U.S. Department of Transportation

Federal Highway Administration

1200 New Jersey Avenue, SE

Washington, DC 20590

202-366-4000

**Federal Highway Administration Research and Technology**

Coordinating, Developing, and Delivering Highway Transportation Innovations

REPORT |

This report is an archived publication and may contain dated technical, contact, and link information |

Publication Number: FHWA-HRT-12-030 Date: August 2012 |

Publication Number: FHWA-HRT-12-030Date: August 2012 |

**PDF Version** (4.44 MB)

PDF files can be viewed with the Acrobat® Reader®

Several types of chemically stabilized materials are used
under pavements as base courses, subbase courses, or treated subgrade. These
include lean concrete, cement stabilized or treated aggregate, soil cement,
lime-cement flyash, and lime-stabilized materials. Typically, the compressive
strength of these materials is used for construction QA and modulus and
flexural strength for pavement design. However, compressive strength testing is
more common than resilient/elastic modulus testing and flexural strength
testing. Industry groups and individual researchers have published several
correlations to estimate chemically stabilized base elastic modulus and
flexural strength from the compressive strength as shown in figure 29 through figure 32. The more common or feasible of these correlations are presented in figure 32. Resilient modulus (*M _{r}*) can be estimated conservatively as
20 percent of the unconfined compressive strength (

The LTPP database does not contain modulus test results for stabilized materials. Limited data were available for modulus tests of LCB layers, which were utilized for model development. Therefore, the discussion on stabilized materials in this report is brief.

Where:

*E*
= Modulus of elasticity, psi.

*f*'* _{c}* = Compressive strength, psi
tested in accordance with AASHTO T 22.

Where:

*E*
= Modulus of elasticity, psi.

*q _{u}* = Unconfined compressive strength,
psi tested in accordance with ASTM D 1633.

Where:

*E*
= Modulus of elasticity, psi.

*q _{u}* = Unconfined compressive strength,
psi tested in accordance with ASTM C 593.

Where:

*M _{r}*

*q _{u}* = Unconfined compressive strength,
psi tested in accordance with ASTM D 5102.

Resilient modulus of unbound materials and soils is a
required input in most pavement design procedures. It has a significant effect
on the computed pavement responses and, hence, pavement performance. Resilient
modulus can be tested directly from the laboratory, backcalculated
using nondestructive test data, or obtained through the use of correlations
with other material strength and index properties such as the California bearing
ratio (CBR), *R*-value, dynamic
cone penetrometer (DCP) value, soil Atterberg limit and gradation properties,
AASHTO soil class, etc.

As a result of extensive research into the
characterization of resilient modulus characterization conducted over the past
four decades, it is now widely recognized that resilient modulus exhibits
stress-state dependency, material dependency, and moisture and temperature
dependency. About 54 percent of State transportation departments use resilient
modulus* _{ }*in routine pavement design.

Of the several approaches put forth to estimate resilient
modulus in the laboratory for design purposes, the one that has gained
considerable traction over time is using a universal constitutive model as
proposed in NCHRP 1-28A (see figure 33).^{(103) }The strength of this
approach is that
two of the resilient modulus dependencies, stress-state and material type, can
be handled by this model form, which is an improvement over previously used
discrete models for coarse- and fine-grained soils which require knowledge of
material behavior prior to applying a function to characterize it.

The nonlinear elastic coefficients and exponents of the
constitutive model are determined by using linear or nonlinear regression
analyses to fit the model to laboratory generated resilient modulus* *test
data.

Where:

*M _{r}*
= Resilient modulus, psi.

_{ }= Intermediate
principal stress = for *M _{r}*
test on cylindrical specimen.

= Minor principal stress/confining pressure.

_{oct} =
Octahedral shear stress.

*P _{a}*
= Normalizing stress (atmospheric pressure).

*k _{1}*,

There have been numerous attempts to estimate resilient
modulus as a function of soil index or soil strength properties over time. One
of the first studies of the resilient properties of soil with the objective of
developing correlation equations for predicting resilient modulus* *from
basic soil test data was conducted by Carmichael and Stuart.^{(104) }They
used the Highway Research Information Service (HRIS) database and developed two
regression models, one for fine-grained soils and another for coarse-grained
soils.^{(104)} Regression models were developed for individual soil
types according to the Unified Classification System (UCS). Variables used in
the models for coarse-grained soils included moisture content and bulk stress. For
fine-grained soils, plasticity index, confining, and deviatoric stresses were
used as predictive variables.

Drumm et al. conducted a resilient modulus study of
cohesive soils based on AASHTO soil classification.^{(105) }They used
deviator stress as the main model parameter. The model coefficients were
derived as functions of liquid limit of soil, degree of saturation, and
unconfined compressive strength.

Two resilient modulus regression models—one each for
fine-grained and coarse-grained Mississippi soils—were developed by George.^{(106)
}Variables used to predict fine-grained soil resilient modulus* *included
soil dry density, liquid limit, moisture content, and percentage passing the
No. 200 sieve. Variables for the coarse-grained soil resilient modulus* *model
included dry density, moisture content, and percentage passing the No. 200
sieve.

A potential benefit of estimating the resilient modulus*
*from physical properties is that seasonal variations in resilient modulus
can be estimated from seasonal changes in a material’s physical properties. A
few of the models from phenomenological studies that relate resilient modulus
to soil properties are presented in figure 34 to figure 48.

Other soil strength parameters have also been used to
estimate resilient modulus. Due to its historical significance in pavement
design, CBR is the most commonly used soil strength parameter for correlation. Direct
correlations between resilient modulus* *and CBR are included in the MEPDG.^{(2)}
Simple correlation equations were developed to predict resilient modulus* *from
standard CBR by several researchers. (See references 107–110.) All these
equations are purely empirical and do not depend on soil properties and stress
state. Figure 49 through figure 58 present a list of correlations between resilient
modulus and other strength parameters.

One should exercise caution in using these correlations
because they may not produce the required input to the MEPDG. The resilient
modulus input is required to be at optimum moisture content and density of the
soil. Most of these correlations do not predict this resilient modulus* *at
optimum moisture content.

The resilient modulus also has been correlated to indices determined from other test devices. A summary of correlations with in-place test methods is presented in figure 59 to figure 67.

Figure 34 was developed for clay type A-7-6. The deviator
stress is 6 psi, the confining pressure is 2 psi, and *M _{r}* is
measured in ksi.

Figure 35 was developed for compacted subgrades. The additional moisture susceptibility correction factor is 0.7 for clay, silty clay, and silty clay loam; 1.5 for clay loam; and 2.1 for loam.

Figure 36 was developed for fine-grained cohesive soils. The deviator stress is 6 psi, and there is no confinement.

Figure 37 was developed for fine subgrade soils containing clay and silts. It was developed using the HRIS database for individual UCS soil types.

Figure 38 was created for coarse granular soils and aggregate bases. It was developed using the HRIS database for individual UCS soil types.

Figure 39 was developed using cohesive subgrades.

Figure 40 was developed using cohesive subgrades.

Figure 41 was developed using undisturbed field samples.

Figure 42 was developed using undisturbed field samples.

Figure 43 was developed using 13 types of fine-grained soils.

Figure 44 was developed using cohesive subgrade soil types A4 through A7-6.

Figure 45 was developed for cohesive soils.

Figure 46 was developed for cohesive soils. The valid for bulk stress is 83 kPa, and the octahedral shear stress is 19.3 kPa.

Figure 47 was developed using fine-grained and coarse-grained soils from the Minnesota Road Research Project test site; applicable only to cohesive soils.

Figure 48 was developed for Texas subgrade data. It is valid for silty to clayey subgrades, and correction factors are provided.

The definitions of the terms used in figure 34 through figure 48 are as follows:

%CLAY = *C* = Clay content in
percent.

%SILT = Silt content in percent.

*%W* = *w* = *w _{c}* = Moisture content.

* _{d}* = Deviation from
the Standard Proctor maximum dry density in pounds per cubic foot.

*w* = Deviation from the
optimum water content in percent.

* _{dr}* = Ratio of
dry density to maximum dry density.

*CH* = 1 for CH type (clay and high plasticity) soil; 0
otherwise.

CLASS = Soil classification (e.g., soil type A7-6 use 7.6 in expression).

*c _{u}* = Uniformity coefficient.

*f(S)* = Normalized saturation by a unit saturation of 1 percent.

*f(**)* = Normalized octahedral
shear stress by a unit stress of 1 psi.

*F _{0}* = 9.8 ksi.

*F _{1}* = Moisture content correction factor.

*F _{2}* = Relative compaction correction factor.

*F _{3}* = Soil plasticity correction factor.

*F _{4}* = Age correction factor.

*F _{5}* = Confining pressure correction factor.

*F _{6}* = Deviator stress correction factor.

*GR* = 1 for gravelly soils (silty gravel, well-graded gravel,
clay gravel, and poorly graded gravel); 0 otherwise.

*LI* = Liquidity index in percent.

*LL* = Liquid limit in percent.

*MH* = 1 for elastic silt type soil; 0 otherwise.

*M _{Ropt}* = Resilient modulus at optimum water content.

PI = Plasticity index.

*PL* = Plastic limit.

*S* = Degree of saturation in percent.

*SM* = 1 for silty sand type soil; 0 otherwise.

*S200* = *S _{200 }= P_{200}* = Percent
material passing the No. 200 sieve.

*w _{opt}* = Optimum water content.

Figure 49 shows reasonable estimates for fine-grained soils with CBR less than or equal to 10.

Figure 50 is currently included in the MEPDG.

Figure 51 was developed for cohesionless soils and is recommended for medium clay sands.

Where:

*A* = 772 to 1,155; recommended 1,000.
*B* = 369 to 555; recommended 555.

Figure 54 was developed for fine-grained soils. The deviator stress is 6 psi, the confinement stress is 2 psi, and the valid for R-value is greater than 20.

Figure 56 is currently included in the MEPDG. The R-value is between 2.3 and 11.

Figure 57 was developed assuming a bilinear *M _{r}*
versus deviator stress behavior.

Figure 58 was developed for clayey subgrade soils and is valid for cohesive soils only where:

*a* = Level of deviator stress.
*S _{u,1%} *= Undrained shear strength at 1 percent axial strain.

Where DCPI is the DCP index in inches per blow.

Figure 60 was developed for subgrade materials using backcalculated FWD modulus values. DCPI is in millimeters per blow.

For figure 61, DCPI is in millimeters per blow.

For figure 62, DCPI is in millimeters per blow.

Figure 63 was developed for both base and subgrade soils materials. DCPI is in millimeters per blow.

Figure 64 was developed for soil types A-4, A-6, A-7-5, and A-7-6. A field DCP test and laboratory test were correlated through statistical analysis. DCPI is in millimeters per blow.

Where:

* _{d}*
= Dry unit weight in kN/m

Figure 65 was developed for soil types A-4, A-6, A-7-5, and A-7-6. Field DCP test and laboratory test were correlated through statistical analysis. DCPI is in millimeters per blow.

Where:

* _{d}*
= Dry unit weight in kN/m

Figure 66 was developed for silty clay and heavy clayey cohesive soils.

Where:

*q _{c}* = Tip resistance (MPa).

Figure 67 was developed for silty clay and heavy clayey cohesive soils.

Where:

* _{ }*=

Recently, the resilient modulus has been predicted using
a two-step approach. First, models to predict parameters *k*_{1}, *k*_{2},
and *k*_{3} of the constitutive equation are developed. Next, the
constitutive equation is used to estimate the resilient modulus. Von Quintus
and Killingsworth, Dai and Zollars, and Santha developed prediction equations
by regressing the coefficients of selected constitutive equations and relating
them to soil physical properties.^{(132–134)} It was observed that the most
influential parameters are moisture content, liquid limit, plasticity index,
and percent passing the No. 200 sieve.

One of the most comprehensive reviews of the resilient
modulus test data measured on pavement materials and soils was made in the LTPP
program.^{(135) }A total of 2,014 resilient modulus laboratory tests that
passed all the QC checks of the LTPP database (i.e., level E data status, 2000
data release) were used in this review. The study verified that the response
characteristics correlate to a form of the constitutive model presented in figure 33. The study correlated resilient modulus data to the physical properties of
the materials and found that the physical properties that influenced the
resilient modulus varied between the different materials and soils. No one
physical property was highly correlated to the modulus. For example, the liquid
limit, plasticity index, and the amount of material passing the smaller sieve
sizes were found to be important for the lower strength unbound aggregate
base/subbase materials, while the moisture content and density were important
as related to higher strength materials. Furthermore, the amount of material
passing the larger sieve sizes was important for the unbound aggregate
base/subbase materials with larger MASs. It also was found that percent clay
and test specimen moisture content or density were important for all soil
groups, while percent silt was important for all soil groups except gravel. It was
also found that to improve correlations, the sample locations (depth) had to be
matched while comparing test results for the same test section or site. Based
on the quality of correlations developed in this study, it was recommended that
the results need to be verified and confirmed after all resilient modulus tests
have been completed. Future model refinement was suggested with a more
comprehensive dataset.

Appendix CC in the MEPDG presents a detailed discussion of
moisture and temperature regime influences on resilient modulus.^{(2) }The
values of the resilient moduli at any location and time within a given pavement
structure are calculated in the MEPDG as a function of the soil moisture and
freeze-thaw influences. The impact of temporal variations in moisture and
temperature on resilient modulus are considered through the composite
environmental adjustment factor, *F _{env}*. The Enhanced
Integrated Climatic model (EICM) is integral to the MEPDG software (the
publication by Larson and Dempsey deals with all environmental factors and
provides soil moisture, suction, and temperature as a function of time, at any
location in the unbound layers from which

*F _{env}* is an adjustment factor, and

Using the latest testing protocol to measure resilient
modulus, AASHTO T 307, Titi et al. performed a comprehensive investigation to
estimate the resilient modulus of various Wisconsin subgrade soils and develop
basic models to estimate the resilient modulus* *from soil properties.^{(28,138)
}Also, a laboratory testing program was conducted on common subgrade soils
to characterize their physical properties. The resilient modulus* *constitutive
equation was used to determine model factors *k*_{1}, *k*_{2},
and *k*_{3}. Titi et al. compared the predictive capability of
these models with those developed by Yau and Von Quintus using LTPP data and
concluded that the two sets of models did not agree.^{(138,135) }Differences
in the test procedures, test equipment, sample preparation, and other
conditions involved with development of the LTPP models and the models of this
study were cited as potential factors for this lack of correlation. Key
prediction models to estimate resilient modulus* *from soil properties are
summarized below.

Based on the results of repeated triaxial load tests
performed on 12 fine-grained and coarse-grained Mississippi subgrades, stress
ratios were used in a bulk stress log-log model to describe their behavior. Subsequently,
soil properties of the same materials were incorporated in the regression
constants of the models. Then, the models were verified using a separate subset
of nine different Mississippi subgrades with good correlation.^{(106,139) }The
resulting equations and constants are shown in figure 68 through figure 73.

The definitions of the parameters used in figure 68 through figure 73 are as follows:

*P _{a}* = Atmospheric pressure.

* = Ratio of dry density to maximum dry density.*

*LL* = Liquid limit in percent.

*w _{c}* = Moisture content in percent.

*w _{cr}* = Ratio of moisture content to optimum moisture content.

#200 = Percent material passing the No. 200 sieve.

* = Intermediate principal stress.*

*c _{u}* = Uniformity coefficient.

The following equation was developed as a combination of the bulk and deviator stress models in an effort to improve the predicted response of resilient modulus test results by including both axial and shear effects.

Santha estimated values for the regression constants in
terms of soil properties using a multiple correlation analysis.^{(134) }The
resulting constants for the analyzed Georgia granular soils are shown in figure 75 to figure 77.

Where:

*w _{c} *= Moisture content.

*w _{opt} *= Optimum moisture content.

*w _{cratio} *=

*COMP* = Degree of compaction.

*SATU* = Percent saturation.

*%SILT* = Silt content in percent.

*%CLAY* = Clay content in percent.

*SW* = Percent swell.

*SH* = Percent shrinkage.

*CBR = *California bearing ratio.

*P _{40}* = Material passing No. 40 sieve in percent.

An equation similar to Uzan’s model using the octahedral
normal stress instead of the bulk stress was used to study eight types of
Louisiana soils.^{(140)} Figure 79 shows the resilient modulus of
Louisiana materials.

Linear regression was then applied to estimate the values of the regression constants in terms of soil properties. The resulting equations are shown in figure 79 through figure 81.

Where:

* _{oct}* = Octahedral
normal stress .

* _{oct}* = Octahedral
shear stress .

*w _{c} *= Moisture content.

*w _{opt} *= Optimum moisture content

*w _{cratio} *=

*LL* = Liquid limit.

*PL* = Plastic limit.

*%SILT* = Silt content in percent.

*%SAND* = Sand content in percent.

* = Optimum density in kN/m*^{3}.

Figure 82 has gained considerable acceptance over time and
is the constitutive model using the same parameters as in figure 33 and proposed in NCHRP Project 1-28A.^{(103) }

The strength of this equation is its ability to handle
two of the resilient modulus dependencies, stress-state and material type. Santha
compared a log-log bulk stress model to figure 82 in modeling Georgia granular subgrade soils and concluded that the model presented in figure 82 provided a better representation of laboratory measurements of resilient modulus.^{(134)}

One of the most comprehensive validations of figure 82 using LTPP resilient modulus test data was performed by Yau and Von Quintus.^{(135)
}The authors first identified anomalous data, verified if the response
characteristics correlated to the constitutive model presented in figure 82, subsequently explored the effect of material type and sampling technique,
and performed a nonlinear regression analysis to establish relationships
between the *k* regression constants in figure 82 and various material properties. The resulting regression equations for unbound and subgrade materials
are presented in figure 83 through figure 115. The definitions of the variables used in the figures are as follows:

*P _{3/8}* = Percent material passing

*P _{4}* = Percent material passing No. 4 sieve.

*P _{40}* = Percent material passing No. 40 sieve.

*P _{200}* = Percent material passing No. 200 sieve.

*%SILT* = Silt content in percent.

*%CLAY* = Clay content in percent.

*LL* = Liquid limit in percent.

*PI* = Plasticity index.

*W _{opt}* = Optimum water content in percent.

*W _{s}* = Water content of the test specimen in percent

* = Maximum dry unit weight of soil in kg/m*^{3}.

* = Dry density of the test specimen in kg/m*^{3}.

Figure 83 through figure 85 show equations for crushed stone (LTPP material code 303) as follows:

Figure 86 through figure 88 show equations for crushed gravel (LTPP material code 304) as follows:

Figure 89 through figure 91 show equations for uncrushed gravel (LTPP material code 302) as follows:

Figure 92 through figure 94 show equations for sand (LTPP material code 306) as follows:

Figure 95 through figure 97 show equations for coarse-grained soil-aggregate mixture (LTPP material code 308) as follows:

Figure 98 through figure 100 show equations for fine-grained soil-aggregate mixture (LTPP material code 307) as follows:

Figure 101 through figure 103 show equations for fine-grained soil (LTPP material code 309) as follows:

Figure 104 through figure 106 show equations for coarse-grained gravel soils as follows:

Figure 107 through figure 109 show equations for coarse-grained sand soils as follows:

Figure 110 through figure 112 show equations for fine-grained silt soils as follows:

Figure 113 through figure 115 show equations for fine-grained clay soils as follows:

Titi et al. evaluated the model presented in figure 82 using repeated triaxial test results performed on various Wisconsin subgrade
soils and developed correlations between the model’s regression constants and
soil properties.^{(138) }Good results were achieved when the
statistical analysis was performed for fine-grained and coarse-grained soils
separately. Researchers also used the LTPP data to compare their correlations
to those developed by Yau and Von Quintus.^{(135)} It was discovered
that the two sets of models did not agree. Differences in the test procedures,
test equipment, sample preparation, and other conditions involved with
development of the LTPP models versus the ones used in the study were cited as
potential factors for this lack of agreement. The equations developed by Titi
et al. are provided in figure 116 through
figure 124.^{(138) }The definitions of the terms used in the figures are
as follows:

*P _{4}* = Percent material passing No. 4 sieve.

*P _{40}* = Percent material passing No. 40 sieve.

*P _{200}* = Percent material passing No. 200 sieve.

*%SAND* = Sand content in percent.

*%SILT* = Silt content in percent.

*%CLAY* = Clay content in percent.

*LL* = Liquid limit.

*PL* = Plastic limit.

*PI* = Plasticity index.

*LI* = Liquidity index.

*w* = Water content.

*w _{opt}* = Optimum water content.

Figure 116 through figure 118 show equations for fine-grained soils as follows:

Figure 119 through figure 121 show equations for non-plastic coarse-grained soils as follows:

Figure 122 through figure 124 show equations for plastic coarse-grained soils as follows: