RESILIENT MODULUS VERSUS INDEX PROPERTIES OF SOILS
by
Andrew J. Suedkamp
B.S., University of Colorado at Boulder, 1997
A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Civil Engineering
2002
This thesis for the Master of Science
degree by
Andrew J. Suedkamp
has been approved
by
NienYin Chang
7/>)/ /
Date
Suedkamp, Andrew J. (M.S., Civil Engineering)
Resilient Modulus versus Index Properties of Soils
Thesis Directed by Professor N. Y. Chang
ABSTRACT
Current mechanistic design for both flexible and rigid pavements is based on the
theory of elasticity. The computer code based on elastic layer theory developed by
the Chevron Corp is among the most frequently used codes for pavement design.
The essential input material property for pavement, base, subbase and subgrade is
their resilient modulus. It is the rebound (or unloading) modulus of elasticity after
a specific number of stress cycles of sample conditioning.
The cyclic triaxial test is the most appropriate test for evaluating the resilient
modulus of materials in a pavement system. Avoiding the highly technical nature
of the cyclic triaxial test and result interpretation, routinely, the resilient modulus is
obtained indirectly from its correlation with CBR (California Bearing Ratio), R
value (Hveem Stabilometer test result), and the unconfined compression strength
from much less sophisticated tests. This oversimplification results in inaccurate
modulus values by using lessthanideal functional relations. Thus, it is most
desirable to evaluate the resilient modulus through appropriate cyclic triaxial tests
using stateof the art equipment. In this study, such equipment is used. In
simulating the vehicular insitu loading conditions, the cyclic triaxial test loading
mechanism imposes a haversine stress wave on a sample under selected confining
in
pressures. Before the imposition of cyclic load, samples are conditioned by strictly
following the 1999 AASHTO test procedures.
Many factors affect the resilient modulus, such as engineering properties of soils,
magnitude and type of traffic loading, vehicle speed, short and long term
environmental variations (moisture content/freezethaw); construction quality
control, and the nature of materials being tested. To achieve accurate test results, it
is critical to replicate all important prevailing factors and samples. In this study
limited but crucial factors are included: dry density, moisture content, liquid limit,
plastic index, group index, grain size analysis, stress amplitude, and confining
pressure. The resulting resilient moduli are formulated as the functions of the
abovementioned influencing factors through regression analysis. Finally, resilient
moduli from cyclic triaxial tests are compared to the values obtained from all
available functional relationships for the purpose of examining their effectiveness.
This abstract accurately represents the content of the candidates thesis. I
recommend its publication.
Signed
IV
ACKNOWLEDGEMENT
I would like to express my gratitude to the following people:
Dr. N.Y. Chang: Without his enthusiasm and commitment to education,
geotechnical engineering, this research would not have been as inclusive and
thorough as we attempted it to be. In addition, his concern for not only the
professional, but also the personal success of his students was above and beyond
and is greatly appreciated.
LieuChing Jiang: Without his faithful dedication in the laboratory, the data
presented herein would never have been compiled or completed in such a precise
manner.
Jeerawat Chaijaruwanich: For enthusiam and willingness to help with statistical
analysis.
GROUND Engineering Consultants, Inc.: For their willingness to invest in the
geotechnical practice through education, equipment, training, and their constant
support and allocation of resources.
Colorado Department of Transportation: For assistance with the laboratory
specimens and commitment to improving the quality of highway construction
through research.
Dick Suedkamp: For encouraging and supporting the pursuit of excellence in
practical geotechnical engineering, in business, and in life.
CONTENTS
Figures...................................................................viii
Tables....................................................................ix
Chapter
1. Introduction.........................................................1
1.1 Problem Statement....................................................1
1.2 Research Objectives..................................................4
1.3 Research Approach....................................................4
1.4 Scope of Study.......................................................5
1.5 Engineering Significance of this Research............................5
2. Literature Review....................................................8
2.1 Definition of Resilient Modulus......................................8
2.2 Evolution of AASHTO Resilient Modulus Procedures / Use...............9
2.3 Previous Research Regarding Factors that Affect Resilient Modulus....9
3. Test Facility.......................................................14
4. Test Procedures and Program.........................................16
5. Data Analysis and Discussion........................................21
6. Formulation of Functional Relations and Comparison Between Lab Test
Results and Model Predictions.......................................30
7. Discrepancies Between Field and Laboratory Resilient Modulus........32
VI
8. Summary, Conclusions and Recommendations for Further Research.........34
Appendix
A. Plots of Resilient Modulus versus Moisture Content with Grain Size
Distribution and Material Properties...............................36
B. Plots of Resilient Modulus versus Index Properties, Rvalue, Density.82
C. Plots of Resilient Modulus versus Index Properties, Rvalue, Density after
Removing the Outlying Results.....................................119
References...............................................................156
vii
FIGURES
Figure
1.01 Current Correlations Between Resilient Modulus and Rvalue...........6
3.01 Resilient Modulus Test Equipment....................................14
3.02 Triaxial Cell With Specimen Inside.................................14
3.03 Resilient Modulus Test Apparatus As Specified By AASHTO T307......15
4.01 Sample Processing..................................................16
4.02 Sample Sieving.....................................................16
4.03 Sample Mold........................................................17
4.04 Placing Specimen Into Mold.........................................17
4.05 Measuring Lifts And Compacting.....................................17
4.06 Filter Paper Placement.............................................18
4.07 Leveling Top Platen................................................18
4.08 Prepared Specimen..................................................18
4.09 Diameter Measurement...............................................18
4.10 Triaxial Cell Loaded...............................................18
4.11 Connecting Triaxial Cell To Machine................................18
4.12 LVDTs Secured In Place.............................................19
viii
TABLES
Table
5.01 Sample Properties........................................................22
5.02 Resilient Modulus Results................................................24
5.03 Interpolated Resilient Modulus Results...................................25
5.04 Coefficient Correlation Matrix...........................................26
5.05 Correlation Coefficients and Equations...................................29
IX
1. Introduction
1.1 Problem Statement
In the recent past, the elastic layer theory was implemented to design pavement
sections. In doing so, the resilient modulus of each layer is required as input to
complete the design and will affect the performance of the entire flexible pavement
section. The resilient modulus is the measurement of the soils ability to rebound
after subjecting it to a load. This translates to the soils ability to resist deformation
when subjected to repeated axial loading with small confining pressures. The
resilient modulus of the subgrade material underlying the pavement surface affect
the required pavement layers thickness with respect to a particular design load and
allowable deformations. Most pavement distress that occurs can be attributed to
deformation of the underlying bases, subbases, and subgrades. Unfortunately, in
the past, performing resilient modulus testing was difficult and expensive.
Therefore, other test procedures were performed and their results were correlated to
obtain resilient modulus values. These correlations are not usually very accurate.
With a national highway paving industry in which billions of dollars are spent
annually, it is impractical to continue to use inaccurate correlations to arrive at one
of the most important factors in pavement design. Therefore, inaccurate
estimations in the resilient modulus potentially result in a pavement section that is
either under or overdesigned.
Typically, the resilient modulus used in pavement design for a base, subbase, or
subgrade material has been achieved through correlations to more conventional,
less sophisticated test procedures. Rvalue, California Bearing Ratio (CBR) and
unconfined compressive strength testing are easily performed and the results are
often correlated to a particular resilient modulus value.
1
In a pavement system, the materials below the pavement providing structural
support are subjected to repeated loading from the traffic imposed on the pavement.
The resilient modulus of the underlying material varies with void ratio, density,
moisture content, amplitude of the loading, frequency of the loading, confining
pressure, and soil variability with respect to soil type, plasticity index, and
gradation. Although the soil type, moisture, density, and void ratio will affect the
results of the CBR, Rvalue, and unconfined compressive strength, these test
methods cannot account for confining pressure or the effects of frequency and
amplitude of repeated loading. The most accurate way of determining the resilient
modulus of soil subjected to given conditions requires resilient modulus testing
using a triaxial chamber with repeated loading capabilities, ideally with confining
pressures and loading which models the insitu condition.
Previously, it has not been practical for those working in the industry to perform
routine resilient modulus testing for each pavement design. The equipment was
expensive and the test procedure was rigorous. However, recent advances with
computer software and equipment have reduced the cost and effort associated with
performing such tests.
Problems relating to stateoftheart pavement design may not be limited to the
determination of the resilient modulus of bases, subbases, and subgrades. Current
AASHTO correlations between resilient modulus and Rvalue for granular soils
often result in resilient modulus values that are seldom, if ever, achieved for
laboratory compacted specimens (most achieved resilient modulus values are
between 25 65 percent less than the correlation indicates). However, most
pavements perform well when founded on subgrades composed of such soils (Al
a, Alb). Locally, the Colorado Department of Transportation (CDOT) has
2
revised the correlation to reduce the error in overpredicting the resilient modulus
for granular soils, but the current equation correlating Rvalue to resilient modulus
still tends to yield resilient modulus values that are rarely obtained for higher
quality granular soils. Additional research should be performed regarding the
effects that actual resilient modulus values have on pavements constructed on
granular soils and modifications to the structural number design equation may be
considered. In addition, moisture content has a tremendous impact on the resilient
modulus. It is important to carefully consider the moisture content of each soil that
is being tested.
Although within the last 40 years considerable research has been performed to
develop correlations between more common laboratory test procedures and the
resilient modulus, newer test procedures for resilient modulus differ from the
procedure used in many of the earlier research projects. For example, previous
resilient modulus test procedures consisted of using confining pressures that were
well above the insitu confining pressures of the base, subbase and / or subgrade
just below the pavement. It is difficult to predict actual confining pressures that act
on insitu materials. In addition, axial loads were applied that appear to be higher
than modem traffic would impose. Current resilient modulus test procedures
appear to be much more consistent with insitu loading and confining conditions.
Therefore, some of the data presented herein may not be perfectly comparable with
previous research performed. It is important that the test procedure closely
simulates the insitu condition that the materials will be subjected to over the
design life.
3
1.2 Research Objectives
The objectives of this thesis are as follows: 1) to formulate the relationship
between the resilient modulus (based on current test procedures) and the standard
index properties and Rvalue, 2) to quantify the effects of moisture content on
resilient modulus, and 3) to present information through literature review as well as
through a large testing program showing that it is more reasonable to rely on actual
resilient modulus testing than questionable correlations to determine the resilient
modulus for use in the design of pavement sections.
1.3 Research Approach
The approach adopted for this study was to quantify the relationship between
resilient modulus and index properties of soils, as well as to quantify the effects of
moisture content on the resilient modulus using data obtained from a largescale
testing program.
Many of the research projects previously performed based conclusions on results
from limited data. In some cases, research was performed on three samples. This
report was prepared based on 45 samples that were each subjected to resilient
modulus testing at three different moisture contents.
The materials were provided by the Colorado Department of Transportation
(CDOT). Prior to resilient modulus testing, CDOT tested each sample for Rvalue,
gradation, and plasticity index. The standard proctor densities and moisture
contents were determined from CDOT testing, as well as testing performed for this
research. All soils tested yielded Rvalues of 50 or less.
4
1.4 Scope of Study
For this research, 135 resilient modulus tests were performed on 45 samples of
material that was provided by the Colorado Department of Transportation (CDOT).
CDOT had performed standard property testing and Rvalue testing for each
sample. Also, moisture/density relationship testing was performed by CDOT and
as part of this research. All soils tested yielded Rvalues of 50 or less. These
samples were subjected to resilient modulus testing at various moisture contents.
The resilient modulus values were plotted against the index properties, Rvalue,
moisture, and density and then the test results were analyzed using regression
analysis to determine correlation relationships. In addition, correlation analysis and
multiregression analyses were performed using the statistical software, R, to
determine which combination of index properties results in the best correlations.
1.5 Engineering Significance of this Research
The significance of this research is as follows:
The number of actual resilient modulus tests that were performed exceeds other
known research works. Increasing the database of test results is important if more
accurate correlations are to be determined, and is also important to determine the
accuracy of correlations that are currently used.
The current correlation used locally by the Colorado Department of Transportation,
as well as the correlation used by AASHTO do not accurately predict the resilient
modulus of roadbed soils. As shown in Figure 1.01, the current correlation tends to
overpredict the resilient modulus. The data obtained throughout this research,
combined with the existing correlations used in pavement design makes a strong
5
case for the pavement design industry to consider cyclic triaxial testing as the sole
method for determining resilient modulus values of roadbed soils.
Figure 1.01: Current Correlations Between Resilient Modulus and Rvalue
(from Colorado Department of Transportation)
R value
Montana (1996)  Current CDOT (NCHRP 128 1972)
Wyuoming (1994) ..... A1 Lower (1982) AASHTO 1993 (A1 Upper 1982)
o Yeh and Su (1989)Suggested (R2 = .2555)
Chang (1994) Least Squares Fit (R2 =.3928)
6
The reduction of the resilient modulus of a particular soil as the moisture content
increases suggests that seasonal or longterm moisture content increases in
pavement bases, subbases, and subgrades should be considered prior to testing.
The research presented demonstrates that performing resilient modulus testing on
samples that are close to optimum moisture content based on Proctor data may
overpredict the resilient modulus. AASHTO test procedures specify that resilient
modulus testing is performed on samples that have been moistureconditioned to
either insitu moisture contents (obtained in the field), the optimum moisture
content (as determined by the Proctor test), or by the governing municipality. In
Colorado, the insitu moisture content five years after completion of paving may be
significantly different than those obtained during the pavement design process in
the field or by Proctor testing.
Lastly, this research shows that it is possible to perform large quantities of resilient
modulus testing. The resilient modulus testing performed for this report was
performed in less than two months. It is possible to perform up to 5 tests per day or
more, inclusive of sample preparation. Technology has advanced to the point were
changes of the cell pressure and loading amplitude are controlled by computer
software. Strains and realtime resilient modulus values are also determined by
computer software. Initially, the equipment is expensive. However, of the billions
of dollars spent annually on the construction or reconstruction of roadways, only a
fraction of the cost is for the actual pavement section design. If longerlasting
roadways result from more accurate pavement designs, a slight increase in costs
associated with pavement designs would be greatly offset by the savings in
maintenance and reconstruction.
7
2. Literature Review
2.1 Definition of Resilient Modulus
The resilient modulus of a material is a measurement of the elastic rebound
stiffness of a pavement material under repeated axial loading and is determined
using an application of stresses in a cyclical manner. This most closely simulates
the repetition of wheel loads acting on a pavement or pavement subgrade/base
material. The test results provide the relationship between the applied stress and
the recoverable deformation of pavement construction materials. The imposed
stresses are usually well below those associated with failure and subsequently fall
below the MohrCoulomb failure envelope. In a resilient modulus test, the sample
is subjected to repeated axial loading along with a constant confining pressure.
Since deformation of the underlying subgrade material often results in pavement
fatigue or rutting, it makes sense that the confining pressure is related to the insitu
confining pressure acting on the subject sample. The resilient modulus is
calculated by measuring the recoverable deformations that occur after each cyclical
load is imposed on a sample and dividing this quantity into to the deviator stress
that was imposed, as shown below:
Mr = Od / Â£a
Where, Â£a = 5 / L and Oj = P/A
8 = recoverable axial deformation
L = original length
P = repeated load
A = cross sectional area
Typically, the resilient modulus is obtained from averaging the recoverable
deformations obtained during the last five loading repetitions of each cycle.
8
2.2 Evolution of AASHTO Resilient Modulus
Procedures / Use
Since the first comprehensive road test performed by AASHO approximately 40
years ago, the pavement design process has evolved to incorporate resilient
modulus of soils for characterizing structural support capacities and layer
coefficients (AASHTO, 1986). The AASHO road test performed in 1962
suggested that 60 to 80 percent of the deflection measured in pavement surfaces is a
result of the deformation of the subgrade soils. This results from an accumulation
of strain induced from the repetition of a load. Subsequent testing and modeling
has been performed and the most recent design guide, released in 1993, states that
the resilient modulus is the definitive material property used to characterize
roadbed soil. By the definition provided by AASHTO, the resilient modulus is a
measure of the elastic property of soil recognizing certain nonlinear characteristics.
AASHTO incorporated the resilient modulus because it is a property that can be
used in mechanistic analysis of multilayered systems for predicting roughness,
cracking, rutting, faulting, etc., because it is recognized internationally for
characterizing materials used in pavement design, and because the resilient
modulus can be determined inplace by nondestructive testing. Unfortunately, the
available correlations to obtain the resilient modulus tends to over predict the
resilient modulus for most soil types.
2.3 Previous Research Regarding Factors
that Affect Resilient Modulus
Within the recent past, much time has been devoted to research regarding the
resilient modulus. Research has been performed to develop proper resilient
modulus test procedures, to correlate resilient modulus to other laboratory test
methods such as the Rvalue, CBR, unconfined compressive strength, and to
develop seasonal environmental effects on the resilient modulus.
9
The composition of the soil, plasticity, gradation, and group index certainly
influence the resilient modulus of soils. Detailed work by Thompson and Robnett,
1976 did not yield a direct correlation between resilient modulus and any single soil
property.
The deviator stress and confining pressure used during the testing procedure also
influences the resilient modulus (Robnett and Thompson, 1976; Brown, 1974; Buu,
1980; Seed, Mitry, Monismith, Chan, 1967). The research performed regarding the
confining pressure indicates that increasing the confining pressure results in an
increased resilient modulus, more so for granular soils than cohesive soils.
Generally, the resilient modulus of soils is greatest under the smallest deviator
stress and the highest confining pressure. However, the deviator stress has a
greater impact on the resilient modulus than the confining pressure.
Moisture content and density have been found to influence the resilient modulus.
Robnett and Thompson (1976) concluded that moisture content significantly affects
the resilient modulus, but its impact is less pronounced with specimens that are
compacted between 95% and 100% of the standard proctor density. The degree of
saturation has a greater impact on the resilient modulus since it is typically an
indication of moisture and density (Thompson and Robnett, 1976). Although
density may reach an equilibrium point with time and water infiltration/drainage,
density has an effect on the resilient modulus. As the density increases, the void
ratio decreases, the effective stress increases, and this generally leads to an increase
in the resilient modulus. However, some studies by Robnett and Thompson (1976)
have shown that for certain soil types, density does not play as crucial of a role as
moisture content. Results presented in this report also tend to show that there is a
general reduction in resilient modulus with an increase in moisture content,
regardless of actual density. The conditioning cycle also provides a means to
10
ensure some degree of compaction of the soil since it is performed until no
reduction in sample height is measured.
The resilient modulus will vary throughout the year as a result of freeze/thaw and
seasonal moisture changes in the subgrade. As the time of year can be related to
moisture content variations of the subgrade, the resulting resilient modulus will be
increased at times of the year when moisture content is lower. In addition, the
resilient modulus will be increased when subgrades are colder, or frozen (Hamilton,
1966). The AASHO Road test showed that reductions of the resilient modulus on
the order of over 70 percent may occur in the spring, while substantial increase may
occur in the winter when compared to the summer values. Robnett and Thompson
(1976) and Elliott and Thornton (1987) also demonstrated that freeze/thaw cycles
significantly reduced the resilient modulus of various finegrained soils.
Chang, Chiang, and Jiang performed work in 1994 in conjunction with the
Colorado Department of Transportation on 20 samples of generally granular
material in an attempt to develop a correlation between the Rvalue and the resilient
modulus. Yeh and Su (1989) performed research on twenty samples with
classifications ranging from A76 to Alb for a report also prepared for CDOT.
These results were included in the work by Chang, Chiang, and Jiang (1994).
However, only limited testing was performed for each soil type in this research, and
the testing was performed with the soils in a saturated condition. This may not be
the most realistic approach because the subgrade soils within this region are seldom
fully saturated. CTL Thompson performed work in 1997 through 1998 in
conjunction with the Metropolitan Government Pavement Engineers Council
(MGPEC) in Denver, Colorado. Part of that scope included testing which
attempted to correlate resilient modulus to Rvalue, CBR, and the unconfined
compression test. Based on work performed by Chang, Chiang, and Jiang, as well
as work performed by Yeh and Su (1989) and CTL Thompson (1997), there is not
11
an available correlation between resilient modulus and other laboratory test
procedures that yields correlation coefficients (R2) greater than 0.8 (CTL, 1997 for
A6 soils using the unconfined compressive strength test), and most values of R2
are around 0.4.
In general, most of the research completed has yielded information that shows
general trends of the resilient modulus when compared to several of the factors
discussed above. In most cases, very few actual resilient modulus tests were
performed.
For a particular soil, moisture in combination with density, has a significant effect
on the resilient modulus of soils. Past studies suggest that the degree of saturation
is a better guideline, combining the effects of both moisture and density. For the
DenverMetro Area, it does not seem practical to perform resilient modulus testing
on saturated or nearly saturated samples. The work performed for this research
suggests that the resilient modulus of a material approximately 2 percent over the
optimum moisture content (as determined by applicable ASTM test procedures)
may cause the resilient modulus to be approximately 30 to 40 percent less than the
resilient modulus of a material with a moisture content at optimum. The resilient
modulus at 4 percent over the optimum moisture content is reduced by
approximately 50 to 60 percent of the resilient modulus of the material at optimum
moisture content. This presents a significant problem in the DenverMetro Area
where overexcavation and moisture treatment of subgrade materials is performed
to reduce the swell potential. In many cases, specifications require that moisture
contents range from optimum to 4 percent above optimum. This range in the
moisture content can cause the soil support values (the resilient modulus) to be
decreased by 50 percent or more. Further complicating this matter is the longterm
tendency for subgrade materials to become generally wetter with time and at
specific times of the year. Therefore, special consideration should be given to
12
resilient modulus values used for design, keeping in mind the possibility of higher
moisture contents of the pavement materials after the construction is completed.
13
3. Test Facility
The resilient modulus testing was performed at the laboratory of GROUND
Engineering Consultants, Incorporated during the spring of 2002. The resilient
modulus machine was manufactured by GCTS in 2001 from Arizona. The testing
equipment (shown in Figures 3.01 through 3.03) follows AASHTO T307 and was
calibrated before and during the resilient modulus testing.
Figure 3.01: Resilient Modulus Test Figure 3.02: Triaxial Cell
Equipment With Specimen Inside.
14
Figure 3.03: Resilient Modulus Test Apparatus As
Specified By AASHTO T307
RESILIENT MODULUS CROSS SECTION
(Not to Scale)
15
4. Test Procedures and Program
Fortyfive samples were delivered to GROUND Engineering Consultants, Inc. The
samples were delivered by CDOT and consisted of cohesive material that yielded
Rvalues of less than 50. CDOT performed testing to determine the liquid limit,
plasticity index, gradation, Rvalue, group index and AASHTO classification for
each sample. The samples were numbered and delivered to the GROUND
Engineering Laboratory in individual bags. Prior to testing, moisture/density
relationships were determined according to ASTM D698. The resulting maximum
dry density and optimum moisture contents were used in the specimen preparation
for the resilient modulus testing.
The following procedure was used for performing the resilient modulus test:
The clay particles within the samples were broken down using a rubber mallet and
sieved over a number four sieve, as shown in Figures 4.01 and 4.02, respectively.
Figure 4.01: Sample Processing Figure 4.02: Sample Sieving
After the samples were sieved over the number four sieve, the moisture content was
obtained from a 200 gram sample of the specimen. Additional moisture was added
to obtain as closely as possible the target moisture content of either optimum, 2
percent above optimum, or four percent above optimum, in accordance with the
procedure outlined in AASHTO T307, ANNEX A1 (moisture conditioning).
16
After the moisture conditioning, the appropriate sample mass was determined based
on the total required volume and at least 95 percent of the standard proctor dry
density. The 4inch inner diameter split mold was prepared with a rubber
membrane liner and filter paper was placed on the bottom (Figure 4.03). Then,
approximately 1/5 of the sample (by mass) was placed (Figure 4.04) and the sample
was compacted in five measured lifts (Figure 4.05), according to ANNEX A4
(kneading compaction).
After the specimens were compacted according to the procedure outlined above,
they were trimmed and filter paper was placed on the top of the sample (Figure
4.06), the top platen was leveled and secured (Figure 4.07), a small vacuum force
was applied, and the split mold was removed (Figure 4.08).
Figure 4.03:
Sample Mold
Figure 4.04:
Placing Specimen
Into Mold
Figure 4.05:
Measuring Lifts
And Compacting
17
Figure 4.06: Figure 4.07: Figure 4.08:
Filter Paper Placement Leveling Top Platen Prepared Specimen
The circumference of the sample was measured at the top, center, and bottom as
shown in Figure 4.09. After the sample has been properly prepared and positioned,
the loading ram was aligned and the cell was placed and secured (Figure 4.10).
Lastly, the loading ram was connected to the machine (Figure 4.11).
Figure 4.09:
Diameter Measurement
Figure 4.10:
Triaxial Cell
Loaded
Figure 4.1 T.
Connecting Triaxial
Cell To Machine
18
The last steps required prior to performing the resilient modulus test were to secure
the LVDTs (Figure 4.12) just after a small seating load was applied to seat the
loading ram securely on the platen. After the loading ram was seated, the LVDTs
were adjusted to ensure that measurements would be made throughout the test as
the sample exhibits deformations.
&
I Figure 4.12: LVDTs Secured In Place
j
After the test specimen and equipment was properly set up the samples were
subjected to resilient modulus testing. The resilient modulus testing was performed
according to AASHTO T307. During the testing, a repeated axial cyclic stress of
fixed magnitude, load duration (0.1 second), and cycle (1.0 seconds) was applied to
the cylindrical test specimen in a cyclical manner, and the specimen was subjected
to a static confining stress provided by means of a triaxial pressure chamber. The
confining medium was air. The total resilient (recoverable) axial deformation
response of the specimen is measured by two LVDTs and used by the computer
software to calculate the resilient modulus.
This loading sequence consists of a conditioning period of at least 500 applications
of a 4 psi axial load with a confining pressure of 6 psi. The conditioning cycle was
performed until no decrease in sample height was observed (measured by the
computer), but no more than 1,000 cycles. After the conditioning cycle was
performed, the specimens were subjected to axial loads of 2 psi, 4psi, 6 psi, 8 psi,
and 10 psi. Each axial load cycle consisted of 100 load repetitions for a load
19
duration of 0.1 second with a 0.9 second rest period. This loading sequence was
performed for each confining pressure of 2 psi, 4 psi, and 6 psi. The resilient
modulus was determined by the computer program by averaging the recoverable
deformations of the last five cycles for each loading sequence. For this research,
the resilient moduli shown are those yielded from the test at a confining pressure of
2 psi and an axial load of 10 psi.
After the completion of each test, the specimens were weighed and moisture
contents were determined so that the actual moisture/density characteristics of the
tested specimen were obtained.
20
5. Data Analysis and Discussion
The results of the laboratory testing program are summarized on Table 5.1.
Included therein are the soil sample numbers, the classifications for each soil and
the group index, liquid limit, plasticity index, grain size analysis, Rvalue, standard
proctor moisture and density, and resilient modulus values obtained at the optimum
moisture content, 2 percent above the optimum moisture content, and 4 percent
above the optimum moisture content.
The resilient modulus tests for each soil type (at the different moisture contents)
were plotted versus the actual moisture content. In most cases, the prepared
specimens were not exactly at the optimum moisture content, 2.0 percent, or 4.0
percent above optimum. The points shown on the plots are the actual test results at
the actual moisture contents, as determined after the test was completed.
Therefore, the resilient modulus values at moisture contents of optimum, 2.0
percent above optimum, and 4.0 percent above optimum were picked off the
resultant curve. These plots, along with sample information and gradation curves
are shown in Appendix A, Figures 1 through 45. The data table of the resilient
modulus results obtained at the specific moisture content and densities obtained
during testing are shown in Table 5.02. Table 5.03 presents the results of the
resilient modulus values at exactly optimum moisture, 2 percent above the
optimum moisture and 4 percent above the optimum moisture. These values were
obtained from the plots of the actual results.
21
Table 5.01 Sample Properties
Soil Data
Sample AASHTO Atterberg Limits
Number Classification RValue Group Liquid Plasticity
Index Limit Index
20010710 A27 29 0 42 17
20010348 Alb 32 0 17 2
20010709 A27 9 1 44 28
20010936 A26 49 0 28 13
21X110353 A24 50 0 28 9
20010556 A26 35 0 33 14
20010586 A24 40 0 27 9
20010855 A26 24 2 40 24
20010511 A26 45 0 37 12
20010324 A27 13 2 54 26
20010510 A26 19 1 37 19
20010321 A24 37 0 27 8
20010856 A27 18 3 41 24
20010316 A4 49 0 37 7
20010320 A6 40 1 34 ^ 15
20010345 A6 14 2 29 15
20010939 A6 21 3 40 21
20010384 A6 21 3 35 18
20010816 A4 44 0 22 7
20010629 A4 23 1 23 10
20010354 A6 17 3 32 17
20010568 A6 8 2 23 13
20010350 A6 17 5 34 19
20010377 A6 10 7 39 24
20010381 A6 15 7 38 23
20010383 A6 12 7 39 23
20010388 A6 14 8 39 20
20010379 A76 14 13 43 28
20010386 A6 8 13 40 24
20010670 A76 27 14 46 21
20010669 A76 23 15 44 21
20010358 A76 11 23 52 31
20010360 A76 15 19 48 24
20010706 A4 19 4 25 8
20010363 A76 5 23 45 29
20010361 A76 8 21 42 26
20010569 A6 10 12 33 16
20010359 A76 10 25 47 28
20010367 A76 6 32 56 34
20010362 A76 7 23 43 25
20010368 A76 6 24 41 27
20010707 A6 19 10 29 12
20010366 A76 6 35 53 36
20010365 A76 11 46 62 43
20010357 A75 26 18 45 15
22
Table 5.01 Sample Properties (continued)
Soil Data (continued)
Sample Number Gradation Analysis Proctor Data (ASTM D 698)
% Passing #4 Sieve % Passing #10 Sieve % Passing #40 Sieve % Passing #200 Sieve Optimum Moisture Maximum Drv Densitv
20010710 77 60 30 15 13.6 115.2
20010348 96 84 33 17 9.4 126.1
20010709 68 47 28 20 11.0 119.7
20010936 67 55 35 22 9.0 127.8
20010353 70 60 38 23 13.0 116.1
20010556 68 61 41 23 13.8 115.9
20010586 79 65 45 24 10.9 121.6
20010855 84 69 45 27 12.1 118.3
20010511 97 93 55 29 16.2 111.6
20010324 80 63 42 30 17.0 109.7
20010510 98 73 46 31 10.9 121.4
20010321 70 60 45 34 13.4 117.6
20010856 96 84 58 35 12.9 117.0
20010316 84 77 63 36 15.7 111.6
20010320 73 63 48 37 12.9 118.8
20010345 94 91 76 39 13.0 118.1
20010939 79 74 62 39 18.0 107.6
20010384 85 75 58 40 13.0 113.7
20010816 99 96 68 41 9.7 123.4
20010629 100 100 80 41 11.1 122.8
20010354 91 85 68 41 12.6 115.9
20010568 100 100 88 45 12.2 117.8
20010350 96 91 77 49 10.8 123.8
20010377 91 81 65 49 13.7 116.2
20010381 92 82 66 49 14.9 113.4
20010383 89 82 67 50 15.3 113.0
20010388 89 83 71 57 16.5 105.9
20010379 95 90 77 60 16.2 109.6
20010386 95 90 79 64 17.4 109.9
20010670 97 94 87 70 19.3 103.4
20010669 96 94 89 73 18.9 104.0
20010358 91 88 83 76 21.9 101.4
20010360 93 90 85 78 21.5 102.3
20010706 99 98 96 80 13.0 117.7
20010363 98 95 90 82 17.2 109.4
20010361 98 96 93 84 19.7 104.8
20010569 100 100 97 85 18.2 106.4
20010359 100 98 95 87 19.7 105.8
20010367 98 97 94 87 23.2 99.8
20010362 100 99 98 90 15.5 109.3
20010368 99 98 96 90 17.4 106.2
20010707 100 100 100 91 14.4 114.5
20010366 100 99 98 92 17.2 110.5
20010365 100 100 98 96 19.9 101.6
20010357 100 100 99 98 21.3 99.0
23
Table 5.02 Resilient Modulus Results
Actual Data Acquired
Samnle Number Resilient Modulus
at Ontimum Moisture at 2% Over Ont. Moisture at 4% Over Ont. Moisture
MR Moist. Density MR Moist. Density MR Moist. Density
20010710 8.351 13.7 108.4 6.604 16.5 109.6 6.248 17.0 109.7
20010348 10.181 9.9 122.4 9.235 11.5 123.8 8,879 13.4 123.8
20010709 11.704 11.2 114.0 8.825 12.9 117.3 7.990 14.4 114.5
20010936 10.425 9.8 121.5 9.698 10.7 122.0 8.196 12.4 122.1
20010353 7.842 13.3 113.1 5.161 14.6 110.5 3.917 16.5 108.7
20010556 8.024 13.9 109.5 4,664 16.4 108.4 4.343 17.0 107.7
20010586 10.750 10.5 116.8 7.588 13.2 114.8 7.591 14.1 114.9
20010855 7.932 12.2 112.7 5.846 14.5 112.6 5.210 16.2 110.7
20010511 8.405 16.9 105.0 5.954 19.2 104.4 5.495 20.6 105.0
20010324 7.972 16.6 104.7 4.702 19.5 103.7 3.511 21.6 102.0
20010510 7.600 11.3 113.7 5,271 13.1 115.3 5,209 16.8 111.1
20010321 11.532 12.3 110.2 5.811 15.4 109.8 4,706 17.7 109.6
20010856 7,790 13.2 110.8 5.427 15.2 110.6 4.003 18.9 106.8
20010316 7.583 16.7 100.0 7.087 18.9 104.6 6.311 20.3 101.8
20010320 17.436 12.2 109.3 7.438 15.1 113.5 5.870 16.4 114.1
20010345 6.378 13.2 111.8 4.817 15.1 113.6 4.234 17.4 109.6
20010939 7,463 17.6 103.2 3.428 20.8 101.9 2.665 22.9 100.3
20010384 6.858 13.3 110.4 5.488 15.2 108.8 4.010 17.6 109.1
20010816 11.218 9.6 118.4 6.795 12.0 117.1 5.794 13.2 113.5
20010629 10.060 11.3 115.6 6.069 14.0 114.7 5.729 14.6 115.8
20010354 7.135 13.3 109.1 4,631 14.9 110.1 3.821 16.6 107.9
20010568 5.778 13.2 111.9 5.243 14.2 115.5 4.934 16.7 111.5
20010350 8.220 11.5 122.8 6.724 12.9 120.5 6,247 14.6 120.1
20010377 7.663 14.0 111.4 4.244 16.0 108.1 3,515 18.1 109.3
20010381 5,636 14.9 110.9 3.839 17.3 108.9 3.551 18.7 106.8
20010383 5.162 15.8 107.0 3.960 17.8 107.1 2,953 19.9 104.4
20010388 4.608 16.9 103.6 3.200 18.8 102.8 2.964 21.0 103.2
20010379 6.740 16.1 101.9 3.799 18.4 97.4 3.380 20.5 103.2
20010386 5.481 17.3 104.3 3.434 19.5 104.2 2.732. 22.0 101.2
20010670 7.992 19.8 94.5 6.552 21.6 96.9 5.210 22.7 95.0
20010669 8.154 18.6 97.8 6.233 21.3 99.6 4.734 22.5 98.7
20010358 4,048 22.7 97.0 3.159 24.0 96.7 2.157 26.1 95.1
20010360 9.699 21.9 95.8 4.861 23.2 96.8 3.018 26.1 94.6
20010706 6.413 13.1 110.2 5.233 14.5 113.9 4.736 16.8 110.5
20010363 6.450 17.6 104.2 3.922 19.3 103.5 2.331 21.6 101.7
20010361 4.012 19.6 103.4 2.283 22.0 101.9 1.909 23.7 98.9
20010569 13,367 17.4 101.9 4.491 20.5 98.5 3.007 22.1 100.6
20010359 5,282 20.0 102.8 2.646 22.9 99.5 1.960 25.2 96.9
20010367 4.256 23.6 96.2 2.730 25.1 94.9 1.785 27.7 93.3
20010362 7.740 16.5 97.8 5.956 17.6 104.2 4.107 20.3 103.3
20010368 5.009 17.3 104.6 2.846 20.1 103.3 2.410 21.6 100.7
20010707 6.638 13.9 109.3 3.842 16.5 110.8 3.456 18.5 107.5
20010366 5,411 17.7 100.9 3.745 19.0 103.9 2.577 21.8 100.9
20010365 4.909 20.2 99.1 3.340 22.4 97.2 2.795 24.1 96.4
20010357 11.229 22.2 95.5 9.406 23.3 92.9 5.238 24.9 94.1
24
Table 5.03 Interpolated Resilient Modulus Results
Interpolated from Graph of Actual Points
Sample Number Resilient Modulus at optimum moisture content Resilient Modulus at 2.0 percent over optimum Resilient Modulus at 4.0 percent over optimum
20010710 8.426 7.313 5.663
20010348 10.663 9.299 8.879
20010709 12.242 8.786 7.248
20010936 10.996 9.473 8.196
20010353 8.801 4.768 3.821
20010556 7.823 5.044 4.228
20010586 10.179 7.797 6.814
20010855 8.122 6.041 5.219
20010511 9.773 6.718 5,564
20010324 7.388 4.670 3.773
20010510 8.619 5.369 5.209
20010321 8.713 5.811 4.779
20010856 8.214 5.511 4.389
20010316 7.601 7.455 6.731
20010320 13.088 7.739 5.414
20010345 5.996 4.833 4,305
20010939 6,757 4.175 2.823
20010384 7.079 5.714 4.254
20010816 10.931 7.097 5.578
20010629 10.489 7.132 5.522
20010354 9.267 4.938 3.821
20010568 6.489 5.243 4.888
20010350 9.510 6.791 6.261
20010377 8.558 4.533 3.524
20010381 5.636 4.067 3.540
20010383 5.494 4.167 3.247
20010388 5.213 3.262 2.971
20010379 6.598 3.987 3.397
20010386 5.392 3.500 2.792
20010670 8.221 6.833 4.312
20010669 8.102 6.844 4,035
20010358 4.789 2.811 2.349
20010360 9.699 4.491 3.175
20010706 6.514 4.965 4,674
20010363 7.209 4.000 2.489
20010361 3.925 2.432 1.909
20010569 9.389 4.878 2.991
20010359 5.592 3.562 2.314
20010367 4,754 2,697 1.823
20010362 10.163 6.078 4.324
20010368 4.989 3.231 2.421
20010707 5.863 3.897 3.462
20010366 6.184 3.511 2.591
20010365 4.241 3.532 2.803
20010357 12.292 9.406 4.162
25
Several statistical analysis approaches were performed to correlate the resulting
resilient modulus values at the three different moisture contents to the Rvalue,
plasticity index, percent passing the 200 sieve, group index, and dry density. In
addition, the data was analyzed with the entire collection of data and then analyzed
the same way after dividing the data into two sets, which consisted of material that
contains over 50 percent passing the No. 200 sieve and material that contains less
than 50% passing the No. 200 sieve. The results of the statistical analysis with
corresponding correlation coefficients (as determined by Microsoft Excel using the
Statistical Analysis, Linear Equation Capability) are shown in Appendix A. A
coeffecient correlation matrix was also obtained by using the statistical software,
RConsole. Table 5.04 shows the correlation coefficients obtained when the
resilient modulus values are compared with the various index properties, group
index, Rvalue and the moisture / density data. Negative numbers indicate an
inverse relationship.
Table 5.04 Resilient Modulus Resilient Modulus Resilient Modulus
Coefficient Correlation at Optimum at 2% over Optimum at 4% over Optimum
Matrix Moisture Content Moisture Content Moisture Content
Rvalue 0.533 0.557 0.608
Group Index 0.464 0.507 0.635
Liquid Limit 0.365 0.401 0.543
Plasticity Index 0.487 0.571 0.640
% Passing #4 0.401 0.267 0.320
% Passing #10 0.404 0.334 0.413
% Passing #40 0.432 0.457 0.595
% Passing #200 0.389 0.464 0.646
Moisture (optimum) 0.417 __
Density (optimum) 0.303 __
Moisture (2% over opt.) 0.493
Density (2% over opt.) 0.456
Moisture (4% over opt.) 0.719
Density (4% over opt.) 0.713
26
The analysis that was performed using Microsoft Excel Statistical Analysis
consisted of fitting a straight line to the existing data using only two data sets at a
time, resilient modulus versus any of the other parameters, and then back calculated
the correlation coefficient and corresponding equation. The RConsole software
was used to determine the correlation coefficients by comparing the resilient
modulus values to each property. After RConsole provided the correlation
coefficients, a multivariant regression analysis was performed using the
parameters with the best correlation coefficients in order to develop relationships
between combinations of the liquid limit, plasticity index, gradation, moisture
content, and density to the resilient modulus.
Using the complete, existing data, correlation coefficients ranging from less than
0.1 to over 0.75. The best correlation using the entire data set was obtained for the
correlation between the resilient modulus at 2 percent over the optimum moisture
content versus the Rvalue of materials that classify as clay (greater than 50 percent
passing the No. 200 sieve). The worst correlations typically were obtained from
the analysis of resilient modulus versus Group Index or maximum dry density (as
determined by ASTM D 698), for soils with greater than 50 percent passing the No.
200 sieve. However, when the entire data set was used, as the moisture content of
the samples subjected to resilient modulus testing increased, the correlation with
the percent passing the No. 200 also increased. This trend is true for plasticity
index and Rvalue as well: As the moisture content increases from optimum, the
correlation of the resilient modulus to the percent passing the No. 200, the plasticity
index, or the Rvalue becomes better, with correlation coefficients of up to 0.4829,
0.4103, and 0.357, respectively, as determined by Microsoft Excel using a bestfit
straight line.
After these general relationships were established, the statistical analysis software,
RConsole was used to perform regression analysis. The correlation coefficients
27
between the resilient modulus at 4 percent above optimum and a combination of
liquid limit, plasticity index, percent passing the Number 4 sieve, moisture and
density yielded a corrected correlation coefficient of 0.755. The results generated
from both Excel and RConsole are shown in Table 5.05 for the comparisons
between resilient modulus and various index properties or resilient modulus versus
individual properties.
If it can be assumed that generally, the resilient modulus of soils increases as the R
value increases and as the plasticity index and percent fines decreases, then several
anomalies are apparent within the data obtained. Approximately 6 of the samples
tested, or 13 percent, yielded much higher resilient modulus values than would be
expected. If these samples are removed from the analysis, then the correlation
coefficients between resilient modulus and the Rvalue, the percent passing the No.
200 sieve, and the plasticity index all approach 0.52, when the resilient modulus at
4 percent over optimum is used. A multivariant regression analysis was not
performed with this data.
28
Table 5.05 Correlation Coefficients and Equations
Resilient Modulus Compared To: Resilient Modulus (% above optimum) R2 Equation (Using RConsole)
Various 0 0.628 RM0=25295.5298.5(PI)789.0(M0)+290.9(LL)+20.2(P200)113.6(DD0)
Various 2 0.577 RM2 = 5774.0 313.2 (PI) + 301.7 (LL) 450.5 (M2) + 23.1 (P10)
Various 4 0.755 RM4=15158.4235.9(P1)+150.8(DD4)+233.3(LL)+27.3(P4)169.7(M4)
Resilient Modulus Compared To : Resilient Modulus (%above optimum) Correlation Coefficient Equation (Using Excel)
Rvalue 0 0.270 RMO = 87.9 (RV) + 6080.8
Rvalue 2 0.320 RM2 = 75.3 (RV) + 3784.0
Rvalue 4 0.357 RM4 = 68.9 (RV) +751.7
PI 0 0.190 RMO = 113.0 (PI) + 10131
PI 2 0.329 RM2 =116.9 (PI)+ 7649.3
PI 4 0.410 RM4 =113.1 (PI)+ 6409.7
P200 0 0.163 RMO = 34.9 (P200) + 9791.3
P200 2 0.229 RM2 = 32.5 (P200) + 7104.4
P200 4 0.483 RM4 = 41.0 (P200) + 6394.1
Where, RMO = Resilient Modulus at Optimum Moisture Content RM2 = Resilient Modulus at 2% over Optimum Moisture Content RM4 = Resilient Modulus at 4% over Optimum Moisture Content PI = Plasticity Index LL = Liquid Limit RV = Rvalue MO = Moisture Content at Optimum M2 = Moisture Content at 2% over Optimum M4 = Moisture Content at 4% over Optimum DDO =Dry Density at Optimum Moisture Content DD2 = Dry Density at 2% over Optimum Moisture Content DD4 =Dry Density at 4% over Optimum Moisture Content P4 = % passing Number 4 sieve P10 =% passing Number 10 sieve P200 = % passing Number 200 sieve
29
6. Formulation of Functional Relations and Comparison
Between Lab Test Results and Model Predictions
Based on the data obtained in this research, the following relationships exist:
A) The resilient modulus of soils is affected by grain size, plasticity, density,
moisture content, confining pressure, and deviator stress.
B) The greater the moisture content of the sample, the closer the relationship is
between resilient modulus and plasticity, percent fines.
C) The best correlation using index properties is obtained when using the
resilient modulus at 4% over the optimum moisture content. The equation,
as generated using multiregression analysis in the statistical software, R
Console, is as follows : Resilient Modulus (4% over optimum) = 235.9
(P.I.) + 233.3 (Liquid Limit) + 27.3 (Percent Passing No.4 sieve) + 150.8
(Dry Density at 4% over optimum) 169.7 (Moisture Content) 15158.4.
This equation yields a corrected correlation coefficient of R2 = 0.76
D) The relationship between resilient modulus and Rvalue when all data is
used and the resilient modulus is at the optimum moisture content yields a
correlation coefficient of 0.27, where, resilient modulus = 87.9(Rvalue) +
6,080). If selected outlying data is removed, the correlation improves (R2 =
0.515, resilient modulus = 91.0(Rvalue) + 5,490). As the resilient modulus
is performed at higher moisture contents, the relationship with Rvalue
increases, especially if the data is filtered to only include samples with
greater than 50 percent passing the No. 200 sieve.
E) The relationship between resilient modulus and percent passing the number
200 sieve provides the best correlation when all data is used and the
resilient modulus is at 4 percent above the optimum moisture content (0.48,
resilient modulus = 41.0(% passing No. 200) + 6,394). If selected outlying
data is removed, the correlation improves (0.44, resilient modulus = 
30
39.3(% passing No. 200) + 6075.5). Unfortunately, the correlation
coefficient decreases as the moisture content decreases (at optimum, 0.16,
resilient modulus = 34.9(% passing No. 200) + 9791).
The data obtained was subjected to regression analysis using Microsoft Excel and
multivariant regression analysis in the statistical software, RConsole. Plots
contained in Appendix A show the individual relationships between resilient
modulus and various index properties, Rvalue, dry density etc.
31
7. Discrepancies between Field and Laboratory
Resilient Modulus
The resilient modulus of a soil can be obtained by laboratory testing and by non
destructive field testing using the falling weight deflectometer. Differences often
exist between the results of the resilient modulus that is obtained in the laboratory
and the results obtained in the field. Although sample preparation can be adjusted
to account for insitu conditions, it is difficult to accurately model the confining
pressure, axial load and temperature variation.
First, insitu conditions will vary throughout the year. This may result in insitu
conditions that vary with respect to moisture, density, and temperature from
laboratory prepared specimens.
Secondly, although theoretical confining pressures exist insitu that can be
calculated, it appears that insitu samples may actually be subjected to a confining
pressure that is between the ko condition and the triaxial confining condition
imposed in the laboratory. For example, a sample directly under the pavement
surface is confined by the surrounding soil. Although it is generally accepted that
pavements tend to deform when the underlying materials yield, the actual condition
that these materials are subjected to insitu may actually be somewhere between the
ko condition, where soil is not permitted to deform laterally, and the confining
pressure simulated in the laboratory. It may be beneficial to perform resilient
modulus testing on samples subjected to both standard confining pressures and
within a solid ring (to simulate ko condition). Ideally, the results could be
compared to actual insitu testing using a plate load test or falling weight deflection
machine. Common sense would suggest that pavement fatigue due to deformation
of the base, subbase, or subgrade is a result of the combination of a reduction of
the void ratio and lateral spreading.
32
Lastly, it is difficult to selectively obtain samples that are perfectly representative
of the materials that compose pavement base, subbase, and subgrade. As shown,
resilient modulus values exhibit general trends, but anomalies exist. It is not
entirely known why occasional samples will exhibit unusual resilient modulus
values. It is possible that in addition to the properties considered above, the
gradation of the materials finer than the Number 200 sieve have an impact on the
resilient modulus of soils. If accurate, representative sampling is not performed,
even accurate resilient modulus testing may result in poorly designed pavement
sections. This is the nature of soils engineering with respect to pavement design
and construction. It would be beneficial to perform correlation analyses between
laboratory resilient modulus values obtained from undisturbed samples using
various confining pressures and falling weight deflection test results of the insitu
material.
33
8. Summary, Conclusions and Recommendations
for Further Research
Based on the scope of work presented herein, the following conclusions may be
made:
A. The cyclical triaxial test is practical and reasonable to perform on a dayto
day basis and provides accurate resilient modulus values. With the amount
of money devoted to the construction and rehabilitation of pavements, either
more accurate correlations must be developed, or pavement engineers must
implement the cyclic triaxial testing as the sole method of obtaining
resilient modulus values for use in design.
B. Correlations between the resilient modulus and index properties or Rvalue
may be possible, but not as accurate as actual resilient modulus testing.
Indirect testing does not regularly provide accurate resilient modulus values
and tends to over predict the Resilient Modulus based on current correlation
equations that are in use. Due to the number of variables that affect the
resilient modulus of soils, a large number of samples will be required in
order to develop accurate correlations. The relationship between resilient
modulus and plasticity index / percent passing the number 200 sieve is
similar to the relationship to the percent Rvalue; their correlation to
resilient modulus is sensitive to moisture content. As the moisture content
increases from optimum, the resilient modulus more closely relates to the
plasticity index, percent passing the number 200 sieve, and Rvalue.
Therefore, it must be established what the proper moisture content should
be at for performing the testing. Longterm estimations of the insitu
moisture content of subgrades should be considered prior to performing
resilient modulus testing.
34
C. Clay materials that are subjected to resilient modulus testing behave more
like granular soils at moisture contents less than or near the optimum
moisture content.
D. The relationship to group index is variable and should not be considered.
Additionally, correlations to density and moisture should not be used since
these parameters may not be constant with seasonal variation and time.
E. A larger database of samples, with testing performed at variable moisture
contents would allow separate relationships to be compared within each soil
classification. Finegrained soils should be tested according to their
classification, for a certain gradation range, plasticity index range and it is
possible that more precise relationships may be obtained. Additional testing
such as the hydrometer analysis should be incorporated into future research.
F. Approximately 13 percent of the test results appeared to be outliers. The
correlations improve significantly if these are removed. Unfortunately,
these anomalies are not inconsistent with other work performed and must be
considered. This condition suggests that other factors, such as clay
mineralogy, may influence the resilient modulus.
G. Additional work should be performed to establish procedures for obtaining
the resilient modulus of granular soils. Previous work has shown that
correlations used to obtain the resilient modulus of granular soils are less
reliable than those used for finegrained soils.
35
APPENDIX A
Plots of Resilient Modulus versus Moisture Content with Grain Size
Distribution and Material Properties
36
Moisture Content (5.)
u>
Gradation Analysis
Sieve
13000
12000
11000
10000
9000
8000
7000
8000
5000
4000
3000
2000
1000
SOIL PROPERTIES
Moisture Content, opt. (%): 18.2
Dry Density, max (pcf): 106.4
Passing 0200 (%): 85
Liquid Limit: 33
Plasticity Index: 16
RValue: io
Sample 0: 20010569
Soil Type: A6 (12)
RESILIENT MODULUS: 4,870 psi
(at 2% over optimum)
Moisture Content (%)
u>
00
Gradation Analysis
Sieve
12000
11000
10000
9000
B000
7000
6000
5000
4000
3000
2000
1000
0
SOIL PROPERTIES
Moisture Content, opt. (%): 15.7
Dry Density, max (pcf): 111.6
Passing #200 (%}; 36
Liquid Limit: 37
Plasticity Index: 7
RValue: 49
Sample #: 20010316
Soil Type: A4(0)
RESILIENT MODULUS: 7,455 psi
(at 2% over optimum)
u>
vO
Gradation Analysis
Sieve
#4 #10 #40 #200
Moisture Content (55)
SOIL PROPERTIES
Moisture Content, opt. (%): 12.9
Dry Density, max (pcf): UB.8
Passing #200 (%): 37
Liquid Limit: 34
Plasticity Index: 15
RValue: 40
Sample #: 20010320
Soil Type: A6 (1)
RESILIENT MODULUS: 7,739 psi
(at 2% over optimum)
Moisture Content {%)
Gradation Analysis
Sieve
SOIL PROPERTIES
Moisture Content, opt. (%): 13.4
Dry Density, max (pcf): 117.6
Passing #200 (%): 34
Liquid Limit: 27
Plasticity Index: 8
RValue: 37
Sample #: 20010321
Soil Type: A2 4(0)
RESILIENT MODULUS: 5,811 psi
(at 2% over optimum)
Moisture Content (%)
Gradation Analysis
Sieve
#4 #10 #40 #200
SOIL PROPERTIES
Moisture Content, opt. (%): 17.0
Dry Density, max (pcf): 109.7
Passing #200 (%); 30
Liquid Limit: 54
Plasticity Index: 26
RValue: 13
Sample #. 20010324
Soil Type: A27(2)
RESILIENT MODULUS: 4,670 psi
(at 2% over optimum)
N)
Moisture Content (X)
Gradation Analysis
Sieve
#4 #10 #40 #200
SOIL PROPERTIES
Moisture Content, opt. (%): 13.0
Dry Density, max (pcf): 110.1
Passing ~#200 (%); 39
Liquid Limit: 29
Plasticity Index: 15
RValue: 14
Sample #: 20010345
Soil Type: A6 (2)
RESILIENT MODULUS: 4,833 psi
(at 2% over optimum)
Moisture Content (%)
Gradation Analysis
Sieve
#4 #10 #40 #200
SOIL PROPERTIES
Moisture Content, opt (%): 9.4
Dry Density, max (pcf). 126.1
Passing #200 (%): 17
Liquid Limit: 17
Plasticity Index: 2
RValue: 33
Sample #: 20010348
Soil Type: AlbfO)
RESILIENT MODULUS: 9,299 psi
(at 2% over optimum)
Moisture Content (55)
Gradation Analysis
Sieve
SOIL PROPERTIES
Moisture Content, opt. (%): 10.8
Dry Density, max (pcf): 123.8
Passing #200 (%): 49
Liquid Limit: 34
Plasticity Index: 19
RValue: 17
Sample #: 2001 .0
Soil Type: A6 (8)
RESILIENT MODULUS: 6,791 psi
(at 2% over optimum)
Moisture Content (%)
Gradation Analysis
Sieve
12000
11000
10000
9000
8000
7000
8000
5000
4000
3000
2000
1000
0
SOIL PROPERTIES
Moisture Content, opt. (%): 13.0
Dry Density, max (pcf): 116.1
Passing #200 (%): 23
Liquid Limit: 28
Plasticity Index: 9
RValue: 50
Sample #; 20010353
Soil Type: A24(0)
RESILIENT MODULUS: 4,768 psi
(at 2% over optimum)
Moisture Content (%)
4^
ON
Gradation Analysis
Sieve
#4 #10 #40 #200
SOIL PROPERTIES
Moisture Content, opt. (%): 12.6
Dry Density, max (pcf): 115.9
Passing #200 {%): 41
Liquid Limit: 32
Plasticity Index; 17
RValue: 17
Sample #: 20010354
Soil Tvpe: A6 (3)
RESILIENT MODULUS: 4,938 psi
(at 2% over optimum)
Moisture Content (X)
Gradation Analysis
Sieve
SOIL PROPERTIES
Moisture Content, opt. (%) 21.3
Dry Density, max (pcf): 99.0
Passing #200 (%): 98
Liquid Limit: 45
Plasticity Index: 15
RValue: 26
Sample #: 20010357
Soil Type: A75(lB)
RESILIENT MODULUS: 9,406 psi
(at 2% over optimum)
Moisture Content (%)
Gradation Analysis
Sieve
SOIL PROPERTIES
Moisture Content, opt. (%): 21.9
Dry Density, max (pcf): 101.4
Passing #200 (%): 76
Liquid Limit: 52
Plasticity Index: 31
RValue: \\
Sample #: 20010358
Soil Type: A76(23)
RESILIENT MODULUS: 3.358 psi
(at 2% over optimum)
Moisture Content (%)
VO
Gradation Analysis
Sieve
SOIL PROPERTIES
Moisture Content, opt. (%): 19.7
Dry Density, max (pcf): 105.8
Passing #200 (%): 07
Liquid Limit: 47
Plasticity Index: 28
RValue: 10
Sample #: 20010359
Soil Type: A76(25)
RESILIENT MODULUS: 3.062 psi
(at 2% over optimum)
Moisture Content (%)
Gradation Analysis
Sieve
SOIL PROPERTIES
Moisture Content, opt. (%): 21.5
Dry Density, max (pcf): 102.3
Passing #200 (%): 78
Liquid Limit: 40
Plasticity Index: 24
RValue: 15
Sample #: 20010360
Soil Type: A76(19)
RESILIENT MODULUS: 4,491 psi
(at 2% over optimum)
Moisture Content (5J)
Gradation Analysis
Sieve
#4 #10 #40 #200
SOIL PROPERTIES
Moisture Content, opt. (%): 19.7
Dry Density, max (pcf): 104.0
Passing #200 (%): 64
Liquid Limit: 42
Plasticity Index: 26
RValue: Q
Sample #: 20010361
Soil Type: A76(21)
RESILIENT MODULUS: 2,533 psi
(at 2% over optimum)
Ui
K>
Gradation Analysis
Sieve
#4 #10 #40 #200
Moisture Content (%)
SOIL PROPERTIES
Moisture Content, opt. (%): 15.5
Dry Density, max (pcf): 109.3
Passing #200 (%): 90
Liquid Limit: 43
Plasticity Index: 25
RValue: 7
Sample #: 20010362
Soil Type: A76(23)
RESILIENT MODULUS: 6.078 psi
(at 2% over optimum)
U\
u>
Moisture Content (/5)
SOIL PROPERTIES
Moisture Content, opt. (%): 17.2
Dry Density, max (pcf) 109.4
Passing #200 (%): 82
Liquid Limit: 45
Plasticity Index: 29
RValue: 5
Sample 20010363
Soil Type: A76(23)
RESILIENT MODULUS: 4,000 psi
(at 2% over optimum)
Moisture Content (%)
Gradation Analysis
Sieve
SOIL PROPERTIES
Moisture Content, opt. (%): 19.9
Dry Density, max (pcf): 101.6
Passing #200 (%): 96
Liquid Limit: 62
Plasticity Index: 43
RValue: n
Sample #. 20010365
Soil Type: A76(46)
RESILIENT MODULUS: 3,660 psi
(at 2% over optimum)
U\
Ui
Gradation Analysis
Sieve
Moisture Content (5)
SOIL PROPERTIES
Moisture Content, opt. {%): 17.2
Dry Density, max (pcf): 110.5
Passing #200 (%): 92
Liquid Limit: 53
Plasticity Index: 36
RValue: 6
Sample #: 2001 0366
Soil Type: A76(35)
RESILIENT MODULUS: 3,511 psi
(at 2% over optimum)
Ln
On
Gradation Analysis
Sieve
#4 #10 #40 #200
Moisture Content (%)
SOIL PROPERTIES
Moisture Content, opt, (%): 23.2
Dry Density, max (pcf): 99.8
Passing #200 (%): 87
Liquid Limit: 56
Plasticity Index: 34
RValue: 6
Sample #: 20010367
Soil Type: A76(32)
RESILIENT MODULUS: 2,697 psi
(at 2% over optimum)
Moisture Content {%)
Gradation Analysis
Sieve
SOIL PROPERTIES
Moisture Content, opt. (%): 17.4
Dry Density, max (pef): 106.2
Passing #200 (%): 90
Liquid Limit: 41
Plasticity Index: 27
RValue: 6
Sample #: 20010368
Soil Type: A76(24)
RESILIENT MODULUS: 3,231 psi
(at 2% over optimum)
Moisture Content {%)
Ui
00
Cradation Analysis
Sieve
SOIL PROPERTIES
Moisture Content, opt. (%): 13.7
Dry Density, max (pcf): 116.2
Passing #200 (%): 49
Liquid Limit: 39
Plasticity Index: 24
RValue: io
Sample #: 20010377
Soil Type: A6 (7)
RESILIENT MODULUS: 4,533 psi
(at 2% over optimum)
VO
Gradation Analysis
Sieve
Moisture Content {%)
SOIL PROPERTIES
Moisture Content, opt (%): 16.2
Dry Density, max (pcf): 109.6
Passing #200 (%): 60
Liquid Limit: 43
Plasticity Index: 28
RValue: 14
Sample #: 20010379
Soil Type: A76(13)
RESILIENT MODULUS: 3,987 psi
(at 2% over optimum)
Moisture Content (%)
Cradation Analysis
Sieve
18 13 14 16 16 17 10 19
18000
11000
10000
9000
6000
7000
6000
5000
4000
3000
2000
1000
0
SOIL PROPERTIES
Moisture Content, opt. {%): 14.9
Dry Density, max (pcf): 113.4
Passing #200 (%): 49
Liquid Limit: 38
Plasticity Index: 23
RValue: 15
Sample #: 20010301
Soil Type; A6 (7)
RESILIENT MODULUS: 4.067 psi
(at 2% over optimum)
Moisture Content (%)
Gradation Analysis
Sieve
#4 #10 #40 #200
12000
11000
10000
0000
8000
7000
6000
5000
4000
3000
2000
1000
0
SOIL PROPERTIES
Moisture Content, opt. (%): 15.3
Dry Density, max (pcf): 113.0
Passing #200 (%): 50
Liquid Limit: 39
Plasticity Index: 23
RValue: 13
Sample #: 20010383
Soil Type: A6 (7)
RESILIENT MODULUS: 4,167 psi
(at 2% over optimum)
Moisture Content (%)
ON
to
Gradation Analysis
Sieve
#4 #10 #40 #200
12 13 14 15 16 1? 10 19
12000
11000
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
Resilient
Modulus at
2% Over
Optimum
SOIL PROPERTIES
Moisture Content, opt. (%): 13.0
Dry Density, max (pcf): 113.7
Passing #200 (%): 40
Liquid Limit: 35
Plasticity Index: IB
RValue: 21
Sample #: 20010384
Soil Type: A6 (3)
RESILIENT MODULUS: 5,714 psi
(at 2% over optimum)
Gradation Analysis
Sieve
#4 #10 #40 #200
Moisture Content (%)
SOIL PROPERTIES
Moisture Content, opt. (%): 17,4
Dry Density, max (pcf): 109.9
Passing #200 (%): 64
Liquid Limit: 40
Plasticity Index: 24
RValue: 13
Sample #: 20010306
Soil Type: A6 (13)
RESILIENT MODULUS: 3,500 psi
(at 2% over optimum)
Moisture Content (%)
Gradation Analysis
Sieve
#4 #10 #40 #200
SOIL PROPERTIES
Moisture Content, opt. (%): 16.5
Dry Density, max (pcf): 105.9
Passing #200 (%): 57
Liquid Limit: 39
Plasticity Index: 20
RValue: 14
Sample #: 2001 0308
Soil Type: A6 (0)
RESILIENT MODULUS: 3,262 psi
(at 2% over optimum)
ON
Ui
Gradation Analysis
Sieve
Moisture Content (55)
SOIL PROPERTIES
Moisture Content, opt. (%): 10.9
Dry Density, max (pcf): 121.4
Passing #200 (%): 31
Liquid Limit: 37
Plasticity Index: 19
RValue: 19
Sample #: 20010510
Soil Type: A26(0)
RESILIENT MODULUS: 5,369 psi
(at 2% over optimum)
Ov
On
Gradation Analysis
Sieve
Moisture Content {%)
SOIL PROPERTIES
Moisture Content, opt. (%): 16.2
Dry Density, max (pcf): 111.6
Passing #200 (%): 29
Liquid Limit: 37
Plasticity Index: 12
RValue: 45
Sample #: 20010511
Soil Type: A26(0)
RESILIENT MODULUS: 6.718 psi
(at 2% over optimum)
ON
J
Moisture Content (7.)
Cradation Analysis
Sieve
#4 #10 #40 #200
SOIL PROPERTIES
Moisture Content, opt. (%). 13.B
Dry Density, max (pcf): 115.9
Passing #200 (%): 23
Liquid Limit: 33
Plasticity Index: 14
RValue: 35
Sample #: 20010556
Soil Type: A26(0)
RESILIENT MODULUS: 5,044 psi
(at 2% over optimum)
On
00
Gradation Analysis
Sieve
Moisture Content (%)
SOIL PROPERTIES
Moisture Content, opt. (%): 12,2
Dry Density, max (pcf): 117.0
Passing #200 (%): 45
Liquid Limit: 23
Plasticity Index: 13
RValue: a
Sample #: 20010568
Soil Type: A6 (2)
RESILIENT MODULUS: 5,243 psi
(at 2% over optimum)
Moisture Content (V.)
ON
O
Gradation Analysis
Sieve
#4 #10 #40 #200
SOIL PROPERTIES
Moisture Content, opt. (%): 18.0
Dry Density, max (pcf): 107.6
Passing #200 (%): 39
Liquid Limit: 40
Plasticity Index: 21
RValue: 21
Sample #: 20010939
Soil Type* A6 (3)
RESILIENT MODULUS: 4,175 psi
(at 2% over optimum)
o
o
Gradation Analysis
Sieve
Moisture Content (X)
SOIL PROPERTIES
Moisture Content, opt. (%): 10.9
Dry Density, max (pci): 121.6
Passing 0200 (%): 24
Liquid Limit: 27
Plasticity Index: 9
RValue: 40
Sample #: 20010586
Soil Type: A24(0)
RESILIENT MODULUS: 7.797 psi
(at 2% over optimum)
\L
sn^rTios ir.
I 5 o c
52: z
n
O
(P
3
I
O 3
0 3 S
.0 3
x r
Â£?f
Percent Passing
70 ^
J5 5'<
sN 2*T3
O ^
1 O >
oi
c ^3
3 W
c
3.*
CO
o
o
o
o
O' 05 J <0
0000c
00000
o o o o a
o
o
o
o
o
o
o
CO
o
o
o
o
CO
to
o>
a
Resilient Modulus (psi)
J
N>
Moisture Content {%)
Gradation Analysis
Sieve
#4 #10 #40 #200
SOIL PROPERTIES
Moisture Content, opt. (%): 10.9
Dry Density, max (pcf): 104 0
Passing #200 (%): 73
Liquid Limit: 44
Plasticity Index: 21
RValue: 23
Sample #: 20010669
Soil Type: A76(15)
RESILIENT MODULUS: 6,844 psi
(at 2% over optimum)
J
U)
Gradation Analysis
Sieve
#4 #10 #40 #200
Moisture Content {7)
SOIL PROPERTIES
Moisture Content, opt. (%): 19.3
Dry Density, max (pcf): 103 4
Passing #200 (%): 70
Liquid Limit: 46
Plasticity Index: 21
R Value: 27
Sample #: 20010670
Soil Type: A76(14)
RESILIENT MODULUS: 6,033 psi
(at 2% over optimum)
Moisture Content (%)
p*
Gradation Analysis
v
v
CL
Sieve
SOIL PROPERTIES
Moisture Content, opt. (%): 13.0
Dry Density, max (pcf): 117.7
Passing #200 (%): 00
Liquid Limit: 25
Plasticity Index: 8
RValue: 19
Sample #: 20010706
Soil Type. A4(4)
RESILIENT MODULUS: 4,965 psi
(at 2% over optimum)
L/i
Gradation Analysis
Sieve
#4 #10 #40 #200
100
90
00
70
c 60
 50
S 40
Â£ 30
20
10
0
Moisture Content (%)
SOIL PROPERTIES
Moisture Content, opt. (%): 144
Dry Density, max (pcf): 114.5
Passing #200 (%); 91
Liquid Limit: 29
Plasticity Index: 12
RValue: ig
Sample 20010707
Soil Type: A6 (10)
RESILIENT MODULUS: 3,897 psi
(at 2% over optimum)
Moisture Content (VI)
ON
Gradation Analysis
Sieve
#4 #10 #40 #200
SOIL PROPERTIES
Moisture Content, opt. (%): 11.0
Dry Density, max (pcf): 119.7
Passing #200 (%): 20
Liquid Limit: 44
Plasticity Index: 28
RValue: 9
Sample #: 20010709
Soil Type: A27(l)
RESILIENT MODULUS: 8,786 psi
(at 2% over optimum)
LL
33 o r "o a s a
' jq o c
Â£. 2. w r
c2aj'?S 2
= a' i S.
 =.=*Â£ n
3 r M / O
Cu ' O 3
3 ^0=!
d
ro^
h x r
cj\
bo i
CO
05
Percent Passing
33 GQ zn
Sg. B
3
CO 3 H *o_
^ 2*n d
o J =*s
<
o Â£ ^ o> CO o
2 w O in  o
1 o
3m0 vl
C o
CO
CO
tJ
M
Resilient Modulus (psi)
Moisture Content (%)
00
Gradation Analysis
Sieve
SOIL PROPERTIES
Moisture Content, opt. (%): 9.7
Dry Density, max (pcf): 123.4
Passing #200 (%): 41
Liquid Limit: 22
Plasticity Index: 7
RValue: 44
Sample #: 20010B16
Soil Type: A4(0)
RESILIENT MODULUS: 7,097 psi
(at 2% over optimum)
'O
Gradation Analysis
Sieve
#4 #10 #40 #200
Moisture Content {%)
SOIL PROPERTIES
Moisture Content, opt. (%): 12.1
Dry Density, max (pcf): 118 3
Passing #200 {%): 27
Liquid Limit: 40
Plasticity Index: 24
RValue: 24
Sample #: 2001 0B55
Soil Type: A26(2)
RESILIENT MODULUS: 6,041 psi
(at 2% over optimum)
Moisture Content {%)
00
o
Gradation Analysis
Sieve
SOIL PROPERTIES
Moisture Content, opt. (%): 12.9
Dry Density, max (pcf): 117.0
Passing #200 (%): 35
Liquid Limit: 41
Plasticity Index: 24
RValue: iq
Sample #: 20010056
Soil Type: A27(3)
RESILIENT MODULUS: 5,511 psi
(at 2% over optimum)
Moisture Content (%)
Gradation Analysis
Sieve
#4 #10 #40 #200
12000
11000
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
1
ta
3
3
O
O
OS
SOIL PROPERTIES
Moisture Content, opt. (%): 9.0
Dry Density, max (pcf): 127.8
Passing #200 (%): 22
Liquid Limit. 28
Plasticity Index: 13
RValue; 49
Sample #: 20010936
Soil Type: A26(0)
RESILIENT MODULUS: 5,760 psi
(at 2% over optimum)
APPENDIX B
Plots of Resilient Modulus versus Index Properties, Rvalue, Density
82
Resilient Modulus (psi)
Resilient Modulus (at optimum moisture) vs Rvalue
for soils with less than 50% Passing No. 200
Resilient Modulus (psi)
Resilient Modulus (at optimum moisture) vs Rvalue
for soils with greater than 50% Passing No. 200
Resilient Modulus (psi)
Resilient Modulus (at 2% over optimum moisture) vs Rvalue
for soils with less than 50% Passing No. 200
Resilient Modulus (psi)
Resilient Modulus (at 2% over optimum moisture) vs Rvalue
for soils with greater than 50% Passing No. 200
Resilient Modulus (psi)
Resilient Modulus (at 4% over optimum moisture) vs Rvalue
for soils with less than 50% Passing No. 200
Resilient Modulus (psi)
Resilient Modulus (at 4% over optimum moisture) vs Rvalue
for soils with greater than 50% Passing No. 200
Resilient Modulus (psi)
Resilient Modulus (at optimum moisture) vs Rvalue
for all soils
Resilient Modulus (psi)
Resilient Modulus (at 2% over optimum moisture) vs Rvalue
for all soils
Resilient Modulus (psi)
Resilient Modulus (at 4% over optimum moisture) vs Rvalue
for all soils
