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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 CTE Models

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.(11) TFHRC initiated an inter-laboratory study during which an error was discovered with the protocol and procedure used to measure concrete CTE. 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 inch/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 Long-Term Pavement Performance Standard Data Release 24.0.(12)

This overestimation of the 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. 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 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 Version 23.0 contained the uncorrected CTE values; therefore, the CTE models developed in this study are not applicable for the corrected data.(10) However, the models demonstrate the ability to develop correlations, and the procedures herein may be repeated for the corrected data.

CTE Model 1: CTE Based on Aggregate Type (Level 3 Equation for MEPDG)

CTE test data were averaged for each aggregate type, which constitutes level 3 inputs for MEPDG. Table 25 lists the average PCC CTE for each aggregate type as found in the literature. The data are in general agreement, providing a degree of confidence in the level 3 MEPDG input recommendations. The average CTE values determined from the data subset are recommended by this study.

Table 25. Prediction model 13 for PCC CTE based on aggregate type, x 10-6 inch/inch/°F.

Aggregate Type

Average From Literature

Average From All LTPP Data

Average From Data Used in Model (Recommended)

Basalt

4.85

5.11

4.86

Chert

6.55

6.24

6.90

Diabase

4.85

5.33

5.13

Dolomite

5.75

5.79

5.79

Gabbro

4.85

5.28

5.28*

Granite

4.55

5.62

5.71

Limestone

4.25

5.35

5.25

Quartzite

6.85

6.07

6.18

Andesite

4.85

4.99

5.33

Sandstone

6.05

5.98

6.33

N

228

 

91

 

*There were no samples with a Gabbro aggregate type in the data used in the model. Hence, the average from the entire dataset is recommended.

Figure 72 shows a plot of recommended CTE values versus average CTE values obtained from other sources. While they are in fairly good agreement, the values recommended from this study are slightly higher for most cases. This can be explained by the overestimation of CTE during testing.

This graph shows an x-y scatter plot of the established portland cement concrete (PCC) coefficient of thermal expansion (CTE) from the Long-Term Pavement Performance (LTPP) data versus the average PCC CTE values noted from past references. The x-axis shows the average CTE for each aggregate type gathered from a literature review, and the y-axis shows the predicted CTE corresponding to each dataset. The solid diamonds represent the average determined from all LTPP data by aggregate type. The hollow squares represent the average CTE by aggregate type obtained from literature. There is a total of nine points under each category. There is also a line of equality, and the data points are concentrated along the line of equality.

Figure 72. Graph. Comparison of average values from other sources and recommended CTE values based on aggregate type from LTPP data.

CTE Model 2: CTE Based on Mix Volumetrics (Level 2 Equation for MEPDG)

The PCC CTE model based on mix volumetrics was established as follows:

CTE subscript PCC equals CTE subscript CA times V subscript CA plus 6.4514 times open parenthesis 1 minus V subscript CA closed parenthesis.

Figure 73. Equation. Prediction model 14 for CTEPCC.

Where:

CTECA = Constant determined for each aggregate type as shown in table 26.

The model statistics are presented in table 26, and details of the range of data used to develop the model are presented in table 27. The model has 89 data points, an R2 value of 44.15 percent, and an RMSE of 0.35006 psi.

Table 26. Statistical analysis results for CTE model based on mix volumetrics.

Parameter

Comment

Estimate

Standard Error

95 Percent Confidence Limits

c

 N/A

6.4514

 

0.1889

 

6.0758

 

6.827

 

d

CTECA for basalt

3

 

0

 

3

 

3

 

e

CTECA for chert

6.4

 

0

 

6.4

 

6.4

 

f

CTECA for diabase

3.4835

 

1.2824

 

0.9337

 

6.0333

 

g

CTECA for dolomite

5.1184

 

0.408

 

4.3071

 

5.9297

 

h

CTECA for gabbro

3.75

 

N/A

 

N/A

 

N/A

 

i

CTECA for granite

4.7423

 

0.4188

 

3.9096

 

5.5749

 

j

CTECA for limestone

3.2886

 

0.3579

 

2.5771

 

4.0001

 

k

CTECA for quartzite

6.1

 

0

 

6.1

 

6.1

 

l

CTECA for andesite

3.6243

 

1.4539

 

0.7336

 

6.515

 

m

CTECA for sandstone

4.5

 

0

 

4.5

 

4.5

 

N/A = Not applicable.

Table 27. Range of data used for CTE model based on mix volumetrics.

Parameter

Minimum

Maximum

Average

Coarse aggregate content

582

 

2,730

 

1,811

 

Coarse aggregate specific gravity

2.42

 

2.86

 

2.65

 

w/c ratio

0

 

0.71

 

0.45

 

Coarse aggregate volume fraction

0.13

 

0.62

 

0.41

 

Mortar volume

0.38

 

0.87

 

0.59

 

 

The predicted versus measured plot and the residual error plots are presented in figure 74 and figure 75, respectively.

This graph is an x-y scatter plot showing the predicted versus the measured values used in the coefficient of thermal expansion (CTE) model based on mix volumetrics. The x-axis shows the measured CTE from 0 to 8, and the y-axis shows the predicted CTE from 0 to 8. The plot contains 89 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 4.11 to 
7.31 inch/inch/°F. The graph also shows the model statistics as follows: y equals 0.4228x plus 3.2012 and R-squared equals 0.4415.

Figure 74. Graph. Predicted versus measured for CTE model based on mix volumetrics.

This graph is an x-y scatter plot showing the residual errors in the predictions of the coefficient of thermal expansion (CTE) model based on mix volumetrics. The x-axis shows the predicted CTE from 
0 to 7, and the y-axis shows the residual error from -2 to 2. The points are plotted as solid diamonds, and there is no significant bias (i.e., the data are well distributed about the zero-error line). This plot illustrates a fair but acceptable error. There appears to be no trend in the data, and the trend line is almost horizontal (i.e., zero slope). The following equations are provided in the graph: y equals -0.0443x plus 0.233 and R-squared equals 0.0014.

Figure 75. Graph. Residual errors for CTE model based on mix volumetrics.

The constant, C, determined as 6.4514, is equivalent to the CTE of the mortar. (At TFHRC, using the AASHTO TP 60 uncorrected values, a CTE value of 6.2 for mortar containing silica sand was determined, validating this equation.(12)) Since the mortar (all components of the mix design except the coarse aggregate) occupies a large volume of the matrix, it was necessary for the model to predict higher CTE for increased mortar proportions (or decreasing coarse aggregate proportions). In optimizing the model and selecting the representative CTE for each aggregate type, it was ensured that the CTE of the aggregate was not above 6.4514.

Figure 76 and figure 77 show a comparison of the predicted CTE values with average values reported in literature for each aggregate type. Figure 78 shows the sensitivity of the model to coarse aggregate content. As expected, CTE decreases as the coarse aggregate content increases (or mortar volume decreases). While this is true for most cases, it was also observed that for aggregates with high CTE values, such as chert and quartzite, the CTE of the aggregate approaches the CTE of the mortar, thereby showing little or no sensitivity to coarse aggregate content. As with all other models, the user is advised to verify model predictions with other sources of information. If possible, both CTE models should be evaluated simultaneously to obtain a range.

This graph is a bar chart showing predicted values using the coefficient of thermal expansion (CTE) model as well as Portland cement concrete CTE values typically reported in literature. The values are reported for several aggregate types, and aggregate type is the category on the x-axis. Starting from the left, the aggregates include basalt, chert, diabase, dolomite, gabbro, granite, limestone, quartzite, andesite, sandstone, conglomerate, syenite, diorite, and peridotite. The y-axis shows concrete CTE from 0 to 8. The CTE model values are shown as blue bars, and the average values from literature are shown as red bars. For each aggregate type category, the blue bar closely matches the red bar.

Figure 76. Graph. Comparison of CTE model prediction with average values reported in literature for each aggregate rock type.

This graph is an x-y scatter plot showing the predicted coefficient of thermal expansion (CTE) values versus the typical values reported in literature for each aggregate rock type. The x-axis shows the typical aggregate specific CTE value reported in literature from 4 to 8 x10-6 inch/inch/ºF, and the y-axis shows the Portland cement concrete 
CTE values from Long-Term Pavement Performance data from 4 to 8 x10-6 inch/inch/ºF. The data are plotted as solid squares and have a linear trend line. The graph also has a 45-degree 
line of equality plotted as a solid line. The points range from 4 to 7 x10-6 inch/inch/ºF. The 
model statistics are also included as follows: y equals 0.4303x plus 3.3629 and R-squared 
equals 0.6709.

Figure 77. Graph. CTE model prediction versus average values reported in literature for each aggregate rock type.

This graph shows the sensitivity of the coefficient of thermal expansion (CTE) model to coarse aggregate content for different aggregate types. The x-axis shows the coarse aggregate content in the mix from 500 to 3,000 lb/yd3, and the y-axis shows the Portland cement concrete CTE from 0 to 
7 x10-6 inch/inch/ºF. The sensitivity is show in the range of 700 to 2,750 lb/yd3. The aggregate types in the order from top to bottom are chert (solid diamonds), quartzite (solid squares), peridotite (x-marks), andesite (solid triangles), and basalt (solid squares). The markers are connected by a solid line for all aggregate types. The two lines representing quartzite and chert remain horizontal, but the lines representing peridotite, andesite, and basalt show a decrease in CTE with increasing coarse aggregate content.

Figure 78. Graph. Sensitivity of the CTE model to coarse aggregate content.


 


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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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