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Publication Number:
FHWAHRT12030
Date: August 2012 
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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, limecement flyash, and limestabilized 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 (q_{u})_{.}^{(95)}
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.^{(17)}
Where:
E = Modulus of elasticity, psi.
q_{u} = Unconfined compressive strength, psi tested in accordance with ASTM D 1633.^{(97)}
Where:
E = Modulus of elasticity, psi.
q_{u} = Unconfined compressive strength, psi tested in accordance with ASTM C 593.^{(99)}
Where:
M_{r}_{ }= Resilient modulus, ksi.
q_{u} = Unconfined compressive strength, psi tested in accordance with ASTM D 5102.^{(101)}
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), Rvalue, 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 stressstate dependency, material dependency, and moisture and temperature dependency. About 54 percent of State transportation departments use resilient modulus_{ }in routine pavement design.^{(102) }Ideally, resilient modulus should be obtained from laboratory measurements; however, standard test procedures such as AASHTO T 307 and NCHRP 128A require substantial time and resources and are not used in routine engineering practice, especially beyond the design phase of the project.^{(28,103)}
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 128A (see figure 33).^{(103) }The strength of this approach is that two of the resilient modulus dependencies, stressstate and material type, can be handled by this model form, which is an improvement over previously used discrete models for coarse and finegrained 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}, k_{2}, and k_{3 }= Regression constants (obtained by fitting M_{r} test data to this equation).
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 finegrained soils and another for coarsegrained soils.^{(104)} Regression models were developed for individual soil types according to the Unified Classification System (UCS). Variables used in the models for coarsegrained soils included moisture content and bulk stress. For finegrained 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 finegrained and coarsegrained Mississippi soils—were developed by George.^{(106) }Variables used to predict finegrained soil resilient modulus included soil dry density, liquid limit, moisture content, and percentage passing the No. 200 sieve. Variables for the coarsegrained 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 inplace test methods is presented in figure 59 to figure 67.
Figure 34 was developed for clay type A76. 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 finegrained 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 finegrained soils.
Figure 44 was developed using cohesive subgrade soil types A4 through A76.
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 finegrained and coarsegrained 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 A76 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, wellgraded 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 finegrained 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 finegrained soils. The deviator stress is 6 psi, the confinement stress is 2 psi, and the valid for Rvalue is greater than 20.
Figure 56 is currently included in the MEPDG. The Rvalue 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 A4, A6, A75, and A76. 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^{3}. w = Water content in percent.
Figure 65 was developed for soil types A4, A6, A75, and A76. 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^{3}. w = Water content in percent.
Figure 66 was developed for silty clay and heavy clayey cohesive soils.
Where:
q_{c} = Tip resistance (MPa). f_{s} = Frictional resistance (MPa). u_{t} = Total pore pressure.
Figure 67 was developed for silty clay and heavy clayey cohesive soils.
Where:
_{ }= _{ }= Confining stress (kPa). _{v }= Vertical stress (kPa). w = Water content. _{d }= Dry unit weight (kN/m^{3}). _{w} = Unit weight of water (kN/m^{3}).
Recently, the resilient modulus has been predicted using a twostep 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 freezethaw 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} can be determined).^{(136)} This moisture prediction capability of the EICM was improved by Zapata and Houston.^{(137) }The resilient modulus at any time or position within the pavement structure is then determined by multiplying the value at optimum with F_{env} ( i.e.,).
F_{env} is an adjustment factor, and M_{ropt} is the resilient modulus at optimum conditions (maximum dry density and optimum moisture content) at any state of stress. Variations of resilient modulus with stress and variations of modulus with environmental factors (i.e., moisture, density, and freezethaw conditions) are assumed to be independent.
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 finegrained and coarsegrained Mississippi subgrades, stress ratios were used in a bulk stress loglog 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} = w_{c }/w_{opt}_{.}
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} = w_{c }/w_{opt}_{.}
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 128A.^{(103) }
The strength of this equation is its ability to handle two of the resilient modulus dependencies, stressstate and material type. Santha compared a loglog 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 ^{3}/_{8}inch sieve.
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 coarsegrained soilaggregate mixture (LTPP material code 308) as follows:
Figure 98 through figure 100 show equations for finegrained soilaggregate mixture (LTPP material code 307) as follows:
Figure 101 through figure 103 show equations for finegrained soil (LTPP material code 309) as follows:
Figure 104 through figure 106 show equations for coarsegrained gravel soils as follows:
Figure 107 through figure 109 show equations for coarsegrained sand soils as follows:
Figure 110 through figure 112 show equations for finegrained silt soils as follows:
Figure 113 through figure 115 show equations for finegrained 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 finegrained and coarsegrained 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 finegrained soils as follows:
Figure 119 through figure 121 show equations for nonplastic coarsegrained soils as follows:
Figure 122 through figure 124 show equations for plastic coarsegrained soils as follows:
Topics: research, infrastructure, pavements and materials Keywords: research, infrastructure, pavements and materials, Pavements, LTPP, material properties, MEPDG, prediction model, Index properties TRT Terms: research, facilities, transportation, highway facilities, roads, parts of roads, pavements Updated: 09/26/2012
