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Publication Number:
FHWAHRT12030
Date: August 2012 
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The data used for this model included SPS sections that had 28day cylinder test results. The data included 42 sets of results after averaging the 28day 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 covary with the predicted variable. The first statistical procedure was a C_{p} analysis wherein various submodels were considered for fit using ANOVA, and the resulting C_{p} and R^{2} values are provided at the end of the SAS^{®} analysis. The results are listed by SAS^{®} in order of the resulting C_{p} value. Also provided in the results are the number of variables (regressors) used in each model and a listing of the variables. The C_{p} analysis results are shown in table 16 for the 28day cylinder strength model.
The C_{p} 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 R^{2} values as listed in the table. The model form used for the analysis was as follows:
Where:
A_{0} = Model intercept determined through the regression.
A_{1} through A_{n} = Regression coefficients.
x_{1} through x_{n} = Parameters included in each submodel.
These results do not imply that all models listed in table 16 are feasible models. C_{p} and R^{2}, 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 C_{p} analysis needs to be further evaluated and verified individually.
Number of Parameters in Model 
C_{p} 
R^{2} 
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 28day compressive strength of PCC cylinders. This procedure typically involves an iterative process and specifically evaluates the following aspects:
Topics: research, infrastructure, pavements and materials Keywords: research, infrastructure, pavements and materials, Pavements, LTPP, material properties, MEPDG, prediction model, Index properties TRT Terms: research, facilities, transportation, highway facilities, roads, parts of roads, pavements Updated: 09/14/2012
