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Publication Number:  FHWA-HRT-12-031    Date:  August 2012
Publication Number: FHWA-HRT-12-031
Date: August 2012

 

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

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PCC Tensile Strength Models

PCC Tensile Strength Model Based on Compressive Strength

This model development served as both a validation and development of a new correlation using the LTPP database. The model form used was a power equation and can be expressed as follows:

f subscript t equals 8.9068 times open parenthesis f prime times c closed parenthesis raised to the power of 0.4785.

Figure 68. Equation. Prediction model 12 for ft.

Where:

ft = Indirect tensile strength of the PCC material.
f'c = Compressive strength of the mix determined at the same age.

The model statistics are presented in table 23. The model was developed using 541 data points with an R2 value of 42.09 percent and an RMSE of 61 psi. Table 24 provides details of the range of data used to develop the model.

 

Table 23. Model statistics for tensile strength prediction model.

Parameter

Estimate

Standard Error

95 Percent Confidence Limits

Coefficient

8.9068

 

2.0204

 

4.9381 to 12.8756

 

Power

0.4785

 

0.0256

 

0.4282 to 0.5288

 

 

Table 24. Range of data used for tensile strength prediction model.

Parameter

Minimum

Maximum

Average

Compressive strength

1,990

12,360

6,763

Tensile strength

316

1,012

600

 

Figure 69 and figure 70 show the predicted versus measured plot and the residual errors plot, respectively. Figure 71 shows the sensitivity of the model to compressive strength. The relationship developed shows that for typical ranges of compressive strength (i.e., 3,000 to 6,000 psi), the PCC tensile strength varies from about 400 to 570 psi, which is a reasonable range for this strength parameter.

This graph is an x-y scatter plot showing the predicted versus the measured values used in the tensile strength model. The x-axis shows the measured tensile strength from 100 to 1,300 psi, and the y-axis shows the predicted tensile strength from 100 to 1,300 psi. The plot contains 541 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 316 to 1,012 psi. The graph also shows the model statistics as follows: N equals 541, R-squared equals 0.4209 percent, and root mean square error equals 61 psi. The following equation is also provided: y equals 0.4231x plus 346.07.

Figure 69. Graph. Predicted versus measured for tensile strength model.

This graph is an x-y scatter plot showing the residual errors in the predictions of the tensile strength model. The x-axis shows the predicted tensile strength from 100 to 1,300 psi, and the y-axis shows the tensile strength (predicted minus measured) from -500 to 500 psi. The points are plotted as solid diamonds, and they appear to show no significant bias (i.e., the data are well distributed about the zero-error line). This plot illustrates a fair degree of errors. There appear to be no trends in the data, and the trend line is almost horizontal (i.e., zero slope). The following equations are provided in the graph: y equals 0.0054x minus 3.2756 and R-squared equals 2E minus 0.5.

Figure 70. Graph. Residual errors plot for tensile strength model.

This graph shows the sensitivity of the tensile strength prediction model to the compressive strength. The x-axis shows the compressive strength from 0 to 16,000 psi, and the y-axis shows the predicted tensile strength from 0 to 1,200 psi. The sensitivity is shown for compressive strength ranges from 1,500 to 14,000 psi, and the data are plotted using solid squares connected by a solid line. The graph shows that with increasing compressive strength, the predicted tensile strength increases.

Figure 71. Graph. Sensitivity of tensile strength prediction model to change compressive strength.

 

 

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