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AUG 15 1266
USE OF ELECTRICAL PRESSURE TRANSDUCERS
TO MEASURE
SOIL PRESSURE
by
RICHARD SWAN LADD
BSCE,
Northeastern University
(1962)
Submitted in partial fulfillment
of the requirements for the degree of
Master of Science
at the
Massachusetts Institute of Technology
1966
/7
Signature redacted
Signature of Author
.
.
.
.
.
.
.
Department of Civil Engineering
June 20, 1966
Signature redacted
.- - - Certified by ...............................
Cetfe0y0
Thesis Supervisor
-
~
Signature redacted
Accepted by ............
Chairman, Departmental Committee
on Graduate Students
~~AL~e
38
ABSTRACT
USE OF ELECTRICAL PRESSURE TRANSDUCERS
TO MEASURE
SOIL PRESSURE
by
RICHARD SWAN LADD
Submitted to the Department of Civil Engineering on June
20, 1966, in partial fulfillment of the requirements for
the degree of Master of Science.
The application of electrical transducers to measure
soil pressures against planar surfaces is described, with
emphasis on the determination of the coefficient of earth
Data are prepressure at rest (K ) for cohesive soils.
sented on the value of Ko for a saturated silty clay
(Boston Blue Clay) as a function of consolidation pressure,
maximum past pressure and overconsolidation ratio. These
data were obtained via a square fixed ring oedometer which
had a Dynisco pressure transducer screwed into one side of
the cell. Although the observed values of K appear reasonable and are consistant with other publis~ed data, the
degree of accuracy is unknown. Attempts to calibrate the
transducer by comparing measured versus applied average
pressures on a planar surface are described. These results
indicated that the measured pressure is directly related to
the applied soil pressure.
Thesis Supervisor: A. E. Z. Wissa
Title: Assistant Professor of Civil Engineering
-2-
ACKNOWLEDGEMENT
The author is indebted to Professors C. C. Ladd,
K.
Hoeg, H.
M. Horn,
and A.
E.
Z. Wissa for their many
helpful suggestions and their guidance in the preparation of this thesis.
-3-
TABLE OF CONTENTS
Page No.
Title Page
1
Abstract
2
Acknowledgement
3
Table of Contents
4
List of Tables
6
List of Figures
7
9
Chapter 1
INTRODUCTION
Chapter 2
MEASUREMENTS OF THE COEFFICIENT
OF EARTH PRESSURE AT REST (K 0
2.1
Scope
11
2.2
Preparation of Boston
Blue Clay
11
Equipment and Related Problems
11
2.3
2.4
Chapter 3
11
2.3.1
Electrical Equipment
11
2.3.2
K 0 Cell
12
Test Procedure
13
2.4.1
Calibration of Pressure
Transducer
13
2.4.2
Trimming Soil Sample
13
2.4.3
Loading Sequence
13
2.4.4
Measurements
21
2.5
Test Results
15
2.6
Comparison with Other Results
16
2.7
Discussion of K
Cell
CALIBRATION OF PRESSURE TRANSDUCER
WITH A SOIL PRESSURE
3.1
Introduction
3.2
Equipment
3.2.1
Disk
-4-
18
21
21
21
21
Page No.
3.3
3.2.2
Electrical Equipment
21
3.2.3
Pressure Cells
22
Test Procedures
Calibration of Pressure
Transducer
22
3.3.2
Trimming Soil Sample
22
3.3.3
Oedometer Unit
22
3.3.4
Triaxial Cell
23
3.3.1
3.4
3.5
3.6
22
Test Results
23
3.4.1
Oedometer Results
24
3.4.2
Triaxial Cell
25
3.4.3
Summary
25
Discussion of Test Results
26
3.5.1
Seating and Arching
Effects
26
3.5.2
Frictional Effects
27
Conclusions and Recommendations
28
Chapter 4
SUMMARY AND CONCLUSIONS
30
Chapter 5
REFERENCES
35
Appendix A
PREPARATION OF BOSTON BLUE CLAY
64
Appendix B
PRESSURE TRANSDUCERS
68
B.1
Pressure Transducers and Associated Instrumentation
68
B.l.1
Design of Gauge
68
B.l.2
Related Electrical
Equipment
B.2
Calibration of Pressure Transducer
69
B.2.1
General
69
B.2.2
Calibration when Excitation
Voltage is Directly Measured
70
B.2.3
Calibration when Excitation
Voltage is Indirectly
Measured
Appendix C
68
LIST OF NOTATIONS
-5-
71
76
* in--------------------------------------------
LIST OF TABLES
No.
Title
Page No.
I
Properties of Boston Blue Clay
37
II
Typical Calibration of Pressure Transducer using VTVM Voltmeter
38
Typical Calibration of Pressure Transducer using Digital Voltmeter
39
IV
Results of K
40
V
Typical Values of Friction Angle for
III
Test on BBC
42
BBC
VI
VII
VIII
Soil Pressure in Consolidation Unit
42
a) With Filter Paper
b) Without Filter Paper
43
44
Soil Pressure Results in Triaxial Cell
without Teflon
45
Soil Pressure Results in Triaxial Cell
with Teflon
-6-
LIST OF FIGURES
Figure No.
1
Title
Page No.
Grain Size Distribution - Boston
Blue Clay
47
2
K
48
3
Volumetric Strain vs. Log Consolidation Stress for Boston Blue Clay
49
Vertical Stress vs. Horizontal Stress
in K Test on Boston Blue Clay
50
Coefficient of Earth Pressure at Rest
vs. Overconsolidation Ratio for Boston
Blue Clay
51
6
Jackson's Triaxial K
52
7
Ko vs. Overconsolidation Ratio for
Several Clays
4
5
Cell
Cell
53
8
Effect of Side Friction on Value of K
9
Disk for Calibration of Transducer
55
10
Oedometer Unit with Transducer
56
11
Triaxial Cell with Transducer
57
12
Pressure System for Triaxial Cell
58
13
Results of Oedometer Test -
14
17
a
a
60
61
Effect of Friction on Stress Distribution in
Oedometer Test
62
Effect of Friction on Stress Distribution
in Triaxial Test
63
-
Results of Triaxial Test with Teflon
Ratio of P /P vs. P
m
16
59
Results of Triaxial Test without Teflon
Ratio of P /P vs. P
m
15
Ratio of
vs. P
-
P /P
54
0
a
a
-7-
LIST OF FIGURES
(Contd.)
Title
Page No.
A-1
Self-Extruding Consolidometer
66
A-2
Method of Slurry Placement
67
B-1
Schematic Diagram of Dynisco Gauge
74
B-2
Voltage Change of 6 Volt Wet Cell
Battery vs. Time
75
Figure No.
Appendix A
Appendix B
-8-
Chapter I
INTRODUCTION
A frequent problem in testing the properties of soil
has been the accurate measurement of soil pressures against
"rigid" surfaces.
This retaining surface is usually used
in direct or indirect measurements of the following soil
properties or stresses:
(1)
Coefficient of earth pressure at rest - K0
(2)
Coefficient
(3)
Coefficient of passive earth pressure - K
(4)
Major principal stress - a1
Minor principal stress - a3
Intermediate principal stress
(5)
(6)
of active
earth pressure -
Ka
p
-2
In some cases the total load is measured and then an
assumption is made relative to the stress distribution.
In
a conventional triaxial test, the stress on the top cap and
bottom platten is assumed equal to the measured load divided
by the area of the sample.
In an oedometer test, the applied
vertical stress is assumed to be uniform and equal to the
applied load divided by the area.
In other cases, a surface
might be instrumentated with strain gauges,
cell.
such as in a K
0
In this case the confining ring of the oedometer has
strain gauges and the lateral pressure is assumed uniform and
proportional to the hoop strain measured by the strain gauges.
An inherent problem in most measuring systems lies in
the assumption relating a computed or measured value to the
true stress at the interface.
(1)
Inaccuracies could arise from:
The existance of shear stresses on planes which
are assumed to be principal planes, such as at the
top and bottom of triaxial samples;
(2)
The presence of shear stresses along the
-9-
circumference of oedometer samples and also along
the top and bottom caps;
(3)
Deflections of the "rigid" surface used to
measure the soil pressures causing arching.
The use of electrical pressure transducers to measure
soil pressures on a plane surface can minimize some of these
problems since the transducer is highly rigid and is designed
to measure pressures directly.
Because pressure transducers
have a flat measuring surface, they can only measure soil
pressures which act against a flat surface.
There are many possible applications for the use of
pressure transducers, some being:
(1)
When one cannot measure the total load, or
if it would be very difficult to do so;
(2)
When edge effects would cause a non-uniform
pressure distribution over most of the surface;
(3)
Whenthe system used to measure total load
would not be rigid enough and yet maintain the required sensitivity;
(4)
To measure the distribution of pressure over
a surface.
-10-
Chapter 2
EARTH PRESSURE AT REST
2.1
(K
)
MEASUREMENTS OF THE COEFFICIENT OF
Scope
K
measurements, obtained by using an electrical
pressure transducer in the side of a square oedometer, are
presented on both normally and over-consolidated Boston
Blue Clay (BBC).
These data are compared with K
measure-
ments obtained from other equipment and procedures on BBC
and on other soils.
2.2
Preparation of Boston Blue Clay
The tests were performed on samples of Boston Blue
Clay consolidated from a dilute slurry, as described in
The soil was obtained from the M.I.T. campus,
Appendix A.
air dried and ground, and mixed with salt water (16 g/l
to form a slurry which was then consolidated one2
Specimens
dimensionally in a large cell to 1.5 kg/cm .
NaCl)
were trimmed from this large batch which had an average
water content of 32%, a void ratio of 0.93, and a degree of
saturation of about 99%.
This soil is a silty clay with a Unified Soil classification of CL.
Table I lists its mineralogic composition,
Atterberg limits and some engineering properties.
size distribution curve is plotted in Fig.
The grain
1 (for the soil
after grinding and after being scalped on a No. 200 sieve).
2.3
Equipment and Related Problems
2.3.1
Electrical Equipment
The transducer was a Dynisco Model APT 25 with a
pressure range of 0 to 200 psia excited by an Allstate 6 volt
-11-
The millivolt output was measured by a
wet cell battery.
VTVM vacuum tube voltmeter model 1477 by Daystrom, Inc.,
Weston Instrument Division.
A full description of the equipment and problems related to their use are presented in Appendix B.
2.3.2
K
Cell
0
Since a flat surface was required, a 2 inch square
cell with a height of 1 inch was made out of 3/4 in. brass
stock (see Fig.
2).
When the cell was designed no provisions were made
to clamp the cell to the bottom stone or to have the dial
supports rigidly connected to the cell.
Therefore changes
in height of the soil could not be measured with a high
A standard platform scale loading frame
degree of accuracy.
(Fig. IX-3 of Lambe, 1951) was used to apply the loads.
One of the main problems in using pressure transducers in this manner is in machining the parts so that the
transducer face will align perfectly with the plane surface
which comes into contact with the soil.
There are three
criteria to meet:
(a)
The transducer face is not recessed or pro-
truding;
(b)
The transducer face is perfectly parallel
with the plane surface;
There is not a large gap surrounding the transAs a rough
ducer face, i.e., less than .0005 in.
guideline, one should not feel any irregularity when
(c)
moving one's finger across the transducer face if
the alignment is proper.
-12-
2.4
Test Procedures
All testing was carried out in a constant temperature
room ( l 0 C)
to help eliminate changes in battery voltage and
in soil properties.
2.4.1
Calibration of Pressure Transducer
The transducer was calibrated both in and out of the
K
cell using the procedure outlined in Appendix B.
Both
calibrations were made to see if the very close tolerances
of the transducer in the cell would affect its calibration,
because in future designs it might be impractical to calibrate the transducer in place.
The results showed the
calibrations to be identical.
Typical calibration results are given in Tables II
and III.
2.4.2
Trimming Soil Sample
Individual test specimens were cut from half moon
chunks of the consolidated batch (see Appendix A)
by using
a wire trimmer wherein four individual wires formed a
square.
The square was a little larger than the K
cell so
that there was a tight fit between the soil and the cell
walls.
The soil was placed in the cell by sliding the cell
down over the soil specimen.
Finally the top and bottom
was trimmed flush with the cell with a wire saw.
2.4.3
Loading Sequence
The loading sequence deviated from the standard procedure of doubling the load,
in that at higher pressure
(above 4 to 8 kg/cm ) the pressure was increased or decreased
2
This enabled more K readings to be taken.
by 2 kg/cm .
There were two load-unload cycles in the test and each
-13-
increment was left on for at least 24 hours.
2.4.4
Measurements
Three measurements were taken: vertical stress on the
soil (av);
horizontal stress
(ah)
from the transducer;
change in height of the sample during loading.
and
The vertical
stress was assumed to be equal to the vertical applied load
The change in height of
divided by the area of the cell.
the sample was obtained by a 0.0001 in. per division Ames
dial which, as previously mentioned, was not securely attached
to the cell.
This fact could have caused inconclusive mea-
surements, although during testing there did not seem to be
any significant errors.
The procedure described below was used to obtain these
measurements:
(a)
One day before the soil was to be placed in the
cell, all of the electrical equipment was connected
and turned on, with the transducer screwed into the
cell.
On the following day the MV reading of the voltmeter was taken to establish the zero reading, i.e.,
(b)
MV .
The electrical connection to the transducer was
then disconnected (Fig. 2)
to facilitate the place-
ment of the soil in the cell.
After the soil was placed in the cell the
transducer was reconnected and the K 0 cell and asso(c)
ciated parts were placed in the loading frame as
shown in Fig. 2.
(d)
2
Before applying a load increment of 1/8 kg/cm
to the soil, the following items were performed
rapidly: Water was added to the container; a tare
reading on the platform scale was taken; the dial
-14-
indicator was set, and the millivolt change was recorded for the calibration resistor.
During each load increment, dial and MV readings
(e)
were taken at time intervals normally used in consolidation testing.
Prior to each load increment the MV change due
to insertion of the calibration resistor was recorded
(f)
to re-establish the calibration factor for the next
increment of load and to see if the final pressure
reading had to be corrected.
2.5
Test Results
Test results at the various vertical stress increments
are presented in Table IV.
From this table the following
plots were made:
(1)
vs.
Volumetric strain vs. vertical stress (AH/H 0
Ov) - Fig. 3.
Vertical stress vs. horizontal stress (v
(2)
h)
(3)
-
vs.
Fig. 4.
Coefficient of earth pressure at rest vs.
overconsolidation ratio
O.C.R.)
-
Fig.
(h
v vs.
/
v or
vs.
5.
The results of other consolidation tests on similarly
prepared BBC with different ring sizes and/or type of ring
This figure shows that
lining are also plotted in Fig. 3.
the volumetric strain during loading is higher in the K
test.
This fact suggests that the sample had more disturbance and/
or that soil was squeezed out of the cell since the top stone
was not recessed in the cell at the start of the test as it
was in the other tests.
When comparing the plots in rebound,
the slope at an O.C.R. of 16 is smallest in the K
factor of about 1.6.
test by a
This suggests that there was more fric-
tion in the K 0 cell than in the other tests.
-15-
When the data are plotted with av vs.
solidated clay, with K
can be established for normally con= 0.48.
This figure also shows that
as the sample is rebounded from a maximum past pressure (a
and as the sample becomes more overconsolidated, K
and eventually becomes greater than 1.
shown in Fig. 5 where K
)
a line representing K
h in Fig. 4,
increases
This relationship is
is plotted against the O.C.R. to a
Fig. 5 also shows that there is a linear relation-
log scale.
ship between K
and log O.C.R.
for an O.C.R. from 1 to 10,
but after an O.C.R. of about 10, K
A maximum K
0
increases very rapidly.
value of 4.6 was measured at the maximum O.C.R.
of 96.
2.6
Comparison with Other Results
Jackson (1963) obtained a K
value of 0.50
similarly prepared normally consolidated BBC.
0.04 for
He used a
triaxial cell (Fig. 6) where the lateral strain was maintained close to zero by controlling the volume of mercury
in a chamber which totally confines the sample and top
loading cap.
Several investigators have reported relationships
between values of K 0 for normally consolidated soils and the
effective stress friction angle,
Simons
P.
Bishop (1958) and
(1958) found good agreement between measured and pre-
dicted values using Jaky's
1-sin T.
(1948) original expression, K0 =
Brooker and Ireland (1965) found that the empirical
relationship K
= 0.95-sin 4 better fit their experimental
data on five clays of low to high plasticity.
Application of the relationship K 0 = 1-sin 4 to BBC
yields K
chosen.
= 0.46 to 0.55 depending upon the value of S
Table V presents values of
compression tests.
W
obtained from triaxial
Values of T vary depending upon:
-16-
Which criteria of failure is used, i.e., maximum obliquity or maximum stress difference;
(1)
(-ah /'v)
at consolidation;
(2)
The value of K
(3)
Type of shear test, i.e., drained or undrained.
When these values are compared with the average K0
value of 0.48 obtained in this investigation, one can only
state that this type of K test yields values which seem to
be reasonable.
There are no other K 0 data on overconsolidated BBC.
The data can only be compared with trends which other investigators have found.
Figure 7 presents a plot of K
versus
overconsolidation ratio to a log scale for:
BBC from this investigation;
Three clays of low to moderate plasticity from
(1)
(2)
Brooker and Ireland (1965).
They employed an oedo-
meter in which a portion of the cell ring was replaced by a steel membrane covering a pressure
chamber filled with oil.
An automatic control device,
actuated by electrical strain gauges on the steel
membrane, controlled the oil pressure such that there
This pressure was equated
was zero lateral strain.
The
to the lateral stress acting on the sample.
vertical stress was carried in increments up to a
value of 2200 psi
(155 kg/cm ) and then reduced in
increments to zero;
The Weald Clay from Henkel and Sowa (1963),
(3)
who controlled the lateral strain in a triaxial
cell.
Their maximum vertical stress was about 12
kg/cm2
One notes that the relationships for the Weald Clay
between K
and O.C.R.
from the two sets of investigators
showed a significant difference.
-17-
This difference could have
been caused by the different experimental procedures, by
the difference in stress level, and/or by slight differences
in soil properties.
The results for BBC obtained in the K
cell follow
0
the same general trends as observed by other investigators
on clays of similar plasticity.
Hence the cell again appears
to yield reasonable data.
2.7
Discussion of K
Cell
In the design of a K
0
cell, the two most important
factors to consider are side friction and the rigidity of
the cell and transducer.
These two items will be discussed
separately.
To measure K
0
properly there should not be any side
friction, but inherently there has to be some side friction
in this type of cell.
(1)
Therefore, several questions arise:
How does this friction, which causes shear
stresses on the transducer's face, affect the transducer in its ability to measure normal stresses?
(2)
To what extent does side friction cause the
actual value of lateral stress to deviate from the
true K
value for no side friction?
0
(3)
What is the effect of side friction on the
vertical stresses on the top and bottom of the
sample?
The amount of side friction can be reduced by lining
the cell walls with teflon and/or by decreasing the height
to width ratio.
However, further research is required to
answer the above questions.
For example, the amount of side
friction could be varied by changing the roughness of the
cell walls and noting the effects on measured K
0
-18-
values.
Another procedure would measure the coefficient of friction
between the wall and the soil and then use this information
to compute the effect on K
0
trated in Fig. 8.
in K
0
from the Mohr's circle, as illus-
The simplified analysis shows a reduction
from 0.48 to 0.42 for a coefficient of friction of 0.31
along the walls of the cell.
Regarding the influence of side friction on vertical
stresses, one could measure the vertical force in the oedometer ring and thereby compute the average vertical stress
on the bottom of the sample, as was done for the study of
compacted soils (M.I.T., 1963).
They found large differ-
ences in top and bottom stresses, especially for heavily
overconsolidated samples.
To measure K
0
movement of the soil.
properly there should not be any lateral
In this case both the confining ring
and the transducer's diaphragm should be absolutely rigid.
Since this is impossible, allowable movements have to be
chosen so that the measured K
0
value is very close to the
"true" value (neglecting friction) •
In choosing these allow-
able movements, one would not only know how the flexibility
of the cell and transducer affects the measured value, but
also how the combined movements affect the measured value.
In determining the allowable wall movement of the
cell, one approach would be to first determine the wall
movement that would cause an active pressure case, and then
design the cell to have a movement which is one tenth to one
hundredth of this value.
In sands an active case of ob3
tained when there is a strain of about 5 x 10- , where the
strain is the lateral wall movement divided by the height
of the sample.
There is very little, if any, published
data on what strain causes an active case in clays, but one
could assume it would be larger than for sands.
Therefore,
a wall movement causing a strain of less than 1/10 of
-19-
5 x 10 3 should be adequate in measuring K
in clays.
Deflection measurements were not taken when hydrostatic water pressures were applied to the cell so an accurate estimate of the deflection of the walls cannot be
quoted.
The calculated deflections, making many simpli-
fying assumptions, is of the order of 0.0004 inches at the
2
maximum horizontal stress of about 6 kg/cm2.
This gives a
strain of 4 x 10 4, which is probably adequate.
In determining the allowable deflection of the transducer's diaphragm there is some literature which discusses
the effect of the rigidity of the gauge on the pressure which
it measures in relation to the assumed applied pressure.
Trollope and Lee (1961)
showed that the gauge can be more
flexible when it is used to measure pressures in clay than in
sand.
They concluded that to measure clay pressures against
a plane surface when using a circular measuring cell, one
should use two design criteria.
These are:
(1)
at maximum
design pressure, the ratio of central deflection to the diameter of the gauge should be less than 1:2000;
(2)
the ratio
of central deflection (dA) to the change in applied pressure
(dp) should be less than 10 5 in./psi.
Therefore, if the
gauge meets these requirements it should measure the pressures accurately providing other effects,
such as seating,
do not five intolerable errors.
For the Dynisco transducer used in these tests,
the
ratio of central deflection to diameter at maximum measured
pressure was approximately 1:3000 and the ratio of dA/dp was
approximately 1.75 x 10-6 in/psi.
Therefore,
the trans-
ducer should have an adequate amount of rigidity to measure the soil pressure accurately.
-20-
Chapter 3
CALIBRATION OF PRESSURE TRANSDUCER
WITH A SOIL PRESSURE
3.1
Introduction
This investigation was aimed at the following question: If a uniform soil pressure acts on a rigid planar
surface, will a pressure transducer inserted into this surface measure the correct pressure?
Because of the diffi-
culty in actually achieving a uniform soil pressure, two
methods of pressure application were employed in order to
study the effects of variable voundary conditions.
3.2
Equipment
3.2.1
Disk
The circular disk with the transducer in its center
It was
was made of stainless steel and is shown in Fig. 9.
machined with great care so that the transducer would fit
properly, but because the transducer was out of shape one
edge of the transducer's face was 5 ten thousands of an inch
above the disk's surface, while the opposite edge was 5 ten
thousands below the disk's surface.
A teflon sheet
(0.005 in. thick) was bonded to the
disk, but not to the transducer's face, with a very thin
film of flexible epoxy.
3.2.2
Electrical Equipment
The transducer was a Dynisco Model APT 25 with a
pressure range of 0 to 200 psi, excited by an Allstate 6
The millivolt output was measured by
volt wet cell battery.
a Keithley or an Electro Scientific Industries voltmeter.
description of these items is given in Appendix B.
-21-
A
3.2.3
Pressure Cells
Two types of cells were used to apply the soil pressure to the disk.
The first was a standard fixed ring con-
solidation unit in which the disk with the transducer became the top cap.
This unit is shown in Fig.
10.
the ring was lined with teflon to reduce friction.
Note that
The
second was a Norwegian triaxial cell which had been modified
to accommodate the disk with the transducer.
is shown in Fig.
3.3
This set up
11.
Test Procedures
All testing was carried out in a constant temperature
room ( 1*C).
3.3.1
Calibration of Pressure Transducer
The transducer was calibrated both in and out of the
disk, with and without the teflon sheet on the surface.
This was done by the procedure outlined in Appendix B, except when the transducer was in the disk.
In this case,
the disk was placed in the triaxial cell and the pressure
was applied by an air regulator.
The results of each cali-
bration proved to be practically identical.
Typical results
of a calibration are given in Table III.
3.3.2
Trimming Soil Sample
The same soil that was used in the K 0 tests was
trimmed to a diameter of about 2.78 inches using a procedure similar to that described in Chapter IX of Lambe
(1951).
The height of the samples was about 0.5 inches.
3.3.3
Oedometer Unit
In a preliminary investigation it was found that
-22-
66
eccentricity of the load on the top cap was a major problem.
Therefore, extreme care was taken when this unit was placed
in the loading frame to prevent this eccentricity.
Filter paper was placed between the soil and the disk
to facilitate removal of the soil from the disk.
The pres-
sure was applied by increasing or decreasing the axial load
in 10,
50, or 100 pound increments (100 lbs. exerted a pres-
sure of about 17 psi).
The load on the soil was cycled
during the test, i.e., the load was reduced to zero and then
reapplied in the above mentioned increments.
Each load was left on for at least 24 hours.
this time,
During
readings were taken on the transducer and sample
height to ensure that an equilibrium condition was obtained.
Loads left on for longer periods of time did not cause any
significant change in the measured pressure.
3.3.4
Triaxial Cell
The trimmed sample was placed on the disk and enclosed in a specially made latex membrane, trying to entrap
A rubber band wrapped around the
as little air as possible.
disk a few times sealed the membrane.
The cell pressure was applied by air pressure using
a Nullamatic air regulator which had a sensitivity of about
To prevent air diffusion through the membrane, the
The pressure was applied
system shown in Fig. 12 was used.
1/8 psi.
in 5 to 10 psi increments.
As in the oedometer test, the
pressure was cycled during the test and each increment of
During each inpressure was left on for at least 24 hours.
crement, transducer and volume change readings were recorded.
3.4
Test Results
The data are presented as a ratio of the measured
-23-
pressure to the applied pressure versus the applied pressure,
i.e.,
P /P
versus P
The data from the oedometer test and
.
the two triaxial tests are summarized in Tables VI, VII, and
VIII, and are plotted in Figs. 13 through 15.
3.4.1
Oedometer Results
Figure 13 shows the ratio of Pm
a versus Pa for the
oedometer test with and without filter paper placed between
This figure shows the following gen-
the soil and the disk.
eral trends:
During loading with filter paper:
When the applied pressure was small (less than
about 10 psi), the error was large, with Pm/Pa greater
(1)
than one.
(2)
At applied pressures greater than 20 to 40 psi,
a remained relatively constant with
the ratio of Pm
a small difference of less than 5%.
During loading without filter paper:
(1)
The ratio of Pm Pa was always less than one,
with a maximum difference of 6%.
During unloading:
(1)
a increased and approached a
The ratio Pm
value of 1.25
0.1 at overconsolidation ratios ex-
ceeding 2 to 3.
In summary, the measured pressure was close to the
applied pressure (within 6%)
during loading, providing the
applied pressure was greater than about 30 psi.
But during
unloading, the measured pressure became much higher than the
At zero
applied pressure, with a difference as high as 35%.
pressure, the measured pressure was essentially zero (note
-24-
that this is not shown in Fig. 13).
3.4.2
Triaxial Cell
The test results (P /P
versus Pa)
from two cycles of
loading for the disk with and without a teflon sheet are
presented in Figs. 14 and 15 respectively.
The following
trends occurred:
(1)
Disk without teflon covering:
During initial loading the ratio PM
a either
increased or decreased (depending on the cycle)
as
the applied pressure was increased from 5 to 20-35
psi, and then remained constant at Pm
1.12 to 1.15.
a equals
During unloading, the ratio decreased
and eventually became equal to 0.8-0.9.
(2)
Disk with teflon covering:
During initial loading the ratio increased
substantially on the first cycle to about unity,
whereas during the second cycle Pm
tween 1.01 and 1.08.
a varied be-
During rebound, both cycles
showed a large reduction in the ratio, which became
as low as 0.67.
3.4.3
Summary
When the pressure was applied by loading the disk in
the oedometer unit,
the measured pressure was generally close
to the applied pressure
(0 to 6% difference) during loading,
but during unloading the measured pressure became substantially larger (15 to 35%) than the applied pressure.
In the case of the uncovered disk inside the triaxial
cell,
the measured pressure was greater than the cell pres-
sure by 10 to 15% during loading at the higher presssures.
When the disk was covered with a teflon sheet,
-25-
the measured
pressure was only about 3% higher.
However, during un-
loading, both with and without the teflon, the measured
pressure became much less
3.5
(35%) than the applied pressure.
Discussion of Test Results
Most of the test results can be explained if the
applied pressure is not uniform across the disk and transducer because of the following boundary conditions:
arching within the soil,
local
seating effects, and friction along
the walls of the oedometer ring, or,
in the case of the tri-
axial cell, along the surface of the disk.
3.5.1
Seating and Arching Effects
On the first cycle of loading all of the tests started
out with initial measured pressures which were either much
too high or too low.
This effect was probably caused by
seating effects and local arching within the soil because
the soil would not be perfectly flat and because the transducer was not perfectly aligned (see Fig.
9).
Although both tests without the teflon gave high initial pressures, while the one test with teflon gave a low
initial pressure, one is not sure whether this change is
caused by the teflon or that the seating effect can give
either a high or low value.
The fact that the ratio Pm
a becomes nearer unity
with increasing applied pressure during the first cycle of
loading is probably explained by a decrease in the effects
of seating and local arching.
These effects appear to nearly
disappear when the applied pressure becomes greater than about
the maximum past pressure, in this case about 20 psi.
The
clay becomes more "plastic" and is capable of flowing into
voids between the soil and the disk.
-26-
It should be pointed out
-
-
that seating and arching effects could vary from test to
test and, of course, from soil to soil, but that these effects
should reach a minimum once the soil reaches a "plastic"
state, provided the transducer alignment and sample trimming
are within reason.
3.5.2
Frictional Effects
Even without seating effects the pressure is not uniform across the disk because friction is present which
causes a change in the stress distribution across the disk.
Oedometer Test
The side friction on the walls of the ring during
loading causes the pressure in the center of the disk to be
lower than the average applied pressure because part of the
The estimated change
applied load is taken up at the walls.
in stress distribution is shown in Fig. 16a.
During unloading this side friction acts in the opposite direction which causes the soil to form an arch with
Figure
the contact area between the soil and disk reduced.
There16b shows the assumed change in stress distribution.
fore the ratio Pm /Pa would increase and become greater than
unity during unloading.
On the second cycle of loading the initial measured
pressures were very high. This could be explained if the
side friction on rebound caused the soil surface to become
rounded. Therefore, the contact area is smaller and the
The reastresses are higher at the center of the top cap.
son why the test without filter paper did not show these
high initial mreasured pressures is unknown.
Triaxial Test
In this case there is no wall friction, but because
-27-
the soil wants to consolidate isotropically (have strain in
both the horizontal and vertical directions)
shear stresses
are developed across the surface of the disk.
During loading these shear stresses caused the measured pressure to be higher in the center as shown in Fig.
17a, but during unloading the opposite is true, see Fig. 16b.
When the disk is covered with the teflon sheet these
shear stresses would be reduced, causing the ratio of PM a
The test results showed this to be
to be closer to unity.
true during loading but not during unloading.
The reason
why the teflon did not help the ratio be be closer to unity
during unloading is not known.
3.6
Conclusions and Recommendations
The test results indicate that:
(1)
It is difficult to apply a uniform soil pres-
sure against a plane surface.
(2)
The pressure measured by the transducer cannot
be related accurately to an average pressure unless
one investigates the effects of the boundary conditions.
(3)
During unloading the difference between the
measured and the applied pressures is much larger
The cause for this large
than that during loading.
difference is not fully understood.
(4)
Seating effects are a function of the stiff-
ness of the soil relative to the applied pressure;
the care with which the transducer is placed in the
plane surface; and how the soil is placed in the
testing apparatus.
(5)
The effects of seating on the first cycle of
loading are thought to be eliminated when the applied
-28-
-
~
pressure is about 1.5 times the maximum past pressure
of the soil.
(6)
The stress distribution across the top stone
in an oedometer unit is thought to be close to uniform
when the soil is normally consolidated or being reloaded, but far from uniform during unloading.
(7)
The placement of a thin sheet of teflon across
the surface of the transducer and the plane surface
apparently does not affect the accuracy with which
the transducer will measure the soil pressure.
(8)
A flat face rigid pressure transducer,
as
used in this investigation, probably measures
accurately the soil pressure which acts across and
directly surrounding the transducer once seating
effects are eliminated.
Further testing is needed to study seating effects,
and how different boundary conditions affect the measured
and applied pressure.
Although all of these studies would
not be directly related to the measurement of K0 , they would
be helpful in understanding how uniform or non-uniform the
applied stresses are in different types of testing equipment.
Finally, a testing program is required to study the
effects of soil moving across the transducer's face, as
occurs in the K
cell.
In this case any protrusion or re-
cession of the transducer could greatly affect the measurements.
However, a sheet of teflon across the plane sur-
face would help to eliminate large errors.
-29-
Chapter 4
SUMMARY AND CONCLUSIONS
A K
cell has been developed in which the lateral
pressure is measured by an electrical pressure transducer.
Test results on remolded BBC indicate that K 0 in the normally consolidated range is 0.48, which is in good agreement with other K 0 data on similar BBC.
dated range, K
In the overconsoli-
increases with increasing O.C.R. and becomes
greater than one at an O.C.R. of about four.
A testing program was initiated to see if this type
of transducer would measure the soil pressure acting across
its face and the area directly surrounding it with a high
degree of accuracy.
This program consisted of applying
pressure to a thin soil cylinder with one face covered by
a stainless steel disk which had a transducer inserted in
its center.
The soil pressure recorded by the transducer
indicated that the applied soil pressure was not uniform
But most of the transducer's
across the stainless steel disk.
readings seemed reasonable because the systems used to apply
this soil pressure had inherent boundary conditions which
would cause this pressure to be non-uniform.
Therefore, it
is the opinion of the author that the transducer measures
the soil pressure directly surrounding the transducer with a
higher degree of accuracy than the assumption that the soil
This may never be proven
pressure on the disk is uniform.
since it is next to impossible to apply a truly known soil
pressure across a plane surface with a transducer in it.
K
There are three basic problems when using this type of
First, there is the problem of rigidity of the cell
cell.
and transducer.
Test
results by others suggest that the trans-
ducer is rigid enough, and as previously discussed (Section
-30-
(2.7) it was concluded that, providing the wall strain is
less than 5 x 10 -,
the value of K
this small amount of strain.
would not be affected by
However, this number is an
engineering approximation which needs further investigation.
Secondly, the main problem with wall friction is most
likely not how it influences the performance of the transducer but rather how this friction causes the horizontal
stress to deviate from the true K
value.
The author pro-
poses that this deviation is caused by two factors:
(1)
Wall friction negates the assumption that the
normal and horizontal stresses are principal stresses.
(2)
Wall friction affects the uniformity of applied
stresses along the top and bottom of the sample, which
must also affect the normal stress applied and measured against the walls of the K
To correct for item (1)
outlined in Fig.
8.
cell.
the author proposes the method
For item (2), no correction is proposed
but two general statements can be made based on the data obtained from placement of the transducer in the top cap of
an oedometer unit.
The normal stress on the walls is probably not
affected very much when the soil is normally con(1)
solidated since the stress on the top cap remained
fairly uniform, e.g., about 5% deviation.
(2)
The normal stress on the walls could be
greatly affected when the soil is highly overconsolidated since the stress on the top cap was not even
close to uniform, e.g., 15 to 35% deviation.
In any case further investigation, as pointed out in Section
2.7,
is required to develop a better understanding of the
problem.
-31-
-1
since there is soil movement across the transducer's face, due to the soil being consolidated, the question arises: does this affect the transducer measurements?
Thirdly,
This problem has not been investigated, but providing the
transducer is flush with the plane surface or covered with a
thin teflon sheet, it is believed that there should not be
any significant amount of error.
In conclusion,
two basic questions have to be asked
and answered relative to the future development and use of
this type of K
cell.
cell better than or equal to
One: Is this type of K
other types of K
cells,
such as an oedometer unit in which
the hoop strain of the confining ring is measured to derive the lateral stress, and an oedometer unit similar to
the one developed by Hendron
(1963), and triaxial tests
such as developed by Jackson (1963) or Bishop and Henkel
(1962)?
In the triaxial type K
cells the wall friction is
eliminated, which is a distinct advantage, but there are
First, it is more difficult to
three major disadvantages.
run and requires either constant attention or elaborate
Secondly, there is continual lateral movements
of the soil sample, i.e., relaxation, then compression. Although these movements can be small (diameter change of about
3 x 10~4 inches) they could cause considerable errors when
automation.
the sample is overconsolidated since there would be a tendency to get a high reading when recompressing the sample
by this amount because the soil is "rigid" compared to the
In the normally consolidated range
confining pressure.
this should not be a major problem since the soil is in a
Thirdly, Bishop (1958) pointed out that
"plastic" state.
in this type of test it is critical that the specimen be
-32-
honogenous regarding its stress-strain characteristics and
that the pore pressure should be uniform throughout the
specimen.
The other types of oedometer units would have the
same problem with wall friction.
Hendron's
(1963) unit has
the advantage that it can go to higher pressures without
losing sensitivity in the low pressure range, that it measures an average pressure, not just a pressure at one point,
and that it has a symmetrical shape.
Its disadvantages are
that it is probably more difficult to operate and is certainly more expensive to build.
This brief discussion leads to the conclusion that a
K
cell using a transducer has the advantage of being sim-
ple, but the results are affected to an unknown degree by
wall friction.
Conversely,
the triaxial K
cell has the
advantage of no side friction, but the relaxation-recompression and non-uniform pore pressure dissipation can also
affect the results and the test is difficult to perform.
Two:
K
Is it worth the effort to perfect this type of
cell by developing a better understanding of how wall
friction and/or wall deflection affects the measured value
of K ?
The answer depends upon the usefulness of K
values
to the soil engineer and whether or not this research yields
additional insight into other problems in soil mechanics.
K
(1)
is usually determined for:
the evaluation of Poisson's ratio and earth
pressures on buried rigid structures.
(2)
laboratory shear strength determinations in
which the soil should be anisotropically consolidated
before shear to represent in situ strength properties.
(3)
aiding the soil engineer in his endeavor to
understand soil behavior.
-33-
These measurements are often required but small deviations
in K
generally have a minor effect compared with the over-
all engineering problem.
As pointed out, in the normally
consolidated range this and other K
cells measure K
within
a reasonable range but in the overconsolidated range this
type and other K
unknown errors.
cells most likely have the largest and
Therefore, in the normally consolidated
range further investigation into wall friction, etc., is
not required, but if good K
values are to be determined in
the overconsolidated range further investigation is needed.
Furthermore, this research would lead to a better understanding of wall friction,
its detrimental effects on consolidation
and direct shear tests,
and a better understanding of the
measurements of earth pressures against a retaining surface.
-34-
Chapter 5
REFERENCES
Bishop, A. W. (1958), "Test Requirements for Measuring the
Coefficient of Earth Pressure at Rest," Proceedings,
Brussels Conference on Earth Pressure Problems, Vol.
I, p. 2.
Bishop, A. W. and Henkel, D. J. (1962), "The Measurement
of Soil Properties in the Triaxial Test," Edward Arnal,
London.
Brooker, E. W. and Ireland, H. 0. (1965), "Earth Pressures
at Rest Related to Stress History," Canadian Geotechnical Journal, Vol. 2, No. 1.
Hendren, A. J. Jr. (1963), "The Behavior of Sand in OneDimensional Compression," Ph.D. Thesis, University of
Illinois, Urbana, Illinois.
Henkel, D. J. and Sowa, V. A. (1963), "The Influence of
Stress History on the Stress Paths Followed in Undrained Triaxial Tests," Laboratory Shear Testing of
Soils, ASTM Special Technical Publication No. 361,
pp. 280-292.
Jackson, W. T. (1963), "Stress Paths and Strains in a
Saturated Clay," Master's Thesis, M.I.T., Unpublished,
Cambridge, Massachusetts.
Jaky, J. (1948), "Pressure in Silos," Proceedings, Second
International Conference on Soil Mechanics and
Foundations, Rotterdam, Vol. 1, pp. 103-107.
Ladd, C. C. (1965), "Stress-Strain Behavior of Anisotropically Consolidated Clays During Undrained Shear,"
Proceedings,
Sixth International Conference on Soil
Mechanics and Foundation Engineering, Montreal, Vol.
I, p. 282.
Lambe, T. W.
(1951), "Soil Testing for Engineers," John
Wiley and Sons, Inc.,
Lambe,
T. W.
New York.
(1964), "Methods of Estimating Settlement,"
Journal of the Soil Mechanics and Foundation Division,
ASCE, Vol. 90, No. SM5, Proc. Paper 4060, September,
1964.
-35-
Lambe, T. W. and Martin, R. T. (1953), "Composition and
Engineering Properties of Soil," Proceedings of
Thirty-Second Annual Meeting of the Highway Research
Board,
M.I.T.
January.
(1960),
"Pore Pressure Measurements during Transient
Loading," The Response of Soils to Dynamic Loadings,
Report No. 5, Dept. of Civil Engineering, November.
M.I.T. (1961), "Effects of Rate of Strain on Stress-Strain
Behavior of Saturated Soils," The Response of Soil to
Dynamic Loadings, Report No. 6, Dept. of Civil Engineering, April.
M.I.T. (1963), "Effective Stress versus Strength: Saturated
Fat Clay," The Response of Soil to Dynamic Loadings,
Report No. 16, Dept. of Civil Engineering, April.
M.I.T. (1963), "Engineering Behavior of Partially Saturated
Soils," Phase Report No. 1, Department of Civil Engineering, May.
Simons, N. E. (1958) Discussion on: General Theory of Earth
Proceedings, Brussels Conference on Earth
Pressure.
Pressure Problems, Vol. 3, pp. 50-53.
Stevens, S. F. (1953), "Effects of Times of Consolidation and
Rebound on the Shearing Strength of Clay," M.S. Thesis,
M.I.T., Unpublished.
Taylor, D. W. (1942), "Research on the Consolidation of
Clays," Department of Civil and Sanitary Engineering,
M.I.T., Serial No. 82.
Trollope, D. H. and Lee, I. K. (1961), "The Measurement of
Soil Pressures," Proceedings, Fifth International Conference on Soil Mechanics and Foundation Engineering,
Vol. II, Paris.
-36-
TA5LE I
COMPO SITIOA/ ANP EANG?/EEPIN&
81e
OF oosToN
PROPERTIES
CLAY
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dh
Il/ite - f5 Yo to 70Y
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45-Y
Quartj - 20 %to 340 %
I/'o;c lati/f 22%
Composition
MnerQ/ogc
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Refertetcos :- lreveo.4, S.f* M/f:5)
5peCille PreW/Ity - e 77z a 01g
fe iyooo NX,.r., (1!5)
1,70rhe, 7.
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FIG. I
GRAIN SIZE DISTRIBUTION
FOR 0OTON BLUE CLAY
MIT
CLASSFICATION
SAND
COARSE MEDIUM
*
__
_
FINE
SILT
COARSE MEDIUM
FINE
CLAY
COARSE MEDIUMJ FINE
___
__
_
_____
90-so -T7O
S 60
050
4c:40
z
10
-
153020--
0 -10
1.0
0.01
0.1
DIAMETER IN MM
0.OOI
0.0001
FY 1
0
ce//
PIA
CRO5:5-.OYE, DAR FOR LOA D/A/
/
Li
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_____________________________________
Coefficict sf Orft/ "
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FIG.
A
?Uu
-52-
CES
L 1
m&L
(MT)
I
3.0 1-
3/
--- 0---
Goove Lake Roave,
r
w /.
2.0
Ar.
v
(ropet I./wle.,V5)
('eo*e/ ( Soa,
WaE/d C/oy, RZ. - 2#
iee/d C/oy,
f
20. % (rw*er
p
/
oston 5/u
. Clay. r. A/37
K, Celf
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/65)
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c
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f re/eod, /f65)
kwm
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a/
for .5eVera
/(p
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32
64-
Fil. d
frictio# ow 1lte of K4
ffect of .5/dc
-
I
measured
1%
F"
4%
KO "Trqg"a-
1
t& a Yb
tv
IFI.Ij
t
m tan
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0
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F/9 9
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42
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PRAINA OE
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TRANSDWCER
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cyc/e
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-
4
a f~
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in psi
90
k
/ 2ft/fT t r/fxi(/ Test Wj
ILi5
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1.03
2, ycle a.O mldem
0.7
AI
0
I0
,to
50
40
p-
60
Applied PrWSSmre in *As;
10
80
Fig. /6
Effect of Frdioi ow Sfrels pisitribution
/,, Ctdo neter Ted.s
Loading ~
%
-
mEA~V4sc
P/FPERENCFr
-
XsOszg
4CrTUAL
35/
Pl,'/rCERWC
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1
0
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b
1si
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fifect- of fr/Ic tn# on 5r5
plstnpatlotl Triaxial
(a) Loud,,,9q
Awmrv~ AcTLJA.
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Aecost/Rec
(&,) 14vodiP79
A65ufiff
A4rUAL
5;#gAe
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I]
Cai-'- /*as suqc
Appendix A
PREPARATION OF BOSTON BLUE CLAY
The Boston Blue Clay
(BBC) used in this investigation
was obtiined from the M.I.T. campus during construction of
the Materials Building pile foundation in September,
1963.
The soil was removed from a auger which had obtained soil
from a depth of between about 40 to 90 feet.
The clay was air dried and ground up by the Sturtevant Mill Co., Boston, Mass., in an air swept pulver mill
with a dust bag collector.
A grinder was used to break up
the chunks so that 100% would pass through a U.S. Standard
No. 100 sieve.
The one problem encountered with this pro-
cedure arose from the fact that the augered clay contained
rocks and/or lumps of shale which could not be completely
removed prior to grinding and were therefore ground up with
the clay.
The air dried ground clay was formed into a slurry
and consolidated in the large oedometer shown in Fig. A-l
using the procedures described below in the M.I.T. Soils
Laboratory.
Ten kilograms of ground clay are added to 15 liters
of demineralized water with a salt content of 16 g/liter.
The salt is added to help make the soil structure similar
to the in situ clay and to cause flocculation.
The soil is
added while the water is being stirred by a very high speed
mixer in a 40 liter pyrex container.
After mixing for about
an hour, the slurry is allowed to settle overnight.
It is
then remixed and poured through a U.S. Standard No. 200
sieve into another container.
The slurry is again remixed
and allowed to settle for a few days.
After syphoning off
the clear water, the denser slurry is remixed and poured
into a 5 gallon metal container where it is heated while
-64-
stirring to help remove trapped air.
After the temperature
has reached about 70 0 C the slurry is added slowly to the
large consolidometer base unit with a 3-foot lucite chamber,
The chamber and consolidometer unit
as shown in Fig. A-2.
was under a vacuum of about 75 cm of mercury before the
slurry was added.
During addition of the soil, the rate of
soil input is varied to keep the vacuum greater than 73 cm
of mercury.
The process takes about one hour.
After the slurry is placed,
a partial (<4" Hg) vacuum
is applied to the bottom drainage valve in order to consolidate the slurry so that its height will fall below the top
of the base unit.
The lucite chamber is then removed and
the piston put in place after applying a slight vacuum to
the piston's drainage lead.
Finally, when the top of the
piston support is below the top of the confining ring, water
repellent transformer oil is added,
the cover is attached
and pressure is applied in the following increments: 0.5,
2
1, 1.5 kg/cm .
A plot of dial change vs. log time is made
to ensure that each increment reaches 100% primary consolidation before the increment is changed.
Following consolidation at 1.5 kg/cm
2
for not less
than 5 days, the soil cake (9.5 in. in diameter by about
5.5 in. high)
is extruded and cut into eight half-moon
chunks with a height of about 1-1/4 in.
These chunks are
stored in water repellent transformer oil (Mobilect No. 33)
until
used for testing.
Samples prepared in this manner had an average water
content of 32%, a void ratio of 0.93, and a degree of saturation of about 99%.
Experience has shown that the soil does
not lose a significant amount of water during storage in
the transformer oil.
-65-
Stainless Steel Shaft
Aluminum Pocking Nut
Aluminum Bushing Holder
Teflon Packing
-Thompson Ball Bushing
To Oil-Nitrogen Accumulator
Top Drain
Aluminum Cover
0" Ring Seal
-+-- ----- Oi I
----
Main
Holding
Rod
(4 Used)
Aluminum
Extrusion Rod (3 Used)
0-"UO" Ring Seal
-
...--- Lucite Piston
Bonded Teflon
Porous Stan
"D. Shelby.Tubing
Soi
Lucite Base Piston
Porous Ston
"O' Ring Seal
- -Bottom
Drain
Aluminum Base
Note:
To extrude, relieve pressure, invert consolidometer ;
remove main holding rods and tighten extrusion rods.
Reapply light pressure sufficient to extrude.
FIGURE A-1
SELF-EXTRUDING CONSOLIDOMETER
-65-
I-
Soil Slurry introduced Here
--- To Vocuum Pump
000
I000
-e 3*ft Lucite Deoiring
column
000
Io
\
0
0000
000
Consolidometer
Soil Slurry
//0
,-101
~iY
FIGURE A-2
II
METHOD OF SLURRY PLACEMENT
n7-
Appendix B
PRESSURE TRANSDUCERS
B.l
Pressure Transducers and Associate Instrumentation
B.l.1
Design of Gauge
The electrical pressure transducer employed in this
research (Model APT 25) is commercially available from Dynisco, Division of American Brake Shoe Company, Cambridge,
Mass.
This "Dynisco" gauge consists of a four-active arm
unbonded strain gauge bridge which senses the deflection of
a small rigid diaphragm (see Fig. B-l).
It has an accuracy of 0.25 per cent of its full scale
output and exhibits a maximum nonlinearity and hysteresis
of less than 0.50% of its full scale output.
It is tempera-
ture compensated between the range of -65 to +300*F with a
maximum drift of 2% F.S./100 0 F.
D.C. voltage (6 volts)
When it is excited by a low
the gauge has an output proportional
to the pressure exerted on the diaphragm.
At full pressure
the output is about 25 to 50 millivolts (M.I.T. 1960 and
M.I.T.
1961).
These gauges are extremely rigid.
The diaphragm de-
flection is about 3.5 x 10~4 in. at full-rated pressure.
The deflection of the diaphragm is a number quoted by Dynisco.
B.l.2
Related Electrical Equipment
(1)
Voltage Source
The voltage source for the transducer was a standard
6 volt wet cell battery obtained from Sears and Roebuck Co.
(2)
Voltage Measuring Equipment
Three different types of voltmeters were used to
-68-
measure the millivolt (MV) output of the transducer.
The first one was a vacuum tube voltmeter (VTM) Model
1477 manufactured by Daystrom, Inc., Weston Instrument DiThis voltmeter can measure
vision, Newark, New Jersey.
-
voltages from zero to 1,000 MV on the following MV scales
0 to 2, to 5, to 10, to 20, to 50, to 100, and to 1000 and
has a 1% accuracy of the reading on each scale.
The second type used was a manual digital type voltmeter manufactured by Keithley Instrument Inc.
gital voltmeter, model 6060T,
This 5 di-
can measure voltages from 0
to 500 volts with a sensitivity of 0.01 MV on the most sensitive range and an accuracy of 0.02% or 20 microvolts,
whichever is larger.
The third type used was a portable manual digital
type voltmeter manufactured by Electro Scientific Industries.
This 5 digital voltmeter model 300 can measure voltages
from 0 to 511.10 volts in five ranges with a maximum sensiThe
tivity of one microvolt on the most sensitive range.
accuracy is 0.02% of the reading or one increment on the
most sensitive decode switch.
B.2
Calibration of Pressure Transducers
B.2.1
General
In general the calibration involves establishing a
relationship between applied pressure, measured output voltage, and excitation voltage.
This relationship should in-
clude the excitation voltage because during long term tests,
i.e., lasting more than a day, the battery voltage can change
enough to cause an appreciable error.
There are two different procedures for obtaining this
relationship, which depend upon the type of voltmeter used.
-69-
In both cases the battery excitation voltage of about 6 volts
is connected to the circuit for at least 2 hours before the
calibration is started. Tests have shown that the voltage
changes with time after the battery is connected to the
transducer, but this change becomes minor after about 2
hours.
This effect is shown in Fig. B-2.
The applied pressure is supplied by a dead weight
gauge tester which has an accuracy of 0.1% of the applied
pressure.
The gauge tester, model ML 23-1, is manufactured
by Chandler Engineering Co., Tulsa, Oklahoma.
B.2.2
Calibration when Excitation Voltage is
Directly Measured
Since the digital voltmeter can measure the excitation
voltage directly with a high degree of accuracy, the following equation can be used to establish a calibration constant
(gauge factor = K) for the relation among applied pressure,
excitation voltage, and output voltage, and to determine
unknown pressures once K is found.
mV
mv
P - PV[ m_ 0] K
e
0
where:
unknown pressure
P
=
P0
= known pressure (usually zero at start of test)
mVm
= measured millivolts at new pressure
mV0
= measured millivolts at known pressure
Ve
= measured excitation voltage at unknown
pressure
V
K
= measured excitation voltage at known pressure
= gauge factor derived during calibration where
changes in pressures are known
-70-
K
=
Note:
V0
-APressure
= Ve since the voltage source does not
V
change during the short period required to
calibrate the transducer.
By using this equation and procedure, measured pressures during tests lasting over a long period will be extremely accurate because excitation voltage changes can be
accounted for and the measuring equipment is more accurate
than the transducer.
B.2.3
Calibration when Excitation Voltage is Indirectly Measured
When the Weston voltmeter is used another procedure
has to be used to take into account any voltage changes
because this meter cannot measure the excitation voltage
directly, as in-the case of the digital voltmeter.
The
procedure used is based on the fact that when a resistor is
added across one of the four active strain gauges making up
the bridge circuit, the circuit's output voltage changes
(see Fig. B-1).
The amount of this voltage change depends
on the value of the added resistance, the characteristics
of the transducer, and the excitation voltage.
Therefore, a resistor can be chosen which would
give a change in output voltage equal b the output voltage
change that takes place when a certain pressure is applied
to the transducer.
The calibration procedure is as follows:
(a)
Resistors are chosen which give a voltage
change of about 75% full scale on each scale that
will be used.
(b)
After the circuit has warmed up for 2 hours,
-71-
-U
the voltage changes are determined for different
known applied pressure changes at the unknown excitation voltage of about 6 volts.
During the above, but between pressure increments, the voltage change due to adding the
(c)
calibration resistors to one arm of the circuit is
measured.
From the mV change/psi (from part b)
(d)
mV change for the resistor
and the
(from part c), one can
determine the equivalent value of the resistor in
psi.
After the establishment of an equivalent psi for each
resistor the transducer is calibrated for any desired excitation voltage.
The equation expressing the transducer electrical
output in terms of pressure has the following form:
K
P -
P
o
=
(mV
m
- mV
)
(Weston Voltmeter)
1 AmVs
where:
mVm
= millivolts measured at new pressure
mV
= millivolts measured prior to change in
pressure
AmVs
= change in millivolts due to adding a calibration resistor
K
= equivalent psi of calibration resistor
determined during calibration
P
= new or unknown pressure
P0
= pressure at mV 1 reading (usually zero)
or pressure before new increment of loading
The equation takes into account the change in exciHowever,
tation voltage from one test to another test.
-72-
in battery voltage.
The procedure is outlined below.
After the pressure change is applied, the calibration
If the magnitude of the
measured voltage changes, a new equation is started.
example follows.
mV )K1,
where K
At the start of the test P - P 0 o=
An
(mvm
-
resistor is continually checked.
= Ke/AmVsl.
If AmVsl changes, the pressure change equation becomes: P - P 1 = (mVm - mv2)K2, where
K2 = K /AmVs2.
mv2 is the mV reading when AmVsl is changed,
and P is the computed pressure when AmVsl is changed.
Although this method would take into account excitation voltages it would not have the accuracy of the calibration procedure explained previously because the voltmeter is not as accurate, and there is a human element in
when one decides that AmVs has changed.
The overall accuracy is approximately 0.5 psi when
the excitation voltage can be measured, and about 1 psi
when the Weston meter is used and the excitation voltage
cannot be measured.
Typical calibrations are presented in Tables II
and III.
It should be mentioned that pressure changes can be
measured with a greater accuracy than these values.
-73-
ykemanic Diagram
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-74-
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Appendix C
LIST OF NOTATIONS
K
Coefficient of earth pressure at rest.
0
Ka
Coefficient of active earth pressure.
K
Coefficient of passive earth pressure.
p
a3
Major principal stress.
03
Minor principal stress.
a2
Intermediate principal stress.
BBC
Boston Blue Clay.
Effective vertical stress.
ah
Effective horizontal stress.
AH/H 0
Volumetric strain.
vi
0 cm
Pm
v
)
O.C.R. Overconsolidation (a Ia
Maximum past pressure.
a
Ratio of the measured pressure to the applied pressure.
Pm
Pressure measured by transducer.
Pa
Assumed applied pressure to transducer.
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