U.S. Department of Transportation
Federal Highway Administration
1200 New Jersey Avenue, SE
Washington, DC 20590
202-366-4000


Skip to content
Facebook iconYouTube iconTwitter iconFlickr iconLinkedIn

Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations

 
REPORT
This report is an archived publication and may contain dated technical, contact, and link information
Back to Publication List        
Publication Number:  FHWA-HRT-15-036    Date:  December 2015
Publication Number: FHWA-HRT-15-036
Date: December 2015

 

Long-Term Pavement Performance Program Determination of In-Place Elastic Layer Modulus: Backcalculation Methodology and Procedures

Chapter 3. Case Studies

The purpose of the case studies conducted in phase I of this project were twofold: (1) select the forward and/or backcalculation methods from the candidates identified in chapter 2 and (2) provide direction for automating the backcalculation process by establishing the decisionmaking criteria in evaluating the results. In addition, results from the case studies were used to confirm the rules of simulation in establishing the pavement structure on an automated basis.

LTPP Test Sections Selected for Case Studies

Test sections from the LTPP SPS and SMP experiments were selected because deflection basins for these experiments were measured at shorter time intervals than for the GPS experiments. Six case studies were used to compare and evaluate the candidate backcalculation and forward calculation programs and to demonstrate the different pre- and post-processing tools to be used for the production runs. The LTPP projects selected for the case studies are listed in table 2. The reasons for selecting these sites are as follows:

Table 2. LTPP test sections used for the case studies.
Pavement Type New Construction Sites Rehabilitation Sites SMP Sites
Rigid North Carolina SPS-2: all sections Oklahoma SPS-6 intact and rubblized sections 49-3011 (Utah)
Flexible Wisconsin SPS-1 sections 0113, 0116, and 0119; Iowa SPS-1 sections 0101, 0106, and 0109 Mississippi SPS-5 control, virgin, and recycled asphalt pavement sections 13-1005 (Georgia)

Comparison of Results from Candidate Backcalculation Programs

This section provides a brief comparison of the results between the candidate backcalculation software packages in terms of the evaluation factors set forth in chapter 2. The BAKFAA and MICHBACK© programs were dropped from further consideration because of issues encountered in executing large batch files for the first few case study sites.(10) For the other four programs, three criteria were used in judging the acceptability of the results from the candidate forward and backcalculation methods: RMSE values, magnitude of the moduli, and comparison to laboratory-measured modulus values.

Deflection Basin Matching—RMSE

Figure 3 summarizes and compares the average RMSE values resulting from the backcalculation of layer moduli at each test section and day of testing. As shown, MODTAG© consistently had lower RMSE values, while MODULUS consistently had higher RMSEs.1 (55) Many of the MODTAG© RMSE values were less than 1 percent. EVERCALC© and MODTAG© also had a higher percentage of stations with less than 2 percent RMSE. Based on the RMSE values, MODTAG© and EVERCALC© consistently resulted in a closer match between the measured and calculated deflection basins. The MODULUS program exhibited higher RMSE values in almost all cases for the two conditions: assuming the presence and absence of an apparent rigid layer or bedrock.

Figure 3. Graph. Comparison of RMSE values between backcalculation programs for flexible pavement sections comparing MODULUS, MODTAG©, and EVERCALC©. This graph shows a comparison of the root mean squared error (RMSE) values between backcalculation programs for flexbiel pavement sections comparing MODULUS, MODTAG©, and EVERCALC©. The x-axis shows RMSE values from EVERCALC© from 0 to 6 percent, and the y-axis shows the RMSE values from other backcalculation programs (MODULUS and MODTAG©) from 0 to 10 percent for the flexible test sections. Two types of data points are shown: MODULUS and MODTAG©. A dashed line represents the line of equality. The graph shows all of the data points for MODULUS are above the line of equality, indicating that the results from MODULUS exhibited a higher RMSE value as compared to EVERCALC©. Some of the data points for the MODTAG© program are below the line of equality.

Figure 3. Graph. Comparison of RMSE values between backcalculation programs for flexible pavement sections comparing MODULUS, MODTAG©, and EVERCALC©.

Figure 4 summarizes and compares the average RMSEs from the best fit forward calculation method and EVERCALC©. As shown, the RMSEs from the best fit method were significantly higher than from the EVERCALC© program. This observation is in line with the authors’ experience from other projects with using the forward calculation equations based on the Hogg model for flexible pavements—the forward calculation program resulted in sets of layer moduli with significantly higher RMSE values than the backcalculation program.(26)

Figure 4. Graph. Comparison of RMSE values between backcalculation programs for rigid pavement sections comparing best fit method and EVERCALC©. This graph shows a comparison of the root mean squared error (RMSE) values between backcalculation programs for rigid pavement sections comparing the best fit method and EVERCALC©. The x-axis shows EVERCALC© RMSE from 0 to 3 percent, and the y-axis shows the best fit method RMSE from 0 to 20 percent for rigid test sections. Four types of data points are shown: North Carolina Seasonal Monitoring Program (SMP) sections, North Carolina other sections, Oklahoma Specific Pavement Studies-6 project, and Utah SMP project. A dashed line represents the line of equality. The graph shows all of the data points are above the line of equality, indicating that the results from the best fit method exhibited a higher RMSE value as compared to EVERCALC©.

Figure 4. Graph. Comparison of RMSE values between backcalculation programs for rigid pavement sections comparing best fit method and EVERCALC©.

Distribution of Elastic Moduli

The range of default elastic modulus values included in the MEPDG was used to define the initial acceptable range of elastic modulus values for comparing the results between different programs for different materials and soils.(1) The percentage of values within the acceptable range of moduli with RMSE less than 2 percent is summarized in the interim report for this project.(13) EVERCALC© exhibited a higher percentage of stations for which moduli were calculated within the typical range for the specific material in question. Backcalculated layer moduli for individual stations were outside the acceptable range of values, but the averages and majority of stations were within the range of typical values.

The distribution of resulting layer moduli for each layer during a day’s testing can be used to investigate the reasonableness of the results. Figure 5 shows the distribution of results for the crushed stone base material at the Georgia 13-1005 site, which exhibits a normal distribution. This type of distribution is typical of many pavement materials. In fact, many of the layers (bound and unbound) exhibit this type of distribution.

Figure 5. Graph. Normal distribution of calculated elastic modulus for a crushed stone base aggregate. This bar graph shows the normal distribution of calculated elastic modulus of a crushed stone base aggregate. The x-axis shows backcalculated elastic modulus values of the aggregate base with an interval of 5 ksi from 10 to 65 ksi, and the y-axis shows the number of observations from 0 to 140. The number of observations with a backcalculated elastic modulus of the aggregate base in the interval of 10 to 15 ksi is about 5, and that number continually increases to a maximum of about 119 in the interval 30 to 35 ksi. It then continually decreases to zero in the interval 60 to 65 ksi.

Figure 5. Graph. Normal distribution of calculated elastic modulus for a crushed stone base aggregate.

Conversely, figure 6 shows a bimodal distribution of results for the weathered soil layer at the Georgia 13-1005 site. A bimodal distribution can reflect a change in the results caused by changing material properties or thickness deviations along the section, compensating errors between two layers, and/or hitting a boundary condition or limit at multiple stations. Based on a review of previous backcalculated layer modulus values in the LTPP database, the results can also exhibit a uniform distribution.(4,46) However, none of the test sections included in the case studies exhibited this type of distribution.

Figure 6. Graph. Bimodal distribution of calculated elastic modulus for the weathered soil layer. This bar graph shows a bimodal distribution of alculated elastic modulus for the weathered soil layer. The x-axis shows backcalculation of weathered soil modulus with an interval of 10 ksi from 10 to 100 ksi, and the y-axis shows the number of observations from 0 to 180. The number of observations with a backcalculation of the wearthered soil modulus in the interval of 10 to 20 ksi is zero and increases sharply to a maximum number of observations of 159 in the interval 30 to 40 ksi. The number of observations then decreases to about 72 for the intervals 40 to 50 ksi and 50 to 60 ksi and then increases to about 121 in the interval 60 to 70 ksi. The number then continually decreases to 3 for the interval 90 to 100 ksi.

Figure 6. Graph. Bimodal distribution of calculated elastic modulus for the weathered soil layer.

Layer Stiffness Properties of Flexible Pavements

Figure 7 through figure 11 provide a comparison of the results from the candidate backcalculation methods in terms of elastic layer moduli for different layer or material types.

Figure 7. Graph. Comparison of backcalculated moduli from the candidate programs for the HMA layer. This graph shows a comparison of backcalculated moduli from the candidate programs for the hot mix asphalt (HMA) layer. The x-axis shows the EVERCALC© HMA surface layer modulus from 100 to 10,00 ksi, and the y-axis shows and the backcalculated HMA surface layer modulus from other programs (MODULUS and MODTAG©) from 100 to 
10,000 ksi. Two types of data are shown: MODTAG© and MODULUS. A dashed line reppresents the line of equality. The individual data points for MODTAG© and MODULUS are scattered around the line of equality suggesting good agreement in results (backcalculated elastic layer modulus for the HMA layer) between all three software programs.

Figure 7. Graph. Comparison of backcalculated moduli from the candidate programs for the HMA layer.

Figure 8. Graph. Comparison of backcalculated moduli from the candidate programs for the asphalt stabilized base layer. This graph shows a comparison of backcalculated moduli from the candidate programs for the asphalt stabilized base layer. The x-axis shows the EVERCALC© backcalculated elastic modulus for a stabilized base layer from 100 to 10,000 ksi, and the y-axis shows the backcalculated elastic modulus for the same stabilized base layer from the other programs (MODULUS and MODTAG©) from 100 to 10,000 ksi. Two types of data are shown: MODTAG© and MODULUS. A dashed line represents the line of equality. The data points are scattered around the line of equality, suggesting the backcalculated moduli for the asphalt stabilized base from MODTAG© and MDOULUS are similar to the results from EVERCALC©. Backcalcualted moduli from MODULUS exhibit more scatter around the line of equality in comparison to MODTAG©.

Figure 8. Graph. Comparison of backcalculated moduli from the candidate programs for the asphalt stabilized base layer.

Figure 9. Graph. Comparison of backcalculated moduli from the candidate programs for the weathered soil layer modulus values. This graph shows a comparison of backcalculated moduli from the candidate programs for the weathered soil layer modulus values. The x-axis shows EVERCALC© backcalculated weathered subgrade layer modulus from 10 to 100 ksi, and the y-axis sshows the backcalculated weathered subgrade layer modulus from other programs (MODULUS and MODTAG©) from 0 to 100 ksi. Two types of data are shown: MODTAG© and MODULUS. A dashed line represents the line of equality. The data points are scattered around the line of equality. MODTAG© produced higher moduli than those from EVERCALC©, while MODULUS© produced lower moduli than those from EVERCALC©. There is a significant amount of scatter between EVERCALC© and the other two programs.

Figure 9. Graph. Comparison of backcalculated moduli from the candidate programs for the weathered soil layer modulus values.

Figure 10. Graph. Comparison of backcalculated moduli from the candidate programs for the natural subgrade modulus values. This graph shows a comparison of backcalculated moduli from the candidate programs for the natural subgrade modulus values. The x-axis shows EVERCALC© natural subgrade modulus from 0 to 100 ksi, and the y-axis shows the natural subgrade modulus from the other programs (MODULUS and MODTAG©) from 0 to 100 ksi. Two types of data are shown: MODTAG© and MODULUS. A dashed line represents the line of equality. The data points are scattered around the line of equality, suggesting the backcalculated moduli for the natural subgrade from MODTAG© and MDOULUS are similar to the values from EVERCALC© except for the higher moduli. Backcalcualted moduli from MODULUS are much higher than from EVERCALC© by more than 60 ksi, while the moduli from MODTAG© are scattered around the line of equality within that same range of the higher moduli.

Figure 10. Graph. Comparison of backcalculated moduli from the candidate programs for the natural subgrade modulus values.

Figure 11. Graph. Comparison of backcalculated moduli from the candidate programs for aggregate base layers. This graph shows a comparison backcalculated moduli from the candidate programs for aggregate base layers. The x-axis shows the EVERCALC© backcalculated aggregate base modulus from 0 to 50 ksi, and the y-axis shows the backcalculated aggregate base modulus from other programs (MODULUS and MODTAG©) from 0 to 60 ksi. Two types of data are shown: MODULUS and MODTAG©. A dashed line represents the line of equality. There are many of the data points above the line of equality, suggesting that MODULUS and MODTAG© result in higher backaclalculated moduli in comparison to those from EVERCALC©.

Figure 11. Graph. Comparison of backcalculated moduli from the candidate programs for aggregate base layers.

The following list summarizes the results related to selection of the backcalculation programs for flexible pavements:

A t-test was used to determine if the average test day results from the two candidate programs with the lower RMSE values (EVERCALC© and MODCOMP©) were statistically indifferent. Table 3 provides a summary for a few of the test sections from three of the case studies. Both EVERCALC© and MODCOMP© resulted in indifferent elastic moduli for many of the test sections. About a fourth of the layers, however, resulted in statistically different datasets. The majority of the test sections with statistically different moduli were those for which the majority of the deflection basins are classified as type II.

Table 3. Comparison of datasets from selected LTPP flexible test sections.
Test Section Number of Test Days Layer Designation EVERCALC© Results MODCOMP© Results Comments
Average Elastic Modulus Standard Deviation of Elastic Modulus Average Elastic Modulus Standard Deviation of Elastic Modulus
Georgia 13-1005 29 Aggregate base 16.38 3.23 23.72 11.91 Statistically different datasets
Subgrade 62.16 2.84 60.25 3.61
Iowa 19-1001 7 Aggregate base 13.98 5.84 13.43 11.84 Statistically indifferent datasets
Subgrade 20.37 1.67 20.41 3.70
Mississippi 28-0501 7 Asphalt-treated base (ATB) 790.4 291.6 918.6 268.8 Statistically indifferent datasets
Subgrade 54.43 15.65 55.35 14.18

Layer Stiffness Properties of Rigid Pavements

The primary material properties needed for completing a rigid pavement rehabilitation design or evaluation in accordance with the MEPDG are the k-value of the lower pavement layers and subgrade, the static elastic modulus for the PCC, and the resilient modulus of aggregate base layers.(1) The area and best fit closed form solution methods were used to estimate the elastic modulus of the PCC and aggregate base layers and the k-value for the combined lower pavement layers and subgrade.

Figure 12 includes a comparison of the elastic modulus calculated with EVERCALC© and the moduli calculated using the area and best fit methods. As shown, the resulting elastic layer moduli from the EVERCALC© program and the area method are variable but have minimal bias between the two. In addition, the unbonded condition of the best fit method has less bias than its bonded condition to EVERCALC©. The bonded condition simply means the two layers are tied together, while the unbonded condition means the two layers are not tied together, and there is no shear transfer between the two layers. This brings up an issue of which method should be used in computing the elastic modulus of the PCC layer, the area or best fit method, as well as which condition should be simulated, bonded, or unbonded.

Figure 12. Graph. Backcalculated layer PCC modulus from EVERCALC© compared to the elastic modulus calculated with the area and best fit methods. This graph shows backcalculated layer portland cement concrete (PCC) modulus from EVERCALC© compared to the elastic modulus calculated with the area and best fit methods. The x-axis shows the EVERCALC© backcalculated PCC layer elastic modulus from 2,000 to 10,000 ksi, and the 
y-axis shows the forward method for calculating pCC modulus from 0 to 10,000 ksi. Three types of data are shown in the graph: the area method, the best fit bonded method, and the best fit unbonded method. A dashed line represents the line of equality. The data points for the area method are generally scattered around the line of equality, suggesting similar mouli to the EVERCALC© program. The data points for the best fit bonded and best fit unbonded methods are significantly below the line of equality, suggesting the moduli from these two methods are significantly lower than those from EVERCAL©.

Figure 12. Graph. Backcalculated layer PCC modulus from EVERCALC© compared to the elastic modulus calculated with the area and best fit methods.

The best fit method (unbonded condition) was selected for rigid pavements because it was used for global calibration for the MEPDG under NCHRP Project 1-37A.(52)

Figure 13 and figure 14 show a comparison of results for the subgrade and aggregate base layers between EVERCALC© and the best fit unbonded condition, while figure 15 shows a comparison of results for PCC layers. The best fit method resulted in significantly different or lower elastic layer moduli than EVERCALC© for PCC (figure 12 and figure 15), while the bias was much less between the computed elastic layer moduli of the base layer between the best fit method and EVERCALC© (figure 14).

Figure 13. Graph. Comparison of forward and backcalculated moduli from the candidate programs for the subgrade layer. This graph shows a comparison of forward and backcalculated moduli from the candidate programs for the subgrade layer. The x-axis shows EVERCALC© weathered subgrade layer from 0 to 100 ksi, and the y-axis shows the weathered subgrade layer from the other programs (MODTAG© and MODULUS). A dashed line represents the line of equality. The individual data points from MODTAG© and MODULUS show a lot of scatter or difference in results between the three programs. The data points from MODTAG© show some results that are significantly greater than the results from EVERCALC©, while some data points from MODULUS are significantly lower than the results from EVERCALC©.

Figure 13. Graph. Comparison of forward and backcalculated moduli from the candidate programs for the subgrade layer.

Figure 14. Graph. Comparison of forward and backcalculated moduli from the candidate programs for the aggregate base layer. This graph shows a comparison of forward and backcalculated moduli from the candidate programs for the aggregate base layer. The x-axis shows the EVERCALC© backcalculated base modulus from 10 to 10,000 ksi, and the y-axis shows the calculated base modulus from the best fit unbonded method from 10 to 100,000 ksi. Three types of data are shown: North Carolina sections, Oklahoma sections, and Utah Seasonal Monitoring Program (SMP) sites. A dashed line represents the line of equality. The data for all three locations are scattered around the line of equality but exhibit a large scatter. The data from the Utah SMP site exhibits the greatest scatter.

Figure 14. Graph. Comparison of forward and backcalculated moduli from the candidate programs for the aggregate base layer.

Figure 15. Graph. Comparison of forward and backcalculated moduli from the candidate programs for the PCC layer. This graph shows a comparison of forward and backcalculated moduli from the candidate programs for the portland cement concrete (PCC) layer. The x-axis shows the EVERCALC© backcalculated PCC modulus from 2,000 to 10,000 ksi, and the y-axis shows the calculated PCC modulus from the best fit unbonded method from 2,000 to 10,000 ksi. Three types of data are shown: North Carolina sections, Oklahoma sections, and Utah Seasonal Monitoring Program (SMP) sites. A dashed line represents the line of equality. The data from the North Carlina sections exhibit a lot of scatter around the line of equality, while the data from the Oklahoma sections and Utah SMP site are generally below the line of equality, suggesting lower moduli from the best fit unbonded method in comparison to the moduli from EVERCALC©.

Figure 15. Graph. Comparison of forward and backcalculated moduli from the candidate programs for the PCC layer.

The t-test was used to determine if the average test day results from the forward and backcalculation programs were statistically indifferent. Table 4 provides a summary for a few of the test sections from three of the case studies for rigid pavements. As shown, the forward and backcalculation methods (best fit method and EVERCALC©) resulted in significantly different PCC elastic moduli for most of the test sections, while about half of the test sections resulted in significantly indifferent elastic moduli for the base layer. This large bias between EVERCALC© and the best fit method can have a critical impact in determining the PCC elastic modulus for input into the MEPDG.(1) This issue of bias is discussed further in the next section.

Table 4. Comparison of datasets from selected LTPP rigid test sections.
Test Section Number of Test Days Layer Designation EVERCALC© Results MODCOMP© Results Comments
Average Elastic Modulus Standard Deviation of Elastic Modulus Average Elastic Modulus Standard Deviation of Elastic Modulus
North Carolina 37-0201 48 PCC 5,795.5 601.3 3,125.5 1,601.8 Statistically different datasets
Aggregate base 46.8 27.4 20.8 10.7
Utah 49-3011 37 PCC 6,584.7 1,167.0 2021.2 570.6 Statistically different datasets
Stabilized base 665.6 718.9 570.6 114.1 Statistically indifferent datasets
Oklahoma 40-0601 7 PCC 4,749.9 418.2 2,461.5 1,099.3 Statistically different datasets
Aggregate base 12.5 4.9 16.4 7.3 Statistically indifferent datasets

Field-Derived and Laboratory-Measured Layer Stiffness Properties

PCC Materials

Static elastic moduli for the PCC layers were extracted from the LTPP database. Figure 16 compares the laboratory-measured elastic moduli and backcalculated values for the PCC layers. As shown, the results from EVERCALC© and the best fit method are highly variable in comparison to the measured PCC static modulus. The average elastic modulus ratio (i.e., E-ratio between the laboratory-measured and field-derived elastic moduli) for the PCC layer are as follows:

Results from the EVERCALC© program exhibited a coefficient of variation of 23 percent for the averages, which is much lower than the best fit method, which had a coefficient of variation of 65 percent for the bonded condition and 44 percent for the unbonded condition.

Figure 16. Graph. Comparison of backcalculated and laboratory-measured PCC moduli. This graph shows a comparison of backcalculated and laboratory-measured portland cement concrete (PCC) moduli. The x-axis shows the laboratory-measured PCC elastic modulus from 2,000 to 8,000 ksi, and the y-axis shows the calculated PCC layer elastic modulus from deflection basins from 0 to 10,000 ksi. Three types of data are shown: EVERCALC© results, best fit results, and best fit unbonded results. A dashed line represents the line of equality. The data from EVERCALC© are consistently above the line of equality or have moduli that are higher than the laboratory-measured PCC elastic moduli, while the data from the best fit results and best fit unbounded methods are consistently below the line of equality have or moduli that are lower than the laboratory-measured PCC elastic moduli.

Figure 16. Graph. Comparison of backcalculated and laboratory-measured PCC moduli.2

The best fit bonded condition significantly underpredicted the measured values, while EVERCALC© overpredicted the measured values. On average, the best fit unbonded condition resulted in no bias.

In summary, there is a significant difference between the resulting PCC elastic moduli from EVERCALC© and the best fit method. The best fit unbonded condition resulted in an unbiased prediction of the laboratory-measured values. Assuming laboratory elastic moduli are used in the global or local calibration effort, an adjustment needs to be made to the EVERCALC© dataset for use with the MEPDG software, similar to using the c-factor for unbound layers.(45,46,1)

HMA and Bituminous Stabilized Materials

Backcalculated elastic layered moduli from deflection basins are used in the MEPDG for the rehabilitation and evaluation of flexible pavements.(1) Dynamic modulus values are estimated using the Witczak regression equation included in the MEPDG to represent the undamaged condition of HMA mixtures. These same values were calculated using the dynamic modulus regression equation from the MEPDG and included in the LTPP databases for the HMA and other bituminous layers.(1)

Dynamic moduli for the HMA layers were extracted from the LTPP database. Figure 17 through figure 26 compare the laboratory estimated dynamic moduli and backcalculated values for the HMA layers. As shown, most of the backcalculation programs underpredict the laboratory-measured values for the loading frequency typically used for the FWD (25 Hz). All three backcalculation programs resulted in similar average values on a day of testing basis for many of the test sections, but not all.

Figure 17. Graph. Comparison of backcalculated HMA surface and binder layer moduli and laboratory-measured moduli from the Iowa SPS-1 project. This graph shows a comparison of backcalculated hot mix asphalt (HMA) surface and binder layer moduli and laboratory-measured moduli from the Iowa Specific Pavement Studies (SPS)-1 project. The x-axis shows test temperature from 0 to 150 ºF, and the y-axis shows modulus of HMA surface and binder from 100 to 10,000 ksi. Three types of data are shown: Iowa EVERCALC©, Iowa MODULUS, and Iowa MODTAG©. Two lines are shown: a solid line represents the dynamic modulus surface mix versus temperature, and a dashed line represents the dynamic modulus binder mix versus temperature. The solid and dashed lines for the dynamic modulus of the surface and binder mixtures, respectively, show the moduli decreasing from the lower to higher test temperatures. The data for the Iowa EVEVRCAL©, Iowa MODULUS, and Iowa MODTAG© are below the solid and dashed lines of dynamic modulus versus temperature relationships.

Figure 17. Graph. Comparison of backcalculated HMA surface and binder layer moduli and laboratory-measured moduli from the Iowa SPS-1 project.

Figure 18. Graph. Comparison of backcalculated HMA base moduli and laboratory-measured moduli from the Iowa SPS-1 project. This graph shows a comparison of backcalculated hot mix asphalt (HMA) base moduli and laboratory-measured moduli from the Iowa Specific Pavement Studies (SPS)-1 project. The x-axis shows test temperature from 0 to 150 ºF, and the y-axis shows modulus of HMA base from 10 to 10,000 ksi. Three types of data are shown: Iowa EVERCALC©, Iowa MODULUS, and Iowa MODTAG©. A solid line represents the dynamic modulus HMA base. The solid line shows the moduli decreasing from the lower to higher test temperatures. The data for the Iowa EVERCAL, Iowa MODULUS, and Iowa MODTAG© backcalculated moduli are below the solid line of dynamic modulus HMA base.

Figure 18. Graph. Comparison of backcalculated HMA base layer moduli and laboratory-measured moduli from the Iowa SPS-1 project.

Figure 19. Graph. Comparison of backcalculated HMA surface and binder layer moduli and laboratory-measured moduli from the Wisconsin SPS-1 project. This graph shows a comparison of backcalculated hot mix asphalt (HMA) surface and binder moduli and laboratory-measured moduli from the Wisconsin Specific Pavement Studies (SPS)-1 project. The x-axis shows test temperature from 0 to 150 ºF, and the y-axis shows the modulus of HMA surface and binder from 10 to 10,000 ksi. Three types of data are shown: Wisconsin EVERCALC©, Wisconsin MODULUS, and Wisconsin MODTAG©. A solid line represents the dynamic modulus of HMA. The solid line shows the moduli decreasing from lower to higher test temperatures. The data for the Wisconsin EVERCAL©, Wisconsin MODULUS, and Wisconsin MODTAG© are slightly below the solid line.

Figure 19. Graph. Comparison of backcalculated HMA surface and binder layer moduli and laboratory-measured moduli from the Wisconsin SPS-1 project.

Figure 20. Graph. Comparison of backcalculated HMA base layer moduli and laboratory-measured moduli from the Wisconsin SPS-1 project. This graph shows a comparison of backcalculated hot mix asphalt (HMA) base layer moduli and laboratory-measured moduli from the Wisconsin Specific Pavement Studies (SPS)-1 project. The x-axis shows test temperature from 0 to 150 ºF, and the y-axis shows modulus of HMA base from 100 to 10,000 ksi. Three types of data are shown: Wisconsin EVERCALC©, Wisconsin MODULUS, and Wisconsin MODTAG©. A solid line represents the dynamic modulus HMA base. The solid line shows the moduli decreasing from lower to higher test temperatures. The data for the Wisconsin EVERCAL, Wisconsin MODULUS, and Wisconsin MODTAG© are along and above 
the solid line.

Figure 20. Graph. Comparison of backcalculated HMA base layer moduli and laboratory-measured moduli from the Wisconsin SPS-1 project.

Figure 21. Graph. Comparison of backcalculated HMA overlay moduli and laboratory-measured moduli from the Mississippi SPS-5 project. This graph shows a comparison of backcalculated hot mix asphalt (HMA) overlay moduli and laboratory-measured moduli from the Mississippi Specific Pavement Studies (SPS)-5 project. The x-axis shows test temperature from 0 to 150 ºF, and the y-axis shows modulus the HMA overlay from 100 to 10,000 ksi. Three types of data are shown: Mississippi EVERCALC©, Mississippi MODULUS, and Mississippi MODTAG©. A solid line represents the dynamic modulus of HMA overlay. The solid line shows the modulus of the HMA overlay decreasing from lower to higher test temperatures. The data for the Mississippi EVERCALC©, Mississippi MODULUS, and Mississippi MODTAG© are along and below the solid line of dynamic modulus. At colder test temperatures, the data are closer to the solid line, but for warmer test temperatures, the data are further below the solid line.

Figure 21. Graph. Comparison of backcalculated HMA overlay moduli and laboratory-measured moduli from the Mississippi SPS-5 project.

Figure 22. Graph. Comparison of backcalculated HMA surface layer moduli of the existing pavement after overlay placement and laboratory-measured moduli from the Mississippi SPS-5 project. This graph shows a comparison of backcalculated hot mix asphalt (HMA) surface layer moduli of the existing pavement after overlay placement and laboratory-measured moduli from the Mississippi Specific Pavement Studies (SPS)-5 project. The x-axis shows test temperature from 0 to 150 ºF, and the y-axis shows modulus HMA existing surface after overlay from 10 to 10,000 ksi. Three types of data are shown: Mississippi EVERCALC©, Mississippi MODULUS, and Mississippi MODTAG©. A solid line represents the dynamic modulus of the existing HMA surface and base. The solid line shows the modulus of the existing HMA surface after overlay decreasing from lower to higher test temperatures. The data for the Mississippi EVERCALC©, Mississippi MODULUS, and Mississippi MODTAG© are slightly to significantly below the solid line except for two data points from Mississippi EVERCALC© that are above it.

Figure 22. Graph. Comparison of backcalculated HMA surface layer moduli of the existing pavement after overlay placement and laboratory-measured moduli from the Mississippi SPS-5 project.

Figure 23. Graph. Comparison of backcalculated HMA moduli of the existing pavement prior to overlay placement and laboratory-measured moduli from the Mississippi SPS-5 project. This graph shows a comparison of backcalculated hot mix asphalt (HMA) moduli of the existing pavement prior to overlay placement and laboratory-measured moduli from the Mississippi Specific Pavement Studies (SPS)-5 project. The x-axis shows test temperature from 0 to 150 ºF, and the y-axis shows modulus HMA existing surface from 100 to 10,000 ksi. Three types of data are shown: Mississippi EVERCALC©, Mississippi MODULUS, and Mississippi MODTAG©. A solid line represents the dynamic modulus HMA existing surface. The solid line shows the modulus of the HMA existing surface decreasing from lower to higher test temperatures. The data for the Mississippi EVERCALC©, Mississippi MODULUS, and Mississippi MODTAG© are scattered along the solid line except for Mississippi MODTAG©, where three data points are significantly below the solid line.

Figure 23. Graph. Comparison of backcalculated HMA surface layer moduli of the existing pavement prior to overlay placement and laboratory-measured moduli from the Mississippi SPS-5 project.

Figure 24. Graph. Comparison of backcalculated existing HMA base layer moduli of the existing pavement prior to overlay placement and laboratory-measured moduli from the Mississippi SPS-5 project. This graph shows a comparison of backcalculated existing hot mix asphalt (HMA) base layer moduli of the existing pavement prior to overlay placement and laboratory-measured moduli from the Mississippi Specific Pavement Studies (SPS)-5 project. The x-axis shows test temperature from 0 to 150 ºF, and the y-axis shows modulus of existing HMA base from 100 to 10,000 ksi. Three types of data are shown: Mississippi EVERCALC©, Mississippi MODULUS, and Mississippi MODTAG©. A solid line represents the dynamic modulus existing HMA base. The solid line shows the modulus of the existing HMA base decreasing from lower to higher test temperatures. The data for the Mississippi EVERCALC©, Mississippi MODULUS, and Mississippi MODTAG© are significantly below the solid line.

Figure 24. Graph. Comparison of backcalculated HMA base layer moduli of the existing pavement prior to overlay placement and laboratory-measured moduli from the Mississippi SPS-5 project.

Figure 25. Graph. Comparison of backcalculated HMA moduli and laboratory-estimated dynamic modulus for the Oklahoma SPS-6 project. This graph shows a comparison of backcalculated hot mix asphalt (HMA) moduli and laboratory-estimated dynamic modulus for the Oklahoma Specific Pavement Studies (SPS)-6 project. The x-axis shows test temperature from 0 to 140 ºF, and the y-axis shows the modulus of HMA overlay from 100 to 10,000 ksi. One type of data are shown: Oklahoma EVERCALC© HMA overlay. A solid line represents the dynamic modulus HMA overlay. The data are scattered along the solid line for the mid-test temperature range of 80 to 100 ºF, while the data are below the solid line within 30 and 80 ºF and above the solid line within 100 and 120 ºF.

Figure 25. Graph. Comparison of backcalculated HMA moduli and laboratory-estimated dynamic modulus for the Oklahoma SPS-6 project.

Figure 26. Graph. Comparison of backcalculated HMA surface moduli and laboratory-estimated dynamic modulus for the Georgia SMP project. This graph shows a comparison of backcalculated hot mix asphalt (HMA) surface moduli and laboratory-estimated dynamic modulus for the Georgia Seasonal Monitoring Program (SMP) project. The x-axis shows the test temperature from 0 to 150 ºF, and the y-axis shows the modulus of HMA surface from 100 to 10,000 ksi. Three types of data are shown: Georgia EVERCALC©, Georgia MODULUS, and Georgia MODTAG©. A solid line represents the dyanic modulus HMA, and it decreases from lower to higher test temperatures. All three types of data are slighly below the solid line.

Figure 26. Graph. Comparison of backcalculated HMA moduli and laboratory-estimated dynamic modulus for the Georgia SMP project.

In summary, there is an insignificant difference between the resulting HMA elastic moduli from EVERCALC©, MODULUS, and MODCOMP©, but none of the programs resulted in unbiased predictions of the laboratory-measured values. This observation is important because it supports the MEPDG methodology for using FWD testing and backcalculated layer moduli of HMA layers for estimating the damage in those layers.(1) The sites that exhibited greater dispersion between the laboratory-estimated (undamaged dynamic moduli) and field-derived (damaged elastic moduli) moduli were found to have stripping or moisture damage and/or extensive cracking reported in the LTPP database.

Unbound Materials

Figure 27 through figure 29 compare the backcalculated elastic moduli from EVERCALC©, MODULUS, and MODCOMP©, respectively, and the laboratory-derived resilient moduli for each site for the weathered soil and subgrade layers. As shown, there is a lot of dispersion between the results, but the results are somewhat consistent with some of the earlier studies.(45,46) The average c-factors calculated for the subgrade layers using the three candidate programs are as follows:

Results from EVERCALC© exhibited a coefficient of variation of 39 percent for the averages, which were about equal to the results from MODCOMP© with a coefficient of 40 percent but much lower than the results from MODULUS, which had a coefficient of variation of 65 percent.

Figure 27. Graph. Comparison of backcalculated moduli of unbound layers using EVERCALC© and laboratory-derived resilient modulus. This graph shows a comparison of backcalcuated moduli of unbound layers using EVERCALC© and laboratory-derived resilient modulus. The x-axis shows resilient modulus of the soil from 0 to 20 ksi, and the y-axis shows EVERCALC© backcalculated modulus from 0 to 70 ksi. Two types of data are shown: natural subgrade layer without rigid layer and weathered subgrade layer without rigid layer. A dashed line represents the line of equality. All data are significantly above the line of equality.

Figure 27. Graph. Comparison of backcalculated elastic moduli of unbound layers using EVERCALC© and laboratory-derived resilient modulus.

Figure 28. Graph. Comparison of backcalculated elastic moduli of unbound layers using MODULUS and laboratory-derived resilient modulus. This graph shows a comparison of backcalcuated elastic moduli of unbound layers using MODULUS and laboratory-derived resilient modulus. The x-axis shows resilient modulus from 0 to 20 ksi, and the y-axis shows the MODULUS backcalculated modulus from 0 to 90 ksi. Two types of data are shown: natural subgrade layer without rigid layer and weathered soil layer without rigid layer. A dashed line represents the line of equality. The data for the natural subgrade layer without a rigid layer are significantly above the line of equality, while the data for the weathered soil layer without a rigid layer are scattered along and above the line of equality.

Figure 28. Graph. Comparison of backcalculated elastic moduli of unbound layers using MODULUS and laboratory-derived resilient modulus.

Figure 29. Graph. Comparison of backcalculated elastic moduli of unbound layers using MODTAG© and laboratory-derived resilient modulus. This the graph shows a comparison of backcalcuated elastic moduli of unbound layers using MODTAG© and laboratory-derived resilient modulus. The x-axis shows resilient modulus of soil from 0 to 20 ksi, and the y-axis shows the MODTAG© backcalculated modulus from 0 to 70 ksi. Two types of data are shown: natural subgrade without rigid layer and weathered soil layer without rigid layer. A dashed line represents the line of equality. All data are significantly above the line of equality.

Figure 29. Graph. Comparison of backcalculated elastic moduli of unbound layers using MODTAG© and laboratory-derived resilient modulus.

CASE STUDY Summary

Candidate programs were used to estimate elastic layer modulus values for the same deflection basins. Observations from the case studies were the same as those documented in the Smith study.(53) EVERCALC© consistently resulted in lower error terms and a higher number of successful modulus determination when considering all deflection basins. When only considering those deflection basins that ran successfully, the MODCOMP© program resulted in the lower RMSE values.

The results from the case studies suggest the use of multiple software packages for various pavement types. Thus, two software packages and one method were selected for use in the production runs for flexible and rigid pavements: EVERCALC© and MODCOMP© for flexible pavements and those two plus the best fit method for rigid pavements. EVERCALC© was selected as the primary package, while MODCOMP© was used to confirm discrepancies or anomalies identified by EVERCALC©. Another reason for selecting MODCOMP© is that EVERCALC© is restricted to five layers, including a rigid layer if present, while MODCOMP© can simulate up to seven layers.


1 MODTAG© includes various data subroutines for evaluating the deflection basin data and uses MODCOMP© for the backcalculation process. MODTAG© was used in the comparison of the programs within the first phase of the project. However, MODCOMP6© was used for the production or batch runs under the second phase of the project.

2 Some of the PCC elastic modulus values from the best fit unbonded condition exceeded 10 million psi, and these are not shown in the figure. These high elastic moduli resulted in a much higher standard deviation than for the EVERCALC© method.

 

 

 

Federal Highway Administration | 1200 New Jersey Avenue, SE | Washington, DC 20590 | 202-366-4000
Turner-Fairbank Highway Research Center | 6300 Georgetown Pike | McLean, VA | 22101