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

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CHAPTER 5. MODEL DEVELOPMENT (3)

Procedures for Model Development

As part of model development, various combinations of model forms (i.e., mathematical relationships) and transformation of dependent/independent variables were evaluated to determine which combination resulted in the best prediction model. The combinations of model forms and transformation of dependent/independent variables is presented in figure 128 through figure 131.

In general, where past literature agreed on some sort of relationship between dependent and independent variables, the relationships were adopted and applied. Where no such agreements exist, all the combinations presented in figure 128 through figure 131 were applied.

Figure 128. Equation. f_c linear model form with no transformation.

Figure 129. Equation. E_c,t nonlinear model form with no transformation.

Figure 130. Equation. k₁ linear model form with transformation.

Figure 131. Equation. k₁ nonlinear model form with transformation.

Both linear and nonlinear statistical techniques were utilized for model development and calibration of the mathematical equations. The two principal SAS^® procedures used for model development were REG and NLIN. Other SAS^® procedures, such as STEP WISE, RSQUARE, and RSREG, were used in selecting the most suitable independent variables for incorporation into the tentative model. In general, using the dependent and independent variables (transformed or otherwise) and mathematical equations representing the model forms identified above, the iterative process in selecting a tentative model was performed as follows:

• Selection of best combination of independent variables—Selection of the best combination of independent variables was performed by using the SAS^® STEP WISE, RSQUARE, RSREG, etc., procedures to determine the best combination of independent variables from the general list of possible independent variables identified as part of the literature review. Selection of the best combination of independent variables was performed based on the p-value of each individual independent variable included in the model. In general, an independent variable with a p-value greater than 5 percent was deemed not significant and was excluded from the model.
• Selection of submodels—For each model, using C_p and VIF determines the best combination of significant independent variables to be included in the tentative model. The aim is to limit the total number of independent variables in the models while minimizing multicollinearity among independent variables, minimizing the error between measured and predicted dependent variable, and maximizing R².
• Maximize R²—The goal is to select independent variables to maximize R² without compromising model robustness characterized by C_p and VIF.
• Minimize error—The goal is to minimize error in predicted and measured dependent variable without compromising model robustness.

PCC Models

The prediction models developed for PCC compressive strength, flexural strength, elastic modulus, tensile strength, and CTE are discussed in detail in this section. The specific tables from which these data were obtained were listed in table 10. The development of the models involved an iterative process, and systematic analyses procedures followed. The process is described in detail for the first model. The various steps are not repeated in great detail for the remaining models, and only results are included.

Data Used in PCC Models

As discussed in chapters 2 and 4, PCC materials data and strength data are available in the LTPP database for both GPS and SPS sections. However, the extent of data available is different for the two experiment types. For the data used for the study, the PCC data come from PCC layers in JPCP, CRCP, and jointed reinforced concrete pavements (JRCPs). All JRCP sections with the exception of one test site belonged to GPS test sites. Also, there was a significant difference in the extent of data available for PCC index properties between the SPS and GPS sections. SPS sections had very detailed mix design information compared to the GPS sections. In addition to the materials information available for GPS sections, the SPS sections contained specific details about the use of SCMs, admixtures, and the gradation of the coarse and fine aggregates.

The following information should be noted about all of the PCC models with regard to data used, data reduction, and assumptions:

• The age at which the test was performed was determined by using the test date and the date of placement.
• Each SPS-2 site consists of 12 rigid pavement sections 500 ft long and constructed with two PCC mix designs in the surface JPCP layer. Six sections were placed using a high-strength mixture with a target flexural strength of 900 psi, and six sections were placed using a low-strength mixture with a target flexural strength of 550 psi. The mix design parameters were the same for all six sections in each strength category. The strength tests were performed at 14 days, 28 days, and 1 year using both cores from the pavement and companion specimens cast during construction. During the data assembly process, data for strengths determined from cores versus cast specimens were separated and averaged for each site and for each age across all sections that represented a given mix. In other words, for a given age, each SPS-2 site provided two data points to the prediction models—one for the low-strength concrete and one for the high-strength concrete. In the data analysis process, codes of 1 and 2 were assigned for the low-strength and high-strength sections, respectively.
• Short-term strength and modulus data were available for SPS sites for 14 days, 28 days, 1 year, and up to 3 years for some sections. Two SPS sections had 10-year strength data.
• For each age, multiple tests were conducted. The analyses used the average strength for each age for all sections (SPS and GPS).
• For correlations between PCC strength parameters, cores were matched with cores and cylinders with cylinders, as necessary.
• The total amount of cement and other SCMs (typically fly ash) was summed to obtain the amount of CMC in SPS sections because this information was readily available for SPS sections. However, the cement content in GPS sections was considered to be the total CMC.
• For SPS sections, coarse and fine aggregate gradations were used to compute MAS and FM.
• Coarse aggregate type was considered a key variable for inclusion in some of the PCC models given its impact on CTE and modulus. As this variable is not countable, the different coarse aggregate types were considered as categorical variables and assigned values of 1 and zero. The aggregate types were basalt, chert, conglomerate, diabase, dolomite, gabbro, granite, limestone, quartzite, syenite, diorite, peridotite, and sandstone.
• Admixtures were considered categorical variables and assigned a value of 1 or zero for the presence or absence of each admixture type. Admixtures included in the list were air entraining agent, fly ash, water reducer, and retarder. Also included were the amounts used in the mix design.
• The curing method adopted for each section was considered as categorical variables (1 and 0) for none, membrane curing, burlap curing, and insulation.
• Mix design variables included the amounts of cement, water, coarse aggregate, fine aggregate, coarse aggregate specific gravity, and fine aggregate specific gravity.
• Cement type in the mix design was considered a categorical variable and included cement types 1, 2, and 3. The database contained one section with type 3 cement.
• LTPP data tables were merged as required for each analysis. The common referencing elements while merging the tables were STATE_ID, SHRP_ID, averaging code, LAYER_NO, and MATERIAL TYPE.

Limitations of All PCC Models

A fundamental limitation for any model is that the relationship that exists between the predicted parameter and the regressors is only valid for the range of data that has been included in the dataset. The statistical modeling procedures, for most part, assume that the variables are normally distributed within the dataset. For example, the relationships developed for PCC properties (e.g., a compressive strength prediction model) are applicable only for mixes with cement types 1 and 2. While one data point with type 3 cement exists in the database (a JRCP section), compared to 500 datasets with type 1 and type 2 cements, the strength gain pattern of a type 3 cement is outcompeted by the other two cement types in the database. As a result, it might not be evident within this dataset that type 3 cements produce higher strengths, especially in the early ages.

The model will reflect the intrinsic trends of the dataset used. For example, the data used for prediction of the 28-day compressive strength contains target low-strength and high-strength mix designs. If the primary means of achieving higher strengths for the States was to increase the cement content, the model will show a high correlation between CMC and strength. However, there are multiple ways to enhance mix compressive strength, such as the use of lower w/c ratios, water reducing agents, higher strength aggregates, curing at higher temperatures and insulation, and the use of type 3 cements. This is critical when the prediction models are implemented for estimating material properties.

The software program developed under the current study calculates the results for the material properties and includes a tool tip that provides the range of values that can be used for each variable. The interface also has a section which lists the basic limitations of the model.

PCC Compressive Strength Models

As discussed in chapter 3, compressive strength is the simplest of PCC strength tests and the most commonly available strength information for PCC materials. For the same reasons, the LTPP database contains extensive compressive strength data for all SPS and GPS sections. Since SPS and GPS data contain different levels of PCC materials information, it was considered meaningful to attempt to group them in different datasets to evaluate if a different subset of regressors emerged as significant for model development.

Compressive strength is considered a fundamental strength parameter and is used at different stages of a project. Many SHAs specify concrete strength requirements by the concrete’s compressive strength, and designers develop pavement layer thicknesses based on compressive strength at 28 days. It is an important qualifier for concrete quality and contractor workmanship. QA testing programs (both contractor QC and agency QA tests) include compressive strength tests on cylinders and cores, and they form the basis for computing strength pay factor in a majority of agencies. Also, the compressive strength of the in situ concrete is used to determine if the pavement can be opened to traffic. Finally, the compressive strength of a core extracted from a pavement ready for rehabilitation is used to estimate the existing structure’s structural capacity in overlay design. The age of the concrete is clearly a parameter of significance in all these cases (except the 28-day strength, which is used for design). Given the extent of data available for PCC materials and compressive strength, the project team considered the following models, which are discussed in detail in this section:

• 28-day cylinder strength model—Suitable for estimating design strength.
• Short-term (1 year) cylinder strength model—Suitable for estimating opening time.
• Short-term (1 year) core strength model—Suitable for in situ strength and opening time.
• All ages core strength model—Suitable for estimating in situ strength at any age.
• Long-term core strength model—Suitable for estimating long-term strength for rehabilitation design.

The procedure used to develop the model is explained in detail for the compressive strength model in the following section. The development of all other models in this study has entailed a similar level of analyses if not more.