Skip to contentUnited States Department of Transportation - Federal Highway Administration FHWA Home
Research Home   |   Pavements Home
REPORT
This report is an archived publication and may contain dated technical, contact, and link information
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

PDF Version (4.44 MB)

PDF files can be viewed with the Acrobat® Reader®

CHAPTER 5. MODEL DEVELOPMENT (5)

Table 17. Regression statistics for the four-variable model suggested by Cp analysis with subset of data that were available for all parameters evaluated.

Parameter

Degrees of Freedom (DF)

Estimate

Standard Error

t-Value

Pr > |t|

VIF

Intercept

1

9,907.383

2,732.919

3.63

0.0023

0

w/c

1

-4,893.05

2,532.455

-1.93

0.0712

3.01113

Cementitious content

1

3.30331

1.56188

2.11

0.0505

3.76626

Coarse_Aggregate_

Mix_Design

1

-1.67238

0.61169

-2.73

0.0147

1.38486

Fine_Aggregate_Mix_Design

1

-1.51914

0.78059

-1.95

0.0694

1.79848

Note: Italicized text indicates that the parameter and statistic do not satisfy the criteria adopted for model development.

The model statistics for table 17 are as follows:

Table 18. Regression statistics for the four-variable model suggested by Cp analysis with complete dataset available for the parameters selected.

Parameter

DF

Estimate

Standard Error

t-Value

Pr > |t|

VIF

Intercept

1

10,789

2,181.11

4.95

<0 .0001

0

w/c

1

-2,050.86

2,200.846

-0.93

0.3607

2.78251

Cementitious content

1

3.57161

1.36819

2.61

0.0153

3.23079

Coarse_Aggregate_

Mix_Design

1

-2.34227

0.51775

-4.52

0.0001

1.25735

Fine_Aggregate_Mix_Design

1

-2.35301

0.64777

-3.63

0.0013

1.39035

Note: Italicized text indicates that the parameter and statistic do not satisfy the criteria adopted for model development.

The model statistics for table 18 are as follows:

Table 19. Regression statistics for the three-variable model suggested by Cp analysis.

Parameter

DF

Estimate

Standard Error

t-Value

Pr > |t|

VIF

Intercept

1

9,381.832

1,569.631

5.98

< 0.0001

0

Cementitious

1

4.57228

0.84557

5.41

< 0.0001

1.24054

Coarse_Aggregate_Mix_Design

1

-2.50707

0.48533

-5.17

< 0.0001

1.11065

Fine_Aggregate_Mix_ Design

1

-2.23659

0.63393

-3.53

0.0016

1.33863

Note: Italicized text indicates that the parameter and statistic do not satisfy the criteria adopted for model development.

The model statistics for table 19 are as follows:

Table 20. Regression statistics for the two-variable model suggested by Cp analysis.

Parameter

DF

Estimate

Standard Error

t-Value

Pr > |t|

VIF

Intercept

1

4,897.511

1,105.332

4.43

0.0002

0

Cementitious content

1

5.80657

0.92386

6.29

< 0.0001

1.02819

Coarse_Aggregate_Mix_Design

1

-2.0405

0.56042

-3.64

0.0012

1.02819

Note: Italicized text indicates that the parameter and statistic do not satisfy the criteria adopted for model development.

The model statistics for table 20 are as follows:

In establishing and optimizing a model, each variable selected has to be significant (p < 0.05) and not show an interaction effect with other variables (VIF > 5). However, the opposite is not true. It is not necessary that a variable with a p-value less than 0.05 and VIF less than 5 be included in a model if it is not meaningful from an engineering standpoint or if it does not show promise based on a sensitivity analysis.

While this evaluation process can be performed in a systematic manner, it cannot be performed in a fully automated manner. Each parameter in each model needs to be assessed manually. Table 17 and table 18 show the regression statistics for the four-variable model shown to produce the best correlation (R2) in table 16. Note that the number of data points in the model is different in the two tables (N = 21 and N = 29 in table 17 and table 18, respectively). Table 17 shows the subset of data that was used in the Cp analysis, wherein 21 observations have data in all fields evaluated; however, 29 observations have data for the parameters selected for the model. R2 in table 17 matches that shown against the four-parameter model in table 16. However, the regressed coefficients and R2 in table 18 correspond to the variables selected for this model, and the contents of table 18 are the proper statistics to report for the model.

The results in table 18 indicate the following:

Removal of the w/c ratio parameter in the three-variable model results in regression statistics shown in table 19. Note that the coarse and fine aggregate contents show trends that counter engineering knowledge even though the parameters are significant to the model. The best two- variable model, shown in table 20, also shares the same concern. Thus, the iterative process needs to evaluate several parameters and balance both statistical and engineering needs. Often, a trial and error method has to supplement the pure statistical approach. The model selection is not based solely on the best R2 value, either.

The final model selected for the estimation of 28-day compressive strength is shown in table 21 and includes the w/c ratio and CMC as the regressors. All 42 observations have been included. The R2 value is 54.4 percent. Although it is compromised relative to the models discussed above, it provides a more meaningful model with a superior predictive ability. RMSE for the model is 871 psi. Table 22 provides details of the range of data used to develop the model. Figure 133 and figure 134 show the predicted versus measured values and the residuals plot for the model, respectively.

 


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).
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.
FHWA
United States Department of Transportation - Federal Highway Administration