
Ks
*5
= 3.24x 10~ 2 cm/hr
" 0.520 cm 3 /cm 3
,n-6- *-
• P = 1.37 gm/cm 3
30 35 40
Soil moisture content 6 (%)
45 20 30 40 50
Soil moisture content (%)
- 46
10'
E5 10-'-
10
10*-
Sample 13
Ks= 3.90 x 10° cm/hr
8i= 0.620 cm 3
/cm 3
p = 0.91 gm/cm 3
10 15 20 25 30 35 40 45 50 55 60 65 70 75
Soil moisture content 8 (%)
I Of
ES io-'-I
10"
Sample 14
Ks=1.83x 10° cm/hr
s= 0.620 cm 3 /cm3
p = 0.92 gm/cm3
30 35 40 45 51
Soil moisture content 6 (%)
E& io-
10"
10
10'
Sample 15
Ks= 3.22x 10° cm/hr
S= 5.80 cm 3 /cm 3
p = 0.94 gm/cm3
15 20 25 30
Soil moisture content 8 (%)
10"
E^ io-
10
10
Sample 16
K$= 2.09x 10° cm/hr
9S= 0.600 cm 3 /cm 3
p = 1.00 gm/cm 3
Soil moisture content 8 (%)
47 -
10"-
£2 10"
10
10"
Sample 1 7
Ks= 2.40x10° cm/hr
s= 0.450 cm 3 /cm 3
p = 1.13gm/cm 3
10'
15 20-J—35>5 30 35 40
Soil moisture content 6 (%)
45 50
Sample 19
•
•
•
10°- ••
••
•_^ •X •E2 io-'-
•> •>
o •DDCo •uo
3 io"1- •
TJ,>-
X •
•
•10"3-
•
K =5.13x 10° cm/hr•
6 =0.590 cm 3 /cm 3
s
•p = 1 .03 gm/cm
10"4-—*-, , ,i i i i
15 20 30 35 40 50 60
Soil moisture content 8 (%)
io1
10"
E•H 10
-
Sample 20
Ks= 4.81 x 10° cm/hr
S= 0.590 cm 3 /cm 3
p = 1.12 gm/cm 3
10•4JL
30 35 55 60
Soil moisture content 6 (%)
10"
10"
E•= 10
L
io-
1020
Sample 1
K = 1.51 x 10° cm/hrS= 0.61 cm 3 /cm 3
p = 0.88 gm/cm 3
25 ~F -
r
-35 40
—r~45 50
-J—55 60
Soil moisture content 6 (%)
- 48 -
10
ES 10
-
io--
10'
Sampl S 2
•
•
2. •
•
S_
•
•
•
•
>_
•
•
s_
•
•
•
K =2.80x 10"' cm/hr
8 = 0.580 cm 3 /cm3
p = 0.86 gm/cm 3
2 5 3'0I
35i
40i i i
45 50 55 60
1U "
Sample 3
•
•
•10"'-
•
••
•
.c •
E •
> •>
o •3
c •oou •
3 io"3- •
> •I •
•
•
tcr»- •
• K$= 5.60x10"' cm/hr
• $= 0.690 cm 3 /cm 3
p = 0.90 gm/cm 3
•
10" 5H
•1 1 1 1 111!30 35 40 45 50 55 60
Soil moisture content 6 {%) Soil moisture content 6 (%)
10
ES 10" 3
10
10
10n
Sample 4
Ks= 1.64 x 10"' cm/hr
6%= 0.710 cm 3
/cm 3
p = 0.82 gm/cm 3
IT 35 40 50 60
Soil moisture content 8 (%)
10
Eo— 10
10
Sample 5
K =4.53x 10"' cm/hr
6 =0.630 cm 3 /cm 3
p = 1.21 gm/cm 3
30 35 40 45 50 55
Soil moisture content 6 (%)
65
- 49 -
10"
ES io~
3-
10 -
i or
Sample 6
K = 7.61 x 10" 2 cm/hr
0^=0.720 cm 3 /cm 3
p = 0.89 gm/cm 3
25 30 35 40 45 50 55 60 65 70
Soil moisture content 6 (%)
Sample 7
•
•
io°- •
•
•~•
.c
£ •
^ 10"'- •> •> •u •
D •C •oo •o •
3 10"2- •
o •>I
•
•
•
io"3-
•
•
•
•
Ks= 4.05x 10° cm/hr
S= 0.540 cm 3 /cm 3
p= 1.30 gm/cm 3
m-4-10 15 20 25 30 35 40 45 50
Soil moisture content 8 (%)
10'
10"
E^ 10"
io-l
r.
Sample 8
Ks= 3.18x 10° cm/hr
s= 4.9Ocm 3
/cm 3
p = 1.36 gm/cm 3
20—r—25 35 45 50
Soil moisture content 6 (%)
10'
10"
E3 io-
10
10"
10
Sample 9
Ks= 4.39x10° cm/hr
9 = 0.400 cm 3 /cm 3
s ,
p = 1.31 gm/cm
15 20 25 30
Soil moisture content 6 (%)
40