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Federal Highway Administration Research and Technology
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Publication Number: FHWAHRT12030 Date: August 2012 
Publication Number:
FHWAHRT12030
Date: August 2012 
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The compressive strength model 4 was developed to provide a strength estimate for in situ strength at all ages of a project and covers both shortterm and longterm estimates. This model provides the ability to assess the strength development over the entire lifetime of a project and make more realistic estimates of distress development. This necessitates the use of both SPS and GPS section data. The shortterm strength data for this model were primarily from SPS sections, and the longterm strength data were controlled by GPS sections. Data from SPS and GPS sections primarily consisted of strength tests for pavement ages less than 3 years and greater than 5 years, respectively. However, this resulted in the use of a limited set of independent parameters for the model. Only information available for GPS sections could be included. For example, gradation parameters of coarse and fine aggregates were not considered when developing this model.This model can be expressed as follows:
Where:
f_{c,t} = Compressive strength at age t years, psi.
w/c = Water to cement ratio.
CMC = Cementitious materials content, lb/yd^{3}.
uw = Unit weight, lb/ft^{3}.
t = Shortterm age, years.
The regression statistics for this model are presented in table 28. The model was developed using 580 data points, and the prediction has an R^{2} value of 55.4 percent and an RMSE value of 992 psi. Table 29 provides details of the range of data used to develop the model. Figure 155 and figure 156 show the predicted versus measured plot and the residual plot, respectively. Figure 157 through figure 160 show the sensitivity of this model to w/c ratio, CMC, unit weight, and age, respectively. Again, the sensitivity plots showing the variation in core compressive strength with changes in w/c ratio, CMC, and unit weight are presented for 28 days, 1 year, and 20 years. The rate of strength gain is much higher in the short term (28 days to 1 year) than during the next 19 years in the long term. The use of the logarithmic function for the age parameter is justified, as these trends mimic actual strength gain in the field or in laboratory cast specimens. Figure 160 can be treated as the strength gain relationship representative of a typical mix (w/c of 0.4, cement content of 600 lb/yd^{3}, and unit weight of 145 lb/ft^{3}).
Variable 
Estimate 
Standard Error 
tValue 
P_{r} > t 
VIF 
Intercept 
6,022.44 
2,028.37 
2.97 
0.0032 
0 
w/c ratio 
854.46 
675.86 
1.26 
0.2069 
2.15941 
Cementitious 
4.8656 
0.5737 
8.48 
< 0.0001 
2.152 
Unit weight 
68.5337 
13.4368 
5.1 
< 0.0001 
1.00604 
Ln(age) 
533.15 
22.3343 
23.87 
< 0.0001 
1.00026 
The model statistics for table 28 are as follows:
Parameter 
Minimum 
Maximum 
Average 
w/c ratio 
0.00 
0.72 
0.43 
Cementitious content 
354 
999 
615 
Unit weight 
120 
163 
145 
Pavement age 
0.0380 
45.3840 
6.4320 
Compressive strength 
1,990 
11,750 
6,430 