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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 (9)

Compressive Strength Model 5: Long-Term Core Strength Model

This model was developed to estimate the long-term strength of cores taken from a pavement. Data from only the GPS sections were utilized, and they included sections greater than 5 years in age. Strength data at multiple ages were available on some of the sections. A preliminary analysis indicated that pavement age was not a significant factor in the model. In other words, for pavements that have been in service for several years, the strength was more a function of its material parameters than age. This suggests that strength gain is relatively minimal after 5 years or is not noticed in a statistical sense. It then becomes reasonable, or perhaps even necessary, from a statistical standpoint to average the strengths for each section.

The model selected for the long-term strength can be expressed as follows:

f subscript c,LT equals -3,467.3508 plus 3.63452 times CMC plus 0.42362 times uw squared.

Figure 161. Equation. Prediction model 5 for fc,LT.

Where:

fc, LT = Long-term compressive strength, psi.

CMC = Cementitious materials content, lb/yd3.

uw = Unit weight, lb/ft3.

The regression statistics for this model are presented in table 30. The model was developed using 201 data points, and the prediction has an R2 value of 18 percent and an RMSE value of 1,179 psi. Table 31 provides details of the range of data used to develop the model. Figure 162 and figure 163 show the predicted versus measured plot and the residual plot, respectively. From observing figure 162, it is evident that this model does not have a good predictive ability, and while there is no significant bias, the error in prediction is fairly high (see figure 163). This model needs to be used with caution, and other means to verify the value would be necessary, such as core tests.

Table 30. Regression statistics for long-term core strength model.

Variable

DF

Estimate

Standard Error

t-Value

Pr > |t|

VIF

Intercept

1

-3,467.3508

1,720.49637

-2.02

0.0452

0

Cementitious

1

3.63452

1.38354

2.63

0.0093

1.024

(Unit weight)2

1

0.42362

0.06634

6.39

< 0.0001

1.024

 

The mode statistics for table 30 are as follows:

Table 31. Range of data used for long-term core strength model.

Parameter

Minimum

Maximum

Average

Cementitious content

354

781

550

Unit weight

134

156

147

Compressive strength

4,315

11,750

7,655

This graph is an x-y scatter plot showing the predicted versus the measured values used in the long-term core compressive strength model. The x-axis shows the measured compressive strength from 4,000 to 12,000 psi, and the y-axis shows the predicted compressive strength from 4,000 to 12,000 psi. The plot contains 201 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 4,315 to 11,750 psi. The graph also shows the model statistics as follows: N equals 201, R-squared equals 0.1803 percent, and root mean square error equals 1,179 psi.

Figure 162. Graph. Predicted versus measured for long-term core compressive strength model.

This graph is an x-y scatter plot showing the residual errors in the predictions of the long-term core compressive strength model. The x-axis shows the predicted compressive strength from 4,000 to 10,000 psi, and the y-axis shows the residual compressive strength from -4,000 to 4,000 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 0.0384x minus 291.07 and R-squared equals 0.0003.

Figure 163. Graph. Residual errors for long-term core compressive strength model.

Relative Comparison of All Compressive Strength Models

The compressive strength models presented in this section reproduce the trends present in the datasets used for each correlation. It is highly recommended that a user estimate the strength based on as many models as possible with the information available at the time of analysis. This might provide a fair assessment of the ranges of compressive strength likely for the project and at different ages.

This section presents a comparison of the various models, and the graphs used for this discussion also include raw data plotted with the various relationships. Figure 164 through figure 168 show the relationship between compressive strength and CMC, w/c ratio, and unit weight, respectively. Figure 167 and figure 168 show the strength gain at short- and long-term ages, respectively.

Note that relationships have been plotted for typical values for all variables, and the raw data used in the models do not necessarily lie on the plots.

This graph shows the sensitivity of four compressive strength models. The x-axis shows the cementitious materials content (CMC) from 300 to 1,100 lb/yd3, and the y-axis shows the predicted compressive strength from 1,000 to 11,000 psi. The sensitivity is shown for CMC and ranges from 350 to 1,000 lb/yd3 for strength predictions at 28 days. The 28-day strength is plotted using different markers for the four models used. The solid diamonds represent the 28-day cylinder model, the solid squares represent the short-term cylinder strength model, the asterisk marks represent the short-term core strength model, and the solid triangles represent the all-ages core strength model. The raw data representing 28-day strengths are plotted as hollow triangles for cylinders and hollow circles for cores. The graph shows that with increasing CMC, the predicted compressive strength increases. The lines are mostly inclined at approximately 30 degrees. The graph also shows that the predictions for all models are within 500 psi of each other for most part. The water/cement ratio is 0.4, the unit weight is 145 lb/ft3, maximum aggregate size is 
0.75 inches, and fineness modulus is 3.0.

Figure 164. Graph. Model compressive strength prediction for varying CMC.

This graph shows the sensitivity of four compressive strength models. The x-axis shows the water/cement (w/c) ratio from 0.2 to 0.8, and the y-axis shows the predicted compressive strength from 1,000 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. The 28-day strength is plotted using different markers for the four models used. The solid diamonds represent the 28-day cylinder model, the solid squares represent the short-term cylinder strength model, the solid circles marks represent the short-term core strength model, and the solid triangles represent the all ages core strength model. The raw data representing 28-day strengths are plotted as hollow triangles for cylinders and hollow circles for cores. The graph shows that with an increasing w/c ratio, the predicted compressive strength decreases. The four plots have different slopes. The graph also shows that the predictions for all models are within 500 psi of each other for w/c ratios of less than 0.50. The raw data are scattered to the top of the models for w/c ratios below 0.38 and between w/c ratios of 0.4 and 0.5. They are spread on both sides of predictions for w/c ratios approaching 0.6. Cementitious materials content is 600 lb/yd3, the unit weight is 145 lb/ft3, and maximum aggregate size is 
0.75 inches.

Figure 165. Graph. Model compressive strength prediction for varying w/c ratio.

This graph shows the model compressive strength prediction for varying unit weights. The x-axis shows the unit weight from 120 to 160 lb/ft3, and the y-axis shows the predicted compressive strength from 1,000 to 11,000 psi. The sensitivity is shown for unit weight and ranges from 125 to 155 lb/ft3 for strength predictions at 1 year. The 28-day strength is plotted using different markers for the two models. The solid triangles represent the core all ages model, and the solid squares represent the core short-term model. The raw data are plotted as hollow triangles for cylinders and hollow circles for cores. The graph shows that with increasing unit weight, the predicted compressive strength increases. The two lines have different slopes; the core all ages line is steeper than the core short-term model line. The raw data are spread on both sides of the predictions. Cementitious materials content is 600 lb/yd3, the water/cement ratio is 0.4, maximum aggregate size is 0.75 inches, and fineness modulus is 3.0.

Figure 166. Graph. Model compressive strength prediction for varying unit weights.

This graph shows the sensitivity of three compressive strength models to the pavement age. The x-axis shows the pavement age from zero to 1 year, and the y-axis shows the predicted compressive strength from 4,000 to 8,000 psi. The models are represented by different markers; the solid triangles represent the cylinder short-term strength, the solid squares represent the core all ages strength, and the solid triangles represent the core short-term strength. The graph shows that with increasing age, the predicted compressive strength increases. Cementitious materials content is 600 lb/yd3, the water/cement ratio is 0.4, the unit weight is 145 lb/ft3, maximum aggregate size is 0.75 inches, and fineness modulus is 3.0.

Figure 167. Graph. Strength gain in the short-term predicted by three models.

This graph shows the sensitivity of long-term strength gain 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 1,000 to 15,000 psi. The models are represented by different markers; the solid squares connected by a solid line represent the core all ages model, and the solid line without any markers represents the long-term strength model. The core all ages model has a steep increase from an zero to 1 year and has a considerable reduction in slope and is almost a flat line after 10 years. The long-term strength model ranges from 5 to 20 years and is a straight line with zero slope, which indicates that it is not affected by age. The hollow circles represent the raw data. Cementitious materials content is 600 lb/yd3, the water/cement ratio is 0.4, the unit weight is 145 lb/ft3, maximum aggregate size is 0.75 inches, and fineness modulus is 3.0.

Figure 168. Graph. Long-term strength gain predicted by the models.

The following observations can be made:

These observations illustrate the benefit of comparing predictions made by the various models available to obtain the range of strength that each project or observation could develop. Any other information to substantiate or validate the strength predictions should be utilized whenever possible, such as strength values from other projects that have used similar materials and mix design.

 


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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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