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Reproducibility of soil compaction curve
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Authors Agah, Hamid, 1939-
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REPRODUCIBILITY OF SOIL COMPACTION CURVE
by
Hamid Agah
A Thesis Submitted to the Faculty of the
DEPARTMENT OF CIVIL ENGINEERING
In Partial Fulfillment of the Requirements For the Degree of
MASTER OF SCIENCE
' In the Graduate College
THE UNIVERSITY OF ARIZONA
19 6 8
STATEMENT BY AUTHOR
This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.
Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.
SIGNED: A
APPROVAL BY THESIS DIRECTOR
This thesis has been approved on the date shown below:
/ ~ / _______H. Sultan
Assoc. Prof. of Civil Engineering
ACKNOWLEDGMENT
The author expresses his appreciation to Dr. H. Sultan, his
thesis director, for the considerable time he spent in making very
constructive criticism in the course of directing this study. This
contribution was invaluable.
Sincere gratitude is extended to Professors R. L. Sloane and
D. Woods for their assistance in this research. They have been a source
of encouragement to the author as outstanding teachers during the course
of his studies.
Finally, this work would not have been possible without the
love, encouragement, patience and support from the authors’ parents.
This I cannot ever adequately acknowledge.
TABLE OF CONTENTS
Chapter Page
LIST OF ILLUSTRATXONSo & o © e ® e e e ® o o 6 8 & ® e o ® e & e e © © e 6 9 9 © B e B e e © ® © VI
LIST OF T A B L E S v l x x
ABSTRACT©@@@@©@@@@@©@@@©©@@@@@©@@@@©©©©@@@@@©@@©@©@@©@0000© xx
I 0 INTRODUCTION @eee@oG«>e@@0@8@@8@©@o@@@8@0@@@@*)060@o0O@@©0@®@o I
IeI SCOpe690ee0tieee©e»®©s©6®oeo»0oeee60eeoe8eaeoceeeeo 2I e 2 Definitions e e e ® e e e e e ® 6 e © e e > 9 e e e < > e e o © ® » e e e © e e e ® e » e e e o 3
EQUIPMENT AND MATERIALS0 e, e e e e e e e o o e e e e e e a e e o e . e e a e e e o e a
2 o I Equipmenteeo®6e®©0ee96oeee»6 e e oeeeeeeoeeoeoeeeeee® 62 e 2 Materials Used © GGe@@ea@0*0@*9@@@@e©e@e6a6@ee8oea@0 D
3 o TEST P ROCEDURE eoeeo®6ee®eeeeeeooe®eeeeGQde©®06®e©6. 09e®©»e0Q 12
3 o 1 P aramete rs oo06OQ©0oo®««©®c/®®0edoe©©0©©eeeeo©©«&0®© 123 © 2 Sample Preparation© ® © © © © © e© ©©©e©©®©©©®®®®©®©©©©©©© 123 © 3 COmpaCtlOn Tests ©®ee»ee0o©ee©e©e©®eeeee»©e8e®©ee®o 13
40 DATA ANALYSIS AND RESULTSee@aeo»e©eeoe**aeoe*@ee@eeee«ea*0@ 16
4 © 1 ASTM Curves ©....... *.......... 164 © 2 Cubic CUrVeS eeeeeeoee*®©©©®©© ©©eoeGoeeeaeee eee©ae© 244 93 Reproducibility Evaluation,.# # e • 294,4 Moisture Content Patterns © ® ©»«e»©»© © 6»8 © © © © © ©»© © © © 364©5 Gradation Change©©©©e©©©©©©©®©©©©®©©©®®©©®©©®*©©©© 39.
Se DISCUSSION OF RESULTSeeeeoeeeeeeeeeeeeeeeeeeoeoeeoeeee®©©©®® 42
9G00Qeo0»0O00e®eeeee0o< 00O6eoeae©eee»ee060O8®eeti@oe®©ei
e e e e e e e o e a o e e ®
5.1 Comparison of Cubic Model vs. ASTM Method.5.2 Controlled Tests5.3 Plasticity5.4 Gradation Effect5.5 Layer-Thickness Effect......5.6 Manual [email protected].@............................ 465.7 Moisture Content Patterns......................... 47
42434445 45
V
TABLE OF CONTENTS— Continued
Chapter Page
6 o CONCLUSIONS e e e e e e e e o e e e e e o e e o e e e e e e e e e e o e e e o e e e e o d e e e e e e e e e 4 9
6 © 1 Summarye e e o e e e e e e e e e e e e e B e e o e o o e c a e e e o e e o e e e e e e e e e 496 a 2 FUture ReSe archo©©e©eeeo0©©o©ee©O9®ee©e®©©eo^e&eQd 50
APPENDIX - LEAST SQUARES SOLUTION FOR THE PARAMETERS OF ACUBIC POLYNOMIAL© e e e e e o o e e e e o e o e o e e e e e e o e o o e o e e © 52
REFERENCESo«o«o«o»«ooO@O9©o®eo0eoae00©0o©0000©©©000e©©e©9Oo 61
LIST OF ILLUSTRATIONS
Figure . Page
1« Rainhart Automatic Tamper No» 662, with the Mold.,.....,.,... 7
2. Range of Gradation of Sand.@@@...,...,,...,@,..@..,@,...@8.,. 10
3, Moisture Density Curves for Controlled Tests Plotted, UsingASTM Standard Method.........e,....,.,........,....,......... 17
Moisture Density Curves for Sand and 10% Kaolinite Plotted,Using ASTM Standard Method..................o...............@ IS
Moisture Density Curves for Sand and 2% Bentonite Plotted,Using ASTM Standard Method..............o.................... 19
Moisture Density Curves for Random Gradation Sand Plotted,Using ASTM Standard Method.............o..................... 20
' p
7. Moisture Density Curves for Variable Layer-ThicknessCompacted Sand Plotted, Using ASTM Standard Method........... 21
8. Moisture Density Curves for Manually Compacted Sand Plotted,Using ASTM Standard Method.............o,...................o .22
9. Moisture Density Mean Curves Plotted, Using ASTM Standard M e t h o d 23
10, Moisture Density Curves for Controlled Tests Plotted, UsingCubic Regression Method, . e . o e . e o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
11. Moisture Density Curves for Sand and 10% Kaolinite Plotted,Using Cubic Regression Method....e........................... 26
12. Moisture Density Curves for Sand and 2% Bentonite Plotted,Using Cubic Regression M e t h o d . . . . . . . e . . . . . . . . . . . . . . . . . 27
13. Moisture Density Mean Curves Plotted, Using Cubic RegressionM e t h o d . . . . . . . . . . d O Q d . e , . . e , o o e , . . o e . e . e . o , o o , . . . . . . . . . . . . . . . . 28
14. Moisture Density Mean Curves for Controlled Tests Plotted,Using ASTM Standard and Cubic Regression Methods............. 30
15. Moisture Density Mean Curves for Sand and 10% KaolinitePlotted, Using ASTM Standard and Cubic Regression Methods.... 31
VI
vii
LIST OF ILLUSTRATIONS— Continued
Figure Page
16o Moisture Density Mean Curves for Sand and 2% BentonitePlotted, Using ASTM Standard and Cubic Regression Methods.e * 32
17. Moisture Density Mean Curves for Random Gradation SandPlotted, Using ASTM Standard and Cubic Regression Methods... 33
18. Moisture Density Mean Curves for Variable Layer-Thickness Compacted Sand Plotted, Using ASTM Standard and Cubic. Regression Methods.......................................... 34
19. Moisture Density Mean Curves for Manually Compacted Sand Plotted, Using ASTM Standard and Cubic Regression Methods... 35
20. Effect of Compaction on Gradation of Sand................... 41
LIST OF TABLES
Table - Page
1. Reproducibility of Compaction in Terms of Standard Deviation of Each Group and Percent of Overlap Area ofMean of Each Group from Mean of Controlled Tests............ 37
2. Effect of Plasticity on Reproducibility of CompactionCurve in Terms of Standard Deviation for Each Parameter..... 38
3. Standard Deviations in Layer Moisture Content (MaximumValue for Each Test)................. 40
A.I. Cubic Regression Coefficients and Correlation Indices, forMoisture-Density Curves ........ 57
A.2. The Deviations of Maximum Density and the Percent OverlapArea from the Mean of the Same Parameter 58
A.3. The Deviations of Maximum Density and the Percent OverlapArea from the Mean of the Same Parameter.................... 59
A.4. The Deviations of Maximum Density and the Percent OverlapArea from the Mean of the Controlled Tests.................. 60
viii
ABSTRACT
The effects of four parameters on the degree of reproducibility
of soil compaction curve were investigated. These parameters were:
placticity; gradation; layer-thickness; and manual compaction. The
variations of the moisture contents within the compacted specimens were
checked to determine their significance. The degree of reproducibility
was computed by four different methods, and compared. Attempts were
made to characterize the moisture-density relationship by mathematical
models. '
CHAPTER 1
INTRODUCTION
The term compaction refers to the practice of artificially
densifying a soil mass by rolling, tamping, vibrating, or other means,
The moisture-density relationship of a soil gives approximate infor
mation on the gradation; the sensitivity to moisture content, and the
load carrying capacity of the soil. The more important reasons for
compaction of soils are: to increase the strength; to reduce compres
sibility, to control volume change tendencies; to control resilience
properties; to decrease permeability; and to reduce frost susceptibility.
Several factors influence the value of density obtained by
compaction. Of primary importance are: the moisture content of the
soil; the gradation and physical properties of the soil; and the type
and amount of compactive effort among others. Of lesser significance is
the temperature of the soil and water. For fine-grained cohesive soils,
the soil structure is a very important factor in affecting the soil
strength.
Thirty five years ago, Proctor (9), a pioneer in the field of
compaction, determined that by moving the soil particles and water into
the soil voids, the soil density can be increased. He determined the
relationship between the compactive effort and the density obtained as
a result of this effort. The compaction test he designed is the basis
of all the present laboratory impact methods of testing. The laboratory
results are hard to duplicate in the field because of differences in
confinement, compactive effort, reuse of soils, layer thickness,
accuracy of measurement and the method of compaction. The-basic
difference between various laboratory methods of testing lies in the
amount and method of application of the compactive energy.
1.1 Scope
In writing specifications for earthwork construction contracts,
it is usually specified that the field density should not be less than
a certain percentage of the maximum dry density obtained in the labo
ratory. Also, the moisture content should be within certain limits from
the laboratory optimum value. Therefore, it is implicitly assumed that
a high degree of reproducibility is expected in conducting the laboratory
compaction tests.
As stated previously several factors do influence the degree of
compaction and obviously many more would influence, to various extents,
the degree of reproducibility of the compaction curve. Consequently,
since the laboratory compaction curve is the basis of the specification
guidelines, it is of interest to investigate its degree of repro
ducibility. Further the quantitative magnitudes of deviations from the
implicit uniqueness assumption are of interest.
The purpose of this investigation is to study the possible effect
of a number of experimental parameters on the degree of reproducibility
of the compaction curve. An attempt also is made to explore the
possibility of establishing a mathematical expression for the compaction
curve, and to measure the degree of reproducibility by a statistical
method.
1.2 Definitions
The following symbols and notations have been adopted for use in
this thesis, and are defined as follows:
Soil Definitions:
Dry density, (y^) - The weight of soil grains per unit volume
of soil mass.
Moisture content, (W) - The weight of moisture filling the soil
voids, as percent of dry weight.
Compaction test - Compacting the soil following a specified
procedure. It is referred to as the test for simplicity.
Compaction curve - The plot of moisture-density relationship
obtained from the compaction test. This is referred to as the
curve for simplicity.
Maximum dry density, (Max. y^) - The density at the peak of the
compaction curve.
Optimum moisture content, (O.M.C.) - The moisture content at the
point of maximum density (peak) on the curve.
Plasticity index, (P.I.) - A measure of the plasticity range of
soils, as measured by the Atterberg Limits, It is usually
expressed as moisture content in percent of dry weight.
Mechanical compaction - The test run by the use of a motor-
operated automatic tamper.
Manual compaction - The test run by the use of a hand-operated
tamper.
Deviation of Maximum dry density, (A Max. y^) - The deviation of
maximum dry density of each test from the maximum dry density of
the mean curve of the group; in percent.
ASTM method - By connecting the test data points with a smooth
curve, a compaction curve is produced. This is the method
designated in the ASTM D 69B-64T test.
Overlap area - The area under a curve bounded by the vertical
lines at _+ 2% of optimum moisture content, and a horizontal line
at 95% of maximum dry density is defined. The portion that the
defined area of any curve has in common with the defined area of
the mean curve, is referred to as the overlap area. When this
overlap area is expressed as a percent of the defined area of
the mean, it is called percent overlap area. This is a method
of measuring the degree of reproducibility of the curves.
Statistical Definitions:
Mean - The value that is computed by adding all the items in a
set, and dividing the total by the number of items used. This
is how the mean curve for each group of the tests was obtained.
Random data - Implies that every individual in the population
has an equal chance of being selected on the next draw. This is
how the random gradation samples were obtained.
Cubic regression curve - I s a type of curve used to describe the
trend of the data. The mathematical expression for the curve is 2 3D = A + B W + C W + F W . Where, D (density) is the dependent
variable and W (moisture content) is the independent variable.
In this work the curve of regression was fitted by the method of
least squares.
Least squares method - Is a method of obtaining the best fit
curve to a set of data points. This unique curve is the one
about which the sum of squares of deviations of the observed
value from the expected value of the dependent variable will be
a minimum. This method is illustrated in the Appendix for a
cubic model.
Standard deviation, (S) - It is a measure of the scatter of
items about the arithmetic mean of the sample. The mathematical
expression is given in the Appendix.
Correlation index, (R) - It is a measure of the closeness of the
points of the curve of relation. Its value ranges from zero for
no correlation to one for perfect correlation. The mathematical 2expression for R is also given in the Appendix.
CHAPTER 2
EQUIPMENT AND MATERIALS
2.1 Equipment
The following compaction equipment was used during the course of
the laboratory work for this study:
Automatic Tamper. The Rainhart Automatic Tamper No. 662 shown
in Figure 1 was used. This method is referred to as mechanical com
paction method. This tamper was cleaned, lubricated and adjusted for
the ASTM test designated D 698 - 64T. This is the so-called Standard
Proctor or Standard AASHO test. The loading speed and the blow spacing
were kept constant through the whole series of tests. The tamper has a
circular segment face (90° angle), with a radius of approximately 2
inches.
The load is lifted by means of a grabber, which is moved by a
cable. This load is released when the grabber reaches the upper end Of
a bar on which it moves. The load falls for the specified height and is
picked up again. The height of the drop is self-adjusting. This tamper
is widely used in the laboratories and is calibrated to apply the same
compactive energy as indicated for method "A" of the ASTM designated
test. It has the same weight of the hammer and the height of the drop
as the manual tamper. It can also be adjusted for the Modified Proctor
test.
6
7
FIGURE 1. Rainhart Automatic Tamper No. 662, with the Mold.
ASTM D 698 - 64T test. The tamper has a flat circular face 2 inches in
diameter and a weight of 5,5 pounds. The tamper has an arrangement that
controls the height of the drop to a free fall of 12 inches above the
surface of the soil in the mold. The load is to be applied vertically
to the soil, and the load spacing should be kept reasonably constant.
The vertical application of the load and the spacing will become more
consistent with experience, but the human factor would undoubtedly be
always present. The soil grains should not be allowed in the space
between the tamper and the cylinder around it, as this would not allow
the completely free fall of the tamper.
Mold, The mold used for all the tests is the one designated by
method "A" of the ASTM test. This is a cylinder of 4 inches in diameter
and a height of 4,584 inches. The volume of the mold is 1/30 cubic feet.
The mold has a detachable collar assembly of approximately 2,5 inches in
height, to permit the preparation of the sample to the desired height,
which is about 1/2 inch above the mold top. The mold and the collar are
fastened firmly to a detachable base plate. The same mold was used
throughout all the tests, and was prevented from rusting by a light
lubrication each day. It was weighed at the beginning of each test.
This mold is shown in Figure 1, attached to the base of the automatic
tamper by two clamps. The mold was held between the feet during the
manual compaction.
2.2 Materials Used
The soils used were sand, sand-kaolinite and sand-bentonite
mixtures. The sand was from a location on the Hughes Access Road, on
the south si4e of Tucson. This sand is being used by the New Pueblo
Construction Company, in asphaltic concrete mixes. The small percentage
(less than 6%) of particles larger than number 4 sieve present in the
sand, was discarded before the soil was brought to the laboratory. This
sand is well-graded with very little fines.
The specific gravity of the sand is 2.67, and it is non-plastic
as was determined by the Atterberg Limits. The grain-size distribution
of the sand as obtained by six sieve analyses is shown in Figure 2.
The range and the selected size distribution for five groups of tests
are shown in this figure.
The kaolinite used is commercially processed and distributed by
the Georgia Kaolin Company of Dry Branch, Georgia. This has the trade
name of Hydrite-UF. The kaolinite has a well defined platey, hexagonal
shape, and has a very small particle size (UF means ultra-fine)(7).
The specific gravity was determined to be 2,72 and the plasticity index
is above 30. Trial samples were run with 4%, 6% and 10% kaolinite re
placing the smallest sand grains. The plasticity index for these
mixtures were 1, 6 and 8 in that order. The sand with 10% kaolinite
having a plasticity index of 8 was selected for a group of tests to
study the effect of plasticity on the degree of reproducibility. This
mixture has approximately the same gradation as the sand selected for
the controlled tests.
100
90
80
70
60
50
40
30
20
10
0 J
RANGE
G R A I N S I Z E IN M M 1
60 40 20S T A N D A R D SIEVE NUMBER
F IGURE 2 R A N G E OF GRADAT ION OF SA N D
11
The bentonite has a plasticity index of around 600, and is
from Wyoming. Trial samples of the sand-bentonite mixture of 2% and
3% bentonite were tested for plasticity. The plasticity index of 2%
bentonite mixture was 14 and the 3% bentonite had a plasticity index
of 30. The bentonite replaced some of the fine particles (passing No,
200 sieve), so that the gradation curve of the mixture is the same as
the controlled sand. The sand with 2% bentonite having a plasticity
index of 14 was selected for another group of tests to study the effect
of plasticity on the degree of reproducibility. With these two mixtures
the plasticities were increased, while the gradation stayed relatively
unchanged.
CHAPTER 3
TEST PROCEDURE
3.1 Parameters
The effect of four factors on the degree of reproducibility is
investigated in this study. These four factors are: gradation; vari
ation in layer-thickness; manual compaction; and plasticity. In
addition, the reproducibility of a group of tests under controlled
condition is determined, and is used as a basis of comparison to
evaluate the influence of the above four factors. Considering the time
limitation of this study, it was decided that five tests in each group
would be a sufficient number, to study the effect of the pertinent para
meter on the degree of reproducibility.
To determine the effect of plasticity on reproducibility of
compaction, the plasticity indices of 8 and 14 were selected after
preliminary testing as indicated previously. These are compared with
the controlled tests, in which the non-plastic controlled gradation sand
was used.
3.2 Sample Preparation
The selected sand of Figure 2 were used for groups of tests in:
this study. Approximately 150 kilograms of sand was obtained from the
location noted previously and air-dried. The hygroscopic moisture
content of the air-dried sand was determined, and was used to correct
12
13
the weight of grain size distribution in preparing the controlled
gradation. This moisture determination was also used to correct the
initial moisture content for all the compaction tests. The sand was
broken into its individual particles by a rubber-tipped pestle, and a
quantity sufficient for twenty five tests was sieved.
Fifteen samples were prepared from the sieved sand by mixing
weighed quantities of each grain size to obtain the selected gradation.
These samples of four kilograms each were prepared for the controlled
test group; variable layer-thickness group; and the manual compaction
group.
Two other groups of samples were prepared with the sieved sand,
in accordance with the selected gradation, and adding the 10% kaolinite
and 2% bentonite as indicated earlier. Finally, five samples were taken
at random from the original unsieved sand, to study the effect of vari
ation in grain size distribution. These samples fall within the range
of the particle size distribution shown in Figure 2.
3.3 Compaction Tests
All the tests were generally conducted in accordance with the
impact-type test, ASTM designation D698 - 64T Method A, commonly referred
to as the Standard Proctor. The total compactive energy for the test is 312,400 ft-lb/ft . For this test the number of layers is three and the
number of blows of the hammer per layer is 25. The 5.5 pound hammer is
dropped for a free fall of 12 inches. The placing of the layers and the
determination of moisture content differed from the ASTM designated
procedure in this study, and they will be discussed here. All the tests
14were conducted in the following manner, except as noted at the end of
this chapter.
General Procedure. For all the test groups the automatic tamper
of Figure 1 was used. For each compaction test six or seven points were
run, at least two of which were on the wet-side of the optimum moisture
content. All the specimens were mixed thoroughly before addition of
water, particularly in the case of the soils with kaolinite and bento
nite. The initial moisture content of 5% was selected after a trial
sample was run. The samples were mixed for this moisture content and
allowed to temper overnight, in accordance with the ASTM procedure. The
moisture content was raised in increments of approximately 2%, and
generally up to a moisture content of 17%.
After each compaction data point was obtained the soil removed
from the mold was completely remixed with the original sample, and then
water was added. During the weighing of moisture samples the soil was
covered with a moist cloth to protect it from surface evaporation. For
each data point an equal weight of soil was used for each layer. This
kept the layer thickness for the tests constant, and was necessary ifJ
the influence of each factor was to be determined independently.
Another variation from the ASTM procedure was the moisture
content determination. For each point on the moisture-density curve,
four moisture samples were obtained. One sample was obtained for each
individual layer, and one for the whole specimen as indicated in the
ASTM procedure. This was done to study the possible significance of
layer moisture content variations. Due to the large number of samples
15
needed for moisture content determinations per test, 30-50 gram
specimens were used for moisture determination instead of 100 grams.
After the compaction tests on the controlled sand samples, a
grain size distribution test was conducted. This was done for the
manual and mechanical compaction to determine their effect on gradation.
Controlled Tests. These tests were conducted using controlled-
gradation sand as indicated in the General Procedure above.
Plasticity Tests. Tests were conducted using the sand with 10%
kaolinite, and the sand with 2% bentonite in the manner indicated by the
General Procedure.
Random Gradation Tests. These tests were conducted on the
random sand samples in the same manner as that indicated in the General
Procedure.
Variable Layer-thickness Tests. Tests were conducted on the
controlled-gradation sand, but the quantity of soil placed was not
weighed, as was the case in the General Procedure. The variations
of the quantities of the soil in the three layers were within the limits
of normal practice. This was done to isolate the effect of layer thick
ness variation on the reproducibility.
Manually Compacted Tests. These tests were conducted on the
controlled-gradation sand, but using the manual tamper instead of the
automatic tamper that was used in the General Procedure.
CHAPTER 4
DATA ANALYSIS AND RESULTS
4.1 ASTM Curves
The moisture-density data points obtained during the thirty
compaction tests are plotted as curves. The points for each test are
connected by a smooth curve, as indicated in the ASTM test procedure
designation D698 - 64T. These are the ASTM curves of Figures 3 through
8. The five tests in each group are plotted in one figure. The data
points are shown on each figure. For each group the mean of the five
curves was computed, and is plotted as the mean curve of the group.
This mean curve was plotted by use of the mean value of dry densities of
five curves at 2% moisture content intervals. The mean value of the
controlled tests was also plotted on all the figures of the non-plastic
soils. The mean curves for all the four groups of tests on sand are
plotted in Figure 9.
In general it can be seen that the data points for the controlled
tests, sand +10% kaolinite, sand +2% bentonite and manual compaction
follow their individual curves closely. The variable layer-thickness
group curves have the largest number of data points that do not fall on
the curves. The sand +2% bentonite group has the best fit of the curves
to the data points of all the groups, and the controlled tests show
better fit than the random gradation group.
16
DRY
DE
NS
ITY
(Y
d)
pcf
126
FIVE TESTS
MEAN OF FIVE T E S T S
MOISTURE CONTENT (W) IN PERCENT
FIGURE 3 M O I S T U R E D EN SI TY CURVES FOR CO NT R OL LE D T E S T S P L O T T E D , USI NG A S T M S T AN D A R DM E T H O D
DRY
DE
NS
ITY
(Y
d)
pcf
126
124
122
120 ' I---
118
F IV E TESTS116M E A N OF FIVE T EST S
114
112
1105 6 127 9 10 II8 13 14 15
MOISTURE CONTENT (W) IN PERCENT
F IGURE 4 M O I S T U R E D E N S I T Y C U R V E S FOR SAND AND 10 % K A O L I N I T E P L O T T E D , USI NG ASTMS T A N D A R D M ET HO D
oo
DRY
DE
NS
ITY
(Y
d)
pcf
126
116 F I V E T E ST S
- - MEAN OF F I V E T E S T S114
112
110 106 7 8 II 125 9 13 14 15MOISTURE CONTENT (w) IN PERCENT
F IG UR E 5 M O I S T U R E D E N S I T Y CURV ES FOR S A N D AND 2 % B E N T O N I T E P L O T T E D , U S I N G AS T M
S T A N D A R D M E T H O D
DRY
DE
NS
ITY
(Y
d )
pc
f
126
F I V E T E ST S124M E A N OF F IV E T E S T S
M E A N OF C O N T R O L L E DJ E S T S22
120
MOISTURE CONTENT (W) IN PERCENT
FIGURE 6 M O I S T U R E D E N S I T Y C U R V E S FOR RANDOM GR AD AT I ON SAND P L O TT E D, USING AST M
S T A N D A R D M E T H OD
K)O
pd (PR)
A1ISN3Q
A
dQ
FIVE TESTS124— MEAN OF F I V E TESTS
M E A N OF CO NT R OL LE DTESTS122
__l
5 6 7 8 9 10MOISTURE CONTENT (W) IN PERCENT
FIGURE 7 M O I S TU R E D E N S I T Y CURV ES FOR V A R I A B L E LAYER-THI CK NESS COMPACTED SAND PL OTT ED,USING A S T M S T ANDARD M ET HO D
to
DRY
DE
NS
ITY
(Y
d )
pcf
128
126
124
122
o I120
118
116F IVE T E ST S
- - M E AN OF FIVE T E ST S114
M E AN OF CO NT R OL LE D TESTS
112
110
MOISTURE CONTENT (W) IN PERCENT
F I G U R E 8 M O I S T U R E D E N S I T Y CURV ES FOR MANUALLY COMPACTED SAN D P L O T T E D , USING A S T MS T A ND AR D METHOD
NJ
DRY
DE
NS
ITY
(Y
d )p
cf
126
X124
122
120
— CONTROLLED TESTS
— M ANUAL COMPACTION
- - RAN DO M GRADATION
V AR IA BL E L AYER —THI CKNES S
114
MOISTURE CONTENT (W) IN PERCENT
FIGURE 9 M O I S T U R E D E N S I T Y MEAN CURVES PLOTTED, USING AS T M STANDARD METHOD
K)UJ
4.2 Cubic Curves
The method of least squares was employed to compute the values
of coefficients for the mathematical expression that would give the
equation of the compaction curve. Initially it was assumed that the
compaction curve would generally have a parabolic shape. The coef
ficients for a parabolic equation were determined by the indicated
method. The values of these coefficients for each test and the mean of
each group were obtained by use of computer programming. The degree of
fit of these curves to the test data points were checked by the use of
correlation index.
Using the parabolic model the correlation indices obtained were
in the acceptable range (above 0.75), however the plotted results showed
that there were considerable divergences in the peak region of the
curves. This is the critical region of the compaction curve, since the
peak point lies within this range. Therefore, the parabolic model was
rejected and the cubic model was tried.
The method of least squares for the cubic equation is illustrated
in the Appendix. The equations for the coefficients of the cubic model
were programmed for the computer. The values of the coefficients of the
cubic equation for some of the individual compaction tests, and those
for the mean curves of all groups are given in Table A.1 in the Appendix.
The correlation indices for the curves are also given in the same table.
The cubic model gave excellent correlation. The correlation
indices ranged from 0.97 to 1.00. The curves obtained using these coef
ficients are presented in Figures 10 through 13. In the first three
DRY
DE
NS
ITY
(*
d)
pcf
126
124
122
120
118
FIVE TESTS116- - MEAN OF FIVE
T E S T S114 r
112
110
M O IS T U R E CONTENT (W) IN PERCENT
FIGURE 10 M O IS T U R E DE N SI TY CUR V ES FOR C O N T R O L L E D T ES T S P L O T T E D , USING CUBI C REGRESSI ON
M E T H O D
K)cn
DRY
DE
NS
ITY
(Y
d )
pcf
M EA N OF F IV E T E ST S
MOISTURE CONTENT (W) IN PERCENT
FIGURE II M O I S T U R E D E N S I T Y CURVES FOR SAND A N D 10 % K A O L I N I T E P L O T T E D , U S I N G CUBICR E G R E S S I O N METHOD
K)O
DRY
DE
NS
ITY
(Y
d)
pcf
126
124
122
120
118FI VE TESTS
116MEAN OF F IVE T E S T S
114
112
110
M O IS T U R E CONTENT (W) IN PERCENT
F I G U R E 12 M O I S T U R E DE N SI TY CURV ES FOR SAND AND 2 % BENTONI TE P L O T T E D , USI NG CUBIC
R E G R E S S I O N MET HOD
N>
DRY
DE
NS
ITY
(Y
d)
pcf
26
24
122 — k
120
C O NT R OL LE D T E S T
MANUAL COMPACTION
RANDOM G RADAT IO N
------------- V A R I A B L E - L A Y E RTHI CKNESS
11010 125 6 7 8 9 14
M O IS TU R E CONTENT (W) IN PERCENT
F IG U RE 13 M O I S T U R E D E N S I T Y M E A N CURVES P L O T T E D , USING CUBIC REGRESSION M E T H O D
N>00
29
figures the curves for all the five tests in each group, as well as
their mean curve are plotted. In Figure 13 the mean curves for the four
non-plastic groups are plotted.
In Figures 14 through 19 the mean curves of each group are
plotted by the ASTM method and by the cubic method, for comparison
purposes. As will be shown later the correlation indices are not a
sufficient criterion for the reproducibility.
4.3 Reproducibility Evaluation
In general four methods are used here to evaluate the degree of
reproducibility of the tests in each group, and to compare each group to
the controlled-tests group.
The first method measures the percent overlap area of the mean
of each group with the mean of the controlled tests. This is an area
that may be specified on a certain construction contract. For this
analysis it was assumed that the specification indicates 95% of the
maximum density and 2% of the optimum moisture content of the com
paction test, as determined by the ASTM D 698 - 64T Method A test. This
is the actual requirement on many contracts. This indicates that any
point within the area bounded by the requirement and the curve would be
acceptable in the field. The boundary of the indicated areas are shown
in Figures 6, 7 and 8.
The overlap area was indicated on each figure and was measured
by a planimeter. The planimeter had a precision of one-hundredth of a
square inch. The average of three readings was recorded as the overlap
area. The measured areas and the computation for this method are shown
DRY
DE
NS
ITY
(
) p
cf
26
124
122
120
A ST M S T AN D A R D
CUBIC REG RE S SI ON
114
110
M O IS TU R E CONTENT (W ) IN PERCENT
F I G U R E 14 M O IS T U R E D E N S I T Y M EA N CURVES FOR C O N T R O L L E D TESTS P L O T T E D USI NG ASTM STANDARDAND C U B I C R E G R E S S I O N M E T H O D S
tzJO
DRY
DE
NS
ITY
(Y
d )
pcf
126
24
x122
120
A S T M STANDARD
CUBIC REGRESSION
MOISTURE CONTENT (W) IN PERCENT
FIGURE 15 M O I S TU R E D E N S I T Y M EA N C U R V E S FOR S A N D AND 1 0 % K A O L I N I T E P L O T T E D , USING
A S T M S T A N D A R D A N D CUBIC R E G R E S S I O N M E T H O D S
tzl
DRY
DE
NS
ITY
(Y
d )
pcf
26
124
22
20
A S T M STANDARD
- - CUBIC REGRESSI ON
M O IS T U R E CONTENT (W) IN PERCENT
FIGURE 16 M O I S T U R E D E N S I T Y M E A N C U R V ES FOR SAND AND 2 % B E N T O N I T E P L O T T E D , USlKlGA S T M S T A N D A R D AND CUBI C R E G R E S S I O N METHODS
wNJ
DRY
DE
NS
ITY
(Y
d )
pcf
126
124
122
120
A S T M STANDARD
- - CUBIC REGRESSI ON
MOISTURE CONTENT (W) IN PERCENT
F I G U R E 17 M O I S T U R E D E N S I T Y M E A N C U R V E S FOR RANDOM G R ADAT I ON SAND P L O T T E D USING A S T MS T A N D AR D AND CUBIC R EG RE SS ION M ET H OD S
(y4
DRY
DE
NS
ITY
(X
d )
pcf
26
24
122
120
116 A S T M S T A ND AR D
CUBIC R E G R E S S I O N
5 76 8M O IS T U R E CONTENT ( W ) IN PERCENT
FIGURE 18 M O I S T U R E D EN SI TY MEAN CURVES FOR VARIABLE L A YE R- THI CKNES S COMPACTED SANDP L O T T E D , U S I N G AS T M STANDARD AND CUBIC REGRESSI ON METHODS
DRY
DE
NS
ITY
(*
d)
pcf
126
124
22
__J120
ASTM STANDARD
- - CUBIC REGRESSION
105 8 126 7 9 13 14MOISTURE CONTENT (W) IN PERCENT
FIGURE 19 M O I S T U R E D E N S I T Y ME AN CURVES FOR M A N U A L L Y COMPACTED S A N D P L O T T E D , USINGA S T M S T A N D A R D AND CUBI C R E G R E S S I O N M ET HODS
in
in Tables A.2, A.3 and A.4 in the Appendix. The overlap area of the
sand-clay mixtures were not compared with the controlled tests on sand,
since they are, essentially, different soils. The results of this
method are presented in Table 1.
The second method assumes that the specification requires 100%
of the maximum dry density. The Arizona Highway Department, for example,
requires 100% of the maximum density for highway base courses, as deter
mined by the method used in this work. The deviation of the maximum
density of the mean of each group from the mean of the controlled tests
is determined. This is expressed as a percent of the maximum density of
the mean of the controlled tests. The results for this method of
analysis'are also presented in Table 1.
The third method measures the standard deviation of the overlap
area of the curves within each group. The results are presented in
Tables 1 and 2. The fourth method measures the standard deviation of
the maximum densities of the curves within each group. The results for
this measure of the reproducibility are also shown in Tables 1 and 2.
The maximum density of each group as well as the optimum
moisture content are also presented in these tables for comparison
purposes. Whenever possible the reproducibility results for the cubic
and ASTM methods were compared. The cubic curves for individual tests
were plotted only for the controlled group, as shown in Table 2.
4.4 Moisture Content Patterns
The nonuniformity of moisture content within the compacted
specimen causes different degrees of compaction in the layers. The
TABLE 1. Reproducibility of Compaction in Terms of Standard Deviation of Each Group and Percent of
Overlap Area of Mean of Each Group from Mean of the Controlled Tests
ASTM METHOD CUBIC METHOD
PARAMETERMax.Yd
pcfO.M.C.
%
&Max.
%
OverlapArea
%
S'.Areas
%
SMax.
%
Max.Yd
pcfO.M.C.
%
AMax. y^
%
Overlap . Area
%
CONTROLLED TESTS 124.0 11.3 0 100 7.7 0.32 123.5 11.3 0 100
RANDOM GRADATION SAND 122.8 11.3 1.0 78 4.9 0.14 122.2 11.3 1.0 75
VARIABLE LAYER THICKNESS SAND 122.8 11.3 1.0 79 10.0 0,28 121.8 11.3 1.4 72
MANUALLY COMPACTED SAND 126.3 10.5 1.9 50 5.2 0.23 125,6 10.5 1.7 52
TABLE 2, Effect of Plasticity on Reproducibility of Compaction Curve in Terms of Standard Deviation
for Each Parameter
ASTM METHOD CUBIC METHOD
PARAMETERP.I. Max.
Ydpcf
O.M.C.%
SAreas
%
S : Max.
% .
Max.Yd
pcfO.M.C.
%
SAreas
%
SMax.
%
CONTROLLED TESTS NP 124.0 11.3 7.7 0.32 123.5 11.3 7.8 0.27
SAND + 10% KAOLINITE 8 124.7 10.3 7.9 0.30 123.7 11.3 4.2 0.18
SAND + 2% BENTONITE 14 121.8 11.5 1.7 0.09 121.1 11.3 4.5 0.24
C/J00
39
standard deviation in the moisture contents between the three layers
in each test are presented in Table 3. The maximum standard deviation
value for each test, and the moisture content at which it occurred are
presented in this table. In addition, the layer within which the
largest moisture content occurred per compacted specimen was noted for
possible variation patterns.
4.5 Gradation Change
The reuse of the soil, for all the six to seven data points in
the compaction test, affects the particle sizes. As the soil is reused
some of the particles break into smaller particles. Grain size analyses
were conducted on specimens compacted by both mechanical and manual
compaction. For comparison purposes, these gradation curves are shown
in Figure 20, along with the controlled grain size distribution before
the compaction.
40
TABLE 3. Standard Deviations in Layer Moisture Content (Maximum Value
for Each Test)
PARAMETER P.I. O.M.C.%" TEST NO. W% S%
1 8.5 .552 13.7 .43
CONTROLLED TESTS NP 11.3 3 15.6 .534 8.4 .295 12.0 .39
1 12.9 .402 14.0 .50
SAND + 10% KAOLINITE 8 10.3 3 9.8 .364 12.7 ,275 13.5 .26
1 15.8 .322 10.8 .30
SAND + 2% BENTONITE 14 11.5 3 10.2 .344 12.3 .305 16.0 .23
1 11.9 .342 15.0 .23
RANDOM GRADATION SAND NP 11.3 3 9.7 .294 12.4 .305 15.7 .40
1 13.2 .562 15.1 .43
VARIABLE LAYER THICKNESS NP, 11.3 3 13.6 .37SAND 4 16.0 .22
5 11.2 . 56
1 14.6 . 352 6.5 .24
MANUALLY COMPACTED SAND NP 10.5 3 14.1 .244 10.3 .305 12.4 .34
100
90
80
70
60
50
40
30
20
10
0
BEFORE COMPACTI ON
■— A F T E R MANUAL COMPACTION
- - AF TE R MECHANI CAL COMPACTION
0.1 1.0G R A I N S I ZE IN MM
2 0 0 140 4 0 20 10 4S T A N D A R D SIZE NUMBER
2 0 E F F E C T OF COMPACTION ON GRADATI ON OF SAND
CHAPTER 5
DISCUSSION OF RESULTS
5.1 Comparison of Cubic Model vs. ASTM Method
The curves plotted by the cubic method and the ASTM method are
compared in Figures 14 through 19. The ASTM curves in general have
higher peaks than the cubic curves. Both methods give approximately
the same optimum moisture content except for the sand-kaolinite mixture.
The curves for the controlled tests, random gradation and manually
compacted groups show close correlation. The sand-bentonite mixture and
the variable layer-thickness group show some divergence between the two
methods. Figure 15 indicates the poor correlation between the two
methods for the sand-kaolinite mixture.
The maximum density deviations and the percent overlap areas of
the sand group show very good correlation between the two methods as
seen in Table 1. The standard deviations of the higher plasticity groups
showed poor correlation between the two methods as outlined in Table 2.
It is likely that a higher order model (e.g. a fourth order equation)
would be more representive for plastic soils. However, the additional ̂
computations involved will outweigh the resulting degree of refinement.
For higher plasticity soils. Table 2 shows poor agreement of the
standard deviations for the two methods, while Table A.1 in the Appendix
indicates that the correlation indices for the cubic model are excellent.
' 42
43This confirms the fact that was stated earlier that the correlation
index is an overall measure of the fit and not particularly indicative
of the fit at the peak region.
It can be stated that the cubic equation is a valid mathematical
expression for the moisture-density relationship of the well-graded sand
used for this study. However, this model is not representative of soils
whose density is very sensitive to moisture content.
5.2 Controlled Tests
The curves in Figure 3 indicate that, with the degree of control
possible in this study, the reproducibility was not perfect. The
standard deviation of the overlap areas, which is the most representative
indication of the degree of reproducibility of the curve is 7.7%. This
indicates that with this degree of control the test cannot be uniquely
conducted. The standard deviation of maximum density is relatively
small (0.32%). However, the overlap area is more representative of the
type of soil and test conducted than the peak point of the curve, whose
determination depends on the chance of obtaining a data point at that
location of the curve. The large standard deviation of overlap areas
can be attributed to the sensitivity of the area to slight changes in
the optimum moisture content.
Although the degree of reproducibility is not perfect with the
imposed control, nevertheless, it is far better than that obtained for
a fine sand by other researchers (6). The deviation of maximum density
for that research was almost four times that obtained with the controlled
tests in this study. In the above mentioned research (6) the results
44
were obtained by five operators, and the control was much less than in
the present study. The optimum moisture contents did not appreciably
vary in this study. This indicates that the compactive energy did not
change during the course of the five controlled tests.
5.3 Plasticity
The standard deviation values for the maximum dry density and
the overlap areas for the sand-kaolinite and the sand-bentonite mixtures
are compared with the controlled tests in Table 2. The degree of
reproducibility of the tests greatly improves with the sand-bentonite
mixture. This is not the case with the sand-kaolinite mixture, which
had a lower plasticity.
The bentonite (predominantly montomorillonitic) has a greater
surface area and plasticity than the kaolinite and is more sensitive to
water. However, the density of the sand-kaolinite mixture proved to be
more sensitive to moisture variations than the density of the sand-
bentonite mixture, as seen in Figures 15 and 16, The larger portion of
kaolinite (10%) as compared to the bentonite portion (2%) in the mixture
is probably the cause of this sensitivity. This larger portion of fines
does also account for the larger maximum densities of the kaolinite
group.
The test results indicate that the degree of reproducibility of
the higher plasticity groups is influenced by the mineral component and
the percentage of fine particles more than the plasticity indices. The
results show that the optimum moisture contents did not exhibit appreci
able variations.
45
5.4 Gradation Effect
The standard deviations for this group are less than that of the
controlled tests as seen in Table 1. This is opposite to what should be
expected. However, in comparing Figures 3 and 6, it can be seen that,
with the random gradation group a larger number of points fall outside
the smoothly drawn curves than with the controlled tests. This points
out the degree of bias introduced by the ASTM method of plotting the
curves.
Figure 9 indicates that the random gradation sand had a lower
maximum density than the controlled tests, and this is reflected in the
overlap area of 78% as shown in Table 1. This is due to a larger per
centage of finer particles (about 2%) in the controlled tests as
compared with that in the random gradation. Method of preparing the
controlled gradation sand introduced the larger percentage of finer
particles.
The results here show that a slight change in the gradation from
the controlled tests causes the area overlap to be reduced to 78%. This
indicates that the reproducibility of the curves is sensitive to small
gradation changes. The optimum moisture contents did not vary appreci
ably in this group.
5.5 Layer-Thickness Effect
Table 1 indicates that the standard deviation of overlap areas
increased to 10%, as compared to 7.7% for the controlled tests. Further
more, the overlap area of this group is 79% when compared with the
controlled test group. There are small variations in the optimum
46moisture contents between the tests in this group, as seen in Figure 7.
These variations in optimum moisture contents are more responsible for
reducing the degree of reproducibility than the small change in the
maximum densities. These variations in the optimum moisture content can
be attributed to the nonuniformity in the moisture content of the layers
(see Table 3), which was due to the variations in layer thicknesses.
The standard deviation of maximum density is small but that is
not a very good indication of the relationship as indicated earlier.
Therefore, it can be stated that variation in layer-thickness, within the
normal limits accepted in practice, significantly influences the degree
of reproducibility.
5.6 Manual Compaction
This factor has the greatest effect on the degree of repro
ducibility of sand than any other group, when compared to the controlled-
tests group. Table 1 shows that the overlap area is 50%, and the
deviation of the maximum density is 1.9% from that of the controlled
tests group. The density of this method is greater than the controlled-
jtests group by the indicated percent, as seen in Figure 13.
These results suggest that the manual tamper applied greater
compactive energy to the sand specimens than the mechanical tamper
(controlled tests). This point is further confirmed by the results of
the gradation analysis of Figure 20 and the lowering of optimum moisture
contents as indicated in Table 1. Similar results were found during the
earlier research on a sandy soil (6). The 1.9% increase in the maximum
density by the use of manual compaction is very close to the 1.7%
47increase obtained in that earlier research. The larger energy applied
causes the greater breakdown of particles; the higher density; the lower
optimum moisture content; and consequently decreases the degree of repro
ducibility of this group of tests, when compared with the controlled-
tests group.
The greater density obtained by the manual tamper may be
attributed to one or more of the following factors:
(a) The application of the load is not completely vertical in
manual compaction, and thus has a horizontal component.
This may have a kneading effect that will increase the
density.
(b) The drag effect of the cable of the mechanical tamper could
reduce the compactive energy of this method.
(c) The poor adjustment of the free fall, among other
factors, also may influence the energy transmitted in the
compact ion test.
The standard deviation of areas for this group is 5,2% as
compared with the 7.7% of the controlled-tests. The greater uniformity
of moisture content in the three layers (Table 3); the larger percentage
of the fines; and the increased energy are probable causes for the
improvement of reproducibility within this group.
5.7 Moisture Content Patterns
The maxima of the standard deviations for the layer moisture
contents are presented in Table 3. It is observed that the large
Majority (70%) of the maximum deviations take place on the wet-side of
48
the optimum. In this region the water has a higher potential mobility
under the application of tamper loads. This may account for the larger
deviations observed in that region."
The moisture content for each data point was computed as the
arithmetic mean of the moisture content of the three layers. As a
result of the greater deviations in the layer moisture contents the data
points are less dependable on the wet-side of the optimum than on the
dry-side of the optimum. This suggests that, in the case of divergence
of the data points from the smooth curve, more weight should be given
to the points on the dry-side of the optimum.
There was no definite pattern indicating which layer has the
maximum moisture content. However, in about half of the tests the
middle layer was observed to have the greatest moisture content of the
three layers. The maximum variation in layer moisture content was
1.1%.
CHAPTER 6
. CONCLUSIONS
6.1 Summary
This study was initiated with the aim of determining the
influence of a number of parameters on the degree of reproducibility of
the compaction curve of soils. It was also intended that this degree of
reproducibility would be measured in a statistical manner, and that
mathematical expressions for the compaction curve would be investigated.
The following conclusions can be drawn from this study:
1. The standard deviation and the percent overlap area were
determined to be valid statistical methods of measuring the
degree of reproducibility.
2. Absolute reproducibility is not obtainable with the degree of
control possible with the present methods of test.
3. The degree of reproducibility increased sharply when 2% bentonite
was added to the sand.
4. Reasonable variations in layer-thickness decreased the degree
of reproducibility.
5. Reproducibility is sensitive to a small change in gradation.
6. Reproducibility showed no appreciable change when 10% kaolinite
replaced the finer particles in the soil.
49
50
7. Manual compaction increases the maximum density as compared to
mechanical compaction. Manual compaction shows poor correlation
as determined by the controlled tests.
8. The reproducibility of the manual compaction (within its group)
was better than that of the mechanical compaction.
9. The maximum deviation in the layer moisture contents generally
occurs on the wet-side of the optimum moisture content.
10. The cubic equation is a good approximation of the moisture-
density relationship of the well-graded sand used in this
research. It is probable that the cubic equation or a
modification of it can be used as the moisture-density curve
equation for any well-graded sand.
11. For high plasticity soils, this cubic expression is not a valid
representation of the moisture-density relationship.
12. Manual compaction and variations in layer-thickness (in that
order) have the largest influence on the reproducibility. These
parameters should be controlled during the compaction tests if
reproducible results are to be expected.
6.2 Future Research
From the analysis of the results of this research the following
suggestions are made for future research:
1. The effect of plasticity should be further studied by using only
one type of clay mineral, to isolate the independent effect of
plasticity on reproducibility.
The effect of compaction method on the reproducibility should
be studied.
The number of tests conducted to study the degree of repro
ducibility should be increased.
The causes of the greater energy transmitted to the soil with
the manual tamper, as compared to the mechanical tamper, should
be investigated.
APPENDIX
LEAST SQUARES SOLUTION FOR THE PARAMETERS OF A CUBIC POLYNOMIAL
MODEL:
DE = A BW CW2 * FW3
WHERE:
Dg = Expected Value of Dry Density
W = Moisture Content
SUM OF SQUARES 2
2 N o N5 = 2 , (D:. - D ) = V (D. - A - BW - CW - FW )
i=l 1 h i=l 1
WHERE:
D^ = Observed Value of Dry Density
N = Number of Observations
MINIMIZE S2 :
as N0 = 2 % (D. - A - BW - CWZ - FW3)(~W2)
SC" i=l 1
(A. 3) 0 = % ^ " A f ̂ ” B % W3 - C f W4 - F f W5i=l i=l i=l 1=1 1=1
as3F"
= 0 =N2 I 1=1 1
A - BW - CW FW3)(-W3)
(A. 4) 0 =N N _ . N . N ' N ,I D.W - A % W - B I W - C % W - F % W
1=1 1=1 1=1 1=1 1=1
CLEARING A FROM EQUATIONS A.l AND A.2 AND ADDING:
r N N N -I N _ ( N X2'0 = I Dj. I W - N y D.W + B N I W - I w. 1=1 1 1=1 i=l 1 . 1=1 '1=1 /
N N N ,q r N N N -1(A.5) ♦ C N y w - I w y w ❖ F. n y w -■ I w % w3
i=i 1=1 i=i i=i 1=1 1=1
CLEARING A FROM EQUATIONS A.2 and A.3 AND ADDING:
N N „ N N -I N N „ / N _\2l0 = I D.W I W - 1 W % D.W * B, I w y w .■ Iw1=1 1=1 1=1 1=1 1=1 i=i '1=1 ^
(A. 6) + Cr N N . N _ N _I W I w4 - I w2 % w3
1=1 1=1 1=1 1=1
CLEARING A FROM EQUATIONS A.3 AND A.4 AND ADDING
N N . N „ N I W % w5 - I W2 % w 1=1 1=1 1=1 1=1
0 =r N N N _ N _
y d .w y w3 - y d .w 3 y w2.1=1 1 i=i i=i 1 i=i
+ B N .,2 r ..,4 NI r i r . i t
Li=l 1=1 \l=l
(A. 7) * CN „ N- N _ N ..% w2 % w5 - I w3 I w4 1=1 1=1 1=1 1=1
4- F - N 2 v ..,6 N 3 % ,.,51% w % w - % w % w1=1 1=1 1=1 1=1 .
54WHEN:
N N NI D I W - n y
1=1 1=1 1=1
. r 2 f ? \ 2S5 N 2 w - y w
1=1 U = 1 /
N N NS n y w - I w y
1=1 1=1 i=i
N 4 N NS n y w4 - I w y
i=i 1=1 i=i
N N Nes I d w y w2 - y
i=i 1 i=i i=i
N= I WNI w3 - ( ! w2)2
1=1 1=1 \i=i jN= I W
NI w4 N - N- y w2 y1=1 1=1 1=1 1=1
N- I w NI w5 N N- 1 "2 I1=1 1=1 1=1 1=1
N - 1 Diw2 N
I_ N
w - y d .w 3 T w2
N= I w2Ny w4 -f ? w3)21=1 i=i \i=l )
N. - 1 w2
NI w5 -N „ NI w3 I w4
1=1 1=1 1=1 1=1N- I w2
NI w6 -N „ NI W3 I w5
1=1 1=1 1=1 1=1
55THUS:
+ BR2 * CR3 + FR4 = 0 (A.8)
S1 + BS2 + CS3 + FS4 = 0 (A.9)
Pj + BP2 + CP3 + PP4 = 0 (A.10)
CLEARING B FROM EQUATIONS A.8 AND A,9 AND ADDING:
(R1s 2 - r 2s1) + c (r3s 2 - r 2s 3) + f (r4s2 - r 2s4) = 0 (A.11)
CLEARING B FROM EQUATIONS A.9 AND A.10 AND ADDING:
CS1P2 - W + C(S3P2 - S2P3̂ + p (S4P2 - S2P4) = 0 (A.12)
WHEN:
Ql * R1S2 - R2S1
^2 = R3S2 “ R2S3
^3 = R4S2 " R2S4
^4 = S1P2 “ S2P1
% " S3P2 ~ S2P3
% " S4P2 - S2P4
THUS:
Qx + CQ2 + FQ3 = 0 (A.13)
56
Q4 + CQ5 * FQ6 = 0. (A„14)
CLEARING C FROM EQUATIONS A.13 AND A.14 AND ADDING:
„ Q2 % - ^ 5' % - ^ 2 %
SOLVING FOR C IN EQUATION A.13:
FQ3 + Q,
SOLVING FOR B IN EQUATION A.8:
CR + FR, = R.B =
R2
SOLVING FOR A IN EQUATION A.l:N N . N 0 N -^ D. - B £ W - C I W - F I W
& i^l 1 1=1 1=1 1=1= , — - ,
CORRELATION INDEX (R):N „
2 A ̂ ̂R = 1.0 N ,I (Dj, - D)2 1=1
WHERE:
N
STANDARD DEVIATION (S):N „I (Di - D)2
S = 1=1 1N - 1
57
TABLE A.I. Cubic Regression Coefficients and Correlation Indices, forMoisture-Density Curves.
Parameter P.I. Test No. A B C F R2
Controlled TestsNP
12345
122.53120.53 115.51 111.24 109.96
-4.688-4.317-2.614-1.034-1.094
.855
.852
.640
.453
.513
-.038 -.039 -.031 -.024 - -.028
.972
.967
.956:
.981
.984Sand + 10% Kaolinite
8
12345
78.4561.6345.2489.7767.55
6.55310.05715.9082.7079.198
-.048 -.259 -.905 .356
-. 297
-.015 - .013 .010
-.029 -.007
.961
.981
.986
.969
.959
Sand t 2% Bentonite
w::12345
112.4757.1399.0799.8296.57
-2.2308.9742.4971.8672.950
.581-.499.082.167.056
-.028.006
-.012-.015-.011
.995
.977
.954
.959
.975
Controlled Tests NP; 114.39 -2.155 .594 -.029 .953
Sand +■ 10% Kaolinite 8 68.47 9.168 -. 285 -.008 .946
Sand * 2% Bentonite 14 m©> 89.53 5.104 -.155 -.005 .949
Random Gradation Sand NP 1 122.45 -4.529 .775 -.033 .940
Variable Layer- Thickness Sand NP 1a 113.38 -1.508 .452 -.022 .939
Manually Compacted Sand NP 114.69 -1.347 .551 -.031 .950
58
TABLE A.2. The Deviations of Maximum Density and the Percent OverlapArea from the Mean of the Same Parameter.
Max. Overlap A Overlap Ave. A Ave. ofParameter P.I. Test No. Yd Area Max. y. Area Max. y , Overlap
. pcf Inches % d % % Areas %
Controlled 1 124.1 3.70 0.1 91Tests 2 125.0 3.23 0.8 79
NP 3 124.2 3.83 0.2 94 0.3 894 123.8 3.40 0.2 845 124.0 4.01 0.0 98
Mean 124.0 4.07 - -
Sand + 10% 1 125.6 2.83 0.7 80Kaolinite 2 124.8 3.43 0.1 97
8 3 124.3 3.37 0.3 96 0.4 924 124.6 3.48 0.1 995 123.8 3.10 0.7 88
Mean 124.7 3.52 - -
Sand + 2% 1 121.7 3.74 0.1 93Bentonite 2 121.7 3.76 0.1 93
14 3 122.0 3.78 0.2 94 0.1 944 121.8 3.76 0.0 935 121.8 3.93 0.0 97
Mean 121.8 4.03 - -
59
TABLE A.3. The Deviations of Maximum Density and the Percent OverlapArea from the Mean of the Same Parameter.
Max. Overlap A Overlap Ave. A Ave. ofParameter Test No. Yd Area Max. v,i Area Max. y. Overlap
. P cf . Inches % d % % Areas %
Random Gradation 1 123.2 3.50 0.3 86Sand 2 123.0 3.88 0.2 95
3 122.8 3.54 0.0 87 0.1 914 122.6 3.68 0.2 905 122.8 3.97 0.0 97
Mean 122.8 4.08 - -
Variable Layer- 1 122.6 3.88 0.2 95Thickness Sand 2 122.0 3.15 . 0.6 77
3 123.0 3.92 0.2 96 0.4 . 894 122.6 4.00 0.2 985 123.8 3.25 0.8 79
Mean 122.8 4.10 - -
Manually Compacted 1 126.5 3.92 0.2 94Sand 2 127.2 3.37 0.7 81
3 126.6 3.72 0.2 89 0.4 864 125.6 3.45 0.6 835 125.7 3.57 0.5 85
Mean 126.3 4.18 - -
60
TABLE A.4. The Deviations of Maximum Density and the Percent OverlapArea from the Mean of the Controlled Tests.
Parameter Test No.Max,YS'
OverlapAreaInches
AMax. y ,
% d
Overlap Ave. A Ave. of Area Max. y. Overlap
% % Areas %
Random Gradation 1 123.2 3.17 0.6 78Sand 2 123.0 3.23 0.8 79
3 122.8 2.98 1.0 73 0,9 754 122.6 2.90 1.1 715 122.8 3.07 1.0 75
Mean 124.0 4.07 - -
Variable Layer- 1 122.6 2.94 1.1 72Thickness Sand 2 122.0 2.42 1.6 60
3 123.0 3.32 0.8 82 1.0 764 122.6 3.14 1.1 775 123.8 3.61 0.2 89
Mean 124.0 4.07 - -
Manually Compacted 1 126.5 1.94 2.0 48Sand 2 127.2 1.46 2.6 36
3 126.6 1.73 2.1 43 1.9 484 125.6 2.29 1.3 565 125.7 2.24 1.4 55
Mean 124.0 4.07 - -
REFERENCES
1. Arizona Highway Department. "Manual of Compaction Control Methods,"Phoenix, Arizona, 1963.
2. American Society for Testing Materials. "Compaction of Soils,"Special Technical Publication No. 377, 1964.
3. American Society for Testing Materials. "ASTM Standards," Part 11,1966.
4. Grim, R. E. Clay Mineralogy, McGraw-Hill, 1953.
5. Highway Research Board. "Symposium on Compaction of Earthwork andGranular Bases," Highway Research Record No. 177, 1967.
6. Johnson, A. W., and J. R. Sallberg. "Factors Influencing CompactionTest Results," Bulletin No. 319, Highway Research Board, 1962.
7. Kell, T. R. "The Influence of Compaction Method on Fabric ofCompacted Clay," unpublished Master's Thesis, The University of Arizona, 1964.
8. Lambe, T. W. Soil Testing for Engineers, John Wiley 8 Sons,Inc.,Tenth Printing, 1965.
9. Proctor, R. R. "Design and Construction of Rolled Earth Dams,"Engineering News Record, August 31, September 7, 21, 28, 1933.
10. Seed, H. B., J. K. Mitchell, and C. K. Chan. "The Strength ofCompacted Cohesive Soils," American Society of Civil Engineers, Proceedings: Research Conference on Shear Strength of CohesiveSoils, Boulder, Colorado, pp. 877-964, 1960.
11. Turnbull, W. J. "Field Investigation, Technique of FieldObservation Including Compaction Control, Soil Stabilization," Proceedings: Third International Conference on Soil Mechanicsand Foundation Engineering, Vol. II, pp. 319-333, Switzerland, 1953.
61
