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TESTING 0F=¥HE 0NE=BINENSIONAL INFILTRATION
EQUATION ON‘SOME MICHIGAN SOILS

presented by

Hmida Mohamed Kar-Kuri

has been accepted towards fulfillment
of the requirements for

M. Sc. 1983

degree in

M

Major profe I

Date May 11, 1983

04639 MS U is an Affirmative Action/Equal Opportunity Institution

 

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TO AVOID FINES return on or before date due.

DATE DUE ‘ DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU Is An Affirmative Action/Equal Opportunity Institution
c:\clvc\dmadunpm3~p.1

 

/ 9p. Edi/é

TESTING OF THE ONE-DIMENSIONAL

INFILTRATION EQUATION ON SOME
MICHIGAN SOILS

By
Hmida Mohamed Kar-Kuri

A THESIS

Submitted to
Michigan State University
In partial fulfillment of the requirement
for the degree of

MASTER OF SCIENCE

Department of Crop and Soil Sciences

1983

ABSTRACT

TESTING OF THE ONE-DIMENSIONAL INFILTRATION
EQUATION ON SOME MICHIGAN SOILS

By

Hmida Mohamed Kar-Kuri

The infiltration and movement of water into soil is of great
importance and concern to mankind and particularly to
agriculturem ILt is important from an economic point of view to
maximize crOp productivity resulting from rainfall (H‘:irrigation
and to manage the associated processes of infiltration,
evapotranspiration and drainage wisely. To assess these
processes accurately, a discription of the physics hunflved is
helpful and should be documented whenever possible.

In this investigatirnu, several columns of Metea and Spinks
sandy loam soils were wetted to preselected distances and/or
preselected periods of time. The horizontal and vertical
soil—moisture distribution profiles were evaluated for soil
columns with slightly different bulk densities. Ekfil moisture
characteristic curves were obtained from capillary rise and
filter paper experiments run on both soils.

Solutions of the one—dimensional Richards' equation were
obtained by a numerical method (FINDIT) using a
:finite—difference, iterative technique. The technique, contrary
to some earlier soluthnmn is extremely accurate for both short
and long periods of time. The infiltration time, the
soil-moisture diffusivity D(@) and conductivity K(®) were

required for sOlving the equation, D(@) being derived from the

Hmida Mohamed Kar—kuri

horizontal wetting profiles and K(O) from the differences between
the horizontal and vertical profiles.

The one-dimensional infiltration equation of Richards' was
tested by comparing experimental infiltration profiles with
calculated profiles. Generally, good agreement was obtained
particularly when considering the variations in bulk density and
temperature, experimental error, etc. in these experiments.
Although satisfactory agreement was obtained for Metea and Spinks
data sets, a second data set for Metea disagreed considerably

with the experimental results.

To my parents

ii

ACKNOWLEDGEMENTS

The author wishes to express his deep appreciation and
indebtedness to Dr. Raymond J. Kunze for help and guidance
throughout the study program, not only serving as chairman of the
guidance committee but contributing many hours of supervision and
words of inspiration making the completion of this work possible.

(Rhm*mwmemsof the guidance committee are also
acknowledged. Gratitude and sincere appreciation are expressed
‘MD Dr. Boyd Ellis from the CrOp and Soil Sciences Department and
especially to Mr. Vincent F. Bralts from the Agricultural
Engineering Department for their advice and encouragement.

To my wierLotfeia, who is very special to me, I give my
thanks for her love, endless support, patience, endurance and
understanding. Without her help and dedication, my graduate
study could never have been achieved.

Speckfl.thafl&3is extended to Ms. Darlene Kriss whose
patience was extremely helpful during the typing and Innaparation
of this manuscript.

The author is also grateful to the Libyan government and
especially to the Sebha Company for Reclamation and Cknmstruction.

who sponsored his study and research work.

iii

TABLE OF CONTENTS

Page
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . vi

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . viii

LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . x
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . 1
I. Objectives . . . . . . . . . . . . . . . . . . . . . 3
LITERATURE REVIEW . . . . . . . . . . . . . . . . . . . 4
I. Theoretical Background . . . . . . . . . . . . . . . 4

1.1. Water movement under saturated conditions . . 4

1.2. Water movement under unsaturated conditions . 6

1.2.1. The deveIOpment of diffusion theory
for unsaturated flow systems . . . . . 7

II. Soil Moisture Diffusivity and Conductivity and their
Measurments . . . . . . . . . . . . . . . . . . . . 10

2.1. Methods for determining soil moisture
diffusivity and conductivity . . . . . . . . . 12

2.1.1. Steady—state method . . . . . . . . . 12
2.1.2. Transient Methods . . . . . . . . . . 13
2.1.3. Pore-size analysis methods . . . . . . 18

III. The Developement of Infiltration Theory and its

Solutions . . . . . . . . . . . . . . . . . . . . . 22
3.1. Theoretical deveIOpment . . . . . . . . . . . 22
3.1.1. Cumulative infiltration . . . . . . . 25

3.1.2. Infiltration rate . . . . . . . . . . 26

3.2. Testing the infiltration equations by
numerical analysis . . . . . . . . . . . . . . 28

iv

IV. Soil Moisture Potential Function .
EXPERIMENTAL PROCEDURE AND ANALYSIS . . . . . . . . . .
I. Materials and Methods .
1.1. Materials . . . . . . . . . . . . . . . . . .
1.2. Preparation of the flow system
1.2.1. Sample preparation . . . . .
1.2.2. Equipment .
1.2.3. Packing of the soil columns . . . .
1.3. Infiltration method .
II. Estimation of Soil Water Potential . . . . . . . .
2.1. Apparatus and supplies . . . .
2.1.1. Procedure . . . . . . . . . . . . . .
RESULTS AND DISCUSSION

I. Horizontal and Vertical Water Movement with
Different Bulk Densities

II. Calculated Soil-Moisture Diffusivity and
Conductivity Functions . . . . . . . . . . . . .

III. Experimental and Calculated Soil—Moisture Profiles.

IV. Demonstration of Generated Data for Modeling
Other Flow System . . . . . . . . . . . . . . . .

SUMMARY AND CONCLUSIONS .
RECOMMENDATIONS FOR FURTHER STUDIES . . . . . . . . . .
APPENDIX

LIST OF REFERENCES . . . . . . . . . . . . . . . . . .

Page
31
34
34
34
35
35
35
38
41
44
44
45

47

47

59

72

80
81
83
85

111

Table

10

11

12

13

14

LIST OF TABLES

Physical properties of soil materials used . . . .

Characterization of soil columns used for
horizontal flow . . . . . . . . . . . . . . . . . .

Characterization of soil columns used for
vertical flow . . . . . . . . . . . . . . . . .

Parameters describing one-dimensional
infiltration experiments with the Metea and
Spinks sandy loam soils

Comparison between measured and calculated hydraulic
conductivities for Metea and Spinks soils

Infiltration time and its relation to 0 —straight
and maximum wetting distances

Horizontal infiltration data on Metea sandy loam at
2175 minutes. Analysis I

Vertical infiltration data on Metea sandy loam at
2270 minutes. Analysis I

Horizontal infiltration data on Metea sandy loam at
6167 minutes. Analysis II

Vertical infiltration data on Metea sandy loam at
2690 minutes. Analysis II

Horizontal infiltration data on Metea sandy loam at
2076 minutes. Analysis III

Vertical infiltration data on Metea sandy loam at
827 minutes. Analysis III

Horizontal infiltration data on Metea sandy loam at
2305 minutes. Analysis IV .

Vertical infiltration data on Metea sandy loam at
840 minutes. Analysis IV. . . . . . . . . . .

Vi

Page

36

52

53

54

66

77

86

88

9O

92

94

96

98

100

Table Page

15 Horizontal infiltration data on Spinks sandy loam at
4500 minutes. Analysis V . . . . . . . . . . . . . 102

16 Vertical infiltration data on Spinks sandy loam at
2020 minutes. Analysis V . . . . . . . . . . . . . 104

17 Horizontal infiltration data on Spinks sandy loam at
1897 minutes. Analysis VI . . . . . . . . . . . . . 106

18 Vertical infiltration data on Spinks sandy loam at
1188 minutes. Analysis VI . . . . . . . . . . . . . 108

vii

Figure

1

1O

11

12

LIST OF FIGURES

Experimental apparatus used for both horizontal and
vertical water movement . . . . . . . . . . . .

Schematic diagram of the soil column packer .

A special device used for adjusting the contact
between the soil surface and the plate .

Distance to the wetting front versus the square root
of time for Metea sandy loam at indicated bulk
densities comprising analyses I and II .

Distance to the wetting front versus the square root
of time for Metea sandy loam at indicated bulk
densities comprising analyses III and IV . . .

Distance to the wetting front versus the square root
of time for Spinks sandy loam at indicated bulk
densities comprising analyses V and VI .

Values of lambda (A) determined by visual distance
to the wetting front divided by the square root of
time for both Metea and Spinks sandy loam at
indicated bulk densities . . . . . . .

Cumulative water volume versus the square root of

time for Metea and Spinks sandy loam at indicated
bulk densities .

Experimental and smoothed soil moisture profiles for
Metea sandy loam at indicated bulk densities and in—
filtration times . . . . . . . . . . . . .

Calculated soil-moisture diffusivity D(®) using both
assumptions (1 & 3) for Metea sandy loam . . . . . .

Calculated hydraulic conductivity using both
assumptions (1 & 3) for Metea sandy loam .

Experimental and calculated soil moisture

characteristics using assumption (2) for Metea
sandy loam . . . . . . . . . . . .

viii

Page

37
39

42

48

49

50

56

57

61

63

64

65

LIST OF FIGURES (Cont'd.)

13

14

15

16

17

18.

19

2O

Calculated soil-moisture diffusivities using
assumption (1) for Metea sandy loam at indicated
bulk densities . . . . . . . . . . . . . . . . . . .

Calculated hydraulic conductivities using

assumption (1) for Metea sandy loam at indicated
bulk densities . . . . . . . . . . . . . . . . . . .

Calculated soil—moisture diffusivities using
assumption (1) for Spinks sandy loam and Metea sandy
loam at indicated bulk densities . . . .

Calculated hydraulic conductivities using assumption

(1) for Spinks and Metea sandy loam at indicated
bulk densities . . . . . . . . . . . . . . . .

Horizontal and vertical soil moisture profiles
obtained for Metea sandy loam soil using assumption
(1) at indicated bulk densities and 2270 minutes .

Horizontal and vertical soil moisture profiles
obtained for Metea sandy loam soil using assumption
(2) at indicated bulk densities and 2270 minutes .

Horizontal and vertical soil moisture profiles
obtained for Metea sandy loam soil using assumption
(3) at indicated bulk densities and 2270 minutes .

Horizontal and vertical soil moisture profiles
obtained for Spinks sandy loam soil using assumption
(1) at indicated bulk densities and 2020 minutes . .

ix

Page

68

69

70

71

73

74

75

76

Symbols

D(0)

LIST OF SYMBOLS

Meaning
transmissivity (cm/min)
arbitrary constant
soil-moisture diffusivity (cmZ/min)
D as a function of O
acceleration due to gravity (cm/secz)
pressure head or suction (cm of water)
cumulative infiltration (cm)
summation indices

unsaturated hydraulic conductivity
(cm/min)

saturated hydraulic conductivity
(cm/min)

calculated conductivity for a specified
moisture content (cm/min)

measured saturated conductivity
(cm/min)

calculated saturated conductivity
(cm/min)

hydraulic conductivity at moisture
content Oi (cm/min)

K as a function of 0

hydraulic conductivity at initial
moisture content

intrinsic permeability
matching factor

number of increments of 0 from
dryness to saturation

Symbols

9X: qy, qz

r1, r2""’ In

S
t

to

t1/2
v0, ai/at

V V V

 

Meaning

number of pore classes up to water
content of interest

flux density (cm3/cm2 min)

flux densities in he x-, y- and 2-
directions (cm /cm min)

largest pore size which remains full
of water

radii of n equal classes of soil
porosity

sorptivity (cm/minl/Z)
infiltration time (min)
total infiltration time (min)

square root of time

infiltration rate (cm3/cm2 min)

Darcy velociti s in x-, y- and 2-
directions (cm /cm min)

wetting distance in vertical direction
(cm)

wetting distance in horizontal direction
(cm)

vertical component of flow attributed
to gravity

volumetric moisture content at
saturation (cm3/cm2)

volumetric moisture content (cm3/cm2)
gravimetric moisture content (cm3/g)
initial moisture content (cm3/cm2)
O as a function of x and t
hydraulic gradient

hydraulic gradient in three-dimensional
space

xi

Symbols
dH/dx

ah/Bx, ah/ay, Bh/az
BO/Bt

BK/Bz

T

A(O)

x, T, w,---, fm

f(o)6r

f(o)6r

Meaning

hydraulic gradient in one—dimensional
space

hydraulic gradients in x-, y- and 2-
directions

volumetric moisture content rate of
change with time

hydraulic conductivity gradient

suction head (cm) or capillary
potential

matric suction gradient in three-
dimensional space

matric suction gradient

volumetric moisture content gradient
vector differential operator
divergence

Boltzmann transformation (cm/minl/Z)

A as a function of 0

parameters which are single-valued
functions of 0

density of water (g/cc)

absolute water viscosity (poise =
g/cm sec)

soil porosity
surface tension (dynes/cm = g/secz)

partial area occupied by pores of
radii p to p + or

Partial area of pores with radii
o to o + 6r

integral sign (operator)

xii

INTRODUCT I ON

The movement of water into and through soil is of great
importance and concern to agriculture. Knowledge of time changes
in soil water content due to the influence of rainfall or
irrigation and the resulting infiltration, evapotranspiration and
drainage is necessary for good land management. To predict water
content changes accurately within the profile, mathematical
equations describing these processes are helpful and should be
used whenever possible. The complex nature of'tflua porous media
and the water held within the pores makes it difficult to specify
directly the forces acting on that water. The description of
soilawater movement depends not only on the forces residimg Ln
the soil but also on the amount of water present. These forces
are related to the total water potential which in turn can be
divided to its four components: (1) gravitational potential,
which relates to position in the gravitational field with respect
to an arbitrary reference elevation; (2) matrL: potential, which
relates to adsorption forces between solid surfaces and the
amount of water present, including the effect of cohesiwmazforces
lxymveen water molecules; (3) osmotic potential, which relates to
forces of attraction between ions and water molecules; and (4)
pneumatic potential, which relates to forces arising from unequal
pressures in the gaseous phase.

lhflersUnfling'fimamechanism by which water moves under

unsaturated conditions into and through soil is extremely

 

important for promoting good soil-plant relationships. The water
movement through the porous media may also be considered as
diffusion phenomena, and analysis achieved by applying diffusion
theory. Diffusion may occur in both liquid and gaseous phases,
the solid matrix determining the diffusion path length and the
cross—sectional area available for diffusion. Diffusive flow of‘
‘water under unsaturated conditions through porous media has been
known and studied for a long period of time, however, relatively
few experimental investigations for testing this theory have been
published.

The inflow , storage and redistribution of moisture in the
soil profile after an irrigation or rainfall event require
knowledge of both soil wetting and drainage processes. Knowledge
of the infiltration rate is necessary for good irrigatdrni system
design and maximization oi'the water absorption capacity of the
soil. Such conservation of our water resource will increase in
importance as our population increases.

Quantitative measurements of the rate at which a diffusion
process occurs in soil are usually expressed in terms of both
diffusivity and conductivity coefficients, both are applicable to
soil water movement. Therefore, the measurement of these
parameters itscpiite necessary if flow, distribution and storage
of moisture within or drainage from the soil are to be rigorously
analyzed.

The mathematical equation for describing water movement in
this study was derived by Richards (1931). The equation is a

combination of the equation of continuity andlknrw”s equation

 

'utilizing gravitational and matric potentials as driving forces.
Since this equation is a non—linear partial differential
equatdrni, it is not readily solvable; however, its solution was
achieved by using the finite difference, iterative method
(FINDITW.. The procedure required the knowledge of the soil
moisture characteristics, the wetting profiles of horizontal and
vertical flow regimes, the wetting times and the initial and
Immndary conditions. llnflcrocomputer was required to solve the
equation by the necessary procedure.

The flow system considenwai in this study was semi—infinite
with water applied at one end of a homogenous sxxfil column. The
semi-infinite cmnflkition required that water never reach the end

of the column

I. Objectives

The objectives of this study were:

1). To examine how well an existing mathematical equation
described the water movement under unsaturated conditions.

2). To collect infiltration data on two of Michigan soils, Metea
(Arenic Hapludalfs; sandy over loamy, mixed, mesic) sandy
loam and Spinks (Psammentic Hapludalfs; sandy, mixed, mesic)
sandy loam and to calculate the respective soil moisture
diffusivity and conductivity functions for wetting
processes.

3). To verify the computations with other experimental evidence.

LITERATURE REVIEW

I. Theoretical Background

1.1. Water Movement under Unsaturated Conditions

Over a century ago, in 1856, a French scientist with the
name of Henri Darcy paved the way to understanding fluid flow
‘through porous media by intrcflucing an equation which described
water flow through saturated sand beds. This equation showed
‘that the flux density of water flow through saturated sand beds
is directly proportional to the hydraulic gradient. The equation
can be presented as:

q = RAH/L . . . . . . . . . . . . (l)

'where q_i13'the flux density, the volume of water flowing through
a unit-cross—sectional area per unit time, K the hydraulic
conductivity and AH/L the hydraulic gradient or<hflying force.
The assumptions in the above equations are that;iflu3 soil volume
considered is sufficiently large relative to individual soil
pwres and microsc0pic heterogeneities permit the averaging of
velocity and potential over the cross sectional area of the soil
(Hillel, 1980).

Equation (1) does not totally satisfy cmr understanding of
water flow through porous media, particularly when flow is
unsteady: Iltllel (1980) pointed out that when the flux changes

with time or the media is non—uniform, the hydraulic head may rnyt

4

'WWH ——'-' _.-'

5

decrease linearly along the flow direction. The variation in the
hydraulic head gradient and/or the conductivity forces
investigators to use more exact and generalized expressions of
Darcy's law. The expression must be in a differential form to
allow for change in the gradient, flux, and conductivity values
for localized regions that comprise the soil system. By
considering Poiseuille's law, Slichter (1899) derived an equation
in which Darcy's law is included in a general form for saturated
porous media. The three-dimensional macroscopic differential
equation is:
q = -KVH . . . . . . . . . . . . . (2)
where VH is the gradient of the hydraulic head in
three-dimensional space. The negative sign which proceeds the
right—hand sideacxf equation (2) is required because the sign of
the driving force is negative resulting in a positive product.
Equation (2) may be written in a one-dimensional form as:
q = -K dH/dx . . . . . . . . . . . (3)

where dH issthe change in hydraulic head along a streamline
segment Cb<. By considering q=v (Kirkham and Powers, 1972) and v
as a vector, having both magnitude and direction, equation (3)

expanded into the y and z directions becomes:

VX = -K Bh/Bx . . . . . . . . . . . (4a)
Vy = -K ah/By . . . . . . . . . . . (4b)
V = —K Bh/Bz . . . . . . . . . . . (4c)

In the above three expressions, a partial derivative has been
used rather than a total derivative to show that one variable may
change independently of the other two.

By combining equatdrni C3) with the equation of continuity,
Slichter (1899) derived an equation for flow of water through
saturated media. This equation is analogous to heat, electricity
sum diffusion flow equations known as Fourier's law, Ohm's law
and Ifirflr's law, respectively. It will be discussed at some

length in connection with unsaturated flow.

1.2. Water Movement Under Unsaturated Conditions

lhflerstanding‘water movement under saturated conditions is
quite important in the area of irrigation, drainage and
infiltration phenomenon. The simplest type of fluid flow exists
when porous media is saturated, that is, all pores are filled
with.iflu3 same fliurl, a condition which seldom if ever occurs in
agricultural soil. For this reason fundamental and mathematical
concepts of unsaturated flow as well as saturatedzflunvnmst be
considered as a continuum.

Em Ufifumafionof water into and moving through
unsaturated porous media is quite complex and difficult 1x3
describe quantitatively. Water movementinnkn'unsaturated
conditions is impeded not only by the fact iflnrt'water is movingr
in partially filled pores, but is further impeded by entrapped
soil air and gases. le>relationship between soil moisture and

soil moisture potential, a tOpic thflivfill be discussed later,

may be further complicated by hysteresis (Hillel, 1980). Neither
soil water conductivity nor water potential associated with
unsaturated flow are easily measured in all ranges of interest
(Baver, 1972). For these reasons and others, the formulation and
solution of unsaturated flow problems very often require the use
of indirect methods of analysis, based upon approximations or
numerical techniques (Hillel, 1980). In subsequent sections the
fundamental concepts and deveIOpment of diffusion theory in

unsaturated porous media are discussed.

1.2.1. The DeveIOpment of Diffusion Theory for Unsaturated Flow
Systems

By combhmhmzthe equation of continuity with Darcy's law,
Richards (1931) extended Slichter's equation to unsaturated flow.
The equation of continuity is a statement of the principle of
conservation of matter and may be written for Luumrturted porous

medium as:

Q)
G)

(5)

ml

r1-
II

I
<1
..D

where EML/Bt is the time rate of change of the volumetric water
content,<3,$7is the vector differential Operator, representing
the three-dimensional gradient in space. The (V.) product is
mathematically called the divergence and designated div.

Therefore, equation (5) also can be written as follows:

ao___.
5E — div q . . . . . . . . . . . (58)

Pu;

 

 

and

29 = _ ESE EST ESE
at (ax+ay+az)......(5b)

'where qxg (yy, qz are the fluxes in the x—, y— and z- directions,
respectively. From Richard's assumption that Darcy'limv is valid
for unsaturated flow, the hydraulic conductivity is now a
function of the matric suction head or soil water potential, V,
[i.e., K = K(T)] and is commonly called the unsaturated
conductivity and in the older literature "the capillary

conductivity" (Richards, 1952). Therefore, equation (2) becomes:

q = -K(w)VH . . . . . . . . . . . (6)

‘where VH is the hydraulic head gradient,tflrufiinmy include both
suction and gravitational components for vertical flow. Also ii?
the unsaturated conductivity is assumed to be a single-valued

function of 0 [i.e., K = K(®)] equation (6) becomes:

q = —K(O)VH . . . . . . . . . . . (6a)

ems used by Nielsen.and Biggar (1961). Substituting equation (6)

in equation (5) yields:

80

—E = v, {K(V)VH} . . . . . . . . . (7)

which_i13'the general equation of water flow in unsaturated soil.

Remembering that H, the hydraulic head, is the sum of the

pressure head (or its negative, the suction head T) and the

gravitational head equation (7) becomes:

0.)
CD

= -v.{K(T) V (T-z)} . . . . . . (8)

Q)
(‘T

By considering Vz as zero for horizontal flow and unity for

vertical flow, equation (8) may be written as:

= -V,{K(y) v y} + 3% . . . . . (9)

0)
CD

Q7
H

:for verticmfil flow. If horizontal flow is to be considered only,
the last term on the right—hand side of equation (9) is omitted

giving:

Q)
Q)

 

= V.{K(V) V T} . . . . . . . . (10)

0)
Ft

or, in a one-dimensional horizontal system:

IN

_0 ,av
_ 8x, {K(y) 5}—{,} . . . . . . . (ll)

0)
CD

 

Q)
rt

Enuations (10) and (11) are nonlinear partial differential
equations. Their solutions, which will be discussed elsewhere in
this study, depend upon the initial and boundary conditions.
Thus, problems iJnnxrving these equations are frequently called
boundary value problems (Ashcroft and Hanks, 1980). Because
these equations readily can.be connected to diffusion type
equations with a transmission coefficient D(0), their diffusion

nature will become evident in the next section.

10

II. Soil Moisture Diffusivity and Conductivity Functions

and their Measurements

TMasofl.moisture diffusivity function, D(0), and
conductivity functions, K(0), must be measured or kxmnni'to
determine the ability of a soil to transmit water. Modeling soil
water flow consisting of infiltration, drainage and
redistribution, require knowledge of these coefficients.
However, their measurement is complicated by iflua:fact that they
are not only a function of soil moisture content,lnm:are also
dependent on its moisture history. Therefrnwe, it is quite
possible to have the same moisture content under a.wetting and
drying condition, but yet have<different diffusivities and
conductivities. This phenomenon is known as hysteresis.

Bearing in mind that hysteresis is most evident in the water
content—pressure relatLMHHUIB of wetting and drying processes,
Childs and Collis—George (1948) introduced the following
equations:

8T

_. We» 39
8x

(9)- _ so
I — K(®)‘é—@ BX' — 13(9) @321 . . . . (12)

K(0)

Here the matric suction gradient aW/ax'is expended by using the
chain rule, under the assumption that there is a unique

relationship between T and 0. In this case, the water content

ll

gradient becomes the driving force instead of the hydraulic

potential gradient. Combining equations (11) and (12) gives:

0)
(D

i
t ax’

{D(e)§—i.} ....... (13)

Q)

The reciprocal of the term BVUQMDis called the "specific moisture
capacity" and is analogous to the specific heat in the theory of‘
heat fltnv. It is also the first derivative of the soil-moisture
characteristic curve at any particular value of O (Klute, 1952).

Similarly, combining equations (9) and (12) results in:

a
8x

80 _ 3 BO
— - 3; {D(@) 5;}-

t (14)

used for describing vertical flow upward by capillarity from a

water table or downward infiltration through the soil surface.

12

2.1. Methods for Determining Soil Moisture

Diffusivity and Conductivity

Determination of D(O) has been underway for a long period of
time. Darcy’s law has long been the basis for measuring
saturated hydraulic conductivity, K(OS), in soils. The constant
and falling—head permeameters are the most common methods of
measuring K((%3) in the laboratory. Klute (1965) has given
details of the constant head method, making it quite easy and
straight forward for anyone who is interested in measuring the
saturated hydraulic conductivity of soil. However, the
measurements of D(O) and K(O) under unsaturated conditions are
more difficult to achieve and can be grouped into three basic
classes: (1) steady-state, (2) transient and (3) pore—size

analysis.

2.1.1. Steady—state Method

This method is restricted entirely to the measurement of the
hydraulic conductivity under unsaturated conditions which
Inandates a constancy in water content, tension (matric potential)
and flux with time. Thus if water flow in the vertical direction
into soil has reached equilibrium the value of the unsaturated
conductivity is numerically equal to the flux density of water
application; i.e. equation (1) becomes q = K (Ashcroft and Hanks,

1980). Richards (1931) deveIOped an apparatus used for such

 

l3

steady-state measurement of unsaturated flow. Iater,ffichards
and Moore (1952) refined and improved Richard's method. Elrick
and Bowman (1964) used this improved method fln'nmasuring
unsaturated conductivities in steady-state analysis. Similarly,
Nielsen and Biggar (1961) constructed a simple apparatus from
stock materials to accomplish the same objectives. Klute (1965)
has given more details on many aspects of this method in part one

of the Methods of Soil Analysis.

 

By combiningl<00) with data from either the desorption or
absorption moisture characteristics as depicted in equation (12),
values of D(0) may be calculated. Attention must be given to the
wetting history of the soil because values of D(0) will change if
calculations are made using the wetting characteristics as

Opposed to the drying characteristic.

2.1.2. Transient Methods

Because water content and hydraulic potential remain
constant at each point in the flow system, steady-state flow
rates do not change with time. In unsteady-state (transient)
flew; these conditions do not exist (Ashcroft and Hanks, 1980)
and the flux density and the volumetric water content change with
distance and time, respectively. Due not only to its complexity
but also because of greater similarity to actual field
conditions, transient state flow has been under intensive
investigation and development by many investigators. Several

techniques have been proposed for determining soil moisture

l4

diffusivity in wetting and drying of soils. Diffusivity in
wetting of a soil column may be determined by measuring the
moisture contents along the flow axis at a given time. On the
other hand, diffusivity of drying soil requires the determination
of outflow data with time under a specified suction or pressure
change.

BeamseD(O)derived from outflow processes is not
sufficiently accurate for inflow processes such as ijrfiltratiorh
D(O) from such techniques will be recognized but not discussed in
any details here. Gardner (1956) was the first to measure D(0)
and l{(O) usirm? outflow of a pressure membrane device. By taking
impedance of the porous plate into account, which was a serious
limitation of Gardner's method, Miller and Elrick (1958)
calculated conductivities up to 3.5 times larger than Gardner's
values. Further modifications of the outflow method were made by
Rijtema (H%%D and by Kunze and Kirkham (1962). Elrick (1963)
tested the outflow method and found that the experimental outflow
did not agree with the theory close to saturation. Deoring
(1965) nmmumxred soil moisture diffusivities of 5 different soils
by using a number of methods, including the one—step method
uprOposed by Gardner (1962). In comparison to other methods, he
found the one—step method to be reasonably accurate. Jackson et
al. (1965) calculated the unsaturated hydraulic conductivity from
outflow data and compared the results with the methods of Childs
and Collis—George (1950), Marshall (1958) and Millington and
Quirk (1960). Their conclusion and those of Bruce and Klute

(1963) suggested that the experimental results did not agree with

15

that predicted by the theory. Rawlins and Gardner (1963)
presented data which showed that D is not a unique function of 0.
Failure of uniqueness implies that either the potential function,
No) or the hydraulic conductivity functions, K(0), or both are
not unique functions of 0. The magnitude of these errors must be
determined before the diffusion equation can be used reliably in
modeling of soil water movements.

Bruce and Klute (1956) introduced the advance of'a.wetting
front method and calculated values of diffusivity by applying
their data to equation (13). Since equation (13) is a non-linear
partial differential equation, Bruce and Klute used the Boltzman

1/2 to transform equation (13) to an

transformation A = xt
ordinary differential equation. This transformation assumes that
the moisture content (0) is a function of a variable (A)
dependent on distance (x) and (t1/2). This transformation allows
(nmatn calculate the diffusivity function, D(0), directly from
the moisture content distribution curve. The NUifial and
boundary conditions for equations (13) enui (14) considered for

water infiltrating into a semi—infinite, homogenous soil with

uniform initial moisture content are:

0(x, t) = On for x' and x > o t = o . . . . . (14a)
0(x, t) = 00 for x' and x = o t > 0 (14b)
0(x, t) = On for x' and x + m t > o . . . . . (14c)

16

where 9n is the initial moisture content, 00 is the moisture
content at saturation, x' and x are the horizontal and vertical
distances, respectively, and t is the time. By substituting the
Imudable A in equation (13), integrating with respect to A and

solving for D(0)X', equation 13 yields:

D(0)x. = -% (Saw, I AdO . . . . . . . . (15)

or in terms of x' and t at constant t:

D(O)X. = fit (3%) f x'dO . . . . . . (l6)

Ox
which can be evaluated in terms of D(0 )x' from the plot
of C>vs A or 0 vs. x', respectively.

Bruce and Klute point<m1t that if soil.i112a column is not
homogeneous, variations of 0, K(0) and D(O) will exist along the
column. They indicated that D(O) increases with moisture content
with a maxmmnnimfltw»near saturation. Childs and Collis—George
(1950) also observed this phenomenon when they calculated the
diffusivity from soil moisture absorption characteristics.

Since therezhs no standard against which the diffusivity
values can be checked, Bruce and Klute concluded that the only
way D(O) can be checked for correctness is to use the function in
calculating the soil moisture profile following varying periods
of infiltration. These calculated profiles can then be compared
with experimentally observed distributions for the same

materials.

17

Even though this method requires a column of homogenous soil
wraituuicrm moisture content, it is much simpler to obtain a
series of diffusivity values with the Bruce and Klute method than
with other methods. It appears to be quite sensitive to
temperature change. Stockinger et al. (1965) observed that the
temperature effect on the advance of a wetting front is quite
pronounced. They concluded that the variable A = (xt7l/2)is
temperature dependent. Jackson (1963) measured the soil—moisture
diffusivity for three different soils at five different
temperatures. He found that the surface tension to viscosity
ratio is the dominant factor influencing the temperature
dependence of soil moisture diffusivity. Ilielsen et ail. (1962)
have suggested that heat evolvement from wetting soil could
account fimrrmnnisothemmfl.conditions and consequential failure
'between experiment and theory. Nielsen and Biggar rigorously
examined the conditions: (1) that Darcy's law is valid iRu~
unsaturated flow and (2) the A(0) 2 xt-l/2 relationship holds
when using oil and water for wetting soil columns horizontally at
(different negative pressures. Their results show deviations for
a linear relationship between x and t1/2 for water entry
pressures more negative than, but not at —2 mb. lflnay concluded
that the values of diffusivity calculated depend upon the
boundary condition at which the water enters the column and,
therefore, these same D values would not be appropriate for the
solution of the diffusion equation for other boundary conditions.

In his cufitticism of Nielsen et al (1962) Peck (1964) states that

Nielsen et al. used initially air-free water but which

l8

subsequently became air-saturated during;later portions of the
experiment, confounding the results. It has been established by
(Christiansen, 1944) that the'variation in the concentration of
air dissolved in the water can alter the hydraulic conductivity

of a porous material considerably.
2.1.3. Pore—size Analysis Methods

Childs and Collis-George (1950), Marshall (1958), and
Millington and Quirk (1959) have calculated the unsaturated
conductiviigr:from capillary-tube analogy and the distribution of
soil pore sizes. These methods are based on the assumptions that
a soil contains distinct pores of various radii which are
randomly distributed in soil, and that when adjacent planes or
sections of the soil are brought into contact with water the
overall hydraulic conductance across the plane depends
statistically tuxni the number of pairs of superposed pores, and
geometrically upon their configurations.

Childs and Collis-George (1950) used an equation for

intrinsic permeability, k, given as:

O
k = M ED Ep_ 02 f(o) 6rf(o) 6r . . . . . . (17)

where M is errmrtching factor obtained by matching calculated and
experimental values of the permeability at a certain point,
:f(D)dr is tuna cross—sectional area corresponding to the range of

pores D to D-+<hy fTo)dr is the area corresponding to the range

19

of pores;c7'to o + dr, and R is the largest pore size of interest
that remains full of water.
Marshall's (1958) equation, adapted from Childs and

Collie-George (1950) can be written as:

@zn-Z 2 2 2 2
= + + +---+ o o o o 18
k —E— (r1 3r2 5r3 (2n_1)rn) ( )
where r1, 133,--—,rn are radii of n equal classes of soil

pmrosity, 9. From capillary rise considerations the equation

r: (Egh’ is substituted in terms of h into equation (18) giving:

k = (% g) —:%l— (h 2 + 3h 2 + 5h; 2 +-——+ (2 n_1)h;2 (19)

where y is the surface tension; h, negative head; 2, density of
'water; g, gravitational acceleration constant and r1 corresponds
to h1, Ir1 < h2, etc. Equation (19) gives intrinsic permeability
(cm2) for various suction values. Unsaturated hydraulic
conductivity is obtained from K(0) = Agk/n, where n is fluid

vescosity. By substituting K(O) in equation (19) one obtains:

_ 2 ¢2n_2
K(0) - (RT 91%;) ———8— (bi + 3h: + 5h: +""" (Zn-Rh; (20)

The accuracy of this method depends upon the accuracy of
measurement of pore-size distributions and will be affected'by
swelling materials as Marshall (1958) points out. Millington and
Quirk (1960) replaced‘P2 in Marshall's equation (20) by @4/3 and
n became the total number of porosity classes. The calculation,
'based upon Poiseuille's law, does not require a matching factor;

however, from a practical point of view a matching factor is

20

needed to adjust the computed and measured conditivities at
saturation (Hillel, 1980). Most of the investigations used the
ratio of observed permeability to calculated permeability at
saturation as the matching factor. Kunze et al. (1968) further
simplified equation (20) by using ¢ instead of<1>2 or d4/3 as
water filled porosity and not the total porosity. Their equation

can be written as:

 

K 3Oh-2y-zd 1
K(O) = _§. 2 (2. -2.)—2 (21)
KSC 2gb j=i 3+1 1 hj
where i=1, 2, ----n., K(0); is calculated conductivity for a

specified moisture content, (Ks/Ksc) is the matching factor which

is the ratio of measured saturated conductivity to calculated

saturated conductivity. The other terms have been defined. They

observed good agreement between experimental and calculated

conductivities especially at lower moisture conmamxh Jackson

(1972) simplified the formula to:
c

I __ Bi -2
k. — K (3;) jii [K2j+1-2i)wj ] [

vaaa

1 <2j_1>w32] (22)
'where Kj_:U3 the hydraulic conductivity at moisture content 01, m
iS‘Hmanumber<fi?increments of 0 from dryness to saturation, j
and i are summation indices, and c is an arbitrary constant.

Since this method is based upon the capillary hypothesis, it
can be expected to apply more to coarse-grained than to
fine-grained soils, as the latter might exhibit phenomena such as
film flow and ionic effects unaccounted for in the simple theory.

Another complication arises where the soil is strongly aggregated

21

and two types of flow occur within and between aggregates
(Hillel, 1980). Finally, for the K(O) values to be applicable to
infiltration theory, these equations must be applied to

adsorption as Opposed to desorption moisture characteristics.

22

III. The Development of Infiltration Theory and its Solutions

3.1. Theoretical Development

Infiltration is the entry Of water into the soil surface and
a consequent wetting of the soil. Physically, it is a common
phenomena encountered in agriculture and hydrology. Experimental
and theoretical work directed toward achieving a satisfactory
understanding of water movement through soils has been carried on
for more than a half century; however, it was only recently that
ea well known series of papers on infiltration theory development
and formulation was published by Philip (1955, 1957a, 1957b,
1957c, 1957a, 1957e, 1957f, 1958).

In his first two papers (1955, 1957a), Philip introduced a
numerical solutmmicfl?diffusion type equations with diffusivity
concentration-dependent. Horizontal and vertical infiltration
satisfying initial and boundary conditions are considered in
these papers. (liven the assumption that the diffusivity versus
moisture content relationship is known, Philip (1955) solved
equation (13) ftn‘lnorizontal flow subjected to (14a), (14b) and
(14c). iRhilip used the Boltzman transformation A(O) = xt-l/2 in
equation (13) along with the D(O) function and found, after
several nwflflumnatical iterations, a stable relationship between A
and O.

Even'flungm.both Philip (1955) and the Bruce and Klute

(1956) methods evolved from equation (13), the Objectives pursued

23

were entirely different. Given a D versus 9 relationship, Philip
calculated the value of x for any 0 and t in horizontal soil. 0n
the other hand, Bruce and Klute (1956) used equation (13) to find
D(0) from given values of x, 0 and t covering the entire range.
Ihxnn his work on horizontal infiltration Philip (1957e) proposed
a new physical prOperty of porous media which he called
sorptivity, S, defined as a measure of the capacimycfi‘soil to
absorb liquids by capillarity.

Philip (1957a) extended his work on horizontal infiltration
to include vertunfl.infiltration by substracting equation (13)

from equation (14). Writing y = x—x', the result is:

L2;

8 8 36 BK
t ‘56 (D $1 332) '1' '56 . . . . . . . . . . . (23)

Q)

with D and K single-valued functions of O, and subject to the

following conditions:

0(x, t) 00 for y=o, t>o . . . . . . . . . (23a)

and

O(x, t) 0,1 for x' + w . . . . . . . . . . (23b)

I.

'where jr:h3 the vertical component of flow attributed to gravity,
positive downward. Using a technique of successive
approximation, Philip (1957a) found a solution expressed in a

power series of t1/2:

1/2 3/2 4/2 m/2

x = At + xt + Vt + mt +---+fm(0)t (24)

where A, X, I, w,———, fm(@) are single—valuedzfinmmdons GfCH
and subject to conditions (23a) and (23b). Equation (24)

provides a theoretical formula for obtaining values of x

24

versus a, useful for comparing calculated and experimental
wetting distances in vertical columns.

The solution of equation (24) is extremely accurate at short
times; however, for long times it fails to converge and hence is
inaccurate. To avoid that, Philip (1957C) used a matching
pmocedure to empirically link the short time solution with that
of long time. Kunze and Nielsen.(1982) compared their solution
with that of Philip using data for the Yolo light clay soil and
found remarkable agreement without using a matching procedure in
both shortenm.long time. Their procedure, is a two—term
solution Of Richard's equation for one dimensional, vertical
infiltrathmucflmeined by a finite-difference, iterative method
(FINDIT). This procedure will be used by the author for
comparisons of calculated and experimental data.

In his theory of infiltration, Philip (1957d) compared his
theoretical moisture distribution curves with experimental curves
of Bodman and Coleman (1944). In their experiments, Bodman and
Coleman divided the soil moisture profile into four zones: a
saturated zone, a transition zone, a transmission zone and a
wetting zone. Philip (1957d) critically examined the basic
assumptions of his mathematical analysis and found that his
analysis predicted all the zones except the transition zone. He
explains that the diffusivity is not a unique function of
moisture content in this zone because Of air entrapment near the
surface, and therefore, his analysis could not predict the

transition zone.

 

 

25

3.1.1. Cumulative Infiltration

Cumulative infiltration is the volume of water that moves
into the surface of the soil profile over a specified time.

Philip (1957b) describes this quantity of water as:

9O
i = f de + Knt . . . . . . . . . . . . . . . (25)
91'1

where i is cumulative infiltration, and Kn is the conductivity at
‘the initial moisture content 9n. The integral term in equation

(25) can be found by integrating equation (24) with respect tx><3

to give:
[90 de = tl/Zf + t f + t3/4f +---+ tm/Zf (26)
O A X to fm
n
9O
where: fA = f AdO,
O
n
60
f = f de,
X
6)n
9O
f? = f TdO, etc
O

26

and when summed yields:

t1/2 2

- = 3/2 m/2

1 IA + t(Kn + IX) + t I? + t fw +---+ t ffm (27)
By reducing equation (27) to only its two terms, Philip attempted
to describe an all-encompassing, simple, general infiltration
equation which seems well suited to the needs of applied
hydrology. This equation in reduced form as given by Philip

(1957e) is:

i = Stl/Z + At . . . . . . . . . . . . . . (28)

where A is a constant, not well defined but related to the
saturated hydraulic conductivity. This equation gave good
results MdHNi tested for goodness Of fit in experimental examples
and was found to be superior when compared to other itrfiltration
equations which were either completely unacceptable or only

moderately acceptable.

3.1.2. Infiltration Rate

TMe infilhmufion.rate can be obtained by differentiating

equation (27) with respect to t and setting Vo = ai/gn;to give:

m
=_3_i=l-% 3% m2“
VO 3t 2t IA + (Kn + IX) + 7t fw + 2t.f(D +---+ 7t ffm

(29)

27

The infiltration rate can also be Obtained by differentiating

equation (28) with respect to t giving:

+ A . . . . . . . . . . . . . . (30)

One serious limitation of both equations (28)znm (30):M3tmat
both S and A are generally treated as constants whose values
depend upon On and.0(). IKunze and Nielsen (1982) were able to
show that A is time dependent and increases to the hydraulic
conductivity, its maximum value, as time approaches infinity.

Philip (1957f, 1958a) also studied the influence Of the
initial moisture content and the water depth (h) on the
infiltration rate, cumulative infiltration, the moisture profile
shape and the advancing rate of the wetting front. The
infiltration rate decreased while the advance of the wetting
front increased at higher initial moisture content. He also
found.iflnit as h increased the infiltration rate and cummulative
infiltration increased by about 2 percent per cm of h, but as
time increased the effect of h on the infiltration rate
diminished and ultimately was negligible.

Pnfldp mum Observed an increase in the depth of the
saturated zone with larger h, the former persisted as time
increased occupying an increasingly larger fraction of the total
wetted profile. He pointed out that the moisture
content-distance gradient in the unsaturated part of the profile
becomes relatively steeper with increasing h.

In his last paper in this series, Philip (1958a) introduced

a new aspect of tension-saturation zone in the area of

28

infiltratdtni. jHe defined the state of tension—saturation to be
that Of a medium in which the volumetric moisture content is
equal to that at V’==3},, but in which T assumes a non—zero
negative value. Philip (1958a) further indicated that the term
"saturation" is reserved for media in which the hydrostatic
pressure is more than zero while "tension-saturation" is for
media with the same moisture content as saturated, but the
hydrostatic pressure is less than zero. In conclusion, he

emphasized the importance of the K(O) and V(O) functions for

characterizing soils hydrologically.

3.2. Testing the Infiltration Equations by Numerical Analysis

The numerical analysis of the infiltration equations has
been studied by many investigators. (Philip, 1955, 1957a; Klute,
1952; lknuzroft et al., 1962; Hanks and Bowers, 1961, 1963; Klute
et al., 1965; Whisler and Klute, 1965; and others) have given
numerical.sxfihrtions for horizontal and/or vertical infiltration
processes. {Mmflr efforts have contributed substantially to our
understandirgg<mf soil water processes. However, these numerical
solutions are only interesting exercises on time computer ii‘rurt
tested against Ixnfl data from the laboratory or the field. For
this reasmdenm.others, Youngs tested Philip's theory by using
his equation to calculate moisture profiles in the laboratory for
homogeneously packed glass beads and slate dust. Good agreement
between theory and experiment was flmnut Nielsen etzflu (1961)

tested the same theory in the field with Monona and Ida silt loam

29

soils and found good agreement between the calculated and
measured profiles in spite of the failure of the soil-water
systemI‘MD fully satisfy the assumed boundary conditions of
equation (14). They also Observed that the experimental and
calculated profiles for the Monona soil were in better agreement
than those of Ida soil. Even though the shape Of the wetting
:front was adequately predicted by the theory for both soils, the
depth Of penetration, on the other hand, was predicted correctly'
only for Monona.

Gupmaand Squ1 (1964) conducted vertical infiltration
experimenmscn1Greenvill silt loam soil using a small positive
head. Using the finite difference technique and Philip's
procedure in their solution, they found a satisfactory agreement
'between.tflu9 theory enui the experiment for drier portions Of the
moisture profile but poor agreement in the saturated zone“
However, as higher conductivities in the saturated and transition
zones were considered, better agreement was found. Using the
jprocedure of Hanks and Bowers (1962), Green et al. (1964) solved
the moisture flow equation for boundary conditions corresrxnuling
approximately to those existing for infiltration into a field
soil. They found the calculated and measured infiltration rates
in good agreement. Another field experiment was conducted on
Panoche clay loam by Nielsen (1965) to measure soil water
movement duidiug infiltration and redistribution. He found that
in order to model the infiltration correctly for four irrigation
treatments, accurate determination of the K vs.C>1%flationship

and other soil parameters had to be established. Rubin and

30

Steinhardt; (1963), (Ni the other hand, compared the experimental
results with mathematical analysis for infiltration and
soil-moisture contents and found poor agreement.
IW'ushu;a,finite—difference, iterative (FINDIT) method
Inrqwsed by Kunze and Nielsen (1982) for calculating soil
moisture Inwxfiles Of Columbia silt loam and Hesperia sandy loam,
Kunze and Nielsen (1983) compared the results with the
experimental infiltration data of Nielsen etzfld (1962). Fair
agreement was obtained for both soils, the lack of better
agreement was attributed to the nature of respective conductivity
functions. Their calculation for soil moisture profiles was
'based upon using integrated mean values of D and K over a range
of time periods and O divisions to get accurate enui predictable
soil moisture profiles. Their method reduced Unacelculations
fer infiltration to a two—term algebraic equation partitioned
convenientljrzhito matric and gravitational components and gives
an asymptotic relationship between the infiltration rate and the
saturated conductivity as time approaches infinity. They
question the need Of always using the diffusion lip procedure

proposed by Philip (1955) which is mathematically taxing.

31

IV. Soil Moisture Potential Function

A:fiuflameo&fl.pr0perty of soil is its ability to retain
water in the fabric as soil moisture. Soil particles will hold a
film Of moisture against strong extraction forces. At any point
below saturation, soil moisture is under a tension analogous to
the tensicnlth a liquid held by capillarity in a tube (Gardner,
1937). This capillary tension increases from zero in a
completely saturated soil to a very large value in air-dry soil.
If a water table exists below the soil surface, vulter moves
upward by capillarity. The tension at any point within the
liquid above the water table is equal to the height cu? the water
above the water table (Gardner, 1937). A measure of the
moisture—holding power over a range of capillary tension not only
furnishes a measure Of the capacity of the soil for water storage
but gives an index of the soil properites as Gardner (1937)
pointed out.

The filter—paper method of measuring water tension or
potential gradually evolved in Europe and tflmalhnited States and
is one of several methods being used by the scientific community.
Hansen (1926) working at the University Cd'Chxpenhagen used
'blotting paper as a carrdtn‘cd‘sugar solutions. The water
potentnilcfi‘the soil was estimated by determining the osmotic
potential of the sugar solution which had the same vapor pressure
as the soil sample under investigation. Stocker (1930) used a

similar procedure with a large number of sugar solution

32

concentrations for better accuracy. Gardner (1934) improved the
method by using a single strip of blotting paper soaked in salt
solution and then measured for weight as an index of potential.
The filter paper method was proposed and reported in the United
States by Gardner (1937) to overcome the limited range of other
methods of measuring soil water potential.

The filter paper method is based upon the assumption that
the water potential of moist soil and filter paper in contact
with the soil will be the same at equilibrium. The method
further assumes that if the soil sample is large compared to the
filter paper, the water potential of the soil will be essentially
the same before and after it is placed in contact with filter
paper. Since filter paper can be obtained with highly uniform
quality, it should be possible to estimate the water potential of
a soil from the gravimetric determination of the water content of
the filter paper in equilibrium with the soil (Al-Khafaf and
Hanks, 1974). McQueen and Miller (1968) modified the procedure
proposed by Gardner (1937) to eliminate some hazards and
difficulties and adapted its use to routine gravimetric soil
moisture determinations. They concluded that the method is
versatile, accurate, convenient and economical and is effective
over the entire tension range from .001 bars to 1,500 bars. They
also concluded that moisture tension may be determined by this
method with an accuracy that is comparable to or better than the
accuracy of other methods with limited ranges.

Preliminary evaluation of the McQueen and Miller (1968)

method was done by Al—Khafaf and Hanks (1974). They used salt

33

solutions, thermocouple psychrometers, pressure plates and soil
columns in their calibration of the method. They found that the
predicted water potential was influenced by the type of contact
of the soil with the filter paper and suggested that one filter
paper be placed beneath the soil (good contactzfln¢liquid flow
and vapor flow) and one filter paper be placed above the soil rnyt
in physical contact (allowing vapor flow only). lurKhafaf and
Hanks (1974) found problems with contact between the filter paper
and soil sample, temperature at equilibrium and temperature
variation during equilibrium. They found that the absolute
temperature was not tOO important but temperature variations with

time had a large effect on the predicted soil water potential.

EXPERIMENTAL PROCEDURE AND ANALYSIS

1. Materials and Methods

1.1. Materials

TwaMidugwisoils1 , the Metea sandy loam (Arenic
Hapludalfs; sandy over loamy, mixed, mesic) and the Equiflns sandy
loam (Psammentic Hapludalfs; sandy, mixed, mesic) were
investigated in this study. The A—horizon, of the Metea soil is
a dark, sandy'ltnnn, approximately 10 cm thick. Permeability is
very rapid in the upper part Of this soil and moderate in the
lower part. The water holding capacity of this series Us
describaieusumderate. The A—horizon, Of the Spinks series is
dark brown, sandy loam, 25 cnlthick. Permeability of this soil
series is described as rapid or moderately rapid. The water
holding capacity of this series is low.

Disturbed samples Of both soils were taken from the Michigan
State University Soils Research Farm in East Lansing, ltxnrted in
the north central portion of Ingham County between 42 and 43
latitude and 84 and 85 longitude. Sampling fCT’IMTUl soils were

taken from the A—horizon between 0 and 10 cm depth.

 

fl

1 Soil survey Of Ingham County, Michigan, United States
Department of Agriculture and Soil Conservation Service in
cooperation with Michigan Agricultural Experiment Station. 1977.

34

   

35

The particle densities and particle size distributions of

both soils are shown in Table 1.

1.2. Preparation of the Flow System

1.2.1. Sample preparation

Soil samples were evenly spread over laboratory benches to
obtain air—dryness and later screened through 1 rmn and 2 nmi
sieves. The screenings were used in an attempt to pack columns

of high and low bulk densities.

1.2.2. Equipment

The infiltration apparatus used for both horizontal and
vertical flow is shown in Figure (1). The water supply system
contains a constant—head burette of 250 ml capacity and divisions
of 1JX)nfl.facilitating measurement of inflow. The soil column
consist£3<xf 2-cm and 1-cm sections of clear glass tubing 3.60 cm
in diameter taped together to form a 1-meter column. Alignment
(If the column was maintained with a trapezoidal—shaped notch cut
into a block of wood. The cover for the notch was transparent
plastic sheeting with a meter stick attached and framed-in by
strong sheet metal. The cover was fastened to the block with
magnets embedded therein to confine the soil column, and
facilitate measurement Of the wetting front. Positions Of the

'wetting front and its rate of movement Mere determined through

36

.mCOAumoaammH oBu mo mwmhm>m OSH ®
.wocume moosowsomuumumEOchm wfiwmn we cmcwmuco +

 

 

 

 

sc.s o.HN em.as smc.m oa-o axeaam
qa.o m.NN om.am nmo.m oano mmumz
AEENOO.OVV AEENoo.Oumo.ov Aafimo.ouoo.mv
hmfic uHHm ecmm Aoo\wv AEOV
® unwflo3 kc udoo mom zuamcoc Lumen Hwom
+ Soauscwuumflc mNHm oaoauhmm oaowuumm

 

 

.VOmD mamflhouwa HAOm mo mOauHOQQHm Hmowwkflm

.H OHLMH

37

.ucmfim>ofi HouOS HMOfluHo>
can Hmucomfihon coon wow wow: msumwmmam kuCoEHHomxm

.H ounwfim

 

   

38

the transparent window by noting the progress Of the wetting

front relative to the meter.

1.2.3. Packing Of the Soil Column

Twenty or more, 2-cm wide glass sections were fastened to
each other by tape followed by an additional 30-sectirnu3 of 1—cm
width. The sections were numbered and arranged in sequential
order forming a cylinder of 70 or more cm in length. TUNE column
was packed in a vertical position and closed from the bottom with
a rubber stopper. To Obtain a uniform bulk density, soil was
added to the column through a special packing device.

Thereckhmrdevice was designed by Dr. A.J. Corey Of
Colorado State University for packing sand. A sketch of the
device and modifications added to serve our purpose is shown in
Fig (2). The device consisted Of a COpper cylinder, 3.2 cm
inside diameter and 10 cm length, connected to a smaller cylinder
Of the same materials Of 90 cm length and 2.0 cm inside diameter.
Two screens roughly 8 cm apart and perpendicular to the axial
dimension were attached at the lower end of each cylinder. The:
screen mesh was such that the soil particles would pass through
without clogging. The upper part Of the smaller tnflxe was capped
by a.diefl:, with four individual and equally spaced Openings Of 2
mm inside diameter, to permit soil to feed continuously into the
device. A supply'funnel was connected to the top of the smaller
tube and kept full with air—dry soil. Some soil.1movement irl'the

funnel was maintained with a small, electrical, kitchen mixer.

 

 

 

 

39

Supply Funnel

/
/

\

Disk with FourIndIvIduaI
Opening:

- '-2.0 cm

 

 

 

 

90 cm
8 cm :>F.Scraens
JL Ann/w
+9.2 cmd
Figure 2. Schematic diagram of the soil column

packer.

40

Before packing commenced, the bottom screen was positioned
approximately 12 cm above the rubber stOpper enclosing the end of
the empty cylinder. This position between the soil surface and
the packing device was maintained by lowering the column with a
jack throughout the filling process. A rotating motion applied
to the column manually was helpful in getting uniform
distributions of falling soil. Experience showed that to obtain
uniform density the distance between the bottom screen of the
packer and the tOp of the packed soil in the column had to be
maintained at a distance of approximately 12 cm at all times.

The purpose of the packing device was to maintain a
continuous and uniform flow of soil from the source into the
column and through the height of fall and striking the screens,
Obtain a homogenous distribution Of soil across the entire column
surface area. The random distribution Of particles across the
entire column area contributes significantly to Obtaining a
column with uniform bulk density.

When the column was filled, the upper part of the column was
plugged with a small amount Of glass wool and a rubber stopper.
If further consolidation of the soil columns was found to be
necessary, the column was drOpped on each stoppered end from a
height of 3 cm 50 times. By increasing the number Of drOps to
100 for each end a slightly greater bulk density was Obtained.
Soil was added to both ends during the latter compacting process
to keep the column filled and consolidation in effect.
Sectioning of the column showed that the bulk density was more

variable at each end than in the middle; hence a 10—cm section

41

was removed from the end to be wetted initially.

To remove the tape from the soil column the later was placed
in a vertical position inside the notched block. By using a
Special device shown in Figure (3), the column was wedged tightly
against a plate to allow removal of the tape without disturbirg;
the soil in the column. Once the tape was removed, the soil
column which remained in the notched block, was covered vfiflfll'the
transparent cover and the meter scale adjusted to the x = 0

point.

1.3. Infiltration Method

Two soil columns were prepared for each soil analysis, one
fcr vertical and the other for horizontal infiltration. Both
were prepared by the same pmocedure as outlined earlier to
achieve maximum uniformity of soil bulk density within and
betWEKNl colunnns. The air entry pressure was maintained at -2 mb
for both vertical and horizontal wetting. The pressuree<xf water
entering flue soil columns was controlled by a fritted glass bead
plate (Nielsen and Phillips, 1958) placed at x = 0 required fer
the solution of the equations (13) and (14) as specified in (14a,
14b and 140). To start an infiltration trial, the ceramic plate
'was filled with water and the desired pressure (—2 mb) applied to
the plate before it was placed in contact with the end of the
column.

letting agentSIuyad for these studies were deaerated tap

water and distilled water saturated with CaS04 following

 

42

.cumHm ecu can momwusm HAOw ecu
com3uon accucoo ecu wcflumnmwm How com: OOH>OU Hmwoomm < .m ounwflm

 

   

43

deaeration. Measurements of time and distance from the water
source were taken simultaneously and commenced the instant
contact was established between the wetted plate and the soil
column. Water entering the columns was concurrently measured in
the constant-head burette. When the flow had proceeded for
desired tmmecn'distance, the water supply was severed and the
column quickly segmented into its 2 cm and 1 cm sections. To
nflnimize<unnfirmed water movement after termination sectioning
commenced art the wetting front constituting the 1—cm sections of
the soil column. The water content of each section was
determined gravimetrically (C?) and converted to volumetric
values (CL,) by using the average bulk density of the entire
column.

Measurement Of wettinngront distances vs. the square root
Of tinue (x vs. t1/73) and soil moisture distribution profiles (0
vs x) were made for both vertical and horizontal columns. Soil
moisture diffusivity and conductivity values were obtained by
using a computer analysis procedure developed by Dr. Raymond J)
ZKunze from the Department OI'CTOp'and Soil Sciences Of Michigan
State University. The computer used by the author for the
analysis was a Hewlett-Packard 9845B microcomputer with internal

tape drives, thermal printer and a HP 7470A plotter.

 

44

II. Estimation Of Soil Water Potential

Soil waterlxytential values needed specifically for K(O)
analysis were determined by suction wetting in the high potential
range and the filter paper method (Gardner, 1937) in the low
potential range. The latter is largely the method of McQueen and
Miller (1968) and Al—Khafaf and Hanks (1974), but with
modifications in an attempt to eliminate some difficulties.

The method is based upon the fact that if a sample of soil
zum filter paper are placed in contact, and one of them is
moistened, water will pass from the moist medium to the dry
medium until equiliOhhmiis attained. If the capillary tension
curve Imus been determined fer'filter paper, the tension for the
soil is readily found by reference to the filter paper curve. A.
point on the absorption moisture characteristic of'muasxdl may
be establishadzfixmlthe known equilibrium tension value and the

measured water content Of the soil.

2.1. Apparatus and Supplies

Beside the equipment requiiwui for gravimetric soil moisture
determinations, the following were needed: (a) an analytical
balance accurate to 0.001 g; (b) constant temperature chamber
(2415 C); (0) filter paper—Schleicher and Schuell No. 589 white
Ritflxni; (d) pentochlorophenol "Dowcide-7" 5.0 mg/ml in 95%

Ethanol; (e) petri-dishes 150 x 15 mm; and (f) plastic electrical

 

   

45

tape to seal petri—dishes during periods of establishing moisture

equilibrium.

2.1.1. Procedure

Predetermined weightscxf moistened soil required to fill a
150 x 15 mm petri—dish at a desired bulk density were packed
'uniformly. One—half of the moistened soil was placed in the dish
and covered with two 9—mm filter papers sandwiched between two
12.5-cm gal. treated with "Dowcide—7". The rest of the moistened
soil was then added, the cover placed on the dish and the entirra
dish sealed with plastic, insulating tape. The samples were
placed in a constant temperature chamber and allowed to
equilibrate for a week. After equilibrium was achieved, the
smaller (9-cm) filter papers were removed and their moisture
content accurately determined with an analytical balance. The
moisture content also was determined on samples of soil in the
nearness Of the filter papers.

To avoid decomposition kw soil organisms, the filter papers
were pre—treated with "pentochlorOphenol" in ethanol.enui allowed
to air dry overnight (McQueen and Miller, 1968).

The gravimetric moisture percentages for the two 9—cm papers
were averaged and from the moisture content—tension curve of
.Al—Khafaf and Eknflmn (1974) the tension of both the filter paper
eufl.the soil were determined. The soil moisture characteristic
curve, particularly for low potential values, was Obtained by

plotting the calculated tension values against the respective

46

soil.1m3isture contents. At high potential values, the soil
moisture characteristic curve was determined from capillary rise
data. Several soil columns with slightly different bulk
densities were prepared by the procedure outlined earlier and
placed upright in contact with a free water'mflfle at Umalower
end facilitated by a fritted glass'bead plate. Glue water level
was adjusted to the lowest height of the soil inside the column
and allowed to equilibrate for three to four weeks. After
equilibrium was achieved, the columns were cut into 2 cm sections
and the gravimetric and volumetric moisture content determined.
The latter values were obtained by using the average bulk density
of the entire column. The moisture contents and associated
heights above the water table were plotted to form the soil

moisture characteristics curve.

 

RESULTS AND DISCUSSION

Three Of six experimental analyses, two cm Metea sandy loam
and one on Spinks sandy loam soil with the corresponding
numerical simulations, are presented here. The numerical results
were Obtained using the computer analysis (FINDIT) proposed by
Kunze and Nielsen (1982). Further developments such as
generating the K function from infiltration.1nwxfiles is new and
has rmrt been published. This investigation is to be one of
several tests for these procedures. All experimental data

obtained for both soils can be found in the Appendix.

I. Horizontal and Vertical Water Movement with Different Bulk
Densities

Six examples of the relationship between the advance of the
wetting front and the square root of time in horizontal flow with
Metea.&wnuly loam and Spinks sandy loam are shown in Figures 4—6.
Each pair of packed soil columns was to fall into a specified
INLUK density range. Packing effort and soil aggregate size were
to effect such changes in bulk density. Wettdiug<distances were
plotted as a.function of time to observe the effect of bulk
density on the water movement. The figures indicate innit as the
bulk density increased the slope (A) of the associated
distance-time”2 line decreased. All curves seem to give a small
positive intercept if a straight line is drawn through the data

by eye or fitted statistically. The phenomenon has not been

47

 

 

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(W3) EDNHISIU

 

49

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50

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(W9) EDNHISIU

 

51

accounted for by theory. Such deviations were reported by
Kirkham and Feng (1949); Biggar and Taylor (1960); Nielsen et al.
(1962); Jackson (1963); and Peck (1964) and are attributed to
inertial forces, bulk density variation within the column,
temperature and experimental error. Since these data were
collected in the laboratory with i 3°C temperature variation, the
temperature and the bulk density variation were likely
contributors to experimental uncertainty and distortion of the
desired A-t1/2 relationship. In any case, the non-linearity of A
with time is evident from these six curves.

Statistical data showing the degree of reproducibility of
bulk density for segments within both horizontal and vertical
soil columns are given in Tables 2 and 3. Actual standard
deviations and the coefficients Of variation within the column
would be expected to be much smaller if the additional error
introduced by sectioning the column were discounted. By
increasing the number Of drOps (See Method and Materials) from 50
to 100 a slightly larger bulk density was Obtained for each
column of Metea soil but the Opposite was true for Spinks soil
(see Table 2 or 3). The effect Of bulk density on water intake
and distance moved is quite noticeable as shown in Table 4. In
general, more water entered the soil and the rate of advance of
the wetting-front was faster in the columns with lower bulk
densities. No explanation can be given why columns wetted with
tap water resulted in larger measured bulk densities than those
wetted with distilled water saturated with CaS04. Student's

t—tests were performed on horizontal and vertical columns wetted

 

 

 

 

 

 

 

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53

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.m cases

 

54

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.4 cases

 

55

with each type Of water. The measured mean differences were
:finum.to be highly significant at the one percent level of
probability. Furthermore, non-significant differences were found
when the same test was performed on pairs of horizontal and
vertical columns used in any of the specified analyses.

A way of testing the assumption that there is a unique
relationship between any A and O is implied in the Boltzmann
transformation, A(@) = xt-1/2, explained by Nielsen et al.
(1962). A unique An-Ihqzrelationship is present if a straight
line is Obtained by ploting An values versus (t/to) where tO is a
total time. Such a plot is shown graphically in Figurra'7. Even
though these data were Obtained for water entering the soil
columns slightly below atmospheric pressure (—2 mb), the
uniquermxns of An versus On seems to be questionable particularly
at short time. Nielsen et al. (1962) obtained larger line
curvatures at more negative water entry pressures. The
non-linearim/cfi'these data indicate A is not a constant for a
specific soil moisture given in A(O) = xt-1/2. The volume of
water which had entered the unit cross—sectional area of two
Metea.euui one Spinks soil column is shown in Figure 8. The flow
equation (13) subjected to the Boltzmann transformatitni, initial
and boundary conditions (14a, b and c) predicts a linear
relationship between cumulative volume versus the sthnne root Of‘
time expressed as i = St1/2 where i is accumulated infiltration
and S is sorptivity, Philip (1957). Two soils gave a
satisfactory agreement with the theory, however, Analysis III

shown in Figure 8 (Metea, BD = 1.47 g/cc) seems to disagree witli

 

56

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RH mHm>lmz¢a ooxm mm.~unm

4

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(Z/IVUIW/Wo) HUHNUW

 

57

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Nm

(Zvu‘o/vao) BEBE/BNI'I'IOA

   

58

theory by giving a curvelinear relationship and increasing
sorptivity with time. The bulk density variation within the soil
column, temperature and experimental error may be part of the
pmoblem as was indicated earlier. The other part would be
whether the Boltzmann transformation and it is application is
always valid. This question is beyond the scope of this
research. IFinally, the issue is further confounded by
consideration of data in Figures 7 and 8. The most acceptable
analysis; hi Figure 7, Analysis III, is the worst in Figure 8 and
vice versa for the other two data sets.

Three Of'the six pairs of horizontal and vertical columns
were chosen'milmapresented as model data for D and K analysis,

designated with "*" in Table 4.

 

 

 

   

59

II. Calculated Soil—Moisture Diffusivity and Conductivity
Functions

The soil-moisture diffusivity and conductivity functions,
D(O) and K(O), are calculated for several assumptions» {The
assumptions are necessary to address the incompatibilities
resulting from bulk density differences, temperature variations,
etc. between horizontal and vertical infiltration pairings.
These ammumnfions were incorporated into the computer analysis
procedure for calculating D(O) and K(@). Calculated distances
were compared with experimentally measured distances and the
degree cu?:fit was judged to be the criterion for testing of both
theory and the FINDIT procedure. Three assumptions were
considered: (1) the horizontal wetting distances, associated
diffusivimylmdues and the moisture characteristic curve for a
given soil are accurate. Accordingly, the FINDIT procedure
analyzes the vertical infiltration data and generates
conductivity values but not necessarily for the original vertical
profile; (2) Huaneasured horizontal and vertical profiles are
accurate, but the measured moisture characteristic is
questionable. If tension values generated from (D/K) functions
are incompatible with measured tension values, FINDIT changes the
measured tension values in the moisture characteristic to conform
'to those generated by the pmrgram; (3) the vertical profile and
the moisture characteristic are accurate, but the horizontal
gprofile and the associated diffusivity values are questionable.

The procedure changes the diffusivity values which, in turn, will

 

 

60

alter the horizontal profile sufficiently enabling the program to
fit the vertical profile. The assumptions can also be presented
in the following abbreviated mathematical formulas: (1) K = DC;
(2) K = DC*; (3) K = D*C where K and D are the conductivity and
diffusivity, respectively, and C the soil moisture capacity, the
latter being the slope (ag/yy) of the soil moisture
characteristic curve at any specific moisture contmnrt. The
symbol "*" following a parameter means that it was allowed to
change according to conditions specified earlier.

TO test these assumptions, the first data set, referred to
as Analysis (I), was prepared for computer input. These data
<consisted of smoothed horizontal and vertical wetting distances
at specified water contents. IBoth scattered (experimental) and
smoothed data for the Metea sandy loam are given in FigureSB.
The smoothed profiles and the associated time values are the
necessary input required for generating the diffusivity and
conductivity functions. Based on the distance —t1/2 relationship
forewarnmdsture content within the horizontal profile at 2175
Ininutes, the horizontal wetting distances for any moisture
contents can be calculated for any other time including 2270
minutes. Repeated solution of equations (13) and (14) subject to
conditions (14a), (14b) and (14c) are required 11) finalize the
generation of the D and K functions for the time values
specified.

The calculation of both functions is based on the vertical
infiltrathmacm?2270 minutes; however, the computer first uses

the given horizontal infiltration time of 2175Imhnmms and its

 

 

 

61

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em.

2

'10A

EV(W°/m°) EMDISION

 

62

associated profile to calculate D values. Alternately, using
vertical time, it then generates the 2270 minute horizontal
profile, the K values from the differences between the horizontal
and vertical profiles and the adsorption soil moisture
characteristic from D and K values given in Figure 12. The
soil—moisture diffusivity and unsaturated hydraulic conductivity'
functions Obtained by such analyses for given assumptions are
presented graphically in Figures 10 and 11. laymn curves follOW'
“the general trend of D and K increasing with increasing moisture
content and terminate with maximum values for D and K near or at
saturations.

fk>make'UMacalculated vertical profile fit the measured
vertical profile,emmfll.changes were required in the horizontal
and vertical profiles resulting in changes of D, K and T
functions as can be seen in Figures 10, 11 and 12 in this section
and in Figures 18 and 19 in the subsequent section. As Figure 10
shows, the change in the diffusivity function is distributed
evenly over iflue entire moisture range, but for conductivity and
(W) the change occurs only in the higher moisture content range“
This suggests tlurtlI and W are interactive and one is dependent
cmrthe other. No other matching factor or approximations were
required for generating these functions using the FINDIT
procedure.

To check if calculated hydraulic conductivities agree in
general with measured saturated hydraulic conductivities, a.
saturated hydraulic conductivity experiment was conducted on both

soils and results compared. The results given in Table 5 appear

 

63

NV.

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64

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65

 

 

 

 

 

 

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.m OHQmH

   

67

to be in fair agreement for both soils; however, Unaseturated
conductivituxsin the infiltration experiments were definitely
differrnrt. Consider that the vertical infiltration time for the
wetting front to reach 700m was 827 minutes in Analysis III
compared to 2270 minues in Analysis I. This suggests that the
fermer has a larger saturated conductivity as shown in Table 5.
.Also, tap water was used for measuring saturated hydraulic
conductivities given in Table 5 and on Metea (Analysis I) whereas
(listilled_inlter saturated with CaS04 was used on Metea (Analysis
III) and Spinks (Analysis V).

The hfilumumaof bulk density on the diffusivity and
conductivity functions shown in Figures 13 and 14, suggest that
.as the bulk density decreased both diffusivity and conductivity
increased. However, this was not true when diffusivity functions
from tflua Metea and.Spinks soils were compared as shown in Figure
15. Mixed results were Obtained when the conductivity functions
for the same soils were compared as shown in Figure 16. The
general shape of these functions and their respective soil
moisture profiles suggest that the solution of the equations
considered herein were equally accurate for all times and

different soils.

 

68

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69

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mv.

 

 

 

 

 

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71

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72

III. Experimental and Calculated Soil-Moisture Profiles

Em amoflmdexperimental horizontal and vertical
irdiltration profiles Obtained under specified assumptions for
Metea and Spinks sandy loam soils are presented in Figures 17—20.
The calculation Of these profiles and the associated D and K
functions are independent processes and can not be done
simultaneously for either horizontal or vertical infiltration
analysis» IEven though the computer procedure gives simultaneous
cnnqmt Of’both functions and the respective moisture profiles,
the D and K functions are generated first during'fiueinterplay
process and then used as input for solving equation (13) and (14)
again to generate the respective moisture profiles for other time
values.

The success of the flow equation in describing soil moisture
profiles is evaluated here by comparing the predicted
distributions with those determined experimentally. For
assumption (1, K 2 DC), the agreement between the calculated and
experimental vertical profiles seems to be quite satisfactory in
Metea and Spinks soils as shown in Figures 17 and 20,
respectively; lunmaver, the differences between the measured and
calculated distances for the Metea soil analysis III, are
considerably larger (see also Table 6). The differences in
measured and calculated vertical profiles are believed to relate
to the compatibility between horizontal and vertical profile

pairs. In the Spinks soil, the difference in bulk density is

 

 

73

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78

equal to .04 g/cc while in Metea (I) it is equal to .01 g/cc;
however, this is not to preclude the possibility of other
experimental errors. Metea (III) on the other hand, showed a
difference of 11.26 cm, a significant lack of agreement, betweewi
predicted and observed vertical profiles (Table 6). This
discrepancy can be attributed to the long horizontal infiltration
time of 2076 minutes versus the short vertical infiltration time
Of 827 minutes, resulting in relatively small D and K values.
Once D values are established, K values have a definite upper
lxnnm.because of‘umaKi= DC relationship. Furthermore, if the
boundary euni initial conditions assumed for the flow system did
not actually exist as a result of experimental error,
discrepancies between predicted and experimental infiltration
profiles could be anticipated.

The calculated profiles could be also in error if the
O—straight choice for either the horizontal or vertical moisture
profiles was uncertain. The concept ofza G-straight, the
distance (x0) from the water source to unsaturated zone, was
introduced by Philip (1958), observed by (Nielsen et al. 1962;
Jackexnl, 1963; and Davidson et al., 1963) and discussed by Kunze
and Nielsen.1 From the concept of capillary rise it is
established that all homogeneous soils will develop a C)-straight
if wetted at zero or small negative pressure. Ikfllisoils used
here exhibit a Cl—straight in their moisture pnuxfiles, shown in

Figure 9 and Figures 17—20.

 

1 Private communications from authors.

. _—.w.._..

_———

 

79

Excellent agreement between the calculated and measured soil
nmisture profiles was obtained for Metea Analysis I under
assuptions 2 and 3 which are presented in Figures 18 and 19.
Similar agreement was Obtained for Metea Analysis III and Spinks

Analysis V but presenting them here would have been redundant.

 

 

 

80

IV. Demonstration of Generated Data for Modeling Other Flow
System

It is quite possilflxe:now to use generated D and K data as a
form Of computer input and the proposed FINDIT procedure for
modeling other flow systems. As was indicated earlier, once D
values are Obtained for a given soil at a specific time, then the
flow equation may be solved fOr any other time to generate new
profiles. This is particularly true with horizontal profiles, iii
fact all.lnxrizontal moisture profiles given in Figures 17—20 are
generated profiles, and may be applied to vertical profiles as
well under the assumptions discussed.

Tins procedures requires only D and K values as input for
each soil. No matching factors or further approximation are
required for solving the flow equation. Changing the boundany
and/or initial condithnmste test their effect on the output is
also pmnvt Of this procedure. This technique is and continues to
be useful in further testing of Equations (13) and (141) and
sometimes is useful to exploit a particular soil character. Once
D and K functions are in hand, it is equally simple to
demonstnwrha capillary rise for a variety of initial and boundary
conditions; however, it is an investigation in itself and is

outside the bounds Of this study.

 

 

SUMMARY AND CONCLUS IONS

An experimental study was conducted on the Metea (Arenic
Hapludalfs; sandy over loamy, mixed, mesic) and Spinks
(Psammentic Hapludalfs; sandy, mixed, mesic) sandy loam soils to
investigate the validity of Richards' equation for describing
one-dimensional flow of water in soil. A numerical simulation
technique, FINDIT, was used for Obtaining the solution of the
Richards' equation by a finite difference, iterative procedure.
The flow system considered in this study was semi-infinte with
water applied at one end of a homogenous, uniform, rigid, porous
material packed in columns. The semi—infinite condition requires
that the wetting front never reach the end Of the column.

To solve the flow equation, the horizontal and vertical soil
moisture profiles and soil moisture characteristic were used in
the computer analysis. To circumvent variations in bulk density
between column pairs, temperature differences during
infiltrations, experimental errors, etc., three assumptions were
invoked for solving the infiltration equation under unsaturated
conditions. These assumptions improved the output of the
moisture profiles and their respective D and K functions.
Results for two experimental runs on Metea soil and one on Spinks
soil are presented and discussed.

Satisfactory agreement between experimental data and
theoretical calculations was obtained when assumption (1) was

considered for Metea Analysis I and Spinks Analysis V. The same

81

 

 

 

 

 

   

82

comparison for Metea Analysis III produced only fair agreement.
When the computer matched the given T and D values according
to assumption (2) and (3), respectively, excellent agreement was
Obtained between experimental and calculated vertical profiles.
A comparison of D and K functions obtained under assumption (1)
‘with those Obtained under assumptions (3) suggests that the
variation due to bulk density, temperature and experimental
errors can be circumvented. Improvement in packing and
sectioning of soil columns resulting in more uniform bulk
densities within columns should lead to more conclusive results.
It may be concluded that the infiltration equation and its
solution considered herein can be used to describe water movement
through unsaturated porous materials. However, further
improvement in the analysis and rigorous testing of some
assumptions on which the equation is based is suggested. The
validity of the Boltzmann transformation is questioned on the
basis of data presented. In spite of the limitations of the
experimental technique, the FINDIT procedure was found to be
quite satisfactory for solvirmrwater flow problems in the soils

tested.

 

 

 

 

RECOMMENDATIONS FOR FURTHER STUDIES

From the results of this study further investigations of
water flow through porous media under unsaturated conditions are
recommended. Terticularly, emphasis in the following areas
should be considered:

1. Continuedzhmprovement for getting rapid, reproducible
means of packing soil columns with uniform bulk density for
further testing Of the flow equations.

2. Woflrshmfld be continued with capillary rise and
measurements of the absorption moisture characteristics. These
results combined with the vertical and horizontal flow data are
bash31x>generating reliable diffusivity and conductivity
functions for a Specific soil.

3. More intensive use should be made of modern technology,
specifically the computer, for solving unsaturated water flow
problems and thereby realizing saving Of time, money and
manpower. Continued develOpment Of computer techniquemszhi these
investigations will be extremely helpful and is highly
recommended.

4. Testing of the (FINDIT) procedure on.very fine to very

coarse textured soils should be of value.

83

 

84

5. Research should continue on diffusion theory to examine
its validity for a wide range of initial and boundary conditicnms
and improve its applicability to the water movement under
unsaturated conditions.

6. Applying What we know theoretically and from laboratory
measurements to field problems is extremely important anni should

be considered in the future work.

 

APPENDIX

EXPERIMENTAL DATA

 

 

86

Table 7. Horizontal infiltration data on Metea sandy loam at
2175 minutes. Analysis I.

 

 

Wetting distance % Mass Bulk density @ % volume % Ave. Volume

 

(cm) (0m) (8/00) (0) (o)
1.00 21.34 1.34 28.52 32.42
3.00 22.62 1.60 36.21 34.37
5.00 24.47 1.58 38.58 37.18
7.00 25.00 1.59 39.69 37.98
9.00 25.91 1.56 40.44 39.36
11.00 25.42 1.56 39.62 38.62
13.00 24.89 1.56 38.78 37.82
14.50 25.47 1.46 37.10 38.69
16.50 25.05 1.54 38.51 38.06
17.50 24.47 1.58 38.76 37.18
18.50 24.10 1.48 35.72 36.62
19.50 24.35 1.58 38.56 37.00
20.50 24.42 1.52 37.14 37.10
21.50 24.45 1-54 37-76 37.15
22.50 24.03 1.58 37.99 36.51
23-50 23.07 1.50 34.49 35.05
24.50 23.32 1.62 37.86 35.44
25.50 22.90 1.41 32.19 34.79
26.50 22.80 1.51 34.47 34.65
27.50 22.07 1.56 34.39 33.53
28.50 22.27 1.42 31.73 33.83
29.50 21.91 1.59 34.82 33.28
30.50 21.51 1.43 30.85 32.68
31.50 20.78 1.46 30.36 31.57
32.50 26.67 1.57 32.40 31.40
33.50 20.53 1.51 31.07 31.19
34.50 20.24 1.48 29.94 30.76
35.50 19.76 1.47 29.02 30.02
36.50 18.94 1.53 28.92 28.78
37.50 19.00 1.64 31.24 28.86
38.50 18.24 1.46 26.61 27.71
1

39.50 17.65 .51 26.71 26.82

 

 

Table 7...continued

87

 

 

40.50 17.04 1.39 23.64 25.89
41.50 16.52 1.56 25.83 25.10
42.50 15.91 1.48 23.48 24.18
43.50 14.87 1.45 21.52 22.59
44.50 13.62 1.54 20.99 20.70
45.50 11.28 1.578 17.78 17.13
45-74 1.501
@ Arithmetic mean = 1.519 g/cc
Standard deviation = .0695
Coefficient of variation = 4.561

t Initial moisture content (0n)

. M—r_*-

 

 

88

Table 8. Vertical infiltration data on Metea sandy loam at
2270 minutes. Analysis I.

 

 

Wetting distance % Mass Bulk density @ % Volume irAve. Volume

 

(cm) (0m) (g/CC) (9) (9)
1.00 21.69 1.56 33.84 33.08
3.00 22.60 1.59 36.02 34.46_
5.00 23.07 1.62 37.30 35.18'
7.00 23.91 1.60 38.20 36.46
9.00 20.57 1.62 33.30 31.36
11.00 25.70 1.55 39.85 39.19
13.00 25.27 1.60 40.38 38.52
15.00 25.70 1.53 39.25 39.19
17.00 25.78 1.54 39.76 39.30
19.00 25.34 1.54 39.14 38.63
21.00 24.52 1.55 37.88 37.38
23.00 24.21 1.61 38.89 36.92
25.00 25.31 1.49 37-79 38-59
27.00 25.02 1.52 37.92 38.15
29.00 25.97 1.43 37.20 39.60
31.00 25.38 1.48 37.65 38.70
33.00 24.87 1.49 37.03 37.92
35.00 25.25 1.45 36.55 38.51
37.00 25.80 1.49 38.34 39.34
39.00 25.37 1.42 35.93 38.68
40.50 25.14 1.62 40.60 38.33
41.50 24.36 1.49 36.23 37.14
42.50 24.71 1.49 36.80 37.68
43.50 24.66 1.49 36.36 37.60
44.50 24.28 1.53 37.04 37.01
45.50 23.86 1.66 39.64 36.38
46.50 23.07 1.41 32.44 35.18
47.50 23.45 1.46 34.29 35.75
48.50 24.01 1.43 34.37 36.60
49.50 24.23 1.51 36.56 36.94
50.40 24.43 1.56 38.10 37.24
51.40 23.82 1.47 35.11 36.32
1

52.40 23.95 .46 34.89 36.52

 

 

Table 8...continued

89

 

53.60 23.74 1.52 36.11 36.20
54.60 23.50 1.50 35.26 35.83
55.60 22.72 1.49 33.79 34.65
56.60 22.73 1.52 34.53 34.66
57.60 22.41 1.44 32.19 34.16
58.60 22.29 1.56 34.69 33.99
59.60 22.06 1.46 32.24 33.63
60.60 21.79 1.53 33.38 33.22
61.60 21.37 1.47 31.32 32.59
62.60 20.61 1.64 33.90 31.42
63.60 19.71 1.41 27.85 30.06
64.60 19.86 1.62 32.07 30.28
65.60 18.97 1.59 30.17 28.92
66.60 17.85 1.49 26.62 27.22
67.60 16.97 1.57 26.65 25.87
68.60 14.88 1.54 22.90 22.68
69.60 12.58 1.64 21.08 19.19
70.00 1.15+
@ Arithmetic mean = 1.525 g/cc
Standard deviation = .0677
Coefficient of variation = 4.44

t Initial moisture content

(9n)

 

 

   

   

90

Table 9. Horizontal infiltration data on Metea sandy loam at
6167 minutes. Analysis II.

 

 

Wetting distance % Mass Bulk density @ % Volume % Ave. Volume

 

(cm) (6m) (g/CC) (G) (0)
1.00 20.86 1.61 33.68 31.68
3.00 21.59 1.52 32.80 33.08
5.00 22.51 1.61 36.14 34.49
7.00 23.28 1.59 37.01 35.67
9.00 24.53 1.59 38.90 37.59
11.00 25.70 1.57 40.39 39.38
13.00 25.40 1.60 40.62 38.92
15.00 26.40 1.50 40.31 40.45
17.00 26.02 1.54 39.96 39.87
19.00 26.09 1.51 39.39 39.97
21.00 25.16 1.56 39.18 38.55
23.00 25.37 1.51 38.40 38.40
25.00 25.13 1.49 37.49 38.49
27.00 24.57 1.53 37.58 37-65
29.00 24.74 1.47 36.31 37.90
31.00 24.02 1.50 36.08 36.80
33.00 24.11 1.53 36.88 36.94
35.00 24.31 1.47 35.66 37.24
36-09 23.55 1.54 36-35 36-35
39.00 23.74 1.48 35.24 36.36
40.50 25.04 1.52 34-99 35-29
41.50 22.82 1.55 35.42 34.97
42.60 23.39 1.54 35.99 35.85
43.50 22.16 1.49 33.08 33.94
44.50 27.12 1.38 37.43 41.55
45.50 22.03 1-50 33-15 33-75
46.50 21.16 1.52 32.14 32.41
47.50 20.86 1.47 30.68 31.97
48.50 21.40 1.51 32.37 32.79
49.50 18.90 1.65 31.14 28.96
50.50 20.47 1.53 31.24 31.36
51.50 20.39 1.44 29.41 31.24
1

52.50 20.27 .63 33.08 31.06

 

Table 9...continued

91

 

53.50 19.84 1.45 28.85 30.39
54.50 19.10 1.54 29.45 29.27
55.50 18.81 1.56 29.34 28.82
56.50 17.84 1.47 26.20 27.33
57.50 18.01 1.57 28.21 27.59
58.50 17.19 1.46 25.02 26.34
59.50 17.44 1.52 26.57 26.71
60.50 16.63 1.55 25.83 25.49
61.50 16.35 1.55 25.38 25.05
62.50 14.89 1.49 22.18 22.81
63.60 15.71 1.69 26.53 24.06
64.60 14.83 1.53 22.63 22.72
65.60 15.89 1.62 25.67 24.35
66.60 13.48 1.45 19.55 20.66
67.60 12.92 1.64 21.21 19.80
68.60 11.86 1.48 17.51 18.18
69.60 10.71 1.57 16.71 16.42
70.00 1.05+
@ Arithmetic mean = 1.532 g/cc
Standard deviation = .0599
Coefficient of variation = 3.90

7 Initial moisture content

(9n)

 

   

92

Table 10. Vertical infiltration data on Metea sandy loam at
2690 minutes. Analysis II.

 

 

Wetting distance % Mass Bulk density @ %_Volume %7Ave. Volume

 

(cm) (0m) (g/CC) (o) (o)
1.00 21.70 1.62 35.15 33.17
3.00 22.88 1.61 36.94 34.96
5.00 25.80 1.55 39.97 39.42
7.00 25.63 1.53 39.20 39.17
9.00 25.21 1.53 38.51 38.52
11.00 25.61 1.54 39.44 39.13
13.00 24.24 1.61 38.93 37.04
15.00 26.01 1.47 38.30 39.74
17.00 26.99 1.49 40.28 41.28
19.00 27.01 1.51 40.75 41.28
21.00 27.43 1.47 40.28 41.91
23.00 27.14 1.51 41.05 41.47
25.00 27.08 1.54 41.62 41.39
27.00 26.85 1.51 40.66 41.03
29.00 25.68 1.52 39.00 39.24
31.00 26.48 1.56 41.19 40.46
33.00 21.43 1.60 34.34 32.75
35.00 26.67 1.54 41.16 40.56
37.00 30.03 1.44 43.26 45.90
39.00 25.25 1.48 37.49 38.58
40.50 25.06 1.57 39.19 38.30
41.50 25.18 1.47 36.94 38.49
42.50 25.24 1.53 38.58 38.58
43.50 24.77 1.44 35.54 37-85
44.50 24.64 1.56 38.49 57.66
45.50 23.69 1.51 35.89 36.20
46.50 23.45 1.60 37.61 35.84
47.50 22.16 1.46 32.29 33.87
48.50 22.69 1.74 39.47 34.68
49.50 23.34 1.64 38.23 35.66
50.40 23.27 1.51 35.13 35.56
51.40 22.76 1.55 35.39 34.78
52.40 22.72 1.51 34.22 34.72

 

 

 

Table 10...continued

93

 

53.50 22.95 1.48 34.00 35.07
54.60 22.60 1.69 38.12 34.53
55.60 22.01 1.49 32.87 33-63
56.60 21.26 1.51 32.09 32.50
57.60 20.10 1.60 32.23 30.72
58.60 19.84 1.46 28.88 30.31
59.60 20.91 1.54 32.13 31.95
60.60 19.82 1.47 29.09 30.29
61.60 19.13 1.49 28.50 29.23
62.60 19.53 1.51 29.54 29.84
63.60 18.80 1.49 28.00 28.73
64.60 17.20 1.45 24.95 26.28
65.60 16.19 1.49 24.04 24.74
66.60 13.92 1.46 20.34 21.27
67.60 12.50 1.50 18.78 19.10
68.00 1.05t
@ Arithmetic mean = 1.528 g/cc
Standard deviation = .0638
Coefficient of variation 2 4.18

t Initial moisture content

(0

n)

 

 

 

94

Table 11. Horizontal infiltration data on Metea sandy loam at
2076 minutes. Analysis III.

 

 

Wetting distance % Mass Bulk density @ % Volume % Ave. Volume

 

(cm) (9m) (g/CC) (9) (0)
1.00 22.07 1.57 34.54 32.54
3.00 21.16 1.57 33.19 31.20
5.00 22.66 1.57 35.50 33.40
7.00 24.07 1.52 36.71 35.71
9.00 24.70 1.53 37.87 36.41
11.00 24.70 1.54 37.93 36.41
13.00 24.94 1.58 39.53 36.77
15.00 25.25 1.53 38.53 37.22
17.00 24.90 1.56 38.86 36.70
19.00 25.12 1.46 36.79 37.03
21.00 26.28 1.50 39.42 38.75
23.00 26.34 1.44 37.90 38.83
25.00 25.86 1.42 36.79 38.13
27.00 24.95 1.43 35.76 36.78
29.00 25.30 1.45 36.71 37.30
31.00 25.14 1.44 36.08 37.06
33.00 24.96 1.40 34.97 36.79
35.00 23.40 1.40 32.76 34.49
37.00 23.93 1.44 34.47 35-28
39.00 23.18 1.44 33.31 34.17
40.50 22.86 1.46 33.38 33.70
41.50 21.70 1.42 30.85 32.00
42.50 22.70 1.42 32.24 33.46
43.50 23.90 1.44 34.37 35.23
44.50 21.67 1.44 31.14 31.95
45.50 20.60 1.41 29.11 30.37
46.50 19.36 1.46 28.20 28.55
47.50 18.46 1.35 24.91 27.22
48.50 18.81 1.40 26.27 27.74
49.50 18.62 1.60 29.82 27.45
50.50 17.46 1.46 25.51 25.74
51.50 17.26 1.54 26.53 25.44
52.50 17.60 1.58 27.77 25.95

 

 

Table 11...continued

95

 

53.50 17.17 1.45 24.87 25.31
54.50 15.79 1.47 23.24 23.28
55.50 15.20 1.45 22.03 22.41
56.50 14.43 1.45 20.94 21.28
57.50 13.48 1.49 20.07 19.87
58.50 12.12 1.46 17.65 17.87
59.50 10.05 1.44 14.46 14.81
60.10 1.007
@ Arithmetic mean = 1.474 g/cc
Standard deviation = .0620
Coefficient of variation = 4.20

t Initial moisture content

(9n)

 

 

 

 

 

 

 

 

 

   

96

Table 12. Vertical infiltration data on Metea sandy loam at
827 minutes. Analysis III.

AL __ _‘

Wetting distance % Mass Bulk density @ % Volume % Ave. Volume

 

 

(cm) (0m) (2/00) (0) (O)
1.00 22.52 1.47 33.20 33.07
3.00 22.62 1.56 35.22 33.22
5.00 23.62 1.53 36.22 34.69
7.00 24.57 1.57 38.51 36.11
9.00 25.29 1.46 37.03 37.14
11.00 25.31 1.51 38.14 37.17
13.00 25.46 1.48 37.59 37.40
15.00 25.17 1.54 38.74 36.97
17.00 25.79 1.45 37.50 37.87
19.00 25.52 1.51 38.65 37.48
21.00 26.31 1.46 38.30 38.63
23.00 26.64 1.46 38.76 39.12
25.00 26.18 1.48 38.86 38.45
27.00 26.54 1.48 39.21 38.97
29.00 25.75 1.41 36.42 37.82
31.00 26.33 1.46 38.38 38.66
33.00 25.75 1.48 38.10 37.82
35.00 25.90 1.47 39.97 38-03
37.00 25.73 1.43 36.89 37.78
39.00 25.44 1.43 36.31 37.36
40.50 25.87 1.49 38-45 37-99
41.50 25.72 1.43 36.84 37.77
42.50 25.77 1.45 37.29 37.85
43.50 25.03 1.48 36.97 36.76
44.50 25.14 1.48 37.28 36.92
45.50 25.37 1.41 35.89 37.26
46.50 25.38 1.51 38.31 37.27
47.50 25.44 1.44 36.57 37.36
48.50 24.78 1.42 35.21 36.39
49.50 24.46 1.42 34.66 35.92
50.50 24.25 1.50 36.46 35.62
51.50 25.03 1.48 37.09 36.77
52.50 25.15 1.49 37.39 36-94

 

 

97

Table 12...continued

 

53.50 27.39 1.42 38.81 40.23
54.50 21.16 1.43 30.34 31.07
55.50 23.55 1.36 31.97 34.58
56.50 23.31 1.50 34.97 34.24
57.50 24.09 1.45 34.83 35.37
58.50 23.01 1.46 33.53 33.80
59.50 29.66 1.40 41.46 43.55
60.50 22.67 1.57 35.58 33.30
61.50 21.76 1.45 31.52 31.96
62.50 21.57 1.43 30.83 31.67
63.50 20.17 1.41 28.49 29.62
64.50 19.66 1.44 28.39 28.87
65.50 19.58 1.52 29.70 28.76
66.50 18.45 1.55 28.51 27.10
67.50 16.42 1.48 24.34 24.12
67.90 15.65 1.47 23.00 23.00
69.01 12.93 1.47 19.00 19.00
69.72 9.52 1.47 14.00 14.00
70.10 1.00+
@ Arithmetic mean = 1.469 g/cc
Standard deviation 2 .0458
Coefficient of variation = 3.12

t Initial moisture content (on)

 

 

 

 

 

98

Table 13. Horizontal infiltration data on Metea sandy loam at
2305 minutes. Analysis IV.

 

 

Wetting distance % Mass Bulk density @77%7Volume % Ave. Volume

 

(cm) (em) (g/CC) (0) (0)
1.00 22.56 1.56 35.21 33.78
3.00 22.11 1.49 32.85 33.11
5.00 22.94 1.56 35.80 34.34
7.00 23.31 1.55 36.06 34.90
9.00 24.46 1.56 38.21 36.62
11.00 25.34 1.54 38.96 37.94
13.00 25.25 1.59 40.19 37.81
15.00 25.63 1.49 38.28 38.38
17.00 26.46 1.50 39.66 39.61
19.00 26.56 1.44 38.36 39.76
21.00 25.22 1.50 37.73 37.76
23.00 25.02 1.47 36.86 37.46
25.00 25.26 1.46 36.94 37.83
27.00 24.38 1.48 36.06 36.50
29.00 24.31 1.48 35.91 36.40
31.00 23.77 1.47 34.95 35-59
33.00 23.22 1.48 34.39 34.77
35.00 23.15 1.46 33.89 34.67
37.00 22.55 1-44 32.53 33.76
39.00 21.96 1.44 31.68 32.88
40.50 21.83 1.49 32.48 32.69
41.50 21.80 1.49 32.38 32.64
42.50 21.40 1.42 30.41 32.04
43.50 20.74 1.45 30.10 31.05
44.50 21.09 1.51 31.93 31.58
45.50 20.97 1.40 29.41 31.39
46.50 19.96 1.49 29.78 29.89
47.50 20.88 1.47 30.68 31.26
48.50 18.61 1.53 28.54 27.87
49.50 19.05 1.49 28.38 28.52
50.50 18.49 1.56 28.79 27.68
51.50 17.54 1.62 28.37 26.27
1

52.50 17.46 .52 26.47 26.14

 

 

  

 

99

Table 13...continued

 

53.50 17.21 1.47 25.36 25.76
54.50 16.27 1.49 24.24 24.37
55.50 14.97 1.52 22.82 22.41
56.50 14.48 1.42 20.54 21.67
57.50 13-34 1.54 20.56 19-97
58.50 12.12 1.54 18.74 18.28
59-50 10.37 1-50 15-53 15-53
60.10 4 .90+
@ Arithmetic mean 1.497 g/cc

Standard deviation = .0480
Coefficient of variation 2 3.21

1 Initial moisture content (0n)

 

  

 

100

Table 14. Vertical infiltration data on Metea sandy loam at
840 minutes. Analysis IV.

 

 

Wetting distance % Mass Bulk density @ %—Volume % Ave. Volume

 

(cm) (9m) (2/00) (9) (e)
1.00 22.35 1.45 32.49 33.13
3.00 23.39 1.51 35.42 34.66
5.00 24.59 1.55 38.17 36.44
7.00 24.80 1.54 38.12 36.75
9.00 25.45 1.45 36.79 37.72
11.00 25.17 1.53 38.49 37.30
13.00 25.18 1.49 37.64 37.32
15.00 25.97 1.51 39.27 38.49
17.00 26.12 1.49 38.84 38.71
19.00 25.75 1.47 37.72 38.16
21.00 26.09 1.42 37.15 38.66
23.00 26.46 1.49 39.42 39.21
25.00 25.52 1.48 37.68 37.81
27.00 25.94 1.44 37.31 38.44
29.00 25.79 1.49 38.35 38.22
31.00 26.12 1.45 37.93 38.72
33.00 26.02 1.50 39.03 38.56
35.00 26.30 1.47 38.61 38.97
37.00 25.85 1.45 37.48 38.30
39.00 25.55 1.45 37.05 37.86
40.50 25.47 1.48 37.75 37.74
41.50 25.08 1.46 36.64 37.17
42.50 25.03 1.46 36.50 36.10
43.50 25.11 1.47 36.97 37.22
44.50 24.63 1.52 37.38 36.51
45.50 25-00 1.54 38.47 37.05
46.50 25.05 1.43 35.73 37.13
47.50 24.69 1.50 36.96 36.59
48.50 24.21 1.47 35.69 35.88
49.50 24.56 1.51 37.21 36.40
50.50 24.56 1.46 35.85 36.40
51.50 24.21 1.49 36.09 35.88
52.50 23.93 1.50 35.81 35.46

 

._... m—-_—- ————‘—-~——— 4

 

 

Table 14...continued

101

 

t Initial moisture content (on)

53.50 23.82 1.47 34.96 35.30
54.50 23.21 1.43 33.11 34.40
55.50 23.46 1.52 35.76 34.77
56.50 22.85 1.46 33.28 33.87
57-50 22-93 1-50 34-33 33-99
58.50 21.73 1.35 29.38 32.20
59.50 21.72 1.59 34.48 32.19
60.50 21.08 1.52 32.13 31.24
61.50 20.73 1.47 30.45 30.72
62.50 19.88 1.47 29.25 29.46
63.50 19.15 1.50 28.69 28.38
64.50 17.98 1.50 26.92 26.64
65.50 16.28 1.48 24.14 24.12
66.50 13.44 1.48 19.91 19.91
67.10 .907
@ Arithmetic mean = 1.482 g/cc
Standard deviation = .0397
Coefficient of variation = 2.68

 

102

Table 15. Horizontal infiltration data on Spinks sandy loam
at 4500 minutes. Analysis V.

 

 

Wetting distance % Mass Bulk dénsity @ %7volume 57Ave. Volume

 

(cm) (9m) (8/00) (0) (G)
1.00 24.88 1.42 35.43 36.33
3.00 25.06 1.51 37.83 36.59
5.00 25.46 1.51 38.52 37.18
7.00 25.53 1.52 38.84 37.28
9.00 27.10 1.52 41.31 39.57
11.00 28.41 1.52 43.08 41.49
13.00 27.66 1.49 41.09 40.38
15.00 26.21 1.58 41.52 38.27
17.00 26.78 1.53 40.86 39.11
19.00 26.74 1.52 40.67 39.05
21.00 27.25 1.44 39.13 39.80
23-00 26-93 1-48 39.79 39-33
25.00 27.40 1.42 38.89 40.01
27.00 27.18 1.45 39.44 39.70
29.00 27.10 1.39 37.65 39.57
31.00 26.66 1.46 38.98 38.94
33.00 26.02 1.43 37.32 38.00
35.00 26.19 1.40 36.79 38.24
37.00 26.13 1.43 37.44 38.16
39.00 25.20 1.41 35.59 36.80
40.50 25.23 1.39 35.09 36.85
41.50 24.26 1.53 37.03 35.42
42.50 24.36 1.43 34.87 35.58
43-50 23.83 1-38 32.78 34.79
44.50 24.18 1.43 34.58 35.30
45.50 24.05 1.42 34.13 35.12
46.50 23.12 1.42 32.73 33.76
47.50 23.44 1.41 33.12 34.23
48.50 22-77 1-51 34.47 33-25
49.50 21.90 1.57 34.39 31.98
50.50 21.70 1.36 29.50 31.69
51.50 21.91 1.32 28.83 32.00
52.50 22.65 1.52 34.49 33.07

 

   

Table 15...continued

103

 

1 Initial moisture content

(on)

53.50 21.67 1.42 30.74 31.64
54.50 21.61 1.45 31.25 31.55
55.50 21.15 1.51 32.01 30.88
56.50 20.52 1.37 28.18 29.97
57.50 20.54 1.45 29.70 29.99
58.50 19.60 1.53 29.91 28.61
59.50 19.39 1.42 27.45 28.32
60.50 19.44 1.52 29.51 28.38
61.50 18.69 1.45 27.11 27.30
62.50 19.66 1.38 27.04 28.71
63.50 17.04 1.50 25.52 24.88
64.50 17.44 1.55 27.07 25.47
65.50 16.47 1.51 24.88 24.05
66.50 15.96 1.40 22.40 23.30
67.50 14.85 1.53 22.66 21.69
68.50 13.54 1.56 21.07 19.77
69.50 10.53 1.36 14.26 15.37
70.00 1.00t
@ Arithmetic mean = 1.460 g/cc
Standard deviation = .0638
Coefficient of variation : 4.37

 

104

Table 16. Vertical infiltration data on Spinks sandy loam at
2020 minutes. Analysis V.

 

 

Wetting distance % Mass Bulk density @ % Volume flTAve. Volume

 

(cm) (9m) (2/00) (6) (6)
1.00 23.45 1.60 37.43 35.14
3.00 24.04 1.55 37.31 36.01
5.00 23.73 1.57 37.22 35.55
7.00 23.52 1.60 37.53 35.24
9.00 25.26 1.50 37.87 37.85
11.00 25.16 1.57 39.57 37.69
13.00 24.62 1.59 39.24 36.89
15.00 24.42 1.58 38.55 36.58
17.00 24.73 1.54 38.15 37.05
19.00 25.09 1.56 39.04 37.60
21.00 24.67 1.55 38.15 36.96
23-00 25-35 1.54 39.12 37.97
25.00 25.29 1.54 38.98 37.88
27.00 25.06 1.56 39.06 37.55
29.00 25.17 1.50 37.81 37.72
31.00 25.85 1.48 38.38 38.74
33.00 26.00 1.49 38.64 38.96
35.00 25.93 1.56 40.48 38.85
37.00 25.85 1.39 36.06 38.74
39.00 25.93 1.49 38.57 38.85
40.50 25.23 1.57 39.59 37.80
41.50 26.00 1.44 37.53 38.96
42.50 25.60 1.50 38.28 38.35
43.50 25.36 1.46 36.99 38.00
44.50 25.46 1.54 39.30 38.14
45-50 25.18 1.50 37.67 37.73
46.50 26.03 1.49 38.80 39.00
47.50 25-30 1.37 34.73 37.91
48.50 25.86 1.52 39.37 38.74
49.50 24.82 1.40 34.76 37.18
50.50 24.86 1.61 40.05 37.24
51.50 24.66 1.47 36.29 36.95
52.50 25.02 1.46 36.50 37.48

 

105

Table 16...continued

 

53.50 24.21 1.55 37.56 36.27
54-50 23-86 1-53 36.55 35-75
55.50 24.25 1.40 33.87 36.33
56.50 23.50 1.41 33.18 35.22
57.50 23.98 1.50 35.92 35.93
58.50 23.60 1.45 34.12 35.36
59.50 23.65 1.48 34.97 35.44
60.50 22.71 1.44 32.64 34.02
61.50 22.75 1.50 34.24 34.09
62.50 21.66 1.48 32.02 32.46
63.50 22.03 1.45 31.83 33.00
64.50 20.81 1.50 31.24 31.18
65.50 20.26 1.45 29.41 30.35
66.50 18.73 1.51 28.31 28.07
67.50 17.85 1.45 25.93 26.75
68.50 15.80 1.54 24.34 23.67
69.50 12.89 1.18 15.21 19.31
70.00 gg 1.007
@ Arithmetic mean = 1.498 g/cc
Standard deviation = .0743
Coefficient of variation = 4.96

1 Initial moisture content (0n)

106

Table 17. Horizontal infiltration data on Spinks sandy loam
at 1897 minutes. Analysis VI.

.4

Wetting distance 7% Mass Bulk density @ % Volume % Ave. Volume

 

 

(cm) (0m) (g/CC) (0) (o)
1.00 24.78 1.49 36.84 35.60
3.00 24.45 1.50 36.76 35.12
5.00 25.02 1.53 38.32 35.94
7.00 25.31 1.53 38.65 36.36
9.00 26.42 1.51 39.74 37.70
11.00 26.96 1.49 40.14 38.74
13.00 26.83 1.57 42.23 38.55
15.00 47.01 1.52 41.18 38.81
17.00 27.20 1.47 40.01 39.08
19.00 27.06 1.43 38.61 38.87
21.00 27.06 1.46 39.42 38.87
23.00 27.41 1.45 39.74 39.38
25.00 27.07 1.39 37.64 38.90
27.00 26.20 1.36 35.71 37.64
29.00 25.79 1.41 36.36 37.06
31.00 25.78 1.39 35.93 37.05
33.00 25.30 1.37 34.71 36.34
35.00 25.24 1.40 35.42 36.26
37.00 25.29 1.40 33.97 34.90
39.00 23.86 1.35 32.23 34.27
40.50 23.79 1.42 33.88 34.17
41.50 23.27 1.46 34.01 33.44
42.50 22.42 1.32 29.70 32.21
43.50 22.61 1.44 32.59 32.48
44.50 21.76 1.34 29.18 31.26
45.50 21.64 1.45 31.38 31.09
46.50 20.67 1.46 30.27 29.70
47.50 20.54 1.33 27.26 29.52
48.50 20.11 1.41 28.37 28.90
49.50 18.29 1.54 28.10 26.27
50.50 18.49 1.45 26.83 26.56
51.50 17.75 1.35 23.99 25.50
52.50 17.03 1.43 24.36 24.47

 

 

107

Table 17... continued

 

53.50 15.57 1.39 21.58 22.36
54.50 12.95 1.45 18.73 18.61
55.10 1.001
@ Arithmetic mean = 1.437 g/cc
Standard deviation 2 .0646
Coefficient of variation = 4.50

1 Initial moisture content (0n)

 

 

 

108

Table 18. Vertical infiltration data on Spinks sandy loam at
1188 minutes. Analysis VI.

 

 

Wetting distance % Mass Bulk density @ % Volumne % Ave. Volume

 

(cm) (9m) (g/CC) (0) (0)
1.00 24.33 1.57 38.15 35.12
3.00 25.45 1.50 38.22 36.73
5.00 26.12 1.50 39.05 37.70
7.00 26.02 1.50 38.99 37.56
9.00 27.24 1.49 40.62 39.32
11.00 26.93 1.50 40.29 38.87
13.00 26.64 1.49 39.77 38.46
15.00 27.11 1.50 40.70 39.13
17.00 27.86 1.47 40.81 40.21
19.00 27.79 1.40 38.95 40.10
21.00 27.72 1.45 40.10 40.01
23.00 28.41 1.42 40.38 41.00
25.00 28.03 1.40 39.34 40.46
27.00 38.14 1.42 39.89 40.61
29.00 28.77 1.44 41.53 41.52
31.00 28-39 1.39 39.57 40.97
33.00 28.10 1.38 38.81 40.56
35.00 28.12 1.42 40.03 40.59
37.00 28.06 1.38 38.68 40.50
39.00 28.38 1.41 40.13 40.97
40.50 27.68 1.40 38.80 39.96
41-50 27.25 1.35 36.71 39-33
42.50 26.86 1.46 39.23 38.76
43.50 28.72 1.40 40.23 41.46
44.50 27.56 1.42 39.20 39.77
45.50 27.64 1.37 37.87 39-89
46.50 26.90 1.46 39.14 38.82
47.50 27.02 1.40 37.91 39.00
48.50 26.04 1.37 35.60 37.59
40.50 27.12 1.53 41.57 39.14
50.50 26.07 1.49 38.84 37.63
51.50 25.83 1.55 40.05 37.28
52.50 25.42 1.36 34.49 36.70

 

 

 

109

Table 18...continued

 

53.50 24.83 1.43 35-61 35-83
54.50 24.81 1.34 33.36 35.82
55.50 24.08 1.51 36.36 34.76
56.50 24.03 1.39 33.34 34.69
57.50 23.38 1.41 32.88 33.74
58.50 22.41 1.55 34.69 32.34
59.50 22.04 1.38 30.38 39.81
60.50 20.66 1.60 32.98 29.82
61.50 19.88 1.45 28.74 28.70
62.50 17.66 1.42 25.09 25.50
63.50 14.06 1.44 20.29 20.29
64.20 1.00+
@ Arithmetic mean = 1.443 g/cc
Standard deviation = .0629
Coefficient of variation = 4.36

I Initial moisture content (0n)

 

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_.u

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