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

 

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.

 

f subscript c equals A subscript 0 plus A subscript 1 times w/c plus A subscript 2 times cementitious content.

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

E subscript c,t equals 375.6 times open parenthesis f prime c subscript 28-day closed parenthesis raised to the power of 1.1 times open parenthesis natural log times the sum of open parenthesis t divided by 0.03 closed parenthesis, closed parenthesis times 0.00524.

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

Natural log open parenthesis k subscript 1 closed parenthesis equals 1.12 plus 2.4 times open parenthesis gamma subscript d closed parenthesis plus 3.6 times LL.

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

Natural log times open parenthesis k subscript 1 closed parenthesis equals 1.12 times open parenthesis gamma subscript d closed parenthesis raised to the power of 1.996 times open parenthesis LL divided by w subscript c closed parenthesis raised to the power of 0.639.

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:

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:

 

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:

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.

 


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