Using Falling Weight Deflectometer Data With Mechanistic-Empirical Design and Analysis, Volume II: Case Study Reports

CHAPTER 2.

CASE STUDY 2: FLEXIBLE PAVEMENT INCLUDING RUBBLIZED CONCRETE PAVEMENT EVALUATION AND OVERLAY DESIGN

PROJECT OVERVIEW

Project 17-0600, located on I-57 near Pesotum, IL, consisted of 14 test sections. Test section 17‑0600 was selected as an HMA surface on a rubblized portland cement concrete (RPCC) layer rehabilitation case study. The original underlying pavement was jointed reinforced concrete pavement (JRCP) with an aggregate base layer. The JRCP was rubblized, and a HMA overlay was placed in 1990. This section is representative of the following selection factors:

The underlying concrete pavement was originally constructed in 1964 (construction number 1), with rehabilitation/repair work performed in 1990 and 1997 (construction numbers 2–4, respectively). Based on LTPP Program core data, the average original pavement cross section consisted of 10 inches (254 mm) of portland cement concrete (PCC) (JRCP) and 7inches (178mm) of aggregate base. The HMA overlay placed in 1990 consisted of a 1.5‑inches (38-mm) HMA surface and a 6.5-inches (165-mm) HMA binder course.

PAVEMENT CONDITION/PERFORMANCE

Pavement condition and performance data can be used to customize (or calibrate) the performance models within the MEPDG software for the specific State using the design procedure.⁽¹⁾ However, the calibration of performance models was beyond the scope of this study. The design inputs after performance model calibration used relatively little distress data, and the design of HMA over RPCC did not use any pavement distress data.

TEST SECTION DATA

The MEPDG design program requires a significant number of inputs, particularly for level 1 analysis. The required design data for the 17-0600 project section were obtained from the LTPP Program’s DataPave database. The required data were not generally complete for any one specific test section within 17-0663; therefore, results for the entire project, and during multiple years, were used to obtain the necessary design inputs. Although the test sections had varying cross sections and maintenance histories, the research team concluded that overall data were sufficient for this study.

Deflection-Testing Data

Deflection data for test section 17-0663 were available from the LTPP Program database for several years of testing, including 1990–1993, 1995, 1997–1998, and 2004. To compare backcalculation results at the time of rehabilitation, deflection data from 1990 were retrieved from the LTPP Program database. Deflection testing was conducted following the LTPP Program protocols.

Equipment

Deflection testing was conducted with two FWD devices. For the 1990–1993, 1995, and 1997–1998 data, a Dynatest® FWD (SN 8002-060) was used; for 2004, a different Dynatest® FWD (SN 8002-130) was used.

Sensor Configuration

Sensors were located at 0, 8, 12, 18, 24, 36, and 60 inches (0, 203.2, 304.8, 457.2, 609.6, 914.4, 1,524 mm) from the center of the load plate for 1990–1993, 1995, 1997–1998 datasets and at 0, 8, 12, 18, 24, 36, 48, 60, and -12inches (0, 203.2, 304.8, 457.2, 609.6, 914.4, 1,219.2, 1,524, -304.8 mm) from the center of the load plate for data collected in 2004.

Number of Drops and Load Levels

Four load level targets—6,000, 9,000, 12,000, and 16,000 lb (2,724, 4,086, 5,448, and 7,264 kg) with four drops at each load level were performed, and data were recorded. Seating drops were also performed, but data were not recorded.

Test Locations/Lanes and Increments

In 1990, immediately before rubblization (construction number 2), FWD testing was conducted on the JRCP at the mid-lane at mid-panel and in the outer wheelpath at both approach and leave joints (for load transfer). For the year after overlay construction (CN 3), FWD testing was conducted in the outer wheelpath and mid-lane of the flexible pavement at 50-ft (15.25-m) intervals along the length of the project.

Temperature Measurements

Temperature measurements were taken using drilled holes in the pavement at depths 1, 2.2, and 3.3 inches (25.4, 55.88, and 83.82 mm) at prescribed time intervals during deflection testing.

Material Properties Data

This section summarizes the data obtained from LTPP database for test section 17-0600 regarding its subgrade, base, HMA and PCC material properties, traffic, climate, and depth of water table or stiff layer.

Subgrade

Six subgrade samples were retrieved from the 17-0600 project location as part of the LTPP Program. However, the soil classification data were only available for five of the samples. The subgrade soil was generally classified as A-6 under the AASHTO soil classification system: three of the subgrade samples were classified as AASHTO A-6, while the other two were classified as AASHTOA‑4.⁽²⁾

Laboratory resilient modulus testing results were available for only one sample of the subgrade materials obtained as part of the LTPP Program data collection. Laboratory resilient modulus testing results for the subgrade sample (BAX04) are illustrated in figure 23. Additional subgrade properties, including Atterberg limits and sieve analysis, are summarized in table 21 and table 22, respectively. Average moisture content was 11.6 percent.

1 psi = 6.89 kPa.
Figure 23. Graph. Summary of LTPP Program laboratory-measured subgrade resilient modulus.

Table 22. Summary of subgrade sieve analysis.

Base Aggregate

Seven coarse aggregate samples were obtained as part of the LTPP Program data collection, and the materials were classified as uncrushed gravel. Laboratory resilient modulus testing results were available for two samples of coarse aggregate materials in the Project 17-0600 sections and are illustrated in figure 24. Additional aggregate properties are summarized in table 23 and table 24.

1 psi = 6.89 kPa.
Figure 24. Graph. Summary of LTPP Program laboratory-measured base aggregate resilient modulus.

Table 23. Summary of base aggregate Atterberg limits.

Table 24. Summary of base aggregate sieve analysis.

PCC Layer

The LTPP Program database contained laboratory compressive strength testing results for 13PCC surface samples from the 17-0600 project section. The compressive strength testing results of cores are summarized in figure 25. Eight of the PCC samples were noted to contain steel reinforcement. The overall average compressive strength was 5,490 psi (37,850 kPa); the average compressive strength of the samples without reinforcement was 4,690psi (32,340 kPa). Average tensile strength testing results were 725 psi (5,000 kPa).

1 psi = 6.89 kPa.
1 lb = 0.454 kg.
Figure 25. Graph. Summary of LTPP Program laboratory-measured compressive strength.

In 1990, the PCC layer was rubblized with a self-propelled resonant frequency breaker. The resulting particle size was noted to range from sand to 152 mm (6 inches) maximum.

HMA Layer

The HMA overlay placed in 1990 consisted of a 6.5-inch (165-mm) binder course and a 1.5-inch (38-mm) surface course. Laboratory testing was conducted for both layers. The resilient modulus testing for each layer is summarized in figure 26. The instantaneous resilient modulus for both layers at 70 °F (21 °C) was approximately 1.1 million psi (7,584,233 kPa). Additional HMA properties for design for the binder course are summarized in table 25 and table 26. It was assumed that the surface layer would be mostly milled off during rehabilitation, so the binder layer properties were more influential.

1 psi = 6.89 kPa.
°F = 1.8 × °C + 32.
Figure 26. Graph. Summary of HMA resilient modulus data from LTPP Program.

Table 25. Summary of existing HMA binder material properties.

Table 26. Summary of existing HMA binder aggregate sieve analysis.

Depth to Rigid Layer/Water Table

The depth to the water table is also required for the MEPDG. However, no data were found for Project 17-0600. In fact, no water table depth data had been reported for the State of Illinois. An average value of 10 ft (3.05 m), considering the mean depth of the water table in a neighboring State, Iowa, was assumed for use in the MEPDG.

Climate/Environment Data

Climate data were obtained from the updated climate files on the MEPDG Web site.⁽⁵⁾ The weather station at Champaign, IL, was used for this study. The general climatic category for the case study location is wet-freeze.

Traffic Data

Traffic data were available from the LTPP Program database. Because evaluating the effect of traffic data on design results was not a primary goal of this study, only basic information was used from the available data (total volume, growth, and vehicle class distribution), with the remaining inputs (such as monthly distribution, hourly distribution, and wheel spacing) kept at their default values in the MEPDG software. An AADTT volume of 5,400 vehicles per day was estimated.

ANALYSIS AND INTERPRETATION OF FWD TESTING DATA

This section presents the data checks and backcalculation analysis of the FWD data, as well as a comparison of the backcalculation results with laboratory testing.

Preprocessing Deflection Data

FWD deflection data were checked for linearity. Figure 27 compares the load versus sensor deflection for a single location before rubblization and after rubblization. The measurements show higher deflections and a slightly more irregular pattern after rubblization. The data were deemed to be acceptable for linear analysis.

The shape of the deflection basins before and after rubblization was also checked. Figure 28 shows typical deflection basins before and after rubblization. The shape of the deflection basin after rubblization is more irregular. This was due to the variability of the rubblized material created during the rubblization process. The irregular shape of the deflection basin after rubblization led to significantly higher RMS values.

Figure 29 illustrates the normalized (9,000-lb (4,086-kg)) deflections along the section for data just before rubblization and shortly after placement of the HMA overlay. As the figure illustrates, the deflections were greater after rubblization, and there was an increase in deflections at the beginning of the section. The data point after rubblization at approximately 300 ft (91 m) had lower normalized deflections than the adjacent points. This may be because of variability in the rubblization process, or it could be variability in one of the other pavement layers.

1 lb = 0.454 kg.
1 mil = 0.0254 mm.
Figure 27. Graphs. Comparison of sample plots for FWD load versus sensor deflection before (top) and after (bottom) rubblization.

1 mil = 0.0254 mm.
1 inch = 25.4 mm.
Figure 28. Graphs. Comparison of typical deflection basins before (top) and after (bottom) rubblization.

1 mil = 0.0254 mm.
1 ft = 0.305 m.
Figure 29. Graph. Normalized deflections along section.

Backcalculation Analysis

The backcalculation of the rubblized cross section was conducted using layered elastic methods. This is because the rubblized PCC no longer acted as a plate and was assumed to behave similar to a granular layer. Three backcalculation programs were used for this backcalculation analysis: (1)MODCOMP©, (2) MICHBACK©, and (3) EVERCALC© to look into the effect of different inverse routines on backcalculated parameters and ultimately on rehabilitation design. In addition, the following layer combinations were used during the backcalculation analysis to determine the most realistic design inputs for the MEPDG software:

• Case I: Four-layer system with HMA, RPCC layer, base, and infinite subgrade.

• Case II: Four-layer system with HMA, combined RPCC layer and base, top 2 ft (0.6 m) of compacted subgrade, and infinite subgrade.

• Case III: Three-layer system with HMA, combined RPCC layer and base, and infinite subgrade.

The seed, minimum, and maximum values for layer moduli for the three- and four-layer backcalculation analyses are shown in table 27 and table 28, respectively.

The backcalculation was performed for each FWD test location for the available test data most closely following rubblization (1990). This allowed for investigation of the effect of construction variability on backcalculation results. The average layer thicknesses shown in table 27 were used in the analysis.

Backcalculation Results

For case I, MODCOMP© results gave unrealistically low granular base layer moduli (average of 11,376 KPa (1,650 psi)). Therefore, MODCOMP© was not used for this case. Figure 30 illustrates the backcalculation results from MICHBACK© and EVERCALC© for the various stations and load levels using a four-layer combination, with separate RPCC and base layers, as described in case I. The results show high variability, especially in the modulus of the rubblized and base layers. A number of locations had a higher modulus for the aggregate base than the rubblized layer. Other locations had base or rubblized layer moduli that reached their maximum limit. The backcalculation results for all these locations had to be excluded from further analysis. The RMS values from MICHBACK© were much higher than those from EVERCALC©.

Figure 31 shows the backcalculation results from all three programs for the various stations and load levels using a four-layer combination, with combined RPCC and base layer, as described in case II. The results again showed very high variability, especially in the modulus of the top 2 ft (0.6 m) of compacted subgrade. On the other hand, the HMA layer moduli were fairly consistent, and the modulus of the combined RPCC and base layer was higher than that of the subgrade layer, which was a desired outcome. Locations that had a higher modulus for the subgrade than the combined aggregate base and rubblized layer were excluded from further analysis. The RMS values from MICHBACK© were the highest, followed by MODCOMP©, and then EVERCALC©.

1 psi = 6.89 kPa.
Figure 30. Graphs. Comparison of MICHBACK© and EVERCALC© backcalculation
results for four-layer system with separate rubblized layer (case I).

1 psi = 6.89 kPa.
Figure 31. Graphs. Comparison of MICHBACK©, EVERCALC©, and MODCOMP© backcalculation
for four-layer system with combined base and rubblized layer (case II).

For case III, only EVERCALC© was used because it gave the lowest RMS values overall, and the backcalculated layer moduli from the different programs were reasonably close to each other.

Figure 32 and figure 33 show the backcalculation results from EVERCALC© for a three-layer system, with combined RPCC and base layer and an infinite subgrade (case III). The results were less variable than those from a four-layer analysis. The most variable layer, nonetheless, was the combined RPCC and base layer. The great majority of the RMS values were below 2 percent.

1 psi = 6.89 kPa.
Figure 32. Graph. EVERCALC© backcalculated layer moduli for three-layer system with combined base and rubblized layer (case III).

Figure 33. Graph. EVERCALC© RMS values for three-layer system with combined base and rubblized layer (case III).

Table 29 through table 31 show the summary statistics of backcalculation results for cases I, II, and III, respectively. Figure 34 through figure 36 show the average backcalculated modulus values for cases I, II, and III, respectively. Overall, the different programs provided comparable backcalculated modulus values when looking at the overall results. Therefore, the research team concluded that using average or median values would provide reasonable input values for design purposes.

The properties of the intact PCC were also backcalculated using early 1990 data. The AREA method was used to determine the PCC elastic modulus to assess the pre- and post-rubblization properties. Details of this analysis were not included here because rigid pavement backcalculation is discussed in the case studies described in chapters 3 and 4, and backcalculation of intact PCC elastic modulus is only intended for a general comparison of modulus results before and after rubblization. The determined average backcalculated PCC elastic modulus was 6,130,000psi (42,264,862 kPa).

Table 29. Summary statistics of backcalculation results for four-layer system with separate rubblized layer (case I) (modulus, psi).

Table 30. Summary statistics of backcalculation results for four-layer system with combined base and rubblized layer (case II) (modulus, psi).

Table 31. Summary statistics of backcalculation results for three-layer system with combined base and rubblized layer (case III) (modulus, psi).

1 psi = 6.89 kPa.
Figure 34. Graph. Summary of average backcalculated moduli for four-layer system with separate rubblized layer (case I).

1 psi = 6.89 kPa.
Figure 35. Graph. Summary of average backcalculated moduli for four-layer system with combined base and rubblized layer (case II).

1 psi = 6.89 kPa.
Figure 36. Graph. Summary of average backcalculated moduli for three-layer system with combined base and rubblized layer (case III).

Backcalculation Modeling Issues and Recommendations

As previously described, the backcalculation results for a rubblized pavement were generally more variable than those of a conventional pavement. The RMS values obtained from MICHBACK© were unacceptably high, while those from EVERCALC© were generally acceptable (below 2percent). However, the backcalculated layer moduli from the different programs agreed reasonably well when averaged across the FWD test locations within the project. Some locations did give unreasonable backcalculation results, and such results should be excluded from the analysis.

The base and rubblized layer moduli exhibited the greatest variability. Combining the base and rubblized layers into a single layer reduced the possibility of erroneous backcalculation results (e.g., a higher base modulus than rubblized layer modulus) and decreased variability in the results. In case II, the 2 ft (0.6 m) of compacted top subgrade had a lower moduli than the natural subgrade; this can be explained by the fact the natural subgrade modulus represents the effective modulus for a halfspace. This value is generally higher because the modulus increases with depth. This increase is due to (1) higher confinement for sandy soils and (2) consolidation for clayey soils. Also, the modulus of the top 2 ft (0.6 m) compacted subgrade has greater variability, which could be attributable to construction variability.

Comparison of Backcalculation and Laboratory Testing Results

To assist in evaluating which layer characteristics would be appropriate to use in the MEPDG software, the results of the backcalculation (field tests) were compared with results obtained from laboratory testing conducted as part of the LTPP Program. While it was outside of the scope of this study to develop new correlations or conversion factors between the two, it was still beneficial to evaluate these relationships and see how they may influence MEPDG input selection.

Unbound Materials

The difference in stress state is often a general argument when comparing field to laboratory results of unbound materials. To compare field (FWD) obtained results with those obtained from laboratory testing (or vice versa), the resilient modulus was estimated for the stress conditions during FWD testing. The stress conditions account for the overburden pressure of the pavement and the stress due to loading. However, it is recommended (and discussed later) to combine the rubblized layer with the base layer, so this issue becomes less important in this case study.

PCC/Rubblized Layer

The different laboratory results for the intact PCC provided substantially different elastic modulus correlations. Based on compressive strength testing, a PCC modulus of 4 million psi (27,579,000 kPa) was estimated; however, a PCC modulus of 8.5 millionpsi (58,605,436 kPa) was estimated based on tensile strength testing. The backcalculated average PCC modulus was 6,130,000 psi (42,264,862 kPa), which was approximately 4.9 million psi (33,784,300 kPa) when applying the recommended dynamic-to-static correction factor of0.8.

For the case I backcalculation (RPCC as an individual layer), the RPCC modulus values ranged from 104,000 to 119,000 psi (717,054 to 820,476 kPa). These values were approximately 2percent of the backcalculated intact static modulus, and were lower than the level 3 recommendation (150,000 psi (1,034,213 kPa)) provided in the MEPDG. When the RPCC was combined with the unbound base, the moduli were even lower. The MEPDG also provides level1 recommendations, which are based on anticipated variability in the fracture process. The fractured slab moduli included in the level 1 discussion were much greater than those backcalculated for the rubblized layer in case study 2.

HMA Layer

Laboratory results for HMA layer modulus for several temperatures are shown in figure 26. Temperature at the time of FWD testing was about 14 °C (58 °F) based on borehole temperature data. Based on the data summarized in figure 26, a corresponding thickness-weighted equivalent laboratory HMA modulus of about 1.6 million psi (11,031,611 kPa) was obtained, compared with average backcalculated moduli ranging from about 1,680,000 to 1,920,000 psi (11,583,192to 13,237,933 kPa), depending on selected layer model and backcalculation program. This translated to a laboratory-to-field (backcalculated) modulus ratio of about 0.83 to0.95.

REHABILITATION DESIGN RESULTS

An HMA overlay rehabilitation design was analyzed for this case study to assess design differences between backcalculated inputs and laboratory-based inputs. The overall design level for this rehabilitation (HMA over JCPC (fractured)) was level 3. The HMA layer design levels can range from 1 through 3, whereas the RPCC design level cannot be changed and the unbound layers can be level 2 or 3 inputs.

Design Criteria and General Inputs

The MEPDG calls for determining the HMA overlay thickness by trial and error. A trial thickness was assumed, and the program was executed to predict the different performance measures (i.e., cracking, rutting, and IRI). For a given desired rehabilitation design life (20years), the level of distress at the design life should not exceed a prescribed limiting value, which is summarized in table 32 for case study 2. A reliability level of 90 percent was selected because it corresponded to the average (expected) performance, which can be compared with the actual observed performance.

For new HMA materials, level 1 analysis requires conducting E* (complex modulus) laboratory testing (ASTM D3496) at loading frequencies and temperatures of interest for the given mixture.⁽⁷⁾ Level 2 analysis does not require E* laboratory testing; instead, the user can input asphalt mix properties (gradation parameters) and laboratory binder test data (from G* testing or other conventional binder tests). The MEPDG software calculates the corresponding asphalt viscosity values; it then uses the modified Witczak equation to predict E* and develops the master curve for the HMA mixture. The same procedure is used for level 3 analysis to estimate the HMA dynamic modulus except that no laboratory test data are required for the binder, and typical values for the selected binder grade are used. The inputs summarized previously in table 25 and table 26 for the existing HMA were used for the new HMA material.

Incorporation of Backcalculation Results with the MEPDG Software

Several analyses were executed with the MEPDG design software (summarized in table 33) to evaluate the influence of the unbound and bound layer inputs, as discussed in the following sections. Version 1.003 of the software was used, as well as the nationally calibrated performance models.

HMA Layer

The MEPDG software does not include the backcalculation-based modulus for an existing HMA layer in a HMA over jointed portland cement concrete pavement (JPCP) (fractured) design. The existing HMA modulus is determined internally based on the HMA mixture properties entered. The required inputs include the aggregate gradation of the asphalt mix and the AC grade (PG in this instance). The new HMA material properties used for this analysis are summarized in table 34 and table 35.

Table 34. Summary of new HMA surface material properties.

Table 35. Summary of new HMA surface aggregate sieve analysis.

PCC/Rubblized Layer

The rubblization option is under “Type fracture” in the JPCP material properties as shown in figure 37. The backcalculated RPCC modulus is also input under the strength properties.

Unbound Materials

For unbound materials (and bedrock), only level 1 analysis calls for FWD testing in rehabilitation and reconstruction designs. However, level 1 for unbound materials is not available in the HMA over JPCP (fractured) design analysis. Level 2 inputs allow the input of a layer modulus or correlation with other strength test data, as shown in figure 38. Level 3 allows the input of a modulus, which is generally based on typical values of the soil classification. The MEPDG lists typical modulus values based on soil classification but warns that they are very approximate and strongly recommends some form of testing, especially noting the use of FWD testing and backcalculation.

1 inch = 25.4 mm.
1 pcf = 16 kg/m³.
1 psi = 6.89 kPa.
1 BTU/h-ft-°F = 1 W/m-°C.
1 BTU/lb-°F = 4,186.8 J/kg-°C.
Figure 37. Screen Capture. RPCC input screen.

Figure 38. Screen Capture. Unbound layer input screen for HMA over JPCP (fractured) design.

The MEPDG notes that the reason for caution is related to using the wrong assumptions: either a fairly strong subgrade material may be erroneously assumed to be semi-infinite while it may actually be less than 1 m (3 ft) thick (e.g., as part of an embankment), or conversely, a weak subgrade soil may be assumed to be semi-infinite while it may, in reality, be overlying a stronger soil or bedrock.

The MEPDG also notes that for granular materials, moduli values that matched FWD backcalculated results were 50 to 70 percent higher than the typical laboratory-tested values, while they were two to three times the typical laboratory determined values for subgrade soils. Guidance in the MEPDG when this report written was to use the previously established coefficients (summarized in table 3.6.8 of the MEPDG (0.35 for subgrade and 0.62 for aggregate base below a flexible pavement)) to adjust backcalculated layer moduli for use in design.⁽¹⁾ The adjusted value should be entered as the modulus for the unbound layer. The layer properties used in the design analysis are summarized in table 33. ICM modeling was also used because data were not available throughout the year.

Evaluation of Design Results

As noted previously, the analyses summarized in table 33 were run with the MEPDG software (version 1.0) using nationally calibrated performance models to evaluate the influence of varying the backcalculation-based inputs. The required HMA overlay thicknesses were determined for each set of inputs, and the change in distress predictions and reliabilities were compared. The required HMA overlay thickness for all analyses was 178 mm (7 inches) to achieve a 90‑percent reliability level. The required HMA overlay thickness was controlled primarily by HMA surface deformation (illustrated in figure 39 for analysis 1), with other distress predictions showing minimal differences between the analyses. A thinner overlay could be selected if maintenance (patching) to repair the rutting was performed in an earlier year.

1 inch = 25.4 mm.
Figure 39. Graph. Summary of required overlay thickness based on surface rutting—analysis 1.

As summarized in table 36, the surface rutting, which controls the overall design, was essentially unaffected by the range of inputs used in the design analyses. In addition, the total rutting had fairly minimal differences between the inputs (or layering) used; that is, the differences did not result in the selection of a different overlay thickness.

SUMMARY

Three backcalculation programs were used to analyze FWD deflection data from various test locations (stations) within the rubblized pavement project. The deflection data showed considerable variability within the project. The RMS values obtained from the MICHBACK© backcalculation program were also very high. It is recommended that one conduct FWD tests at multiple locations and use the average of backcalculated layer moduli. This should provide consistent service life predictions irrespective of the backcalculation program used, and therefore result in a similar recommended overlay design.

For an HMA overlay on rubblized concrete pavements, the critical performance measure in the MEPDG software is surface rutting. However, surface rutting can be addressed through maintenance at some intermediate year (less than 20 years), and a thinner HMA overlay would be acceptable. The surface rutting predictive model is mainly sensitive to HMA overlay thickness and HMA and rubblized layer moduli. Therefore, care should be taken in selecting the modulus for the rubblized layer. In this particular case, the RPCC modulus was slightly lower than the suggested level 3 input in the MEPDG. It may be useful to combine the rubblized layer with the existing unbound base layer when using some backcalculation programs (for example MICHBACK©, in this case study). The remaining unbound layer moduli should be entered as the adjusted backcalculated values (until ongoing studies are completed, the correction factors developed by Von Quintus and Killingsworth should be applied to the backcalculation results), but the existing HMA modulus determined by backcalculation could not be used at the time of this research.⁽⁷⁾