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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 (8)

Compressive Strength Model 4: All Ages Core Strength Model

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 short-term and long-term 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 short-term strength data for this model were primarily from SPS sections, and the long-term 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:

f subscript c,t equals -6,022.44 minus 854.46 times w/c plus 4.8645 times CMC plus 68.5337 times uw plus 533.15 times natural log open parenthesis t closed parenthesis.

Figure 154. Equation. Prediction model 4 for fc,t.

Where:

fc,t = Compressive strength at age t years, psi.

w/c = Water to cement ratio.

CMC = Cementitious materials content, lb/yd3.

uw = Unit weight, lb/ft3.

t = Short-term 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 R2 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/yd3, and unit weight of 145 lb/ft3).

Table 28. Regression statistics for all ages core strength model.

Variable

Estimate

Standard Error

t-Value

Pr > |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:

Table 29. Range of data used for all ages core strength model.

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

 

This graph is an x-y scatter plot showing the predicted versus the measured values used in the all ages core compressive strength model. The x-axis shows the measured compressive strength from zero to 12,000 psi, and the y-axis shows the predicted compressive strength from zero to 12,000 psi. The plot contains 580 points, which correspond to the data points used in the model. The graph also shows a 45-degree line that represents the line of equality. The data are shown as solid diamonds, and they appear to demonstrate a good prediction. The measured values range from 1,990 to 11,750 psi. The graph also shows the model statistics as follows: N equals 580, R-squared equals 0.5538 percent, and root mean square error equals 992 psi.

Figure 155. Graph. Predicted versus measured for all ages core compressive strength model.

This graph is an x-y scatter plot showing the residual errors in the predictions for the all ages core compressive strength model. The x-axis shows the predicted compressive strength from zero to 12,000 psi, and the y-axis shows the residual compressive strength from -6,000 to 6,000 psi. The points are plotted as solid diamonds, and they appear to show no significant bias (i.e., the data are well distributed about the zero-error line). There appears to be no trend in the data, and the trend line is almost horizontal (i.e., zero slope). The following equations are provided in the graph: y equals -0.002x plus 79.723 and R-squared equals 5E minus 0.6.

Figure 156. Graph. Residual errors for all ages core compressive strength model.

This graph shows the sensitivity of the all ages core compressive strength model to the water/cement (w/c) ratio. The x-axis shows the w/c ratio from 0.2 to 0.8, and the y-axis shows the predicted compressive strength from 3,000 to 11,000 psi. The sensitivity is shown for w/c ratio ranges from 0.25 to 0.70 for strength predictions at 28 days, 1 year, and 20 years. The 28-day strength is plotted using solid squares connected by a solid line, the 1-year strength prediction data are shown using solid triangles connected with a solid line, and the 20-year strength data are plotted using solid diamonds connected by a solid line. The graph shows that with increasing w/c ratio, the predicted compressive strength decreases. Cementitious materials content is 600 lb/yd3, and the unit weight is 145 lb/ft3.

Figure 157. Graph. All ages core compressive strength sensitivity to w/c ratio.

This graph shows the sensitivity of the all ages core compressive strength model to the cementitious materials content (CMC). The x-axis shows CMC from 300 to 1,100 lb/yd3, and the y-axis shows the predicted compressive strength from 3,000 to 11,000 psi. The sensitivity is shown for CMC ranges from 350 to 1,000 lb/yd3 for strength predictions at 28 days, 1 year, and 20 years. The 
28-day strength is plotted using solid squares connected by a solid line, the 1-year strength prediction data are shown using solid triangles connected with a solid line, and the 20-year strength data are plotted using solid diamonds connected by a solid line. The graph shows that with increasing CMC, the predicted compressive strength increases. The water/cement ratio is 0.4, and the unit weight is 145 lb/ft3.

Figure 158. Graph. All ages core compressive strength sensitivity to CMC.

This graph shows the sensitivity of the all ages core compressive strength model to the unit weight. The 
x-axis shows the unit weight from 120 to 160 lb/ft3, and the y-axis shows the predicted compressive strength from 3,000 to 11,000 psi. The sensitivity shown for unit weight ranges from 125 to 155 lb/ft3 for strength predictions at 28 days, 1 year, and 20 years. The 28-day strength is plotted using solid squares connected by a solid line, the 1-year strength prediction data are shown using solid triangles connected with a solid line, and the 20-year strength data are plotted using solid diamonds connected by a solid line. The graph shows that with increasing 
unit weight, the predicted compressive strength increases. Cementitious materials content is 
600 lb/yd3, and the water/cement ratio is 0.4

Figure 159. Graph. All ages core compressive strength sensitivity to unit weight.

This graph shows the sensitivity of the short-term core compressive strength model to the pavement age. The 
x-axis shows the pavement age from zero to 20 years, and the y-axis shows the predicted compressive strength from 3,000 to 11,000 psi. The sensitivity is shown for pavement ages from zero to 1 year, and the data are plotted using solid squares connected by a solid line. The graph shows that as the pavement ages, the predicted compressive strength increases. Cementitious materials content is 600 lb/yd3, the water/cement ratio is 0.4, and the unit weight is 145 lb/ft3.

Figure 160. Graph. All ages core compressive strength sensitivity to age.

 


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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.
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