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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 (18)

Using the JPCP deltaT Model

This section provides an example for the use of the JPCP deltaT model developed under this study. The section used to describe the process is the LTPP SPS-2 section 04_0213 located in Maricopa County, AZ, and constructed in July 1993.

 

The following latitude, design, and material inputs required for the deltaT prediction model can be obtained from the MEPDG inputs:

The temperature range input to this model is the difference between the mean monthly maximum and minimum temperatures for the month of July from historical climate data records (as climate data included in the MEPDG). If the user does not have this information readily available, the data to compute the temperature range can be determined from the output file of the MEPDG analysis of this section. The output file (e.g., titled “04_0213.xls”) contains a worksheet titled “Climate” with key climate data for the specific location (or the virtual climate station created). This worksheet includes the monthly climate summary with minimum and maximum temperature by month for all years of data used under the headings “Min. Temp. (ºF)” and “Max. Temp. (ºF),” respectively. (Note that this summary also consists of “Average Temp. (ºF),” “Max. Range (ºF),” “Precip. (in.),” “Average Wind (mph),” “Average Sun (%),” “Number Wet Days,” and “Max. Frost (in.).” However, these data are not of relevance to the deltaT model).

For the month of July, the average minimum and maximum temperatures are 73 and 111.7 °F, respectively. The difference between these temperatures is 38.7 °F.

Using these inputs, the deltaT gradient can be calculated as -1.7457138 °F/inch. For the slab thickness of 8.3 inches, this is equivalent to a deltaT of -14.5 °F. This value is significantly higher than the default of -10 °F/inch. This input can be revised in an MEPDG file and reanalyzed to evaluate the predicted transverse cracking performance.

deltaT—CRCP Design

Generating Dependent Variable Data

The procedure followed to obtain the dependent variable—the CRCP deltaT producing the closest prediction to field distress—shared several commonalities that followed to generate the deltaT for JPCP. Punchout prediction was the basis for selecting the optimum deltaT with minimized errors. The CRCP design files used for the calibration of the MEPDG models were run at deltaT values of -2.5, -5.0, -7.5, -10, -12.5, and -15 °F. The punchout predictions at all these values of deltaT were compared against field measured punchouts. The value corresponding to the least sum of squared errors for the prediction at all ages combined was selected as the optimum deltaT for that section. This selection of an optimum value for all the sections used in the calibration generated the dependent variable dataset.

 

CRCP deltaT Gradient Model Development

As with the JPCP deltaT gradient model, the dependent variable CRCP deltaT data correlated well with the material, design, and climate parameters when transformed from deltaT temperature differential to deltaT temperature gradient. Step-wise regression and Cp analyses were performed to select the variables that best correlated to the dependent variable and to select the best combination of variables to develop the model. It was observed that coarse aggregate type was significant. After an iterative process to optimize the model, the equation developed to estimate the deltaT gradient variable is as follows:

DeltaT divided by inch equals 12.93007 minus 0.15101 times MaxTemp minus 0.10241 times MaxTempRange plus 3.279 times Chert plus 1.55013 times Granite plus 1.40009 times Limestone plus 2.01838 times Quartzite plus 0.11299 times PCCTHK.

Figure 225. Equation. Prediction model 16 for deltaT/inch.

Where:

deltaT/inch = Predicted gradient in CRCP slab, °F/inch.

MaxTemp = Maximum temperature for the month of construction, °F.

MaxTempRange = Maximum temperature range for the month of construction, °F.

PCCTHK= JPCP slab thickness, inch.

Chert =1 if PCC mix coarse aggregate is chert, or 0 if otherwise.

Granite = 1 if PCC mix coarse aggregate is granite, or 0 if otherwise.

Limestone = 1 if PCC mix coarse aggregate is limestone, or 0 if otherwise.

Quartzite = 1 if PCC mix coarse aggregate is quartzite, or 0 if otherwise.

The model considers climate (MaxTemp and MaxTempRange), design parameters (PCCTHK), and material (Aggregate type) parameters. The model statistics are presented in table 55. The model was developed with 35 data points and has an R2 value of 82.5 percent and an RMSE value of 0.27932 psi. Table 56 provides details of the range of data used to develop the model. Figure 226 shows the predicted versus measured for the proposed CRCP deltaT gradient model, while figure 227 shows the residual errors. Note that the measured data refers to the deltaT gradient determined by matching MEPDG prediction to field performance.

Table 55. Regression statistics for CRCP deltaT model.

Variable

DF

Estimate

Standard Error

t-value

Pr > t

VIF

Intercept

1

12.93007

1.98459

6.52

< 0.0001

0

MaxTemp

1

-0.15101

0.01793

-8.42

< 0.0001

3.46347

MaxTempRange

1

-0.10241

0.01869

-5.48

< 0.0001

2.00933

Chert

1

3.279

0.30508

10.75

< 0.0001

2.24965

Granite

1

1.55013

0.22656

6.84

< 0.0001

4.96262

Limestone

1

1.40009

0.18956

7.39

< 0.0001

4.00053

Quartzite

1

2.01838

0.39449

5.12

< 0.0001

1.93773

PCCTHK

1

0.11299

0.0705

1.6

0.1207

1.68624

 

 

The model statistics for table 55 are as follows:

Table 56. Range of data used for CRCP deltaT model.

Parameter

Minimum

Maximum

Average

Maximum temperature

78.4

99.2

90.3

Temperature range

24.8

40.4

30.4

Chert

0

1

0.06

Granite

0

1

0.31

Limestone

0

1

0.46

Quartzite

0

1

0.03

PCC thickness

5.6

9.5

8.4

 

This graph is an 
x-y scatter plot showing the predicted versus the measured values used in the continuously reinforced concrete pavement (CRCP) deltaT model. The x-axis shows the deltaT gradient estimated by matching the Mechanistic-Empirical Pavement Design Guide and field performance from -3 to 0 Fahrenheit/inch, and the y-axis shows the predicted deltaT gradient from -3 to 0 Fahrenheit/inch. The plot contains 35 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 -2.67 to -0.30 °F/inch. The graph also shows the model statistics as follows: y equals 0.825x minus 0.2629 and R-squared equals 0.825.

Figure 226. Graph. Predicted versus measured for CRCP deltaT model.

This graph is an x-y scatter plot showing the residual errors in the predictions of the continuously reinforced concrete pavement (CRCP) deltaT model. The x-axis shows the deltaT gradient estimated by matching the Mechanistic-Empirical Pavement Design Guide and field performance from -2.5 to 0 Fahrenheit/inch, and the y-axis shows the predicted deltaT gradient from -2.5 to 2.5 Fahrenheit/inch. 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). There appears to be no trend in the data, and the trend line is almost horizontal (i.e., zero slope). The graph provides the following equations: y equals 8E minus 07x minus 8E minus 05 and R-squared equals 3E minus 12.

Figure 227. Graph. Residual errors for CRCP deltaT model.

Figure 228 through figure 231 show the sensitivity of the deltaT differential calculation to the parameters maximum temperature of the project location, maximum temperature range, CRCP slab thickness, and geographic location, respectively. The trends observed in the model—CRCP deltaT increasing with increasing maximum temperature and increasing temperature range—are reasonable. While the effect of slab thickness shows a linear relationship with the deltaT gradient, the magnitude of the coefficient for this variable results causes the deltaT differential (CRCP deltaT gradient × thickness) to assume a nonlinear relationship with the deltaT differential, peaking at about 10 inches. Figure 231 shows the deltaT predictions for projects selected from LTPP sites in Texas, Illinois, Virginia, Mississippi, Oregon, and Georgia.

This graph shows the sensitivity of the continuously reinforced concrete pavement (CRCP) deltaT prediction model to the maximum temperature. The x-axis shows the maximum temperature from 70 to 110 Fahrenheit, and the y-axis shows the predicted deltaT  in a 10-inch slab from -30 to 20 Fahrenheit. The sensitivity is shown for temperature ranges from 76 to 100 Fahrenheit, and the data are plotted using solid diamonds connected by a solid line. The graph shows that with increasing temperature, the predicted deltaT decreases.

Figure 228. Graph. Effect of maximum temperature on CRCP deltaT prediction model.

This graph shows the sensitivity of the continuously reinforced concrete pavement (CRCP) deltaT prediction model to a range of temperatures. The x-axis shows the temperature range from 20 to 50 Fahrenheit, and the y-axis shows the predicted deltaT in a 10-inch slab from -25 to 0 Fahrenheit. The sensitivity is shown for temperatures ranging from 24 to 40 Fahrenheit, and the data are plotted using solid diamonds connected by a solid line. The graph shows that with increasing temperature, the predicted deltaT decreases.

Figure 229. Graph. Effect of temperature range on CRCP deltaT prediction model.

This graph shows the sensitivity of the continuously reinforced concrete pavement (CRCP) deltaT prediction model to a range of slab thicknesses. The x-axis shows the slab thickness from 6 to 
14 inches, and the y-axis shows the predicted deltaT from -12.1 to -11.4 Fahrenheit. The sensitivity is shown for thicknesses ranging from 8 to 12 inches, and the data are plotted using solid diamonds connected by a solid line. The graph shows that in the range of 8 to 10 inches with increasing thickness, the predicted deltaT decreases. In the range of 10 to 12 inches with increasing thickness, the predicted deltaT increases.

Figure 230. Graph. Effect of slab thickness on CRCP deltaT prediction model.

This graph is a bar chart showing the predicted deltaT values for continuously reinforced concrete pavement (CRCP) sections in the Long-Term Pavement Performance sites in various locations. The data are categorized by the location, which, starting from the left, are Texas—cold climate, Texas—hot climate, Illinois, Mississippi, Oregon, Georgia, and Virginia. The y-axis shows the deltaT in a 10-inch slab from zero to -40 Fahrenheit. The values plotted are also labeled on the solid bars and are 
-1.3, -31.0, -11.4, -1.5, -25.1, -14.5, and -12.4 Fahrenheit, respectively.

Figure 231. Graph. Effect of geographic location on CRCP deltaT prediction.

The sensitivity analyses show reasonable trends but do not demonstrate that the model is robust. From an engineering standpoint, it is not clear if the range of predicted values and their magnitudes are practical and realistic. The wide range of deltaT will have a significant effect on design thickness. The data used to develop the model show very strong correlations, and it is likely that the predictions are valid, at least within a certain range of inputs. The current analyses and the data available are not adequate to determine these ranges. It is therefore recommended that this model be used with extreme caution.

 


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