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USE OF ELECTRICAL PRESSURE TRANSDUCERS

TO MEASURE SOIL PRESSURE

by

RICHARD SWAN LADD

BSCE, Northeastern University

(1962)

Submitted in partial

of the requirements for

fulfillment

the degree

Master of Science

at the

Massachusetts Institute

1966

of Technology

/7Signature redacted

Signature of Author . . . . . . .. . ...

Department of Civil EngineeringJune 20, 1966

Signature redacted

Certified by ............................... .- - - - -Cetfe0y0 Thesis Supervisor

Signature redacted

Accepted by ............Chairman, Departmental Committee

on Graduate Students

of

~~AL~e

38ABSTRACT

USE OF ELECTRICAL PRESSURE TRANSDUCERS

TO MEASURE SOIL PRESSURE

by

RICHARD SWAN LADD

Submitted to the Department of Civil Engineering on June20, 1966, in partial fulfillment of the requirements forthe degree of Master of Science.

The application of electrical transducers to measuresoil pressures against planar surfaces is described, withemphasis on the determination of the coefficient of earthpressure at rest (K ) for cohesive soils. Data are pre-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. Thesedata were obtained via a square fixed ring oedometer whichhad a Dynisco pressure transducer screwed into one side ofthe cell. Although the observed values of K appear rea-sonable and are consistant with other publis~ed data, thedegree of accuracy is unknown. Attempts to calibrate thetransducer by comparing measured versus applied averagepressures on a planar surface are described. These resultsindicated that the measured pressure is directly related tothe applied soil pressure.

Thesis Supervisor: A. E. Z. Wissa

Title: Assistant Professor of Civil Engineering

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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 prepara-

tion of this thesis.

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TABLE OF CONTENTS

Page No.

Title Page

Abstract

Acknowledgement

Table of Contents

List of Tables

List of Figures

Chapter 1

Chapter 2

Chapter 3

INTRODUCTION

MEASUREMENTS OF THE COEFFICIENT

OF EARTH PRESSURE AT REST (K 02.1 Scope

2.2 Preparation of BostonBlue Clay

2.3 Equipment and Related Problems

2.3.1 Electrical Equipment

2.3.2 K Cell0

2.4 Test Procedure

2.4.1 Calibration of PressureTransducer

2.4.2 Trimming Soil Sample

2.4.3 Loading Sequence

2.4.4 Measurements

2.5 Test Results

2.6 Comparison with Other Results

2.7 Discussion of K Cell

CALIBRATION OF PRESSURE TRANSDUCERWITH A SOIL PRESSURE

3.1 Introduction

3.2 Equipment

3.2.1 Disk

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6

7

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11

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12

13

13

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21

15

16

18

21

21

21

21

Chapter 4

Chapter 5

Appendix A

Appendix B

Appendix C


3.2.3 Pressure Cells

3.3 Test Procedures

3.3.1 Calibration of PressureTransducer


3.3.3 Oedometer Unit

3.3.4 Triaxial Cell

3.4 Test Results

3.4.1 Oedometer Results

3.4.2 Triaxial Cell

3.4.3 Summary

3.5 Discussion of Test Results

3.5.1 Seating and ArchingEffects

3.5.2 Frictional Effects

3.6 Conclusions and Recommendations

SUMMARY AND CONCLUSIONS

REFERENCES

PREPARATION OF BOSTON BLUE CLAY

PRESSURE TRANSDUCERS

B.1 Pressure Transducers and Asso-ciated Instrumentation

B.l.1 Design of Gauge

B.l.2 Related ElectricalEquipment

B.2 Calibration of Pressure Transducer

B.2.1 General

B.2.2 Calibration when ExcitationVoltage is Directly Mea-sured

B.2.3 Calibration when ExcitationVoltage is IndirectlyMeasured

LIST OF NOTATIONS

Page No.

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* in--------------------------------------------

LIST OF TABLES

No. Title Page No.

I Properties of Boston Blue Clay 37

II Typical Calibration of Pressure Trans-ducer using VTVM Voltmeter 38

III Typical Calibration of Pressure Trans-ducer using Digital Voltmeter 39

IV Results of K Test on BBC 40

V Typical Values of Friction Angle for 42BBC

VI Soil Pressure in Consolidation Unit 42

a) With Filter Paper 43b) Without Filter Paper 44

VII Soil Pressure Results in Triaxial Cellwithout Teflon 45

VIII Soil Pressure Results in Triaxial Cellwith Teflon

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LIST OF FIGURES

Figure No.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

Title Page No.

Grain Size Distribution - BostonBlue Clay 47

K Cell 48

Volumetric Strain vs. Log Consoli-dation Stress for Boston Blue Clay 49

Vertical Stress vs. Horizontal Stressin K Test on Boston Blue Clay 50

Coefficient of Earth Pressure at Restvs. Overconsolidation Ratio for BostonBlue Clay 51

Jackson's Triaxial K Cell 52

Ko vs. Overconsolidation Ratio forSeveral Clays 53

Effect of Side Friction on Value of K 540

Disk for Calibration of Transducer 55

Oedometer Unit with Transducer 56

Triaxial Cell with Transducer 57

Pressure System for Triaxial Cell 58

Results of Oedometer Test - Ratio ofP /P vs. P 59

Results of Triaxial Test without Teflon -Ratio of P /P vs. P 60m a a

Results of Triaxial Test with Teflon -Ratio of P /P vs. P 61

m a aEffect of Friction on Stress Distribution inOedometer Test 62

Effect of Friction on Stress Distributionin Triaxial Test 63

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LIST OF FIGURES (Contd.)

Figure No.

Appendix A

A-1

A-2

Appendix B

B-1

B-2

Title Page No.

Self-Extruding Consolidometer

Method of Slurry Placement

Schematic Diagram of Dynisco Gauge

Voltage Change of 6 Volt Wet CellBattery vs. Time

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66

67

74

75

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 of active earth pressure - Ka

(3) Coefficient of passive earth pressure - Kp

(4) Major principal stress - a1(5) Minor principal stress - a3(6) Intermediate principal stress -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, such as in a K0

cell. 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. Inaccuracies could arise from:

(1) 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

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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 re-

quired sensitivity;

(4) To measure the distribution of pressure over

a surface.

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Chapter 2

MEASUREMENTS OF THE COEFFICIENT OF

EARTH PRESSURE AT REST (K )

2.1 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

Appendix A. The soil was obtained from the M.I.T. campus,

air dried and ground, and mixed with salt water (16 g/l

NaCl) to form a slurry which was then consolidated one-2

dimensionally in a large cell to 1.5 kg/cm . Specimens

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 classi-

fication of CL. Table I lists its mineralogic composition,

Atterberg limits and some engineering properties. The grain

size distribution curve is plotted in Fig. 1 (for the soil

after grinding and after being scalped on a No. 200 sieve).

2.3 Equipment and Related Problems


The transducer was a Dynisco Model APT 25 with a

pressure range of 0 to 200 psia excited by an Allstate 6 volt

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wet cell battery. The millivolt output was measured by a

VTVM vacuum tube voltmeter model 1477 by Daystrom, Inc.,

Weston Instrument Division.

A full description of the equipment and problems re-

lated to their use are presented in Appendix B.

2.3.2 K Cell0

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

degree of accuracy. A standard platform scale loading frame

(Fig. IX-3 of Lambe, 1951) was used to apply the loads.

One of the main problems in using pressure trans-

ducers 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;

(c) There is not a large gap surrounding the trans-

ducer face, i.e., less than .0005 in. As a rough

guideline, one should not feel any irregularity when

moving one's finger across the transducer face if

the alignment is proper.

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2.4 Test Procedures

All testing was carried out in a constant temperature

room ( l0 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 cali-

brate the transducer in place. The results showed the

calibrations to be identical.

Typical calibration results are given in Tables II

and III.


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 pro-

cedure of doubling the load, in that at higher pressure

(above 4 to 8 kg/cm ) the pressure was increased or decreased2

by 2 kg/cm . This enabled more K readings to be taken.

There were two load-unload cycles in the test and each

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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; and

change in height of the sample during loading. The vertical

stress was assumed to be equal to the vertical applied load

divided by the area of the cell. The change in height of

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.

(b) On the following day the MV reading of the volt-

meter was taken to establish the zero reading, i.e.,

MV . The electrical connection to the transducer was

then disconnected (Fig. 2) to facilitate the place-

ment of the soil in the cell.

(c) After the soil was placed in the cell the

transducer was reconnected and the K cell and asso-0

ciated parts were placed in the loading frame as

shown in Fig. 2.

(d) Before applying a load increment of 1/8 kg/cm2

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

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indicator was set, and the millivolt change was re-

corded for the calibration resistor.

(e) During each load increment, dial and MV readings

were taken at time intervals normally used in consoli-

dation testing.

(f) Prior to each load increment the MV change due

to insertion of the calibration resistor was recorded

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) Volumetric strain vs. vertical stress (AH/H0vs. Ov) - Fig. 3.

(2) Vertical stress vs. horizontal stress (v vs.

h) - Fig. 4.

(3) Coefficient of earth pressure at rest vs.

overconsolidation ratio (h v vs. / v or vs.O.C.R.) - Fig. 5.

The results of other consolidation tests on similarly

prepared BBC with different ring sizes and/or type of ring

lining are also plotted in Fig. 3. This figure shows that

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 test by a

factor of about 1.6. This suggests that there was more fric-

tion in the K cell than in the other tests.0

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When the data are plotted with av vs. h in Fig. 4,

a line representing K can be established for normally con-

solidated clay, with K = 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 increases

and eventually becomes greater than 1. This relationship is

shown in Fig. 5 where K is plotted against the O.C.R. to a

log scale. Fig. 5 also shows that there is a linear relation-

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 increases very rapidly.

A maximum K value of 4.6 was measured at the maximum O.C.R.0

of 96.

2.6 Comparison with Other Results

Jackson (1963) obtained a K value of 0.50 0.04 for

similarly prepared normally consolidated BBC. He used a

triaxial cell (Fig. 6) where the lateral strain was main-

tained 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 for normally consolidated soils and the0

effective stress friction angle, P. Bishop (1958) and

Simons (1958) found good agreement between measured and pre-

dicted values using Jaky's (1948) original expression, K0 =

1-sin T. 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 = 1-sin 4 to BBC0

yields K = 0.46 to 0.55 depending upon the value of S

chosen. Table V presents values of W obtained from triaxialcompression tests. Values of T vary depending upon:

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(1) Which criteria of failure is used, i.e., maxi-

mum obliquity or maximum stress difference;

(2) The value of K (-ah /'v) at consolidation;

(3) Type of shear test, i.e., drained or undrained.

When these values are compared with the average K0value 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 data on overconsolidated BBC.0

The data can only be compared with trends which other inves-

tigators have found. Figure 7 presents a plot of K versus

overconsolidation ratio to a log scale for:

(1) BBC from this investigation;

(2) Three clays of low to moderate plasticity from

Brooker and Ireland (1965). They employed an oedo-

meter in which a portion of the cell ring was re-

placed 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

was zero lateral strain. This pressure was equated

to the lateral stress acting on the sample. The

vertical stress was carried in increments up to a

value of 2200 psi (155 kg/cm ) and then reduced in

increments to zero;

(3) The Weald Clay from Henkel and Sowa (1963),

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. This difference could have

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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 same general trends as observed by

on clays of similar plasticity. Hence

to yield reasonable data.

the K cell follow 0

other investigators

the cell again appears

2.7 Discussion of K Cell

In the design of a K cell, the two most important 0

factors to consider are side friction and the rigidity of

the cell and transducer. These two items will be discussed

separately.

To measure K properly there should not be any side 0

friction, but inherently there has to be some side friction

in this type of cell. Therefore, several questions arise:

(1) How does this friction, which causes shear

stresses on the transducer's face, affect the trans

ducer 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 values. 0

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Another procedure would measure the coefficient of friction

between the wall and the soil and then use this information

to compute the effect on K0

from the Mohr's circle, as illus

trated in Fig. 8. The simplified analysis shows a reduction

in K0

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 oedo

meter 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 properly there should not be any lateral 0

movement of the soil. 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 value is very close to the 0

"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 ob

tained when there is a strain of about 5 x 10-3 , 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

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5 x 10 3 should be adequate in measuring K in clays.

Deflection measurements were not taken when hydro-

static water pressures were applied to the cell so an accu-

rate 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 the2

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 trans-

ducer'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 dia-

meter 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 pres-

sures 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 mea-

sure the soil pressure accurately.

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Chapter 3

CALIBRATION OF PRESSURE TRANSDUCER

WITH A SOIL PRESSURE

3.1 Introduction

This investigation was aimed at the following ques-

tion: If a uniform soil pressure acts on a rigid planar

surface, will a pressure transducer inserted into this sur-

face 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

was made of stainless steel and is shown in Fig. 9. It was

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.


The transducer was a Dynisco Model APT 25 with a

pressure range of 0 to 200 psi, excited by an Allstate 6

volt wet cell battery. The millivolt output was measured by

a Keithley or an Electro Scientific Industries voltmeter. A

description of these items is given in Appendix B.

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3.2.3 Pressure Cells

Two types of cells were used to apply the soil pres-

sure to the disk. The first was a standard fixed ring con-

solidation unit in which the disk with the transducer be-

came the top cap. This unit is shown in Fig. 10. Note that

the ring was lined with teflon to reduce friction. The

second was a Norwegian triaxial cell which had been modified

to accommodate the disk with the transducer. This set up

is shown in Fig. 11.

3.3 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, ex-

cept 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.


The same soil that was used in the K tests was0

trimmed to a diameter of about 2.78 inches using a proce-

dure 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

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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. During

this time, 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 en-

closed in a specially made latex membrane, trying to entrap

as little air as possible. A rubber band wrapped around the

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

1/8 psi. To prevent air diffusion through the membrane, the

system shown in Fig. 12 was used. The pressure was applied

in 5 to 10 psi increments. As in the oedometer test, the

pressure was cycled during the test and each increment of

pressure was left on for at least 24 hours. During each in-

crement, transducer and volume change readings were recorded.

3.4 Test Results

The data are presented as a ratio of the measured

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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

the soil and the disk. This figure shows the following gen-

eral trends:

During loading with filter paper:

(1) When the applied pressure was small (less than

about 10 psi), the error was large, with Pm /Pa greater

than one.

(2) At applied pressures greater than 20 to 40 psi,

the ratio of Pm a remained relatively constant with

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) The ratio Pm a increased and approached a

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

applied pressure, with a difference as high as 35%. At zero

pressure, the measured pressure was essentially zero (note

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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 a equals

1.12 to 1.15. 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 a varied be-

tween 1.01 and 1.08. 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 substan-

tially 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, the measured

-25-

pressure was only about 3% higher. However, during un-

loading, both with and without the teflon, the measured

pressure became much less (35%) than the applied pressure.

3.5 Discussion of Test Results

Most of the test results can be explained if the

applied pressure is not uniform across the disk and trans-

ducer because of the following boundary conditions: local

arching within the soil, 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 trans-

ducer was not perfectly aligned (see Fig. 9).

Although both tests without the teflon gave high ini-

tial 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. It should be pointed out

-26-

- -

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 uni-

form 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

applied load is taken up at the walls. The estimated change

in stress distribution is shown in Fig. 16a.

During unloading this side friction acts in the oppo-

site direction which causes the soil to form an arch with

the contact area between the soil and disk reduced. Figure

16b shows the assumed change in stress distribution. There-

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

stresses are higher at the center of the top cap. The rea-

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 mea-

sured 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 ato be closer to unity. The test results showed this to be

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 con-

ditions.

(3) During unloading the difference between the

measured and the applied pressures is much larger

than that during loading. The cause for this large

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 re-

loaded, 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 mea-

surements. 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 in the nor-0

mally consolidated range is 0.48, which is in good agree-

ment with other K data on similar BBC. In the overconsoli-0

dated range, K 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

across the stainless steel disk. But most of the transducer's

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

pressure on the disk is uniform. This may never be proven

since it is next to impossible to apply a truly known soil

pressure across a plane surface with a transducer in it.

There are three basic problems when using this type of

K cell. First, there is the problem of rigidity of the 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 would not be affected by

this small amount of strain. 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 trans-

ducer 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 mea-

sured against the walls of the K cell.

To correct for item (1) the author proposes the method

outlined in Fig. 8. For item (2), no correction is proposed

but two general statements can be made based on the data ob-

tained from placement of the transducer in the top cap of

an oedometer unit.

(1) The normal stress on the walls is probably not

affected very much when the soil is normally con-

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 overconsoli-

dated 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

Thirdly, since there is soil movement across the trans-

ducer's face, due to the soil being consolidated, the ques-

tion arises: does this affect the transducer measurements?

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.

One: Is this type of K cell better than or equal to

other types of K cells, such as an oedometer unit in which

the hoop strain of the confining ring is measured to de-

rive 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

three major disadvantages. First, it is more difficult to

run and requires either constant attention or elaborate

automation. Secondly, there is continual lateral movements

of the soil sample, i.e., relaxation, then compression. Al-

though these movements can be small (diameter change of about

3 x 10~4 inches) they could cause considerable errors when

the sample is overconsolidated since there would be a ten-

dency to get a high reading when recompressing the sample

by this amount because the soil is "rigid" compared to the

confining pressure. In the normally consolidated range

this should not be a major problem since the soil is in a

"plastic" state. Thirdly, Bishop (1958) pointed out that

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 mea-

sures 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 cer-

tainly 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-recom-

pression and non-uniform pore pressure dissipation can also

affect the results and the test is difficult to perform.

Two: Is it worth the effort to perfect this type of

K 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 is usually determined for:

(1) 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 cells most likely have the largest and

unknown errors. 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 understand-

ing 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 theCoefficient 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 Measurementof Soil Properties in the Triaxial Test," Edward Arnal,London.

Brooker, E. W. and Ireland, H. 0. (1965), "Earth Pressuresat Rest Related to Stress History," Canadian Geo-technical Journal, Vol. 2, No. 1.

Hendren, A. J. Jr. (1963), "The Behavior of Sand in One-

Dimensional Compression," Ph.D. Thesis, University ofIllinois, Urbana, Illinois.

Henkel, D. J. and Sowa, V. A. (1963), "The Influence of

Stress History on the Stress Paths Followed in Un-

drained 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 andFoundations, Rotterdam, Vol. 1, pp. 103-107.

Ladd, C. C. (1965), "Stress-Strain Behavior of Anisotro-pically 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," JohnWiley and Sons, Inc., New York.

Lambe, T. W. (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 ofThirty-Second Annual Meeting of the Highway ResearchBoard, January.

M.I.T. (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-StrainBehavior of Saturated Soils," The Response of Soil toDynamic Loadings, Report No. 6, Dept. of Civil Engi-neering, 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 SaturatedSoils," Phase Report No. 1, Department of Civil Engi-neering, May.

Simons, N. E. (1958) Discussion on: General Theory of Earth

Pressure. Proceedings, Brussels Conference on Earth

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 Con-ference on Soil Mechanics and Foundation Engineering,Vol. II, Paris.

-36-

TA5LE I

COMPO SITIOA/ ANP EANG?/EEPIN& PROPERTIES

OF oosToN 81e CLAY

MnerQ/ogc Composition C/d Sf1'fct;n dh

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Quartj - 20 %to 340 % I/'o;c lati/f 22%

Ck/orite - sometlwe5 preweNt Perceift w/ils 2 0c1*4rors- 50%

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Compref ioll Index Cc -d-34

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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 Sturte-

vant 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,

as shown in Fig. A-2. The chamber and consolidometer unit

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 consoli-

date 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 consoli-

dation before the increment is changed.

2Following consolidation at 1.5 kg/cm 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 satur-

ation of about 99%. Experience has shown that the soil does

not lose a significant amount of water during storage in

the transformer oil.

-65-

Top

MainHoldingRod(4 Used)

Porous Stan

Porous Ston

Stainless Steel Shaft

Aluminum Pocking Nut

Aluminum Bushing Holder

Teflon Packing

Drain -Thompson Ball Bushing

To Oil-Nitrogen Accumulator

Aluminum Cover0" Ring Seal

-+-- ----- Oi I---- Extrusion Rod (3 Used)

Aluminum 0-"UO" Ring Seal

- ...--- Lucite Piston

Bonded Teflon

"D. Shelby.TubingSoi

Lucite Base Piston

"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-

Soil Slurry introduced Here

--- To Vocuum Pump

-e 3*ft Lucite Deoiringcolumn

\ 0

000

I000

000 Io

0000

000

Soil Slurry

//0

~iY II

Consolidometer

FIGURE A-2 METHOD OF SLURRY PLACEMENT

n7-

I-

,-101

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 Dyn-

isco, 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./1000 F. When it is excited by a low

D.C. voltage (6 volts) 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 Dyn-

isco.

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 Di-

vision, Newark, New Jersey. This voltmeter can measure

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 volt-

meter manufactured by Keithley Instrument Inc. This 5 di-

gital voltmeter, model 6060T, can measure voltages from 0

to 500 volts with a sensitivity of 0.01 MV on the most sen-

sitive 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 sensi-

tivity of one microvolt on the most sensitive range. The

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 vol-

tage, 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 follow-

ing 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 mvP - PV [ m _ 0] K

e 0

where:

P = unknown pressure

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 = measured excitation voltage at known pressure

K = gauge factor derived during calibration where

changes in pressures are known

-70-

V0K = -APressure

Note: V = Ve since the voltage source does not

change during the short period required to

calibrate the transducer.

By using this equation and procedure, measured pres-

sures during tests lasting over a long period will be ex-

tremely 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 Indi-

rectly 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 ex-

citation voltage of about 6 volts.

(c) During the above, but between pressure in-

crements, the voltage change due to adding the

calibration resistors to one arm of the circuit is

measured.

(d) From the mV change/psi (from part b) and the

mV change for the resistor (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 exci-

tation voltage.

The equation expressing the transducer electrical

output in terms of pressure has the following form:

K

P - P = (mV - mV ) (Weston Voltmeter)o m 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 cali-

bration resistor

K = equivalent psi of calibration resistor

determined during calibration

P = new or unknown pressure

P0 = pressure at mV1 reading (usually zero)

or pressure before new increment of loading

The equation takes into account the change in exci-

tation voltage from one test to another test. However,

-72-

in battery voltage. The procedure is outlined below.

After the pressure change is applied, the calibration

resistor is continually checked. If the magnitude of the

measured voltage changes, a new equation is started. An

example follows. At the start of the test P - P0 = (mv -o mmV )K1, where K = Ke/AmVsl. If AmVsl changes, the pres-

sure change equation becomes: P - P1 = (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 exci-

tation voltages it would not have the accuracy of the cali-

bration procedure explained previously because the volt-

meter 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-

ykemanicpyi~co

F

Diagram67auge

PREs$URE

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a I

C N

TR/CAL CoaVNEcT/0N5

SMAIN WIRES

CALIOXATIOA/

Exc/rATroM

-74-

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ime 1* mig fes

0

I'

0

0

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/H0 Volumetric strain.

O.C.R. Overconsolidation (a Ia )vi v0 cm Maximum past pressure.

Pm a Ratio of the measured pressure to the applied pressure.

Pm Pressure measured by transducer.

Pa Assumed applied pressure to transducer.

-76-

AUG 15 1266

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Transcript of AUG 15 1266