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thesis entitled

"An Infiltrometer To Measure And
Analyze The In-situ Sorptivity."

presented by

Fei-Jan Kao

has been accepted towards fulfillment
of the requirements for

14.8. degree in Agricultural Engineering

 

March 23 , 1998

 

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ma alumnus-p.14

AN INFILTROMETER TO MEASURE AND ANALYZE THE lN-SITU
SORPTIVITY

By

Fei-Jan Kao

A THESIS
Submitted to
Michigan State University

in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Agricultural Engineering

1998

ABSTRACT

AN INFILTROMETER TO MEASURE AND ANALYZE THE IN-SITU
SORPTIVITY

By

Fei-Jan Kao

The proposed infiltrometer is an non-electronic system to
measure the soil sorptivity in the field. It is low-cost, portable, reliable,
and simple for installation and use. In additional to the soil sorptivity,
this infiltrometer can also be used to determine the soil hydraulic
conductivity and macroscopic capillary length. In our research, we
suggest a new method instead of the conventional cumulative

infiltration vs. time"2

diagram to analyze the field data. Even when the
true infiltration is not measured at the very start, we can still obtain the
correct sorptivity using the suggested analysis. Two new parameters,
initial infiltration and lag time, are introduced in the sorptivity

determination. In order to calculate the soil sorptivity more accurately,
it is necessary to evaluate the initial infiltration in the field. The lag
time is the duration between the onset of the soil infiltration and the

start of the measurement and should be used to examine the reliability

of the result of field experiments.

ACKNOWLEDEGMENTS

I would like to express my sincere gratitude to my committee
chairman, Dr. George Merva, for his advice, help, and encouragement

given during the course of my studies and research.

I am also grateful for the help and guidance offered by the other
members of my committee, Dr. Robert Von Bernuth and Dr. Harold

Belcher.

I would also like to thank Richard Wolthuis for his help and

advice.
Finally, a special thank to my parents and my girl friend, Ya-

Hsien Chen, for supporting me through each of the deadlines for the

completion of this thesis which came and went.

TABLE OF CONTENTS

List of Tables

List of Figures

III.
IV.

VI.

VII.

Introduction

Literature Review

A. Non-tension lnfiltrometer
B. Tension lnfiltrometer

C. Problems with Current In-Situ lnfiltrometer
Fundamentals

Objectives

System Design

A. Proposed System

B. System Prototype
Instructions for Field Use

A. Setting the Potential

B. Site Preparation

C. System Installation

D. Soil Sample Water Content
E. Required Measurement Time
Test System I

A. Test 1 Results

B. System Modifications

vi

vii

V0101

1 3
15
16
16
1 8
23
23
23
23
24
25
26
26
29

C. Test 2 Results

D.
E.

Problems and Analysis

Re-analysis of Test 2

VIII. Error Analysis

A.
B.
C.
D.

Empirical Equation for Real Flow
Experiment Design
Regressions and Results

Discussions

IX. Test System II

A.
B.
C.
D.

Results for Site 1
Results for Site 2
Results for Site 3

Discussions

X. Recommendations

XI. Conclusions

Appendices

A. Component Specifications

B.

Experimental Data for Field Tests

C. Experimental Data for Error Analysis

List of References

32
32
42
45
45
46
46
49
50
50
53
57
61
67
73

75
77
87
88

Table 1.
Table 2.

Table 3.
Table 4.
Table 5.
Table 6.
Table 7.

LIST OF TABLES

Experimental data for Test 1.

Comparison of regression results generated by different
numbers of points.

Comparison of results from different tests at site 1.
Comparison of results from different tests at site 2.
Comparison of results from different tests at site 3.
Comparison of results from different tests at site 3.

The recommended range of lag time for different soils.

vi

27

53
57
57
61

Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.

Figure 8.
Figure 9.

Figure 10.

Figure 1 1.

Figure 12.

Figure 13.

Figure 14.

Figure 15.
Figure 16.
Figure 17.

LIST OF FIGURES

Proposed system for sorptivity measurement.
Designed sample cup.

Prototype for sorptivity measurement.
Designed flow meter.
Cumulative infiltration vs. time"2
Modified system for sorptivity measurement.

Relative position of the soil surface and top of the
sample cup.

Cumulative infiltration vs. time diagram for Test 2.

Cumulative infiltration vs. time"2 diagram for Test 2.

Cumulative infiltration vs. time diagram for constant
head and falling head flow.

Cumulative infiltration vs. time diagram for ideal
sorptivity flow and experimental sorptivity flow.

Cumulative infiltration vs. time"2 diagram for ideal

sorptivity flow and experimental sorptivity flow.

Cumulative infiltration v. time diagram for ideal
sorptivity flow and experimental sorptivity flow with
initial infiltration.

Square of cumulative infiltration vs. time diagram
for ideal sorptivity flow and experimental sorptivity
with initial infiltration.

Cumulative infiltration2 vs. time diagram for Test 2.
Designed system for error analysis.

Regression curve for the result of error analysis.

vii

diagram for Test 1.

17
19
20
22
28
30

31
33

35

37

38

40

41
43
47
48

Figure 18.
Figure 19.
Figure 20.
Figure 21.

Figure 22.
Figure 23.
Figure 24.
Figure 25.
Figure 26.
Figure 27.
Figure 28.
Figure 29.
Figure 30.
Figure 31.

Result of the first for Capac loam.
Result of the second test for Capac loam.
Result of the first test for Riddles-Hillsdale sandy loam.

Result of the second test for Riddles-Hillsdale sandy
loam.

Result of the third test for Riddles-Hillsdale sandy loam.

Result of the first test for Granby loamy fine sand.
Result of the second test for Granby loamy fine sand.
Result of the third test for Granby loamy fine sand.
Result of steady state flow for the first test at site 3.
Result of steady state flow for the second test at site 3.
Result of steady state flow for the third test at site 3.
Recommended sample cup and porous plate.
Recommended water reservoir with adding tube.

Recommended flow meter with parallel tubing.

viii

51
52

55

58
59
60
62
63

69
70
72

I. Introduction

Today, the demand for the high quality water is increasing while
depletion of the fresh water supply is occurring all over the world.
Agricultural practices are a major cause of this depletion and, in some
areas, cause considerable degradation of the water quality as well as
the supply. This problem can be improved by effective management
of agricultural water use and a good understanding of soil and water

interaction.

Engineers are particularly interested in the soil infiltration and
movement of water through the soil profile. This understanding is
necessary for hydrological modeling and irrigation planning, since
infiltration is the sole source of soil water to support the growth of
vegetation and of the ground water supply of wells, springs, and
streams. In addition, construction of roads, dams, and buildings also
require detailed knowledge of soil properties, including soil infiltration.

Many researchers have been studying soil infiltration for decades.

Philip (1969) intensively studied the infiltration of ponded water
into soil and proposed that infiltration depends on two major
parameters, sorptivity and hydraulic conductivity. Sorptivity is a soil
water property that innately contains information on the soil hydraulic

conductivity and diffusivity. Generally, sorptivities can be measured

2

more accurately and easily than unsaturated hydraulic conductivity
and diffusivity, so it is worthwhile to consider determining the latter

parameters in this indirect way.

In order to measure the sorptivity in the field on undisturbed soil,
there is an obvious need for a simple and reliable device. To serve
this need, several instruments have been designed and built in the

past for to be used in practical field applications.

In 1969, Talsma (1969) designed the very first infiltrometer to
measure the in-situ sorptivity by applying Philip's equation. Similar
to Talsma's device, a twin ring method (Scotter et al.,1982) involved
measuring the steady state infiltration of ponded water. In addition,
the Guelph permeameter (Reynolds and Elrick, 1985), and a portable,
microcomputer-controlled drip infiltrometer designed by Bridge and
Ross(1985) were also used in the field. However, Taslsma's device
and the other devices for the determination of the in-situ sorptivity are
restricted to water supply potential greater than zero. They have the
disadvantages that supply potential decreases during measurement
and the macropores of soil possibly influence the result of the

sorptivity measurement (Perroux and White, 1988).

To prevent macropores from dominating saturated sorptivity
measurements, Dixon (1975) designed the single-ring, single-square
and double-square closed-top infiltrometers to measure saturated
sorptivity under a small suction. Similar to Dixon's device, Dirksen

(1975) designed an apparatus for determination of sorptivity by one

dimensional absorption into short columns of a loamy sand.
Nowadays, Perroux and White's technique (1988) is widely used in
many designs of instruments to determine the in-situ sorptivity. An
automated tension infiltrometer designed by Arkeny et al. (1988), and
another tension infiltrometer built by Logsdon and Jaynes (1993) were
a modification of an early version of Perroux and White's disk
permeameter. However, the disk permeameter is not able to restrict
the infiltration to one direction and can not ensure good contact
between soil surface and porous disk. Moreover, the method
suggested by Talsma (1969) to determine the field sorptivity using a
tension infiltrometer creates some errors in the data analysis during

the determination of sorptivity.

The system proposed in this work is an infiltrometer to measure
the soil sorptivity under a supplied water potential (-10 mm to -150 mm)
in the field. It is low-cost, portable, reliable, but simple to install and
use. The infiltrometer uses a sharpened edge metal cylinder for the
sample cup to avoid soil disturbance and air infiltration into the soil
during conduct of the test; furthermore, the cup ensures flow in one
direction during early infiltration. A designed flow meter is used to
determine the infiltration rate during operation of measurement. In
additional to the soil sorptivity, this instrument can be used to rapidly
determine other hydraulic properties (eg hydraulic conductivity,
macroscopic capillary length, etc.) of field soil. A modification of
Talsma's method to analyze the soil sorptivity from the field data is
proposed in this paper. In addition, two new parameters, initial

infiltration and lag time, are introduced for the determination of the

4

in-situ sorptivity. The initial infiltration and lag time are
recommended to be criteria for examining the reliability of the result

for each experiment.

ll. Literature Review

A. Non-tension lnfiltrometer

Talsma (1969) described a typical method for determining
sorptivity in the field. The measurements were made on large
samples enclosed within 300 mm diameter, 150 mm high, infiltrometer
rings pushed into the soil. Water was rapidly ponded in the rings to
depth of about 30 mm; the subsequent drop in water level was noted at
regular time intervals from 10 to 15 seconds, on a sharply inclined
aluminum scale graduated at 2 mm intervals over 200 mm length. The
scale was suspended from the rim of the infiltrometer with adjustable
bolts, allowing variation of the angle of inclination to the horizontal
soil surface, which varied in practice from 4° to 15° (giving an accuracy
of depth measurement between 0.07 and 0.25 mm), depending on the
rate of drop of water level. Talsma's device is restricted to water
supply potentials greater than zero. It has the disadvantage that
water supply potential decreases during measurement (Perroux and

White, 1988).

Similar to Talsma's device, a twin ring method which was
mentioned by Scotter et al. (1982) involved measuring the steady state
infiltration of ponded water from two rings of different radii that had

been lightly pressed 10 mm into the soil, just far enough to prevent

5

6

lateral leakage when water was ponded. The radii of rings range from
0.025 to 0.204 m depending on the soil types which were tested. This
method of measuring sorptivity is simple and needs a minimum of

equipment. This method also tried to minimize soil disturbance and
error in measurement due to smearing, compaction or cracking. The
twin ring method is also limited to positive supply potential and has the

disadvantage that supply potential decreases during measurement.

Reynolds and Eleric (1985) applied the Guelph permeameter to
determine the in situ sorptivity. In the field, two wells with radii 0.02
m and 0.03 m, were used. The wells were dug with different
diameters of augers. The depth of the wells varied from 0.25 to 0.35
m below the soil surface. Within each well, an initial depth of ponding
of 0.1 m was used to obtain first flow rate corresponding to the initial
depth, and followed immediately afterward with a second depth of 0.15
m to obtain second flow rate corresponding to the second depth. The
sorptivity and hydraulic conductivity can then be computed.
Reynolds and Elrick tried to minimize the influence of smearing and
compaction of well wall by the auger, siltation of the well during the
course of measurement, and entrapment of air during the initial filling
of the well. Like Talsma's device, the Guelph permeameter can only
measure the sorptivity and hydraulic conductivity with supply potential
greater than zero and has the same disadvantage of supply potential

decreasing during measurement.

A portable, microcomputer-controlled drip infiltrometer,

designed by Bridge and Ross (1985), was used to determine the

sorptivity and hydraulic conductivity in the field. The main
components of the drip infiltrometer are gravity supply tank, a
measuring cylinder with water level sensor and solenoid inlet and
outlet valves, a 1 m2 dripper unit and swing support, a stepper motor to
swing the dripper, and a microcomputer control system. The
microcomputer controls the amount of water delivered from and added
to the measuring cylinder. When more water must be delivered to
satisfy the set rate, the microcomputer opens the outlet valve,
switches on the stepper motor and moves the unit through 100 mm to
the other side of its travel. The outlet valve is then closed, the
stepper motor switched off and the cylinder refilled if necessary. The
dripper unit is constructed of lightweight PVC conduit and is fixed on
the swing frame. The measuring cylinder, level sensor, solenoid
valves and stepper are assembled as an integrated unit mounted on a
support stand. The advantage of the drip infiltrometer is that it is an
automatically recording device. The disadvantages are i) the whole
unit is comparatively large and can not easily change sites, ii) high
building and maintenance costs, and iii) operation only at water supply

potential greater than zero.

B. Tension lnfiltrometer

Dixon (1975) designed the single-ring, single-square and
double-square closed-top infiltrometer. The first of three closed-top
infiltrometers designed and used was the single-ring device. This
infiltrometer consists of an acrylic ring (150 mm ID.) closed at the top

except for connections to two water manometers and to an air pressure

8

regulator. To initiate an infiltration run, the closed-top ring is (i)
closed at the bottom with a disk of plastic film, (ii) filled with water, (iii)
placed upon the soil surface area to be tested, (iv) opened at the
bottom by slipping out the film, and (v) sealed on the soil surface with
a wet soil paste. Cumulative infiltration can be determine by
observing manually the drop of water level in the closed-top ring. For
automatic recording, the water manometer air lines are connected to
the two bellows of an air pressure recorder. Automatic recording by
this method is limited to some specific modes of operation. The
single-ring infiltrometer was designed to simulate effective surface
heads ranging from -30 mm to +10 mm of water. This device appears
somewhat cumbersome, and is only for routine field use (Perroux and

White, 1988).

Dirksen (1975) designed an apparatus for determination of
sorptivity by one dimensional absorption into short columns of a loamy
sand. In the field, the soil is contained in a sharp-edged cylinder (10
mm long and 150 mm in diameter) which is pushed into the soil and the
soil surface out even with the top of the cylinder. Contact can be
improved at times by sieving a very thin layer of local, dry soil over the
cylinder before placing the ceramic plate on the top of it. The plate
diameter should be kept as large as possible to smooth the effect of
soil inhomogeneities and to facilitate accurate volumetric
measurements. Water is supplied to the soil surface through a
porous ceramic plate from a horizontal graduated pipette. The
receding water meniscus in the pipette (4 mm ID.) could be read to

0.001 ml3. The pressure head was maintained constant by means of

9

a Mariotte-type regulator before the plate was placed against the soil
surface. This allowed for accurate determination of initial volume

and starting time. Air could escape at the bottom of the soil columns.
Dirksen's permeameter provides a simple concept of design; however

it is not used much in the field.

Clothier and White (1981) simplified Dirksen's device and
designed a sorptivity tube for field measurements. The sorptivity
tube is basically a Mariotte bottle in which supply potential was
determined by the bubbling pressure of a capillary or hypodermic
needle through which air entered a water reservoir. In the field, the
soil is contained in a thin walled perspex cylinder (95 mm long and 86
mm ID.) which is pushed into the soil and the soil surface out even with
the top of the cylinder. Water was supplied to the soil via a sintered
glass plate sealed at the upper end by a stopcock. Once the stopcock
is closed, water can move into the cylinder through the porous plate
only if air enters through the hypodermic needle. The practical range
of supply potential was from -0.1 m to 0 m water. The sorptivity tube
has been used in a variety of hydrological and soil management
studies; however, for soil with high sorptivity, the air entry through the
hypodermic needle was insufficient to maintain supply potential
constant. This is the major limitation of this device (Perroux and

White, 1988).

Perroux and White (1988) modified the sorptivity tube for
application as a disk permeameter. In their design, the hypodermic

needle in the sorptivity tube is replaced by a bubbling tower. The

10

water level in the bubbling tower is used to control the supply potential.
The cylinder in the sorptivity tube is replaced by a 200 mm diameter
disk to reduce the soil disturbance. The disk is made of clear
material to enable the operator to check for air leakage. The bottom of
the disk is milled to form a shallow reservoir, which is enclosed by a
water supply membrane, a fine mesh nylon screen. The membrane is
supported by a steel mesh backing and two or more layers of material.
The infiltrometer is constructed of polycarbonate plastic. Both the
water reservoir tubes and bubbling tower have metal distance scales
attached. The reservoir and bubbling tower can be detached from
permeameter during transportation. This also permits the use of
reservoirs of various diameters which depends on the type of soil
which is tested. The disk permeameter can be operated at both

supply potential less than zero and greater than zero.

Arkeny et al. (1988) designed an automated tension infiltrometer
whose major components are a bubble tower, a Mariotte column (water
reservoir), a base for soil contact, and a transducer-equipped data
logger for data collection and storage. The bubble tower has four
air-entry ports that control tension by allowing air entry at different
distances below the water level. The port can be present to tensions
from 0.02 m to 0.5 m, and valves are used to switch from one port to
another. The bubble tower is connected to the water reservoir with
1.6 mm ID. polypropylene tubing (bubbling tube). Interchangable
water reservoir of different diameters are employed because the
volume of water infiltrating into the soil is calculated from the height

change of water in the reservoir. A mesh nylon filter is used for soil

11

contact. The filter is backed by a circular acrylic faceplate which has
approximately one 2 mm hole per 10 mm2 to allow water flow.
Measurement of infiltration can be automated by the use of data logger
and two pressure transducers and the operation range of the
automated tension infiltrometer is from 0.02 to 0.5 m of water tension

and for infiltration rates of 1 x 10-3 to 5 x 10“ mls.

Logsdon and Jaynes (1993) designed a tension infiltrometer
which was a modification of an early version of Perroux and White's
disk permeameter. Variations from the disk permeameter were that
reservoir and bubble tube were not interchangable, membranes were
used in place of interfacing for the spacing material in the base, and
the infiltrometers were automated with transducers, as described by
Ankeny et al. (1988). The wetting area diameter of the infiltrometer
base was 230 mm. Soil was scraped off level before making the
measurements since most of the measurements were made subsurface;
therefore, no contact material was necessary to obtain hydraulic

contact between infiltrometer and soil.

C. Problems with Current ln-Situ lnfiltrometer

Presently, the disk permeameter is most commonly used to
determine the in-situ sorptivity. However, there are some problems
encountered when applying the disk permeameter in the field. The
sorptivity is derived from one dimensional flow (Philip, 1969);
nevertheless, the disk permeameter is not able to restrict the

infiltration in one direction. This means the derived sorptivity may

12

contain error and may not represent the true characteristic of the field
soil. In addition, the disk permeameter does not ensure good contact
between soil surface and porous disk. This allows air leaking into the
soil sample during the experiment and influencing the outcome of the
field test. Another disadvantage of the disk permeameter is the
limitation of measurement. For the disk permeameter, the infiltration
rate is determined by recording the differential of falling water levels in
the reservoir. Because of the limitation of minimizing the cross
sectional area of the water reservoir, for slow infiltration (e.g. clay), it
will take a long time to obtain enough data to generate the soil

sorptivity.

All of the previously mentioned devices allow some early
infiltration into soil before the beginning of the measurement because
it is difficult to design an non-electrical infiltrometer to set up the
supply tension to the desired value immediately at the start of the
infiltration. . However, people overlooked the early infiltration and
omitted it. This will create significant errors in the result of the

sorptivity measurement.

Ill. Fundamentals

Talsma (1969) applied Philip’s (1969) infiltration theory and
presented the following equation to model the early stage of one
dimensional water infiltration into the soil.

I l

.=—,—zs,,t2 (1)
m1,"

Where:
i = cumulative infiltration
I = cumulative volume of infiltration
r0 = radius of soil sample
t = time from start of infiltration
$0 = sorptivity

In Eq. (1), the sorptivity So is the slope of the plot of i vs. t”

White and Sully (1987) introduced the macroscopic capillary
length kc defined by
beg,

kc : (ewel —9dry )Kll (2)

 

Where:
9..., = the initial volumetric water content

9.... = the final water content at the supply potential ‘110

13

14

K0 unsaturated hydraulic conductivity at To

0"
II

0.55, a representative value for soil

Wooding (1968) used a disk under steady state conditions and

obtained
Q, 41,
-—‘2zK,,+K,,-—— (3)
TIT“ TITO

Where:

00 = steady state flow rate of infiltration
The first term on the right of Eq. (3) essentially represents the
contribution of gravity to the total flow and the second term contains

the contribution due to capillarity.

The relationship between the hydraulic conductivity K0 and the

sorptivity So is obtained by combining Eq.s (2) and (3).

0,, __ 4bSE,
"r02 ”Mews _9dry)

()—

 

 

(4)

Thus, to estimate the unsaturated hydraulic conductivity from Eq. (4),
one must determine the Sorptivity, the steady flow rate, the initial
volumetric water content, and the final water content at the supply

potential We.

IV. Objectives

The objectives of this project are as follows:

To develop an infiltrometer that is portable, durable, reliable,
and simple in design with an accuracy of :t 10% of readings.
To design a system that prevents air infiltration into the soil
during the test, and that has a water capacity for long term
operation.

To test the system in sand, silt, loam and clay texture soils.
To analyze the field data and consider the propriety of the

conventional method of the sorptivity determination.

15

V. System Design

The sorptivity infiltrometer system is intended to be portable,
durable, reliable, but simple in design and has an accuracy of t 10%.
The instrument prototype should be able to execute a test without air
infiltration into the soil during conduct of the test, and should have a
water capacity for long term operation. In addition, the system should

be satisfactory for sand, silt, loam, or clay textured soils.

A. Proposed System

The system (Fig. 1) as designed in prototype is comprised of
four components: sample cup, water reservoir, potential tube, and flow

meter.

A sample cup was chosen because it will restrict flow in the soil
to one dimension, and will prevent air leakage into the sample during
execution of the test. The sample cup is made of steel and designed

to be driven into the soil.
The water reservoir supplies water for in-situ tests and holds

enough water for a long term experiment. The potential tube is of clear

plastic so that the height of the water column can be viewed, making it

16

17

 

 

 

 

 

 

mm

 

 

 

 

 

 

 

 

 

 

 

2 Water mentor
L_, 2
Flow motor
~—E——
soil surface
Sample up

Figure 1. Proposed system for sorptivity measurement.

18

possible to control the potential during the test. The water reservoir

and the potential tube are connected by tygon tubing.

A flow meter consisting of a length of clear tubing of relatively
small diameter resting next to a calibrated surface is used to determine
the rate of flow of water during the test. In operation, a bubble of air
is injected into the tubing, and the time required for the bubble to travel
a set distance is used to determine the rate of flow. If the roughness
of the tubing is very small, the velocity of the bubble should be close

to the velocity of water in the flow meter

8. System Prototype

The sample cup (Fig. 2) consists of a cylinder 104 mm diameter
and 125 mm long, with a removable top fastened together by four
screws. The removable top has the advantage that the condition of the
soil surface within the core can be observed. If necessary, a layer of
porous sand can be applied to the soil surface prior the test. The
removable top contains an inlet and an outlet (to expel the trapped air).

A gasket is used to seal the top to the sample chamber.

The water supply reservoir (Fig. 3) is constructed of a clear
polycarbonate tube, 200 mm inside diameter and 200 mm long with a
capacity of 6 liters. The top of the reservoir contains a water inlet, an
air outlet and a water outlet connecting to the potential control tube.
The air outlet will accept a small pump which can be used to exhaust

air from the reservoir prior to commencing the infiltration, if desired.

19

Removable top

 

air outlet
water inlet screw hole

 

Lg'

 

I".

 

 

 

 

Steel cylinder

sharpened edge

Figure 2. Designed sample cup.

20

 

 

 

 

 

 

 

 

 

 

 

 

air inlet tube
._ f
1r— Y
é water inlet air outlet
° 4.1
z, : I I
2 ° Water reservoir
0 : Z3 Z1
2’. ll: ‘1 I Flaw meter
° . :b—E—
Ball valve air ouflet
l 2’ -—L—&-| soil surface

 

 

 

Samploctp

Figure 3. Prototype for sorptivity measurement.

21

The potential tube is 50 mm inside diameter and 350 mm long. It
contains an air inlet tube of 3 mm inside diameter which can be
adjusted vertically throughout it entire length thus determining the
potential at which water may enter the soil in the sample cup. The
supply potential can be set from -10 mm to -150 mm water height. Both

the reservoir and the potential tube rest on a small wooden stand.

The flow meter (Fig. 4) connects the water reservoir and the
sample cup. A segment of 3.2 mm inside diameter tubing lies adjacent
to a ruler. Air is injected into the flow meter using a hypodermic
syringe. At the far end of the flow meter, a vertical tube traps the
bubble, preventing it from entering the soil. The designated distance
of bubble movement is L, and the duration of bubble movement is tb.
Thus the volumetric rate of the water within the meter is determined by

Lbltb multiplying the cross sectional area of the tubing in flow meter.

T To sample cup

Bubble trap

 

 

 

22

Ruler

/'

 

 

IIUIIITIUTIFITUITTIIIIUII[VIII]

Syn’nge

 

 

Ijfi—

 

O .

 

 

 

 

......................................................................................................

Figure 4. Designed flow meter.

From reservoir

VI. Instructions for Field Use

A. Setting the Potential

Before testing the system in the field, supply potential is set by
altering the height of the air inlet tube in the potential control tube as
shown in Fig. 3. The supply potential at the soil surface is z, + 22 -
23 - z... The value of 22 is the height of the wooden stand and is fixed.
Since the value of 21 decreases while the infiltration proceeds and 23
has the same decreasing rate as 21, 21 + z; -z;. will remain constant.
The supply potential is varied by only changing 24, the height of the air

inlet tube.

8. Site Preparation

The instrument is only tested on bare soil. If the soil is not flat

and even, it will be necessary to level it.

C. System Installation

In the first period, testing was performed in sandy soil only since
sandy soil responds quickly. The system was tested on the Michigan
State University research farm using following procedures:

i) Hammer the cylinder 100 mm deep into the soil, and level the

23

24

soil sample (if necessary) with a spatula, trying not to disturb the
condition of the top soil. Attach the top of sample cup using the
four screws.

ii) Place the water reservoir beside the sample cup, connect it to
the flow meter and the potential tube with the interconnecting
tubing.

iii) Set the depth of the air inlet tube, 24, to the desired position.
iv) Make sure the air outlet of the sample cup is open, and then
fill the sample cup with water by turning on the ball valve. Once
water exits from the air outlet, shut off air outlet at both the water
reservoir and sample cup immediately.

v) When the air inlet tube begins bubbling, start measuring as
soon as possible. Inject 0.1 ml air into the flow meter every
minute and record the time of bubble movement tb through the

designated distance L., by using a portable computer.

D. Soil Sample Water Content

The initial water content, supply water content, and the bulk
density are needed to calculate the hydraulic conductivity. At least
two samples should be taken for each test to determine the initial water
content and bulk density. Samples are taken approximately 250 mm

from the center of the sample cup.

After the completion of infiltration, dig out the sample cup with a
shovel, remove the tubing, and quickly reverse the sample cup to allow

excessive water to drain out. Sample the top 2 to 3 mm of soil for

25

supply water content determination.

Once the samples are taken, they should be placed in tin cans
and capped with a lid , then stored in plastic bags and sealed for

transportation.

E. Required Measurement Time

Both the duration of sorptivity and time of approaching to steady
state depend on the soil. The duration of sorptivity flow can rage
from 0.02 to 1 hour. The time required to approach steady state flow

ranges from 0.2 to 6 hours (Perroux and White, 1988).

VII. Test System I

A. Test 1 Results

The flow rate, Q, at every minute is derived from multiplying the
velocity of the bubble, Lb/tb, by the cross sectional area of the tubing
in the flow meter. Moreover, the cumulative infiltration, i, at any time
t is the total amount of water, I, which has flowed into the soil divided
by the cross sectional area of the sample cup, A0. The calibrated
cross sectional area of flow meter and sample cup is 7.92 mm2 and
8413 mmz. According to Eq. (1 ), the sorptivity So calculated from the
early time data near the origin of the i vs. t"2 diagram. The slope of
the straight line portion is So, the sorptivity, and it has the dimensions

of length / time“.

Test 1 was run on Oct. 5'", 1997. The results are shown in
Table 1 and the i vs. t"2 diagram is shown as Fig 5. The curve relating
i to t"2 for water in Fig.5 is found to be non-linear, making the
determination of a sorptivity impossible. Theoretically, the

1/2

relationship between the cumulative infiltration and time during the

early infiltration, i and t"2

should behave close to a straight line. This
unexpected result is due to the fact that the readings from which the i
to t"2 ratio was found right after the air inlet tubing began bubbling.

However, some infiltration occurred before the bubbling began.

26

27

Table1. Experimental data of Test 1

 

Test 1

Date: 1015/97

Location: Research farm land at M.S.U.
Soil type: Granby loamy fine sand
Supply potential: -20 mm

 

 

Lb = 150 mm

Time t b Q Timem I i

(min) (sec) (ml) (seem) (ml) (mm)
0 0.00 0.00 0.00 0.00 0.00
1 7.57 9.12 7.75 9.12 1.08
2 7.87 8.77 10.95 17.89 2.13
3 8.07 8.55 13.42 26.44 3.14
4 8.27 8.35 15.49 34.79 4.13
5 8.47 8.15 17.32 42.94 5.10
6 8.63 8.00 18.97 50.94 6.05
7 8.63 8.00 20.49 58.94 7.00
8 8.70 7.93 21.91 66.87 7.94
9 8.91 7.75 23.24 74.62 8.87
10 8.96 7.70 24.49 82.32 9.78
11 8.97 7.70 25.69 90.02 10.69
12 9.09 7.59 26.83 97.61 11.60
13 9.10 7.59 27.93 105.19 12.50
14 9.16 7.54 28.98 112.73 13.39
15 9.20 7.51 30.00 120.24 14.28
16 9.20 7.51 30.98 127.74 15.18
17 9.23 7.48 31.94 135.22 16.07
18 9.39 7.35 32.86 142.57 16.94
19 9.55 7.23 33.76 149.80 17.80
20 10.02 6.89 34.64 156.69 18.62
22 9.77 14.14 36.33 170.82 20.29
24 9.82 14.07 37.95 184.89 21.97
26 9.89 13.97 39.50 198.85 23.62
28 9.62 14.35 40.99 213.20 25.33
30 9.62 14.35 42.43 227.54 27.03
32 9.69 14.255 43.82 241.80 28.73

 

 

Cum. Infiltration (mm)

28

 

 

30

25»

20L

15~

 

l l A l

10 20 30 40

Time"2 (seem)

Figure 5. Cumulative infiltration vs. time"2 diagram for Test 1.

 

29

Therefore, the start point of the cumulative infiltration in Fig. 5 was not
at the origin. In order to get the actual results of the field test, it is
necessary to estimate the amount of infiltration which has taken place

before the bubbling starts.

B. System Modifications

In order to evaluate the volume of the initial infiltration

lo ,infiltration which occurs before bubbling begins, a portable digital
scale was placed under the water reservoir as Fig 6. The 2; distance
now will be the height of the scale. The capacity of the scale chosen
was 30 kg and the readability is 0.001 kg. The scale was not sensitive
enough to estimate the sorptivity flow but it is enough to evaluate the
initial infiltration. When the specific weight of water is unity as 1, the
volume of gross initial infiltration Imus, the amount of total filling water
before the time of bubbling happens, can be decided by the digital

scale.

Another quantity, V0, must be determined in order to evaluate lo.
In Fig 7, V0 is the volume between the soil surface and the inlet of the
removable top and it varies according to the height of ho. In most
tests, ho is forced to be 10 mm by filling a thin layer of dry fine sand or
placing a porous plate on the soil surface. Thus, Io can be calculated

by

I0 = 'gross ' V0 (5)

While

30

 

 

 

Watermervol'

 

 

Flowmeter

 

 

 

 

 

 

0"“ 8"” 1 ~——fi‘- soil surface

 

 

 

Salaam

Figure 6. Modified system for sorptivity measurement.

31

 

 

 

 

 

 

 

[T J
h fir [1‘ V '
o__,t _________ .---0 .......... Soil Surface
fine sand
Sample Cup
( l

 

 

 

 

Figure 7. Relative position of the soil surface and top of sample cup.

32

V0 can be determined in the laboratory. In this prototype instrument,

the calibrated V0 was 98 ml.

C. Test 2 Results

In order to obtain more data, lb was measured every 30 seconds
in Test 2 following the same procedures of Test 1. The height of ho
was set at 10 mm and the supply potential was set at -50 mm. lo can
also be determined during the test. Test 2 was run on Oct. 10th, 1997.
In this test, the volume of initial infiltration Io was 42 ml, and the
infiltration data were shown in Appendix B and plotted in Fig. 8 and Fig.
9. In Fig. 9, it can be seen that the early time relationship was more

linear if ignoring the start point.

D. Problems and Analysis

Before deriving the soil sorptivity, two assumptions should be
made:

i) Assume equal amount of water lo infiltrate into two identical

soils within different times to and t1 (Fig. 10), one (C1) under a

constant head ‘1", and another (02) starting at a later time, but

under a falling head which will reach ‘Po at A and then remain

constant. If to is greater than t1 by an appropriate amount, at A

the soils will reach the same water content wo.

ii) Two identical soils which possess the same water content

and potential head will possess the same infiltration rate at any

time.

Cum. Infiltration (mm)

33

 

30

25-

20

T

15~

10~

l_ 1 1 i 1 l l

 

 

 

200 400 600 800 1000 1200 1400

Time (see)

Figure 8. Cumulative infiltration vs. time diagram for Test 2.

1600

Cum. Infiltration (mm)

 

25 ~

20 ~

10 _

 

l i l l l l

 

 

5 10 15 20 25 30 35

Time"2 (seem)

Figure 9. Cumulative infiltration vs. time"2 diagram for Test 2.

40

Cum. Infiltration, i

35

 

 

A
T A ----------------- I (wmq’o)
. c, g
I0 C2 i
0'h— t1—el
l+— to —4 Time

Figure 10. Cumulative infiltration vs. time diagram for
constant head and falling head flow.

36

In Figure 11, C, is the curve of an ideal sorptivity flow measured
with a constant supply potential We at any time. In fact, C1 is an ideal
curve because it is very difficult to design an non-electronic
infiltrometer to set the supply potential to a desired value immediately
at the start of the infiltration. The curve C; is from an experimental
sorptivity flow which can be determined by the proposed infiltrometer.
Once the experiment begins, the potential head of C2 decreases during
the water filling into the soil and reaches the desired potential We at A,
at which time it remains constant and the air inlet tube starts bubbling.
At A, both flows possess the initial infiltration i0 and reach the same
supply potential. According to the assumption, the curve C1 and 02
should meet at A, and thereafter C1 and C2 possess the same
infiltration rate and can be considered identical. Within a short time
increment dt, both have the same sorptivity which will be the slope of

the straight line portion (Fig. 12),

_ di
(t0 + dt)"3 — to"2

 

(6)

ll
where di is a small infiltration increment within dt. To determine So
from the experimental sorptivity flow, it is needed to measure to;
however, to is derived from the ideal sorptivity flow and cannot be

measured by any available infiltrometer. The to can be determined

only when lo and So are given, as expressed in the following equation,

to = (lo/So)2 (7)

Cum. Infiltration, i

37

/\ (g+dtr+dn
:(tm i0)

 

p-------_--

.9

 

l

l¢——— to ——>l
Time
Figure 11. Cumulative infiltration vs. time diagram for

ifldeal sorptivity flow and experimental sorptivity
ow.

Cum. Infiltration, i

38

  
  

 
 

(itofdtlm.io+di)

So = di/[(to+dt)1l2'tom]

 

h—— t01’2——>l
Time"2

Figure 12. Cumulative infiltration vs. time"2 diagram for
iffleal sorptivity flow and experimental sorptivity
ow.

39

Since the measurement begins at A (whenever the supply
potential reaches the desired value), to would be the lag time between
the start of the measurement and the ideal sorptivity flow. In the past,
most researchers ignored to (let to = 0 in Eq.(6)) and derived the
sorptivity as di/dt‘”. This will result some errors in the sorptivity
determination during the data analysis. Moreover, if the to exceeds
the duration of the sorptivity flow, the sorptivity phenomena ceases
and can not be measured by the infiltrometer. In order to determine
the correct sorptivity form the experimental data without measuring to,

1/2

a conversion of the i vs. t expression can be made to solve the above

problem.

In Fig. 13, C1 is the curve of an ideal sorptivity flow. C2' is the
coordinate shift of C; (Fig. 11). Thus 01 and C2' should be the
identical flow after A and A'. According to Eq. (1 ), i is equal to Sat“.
Therefore, by squaring both side of Eq. (1 ), i2 can be expressed as Sozt.
If the data are plotted with i2 on the ordinate versus time on abscissa
(Fig. 14), the slope of the straight line portion is the square of the
sorptivity. Moreover, the sorptivity of C1 and 02' at any time can be

expressed by

 

. _ (i, + di)2 — if

8.; d, (8)

The above derivation shows the sorptivity of an infiltration remains

constant regardless of the start points. This result corresponds with

40

C.

(g+dth+dn

Cum. Infiltration, i

 
 

 

 

Time

Figure 13. Cumulative infiltration vs. time diagram for
ideal sorptivity flow and experimental sorptivity
flow with initial infiltration.

Square of Cum. Infiltration, i2

41

 

   

(to+dt,[io+di]2)

502: [(io+di)"2-io"2]ldt

 

 

+-—— t, ——.l
Time
Figure 14. Square of cumulative infiltration vs. time diagram

for ideal sorptivity flow and experimental
sorptivity flow with initial infiltration.

42

the definition of the sorptivity. As a result, it is virtually impossible to
avoid some initial infiltration during a sorptivity measurement. In
order to determine the sorptivity from Eq. (8), it is necessary to
measure the initial infiltration. Hopefully, it is much easier to
evaluate io in the field than to. Using this approach instead of the
conventional i vs. t”2 diagram, the sorptivity can be determined

correctly from the experimental data without measuring to.
E. Re-analysis of Test 2

. The result of Test 2 was re-plotted in i2 vs. time diagram and
presented in Fig. 15. The slope of the straight line derived from the
early time data was found to be 0.256. Therefore, the square of the
sorptivity 802 = 0.256 mmzlsec and So = 0.506 mmlsec‘”. The to can
be calculated from Eq. (7) and was about 90 seconds. Since to was

short, the sorptivity flow would probably still happen within the

regression range.

The straight line portion was determined by eye; however, a
visual determination does not strongly influence the result. Table 2
shows the differences between the results of regression generated by
different numbers of points. Using 2 points to 10 points, the deviation
of the sorptivity is under 12% of the reading. This result shows that
the determination of the straight line portion by eye would not cause

intolerable error.

700

600

500

400

‘s‘

200

Square of Cum. Infiltration (mmz)

100

43

 

 

  

y = 0.2558x + 22.336
R2 = 0.9944

   

 

L

500 1000 1500
Time (see)

Figure 15. Cumulative infiltration2 vs. time diagram for Test 2.

44

Table 2. Comparison of regression results generated by
different numbers of points

 

 

 

 

 

 

 

 

 

 

NUMBERS OF s2 R2 8
POINTS (mm’IS) (mm/Sm)
2 0.198 1 0.445
3 0.207 0.9993 0.455
4 0.216 0.9987 0.464
5 0.220 0.9990 0.470
6 0.227 0.9903 0.476
7 0.233 0.9979 0.432
a 0.240 0.9969 0.490
9 0.248 0.9954 0.499
10 0.256 0.9944 0.506

 

 

 

 

 

 

VIII. Error Analysis

The velocity of the bubble is determined by its travel distance
divided by its travel time. This was used to determine the velocity of
the real flow in Test 1 and Test 2. The real flow is defined as the water
flow minus the injected air bubbles into the flow meter. If the
roughness of the tubing is very small, the movement of the bubble will
be close to the real flow. The error analysis performed on the flow
meter was mainly concerned with the relationship between the velocity
of the injected bubbles and the real flow rate. This project was done in
the laboratory in order to derive the empirical equations for the bubble

movement and real flow for the field use.

A. Empirical Equation for Real Flow

The empirical equation for this project is defined by the following

form:

0 = cm,"2 (9)
Where:

Q = discharge of real flow

Vb = velocity of injected bubble

c1, c2 = constants from the regression

45

46

The volume of each injected bubble was assigned 0.1 ml which is

corresponding to the field use.

B. Experiment Design

Basing on the empirical equation, the schematic diagram of the
designed system to be used for this experiment is shown in Fig. 16.
The flow rate is varied by changing the water level in the water
reservoir. A hypodermic needle was used to inject 0.1 ml air bubble
into the flow meter (3.2 mm l. D.). The velocity of the bubble is
calculated by measuring its travel distance and travel time. A digital
scale with a pan on it was located at the end of the flow meter. By
measuring the outflow within a certain time the flow rate of real flow can
be determined. Since the size of the water reservoir (about 209 mm l.
D.) is comparatively large, within a short time increment, the pressure

head and the flow rate remain constant.

C. Regressions and Results

The experiment was done in the laboratory at about 15 °C of
water temperature which was the most common condition in the field
tests. The experimental data is shown in appendix C. By plotting the
0 vs. Vb in logarithmic scale (Fig. 17) The slope of the straight line is
found to be c1, and the interception is found to be log c2. The

regression equation can then be determined as follows:

0 = 4.647 v., ”33‘ (10)

47

 

 

 

Water reservoir

water level

Flowmeter

 

 

 

 

Scale

 

 

Figure 16. Designed system for error analysis.

log 0

48

 

 

0.9 ~

0.8 ~

 

0.7 y = 0.9331x + 0.6673

/ R2 = 0.9998

 

 

 

0 0.1 0.2 0.3 0.4 0.5
log Vb

Figure 17. Regression curve for the result of error analysis.

49

The r2 for the regression curve is 0.9998 which provides a strong
confidence for the result of the regression. The unit of Q is
milliliters per minute and while the unit of Vb is centimeters per
second. The operation range of the empirical equation was from 3
mllmin to 15 mllmin. The Eq. (10) can be easily used to estimate the

real flow by using the flow meter in the field.
E. Discussions

The empirical equation was derived from the experimental data
by simulating the field condition in the laboratory. Eq. (10) provide an
accurate means to determined the discharge of a small flow. According
to the experiment, the original mean square error was 0.32 ml’lminz,
and was reduced to 0.001 mlzlminz by applying Eq. (10) to predict the
real flow. This result provides more accuracy than just using the
bubble velocity to represent the velocity of the real flow. The operation
ranges for the Eq. (10) is from 3 mllmin to 15 mllmin which is the most
common range for the sorptivity flow of sand and loam. For very clayey
soil, the infiltration rate is much smaller than 3 mllmin and can not be
simulated in laboratory; therefore, the velocity of the bubble is used to
represent the velocity of real flow. Even under these conditions, the
flow meter is still an easy way to estimate this kind of flow. This
analysis shows that the flow meter can be possibly applied in many
different fields especially when the flow is slow and can not be

determined by any other methods.

IX. Test System ll

According to the derivation in the previous paragraphs, the
sorptivity is able to be estimated accurately in i2 vs. t diagram.
Moreover, the Eq. (10) provides more accuracy to predict the real flow
by the bubble velocity. The designed infiltrometer was applied on
three different soil textures in order to test its operation ranges. Two
tests were performed on Capac loam and three tests were done on
Riddles-Hillsdale sandy loam and Granby loamy fine sand. Each test

was tested under different supply potentials.
A. Results for Site 1

At site 1, two tests were conducted on Capac loam. The
experiments were operated under different supply potential, ‘Po, on
October 19th, 1997 at the Michigan State University research farm at
East Lansing. The data are shown in Appendix B and plotted in Fig.
18 and Fig. 19 The slope of the straight line in Fig. 18 and Fig. 19 is
the square of sorptivity for the field soil. The results for each test are
shown in tabular form in Table 3. The duration for both tests was over
80 minutes. The sorptivity of the first test was 0.401 mmlmin"2 and
the sorptivity of the second test was higher and was 0.362 mm/min‘”.
The V“... is the volume of the total infiltration which can be determined

by observing the differential between the initial and finial weight on the

50

N
0|

N
0

Square of Cum. Infiltration l (mmz)
3 8

51

 

 

  

 

 

O
O
O
O
O
O
O
O
O
O
0
O
O
O
O
0
y = 01611:: + 1.627
R2 = 0.9954
20 40 60 80

Time (min)

Figure 18. Result of the first test for Capac loam.

100

Square of Cum. Infiltration (mm?)

52

 

.5 .L .L .2
O N :5 GD
0
O
O

Q
T

 

y = 0.1305x + 1.3894
R2 = 0.9995

   

 

 

 

o 1 L
0 20 40 60 80

Time (min)

Figure 19. Result of the second test for Capac loam.

100

digital scale during the infiltration.
by the flow meter and would be the total amount of the cumulative
infiltration.

close to the v..,,.. determined by the scale.

53

intolerable error happened during the tests.

The Vim. can also be estimated

In both tests, the V“... determined by the flow meter was

This result shows no

Table 3. Comparison of results from different tests at site 1.

 

 

 

 

 

 

 

 

 

 

 

No. Tension lo 32 v m. v m... to
To (ml ) (mm’lmin) ("when“) by scale by flow meter (min)
1 -10 mm 11 0.161 0.401 44 ml 44.4 ml 10.63
2 -30 mm 10 0.131 0.362 32 ml 31.2 ml 10.78

 

B. Results for Site 2

 

At site 2, three tests were conducted on Riddles-Hillsdale sandy
loam. The tests were operated on November 91h, 1997 at the
research farm on university property at East Lansing. The data are
shown in Appendix B and plotted in Fig. 20 to Fig. 22. The results for
each test are shown in Table 4. The operation time for all three tests
was 40 minutes. The sorptivity of the first test (Fig. 20) was 0.282
mmlsecm, and the sorptivity of the second test (Fig. 21) was 0.260
mmlsec‘”. The sorptivity of the third test (Fig. 22) was 0.239

mm/sec‘”. The lag time to for each test was around 2 minutes. For
all three tests, the difference between the Vim. determined by the flow
meter and v.,... determined by the scale was less than 3% of total

infiltration.

Square of Cum. Infiltration (mmz)

350

300 .

250 ~

200 —

150 ~

100 ~

0|
O

54

 

 

  
 

y = 0.0794x + 8.6275

 

 

R2 = 0.9934
500 1000 1500 2000 2500
Time (see)

Figure 20. Result of the first test for Riddles-Hillsdale sandy loam.

350

N
OI
O

200

150

Square of Cum. Infiltration (mmz)

55

 

300 ~

y = 0.0677): + 7.2074

 

 

 

 

R’ = 0.9908
0 500 1000 1500 2000 2500
Time (see)

Figure 21. Result of the second test for Riddles-Hillsdale sandy loam.

56

 

 

 

 

 

300

«A 250 -

E

.5.

0

C

,9 200 - o
H

E o

2 e

I: o

5: 150 ~ 0 °

E 4’

3 o

o ,0

“a 100 ~ .0

2 0

fl

8

m 50

y = 0.0572x + 7.3034
R’ = 0.9959
0 l
0 500 1 000 1 500 2000
Time (see)

Figure 22. Result of the thired test for Riddles-Hillsdale sandy loam.

57

Table 4. Comparison of results from different tests at site 2.

 

 

No. Tension l0 s2 s v .0... v M... t.
‘P 0 (ml 1 (mm’lsec) (nun/seem) by scale by flow meter (sec)
1 -10 mm 27 0.0794 0.282 152 ml 150.4 ml 129.5

 

-30 mm 25 0.0677 0.260 154 ml 152.6 mi 130.6
3 -50 mm 24 0.0572 0.239 142 ml 139.6 mi 142.4

 

 

 

 

 

 

 

 

 

 

 

C. Results for Site 3

At site 3, three tests were conducted on Granby loamy fine sand.
The tests were operated on November 14th, 1997 at the research farm
on university property at East Lansing. The data are shown in
Appendix B and plotted in Fig. 23 to Fig. 25. The operation time for
all three tests was 30 minutes. The sorptivity of the first test (Fig. 23)
was 0.480 mm/sec‘”, and the sorptivity of the second test (Fig. 24) was
0.473 mmlsec‘”. The sorptivity of the third test (Fig. 25) was 0.409
mmlsecm. For the third test, to increased to 97 seconds because the
infiltrometer needed more time to reach the higher supply potential.
For all three tests, the difference between the v..... determined by the
flow meter and Vim. determined by the scale was less than 3% of total

infiltration. The results for each test are shown in table 5.

Table 5. Comparison of results from different tests at site 3.

 

 

No. Tension In S2 S V m. V m. to
\P 0 (ml ) (mn’lsec) ("mime”) by scale by flow meter (min)
1 -20 mm 28 0.231 0.480 304 ml 301 ml 49

 

2 -40 mm 30 0.224 0.473 296 ml 293 ml 57
3 -80 mm 34 0.167 0.409 232 ml 231 ml 97

 

 

 

 

 

 

 

 

 

 

 

58

 

 

 

 

1400
O

A 1200 - e
N

E O

E 0

TE 1000 ~ 0

.9 0

E e

2 ~ 0

a: 600 .

5 .

' e

g 600 ~ .

0 e

"5 . °

2 400 ~ 0

a O

a O

U' . °

"’ 200 ~ . 0 y = 0.231): + 6.2137

/ R’ = ”925
o l t
0 500 1000 1500 2000
Time (see)

Figure 23. Result of the first test for Granby loamy fine sand.

A

Square of Cum. Infiltration (mm2

59

 

 

 

 

1400
1200 — o
O
O
1000 ~ °
0
O
O
800 ~ 0
O
O
600 r e .
O
O
O
400 ~ 0
O
O
O
. O
200 ~ . e y = 0.22351: + 10.355
/ R2 = 0.9943
0 r ‘ T
0 500 1000 1500 2000
Time (see)

Figure 24. Result of the second test for Granby loamy fine sand.

60

 

 

 

 

600
O

700 ~ ’
NA .
E e
E, 600 ~ 0
C 0
.2 e
a
to 500 —
E . °
1:

O

5_ 400 - e
E O
3 O
U 300 - o
u— 0
O 0
Q) 0
a 200 ~ , °
3 O
o- .0
(D ,.o y = 0.1668x + 14.669

100 ~ 0 2

R = 0.9954
0 l 1
0 500 1000 1500 2000
Time (see)

Figure 25. Result of the third test for Granby loamy fine sand.

61

In addition to the sorptivity, the macroscopic capillary length kc
and the hydraulic conductivity can also be determined by applying
Eq.s (2) and (4). The initial water content 8,", and final water content
8w... were measured during the tests and shown in Table 6. The
steady state flow rate (II/m2 is found by plotting the cumulative
infiltration during the last part of the infiltration as a function of time.
The plot should be linear at large time. The slope of this line is the
steady state flow rate Q/Tti'z. The plots are shown in Fig. 26 to Fig. 28
and the results are shown in Table 6. The soil hydraulic conductivity
at -20 mm supply potential was 17 mm/hr, at -40 mm was 14 mm/hr, and
at -80 mm was 11.8mm/hr. The macroscopic capillary length for each
test was 110 mm, 108 mm, and 118 mm. For many field soils kc is
close to 100 mm (White and Sully, 1987), so the results were

consistent to the field situation.

Table 6. Comparison of results from different tests at site 3.

 

 

 

 

No. Tension S Qlur’ 0..., 9,... K. to
1.110 (nmisecm) (muses) (Whr) (run)
1 -20 mm 0.480 0.0176 0.05 0.292 17 110
2 -40 mm 0.473 0.0165 0.05 0.290 14 108
3 -80 mm 0.409 0.0128 0.05 0.287 11.8 118

 

 

 

 

 

 

 

 

 

 

D. Discussions

According the results, the soil had higher sorptivity under less
supply potential in each site. This outcome is consistent to the field

situation, since the higher negative supply potential would restrict the

62

 

&
O

U
0|

(A
O

M
(II

  

y = 0.0176x + 4.0165

   

Cum. Infiltration (mm)
N
O

 

 

 

R’=0.9969
15 ~
10 »
5 .
0
500 700 900 1100 1300 1500 1700 1900
Time (see)

Figure 26. Result of steady state flow for the first test at site 3.

63

 

35

15—

 

Cum. Infiltration (mm)

d
O
I

 

  

y = 0.0165x + 5.0996

R’ = 0.9991

 

 

500 700 900 1100 1300
Time (sec)

1500

1900

Figure 27. Result of steady state flow for the second test at site 3.

Cum. Infiltration (mm)

64

 

30

25~

20~

 

15 »
y = 0.0128x + 4.3665

   

10e

 

 

 

500 700 900 1100 1300 1500 1700
Time (see)

Figure 28. Result of steady state flow for the third test at site 3.

1900

65

soil to absorb water from the surface.

In site 3, the soil hydraulic conductivity for each test was much
smaller than the steady state flow rate, Q/itrz. This result
demonstrates the fact that the soil absorption dominated the
infiltration when the soil infiltration is operated under some negative

supply potential.

The difference between the Via... determined by the flow meter
and V“... determined by the scale was considered as a parameter,
AV.°..., to examine the accuracy of each test. For all the tests, the
AV..... was less than 3% of the total infiltration. This result verifies
the high accuracy of the designed flow meter and shows using the flow

meter to estimate a small infiltration is a feasible and accurate device.

The to is an important parameter in sorptivity measurement,
since if the to is greater than the duration of the sorptivity flow, the
measured sorptivity can not represent the true characteristic of the
tested soil. In site 1, the to for each test was about 10 minutes. By
field experiences, the duration of the sorptivity flow for Capac loam
was over 30 minutes; therefore, the sorptivity flow was possibly still
taking place, since to for both tests was much less than 30 minutes. In
site 2, the to for each test was around 2 minutes. According to the
field experiences, the duration of the sorptivity flow for Riddles-
Hillsdale sandy loam would hold over 5 minutes which is greater than
to of all three tests in site 2. Therefore, the sorptivity flows were

assure to happen. In site 3, the to for each test was around 1 to 1.5

66

minutes which should be small enough to assure the proceeding of the
sorptivity flow.

For the first test in site 1, the soil sorptivity was 0.401 mm/hr"2
when the volume of initial infiltration, lo, was equal to 11 ml. However,
the sorptivity would decrease to 0.204 mmlhr"2 by omitting the initial
infiltration (let i0 = 0). Therefore, even 11 ml of initial infiltration
would possibly create 100% of error in the sorptivity determination.
This shows the volume of initial infiltration, la, is another important
parameter which needs to be decided in sorptivity measurement

especially for clayey soil.

According to the field experiences, the operation range of the
flow meter was from 1 mllmin to 20 mllmin. Within this range, the flow
rate was able to be determined accurately and conveniently by the flow
meter. For some tests done in clay, the infiltration rate was much

smaller than 1 mllmin and was not able to be measured by this device.

X. Recommendations

There are several suggestions that would improve the system but
have not been tested. In the first version of the designed infiltrometer,
some problems related to the determination of the initial infiltration and
the flow rate were discovered. The first was matching the operation
range of flow meter with the infiltration rate of soils. As mentioned
before, the applicable range of the flow meter was from 1 mllmin to 20
mllmin, however, the infiltration rate of some clays was under this
range. This means the flow meter can not measure such a small flow
accurately. The flow rate is relative to the cross sectional area of the
sample cup. Since this was a prototype version of the system, the size
of the sample cup was determined to be adequate for field tests and no

further attempts were made to correct the problem.

In order to create the flow, a bigger sample cup is necessary to
be applied. A 200 mm I. D. and 50 mm length sample cup is suggested
to be used in the future for clay. By using the suggested sample cup,
the flow can increase to as much as about four times than the
prototype. For clay, the 50 mm length cup should be long enough to
assure the proceeding of the one dimensional flow within the sample
cup during the early infiltration. The top of the sample cup should be

still detachable as the prototype for convenient installation.

67

68

The second problem encountered was the calibrated volume of
the upper room in the sample cup, V0 (Fig. 7). The accuracy of the V0
would hugely influence the result of lo, volume of the initial infiltration.
Since in the previous tests, Vo was forced to desired value by filling dry
fine sand on the soil surface, it was difficult to set Vo accurately by this
method. A detachable metal plate with 1 mm pores (Fig. 29) is
suggested to fixed at a desired position in the sample cup to solve this
problem. According to Clothier and White (1981), pores having a
diameter over 0.76 mm will not affect infiltration of water. Beneath the
porous plate, a thin layer of dry fine sand was used to ensure good
contact between the plate and the field soil without influencing the
sorptivity flow (Clothier and White, 1981 ). By adding the porous plate
in the sample cup, V0 will be constant, and both V0 and lo can be

calibrated more accurately.

Furthermore, the determination of the amount of the initial
infiltration lo was another problem needed to be solved. In the
prototype, the lo was measured by a digital scale which is much more
expensive than the infiltrometer. To reduce the cost of this project,
some modifications are suggested to be done on the water reservoir. In
Fig. 30, a 38 mm l. D. and 150 mm length tube is added on the
prototype. The adding tube should be made by clear material and have
scales on the wall in order to observe the water level. By recording the
differences between the height of water surface, the volume of the
initial infiltration Io can be determined easily. The advantages of this
two sectional tube design are: i) lower cost for the determination of lo

than prototype, ii) contain more water for long term experiment than

69

Emmdmmefim

l_l'FII

 
  
  
  
  
 

  
  
  
   
    
   

000000
0000000000
OOOOOOOOOOOO
00000000000000
00000000000000
OOOOOOOOOOOOOOOO

OOO OOOOOOOOOOOO

V0 10mm

ShmfleCmi

 

 

sharpened edge

Figure 29. Recommended sample cup and porous plate.

70

 

 

 

 

 

 

 

 

 

_E_L,
Y .
.. C
0 Adan Tube

.8 Z
_3_ o
i 2 i
a 3 3

Z 3 Want reservolr

I: o: i! —>To Sample Cup

 

 

 

 

 

 

Figure 30. Recommended water reservoir with adding tube.

71

disk permeameter, and iii) the system has lower gravity center than

disk permeameter to avoid wind effect and decline in the field.

The other problem was the reduction of the initial infiltration.
Since the lag time to is changing with the lo, if the lo can be reduced, the
to will also decrease. This can ensure that the sorptivity flow still
happen at the beginning of the measurement. In the prototype, the
interconnecting tubing between the water reservoir and the sample cup
was 3.2 mm inside diameter. Since the small tubing restricted the flow
rate of filling water, this created more time and water to fill up the
sample cup. A double tubing design (Fig. 31) is recommended to solve
this problem. A 0.95 mm I. D. tubing is placed parallel to the flow meter
and connected by two Y adapters. The parallel tubing will carry most
water to the sample cup during the water filling. Once the sample cup
is filled, shut the stopcock, and then the water will flow only through the
flow meter. This device can reduce the la and to effectively and will
increase the accuracy of the sorptivity measurement. The
recommended range of to for each soil is shown in Table 7 and decided
by field experiences. If the calculated to is over this range, the

sorptivity would probably cease before the measurement starts.

Table 7. The recommended range of lag time for different soils.

 

TYPE OF SOIL RANGE OF T0
Sand to < 3 minutes
Loam to < 7 minutes
Clay to < 20 minutes

 

 

 

 

 

 

 

T0 sample cup

72

Bubble trap

Ruler

   
  

Y Adapter Y Adapter

4——
From reservoir

Figure 31. Recommended flow meter with parallel tubing.

XI. Conclusions

The designed permeameter is an non-electronic system to
measure the soil sorptivity in the field. It is low-cost, portable, reliable,
and simple for installation and use. The infiltrometer can execute a
test without air infiltration into the soil during conduct of the test, and
can ensure the flow in one dimension during the early infiltration.
Moreover, it has a large water capacity sufficient for a long term
experiment and is satisfactory for sand, silt, loam, or clay textured
soils. Moreover, the infiltrometer enables tests to be run under -10 mm
to -150 mm water potential, and can measure a flow ranging 1 mllmin
to 20 mllmin with tolerable error. In additional to the soil sorptivity,
this instrument can be used to determine other hydraulic properties,
(e.g. hydraulic conductivity, macroscopic capillary length, etc.) even
in clay textured soils.

In the past, the i vs. 1‘”

diagram was used to determine the
sorptivity through the application of Philip's equation. However, the
derived sorptivity included some errors form the data analysis. The
method proposed in this text enables the analysis of the soil sorptivity
from the field data. Instead of the conventional i vs. t"2 diagram, the
sorptivity is determined from an i2 vs. t diagram, even when the true

infiltration is not measured at the very start.

73

74

Two new parameters, initial infiltration and lag time, were
introduced in the determination of the sorptivity. The initial infiltration
is the amount of water infiltrated into soil before the infiltrometer water
potential reaches the desired value. The initial infiltration becomes
the interception in the i2 vs. t diagram and can be measured at the onset
of infiltration by the designed infiltrometer. The lag time is the duration
between the onset of Infiltration and the start of the measurement. It
can be derived from the initial infiltration and the derived sorptivity.
The lag time should be used to examine the reliability of the result of
each experiment, since If the lag time is greater than the duration ofthe
sorptivity flow, the derived sorptivity can not represent the true
characteristic of the tested soil. Both initial infiltration and lag time are

important for the determination of the sorptivity.

APPENDICES

APPENDIX A

APPENDIX A

COMPONENT SPECIFICATIONS
(All information given is from manufacture's system user's guide)
Digital Scale (K Tron DS-1)

* Size
330 mm WX 124 mm H X225 mm D.
* Capacity
30 kg (66 lb).
* Readability
060 kg (15 lb): 0.001 kg (0.003 lb).
60-15 kg (30 lb): 0.005 kg (0.01 lb).
15-30 kg (66 lb): 0.010 kg (0.02 lb).
* RS232 communications
An R8232 port, accessible from a program, to communicate with the
data logger.
* Battery capacity
12 VDC, 1.4 AH.

Digital Scale (Denver Instrument, XL-500)

* Pan Size
140 mm X 140 mm.
* Capacity
500 g.
* Readability
0.01 g.
* Response Time (avg)
3 sec.
* RS232 communications
An R8232 port, accessible from a program, to communicate with the
data logger.

Computer (Panasonic CF-1508)
* Size and weight

309 mmWX62 mm HX250 mm D.
2.9 kg (6.4 lb).

75

76

* CPU

V20, 8 MHz.
* Memory

640 K bytes.
* Storage

3 1/2" Floppy Disk Driver.

(720 K bytes double-sided, double density)
* Software

MS-DOS 3.30, GW-BASIC 3.2.
* Battery capacity

6 VDC, 1.8 AH.

APPENDIX B

APPENDIX B

Experimental Data for Field Tests

 

Experimental data for Test 2

 

~2

 

t(sec) t2 Q(ml) I(m|) i(mm) I
0 0.00 42.00 42.00 4.99 24.92
30 5.46 4.73 45.73 5.55 30.65
60 7.75 4.68 51.41 6.11 37.35
90 9.49 4.60 56.02 6.66 44.33
120 10.95 4.19 60.20 7.16 51.21
150 12.25 4.39 64.59 7.66 56.94
180 13.42 4.13 66.72 6.17 66.71
210 14.49 4.34 73.05 8.68 75.40
240 15.49 4.43 77.49 9.21 64.63
270 16.43 4.17 61.65 9.71 94.20
300 17.32 4.09 65.74 101910367
330 16.17 4.13 69.67 106811411
360 16.97 3.32 93.19 110812270
390 19.75 4.09 97.26 115613370
420 20.49 2.95 100.23 11.91 141.94
450 21.21 3.66 104.09 12.37 153.06
480 21.91 3.77 107.67 128216439
510 22.56 3.61 111.46 132517557
540 23.24 3.56 115.06 136818704
570 23.67 3.52 116.56 140919666
600 24.49 3.15 121.73 14.47 209.35
660 25.69 6.98 126.71 15.30 234.06
720 26.83 6.07 134.76 16.02 256.66
780 27.93 6.96 141.77 16.65 263.95
640 26.96 6.87 146.64 17.67 312.13
900 30.00 6.98 155.62 16.50 342.15
960 30.98 6.93 162.54 19.32 373.29
1020 31.94 7.01 169.56 20.15 406.20
1060 32.86 7.01 176.57 20.99 440.47
1140 33.76 7.13 163.70 21.64 476.78
1200 34.64 6.98 190.66 22.67 513.72

77

1260
1 320
1 380
1440

35.50
36.33
37.15
37.95

7.10
7.22
7.22
7.07

78

197.79 23.51 552.70
205.00 24.37 593.78
212.22 25.23 636.33
219.30 26.07 679.46

 

Experimental data for the first test at site 1

 

-2

 

t(min) Q(ml) l(ml) i(mm) l
0 11.000 11.000 1.308 1.710
1 0.455 11.455 1.362 1.854
2 0.455 11.910 1.416 2.004
3 0.422 12.332 1.466 2.149
4 0.377 12.708 1.511 2.282
5 0.373 13.081 1.555 2.417
6 0.373 13.454 1.599 2.557
7 0.370 13.824 1.643 2.700
8 0.367 14.191 1.687 2.845
9 0.366 14.556 1.730 2.994
10 0.385 14.942 1.776 3.154
12 0.776 15.718 1.868 3.490
14 0.770 16.488 1.960 3.841
16 0.776 17.263 2.052 4.211
18 0.775 18.038 2.144 4.597
20 0.731 18.770 2.231 4.977
22 0.771 19.541 2.323 5.395
24 0.770 20.311 2.414 5.829
26 0.776 21.087 2.506 6.282
28 0.760 21.847 2.597 6.743
30 0.770 22.617 2.688 7.227
33 1.077 23.694 2.816 7.932
36 1.171 24.865 2.956 8.735
39 1.195 26.060 3.098 9.595
42 1.051 27.110 3.222 10.384
45 1.085 28.195 3.351 11.232
48 1.104 29.299 3.483 12.128
51 1.080 30.379 3.611 13.039
54 1.095 31.474 3.741 13.996
57 1.055 32.528 3.866 14.949
60 1.085 33.613 3.995 15.963
63 1.052 34.665 4.120 16.978
66 1.095 35.760 4.251 18.068

69
72
75
78
81
84
87 _
90

1.054
1.074
1.081
1.093
1.072
1.084
1.097
1.088

79

36.814
37.888
38.969
40.063
41.134
42.218
43.315
44.402

4.376
4.504
4.632
4.762
4.889
5.018
5.149
5.278

19.148

20.282
21 .456
22.677
23.906
25.182
26.507
27.856

 

Experimental data for the second test at site 1

 

~2

 

1 (min) Q (ml) l (ml) i (mm) l

0 10.000 10.000 1.189 1.413
1 0.456 10.456 1.243 1.545
2 0.419 10.875 1.293 1.671
3 0.402 11.277 1.340 1.797
4 0.390 11.667 1.387 1.923
6 0.748 12.415 1.476 2.178
8 0.700 13.116 1.559 2.430
10 0.642 13.758 1.635 2.674
12 0.631 14.389 1.710 2.925
14 0.624 15.012 1.784 3.184
16 0.610 15.622 1.857 3.448
18 0.557 16.179 1.923 3.698
20 0.575 16.754 1.991 3.966
22 0.565 17.319 2.059 4.238
24 0.556 17.875 2.125 4.514
26 0.559 18.434 2.191 4.801
28 0.530 18.964 2.254 5.081
30 0.528 19.492 2.317 5.368
32 0.526 20.018 2.379 5.661
34 0.508 20.526 2.440 5.953
36 0.520 21.046 2.502 6.258
38 0.511 21.557 2.562 6.566
40 0.480 22.037 2.619 6.861
42 0.466 22.502 2.675 7.154
44 0.443 22.945 2.727 7.438
47 0.708 23.652 2.811 7.904
50 0.708 24.360 2.895 8.384
52 0.541 24.900 2.960 8.760
55 0.712 25.613 3.044 9.269

59
61
63
65
67
69
71
73
75
77
79
81

0.832
0.467
0.480
0.491
0.472
0.525
0.507
0.501
0.525
0.501
0.531
0.455

80

26.445
26.912
27.392
27.883
28.354
28.879
29.386
29.887
30.412
30.913
31.444
31.899

3.143
3.199
3.256
3.314
3.370
3.433
3.493
3.552
3.615
3.674
3.737
3.792

9.880
10.232
10.601
10.984
11.359
11.784
12.201
12.620
13.067
13.501
13.969
14.376

 

Experimental data for the first test at site 2

 

-2

 

 

t(sec) 0 (ml) l (ml) 1 (mm) l
0 27.000 27.000 3.209 10.300
60 4.190 31.190 3.707 13.744
120 4.110 35.299 4.196 17.605
180 4.104 39.403 4.684 21.936
240 4.004 43.407 5.159 26.620
300 3.805 47.212 5.612 31.492
360 3.789 51.001 6.062 36.750
420 3.763 54.764 6.509 42.373
480 3.719 58.483 6.951 48.323
540 3.510 61.993 7.369 54.299
600 3.452 65.445 7.779 60.513
660 3.342 68.787 8.176 66.851
720 3.325 72.1 12 8.572 73.471
780 3.325 75.438 8.967 80.404
840 3.309 78.747 9.360 87.613
900 3.291 82.038 9.751 95.088
960 3.239 85.277 10.136 102.745
1020 3.224 88.500 10.519 110.659
1080 3.149 91.649 10.894 118.674
1140 3.141 94.790 11.267 126.948
1200 2.907 97.698 11.613 134.855
1320 5.612 103.310 12.280 150.793
1440 5.384 108.694 12.920 166.921
1560 5.258 113.952 13.545 183.460
1680 5.230 119.182 14.166 200.687

81

1800 5.143 124.325 14.778 218.381
1920 5.194 129.519 15.395 237.011
2040 5.300 134.820 16.025 256.807
2160 5.143 139.962 16.636 276.771
2280 5.214 145.177 17.256 297.777
2400 5.195 150.372 17.874 319.471

 

Experimental data for the second test at site 2

 

-2

 

1 (sec) 0 (ml) l (ml) i (mm) I
0 25.000 25.000 2.972 8.830
60 3.722 28.722 3.414 11.656
120 3.700 32.423 3.854 14.852
180 3.682 36.104 4.291 18.417
240 3.646 39.750 4.725 22.324
300 3.585 43. 335 5.151 26.533
360 3.585 46.920 5.577 31 .104
420 3.581 50.501 6.003 36.033
480 3.567 54.068 6.427 41 .303
540 3.563 57.632 6.850 46.927
600 3.546 61.178 7.272 52.879
660 3.419 64.596 7.678 58.954
720 3.368 67.965 8.079 65.262
780 3.368 71.333 8.479 71.892
840 3.353 74.686 8.877 78.809
900 3.335 78.021 9.274 86.004
960 3.301 81.322 9.666 93.436
1020 3.287 84.610 10.057 101.143
1080 3.285 87.895 10.447 109.150
1140 3.239 91.133 10.832 117.342
1200 3.207 94.340 11.214 125.745
1320 6.182 10052311948 142.766
1440 6.067 10658912670 160.519
1560 5.912 11250213372 178.820
1680 5.870 118.372 14.070 197.969
1800 5.687 12405914746 217.449
1920 5.659 12971815419 237.739
2040 5.545 135.264 16.078 258.500
2160 5.674 14093816752 280.642
2280 6.020 146.957 17.468 305.127
2400 5.650 152.607 18.139 329.040

 

82

 

Experimental data for the third test at site 2

 

~2

 

t (sec) 0 (ml) | (ml) i (mm) l
0 24.000 24.000 2.853 8.138
60 3.904 27.904 3.317 11.001
120 3.520 31.425 3.735 13.952
180 3.371 34.795 4.136 17.106
240 3.174 37.969 4.513 20.368
300 3.142 41.111 4.887 23.879
360 3.058 44.170 5.250 27.564
420 3.058 47.228 5.614 31.514
480 3.051 50.279 5.976 35.716
540 3.013 53.292 6.334 40.125
600 3.013 56.305 6.693 44.791
660 2.930 59.235 7.041 49.574
720 2.923 62.158 7.388 54.587
780 2.922 65.080 7.736 59.841
840 2.916 67.996 8.082 65.323
900 2.903 70.899 8.427 71 .020
960 2.896 73.795 8.771 76.939
1020 2.896 76.690 9.116 83.096
1080 2.882 79.573 9.458 89.459
1140 2.863 82.436 9.799 96.013
1200 2.863 85.299 10.139 102.798
1260 2.856 88.155 10.478 109.797
1320 2.836 90.991 10.816 116.975
1380 2.830 93.821 11.152 124.365
1440 2.824 96.645 11.488 131.965
1500 2.726 99.372 11.812 139.516
1560 2.824 102.196 12.147 147.559
1620 2.775 104.971 12.477 155.680
1680 2.780 107.751 12.808 164.036
1740 2.630 110.381 13.120 172.141
1800 2.698 113.078 13.441 180.657
1920 5.382 118.460 14.081 198.263
2040 5.149 123.609 14.693 215.874
2160 5.204 128.814 15.311 234.435
2280 5.429 134.243 15.957 254.612
2400 5.318 139.561 16.589 275.185

 

 

83

 

Experimental data for the first at site 3

 

-2

 

t(sec) Q(ml) I(ml) i(mm) l
0 28.000 28.000 3.328 11.077
20 3.741 31.741 3.773 14.235
40 3.535 35.276 4.193 17.582
60 3.454 38.730 4.604 21.193
80 3.573 42.303 5.028 25.284
100 3.535 45.838 5.448 29.686
120 3.409 49.247 5.854 34.265
140 3.375 52.622 6.255 39.123
160 3.300 55.922 6.647 44.183
180 3.170 59.092 7.024 49.335
200 3.130 62.221 7.396 54.699
220 3.115 65.336 7.766 60.312
240 3.068 68.404 8.131 66.109
260 3.103 71.507 8.500 72.244
280 3.144 74.652 8.873 78.736
300 3.004 77.656 9.230 85.202
360 9.069 86.725 10.308 106.264
420 9.069 95.794 11.386 129.651
480 8.983 104.778 12.454 155.108
540 8.905 113.682 13.513 182.593
600 9.019 122.702 14.585 212.716
660 8.918 131.620 15.645 244.762
720 9.062 140.683 16.722 279.627
780 9.204 149.887 17.816 317.412
840 8.944 158.830 18.879 356.422
900 8.831 167.662 19.929 397.160
960 8.880 176.542 20.984 440.345
1020 8.705 185.247 22.019 484.843
1080 8.718 193.965 23.055 531.549
1140 8.983 202.948 24.123 581.926
1200 8.944 211.892 25.186 634.345
1260 9.025 220.916 26.259 689.530
1320 8.864 229.780 27.313 745.973
1380 8.849 238.629 28.364 804.538
1440 8.996 247.626 29.434 866.343
1500 8.913 256.539 30.493 929.833
1560 8.838 265.377 31.544 995.002

 

1620
1680
1740
1 800

8.819
9.037
8.887
8.913

84

274.196 32.592
283.233 33.666
292.119 34.722
301.033 35.782

1062.235
1 133.405
1205.644
1280.341

 

Experimental data for the second test at site 3

 

-2

 

t (sec) Q (ml) I (ml) i (mm) l
0 30.000 30.000 3.566 12.716
20 3.541 33.541 3.987 15.895
40 3.528 37.069 4.406 19.414
60 3.441 40.511 4.815 23.186
80 3.320 43.830 5.210 27.142
100 3.398 47.229 5.614 31.514
120 3.086 50.314 5.981 35.767
140 3.136 53.450 6.353 40.364
160 3.048 56.498 6.716 45.099
180 3.046 59.544 7.078 50.092
200 2.988 62.531 7.433 55.245
220 2.915 65.446 7.779 60.515
240 3.068 68.514 8.144 66.322
260 2.949 71.463 8.494 72.155
280 3.004 74.468 8.852 78.349
300 3.004 77.472 9.209 84.799
360 8.909 86.381 10.268 105.424
420 8.744 95.125 11.307 127.847
480 9.033 104.158 12.381 153.280
540 9.033 113.192 13.454 181.020
600 8.849 122.041 14.506 210.430
660 8.804 130.845 15.553 241.888
720 8.983 139.829 16.621 276.242
780 9.217 149.046 17.716 313.861
840 8.870 157.916 18.770 352.330
900 8.962 166.878 19.836 393.456
960 8.907 175.785 20.895 436.580
1020 8.832 184.617 21.944 481.553
1080 8.373 192.991 22.940 526.226
1140 8.243 201.234 23.919 572.140
1200 8.455 209.690 24.924 621.230
1260 8.772 218.461 25.967 674.291
1320 8.438 226.900 26.970 727.387

1380
1440
1500
1560
1620
1680
1740
1800

8.129
8.125
8.262
8.554
8.174
8.374
8.595
8.174

85

235.029
243.154
251.416
259.969
268.144
276.518
285.113
293.287

27.936
28.902
29.884
30.901
31.873
32.868
33.890
34.861

780.442
835.334
893.066
954.867
1015.859
1080.299
1 148.504
1215.303

 

Experimental data for the third test at site 3

 

-2

 

 

t (sec) 0 (ml) I (ml) i (mm) I
0 34.000 34.000 4.041 16.333
30 3.806 37.806 4.494 20.194
60 3.760 41.567 4.941 24.411
90 3.741 45.308 5.385 29.003
120 3.659 48.967 5.820 33.876
150 3.626 52.593 6.251 39.079
180 3.565 56.157 6.675 44.556
210 3.492 59.649 7.090 50.269
240 3.448 63.097 7.500 56.248
270 3.380 66.476 7.902 62.435
300 3.353 69.829 8.300 68.892
330 3.353 73.181 8.699 75.666
360 3.296 76.478 9.090 82.636
390 3.309 79.787 9.484 89.942
420 3.313 83.100 9.878 97.566
450 3.125 86.225 10.249 105.042
480 3.247 89.472 10.635 113.103
510 3.237 92.709 11.020 121.433
540 3.237 95.945 1 1.404 130.060
570 3.036 98.981 11.765 138.422
600 3.212 102.193 12.147 147.551
660 6.445 108.638 12.913 166.748
720 6.445 115.083 13.679 187.119
780 6.445 121.527 14.445 208.664
840 6.375 127.902 15.203 231.130
900 6.420 134.323 15.966 254.915
960 6.470 140.792 16.735 280.062
1020 6.445 147.237 17.501 306.288
1080 6.230 153.467 18.242 332.757

 

86

1140 6.498 159.965 19.014 361.532
1200 6.466 166.431 19.783 391.350
1260 6.470 172.900 20.552 422.367
1320 6.470 179.370 21.321 454.566
1380 6.470 185.839 22.090 487.948
1440 6.420 192.259 22.853 522.244
1500 6.593 198.852 23.636 558.674
1560 6.494 205.346 24.408 595.762
1620 6.473 211.820 25.178 633.914
1680 6.396 218.215 25.938 672.773
1740 6.494 224.710 26.710 713.415
1800 6.523 231.233 27.485 755.436

 

Experiment data for initial water content and
final water content of each replication at site 3

 

 

B.K.= 1470 kg/F
W1 W2 W3 W.C. Volumetric
(9) (9) (9) W W-0 (96)
Test1 21.6 139.76 120.22 19.674 29.215
Teslz 22.44 119.65 103.63 19.731 29.005
Test3 21.93 133.59 115.37 19.499 26.664
Before 22.1 140.11 136.3 3.336 4.904

Where
W1: weight of tin can
W2: weight of tin can and wet soil
W3: weight of tin can and dry soil

APPENDIX C

 

APPENDIX C

Experimental Data for Error Analysis

 

 

 

 

 

 

87

Vb Q 109 Vb 109 Q Qbefore Qafter Errbefore2 Errafter2
(cm/sec) (ml/min)
0.894 4.189 -0.048 0.622 4.188 4.249 2E-06 0.0036
1.054 4.932 0.023 0.693 4.881 5.007 0.0026 0.0057
0.972 4.532 -0.012 0.656 4.525 4.617 6E—05 0.0071
1.119 5.152 0.049 0.712 5.161 5.316 7E-05 0.0266
1 .249 5.704 0.097 0.756 5.720 5.936 0.0003 0.0534
1.167 5.356 0.067 0.729 5.369 5.545 0.0002 0.036
1.280 5.796 0.107 0.763 5.850 6.080 0.0029 0.0805
1.393 6.331 0.144 0.801 6.333 6.619 3E-06 0.0829
1.501 6.752 0.176 0.829 6.787 7.129 0.0013 0.1425
1.411 6.415 0.150 0.807 6.408 6.703 5E-05 0.0832
1.319 6.002 0.120 0.778 6.018 6.267 0.0003 0.0702
1.386 6.310 0.142 0.800 6.303 6.586 5E-05 0.0758
1.514 6.856 0.180 0.836 6.841 7.190 0.0002 0.1119
1.612 7.333 0.207 0.865 7.256 7.658 0.0061 0.1052
1.930 8.583 0.285 0.934 8.581 9.167 2E-06 0.3408
2.408 10.555 0.382 1.023 10.553 11.441 4E-06 0.7851
2.945 12.735 0.469 1.105 12.733 13.991 8E-06 1.5773
3.211 13.803 0.507 1.140 13.800 15.252 1E-05 2.0991
Sum square error: 0.001 0.3159
Vb : velocity of bubble.
: discharge of real flow.
OW. : predicted flow rate by velocity of bubble.
Qat'ter : predicted flow rate by Eq. (10).
Errm“. : error between OWN. and Q.
Err...“ : error between 0.7... and Q.

 

 

LIST OF REFERENCES

LIST OF REFERENCES

Ankeny, M. D. , T. C. Kaspar, and R. Horton. 1988. Design for an automated
tension infiltrometer. Soil Sci. Soc. Am. J. 52:893-896.

Bridge, B.J., and P. J. Ross. 1985. A portable microcomputer-controlled drip
infiltrometer. I . design and operation. Aust. J. Soil Res. 23:383-391.

Clothier, B. E., and l. White. 1981. Measurement of sorptivity and soil water
diffusivity in the field. Soil Sci. Sco. Am. J. 45:241-245.

Dirksen, C. 1975. Determination of soil water diffusivity by sorptivity
measurement. Soil Sci. Sco. Am. Proc. 39:22-27.

Dixon, R. M. 1975. Design and use of closed-top infiltrometers. Soil Sci.
Soc. Am. Proc. 39:755-763.

Logsdon, S. D., and D. B. Jaynes. 1993. Methodology for determining
hydraulic conductivity with tension infiltrometer. Soil Sci. Sco. Am. J. 57:
1426-1431.

Perroux, K. M., and l. White. 1988. Design for disk permeameters. Soil Sci.
Sco. Am. J. 52:1205-1215.

Philip, J. R. 1969. Theory of infiltration. Adv. Hydrosci. 5:215-296.

Reynolds W. D., and D. E. Eleric. 1985. In situ measurement of field-
saturated hydraulic conductivity, sorptivity, and the alpha-parameter using
the Guelph permeameter. Soil Sci.140:292-302.

Scotter, D. R., B. E. Clothier, and E. R. Harper. 1982. Measuring saturated
hydraulic conductivity and sorptivity using twin rings. Aust. J. Soil Res.
20:295-304.

Talsma, T. 1969. In situ measurement of sorptivity. Aust. J. Soil Res. 7:269-
276.

White, I, and M. J. Sully. 1987. Macroscopic and microscopic capillary length
and time scales from field infiltration. Water Resour. Res. 23: 1514-1522.

Wooding, R. A. 1968. Steady infiltration from a shallow circular pond. Water
Resour. Res. 421259-1273.

88

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