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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 (14)

PCC Tensile Strength Models

The data assembly and data reduction were same as that performed for the other PCC models. Both SPS and GPS section data were used in the development of this model. PCC tensile strength is a critical input to the CRCP models in the MEPDG. It is most likely that compressive strength test results could be available for the PCC materials being used in CRCP design/ construction. The intent, therefore, was to correlate PCC tensile strength data to the compressive strength. Past studies have correlated the tensile strength to the flexural strength of the mix. However, flexural strength test results are available only for the SPS sections, thereby drastically reducing the dataset that can be used to generate a tensile strength model based on flexural strength.

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 c closed parenthesis raised to the power of 0.4785.

Figure 200. 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 45. The model was developed using 541 data points, with an R2 value of 42.1 percent and an RMSE value of 61 psi. Table 46 provides details of the range of data used to develop the model. Figure 201 and figure 202 show the predicted versus measured plot and the residual errors plot, respectively.

Table 45. 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

 

The model statistics for table 45 are as follows:

Table 46. 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

 

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 equations are also provided: y equals 0.4231x 
plus 346.07 and R-squared equals 0.4209.

Figure 201. 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 202. Graph. Residuals error 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 zero to 16,000 psi, and the y-axis shows the predicted tensile strength from zero to 1,200 psi. The sensitivity is shown for compressive strength and 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 203. Graph. Sensitivity of tensile strength prediction model to change compressive strength.

Figure 203 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.

PCC CTE Models

PCC CTE, which has gained higher importance in recent pavement analysis procedures as a material parameter influencing performance, has been included in the TST_PC03 table of the LTPP database for both SPS and GPS sections. The TST_PC03 table in the LTPP Standard Data Release 23.0 contained 228 CTE test results.(3) These test data contained multiple CTE measurements on a given 500-ft section. Each CTE test result was accompanied by the aggregate type and rock type determined by visual examination of the core used for CTE measurements. The reasons for collecting this information at the time of CTE tests can be easily perceived. Coarse aggregate mineralogy and concrete moisture content have the highest influence of all material parameters on PCC CTE values. Testing for CTE was done with the concrete saturated so that this variable was eliminated. Additional data and corrected data have been added to the LTPP Standard Data Release 24.0.(142)

Additionally, aggregate type data were obtained from the materials tables, as explained in chapter 4. It is also noted that fine aggregates in PCC are usually silica natural sand. There is no indication of fine aggregate type in the LTPP database. Specific tables from which aggregate type information were extracted and assembled in the database include SPS2_PCC_MIXTURE_ DATA, RHB_PCCO_AGGR, SPS8_PCC_MIXTURE_DATA, and INV_PCC_MIXTURE for SPS-2, SPS-7, SPS-8, and GPS sections. Reviewing and comparing the aggregate type reported in the CTE and materials tables revealed the following:

In developing CTE correlations, the following assumptions and data reduction methods were made:

Two model types were developed, either of which could be used depending on the level of information available. These models are equivalent to level 3 and level 2 MEPDG inputs. The level 3 model provides default CTE values depending on the coarse aggregate rock type used in the PCC mix. This is equivalent to the CTE values suggested by Mallela et al. but covers a larger database of CTE test results.(15) The level 2 model provides a correlation based on mix volumetrics and uses existing model forms. The regressed constants in the model were obtained from the database assembled for this study.

Current Issue with CTE Overestimation in LTPP Data

CTE tests of the PCC specimens from LTPP sections were performed by FHWA’s Turner-Fairbank Highway Research Center (TFHRC) using the AASHTO TP 60 protocol.(24) TFHRC initiated an inter-laboratory study during which an error was discovered with the protocol and procedure used to measure concrete CTE.(144) The source of the error was in the assumption of a single CTE value for the calibration specimen. Testing performed at independent laboratories revealed that a CTE value must be determined for each calibration specimen, and the calibration specimen should be tested over the same range of temperature over which the concrete CTE is determined—50 to 122 °F. Not meeting these two conditions caused an overestimation of the reported CTE by approximately 0.83 inches/inch/°F. Since all of the initial LTPP testing for CTE had been done in one laboratory with one calibration specimen, the calibration offset can be corrected in the database, and it has been corrected in LTPP Standard Data Release 24.0.(3,145,142)

This overestimation of CTE has significant ramifications, especially in light of the fact that the TFHRC has tested over 2,100 specimens for the LTPP program and the fact that the LTPP database was the primary source for the national calibration of the AASHTO MEPDG rigid pavement performance models.(1) The national calibration coefficients for all JPCP and CRCP performance models may be invalid, and the models may need to be recalibrated. As a result, local implementation efforts also may be delayed.

The impact of this error in the CTE values on the current study was described in an internal status report submitted to LTPP. LTPP Standard Data Release 23.0 contained the uncorrected CTE values, and therefore, the CTE models developed in this study are not applicable for the corrected data.(3) However, the models demonstrate the ability to develop correlations, and the procedures herein may be repeated for the corrected data.

 


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