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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 (4)

Compressive Strength Model 1: 28-Day Cylinder Strength Model

The data used for this model included SPS sections that had 28-day cylinder test results. The data included 42 sets of results after averaging the 28-day cylinder strength for each site and for each mix design.

All material properties discussed in the section, Data Used in PCC Models, in chapter 5 of this report were evaluated to verify if they co-vary with the predicted variable. The first statistical procedure was a Cp analysis wherein various submodels were considered for fit using ANOVA, and the resulting Cp and R2 values are provided at the end of the SAS® analysis. The results are listed by SAS® in order of the resulting Cp value. Also provided in the results are the number of variables (regressors) used in each model and a listing of the variables. The Cp analysis results are shown in table 16 for the 28-day cylinder strength model.

The Cp analysis summary indicates that 42 observations were read. There were missing data for certain PCC mix parameters. For example, the amount of coarse aggregate in the mix design and the amount of fine aggregate in mix design were missing in 13 cases, while the information on admixtures was missing in 21 cases. A summary indicates that only 21 observations had values for all variables considered in the model. Using a subset of 21 datasets, the potential prediction models created produced the R2 values as listed in the table. The model form used for the analysis was as follows:

f subscript c equals A subscript 0 plus A subscript 1 times x subscript 1 plus A subscript 2 times x subscript 2 plus A subscript 3 times x subscript 3 plus A subscript 4 times x subscript 4…plus A subscript n times x subscript n.

Figure 132. Equation. fc model form.

 

Where:

A0 = Model intercept determined through the regression.

A1 through An = Regression coefficients.

x1 through xn = Parameters included in each submodel.

These results do not imply that all models listed in table 16 are feasible models. Cp and R2, as explained earlier, do not indicate whether the parameters included in the model, or submodel in this case, are significant, exhibit multicollinearity, or physically explain the trend. Each submodel suggested by the Cp analysis needs to be further evaluated and verified individually.

Table 16. Cp selection method for 28-day cylinder compressive strength model.

Number of Parameters in Model

Cp

R2

Variables in Model

4

1.0058

0.8184

w_c

cementitious Coarse_Aggregate_Mix_Design

Fine_Aggregate_Mix_Design

4

1.2802

0.8143

cementitious AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

2

1.5747

0.7493

cementitious Coarse_Aggregate_Mix_Design

3

1.807

0.7761

cementitious Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

4

1.8277

0.806

w_c MASm15pct_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

3

1.8478

0.7755

w_c cementitious Coarse_Aggregate_Mix_Design

3

2.0836

0.7719

cementitious AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design

5

2.2057

0.8305

w_c cementitious FM Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

3

2.3622

0.7677

w_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

4

2.4771

0.7962

cementitious MASm15pct_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

5

2.4789

0.8264

cementitious FM AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

4

2.5453

0.7952

w_c FM Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

3

2.5577

0.7647

cementitious MASm15pct_W_c Coarse_Aggregate_Mix_Design

5

2.7348

0.8225

w_c cementitious MASm15pct_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

5

2.9597

0.8191

w_c cementitious AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

5

2.9672

0.819

w_c cementitious AVG_UNIT_WT2 Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

5

2.97

0.819

w_c cementitious AVG_UNIT_WT Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

5

2.9955

0.8186

cementitious AVG_UNIT_WT2 AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

5

3.0046

0.8185

cementitious AVG_UNIT_WT AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

5

3.04

0.8179

w_c MASm15pct_W_c FM Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

4

3.1679

0.7857

cementitious FM Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

5

3.2171

0.8152

cementitious MASm15pct_W_c AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

3

3.4873

0.7507

cementitious FM Coarse_Aggregate_Mix_Design

5

3.4917

0.8111

AVG_UNIT_WT2 MASm15pct_W_c AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

5

3.4928

0.8111

w_c AVG_UNIT_WT2 MASm15pct_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

5

3.4971

0.811

w_c AVG_UNIT_WT MASm15pct_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

5

3.5058

0.8109

cementitious MASm15pct_W_c FM Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

5

3.5095

0.8108

AVG_UNIT_WT MASm15pct_W_c AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

2

3.5215

0.7199

w_c cementitious

5

3.5431

0.8103

w_c MASm15pct_W_c AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

3

3.5548

0.7496

cementitious AVG_UNIT_WT2 Coarse_Aggregate_Mix_Design

3

3.5574

0.7496

cementitious AVG_UNIT_WT Coarse_Aggregate_Mix_Design

4

3.6023

0.7792

FM AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

3

3.6744

0.7478

AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

2

3.711

0.717

cementitious MASm15pct_W_c

4

3.7405

0.7771

w_c cementitious AVG_UNIT_WT2 Coarse_Aggregate_Mix_Design

4

3.7435

0.777

cementitious AVG_UNIT_WT2 AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design

4

3.7458

0.777

MASm15pct_W_c AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

4

3.7472

0.777

w_c cementitious AVG_UNIT_WT Coarse_Aggregate_Mix_Design

4

3.7504

0.7769

w_c cementitious AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design

4

3.757

0.7768

cementitious AVG_UNIT_WT AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design

4

3.7817

0.7765

w_c cementitious FM Coarse_Aggregate_Mix_Design

4

3.8069

0.7761

cementitious AVG_UNIT_WT Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

4

3.807

0.7761

cementitious AVG_UNIT_WT2 Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

4

3.8079

0.7761

w_c cementitious MASm15pct_W_c Coarse_Aggregate_Mix_Design

2

3.9079

0.7141

cementitious AVG_UNIT_WT_W_c

4

4.0157

0.7729

cementitious FM AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design

4

4.034

0.7726

w_c AVG_UNIT_WT_W_c Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

6

4.0832

0.8324

w_c cementitious MASm15pct_W_c FM Coarse_Aggregate_Mix_Design Fine_Aggregate_Mix_Design

 

Table 17 to table 20 show examples of submodels evaluated in the selection of the optimized model for the prediction of 28-day compressive strength of PCC cylinders. This procedure typically involves an iterative process and specifically evaluates the following aspects:

 


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