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Federal Highway Administration Research and Technology
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REPORT 
This report is an archived publication and may contain dated technical, contact, and link information 

Publication Number: FHWAHRT12031 Date: August 2012 
Publication Number:
FHWAHRT12031
Date: August 2012 
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The following model recommended for predicting the resilient modulus of unbound materials is based on the constitutive equation for modeling resilient modulus behavior when subjected to various stress states:
Figure 100. Equation. M_{r}.
Where:
=
Bulk stress = .
= Principal stress.
= Confining pressure.
P_{a} = Atmospheric pressure.
= Octahedral normal stress =1/3
().
k_{1}, k_{2}, k_{3} =
regression constants that are a function of soil properties, as
defined in figure 101 through figure 103 of this report.
This model can be used for various soil types, and the model attributes (k_{1}, k_{2}, and k_{3}) for a given soil type remain the same regardless of stress state. Furthermore, models used to predict constitutive model attributes for a given set of soil properties are recommended to characterize resilient modulus behavior rather than developing models individually for each possible combination of expected stress states.
Figure 101. Equation. Prediction model 18 for k_{1}.
Model statistics for k_{1} are as follows:
Figure 102. Equation. Prediction model 19 for k_{2}.
Model statistics for k_{2} are as follows:
Figure 103. Equation. Prediction model 20 for k_{3}.
Where:
PCTHALF = Percent passing ^{1}/_{2}inch sieve. LL = Liquid limit, percent. OPTMOIST = Optimum moisture content, percent. PCTNO80 = Percent passing No. 80 sieve. PCTGRVL = Percent gravel fraction (0.078 to 2.36inch size). D_{10} = Maximum particle size of the smallest 10 percent of soil sample.
In the development of these models, a wide range of k_{1}, k_{2}, and k_{3} parameters were used, which varied by soil class. Histograms showing the distribution of k_{1}, k_{2}, and k_{3} values by soil class are shown in figure 104 through figure 106, respectively.
Figure 104. Graph. Resilient modulus parameter k_{1} for unbound material types included in the model development database.
Figure 105. Graph. Resilient modulus parameter k_{2} for unbound material types included in the model development database.
Figure 106. Graph. Resilient modulus parameter k_{3} for unbound material types included in the model development database.
Model prediction accuracy and reasonableness were evaluated by reviewing the plot of predicted and measured resilient modulus for all individual resilient modulus test values used in model development as presented in figure 107. Figure 108 presents a plot of measured and predicted resilient modulus versus bulk stress for all fine and coarsegrained materials included in the model development database.
Figure 107. Graph. Plot of measured versus predicted resilient modulus (using k_{1}, k_{2}, and k_{3} derived from figure 101 through figure 103).
Figure 108. Graph. Plot showing predicted and measured resilient modulus versus bulk stress for fine and coarsegrained soils.
Sensitivity analysis results are presented in figure 109 through figure 115. The results of the sensitivity analysis are summarized as follows:
Figure 109. Graph. Effect of material type (AASHTO soil class) on predicted resilient modulus.
Figure 110. Graph. Effect of percent passing ^{1}/_{2}inch sieve on predicted resilient modulus.
Figure 111. Graph. Effect of liquid limit on predicted resilient modulus.
Figure 112. Graph. Effect of optimum moisture content on predicted resilient modulus.
Figure 113. Graph. Effect of No. 80 sieve on predicted resilient modulus.
Figure 114. Graph. Effect of gravel content on predicted resilient modulus.
Figure 115. Graph. Effect of effective size on predicted resilient modulus.