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This is to certify that the

thesis entitled

A NEW EXPERIMENTAL METHOD FOR MEASURING
WATER CHARACTERISTIC CURVES OF SOILS

presented by

Gholamreza Rakhshandehroo

has been accepted towards fulfillment
of the requirements for

M.S. , Civil & Environmental
degree in

 

 

Engineering

ajor professor

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A NEW EXPERIMENTAL METHOD FOR MEASURING

WATER CHARACTERISTIC CURVES OF SOILS

BY

Gholamreza Rakhshandehroo

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Civil and Environmental Engineering

1992

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A A

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C1, 79,;

ABSTRACT

A NEW EXPERIMENTAL METHOD FOR MEASURING
WATER CHARACTERISTIC CURVES OF SOILS

BY
G. Reza Rakhshandehroo

A new experimental method by which one can measure
saturation as a function of capillary pressure in a soil
sample was investigated. The method imposed a saturation on a
sample and measured resulting capillary pressure. After each
drainage increment a period of time was required for the
sample to come to internal static equilibrium. In this paper,
this was referred to as the "redistribution time". The effect
of hydraulic gradient on both drainage time and redistribution
time at different saturations was investigated.

The results showed that data obtained by this new method
and the traditional method agree. Increasing the hydraulic
gradient when high saturations exist speeded the drainage up
but increased the redistribution time. At lower saturations a
higher hydraulic gradient retarded both the drainage and
redistribution processes.

Seven experiments determined the internal moisture
profiles at the end of a drainage step which found not
reproducible. It. was postulated. that 'the shape of such
profiles depend on the internal microscopic structure of the

sample.

ACKNOWLEDGEMENTS

First and foremost I would like to thank professor Arthur
T. Corey for presenting his invaluable course in the mechanics
of immiscible fluids in jporous media. His guidance and
assistance to complete this thesis were also greatly
appreciated.

My sincere thanks to my major advisor Dr. Roger B.
Wallace for his encouragement, support and patience throughout
my thesis. Furthermore, I would like to thank the members of
my thesis committee, professor David C. Wiggert and Dr. Susan
Hasten.

In addition, I wish to thank my office mates and friends
who have made my study easier and my life more enjoyable.

Finally I greatly thank my family. My father and mother
have provided me with the motivation to continue my study. My
wife has continuously encouraged me to complete my master's

work.

ii

QHAEIEB

TABLE OF CONTENTS

LISTOF FIGURES ......OOOOOOOOOOOOOOOOO.

LISTOF 8mm ......OOOOOOOOOOOOOOOOOO

CHAPTER 1 INTRODUCTION .............................

m2 PROBLHSTATMT ......OOOOOOOOOOOOOOOOOO

General

Background ................................

Objecti
Theory

Physics

ves ......OOOOOOOO......OOOOOOOOOOOO

of The Problem ....................

EQUIPMENT AND PROCEDURE ..................

General

Pressure Cell .............................

Burette

Pressure TranSducer ......OOOOOOOOOOOOOOOOO

Valves
Set up

3.6.1
3.6.2

3.6.3
3.6.4

3.6.5

And Procedure ......OOOOOOOOOOOOOOO.

Set up .............................
New Method Procedure for
Determination of Pc(S) ..............
Traditional Method Procedure for
Determination of Pc(S) ..............
Procedure for Determining moisture
Profiles Within the Soil Samples ...
Procedure for Determining the
Influence of Hydraulic Gradient......

iii

10

12

21

21

21

24

24

25

27

27

28

32

34

35

CHAPTER 4

iv
RESULTS AND DISCUSSION ...................
General ....................OOOOOOOOOOO....

Water Characteristic Curves ...............

4.3 Moisture Profiles Within the Soil Samples ..

APPENDIX

REFERENCES

Influence of the Hydraulic Gradient
on the Drainage and Redistribution Times ..

CONCLUSION AND RECOMMENDATIONS ...........

37

37

37

50

52

59

LIST OF FIGURES

EIEUBE

1 Schematic of Experimental Apparatus ..........

2 Pressure Cell Schematic ......................

3 Water Characteristic Curve ...................

4 Redistribution Time at Different Saturations .

5 Moisture Profile Within the Soil Samples .....

6 Drainage Time Under Different Gradients ......

7 Redistribution Time Under Two Gradients ......

A-l Calibration Curves

22

23

38

43

46

48

53

LIST OF SYMBOLS

flux through a unit cross sectional area; [L/T]
hydraulic conductivity; [L/T]
hydraulic head; [L]

distance from the origin in the direction of flow; [L]

”I." :3 NH,

radius of curvature of the interface; [L]
a interfacial tension; [F/L]

P; capillary pressure across an interface; [F/L’].
V output voltage; [v]

IL capillary pressure head; [cm of water]

vi

CHAPTER 1

INTRODUCTION

Water flow in soil is of great importance to engineering,
'hydrology’and.agriculture. The laws under which water flows in
fully saturated soil have been studied extensively' both
experimentally and theoretically, however, flow in unsaturated
zone needs more study.

In the unsaturated or vadose zone, soil water content
depends on the difference in water and air pressure within the
soil. In the vadose zone, water pressure is usually less than
that of the air. The greater the soil water content, the
smaller the difference between air and water pressures. The
functional relationship, however, depends on the type of soil
and is also subject to hysteresis. Curves depicting water
content (or saturation) as a function of pressure difference
(between soil air and water) are called "water characteristic
curves". These curves can be obtained. either through a
drainage or wetting cycle. Starting with fully saturated soil
(with water) and decreasing the soil water content
successively completes a drainage (or drying) cycle. The

wetting (or inhibition) cycle, on the other hand, requires

2
addition of water to initially dry soil. These curves are also
called "water retention" or "capillary pressure vs.
saturation" curves.

This thesis presents results Vof experiments which
generate water characteristic curves for a given soil sample
using a different method than those traditionally employed.
The "pressure equilibrium" method, which has not been
previously studied with this design and accompanying simple
procedure, is reported and the results are compared to the
traditional method of generating data.

The basic concept of this neW'method is to impose a known
saturation on the soil sample and measure the resulting
pressure difference under a static fluid (no flow) condition.
The set up is designed to make the overall measurements
faster. The use of a reluctant pressure transducer and
associated electrical instruments makes the pressure
difference measurements more reliable. A modified pressure
cell technique is employed so that the size of the sample is
relatively small and changing the sample saturation requires
removal or addition of less wetting phase.

This thesis is divided into five chapters and an
appendix. Chapters 2 and 3 present theory and experimental
procedures used in this study, respectively. Comparison of
results obtained from different equilibration techniques, as
well as details of this new method, are presented in Chapter

4 of the thesis. The last chapter contains conclusions based

3
on the results and some recommendations for future work. The
Appendix contains the procedure to calibrate the pressure
transducer along with some data and also a list of apparatus

components with names and addresses of parts providers.

CHAPTER 2

PROBLEM STATEMENT

2.1. General

Water characteristic curves have been generated by many
investigators using a variety of different laboratory
techniques. Topp, etmal. (1967), havercompared.curves obtained
by different methods and have shown that the results are
dependent on the state of flow of the water. However, it is a
common practice to use the water characteristic curves
obtained under static condition of fluids in most cases.

This chapter presents a review of traditional methods for
developing water characteristic curves along with a brief
explanation of the new apparatus and approach employed in this
study. This is followed by the objectives of this work. The

theory and the physics of new system are described at the end.

2.2. Background

Richards published the first plots of water
characteristic: curves, in 1928. These curves ‘usually’ are
determined on samples by changing the pressure difference

across the air-water interface (the capillary pressure) in

5
increments and letting the water content adjust until
equilibrium is achieved. The apparatus used to make such
measurements is called a "pressure cell". The pressure cell
was first described by W. Gardner et a1. (1922).

The pressure cell method involves placing a soil sample
in contact with a "pressure plate" or capillary barrier and
controlling water and/or air pressures. The pressure plate is
an essential component of a pressure cell. It is a porous
plate made of glass, ceramic or a thin sheet of metal. In any
case, the pressure plate has very small pores so that, when
saturated, it allows only water and not air to pass through
its pores over a range of capillary pressures chosen to study
the saturation characteristics of the soil sample. The
pressure difference at which air breaks through the plate is
called the bubbling point or air entry pressure. Hence, any
pressure difference less than the bubbling point applied
across the plate is transmitted to the soil water in the cell.
This feature of the pressure plate provides an efficient way
t0<developrcapillary'pressures in the soil sample in the range
of interest.

Capillary pressures are usually controlled by
incrementally changing air pressure inside the cell on one
side of the pressure plate and letting water pass through the
plate and come to equilibrium with some known pressure on the
other side of the plate. Once equilibrium is achieved, soil

water pressure at any point inside the sample can be

6
determined, by knowing capillary pressure across the plate. If
the sample height is small compared to pressure head
differences applied across the plate, then a single capillary
pressure can be assumed for the whole sample.

Depending on whether one is drying or wetting the sample,
water will pass through the plate and either out of or into
the sample. Once the air pressure inside the cell is increased.
by an increment, water will initially pass through the plate
relatively fast because of the large hydraulic gradient across
the plate. As water pressure across the plate approaches
equilibrium, the gradient gets smaller and so does water flow
through the plate. As a result, letting soil water come to
equilibrium under a constant boundary pressure difference
takes a long time, which may be on the order of days.

A variations of the pressure cell described above, was
introduced by Su and Brooks (1980). In their procedure, the
top of the pressure cell is open to the atmosphere. The method
lets soil water drain out of the cell through the plate at the
bottom and it can be added to the soil from the open top. As
a result, the method enables investigator' to get ‘water
characteristic curves during the wetting cycle and the drying
cycle.

In their method a major improvement was achieved in that
the method shortened the length of time required to generate
a water characteristic curve. The basic idea of their

procedure is to hold soil air at atmospheric pressure while,

7

in the drying cycle, a relatively high suction is applied to
the soil water. Water is allowed to drain out of the soil into
a burette that monitors the water content volumetrically. Once
a desired volume of water is drained out, water suction is
carefully reduced to stop the drainage and soil water suction
is simply computed from the suction necessary to stop
drainage. A slightly modified approach is employed to obtain
wetting cycle data. In this procedure, capillary pressure and
saturation on either drainage or wetting cycles is recorded
when a pressure equilibrium is established. This is in
contrast to the previously discussed procedures that wait for
saturation to equilibrate with the applied pressures. By their
method one can get data for the whole water characteristic
relationship of a sample in a relatively short period of time.

One difficulty with the Su and Brooks method is that
great care must be taken in adjusting water suction to stop
drainage out of the cell. This is necessary because the
occurrence of pressure equilibrium is established by the
relatively tricky task of establishing a stable position of
the meniscus in the outflow tube. Although they did not
describe it as time dependent, the suction required to
stabilize the meniscus would appear to be time dependent which
could make the static equilibrium condition more difficult to
identify. Failure to establish equilibrium would cause
unwanted flow into or out of the cell which could change the

status of the experiment from drainage to wetting or vice

versa at some points.

The pressure cell technique, in general, is the most
commonly used experimental procedure to measure capillary
pressure as a function of saturation. There are several other
variations of the technique that have been used. Details of
the variations, as well as other techniques, are described in

the literature.

2.3. Objectives

The main purpose of this thesis is to investigate a new
method for obtaining water characteristic curves for soil
samples. The method includes a new experimental design and
proper procedures. The basic principal of this method, as in
Su and Brooks method, is recording data once pressure
equilibrium in water is achieved rather than imposing a
constant capillary pressure on the sample and waiting for the
saturation equilibrium. The intent in the new method is to
provide water characteristic curves faster than previous
methods and not to take the risk of unwanted back-flow into
the sample. The design is established to make measurements
easier and at the same time more reliable than previous
methods. This thesis will mainly investigate how'well this new
method could provide consistent and meaningful results and
meet the mentioned expectations.

The second objective is to compare the data obtained by

this method and.the traditional method. This method is capable

9
of providing data based on both the traditional and the new
method. Therefore, the investigator can make a quantitative
comparison of results from the two methods. It is preferred
for the comparison to be made on one packed soil sample.

This method applies more controls on the system compared
to the traditional method. For example theidrainage process is
forced to occur in a desired manner by controlling the
hydraulic gradient. On the other hand, the drainage is
controlled and stopped externally when a desired volume of the
wetting phase has drained out. As a result of above controls
1) a moisture profile forms within the soil sample at the end
of’a drainage period and, 2) if this internal moisture profile
is not at static equilibrium condition, it will take some time
for the moisture to redistribute and come to a static
equilibrium condition. The drainage and .redistribution
processes are discussed in the next sections.

The third objective in this thesis is to study the
resulting moisture profile within the soil sample at the end
of a drainage period. It seems that the shape of such profile
is critical with regard to the redistribution time. This study
will address issues such as: a) How the moisture content
varies along the height of a sample, b) What could the reason
be for the formation of such profiles and, c) How far the
profile is from being at a static equilibrium condition.

The last objective is to investigate how the controls in

the new method can effect the drainage and redistribution

10
times. Results of this investigation could lead to an optimum
criterion that minimizes the sum of drainage and
redistribution time at each drainage increment. Note that the
overall time to generate the entire water characteristics
curve is sum of the drainage and redistribution times at
several drainage increment. Therefore, any condition that
reduces the drainage and redistribution time will contribute

to shortening the time to generate water characteristic curve.

2.4. Theory

A fluid in porous media can be in thermal, chemical
and/or mechanical equilibrium. The first two types of
equilibrium are out of the scope of this work. Here the
assumption is made that temperature gradients and chemical
reactions do not exist in the fluid itself, nor between the
fluid and its surroundings. Mechanical equilibrium is of
interest in this study and occurs when there are no unbalanced
driving forces on the fluid.

In the analysis of unsaturated flow problems, water
characteristic curves can be developed under three different
flow conditions: static (no flow), steady and unsteady flow.
It has been shown that the flow condition has an influence on
the relationship between capillary pressure and saturation,
Topp et al (1967). Despite this fact, it has been common
practice to use data based on a static equilibrium technique

and apply it in the analysis of all unsaturated flow problems.

11
In static methods, capillary pressures and saturations are
determined once the fluids are in a static condition i.e. when
mechanical equilibrium is achieved. However, in order to
measure capillary pressure at different saturations, flow of
wetting phase into or out of the sample is inevitable.

It is an important fact that in the experiments to
generate water characteristic curves under a condition of
mechanical equilibrium the fluid particles should be at static
equilibrium condition both externally and internally. The
external static condition is established when the fluid
particles in the system that are outside the scil sample and
barrier are stagnant. Here after, for the purpose of this
discussion, the soil sample and barrier will be described as
a unit and referred to as the 'sample’. Note that in order to
maintain the external static condition the net driving forces
on each fluid particle outside the ’sample’ should be zero. In
this case there would not be any flow of fluids into or out of
the 'sample'. As a result, a fixed saturation of the fluids
would be held in the soil sample. The external static
condition does not necessarily require the fluid particles
inside the 'sample' to be static. They are free to move inside
the soil matrix and at the upper face of the capillary
barrier.

The internal static condition, on the other hand, is
established when the fluid particles everywhere inside the

'sample’ come to a static equilibrium condition. In this

12
situation the fluid particles would be at equilibrium with
other fluid particles inside the matrix. Furthermore, it seems
that once the internal static condition is achieved, the
entire fluid system would be at true mechanical equilibrium.

The static fluid condition, for the purpose of this
thesis, is the condition at which all fluid particles are in
static mechanical equilibrium. Hence, there is no fluid motion
anywhere in such a system.

Looking at unsaturated flow closely, we recognize that
both the wetting and the non wetting fluids may flow. For
example once a rigid, water saturated soil starts draining, as
water drains out of soil, air enters. In other words, water
will not initially drain out from a rigid soil matrix until
air finds its way into the matrix to replace the drained
water. Furthermore, in this work the assumption is made that
the air density is negligible. Consequently, in unsaturated
soil where the air exists as a continuous phase, it is assumed
that air pressure is everywhere the same.

All experiments were run on disturbed sandy soil samples
using air and Soltrol‘. However, the same technique can be
applied on any type of soil sample with any gas or liquid
which is of interest. As mentioned before, the design and

procedure are applicable to both wetting and drainage cycles.

 

1A light hydrocarbon used as a wetting phase in most related
research laboratories. It is more stable than water in regard to
concerned chemical and physical characteristics.

13

2.5. Physics of the Problem

A review of the physical behavior of the system during
two different periods is in order. The first period of
interest is the drainage period. Drainage starts with the
sample fully saturated. The air pressure is applied on top of
the cell to initiate drainage. This occurs as the wetting
phase is progressively replaced by air. The physics of the
drainage process, which is basically the same in this study
and the traditional method, is discussed below. The second
period occurs in the new method when drainage from the
'sample' is forced to stop and covers the time required to
establish an internal static condition.

Let us first introduce some basic concepts that are
relevant to this analysis. Darcy's equation governs flow in
the system. This equation in its simple form states that:

___d_H
f—KdL

where f is the flux through a unit cross sectional area [L/T],
K is the hydraulic conductivity [L/T] , H is the hydraulic head
[L], and L is the distance from the origin in the direction of
flow [1.]. The term dH/dL is the hydraulic gradient. In a
saturated system the conductivity K is constant, whereas, in
unsaturated media it is a function of the capillary pressure.
In this section we will make use of Darcy's equation
qualitatively.

Another basic relevant.equation is Laplace's equation of

l4
capillarity. This equation relates capillary pressure across

an interface to the radius of curvature of the interface.

 

where R is the radius of curvature of the interface [Id, 0

is the interfacial tension [F/L] , and Pc is the capillary
pressure across the interface [F/L’].

In an unsaturated porous media the radius of curvature of
the interface is an indication of saturation. The smaller the

radius, the less the saturation. For a given fluid pair the
interfacial tension 0 is constant. Then Laplace's equation

requires that the capillary pressure remain constant in order
for the saturation to remain constant. Increase in ‘the
capillary pressure, for instance, implies that the interface
has moved towards the corner in a pore space. It results in a
smaller radius of curvature and less saturation when the
fluids return to a static situation. Obviously the interface
adjustment, which is related to the saturation change, may
take some time to occur since it requires addition or removal
of some of the wetting phase to the pore space.

In the pressure cell study, the experiment starts when
the sample is fully saturated, Then the air pressure on topiof
the cell is increased and held constant at a high pressure.

The interface, which is originally horizontal, is not capable

15

{of holding any capillary pressure. As a result, the pressure
in the air is,totally transmitted to the wetting phase across
the interface. At the same time, the wetting phase pressure on
the other side of the cell is almost constant and smaller than
that of air. This situation produces an hydraulic gradient in
the wetting phase that, according to Darcy’s law, drains the
wetting phase from the sample. The hydraulic gradient, and
therefore the drainage flux, depend on the capillary pressure
across the cell. For instance, given a conductivity and a
wetting phase pressure at the bottom of the cell, the greater
the air pressure the higher the drainage flux out of the
sample.

As theidrainage proceeds, air'will break.through the soil
matrix. It will exist as a continuous phase throughout the
sample. Consequently, an interface with some curvature will be
formed in the pore spaces. At the bottom boundary of the
sample, on topiof the pressure plate, an important development
will occur. The air pressure is too small to force air through
the plate. So an interface will form at the top surface of the
plate that represents the applied capillary pressure according
to Laplace’s equation. This interface can be expected to
develop its full curvature more quickly than the interface
inside the matrix because: 1) it requires much less wetting
phase desaturation due to its smaller pores compared to pores
that are internally desaturating in the soil, 2) the distance

that the wetting phase fluid particles must move in order to

16
let the interface curvature develop in the plate is shorter
compared to that in the soil, and 3) the conductivity of the
path along which the particles move is usually greater in the
plate since it remains fully saturated whereas the soil sample
does not. At this point, the difference in radii of curvatures
on top of the plate and inside the soil matrix will results in
a pressure difference within the wetting phase between the two
locations. This pressure difference could produce a hydraulic
gradient that according to Darcy’s law is the reason for the
drainage out of the soil sample.

While the drainage is proceeding, the interface inside
the soil matrix will retreat and move towards the corner of
the pore spaces. It is only by this retreatment that some
volume of the wetting phase could be removed from a:rigid pore
space. The interface at its new position has a smaller radius
of curvature and is bearing a greater portion of the applied
force SO‘that.aigreater capillary pressure exists as described
by Laplace's equation. As a result of such retreatment, the
wetting phase pressure adjacent to the interface will
decrease. This pressure drop will, in turn, decrease the
hydraulic gradient in the wetting phase across the plate,
assuming that the wetting phase pressure at the bottom of the
cell remains constant. In addition, the wetting phase
conductivity K of the soil decreases logarithmically as the
drainage proceeds. Decreases in the hydraulic gradient and

conductivity throughout the soil sample result in a decaying

17
type drainage flux over time according to Darcy’s equation.

This decaying behavior of the drainage flux over time
makes the drainage process "lengthy". It is the main
difficulty with the traditional method of generating water
characteristic curves. The method requires the gradient and
the drainage to decay to practically zero. Therefore, it will
take a relatively long time, especially at low saturations.

Two controls are employed in this study to deal with the
length of the drainage time. First, the air pressure on toprof
the cell is controlled to make the drainage faster. As
discussed before, higher air pressure causes a higher
hydraulic gradient in the wetting phase. This could be used to
increase the initial drainage flux out of the sample according
to Darcy's equation. However, as the drainage proceeds this
does not prevent the hydraulic gradient or the conductivity
from dropping.

Secondly, once a desired volume of the wetting phase is
drained out, and before the hydraulic gradient decays
significantly, the drainage is stopped externally. In other
words, the drainage increment is controlled as a variable. By
employing both of the above controls, the new method could
make the drainage occur faster compared to the traditional
procedure.

The second period in physical behavior of the system is
referred to as the "redistribution" period. Su and Brooks

(1980) have referred to a somewhat similar behavior as the

18
"pressure equilibrium" period. Despite the fact that their
procedure is different from the procedure employed in this
study, the physical responses of the two systems are similar.
This period is discussed here from both points of views.

In the new method the redistribution period starts when
drainage is stopped. At this moment the external static
condition is, for all practical purposes, achieved and a fixed
saturation is imposed on the 'sample’. As discussed earlier,
right before stopping the drainage the interface on top of the
plate is almost fully developed and.the wetting'phase pressure
in the plate is close to zero. When the drainage is stopped
externally, flow of the wetting phase from the soil into the
plate will still occur due to the existing hydraulic gradient.
Therefore the interface in the soil and on top of the plate
will retreat accordingly. This retreatment will decrease the
overall pressure of the wetting phase in the soil and increase
that in the plate. This internal flow will go on until the
wetting phase pressure in the soil and in the plate are
equilibrated. Then the flow will stop and the internal static
condition will be established.

The redistribution period could also be analyzed from a
different point of view. Consider the moisture profile within
the soil sample at the beginning and at the end of this
period. Noting that the wetting phase has been flowing out of
the sample right before stopping the drainage, one may

conclude that the moisture profile at the beginning of this

19

period would not be at a static equilibrium condition. On the
other hand, by definition, at the end of the period the
moisture profile within the sample must be at static
equilibrium condition. From this point of view, the second
‘period represents the redistribution of moisture inside the
'sample'. For the final equilibrium to be established, this
internal redistribution is accompanied by a small amount of
moisture flowing from the soil into the plate. Note that
despite a known overall saturation of the ’sample', a single
capillary pressure can not be assigned to the sample during
this period. The reason is again the dynamics of the internal
moisture redistribution, as described earlier.

In order to obtain the approximate shape of the moisture
profile within the sample at the end of a drainage step, a set
of supplementary experiments was conducted. It was assumed
that the hydraulic gradient and drainage increment have an
effect on the shape of such profiles. Therefore, a relatively
high pressure gradient was applied to the wetting phase to
drop the sample saturation from 100 to 50 percent in one step.
The intent was to create a nonuniform moisture profile that
could not redistribute to a static equilibrium condition
before the moisture distribution could. be ‘measured. The
moisture distribution was measured by removing soil samples
from different regions of the sample and oven drying them.

Several additional experiments were conducted to

investigate the effect of the two controls employed in this

20
new method on the drainage and redistribution times. Based on
a simple analysis, it seemed likely that the hydraulic
gradient has the predominant role both theoretically and
practically compared to the drainage increment. Therefore, the
drainage and redistribution times were measured under two

different hydraulic gradients for equal drainage increments.

CHAPTER 3

EQUIPMENT AND PROCEDURE

3.1. General

This chapter contains a description of each component of
the apparatus, including the pressure cell, burette, valves
and pressure transducer with its required accessories (Figure
1). The last.sectionidescribes the experimental design, set.up

and procedure.

3.2. Pressure Cell

The pressure cell used, like those previously described,
is a small cell composed of an inner cylinder, outer cylinder
and two end caps (Figure 2).

The cell had an inside diameter of 5.6 cm and an
effective internal height of 3.2 cm. It was designed short so
that saturation remained fairly constant over the height of
the sample. The short cell also allowed for easy soil packing
and minimized drainage time.

To minimize diffusion of liquid through the body of the
cell, it was made of aluminum. A round ceramic plate with

epoxy paint sealing the edge was used as a capillary barrier

21

22

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23

To Air Pressure
(or Suction)

 

 

 

 

 

 

 

 

 

 

 

 

‘ ‘ Top Cap
Outer ’/
Cylinder \ ‘—
\ Inner
Cylinder
Sa I
mp e \ Screw
Filter
Paper N 0
II It rings
Pressure /—
Plate
liottom
,_LJ Cap
To Burette

and Transducer

Figure 2.
Pressure Cell Schematic

24
to transmit suction to the soil water. Two O-rings on the top
and bottom of the pressure plate along with the epoxy provided
a seal, while on the top of the cell a single O-ring was used.
A paper filter placed on the topiof plate prevented clay-sized
particles from entering the plate. Side screws were provided
to fix the inner cylinder relative to the outer one in order
to permit the bottom seal to be achieved before packing soil

into the cell.

3.3. Burette

A glass, 25 ml burette with a bottom stop cock and 0.1 m1
graduations was used during the experiment. The stop cock was
a high quality, zero-displacement valve. It was used to stop
and start the drainage in order to impose known saturations on
the sample. Thick-walled Teflon tubing was usedto connect the
burette to the cell and transducer, Figure 1. The liquid
content of the sample was monitored volumetrically using this

burette.

3.4. Pressure Transducer

The most critical device used in the experiment was the
pressure transducer and its associated components. A very
sensitive variable reluctance pressure transducer was used
(model number CJVR, C.J.Enterprises, Tarzana, CA). It was
designed to measure low and medium gage, as well as,

differential pressures. Using a carrier demodulator and

25

voltmeter, the transducer produced a 0 to :10 volt DC output
in response to a 0 to maximum pressure difference on its
diaphragm.

A brief technical description of the transducer from the
manufacturer's manual states:
"The transducer consists of basically a flat pressure
sensing diaphragm (field replaceable) clamped between two
matched case halves each containing electrical pick off
coils. Applied pressure deflects the diaphragm which is
detected by the two pick off coils. When the coils are
connected as two opposing legs of a bridge circuit, the
resultant bridge output is proportional to pressure.
Bleed screws are provided in both case halves to

facilitate . complete liquid filling for dynamic
measurements."

The pressure transducer was connected across the ends of
the cell. One port was always filled with Soltrol, whereas,
the other port was connected to the air source as shown in
Figure 2. This pressure measurement reflects the pressure
difference between air and Soltrol i.e. the capillary

pressure, .P , across the plate.

C

A calibration curve was frequently developed to convert
output voltage into pressure difference. Characteristics of
the transducer and other related electrical devices were
investigated and shown to be satisfactorily stable. A typical

result is discussed in the Appendix.

3.5. valves

Besides the burette valve, which, was previously

26

described, three other valves were used in the system (Figure
1). They are referred to as the 3-way valve, air valve and
vacuum saturation valve. The vacuum saturation valve was used
for initially saturating the plate and the soil. It had two
important characteristics. First, it was capable of providing
adequate seal when a relatively high vacuum (around 700
millibar) was imposed on the air phase at the top of the cell
to take the air out. Secondly, it was a displacing valve (not
a desired characteristic) that was capable of a fairly fine
regulation of valve opening and therefore liquid flow. With
this valve, the Soltrol inflow to the cell to initially
saturate the sample was kept to a reasonably low rate. This
was judged necessary as a relatively high inflow rate could
have changed the internal structure of the packed sample,
especially at the unrestrained top surface of the soil. The
internal volume of this valve was measured and accounted for
during the experiment. Once the sample was saturated, the
vacuum was released and this valve was left open for the rest
of the experiment.

The air valve was a three-way stopcock. It had.a rotating
core with T-shape opening. It connected all three air lines
during the experiment. In order to initially vacuum saturate
the sample, this valve was set so that the suction was
transmitted only to the cell. During the calibration, however,
the air pressure was applied only on the transducer through

this valve.

 

27

The 3-way valve on the liquid side was a 3-way ball valve
with directional flow switching. It had an inlet port that
could.be connected to either'of the other two ports. The inlet
port was connected to the transducer. During the experiment
this valve was positioned so that the transducer'was connected
to the pressure cell. For calibration purposes and during the
initial vacuum saturation of the sample, the valve was used to,
isolate the cell and connect the transducer to the constant
pressure head Soltrol reservoir. The calibration setup and

procedure are discussed in the next section.

3.6. Set up and Procedure

3.6.1. Set up

The procedure used here, as discussed before, is a

variation of traditional pressure cell technique. The main
differences are:

1. A desired saturation is imposed on the sample and the
resultant capillary pressure is measured, as opposed
to the traditional method that leaves the soil under
a constant capillary pressure to come to saturation
equilibrium over time.

2. A pressure transducer along with a carrier
demodulator and voltmeter are used to monitor
the capillary pressure. The setup allows a quick,
reliable measurement.

3. An aluminum cell is used to minimize the effect of

28
diffusion through the cell body.

These differences enable the investigator to obtain the
whole water characteristic curve in a more convenient manner
than with other static devices and procedures. The design
allowed data to be obtained both by this new method and the
traditional method. Figure 1 shows the setup schematically.

The transducer was wired to the carrier demodulator and
a voltmeter. It had a sensitive replaceable diaphragm and
because of the type of soil sample a 0-1 psi diaphragm was
employed. The demodulator was set so that the output signal
had the maximum. possible value when the transducer ‘was
subjected to the maximum pressure difference. By setting the
controls on the demodulator, a 0-10 volt output was registered
on the voltmeter when the transducer was subjected to its full
range of pressure differences. By locating the transducer at
the same elevation as the midpoint of the sample, it directly
provided capillary pressure corresponding to the mid sample

position whenever the fluids were static.

3.6.2. New Method Procedure for Determination of Pc(S)

The general procedure was to remove a specified volume of
water from the soil and measure the resulting capillary
pressure. The drained volume was determined with the graduated
burette and the saturation was calculated. The capillary
pressure was measured with the pressure transducer which was

connected to a voltmeter. The voltage signal was registered on

 

29
the voltmeter and.was converted to capillary pressure by using
the calibration data.

Vacuum saturating the space beneath the plate and the
plate itself was the first step. The vacuum saturation valve
was closed and the burette valve opened. An oven dried
pressure plate was employed and the vacuum was created by
applying 700 millibar air suction on top of the plate. Then
the vacuum saturation valve was opened.to let Soltrol saturate
the space and the plate. When the saturation process was
complete the air suction was removed.

Any air trapped inside the space was identified and
removed by turning the cell over and applying a small suction
on top of the burette. Then the burette valve was closed. A
paper filter was placed on top of the pressure plate and the
system was weighted.

» A fine sandy air-dried soil was packed on the filter
paper and plate: the soil had a free top surface. The packing
device was a 20 cm long, 3 cm diameter tube with a 2 mm mesh
screen at the bottom to help uniformly distribute the soil
particles. The tube was placed on the plate, filled with the
soil, pulled up slowly and rotated uniformly until the cell
was almost filled up. The cell was dropped 10 times from an
elevation of 3 cm. Then the free top of the soil was hammered
by dropping a 1.5 kg weight 10 times from a 1 cm elevation.
When the packing was complete, the system was weighted again

and vacuum saturated, in place, within the cell.

30

Vacuum saturating the soil was almost the same as vacuum
saturating the plate. As rationalized earlier, the vacuum
saturation valve was used to insure a small flow rate of
Soltrol during saturation. First the sample was over
saturated. Then the high vacuum was removed and the vacuum
saturation valve was totally opened. The system was left under
a small hydraulic gradient for a long time so that excess
Soltrol would drain out. The volume of Soltrol necessary to
fully saturate the sample was monitored with the burette. It
was corrected for the small volume added to the system by
totally opening the displacement valve (vacuum saturation
valve) and was considered to be the total pore volume. At the
end, the pressure transducer along with the Soltrol reservoir
and other electrical devices were connected to the system as
shown in Figure 1.

I Before starting the experiment, the transducer was
calibrated. It was also frequently calibrated in place during
the experiment. Calibration was achieved by positioning the
air valve and the 3-way valve in Figure 1 such that the
pressure cell and burette were isolated from the transducer.
Transducer calibration was accomplished by controlling the
regulated air pressure on one side of the transducer and
connecting a static Soltrol reservoir to the other side. Data
for calibration were obtained by progressively increasing the
air pressure on the transducer and decreasing it.back to zero.

Air pressure was monitored with a U-tube water manometer. The

31
accuracy of the calibration procedure is discussed in the
Appendix.‘

The drainage branch of a water characteristic curve was
initiated by positioning the air valve so that air pressure
was applied to both the transducer and the cell. The 3-way
valve was set to connect the transducer to the cell and
isolate the Soltrol reservoir. With the burette valve closed,
relatively high air pressure was applied to the top of the
cell. Soltrol was then allowed to drain.out of the sample into
the burette under a relatively high pressure gradient by
opening the burette valve. When the desired volume of Soltrol
was drained into the burette, the burette valve was closed
again. Saturation of the sample at that point was calculated
from the known Soltrol drainage and the initial Soltrol volume
in the pore space. Output voltage was read on the voltmeter
and converted to capillary pressure by using the calibration
curve.

The process of desaturating the sample and measuring
capillary pressure and saturation went on by opening and
closing the burette valve and reading the voltmeter and
burette. Smaller drainage increments were employed where the
water characteristic curve exhibited large values of dS/ch.

Once a specified volume of Soltrol was drained out.of the
sample, a period of waiting was required for the system to
equilibrate (redistribution period) before additional Soltrol

was drained. During this time Soltrol was not allowed toidrain

 

32
out, but the voltage signal on the voltmeter was observed to
drop to some stable value asymptotically. As rationalized
earlier, this transient time was attributed to the
redistribution of the moisture inside. the sample. In this
study, the ‘time required for ‘voltmeter stabilization is
referred to as "redistribution time".

During redistribution, the voltage was recorded
periodically until it approached a stable value. However, the
length of time required to achieve internal equilibrium was
not well defined because it is approached asymptotically.
Furthermore this time was observed to depend upon saturation.
Therefore, the actual time recorded as necessary to achieve
redistribution was dependent on the operator's judgement. In
this study the voltage was recorded for a long time after each
drainage step to insure that most of the change in capillary
pressure had occurred. Despite the subjectivity associated
with the determination, a consistent criteria was used

throughout the experiments.

3.6.3. Traditional Method.Procedure for'Determinationiof

p43)

The second objective of this study was to compare the
results obtained by this newrmethod.and'the traditional method
quantitatively. To achieve that, in between the new method
points and within the same run, some data were collected by

allowing the sample Soltrol saturation to equilibrate under an

33
applied pressure difference. The procedure was as follows:

The drainage curve was. developed. by increasing air
pressure to its maximum value in four steps. Within each step,
data were obtained using the previously described procedure.
At the end of each step the burette valve was left open for a
relatively long time so that the soil sample could drain to
equilibrium under the imposed pressure difference. Then a
single data point was recorded that was based on the
traditional method. An indication of the occurrence of true
equilibrium was obtained by shutting the burette valve off and
determining that no significant change on the voltmeter could
be observed. This would occur if no outflow'had.been occurring
when the valve was closed which indicated, by definition, that
equilibrium existed. By this technique, data were obtained
using both the traditional method and the new method on a
drainage cycle.

At the end of each experiment the Soltrol mass balance
was checked by oven drying the sample. In addition, the
transducer was recalibrated. Comparison of before and after
calibration curves show sufficient consistency in basic
characteristics of the electrical devices used in the
experiment. The Appendix includes a set of such curves.

Although only drainage cycle curves were generated in
this study wetting cycle curves could have been measured.
These would be initiated after the Soltrol was brought to

residual saturation on the drainage cycle.

 

34
3.6.4. Procedure for Determining Moisture Profiles Within
the Soil Samples

To achieve the third objective seven experiments were
conducted.to:measure the moisture profile within the sample at
the end of a drainage step. The air valve and 3-way valve were
positioned to isolate the transducer and the Soltrol reservoir
since no measurement of the capillary pressure was needed in
these experiments. The soil was packed and vacuum saturated in
the same way as explained earlier. The soil sample was brought
to a fully saturated condition while the saturation was
monitored by the burette. At this time the burette and vacuum
saturation valves were fully open.

Desaturation of the sample was initiated by applying 70
mbar air pressure to the top of the cell. As a result, Soltrol
was driven out of the soil under a relatively high hydraulic
gradient. When the Soltrol saturation was reduced to
approximately 0.5, the burette valve was closed and the air
pressure reduced to atmospheric. The soil sample was
stratified into three layers. Each layer was divided into
three smaller samples. The samples were weighted, oven dried
and weighted again. The Soltrol saturation of each sample was
computed and a coarse moisture profile developed. In addition,
the total saturation was checked by the mass balance.

The stratifying process was conducted as quickly as
experimentally possible to minimize internal moisture

redistribution during this process. On average, 95% of the

 

35
mass of soil samples was collected and oven dried for

saturation determination during the stratifying process.

3.6.5. Procedure for Determining the Influence of
Hydraulic Gradient

The final set of experiments measured the drainage and
redistribution times at different saturations under two
different hydraulic gradients. These experiments were
performed using the new method procedure except that the air
pressure was periodically adjusted in order to maintain a
constant hydraulic gradient. Two soil samples were packed and
vacuum saturated as explained earlier. The transducer was
connected to the system and calibrated before running the
experiment.

With the burette valve closed, the air pressure was
applied on top of the first sample so that the voltmeter
registered 2 volts. By opening the burette valve, Soltrol was
allowed to drain out of the sample into the burette. During
the drainage increment, the air pressure was adjusted so that
the voltmeter remained stable at 2 volts. The time required to
drain the required volume of Soltrol was monitored with a
stopwatch. At the end of the drainage step, the redistribution
time was determined. The experiment continued by progressively
desaturating the sample until the times required became too
large. The second sample was subjected to a 4 volts gradient

during the drainage. Except for this, it was desaturated in

 

36
the same way as the first sample. The drainage increments were

the same in both cases.

CHAPTER 4

RESULTS AND DISCUSSION

4.1. General

An example of a water characteristic curve on a drainage
cycle obtained. by the procedure previously' described is
presented in this chapter. The results of the supplementary
experiments and the drainage time measurements are presented
next. The last section includes a general discussion on the
redistribution process in the new method and the results of

the redistribution time measurements.

4.2. Water Characteristic Curves

A typical water characteristic curve obtained by the
described procedures is shown on Figure 3. Solid squares
represent data from the traditional method, where open squares
are data recorded by the new method. The wetting phase
saturation of the sample is shown on the horizontal axis and
the capillary head in centimeters of water is on the vertical
axis. The data were obtained on a single drainage cycle
experiment on one packed sample. Soltrol was used as the

wetting phase and air as the non wetting phase.

37

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The probable error in values of He resulting from
uncertainty in the calibration, is represented by the height
of the squares. The contribution to this error due to the
uncertainty of the true end of redistribution is not shown on
the figure. This error was partly discussed in the last
chapter and. will be discussed further in the following
section. The inconsistency in the data especially at very low
saturations could be mostly the result of the subjectivity in
identifying the true end of redistribution.

As shown in Figure 3, data from both methods appear to
fit on a single smooth curve. This indicates that the water
characteristic curve obtained by this new method has the same
characteristics as the old curve and therefore such a curve
could have the same applications as the traditional one. The
data denoted by numbers are those for which data in the form
of voltage as a function of time were collected during the
redistribution period.

The fact that the voltmeter did not register a constant
stable voltage at the end of a drainage step is shown in
Figure 4. This figure shows the voltage history at 5
saturation points. These points are labeled in Figure 3. The
vertical axis is the voltage registered on the voltmeter at
any time. The horizontal axis is the time that the voltmeter
was monitored. Note that during these transition periods the
drainage had been stopped by closing the burette valve (Figure

1) and the soil system was under an external static condition.

 

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The voltmeter sensitivity' was one 'millivolt. It is
equivalent to less than 0.1 mm of water when converted to
pressure head. This level of accuracy was more than adequate
for the system under consideration. Thetime was also measured
accurately with a stopwatch. Therefore the margin of error in
the data shown in Figure 4 is probably less than 1% in all
cases.

The main difficulty in analyzing the redistribution
process is associated with the definition of redistribution
time. It is the time required for the voltmeter to become
"stable". As shown in Figure 4 the voltmeter drops to a final
value asymptotically. Therefore, in a certain sense it will
never become "stable" as it only becomes stable as t~w.

Figure 4 shows that in some cases the rate of the drop is
smaller and therefore it takes longer for the voltmeter to
stabilize. One may conclude that the data determining the
redistribution time and therefore the corresponding voltage at
those cases are less accurate. Note that during the main
experiment a long time was considered for the voltmeter
stabilization at each point. The attempt was to capture the
voltage drop as much as possible.

Figure 4 shows that at low saturations the redistribution
process is slower. In other words, it takes longer for the
system to come to an internal static condition. It seems that
the low conductivity and relatively large drainage increment

could cause the delay. On the other hand at high saturations,

42
especially with small drainage increments, it is on the order
of minutes for the redistribution precess to take place. Again
the high conductivity there, could be the main reason for this
behavior. .

The voltage drop, by itself, shows that the capillary
pressure across the cell is dropping. Noting that a constant
high air pressure was applied on top of the cell, Figure 4
reveals that the wetting phase pressure:in the plate increases
during the redistribution process. It confirms the physical
analysis of the behavior of the system during the

redistribution process presented in Chapter 2.

4.3. Moisture Profiles Within the Soil Samples

The data from seven experiments are shown in Figure 5.
The vertical axis represents the height of the soil sample
which was divided into three equal layers. Layers 1, 2 and 3
refer to the bottom, middle and top layers, respectively. Each
moisture profile in this figure depicts the saturation of the
various layers of a particular packed soil sample after it has
been drained from 100% to around 50% saturation in one step.

As described before, three smaller samples were collected
at each layer. It was observed that of all possible moisture
profiles in a packed sample the vertical moisture profile was
the dominant and more consistent one. Therefore, the average
saturation of the three samples for each layer is shown in

Figure 5. Saturation of the samples at each layer is provided

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in the Appendix.

As mentioned earlier, an average of 5% of the mass of the
soil sample was lost during the stratifying procedure. The
average saturation error associated with the data shown in
Figure 5 is i0.8%. It was computed from the mass balance check
at the end of each experiment by oven drying the samples. The
layer’s heights were chosen to be equal in each soil sample.
The average error in layer height is i3%.

To analyze the profiles shown in Figure 5 let us first
discuss why some regions in a single sample have higher
moisture contents than other regions. According to the physics
of the flow, the drainage will first occur locally along the
path of least resistance. This path possibly includes the
biggest pores that are filled with the wetting phase at the
time. It is reasonable to believe that.in.a packed soil sample
these paths and pores are located randomly.

By the above analysis the inconsistency between the
saturation profiles of different samples, shown in Figure 5,
could.be rationalized- The profiles in this figure reveal that
the drainage process within different samples occurs
preferentially from different regions. These regions seem to
be located in the samples without any consistent order. The
reason could be the fact that each packed soil has randomness
with regard to positioning of the pores and the least
resistant paths. It is a microscopic property of a particular

packed soil and can not be repeated by following the same

45

macroscopic packing procedures.

4.4. Influence of the Hydraulic Gradient on the Drainage
and Redistribution Times 1

Figure 6 depicts the results of the experiments on the
drainage process. They measured the drainage time for equal
drainage increments under two different hydraulic gradients.
They were performed on two different samples. Hydraulic
gradients are given in volts which can be converted to the
differential pressure head using the calibration curve. The
time to drain the sample from a higher to lower saturation has
been plotted at the lower saturation on the vertical axis.

Drainage time was measured accurately using a stopwatch
which recorded time to the nearest hundredth of a second. The
saturation was monitored by the burette. The maximum error in
saturation due to propagation of the burette reading error was
10.5%. The mass balance was checked at the end of the
experiment by oven drying the sample. The measured error was
-2% saturation. The loss was probably due to Soltrol that
remained on the surface of the cell.

As shown in Figure 6, at high saturations the wetting
phase will drain.out.more quickly under higher gradients. This
is consistent with the expectation based on Darcy’s equation
presented earlier. At high saturations an average conductivity
could be assigned to the entire sample. Then, neglecting

conductivity variation over time and space, the drainage flux

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out of the sample is directly proportional to the hydraulic
gradient.

At low saturations, however, Figure 6 shows that the
higher gradient retards the drainage process. The reason could
be explained by considering conductivity variations inside the
sample. As discussed earlier, drainage occurs in some regions
of the sample first. Applying a high gradient could desaturate
these regions considerably. Therefore conductivity of the
sample would locally drop to a low value. Further drainage
from the sample may require flow of the wetting phase through
this region. In this situation the low conductive region would
delay the overall flux out of the sample.

Results from the experiments investigating the
redistribution time are depicted in Figure 7. The figure shows
the results on two packed soil samples each drained under a
different hydraulic gradient. The vertical axis shows the
redistribution time. The saturation of the sample is on the
horizontal axis. Since the redistribution occurs when a fixed
saturation exists in the sample, unlike in the case of
drainage time, the redistribution time is assigned to a
saturation point.

The packed soil samples used in this last study were
those used to develop Figure 6. The drainage and
redistribution times were recorded on the same samples in a
single run. Therefore, the errors associated with the

measurements of the time and saturation are the same as

48

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discussed with regard to Figure 6. However, the determination
of the redistribution time has an inherent uncertainty due to
its indeterminate character by definition. This was discussed
earlier in the last section. I

In Figure 7 for saturations greater than 30%, data for
the two gradients can not be significantly distinguished from
one another due to the margin of error associated with each
one. However, since the redistribution time measurements were
conducted consistently throughout the experiment, one may draw
a conclusion from those data. For example, it may be
interpreted that the higher gradient causes a longer
redistribution time, in general. At low saturation, the higher
gradient causes such a longer redistribution time that the
conclusion is obvious and undoubted.

The behavior of the system during redistribution (Figure
7) may be deduced from Darcy's equation in a similar way to
what was done with regard to drainage (Figure 6). The only
difference is that the drainage is a process in which the
wetting phase flows out of the soil sample where the
redistribution process considers internal flow of the wetting
phase. However, both processes are governed by the same
concepts and equations.

Note that the drainage increment may have an effect on
the drainage and redistribution time under any gradient. This

effect was not considered in this study.

CHAPTERS

CONCLUSION AND RECOMMENDATION

C 5'0 5:

Consistent results could be obtained by the new method by
applying the explained procedures.

Water characteristic curves obtained by the new method
agree with the traditionally generated data.

By' using' more controls, this method. generates more
reliable results more easily, compared to previous
methods. The controls include valves to set the
saturation , a pressure transducer to track Pc , and
capability to alter the hydraulic gradient.

The new' method could require less overall time to
generate Pc(S) curves, by using the controls.

Very accurate measurements of capillary pressure are made
by using a sensitive pressure transducer.

The method establishes the external and internal static
equilibrium conditions at two separate stages.

Once the external static condition is imposed on the
system,an internal moisture profile exists inside the
soil sample that. may not. be at static equilibrium
condition.

The exact shape of such profile may depend on the
internal structure of the sample and may not be
reproducible through same packing procedures.

The method requires a waiting period for the internal
moisture to redistribute. Redistribution of moisture
inside the sample is necessary for establishing the
internal static equilibrium condition.

50

 

51

The hydraulic gradient causing the internal
redistribution of moisture drops to zero asymptotically.

Other things being equal, the redistribution time is
longer at lower saturations.

Results show 'that. at lower saturations, the higher
hydraulic gradient retards both the drainage and
redistribution. At higher saturations the higher
hydraulic gradient makes the drainage and redistribution
occur faster.

The drainage and redistribution times may also depend on
the drainage increments.

MW

Get the entire Pc(S) curve by the new method several
times. Look for reproducibility of the curve.

Determine the internal moisture profile at the end of
drainage without destroying the soil sample. Look for
reproducibility of the profiles.

Try several hydraulic gradients to monitor the drainage
and redistribution times at.different saturations. Look
for the optimum gradient at every saturation.

Apply suction on top of the burette to drain the sample.
Look for any difference in the drainage and
redistribution times compared to applying air pressure on
top of the cell.

Numerically simulate the drainage and redistribution
processes. Compare the internal moisture profile at the
end of drainage and also the drainage and redistribution
times to experimental results.

Look at the effect of drainage increment on the overall
time to generate Pc( S) curves.

APPENDIX

APPENDIX

During the course of the experiment, the valves and
manometer were placed in the system.and.positioned.so that the
set up could function for both the experiment and transducer
calibration (Figure 1). The positioning of the valves is
discussed in the set up and procedure section.

Figure A-l shows two different calibration curves one
obtained before and one obtained after an experiment that
lasted two days. Pressure head difference across the
transducer, in centimeters of water is shown on the vertical
axis and the output voltage on the horizontal axis. Each
calibration curve was obtained by increasing air pressure from
zero to maximum and decreasing it back to zero in a step wise
manner.

The method of least squares was used to fit a straight
line to the data. Based on that, the equation for the 95%

confidential interval is:
PM = -.854 + 7.735 V i 0.458

where, V is output voltage, and H; is the capillary pressure

52

53

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54
head in cm of water. This interval is shown on Figure A-l.
Figure A-l suggests that basic properties of the
transducer remained constant over this two day period. The
transducer was recalibrated for each.experiment.to account for

small amounts of drift.

55

Part List:

Aluminum cell was made at the Research Complex-Engineering
Machine shop

5/8" x 1/4", 1 Bar High Flow Ceramic Plate (Part No. 604D02-
B1M3 Soil Moisture Equipment Corp. Santa Barbara, CA.)

Viton O-ring (National O-rings Company, Detroit Ball
Bearing, Lansing, MI)

0.062" ID x 1/8" OD Teflon Tube (Upchurch Scientific Inc.,
Oak Harbor, WA)

Variable Reluctance Pressure Transducer, Model No. CJVR
(C.J. Enterprises Tarzana, CA)

Carrier Demodulator Model No. CJCD—2061 (C.J. Enterprises
Tarzana, CA)

Bench Digital voltmeter (Part No. 8050A John Fluke MFG. Co.
Plymouth, MI)

3-way Ball Valve Model No. ZZ-BZXJ-SSP (Parker Hannifin
Corp., Instrumentation Valve Division, Jacksonville, AL)

Air Valve (Three-way stopcock, Chemistry shop at MSU,
E.Lansing, MI)

Soltrol 170 Cat. No. AP1700 (Phillips 66 Company, Borger,
TX)

25 ml. Burette with stop cock (Chemistry shop at MSU,
E.Lansing, MI)

56

Experiments to determine the moisture profile at the end of drainage

Experimental Run

1 2 3 4 5 6 7
Sample 1 40.7 36.1 40.4 49.4 39.9 48.5 39.0
Top Layer Sample 2 40.7 48.5 46.7 ' 47.2 43.0 48.5 41.3
Sample 3 48.4 55.0 37.5 50.1 44.3 53.5 34.8
Sample 1 47.4 42.8 55.3 43.5 45.7 56.2 47.3
Mid.Layer Sample 2 56.1 45.7 57.4 49.3 41.7 51.7 54.2
Sample 3 45.0 44.5 47.5 45.7 39.3 52.1 52.2
Sample 1 47.8 51.8 56.4 54.1 56.0 39.5 62.9
Bot.Layer Sample 2 46.5 57.4 57.2 50.4 65.9 44.3 57.0
Sample 3 44.8 51.6 59.2 46.9 69.4 49.0 52.3

57

PRESSURE TRANSDUCER
VARIABLE RELUCTANCE--- MODEL CJVR

RANGES OF 0.1 T0 500 PSIG 5 PSID

ACCEPTS CORROSIVE LIQUIDS & GASES
LOW VIBRATION & SHOCK SENSITIVITY
HIGH NATURAL FREQUENCY

4 t! 4

DESCRIPTION

The Model CJVR Variable Reluctance Pressure Transducer is designed to
measure low and medium gage and differential pressures. In typical
AC excited bridge circuits, the system provides a full scale output
of approximately 25 millivolts per volt input at SKHz. The trans-
ducer will operate with most carrier systems operating at a frequency
between 3KHz and IOKHz. With C.J. carrier demodulators CJCD and most
Pace carrier systems. the transducer will deliver a 0 to :SVDC or
:lOVDC output. Constructed primarily of 400 series stainless steel.
the transducer consists of basically of a flat pressure sensing dia-
phragm (field replaceable) clamped between two matched case halves
each containing electrical pickoff coils. Applied pressure deflects
the diaphragm which is detected by the two pickoff coils. When the
coils are connected as two opposing legs of a bridge circuit, the
resultant bridge output is proportional to pressure. The pickoff
coils are hermetically sealed in the case so as to isolate them from
the pressure media. Bleed screws are provided in both case halves to
facilitate complete liquid filling for dynamic measurements.

 

SPECIFICATIONS ‘

RANGES: 0.1 to 500 psi gage & differential

LINEARITY: :1/2% full scale (best fit straight line)

HYSTERESIS: 1/2% full scale

OVERPRESSURE: 2 times range with 1/2% F.S. maximum zero shift

LINE PRESSURE: 25 times range or 500 psi, whichever is less

OUTPUT: 25 mv/V nominal e SKHz

INDUCTANCE: 10 mh/coil nominal @ SKHz, zero balance within 20% F-So

PRESSURE MEDIA: Corrosive liquids & gases both sides compatible with
400 series stainless steel, Buna "N" and silver

TEMPERATURE: Operational from -65° to +250°F. Compensated from 0° to
+170°F. with nominal deviation from 70°F. calibration 0f
3% F.S.

PRESSURE CAVITY: 4 x 10'3 cubic inches

VOLUMETRIC 4 x 10‘4 cubic inches

DISPLACEMENT: _

WEIGHT: 15 ounces

.—.—-—— 14° . '——1.38—-"
36. PRESSURE III-27NPT

_ ‘.J. ‘

{—— -/I-- ""I

1.20

I._._ /-¢- -£

/ [’05. PRESSURE III-27"" / \.P08. BLED SCRDI
NEG. ILnD SCREW ELECTRICAL COMR

HR-C- 12$ . HATES
HIT" HR-l-ZIC

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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C. J. ENTERPRISES

division of C. J. Instruments. Inc.
P. 0. BOX 834 TARZANA, CA 91356 (818) 996-4131

58

CARRIER DEMODULATOR
FOR VARIABLE RELUCTANCE TRANSDUCERS .
MODELS CJCD-Rlll, CJCD-A 11M, AND CJCD-RlliD

FEATURES

“ llSVAC INPUT

* UP TO ilOVDC OUTPUT

* SMALL RUGGED CONSTRUCTION

* OPERATES WITH C.J. 6 PACE TRANSDUCERS

IDESCRIPTION

The Model CJCD-élll Carrier Demodulator. designed for operation on unregulated IISVAC.
60Hz. operates with C.J. and Pace variable reluctance transducers to provide up to 0-10
or :IOVDC full scale output for voltage controlled telemetry and other DC systems. Ex-
citation of 8 volts pk-pk at 4 KB: is applied to a bridge including the two inductance
arms of the transducer. A solid-State amplifier and demodulator converts the bridge
output to DC. Response time is less than 50 milliseconds. The assembly is packaged in

a small lightweight aluminum housing with external digital turns-counting dials for zero
and span control. Models CJCD-bllLM and CJCD-éllID are the same as the basic Model CJCD-

bill except the CJCD-blllh incorporates a dial indicating readout and the CJCD—blllIJin-
corporates a digital readout.

SPECIFICATIONS

POWER REQUIREMENTS: IISVAC. 60 Hz (specials available for DC operation)
REGULATION: Better than 0.22 from a voltage level of 105 to IZSVAC at frequen-
cies from 50 to 7082.

OUTPUT: Full scale is adjustable from :IVDC to :10VDC into a 1000 ohm load
or greater with a 10 turn digital turns counting dial.

 

 

 

 

 

 

 

 

 

 

 

 

ZERO: Adjustable up to 3752 of full scale with a 10 turn digital turns
counting dial.
RESPONSE: Less than 50 milliseconds.
ACCURACY: Better than 20.52 F.S. including linearity 6 drift.
TEMPERATURE: 32°F. to I60'F.
THERMAL EFFECT: 0.032 F.S./°F. maximum.
WEIGHT: 24 ounces
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MODELS “€0-01!!! 6 CJCD-CIIID
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C. J. ENTERPRISES

division of C. J. Instruments, Inc.

P. 0. BOX 8314 TARZANA, CA 91356 (818) 996-4131

I

 

 

 

 

REFERENCES

Bear J., 1979, Hydraulics of Ground Water, Mc.Graw Hill Inc.,
pp.190-224

Collins R.E., 1961, Flow of Fluids Through Porous Materials,
Reinhols publishing Corp. New York

Corey A.T., 1986, Mechanics of Immiscible Fluids in Porous
Media, Water Resources Publications, pp.26—55

Corey A.T., Brooks R.H., 1975, Drainage Characteristic of
Soils, Soil Science Society'of America Proceeding Vol. 39

Freeze R.A., Cherry J.A., 1979, Ground Water, Prentice Hall
Inc., pp.18-45

Gardner W., Israelsen O.W., Edlefsen N.W. and Clyde H., The
Capillary Potential Function and its Relation to
Irrigation Practice, Physical Review, Second Series
July-December, 1922, p. 196

Lenhard R.J. and Parker J.C., Measurement And Prediction of
Saturation-Pressure Relationships in Three-Phase Porous
Media System

Richards L.A., The Usefulness of Capillary Potential to Soil
Moisture and Plant Investigators, Journal of Agricultural
Research, Vol. 37, No.1, 1928, pp.719-742

Su C., Brooks R.H., 1980, Water Retention Measurements for
Soils, Journal of Irrigation and Drainage Division, ASCE,
Vol. 106 No. IR2

Top G.C., Klute A. and Peters D.P., 1967, Comparison of
Water Content-Pressure Head Data Obtained by Equilibrium,
Steady State and Unsteady State Methods, Soil Science
Society of America Proceeding Vol. 31

White N.F., Duke H.R., Sunada D.K., Corey A.T., 1972,

Boundary Effects in the Desaturation of Porous Media,
Soil Science Society of America Vol. 113

59

MICHIGAN STATE UNIV. LIBRARIES
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