User’s Guide: Estimation of Key PCC, Base, Subbase, and Pavement Engineering Properties From Routine Tests and Physical Characteristics

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CHAPTER 2. MODEL DEVELOPMENT

The LTPP study database, Long-Term Pavement Performance Standard Data Release Version 23.0, was used to develop the models.⁽¹⁰⁾ Material properties and pavement engineering properties for which develop predictive models were developed were selected based on the following:

• Material inputs requirements for the MEPDG design procedure and the sensitivity of the specific parameter for performance prediction.
• Typical agency needs for determining material properties during QA.
• Typical agency needs for determining material properties during routine pavement management functions.
• Data availability in the LTPP database.

Predictive models were developed for PCC compressive strength, PCC flexural strength, PCC elastic modulus, PCC tensile strength, lean concrete base (LCB) modulus, and unbound materials resilient modulus. In addition, rigid pavement design feature inputs properties were developed using the MEPDG calibration data. These include the JPCP and CRCP deltaT parameters. For all PCC material properties, multiple models were developed for use in different project situations and to provide user prediction model alternatives depending on the extent of mix design information available.

In developing the models, a uniform set of statistical criteria were used to select independent parameters to define a relationship as well as to mathematically formulate prediction functions. The analyses examined several statistical parameters in choosing the optimal model and in determining the predictive ability of the model. In general, the optimal set of independent variables (Mallows coefficient, C_p), the interaction effects (variance inflation factor (VIF)), the significance of the variable (p-value), and the goodness of fit (R²) were verified. Additionally, the study validated or refined existing models and developed new relationships. In the analyses, the following general observations were made:

• PCC compressive strength could be correlated to several index properties. It was found to increase with decreasing water/cementitious (w/c) ratio, increasing cementitious materials content (CMC), increasing curing time, increasing unit weight, decreasing maximum aggregate size (MAS) for a given level of w/c ratio, and decreasing fineness modulus (FM) of the sand.
• PCC flexural strength could be correlated to the compressive strength using a power model. These relationships were validated and refined using the LTPP data. It also could be correlated to the w/c ratio, unit weight, CMC, and curing time. The correlation was improved significantly in the new models with the additional parameters. The flexural strength increased proportionally with all parameters listed except w/c ratio, with which it had an inverse relationship.
• PCC elastic modulus could be correlated to the compressive strength and unit weight using a power model, as has been done in past studies. These relationships were validated and verified with the data used in this study. Predictions could be made based on aggregate type, unit weight, compressive strength, and age with improved correlation. The elastic modulus increases with an increase in magnitude of all parameters listed.
• PCC tensile strength was found to correlate well with the compressive strength using a power relationship.
• The coefficient of thermal expansion (CTE) of PCC was most sensitive to the coarse aggregate type and the volumterics of the mix design.
• JPCP deltaT negative gradient was found to increase with an increase in temperature range at the project location for the month of construction and slab width and with a decrease in PCC thickness, unit weight, w/c ratio, and latitude of the project location.
• CRCP deltaT negative gradient was found to increase with an increase in maximum temperature at the project location for the month of construction and maximum temperature range and decrease with the use of chert, granite, limestone, and quartzite.
• The modulus of LCB was found to correlate well with its 28-day compressive strength based on a power model.
• The prediction of resilient modulus was possible using parameters k₁, k₂, and k₃ of the constitutive model as follows:
  • The parameter k₁ was found to increase with a decrease in percent passing the ¹/₂-inch sieve, an increase in liquid limit, and a decrease in optimum moisture content.
  • The parameter k₂ was found to increase with a decrease in percent passing the No. 80 sieve, liquid limit, and percent gravel and an increase in the maximum particle size of the smallest 10 percent of the soil sample.
  • The parameter k₃ was dependent on the soil classification (coarse-grained versus fine-grained materials).

List of Models

The following models have been developed under this study.

PCC compressive strength models include the following:

• Compressive strength model 1: 28-day cylinder strength model.
• Compressive strength model 2: Short-term cylinder strength model.
• Compressive strength model 3: Short-term core strength model.
• Compressive strength model 4: All ages core strength model.
• Compressive strength model 5: Long-term core strength model.

PCC flexural strength models include the following:

• Flexural strength model 1: Flexural strength based on compressive strength.
• Flexural strength model 2: Flexural strength based on age, unit weight, and w/c ratio.
• Flexural strength model 3: Flexural strength based on age, unit weight, and CMC.

PCC elastic modulus models include the following:

• Elastic modulus model 1: Model based on aggregate type.
• Elastic modulus model 2: Model based on age and compressive strength.
• Elastic modulus model 3: Model based on age and 28-day compressive strength.

The PCC indirect tensile strength model is as follows:

• PCC indirect tensile strength model: Model based on compressive strength.

PCC CTE models include the following:

• CTE model 1: CTE based on aggregate type (level 3 equation for MEPDG).
• CTE model 2: CTE based on mix volumetrics (level 2 equation for MEPDG).

The JPCP design deltaT model is as follows:

• JPCP deltaT model: JPCP deltaT gradient based on temperature range, slab width, slab thickness, PCC unit weight, w/c ratio, and latitude.

The CRCP design deltaT model is as follows:

• CRCP deltaT model: CRCP deltaT gradient based on maximum temperature, maximum temperature range, and aggregate type.

The LCB elastic modulus model is as follows:

• Elastic modulus model: Elastic modulus based on 28-day compressive strength.

The unbound materials resilient modulus is as follows:

• Resilient modulus model: Resilient modulus using constitutive model based on gradation, Atterberg limits, optimum moisture content, and soil classification.

Practical Guide and Software Program

The models described in this user’s guide have been incorporated into a user friendly software program, Correlations, which was developed under this study and can be used independently from the MEPDG. The software was developed on the Microsoft.NET platform to be compatible with the latest versions of the Microsoft Windows^® operating systems. It uses a modern user interface library to provide a familiar look and feel. It features multiple windows on the user interface that are initially docked inside the main window. These windows can be moved separately from the main window for better viewing of the inputs or results.

The program interface features tabs for PCC, design features, stabilized materials, and unbound materials. Models that belong to each of these categories are made available through a series of radio button selections placed in an accordion control. This placement not only provides the ability to make multiple selections, but it also conserves screen space so that the results of the calculations can be placed for easy viewing. Once a model is selected, the entry area adds controls for the available inputs of the model. Figure 2 shows a screenshot of the program and displays the various tabs and general layout of the user interface.

Figure 2. Screenshot. View of Correlations user interface.

On all screens of the software, tooltips are provided for feedback on input range. Calculations occur after all necessary values have been input. Information about each model is available in an information window initially located at the bottom of the screen. This information is context-sensitive to the specific selections that the software user has made. Results of each calculation are displayed prominently in the results area window initially placed on the right side of the main window.