Estimation of Key PCC, Base, Subbase, and Pavement Engineering Properties From Routine Tests and Physical Characteristics

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CHAPTER 5. MODEL DEVELOPMENT

This chapter discusses the statistical analyses performed to develop the predictive models and the sensitivity analyses used to validate the models. All statistical analyses were performed using the SAS^® software program.

Statistical Analyses Methods Adopted

After data assembly was completed, predictive relationships for the parameters identified in table 6 through table 8 were considered for statistical analyses. The following approaches/ options were considered for developing the various models:

• Refinement of existing models—Refinement of existing ACI PCC compressive strength-flexural strength relationship or the MEPDG PCC strength gain model.
• Development of new models—A predictive model to determine CTE based on PCC mix constituent properties.
• Development of empirical models specific to MEPDG performance—A predictive model to determine deltaT for JPCP design.

Formulating Data for Statistical Models

Data were formulated in three distinct types depending on the nature and extent of data available for each parameter and the intended use of the predicted variable. Within each type, different model forms can be adopted depending on the relationship the dependent parameter holds with the independent variables. The three primary data formulation types adopted are data formulation types 1 through 3 and are discussed in the following sections.

Data Formulation Type 1

• Model description—Simple mathematical correlation between a dependent parameter and continuous predictors or independent variables.
• Dependent variable type and data source—Continuous variable from the LTPP database.
• Independent variable type and data source—Continuous variable from the LTPP database.
• Correlation—Direct mathematical correlation between dependent and independent variables.
• Example predictive model—Compressive strength of PCC predicted as a function of aggregate type, cement content, air content, w/c ratio, unit weight, admixtures, and SCMs. Additionally, k₁, k₂, and k₃ coefficients of the resilient modulus universal constitutive model for unbound materials and soils are predicted as a function of aggregate gradation parameters and index properties.
• Model inference space—Applicable to materials representative of the materials in the LTPP database and limited to the ranges of material properties (i.e., data points) used in the model.

Data Formulation Type 2

• Model description—Simple correlation between a dependent parameter and categorical predictors or independent variables.
• Dependent variable type and data source—Continuous variable from the LTPP database.
• Independent variable type and data source—Categorical variable from the LTPP database.
• Correlation—Average value of the predicted value determined from the database for each category of independent variable. A direct correlation between dependent and independent variables still exists.
• Example predictive model—CTE predicted as a function of aggregate type.
• Model inference space—Applicable to materials representative of the materials in the LTPP database and limited to the ranges of material properties used in the model.

Data Formulation Type 3

• Model description—Relationship between a dependent parameter and predictor variables for dependent variable values established by matching field performance to MEPDG predicted performance in LTPP sections used in MEPDG calibration.
• Dependent variable type and data source—Parameter established by trial and error for each calibration section so that predicted performance matches field performance for each section.
• Independent variable type and data source—Continuous variables from the LTPP database.
• Correlation—Dependent variable determined from trial and error correlated to independent variables from the LTPP database through simple mathematical correlation.
• Example predictive model—The current MEPDG calibration models have used a uniform value of -10 °F for deltaT in JPCP and CRCP designs, as this value was found to provide the least error term overall in the cracking model. This project will determine the deltaT term required to minimize the error in prediction for each calibration section individually, which represents the deltaT term that best explains the performance of the pavement based on MEPDG calibration. The array of deltaT terms correlates to the independent variables from the LTPP database such as base type, construction time, PCC properties (unit weight, compressive strength, etc.), and climatic variables. Another example for a parameter that can be predicted using a type 3 model is EI in JPCP faulting model prediction. The value resulting in the best faulting prediction can be correlated to material (base material), design (dowels/no dowels), and climate (precipitation) parameters.
• Model inference space—Specific to MEPDG performance prediction. The MEPDG distress model calibration is built into the predictive relationship proposed and therefore is applicable only to derive MEPDG-specific inputs. However, relative comparisons are valid. For example, deltaT determined from this relationship for different locations will explain the relative potential for developing upward/downward curling at these locations.

Table 13 to table 15 provide summaries of the model types evaluated for developing predictive relationships for PCC, stabilized, and unbound materials, respectively.

Table 13. Model types used to derive predictive relationships for PCC material properties or design features
for rigid pavements.

N/A = Not applicable.

Table 14. Model types used to derive predictive relationships for stabilized materials.

*All other material types have been excluded from this table, as the database provides data for LCB elastic modulus only.

Table 15. Model types used to derive predictive relationships for unbound materials.