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Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations
REPORT 
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Publication Number: FHWAHRT12030 Date: August 2012 
Publication Number:
FHWAHRT12030
Date: August 2012 
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Variable 
DF 
Estimate 
Standard Error 
tValue 
P_{r} > t 
VIF 
Intercept 
1 
4028.41841 
1681.71576 
2.4 
0.0215 
0 
w/c ratio 
1 
3486.3501 
2152.99857 
1.62 
0.1134 
2.40903 
Cementitious content 
1 
4.02511 
1.32664 
3.03 
0.0043 
2.40903 
The model statistics for table 21 are as follows:
Parameter 
Minimum 
Maximum 
Average 
w/c ratio 
0.27 
0.71 
0.42 
Cementitious content 
376 
936 
664 
Compressive strength 
3,034 
7,611 
5,239 
The recommended 28day compressive strength model is as shown in figure 135.
Where:
f’_{c,}_{28d}= 28day compressive strength, psi.
w/c = Water to cementitious materials ratio.
CMC = Cementitious materials content, lb/yd^{3}.
Figure 136 and figure 137 show the sensitivity of this model to w/c ratio and CMC. The change in compressive strength appears reasonable for both of the parameters for the range of values evaluated. They are also consistent with the data in the database. Within practical ranges, a change in CMC from 500 to 650 lb/ft^{3} increases the 28day strength from approximately 4,700 to 5,300 psi for a w/c ratio of 0.4. Likewise, a decrease in the w/c ratio from 0.5 to 0.35 increases the strength from 4,700 to 5,200 psi.
Cylinder strength data were available for the SPS sections at pavement ages of 14 days, 28 days, and 1 year for a majority of the sections. Although two sections with strength data at 10 years were available, data in the model were limited for ages up to 1 year. Therefore, this model predicts the strength up to an age of 1 year.
Since this model utilizes only SPS data, a large set of independent variables was available for evaluation. Additionally, it is likely that this model will be used after approval of the mix design for a project or possibly even after initial construction, during which time more mix design parameters will be known for accurate prediction. The model developed includes pavement age as an independent parameter. Because the dataset includes multiple measurements or repeated readings of the same section, this parameter has been treated with a hierarchical modeling approach.
This model was established as shown in figure 138.
Where:
f_{c,t} = Compressive strength at age t years, psi.
CMC = Cementitious materials content, lb/yd^{3}.
w/c = Water to cement ratio.
uw = Unit weight, lb/ft^{3}.
t = Shortterm age, years.
The regression statistics for this model are presented in table 23, and details of the range of data used to develop the model are presented in table 24.
Variable 
DF 
Estimate 
Standard Error 
tValue 
P_{r} > t 
VIF 
Intercept 
1 
6,358.60655 
1,213.09762 
5.24 
< 0 .0001 
0 
Cementitious 
1 
3.53012 
0.90968 
3.88 
0.0002 
2.15941 
(w/c) × unit weight 
1 
34.24312 
11.00358 
3.11 
0.0026 
2.152 
Ln(age) 
1 
633.3489 
87.49625 
7.24 
< 0.0001 
1.00604 
The model statistics for table 23 are as follows:
Parameter 
Minimum 
Maximum 
Average 
w/c ratio 
0.27 
0.69 
0.43 
Cementitious content 
376 
936 
660 
Unit weight 
124 
151 
143 
Pavement age 
0.0384 
1.0000 
0.3081 
Compressive strength 
2,480 
10,032 
5,256 
The model was developed using 79 data points, and the prediction has an R^{2} value of 66.6 percent and an RMSE value of 789 psi. The reason for an improved R^{2} compared to the 28day strength model is not clear from these analyses. Figure 139 and figure 140 show the predicted versus measured plot and the residual plot, respectively.