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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 (10)

PCC Flexural Strength Models

The first step with the development of PCC flexural strength model was to assemble the relevant data in a manner appropriate for model development, followed by the actual statistical analyses. Statistical analyses to develop prediction models for flexural strength involved the validation of existing models and model forms as well as the development of new models to predict flexural strength.

The validation of existing models was a relatively straightforward exercise that involved fitting the data assembled in this study to the most commonly referenced model forms. Flexural strength has been correlated to compressive strength in previous models. Furthermore, in the development of new models, attempts were made to provide relationships as a function of readily available information. This study therefore attempted to develop models based on the compressive strength, as well as material properties and age. This provides options on which models to use, depending on the parameters and mix design information available.

The following are key points to note about flexural strength data:

Validation of Existing Models

Previous attempts have been made to correlate PCC flexural strength to the compressive strength, as discussed in chapter 2. These correlations generally have used a power model of the following form:

M subscript r equals a times f prime subscript c raised to the power of b.

Figure 169. Equation. Mr.

Where:

a = 7.5 to 11.7 for b = 0.5.

a = 2 to 2.7 for b = 0.67.

The data assembled from the LTPP database was used to develop models with b = 0.5 and 0.67. Table 32 shows a summary of the models developed. The regressed constants, a and b, were found to be within the range of values reported by the other studies discussed in chapter 2. This validation not only provides feasible models, but it also confirms that the data being used in this study can reasonably represent the broad range considered in the various studies. The correlations are presented in figure 170 and figure 171 for the power models with exponents of 0.5 and 0.67, respectively.

Table 32. Power models developed for flexural strength prediction using LTPP data for validation.

Model

a

b

R2

N

[any value]

10.3022

0.5

0.446

185

2.4277

0.67

0.449

185

 

This figure is an x-y scatter plot showing the predicted versus the measured values used for validating 0.5 power flexural strength model. The x-axis shows the measured modulus of rupture from 100 to 1,300 psi, and the y-axis shows the predicted modulus of rupture from 100 to 1,300 psi. The plot contains 185 points, which correspond to the data points used in the model. The graph also shows a 45-degree line that represents the line of equality. The data are shown as solid diamonds, and they appear to demonstrate a good prediction. The measured values range from 467 to 1,075 psi. The graph also shows the model statistics as follows: N equals 185, 
R-squared equals 0.4460 percent, and root mean square error equals 84 psi.

Figure 170. Graph. Predicted versus measured for validating 0.5 power flexural strength model.

This graph is an x-y scatter plot showing the predicted versus the measured values used for validating 0.667 power flexural strength model. The x-axis shows the measured modulus of rupture from 100 to 1,300 psi, and the y-axis shows the predicted modulus of rupture from 100 to 1,300 psi. The plot contains 185 points, which correspond to the data points used in the model. The graph also shows a 45-degree line that represents the line of equality. The data are shown as solid diamonds, and they appear to demonstrate a good prediction. The measured values range from 467 to 1,075 psi. The graph also shows the model statistics as follows: N equals 185, 
R-squared equals 0.4493 percent, and root mean square error equals 111 psi.

Figure 171. Graph. Predicted versus measured for validating 0.667 power flexural strength model.

 


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The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). Provide leadership and technology for the delivery of long life pavements that meet our customers needs and are safe, cost effective, and can be effectively maintained. Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
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