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Publication Number: FHWA-RD-02-042
Date: October 2000

Modified Asphalt Binders in Mixtures - Topical Report: Permanent Deformation Using A Mixture With Diabase Aggregate

6. Cumulative Permanent Shear Strain

Cumulative permanent shear strain was measured at 7.0-percent air voids, 50°C, and 5,000 cycles. The applied shear stress was 69 ±5 kPa. The loading time was 0.1 s and the rest time was 0.6 s. Three replicate specimens were tested per mixture. Cumulative permanent shear strain is generally a better measure of rutting resistance compared to G* and G*/sind because it accounts for changes in the amount of damage from cycle to cycle. Lower cumulative permanent shear strains indicate more resistance to rutting.

The average data for all asphalt binders and mixtures are given in table 9. Rankings for the 11 asphalt mixtures are given in table 10. CMCRA fell into three groups: A, B, and C. Six of the 11 mixtures fell into group C. Six mixtures also fell into group D. This means that even though some of the mixtures had significantly different cumulative permanent shear strains, the range in the strains is relatively low compared to the variability of the strains from replicate specimen to replicate specimen. Table 10 also shows that grafting did not improve the rutting resistance of EVA, and its effect on SBS was not significant.

The replicate strains are given in table 11. The coefficients of variation range from 8.2 to 24.1 percent. Coefficients around 20 percent and lower are generally desirable for asphalt mixture tests. The data indicate that studies on the SST should be done to determine if testing four or five replicate specimens decreases the range in the coefficient of variation.

Figure 11 shows that there was no correlation between the cumulative permanent shear strains and the G*/sind's of the asphalt binders at 50°C and 10.0 rad/s. The r2 was 0.08. The r2 using the data from all 16 materials was 0.43, which is also poor.A log-log transformation increased the r2 to 0.68. As shown by figure 12, the log-log relationship provided a trend of decreasing cumulative permanent shear strain with increasing G*/sind.

The high-temperature PG's provided relationships as good or better than those provided by G*/sind at 50°C, even though the PG's were 17 to 27°C higher than the SST test temperature of 50°C. The r2 was 0.68 for the 11 materials. The data are shown in figure 13. However, the data for the PG 64-28 materials might have inflated the r2. Without this data point, the r2 was only 0.39.

The r2 between high-temperature PG and cumulative permanent shear strain for all 16 materials was 0.69 using no transformation and 0.76 using a log-log transformation. The latter relationship, given in figure 14, shows that there is a trend of decreasing cumulative permanent shear strain with increasing G*/sind. Based on this relationship, an increase of one high-temperature PG, from 70 to 76, would decrease the cumulative permanent shear strain from 28 750 to 18 100 mm/m at 50°C, which is a 37-percent reduction.

The time-temperature superposition principle indicates that data taken at high temperatures and short loading times can be used to calculate data at lower temperatures and longer loading times. This principle and the higher r2's provided by the high-temperature PG's compared to G*/sind at 50°C and 10 rad/s indicate that G*/sind's at a frequency lower than 10.0 rad/s should correlate better with cumulative permanent shear strain. G*/sind's for the 16 materials at 50°C and 10.0, 2.0, and 0.125 rad/s are given in table 12. The latter two frequencies were chosen because the G*/sind's of the five asphalt binders used in the Superpave Validation Study were measured at these frequencies. For the 11 materials, frequencies of 10.0, 2.0, and 0.125 rad/s provided r2's of 0.06, 0.55, and 0.89, respectively, using log-log transformations. For the 16 materials, frequencies of 10.0, 2.0, and 0.125 rad/s provided r2's of 0.68, 0.83, and 0.93, respectively, using log-log transformations. The relationships using 0.125 rad/s are shown in figures 15 and 16. To avoid having a negative log G*/sind, the unit for G*/sind in these two figures was changed from kPa to Pa.

Table 2. Descriptions of the asphalt binders.

Name of Asphalt Percent Polymer PG of Base Asphalt Description Provided by the Source Trade Name Source
Unmodified
Asphalts
0 Not Applicable PG 52-34, PG 64-28, PG 70-22 Not Applicable Citgo Asphalt Refining Co.
Air-Blown
Asphalt
0 52-34 Air-Blown Asphalt Without Catalyst Not Applicable Trumbull and
Owens Corning
Elvaloy 2.2 50% 52-34
50% 64-28
Ethylene Terpolymer Elvaloy DuPont
SBS Linear 3.75 58.9% 52-34
41.1% 64-28
Styrene-Butadiene-Styrene Dexco
Vector 2518
TexPar Labs and Johns Manville
SBS Linear Grafted 3.75 58.9% 52-34
41.1% 64-28
Styrene-Butadiene-Styrene
and 0.05% Additive
Dexco
Vector 2518
TexPar Labs and Johns Manville
SBS Radial Grafted 3.25 58.9% 52-34
41.1% 64-28
Styrene-Butadiene-Styrene
and 0.05% Additive
Shell 1184 TexPar Labs and Johns Manville
EVA 5.5 52-34 Ethylene Vinyl Acetate Exxon
Polybilt 152
TexPar Labs and Johns Manville
EVA
Grafted
5.5 52-34 Ethylene Vinyl Acetate
and 1.35% Additive
Exxon
Polybilt 152
TexPar Labs and Johns Manville
ESI 5.0 52-34 Ethylene Styrene Interpolymer ESI Dow and PRI
CMCRA 5.0 64-28 Chemically Modified
Crumb Rubber Asphalt
CMCRA FHWA

Table 3. Performance grade (PG) for each asphalt binder.

Trade Name: PG 52 Unmodified PG 64 Unmodified PG 70 Unmodified Air-Blown Asphalt Elvaloy EVA EVA Grafted
PG: 52-28 64-28 70-28 70-28 76-28 70-28 70-28
Continuous PG:1 54-33 67-28 71-28 74-28 76-31 70-31 73-31
PG From the Supplier: 52-34 64-28 70-22 73-28 74-29 73-31 75-31
Original Asphalt Binder
Temperature at a G*/sind of 1.00 kPa and 10 rad/s, C 55 67 73 74 76 70 76
RTFO Residue
Temperature at a G*/sind of 2.20 kPa and 10 rad/s, C 54 67 71 74 77 75 74
RTFO/PAV Residue
Temperature at a G*sind of 5000 kPa and 10 rad/s, C 8.1 20 24 21 14 13 14
BBR Temperature at a Creep Stiffness of 300 MPa and 60 s, C + 10°C -33 -28 -28 -29 -31 -31 -32
BBR Temperature at an m-value of 0.30 and 60 s, C + 10°C -36 -30 -29 -28 -33 -31 -31
Critical Cracking Temperature From the BBR and Direct Tension, C -35 -28 -27 -28 -34 -31 -33

1The low-temperature continuous PG is the PG provided by the BBR.

Table 3. Performance grade (PG) for each asphalt binder (continued).

Trade Name:  SBS Linear  SBS Linear Grafted  SBS Radial Grafted  ESI  CMCRA 
PG: 70-28 70-28 70-28 76-28 76-28
Continuous PG:1 72-31 72-33 71-32 76-31 76-29
PG from the Supplier: 72-28 74-29 73-28 Unknown 76-28
Original Asphalt Binder
Temperature at a G*/sind of 1.00 kPa and 10 rad/s, C 75 75 74 77 76
RTFO Residue
Temperature at a G*/sind of 2.20 kPa and 10 rad/s, C 72 72 71 76 76
RTFO/PAV Residue
Temperature at a G*sind of 5000 kPa and 10 rad/s, C 18 15 16 9.2 18
BBR Temperature at a Creep Stiffness of 300 MPa and 60 s, C + 10°C -32 -33 -32 -31 -29
BBR Temperature at an m-value of 0.30 and 60 s, C + 10°C -31 -34 -32 -31 -29
Critical Cracking Temperature From the BBR and Direct Tension, C -33 -34 -34 -29 -29

1The low-temperature continuous PG is the PG provided by the BBR.

Table 4. Aggregate properties for the diabase.

Aggregate Gradations, Percent Passing:

Sieve Size (mm)

61% No. 68 Diabase 30% No. 10 Diabase 8% Natural Sand 1% Hydrated Lime Blend

25.0

100.0       100.0

19.0

97.9       98.7

12.5

60.7       76.0
9.5 37.7 100.0 100.0   62.0
4.75 9.2 99.2 95.8   44.0
2.36 2.2 75.6 88.2   32.1
1.18 1.7 52.5 74.8   23.8
0.600 1.4 37.8 46.0   16.9
0.300 1.3 27.9 14.1   11.3
0.150 1.1 19.6 4.8   7.9
0.075 0.9 12.5 2.9 100.0 5.5

Specific Gravities and Percent Absorption:

Bulk Dry

2.943 2.914 2.565   2.892

Bulk SSD

2.962 2.945 2.601   2.916
Apparent

2.999

3.007 2.659 2.262 2.961
% Abs

0.6

1.1 1.4   0.8

Flat and Elongated Particles at a 3-to-1 Length-to-Thickness Ratio, Percent by Mass:

 

21

NA NA    

Los Angeles Abrasion, Percent Loss by Mass:

  14 NA NA    
Fine Aggregate Angularity:
  NA 49 45    

Bulk Dry = Bulk Dry Specific Gravity
Bulk SSD = Bulk Saturated-Surface Dry Specific Gravity
Apparent = Apparent Specific Gravity
% Abs = Percent Water Absorption
NA = Not Applicable

Figure 2. Graph. Aggregate Gradation. This graph shows the aggregate gradation for the "blend" reported in table 4. It shows the cumulative percent passing in millimeters for each sieve size listed in table 4 raised to the 0.45 power, in millimeters. The aggregate gradation is very close to the Superpave maximum density line for a 19.0-millimeter nominal maximum aggregate size.

Figure 2. Aggregate gradation.

Table 5. Volumetric properties of the mixture.

Mixture Property Diabase Mixture Without Hydrated Lime Specification

Asphalt Binder Content

Total Asphalt Binder Content, Percent by Mixture Mass 4.85  
Effective Asphalt Binder Content, Percent by Mixture Mass 4.15  
Asphalt Binder Absorption, Percent by Mixture Mass 0.7  
Effective Asphalt Binder Content, Percent by Total Volume 10.8  

Voids Analyses

Maximum Specific Gravity of the Mixture 2.702  
Effective Specific Gravity of the Aggregate 2.948  
Total Air Voids, Percent by Volume 3.2 4.0
Voids in the Mineral Aggregate (VMA), Percent by Total Volume 14.0 Minimum of 13.0
Voids Filled With Asphalt (VFA), Percent by Total Volume 77 65 to 78

Dust Content

Dust Content, Percent Finer Than 75 m by Aggregate Mass 5.5  

Dust-to-Binder Ratios

Dust by Aggregate Mass to Total Binder Content by Mixture Mass 1.1  
Dust by Aggregate Mass to Effective Binder Content by Mixture Mass 1.3 0.6 to 1.6
Dust by Mixture Mass to Effective Binder Content by Mixture Mass 1.2  
Dust by Volume to Effective Binder Content by Volume 0.42  

Table 6. G*/sind's of all binders and mixtures with the
materials listed from the highest to lowest mixture G*/sind.

Asphalt Binder or Mixture Designation Binder Mixture
High Temp. PG G*/sind, 50°C (kPa) G*/sind, 50°C (MPa) G*,50°C (MPa)
10.0 rad/s 10.0 rad/s 10.0 Hz 10.0 Hz
Novophalt (Validation Study) 77 60.2 101.5 84.5
Styrelf (Validation Study) 88 76.0 98.1 78.5
EVA Grafted 74 35.8 87.0 74.5
Air-Blown 74 49.1 85.8 75.8
PG 70-22 71 40.7 83.9 78.9
EVA 75 26.3 83.9 72.0
ESI 76 32.3 75.1 65.9
CMCRA 76 44.3 71.6 61.5
SBS Radial Grafted 71 25.1 55.1 50.1
AC-20 (Validation Study) 70 30.7 50.5 46.7
SBS Linear Grafted 72 25.6 47.8 43.9
SBS Linear 72 25.4 47.8 43.7
Elvaloy 77 28.7 46.4 39.7
PG 64-28 67 22.2 43.8 41.0
AC-10 (Validation Study) 65 15.9 29.1 26.9
AC-5 (Validation Study) 59 7.5 19.9 17.6
Unmodified Asphalt Binders Only
PG 70-22 71 40.7 83.9 78.9
AC-20 (Validation Study) 70 30.7 50.5 46.7
PG 64-28 67 22.2 43.8 41.1
AC-10 (Validation Study) 65 15.9 29.1 26.9
AC-5 (Validation Study) 59 7.5 19.9 17.6

Figure 3. Diagram of Superpave Shear Tester chamber. It shows a vertical actuator that is used to maintain a constant specimen height during testing and a horizontal actuator (shear table) used to apply the shear stress. There are two horizontally mounted linear variable differential transformers that measure the shear strain in the specimen during loading and rest. The specimen is tested in an enclosed steel chamber so that the test temperature can be maintained.

Figure 3. Diagram of SST chamber.

Figure 4. Photo. Superpave Shear Tester. This is a photo of the Superpave Shear Tester chamber shown in figure 3. In addition, it shows thermocouples attached to the asphalt mixture specimen, which record the temperature during testing.

Figure 4. Superpave Shear Tester.

Table 7. G*/sind's of the 11 binders and mixtures with the
materials listed from the highest to lowest mixture G*/sind.

Asphalt Binder or Mixture Designation Binder Mixture
High Temp. PG G*/sind 50°C (kPa) G*/sind at 50°C (MPa)
10.0 rad/s 10.0 rad/s 10.0 Hz
EVA Grafted 74 35.8 87.0 A          
Air-Blown 74 49.1 85.8 A          
PG 70-22 71 40.7 83.9 A          
EVA 75 26.3 83.9 A          
ESI 76 32.3 75.1   B        
CMCRA 76 44.3 71.6   B        
SBS Radial Grafted 71 25.1 55.1     C      
SBS Linear Grafted 72 25.6 47.8     C D    
SBS Linear 72 25.4 47.8     C D    
Elvaloy 77 28.7 46.4       D    
PG 64-28 67 22.2 43.8       D    
  10.0 rad/s 2.0 rad/s 2.0 Hz
EVA Grafted 74 14.3 41.1 A            
EVA 75 12.1 39.3 A B          
Air-Blown 74 14.2 38.6 A B          
CMCRA 76 13.9 37.8   B          
ESI 76 8.9 34.5     C        
PG 70-22 71 10.2 29.9       D      
Elvaloy 77 10.0 25.5         E    
SBS Radial Grafted 71 7.6 24.9         E F  
SBS Linear Grafted 72 8.0 21.1           F G
PG 64-28 67 5.4 20.5             G
SBS Linear 72 7.7 20.4             G

Table 8. Replicate data for G*/sind at 50oC.

Asphalt Binder or Mixture Designation Specimen No. 1 Specimen No. 2 Specimen No. 3 Average (MPa) CV1(percent)
  Frequency = 10.0 Hz
EVA Grafted 85.5 91.3 84.3 87.0 4.3
Air-Blown 86.0 86.8 84.5 85.8 1.4
PG 70-22 94.0 69.9 87.8 83.9 14.9
EVA 79.5 84.3 87.8 83.9 5.0
ESI 80.3 71.1 73.8 75.1 6.3
CMCRA 68.1 76.9 69.7 71.6 6.5
SBS Radial Grafted 56.6 55.3 53.5 55.1 2.8
SBS Linear Grafted 41.8 51.4 50.3 47.8 11.0
SBS Linear 48.7 45.8 48.8 47.8 3.6
Elvaloy 45.0 46.1 48.1 46.4 3.4
PG 64-28 41.5 41.8 48.2 43.8 8.6
  Frequency = 2.0 Hz
EVA Grafted 41.1 42.7 39.4 41.1 4.0
EVA 38.1 39.2 40.7 39.3 3.3
Air-Blown 38.5 39.6 37.8 38.6 2.3
CMCRA 35.9 40.7 37.3 37.8 6.5
ESI 37.0 33.1 33.4 34.5 6.3
PG 70-22 28.1 27.6 34.1 29.9 12.1
Elvaloy 24.1 26.1 26.3 25.5 4.8
SBS Radial Grafted 25.2 25.5 24.1 24.9 3.0
SBS Linear Grafted 20.5 23.0 22.8 21.1 6.3
PG 64-28 20.9 19.5 21.0 20.5 4.1
SBS Linear 20.9 19.7 20.7 20.4 3.1

1CV = Coefficient of Variation, percent = (standard deviation ÷ average)*100.

Figure 5. Graph. The absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt mixture versus the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt binder using the 11 asphalt binders. This graph shows that the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt mixture increases with an increase in the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt binder using the 11 asphalt binders. The data are reported in table 6. The R-square of 0.50 indicates that the relationship is poor. The relationship is relatively flat. The equation of the line is Y equals 1.41 X plus 20.5.

Figure 5. G*/sind of the asphalt mixture vs. G*/sind
of the asphalt binder using the 11 asphalt binders.

Figure 6. Graph. The absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt mixture versus the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt binder using all 16 asphalt binders. This graph shows that the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt mixture increases with an increase in the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt binder using the 16 asphalt binders. The data are reported in table 6. The R-square of 0.72 indicates that the relationship is fair. This relationship is better than the relationship for the 11 asphalt binders because the 5 additional data points increased the range in the data. The equation of the line is Y equals 1.24 X plus 22.0.

Figure 6. G*/sind of the asphalt mixture vs. G*/sind
of the asphalt binder using all 16 asphalt binders.

Figure 7. Graph. The absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt mixture at 50 degrees Celsius versus high-temperature performances grades using the 11 asphalt binders. This graph shows that the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt mixture increases with an increase in the high-temperature performance grade of the asphalt binder using the 11 asphalt binders. The data are reported in table 6. The R-square of 0.14 indicates that the relationship is very poor. The data are highly scattered. The equation of the line is Y equals 2.31 X minus 103.

Figure 7. G*/sind of the asphalt mixture at 50°C vs.
high-temperature PG using the 11 asphalt binders.

Figure 8. Graph. The absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt mixture at 50 degrees Celsius versus high-temperature performances grades using all 16 asphalt binders. This graph shows that the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt mixture increases with an increase in the high-temperature performance grade of the asphalt binder using the 16 asphalt binders. The data are reported in table 6. The R-square of 0.59 indicates that the relationship is poor. The data are scattered. This relationship is better than the relationship for the 11 asphalt binders because the 5 additional data points increased the range in the data. The equation of the line is Y equals 3.03 X minus 156.

Figure 8. G*/sind of the asphalt mixture at 50oC vs.
high-temperature PG using all 16 asphalt binders.

Figure 9. Graph. The absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt mixture at 2.0 Hertz versus the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt binder at 2.0 radians per second using the 11 asphalt binders. This graph is identical to figure 5, except that the absolute value of the complex shear modulus divided by the sine of the phase angles are at 2.0 Hertz and 2.0 radians per second instead of 10.0 Hertz and 10.0 radians per second. The absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt mixture increases with an increase in the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt binder using the 11 asphalt binders. The data are reported in table 7. The R-square of 0.81 indicates that the relationship is good, although there is some scatter in the data. The equation of the line is Y equals 2.41 X plus 5.68.

Figure 9. G*/sind of the asphalt mixture at 2.0 Hz vs. G*/sind
of the asphalt binder at 2.0 rad/s using the 11 asphalt binders.

Figure 10. Graph. The absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt mixture at 2.0 Hertz versus the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt binder at 2.0 radians per second using all 16 asphalt binders. This graph shows that the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt mixture increases with an increase in the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt binder using the 16 asphalt binders. As in figure 9, the absolute value of the complex shear modulus divided by the sine of the phase angle are at 2.0 Hertz and 2.0 radians per second. The R-square of 0.85 indicates that the relationship is very good, with low scatter. In this figure, an exponential correlation was used because it provided a higher r-square than a linear arithmetic correlation. The exponential equation is Y equals 7.55 times X raised to the 0.59 power.

Figure 10. G*/sind of the asphalt mixture at 2.0 Hz vs. G*/sind
of the asphalt binder at 2.0 rad/s using all 16 asphalt binders.

Table 9. G*/sind's of the asphalt binders vs. cumulative permanent shear strain.

Asphalt Binder or Mixture Designation Binder Mixture Pavement
High Temp. PG G*/sind, 10.0 rad/s, 50°C (kPa) Shear Strain, 50°C (mm/m) Relative ALF Rut Depth (mm)
Styrelf (Validation Study) 88 76.0 10 500 6.1
EVA 75 26.3 13 600 7.3
Novophalt (Validation Study) 77 60.2 14 100 7.5
Elvaloy 77 28.7 14 600 7.7
EVA Grafted 74 35.8 15 400 8.0
CMCRA 76 44.3 19 100 9.7
SBS Radial Grafted 71 25.1 21 300 10.4
Air-Blown 74 49.1 21 300 10.4
ESI 76 32.3 22 700 11.0
SBS Linear Grafted 72 25.6 23 200 11.2
PG 70-22 71 40.7 23 900 11.4
SBS Linear 72 25.4 26 500 12.5
AC-20 (Validation Study) 70 30.7 36 200 16.4
PG 64-28 67 22.2 38 600 17.3
AC-10 (Validation Study) 65 15.9 61 300 26.4
AC-5 (Validation Study) 59 7.5 85 500 36.1

Unmodified Asphalt Binders Only

PG 70-22 71 40.7 23 900 11.4
AC-20 (Validation Study) 70 30.7 36 200 16.4
PG 64-28 67 22.2 38 600 17.3
AC-10 (Validation Study) 65 15.9 61 300 26.4
AC-5 (Validation Study) 59 7.5 85 500 36.1

Table 10. Statistical rankings for the 11 asphalt
mixtures based on cumulative permanent shear strain.

Asphalt Binder or Mixture Designation

 
Binder Mixture
High Temp. PG G*/sind, 10.0 rad/s, 50°C (kPa) Cumulative Permanent Shear Strain, 50°C (mm/m)
EVA 75 26.3 13 600 A          
Elvaloy 77 28.7 14 600 A          
EVA Grafted 74 35.8 15 400 A B        
CMCRA 76 44.3 19 100 A B C      
SBS Radial Grafted 71 25.1 21 300   B C D    
Air-Blown 74 49.1 21 300   B C D    
ESI 76 32.3 22 700     C D    
SBS Linear Grafted 72 25.6 23 200     C D    
PG 70-22 71 40.7 23 900     C D    
SBS Linear 72 25.4 26 500       D    
PG 64-28 67 22.2 38 600         E  

Table 11. Replicate data for the cumulative permanent shear strains.

Asphalt Mixture Cumulative Permanent Shear Strain at 50°C (mm/m) CV1 (percent)
Specimen No. 1 Specimen No. 2 Specimen No. 3 Average
EVA 15 100 12 900 12 800 13 600 9.6
Elvaloy 13 300 14 400 16 000 14 600 9.3
EVA Grafted 13 800 17 100 15 300 15 400 10.7
CMCRA 22 200 16 620 18 490 19 100 14.9
SBS Radial Grafted 16 200 21 400 26 300 21 300 23.7
Air-Blown 16 100 22 200 25 700 21 300 22.8
ESI 20 580 24 040 23 510 22 700 8.2
SBS Linear Grafted 21 500 18 600 29 400 23 200 24.1
PG 70-22 18 200 26 000 27 500 23 900 20.9
SBS Linear 29 500 23 400 26 700 26 500 11.5
PG 64-28 41 290 42 030 32 410 38 600 13.9

1CV = Coefficient of Variation, percent = (standard deviation ÷ average)*100.

Figure 11. Graph. The cumulative permanent shear strain versus the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt binder at 10.0 radians per second using the 11 asphalt binders. This graph shows that the cumulative permanent shear strain of the asphalt mixture did not correlate to the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt binder using the 11 asphalt binders at 50 degrees Celsius. The data are reported in table 9. The R-square of 0.08 indicates that the relationship is very poor. The relationship is flat and scattered.

Figure 11. Cumulative permanent shear strain vs. G*/sind
of the asphalt binder at 10.0 rad/s using the 11 asphalt binders.

Figure 12. Graph. Log cumulative permanent shear strain versus log the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt binder at 10.0 radians per second using all 16 asphalt binders. This graph shows that the cumulative permanent shear strain of the asphalt mixture decreases with an increase in the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt binder using the 16 asphalt binders. The data are reported in table 9. The R-square of 0.68 indicates that the relationship is poor to fair. This relationship is better than the relationship for the 11 asphalt binders because the 5 additional data points increased the range in the data. Even so, the data are highly scattered. The equation of the line is Y equals negative 0.854 X plus 5.638.

Figure 12. Log cumulative permanent shear strain vs. log G*/sind
of the asphalt binder at 10.0 rad/s using all 16 asphalt binders.

Figure 13. Graph. Cumulative permanent shear strain at 50 degrees Celsius versus high temperature performance grade using the 11 asphalt binders. This graph shows that the cumulative permanent shear strain of the asphalt mixture decreases with an increase in the high-temperature performance grade using the 11 asphalt binders. The data are reported in table 9. The R-square of 0.68 indicates that the relationship is poor to fair. The data are highly scattered. The equation of the line is Y equals negative 1,958 X plus 165,124.

Figure 13. Cumulative permanent shear strain at 50°C
vs. high-temperature PG using the 11 asphalt binders.

Figure 14. Graph. Log cumulative permanent shear strain at 50 degrees Celsius versus log high-temperature performance grade using all 16 asphalt binders. This graph shows that the log cumulative permanent shear strain of the asphalt mixture decreases with an increase in the log high-temperature performance grade using the 16 asphalt binders. The R-square of 0.76 indicates that the relationship is fair. There is a moderate amount of scatter. This relationship is better than the relationship for the 11 asphalt binders because the additional 5 data points increased the range in the data. The equation of the line is Y equals negative 5.621 X plus 14.83.

Figure 14. Log cumulative permanent shear strain at 50°C
vs. log high-temperature PG using all 16 asphalt binders.

Table 12. G*/sind's of the asphalt binders at 10.0, 2.0, and 0.125 rad/s with
the asphalt binders listed from highest to lowest G*/sind using 0.125 rad/s.

Asphalt Binder G*/sind at 50°C (kPa)
10.0 rad/s 2.0 rad/s 0.125 rad/s
Styrelf (Validation Study) 76.0 31.8 5.230
EVA 26.3 12.1 2.744
EVA Grafted 35.8 14.3 2.312
Novophalt (Validation Study) 60.2 19.1 2.000
Elvaloy 28.7 10.0 1.597
CMCRA 44.3 13.9 1.541
Air-Blown 49.1 14.2 1.390
SBS Linear Grafted 25.6 8.0 0.917
ESI 32.3 8.9 0.868
SBS Linear 25.4 7.7 0.811
PG 70-22 40.7 10.2 0.808
SBS Radial Grafted 25.1 7.6 0.802
AC-20 (Validation Study) 30.7 9.0 0.635
PG 64-28 22.2 5.4 0.405
AC-10 (Validation Study) 15.9 4.4 0.348
AC-5 (Validation Study) 7.5 2.1 0.130

Figure 15. Graph. Log cumulative permanent shear strain versus log absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt binder at 0.125 radians per second using the 11 asphalt binders. This graph shows that log cumulative permanent shear strain of the asphalt mixture decreases with an increase in the log absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt binder at a frequency of 0.125 radians per second using the 11 asphalt binders. The asphalt mixture data are in table 9, while the asphalt binder data are in table 12. The R-square of 0.89 indicates that the relationship is very good. The amount of scatter is low. The equation of the line is Y equals negative 0.506 X plus 5.87.

Figure 15. Log cumulative permanent shear strain vs. log G*/sind
of the asphalt binder at 0.125 rad/s using the 11 asphalt binders.

Figure 16. Graph. Log cumulative permanent shear strain versus log absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt binder at 0.125 radians per second using all 16 asphalt binders. This graph shows that the log cumulative permanent shear strain of the asphalt mixture decreases with an increase in the log the absolute value of the complex shear modulus divided by the sine of the phase angle of the asphalt binder at a frequency of 0.125 radians per second using the 16 asphalt binders. The asphalt mixture data are in table 9, while the asphalt binder data are in table 12. The R-square of 0.93 indicates that the relationship is excellent. The amount of scatter is very low. The equation of the line is Y equals negative 0.607 X plus 6.2.

Figure 16. Log cumulative permanent shear strain vs. log G*/sind
of the asphalt binder at 0.125 rad/s using all 16 asphalt binders.

The following equation was provided by the five asphalt binders used in the Superpave Validation Study:

RD = 1.87 + 0.0004 (CPSS)
r2 = 0.92 (2)

where:

RD = Rut depth in the asphalt pavement layer at 58°C, mm.
CPSS = Cumulative permanent shear strain at 5,000 cycles and 50°C, mm/m.

The rut depths provided by equation 2 are included in table 9. Substituting the cumulative permanent shear strains of 28 750 to 18 100 mm/m into equation 2 provided rut depths of 13.4 and 9.1 mm, respectively. Therefore, an increase in PG from 70 to 76 provides a 32-percent reduction in rut depth. In the Superpave Validation Study, a change in strain from 28 750 to 18 100 mm/m would have provided a 50-percent reduction in rut depth. The applicability of equation 2 is questionable, but both studies indicate that an increase in PG from 70 to 76 should provide a significant decrease in the rate of pavement rutting for the particular mixture tested in this study.

In the Superpave Validation Study, Novophalt had the lowest cumulative permanent shear strain at 40°C at a 95-percent level of significance. Novophalt also had the highest resistance to pavement rutting at the three pavement test temperatures that were used: 58, 70, and 76°C. The data at 50°C in table 9 shows that Styrelf is ranked above Novophalt, although the strains for these two mixtures are not significantly different. Because the Novophalt mixture was more resistant to rutting according to both RSCH at 40°C and the pavement tests at 58, 70, and 76°C, it should have been more resistant to rutting when tested by RSCH at 50°C. This suggests that the change in ranking was the result of substituting diabase dust for hydrated lime. This change in ranking decreases the confidence in equation 2, even though the r2 of 0.92 is high.

7. French PRT

The French PRT tests a slab for permanent deformation using a smooth, rubber tire inflated to 600 ±30 kPa.(1) Each slab had a length of 500 mm, a width of 180 mm, and a thickness of 50 mm. The applied load was 5000 ±50 N and the test temperature was 70°C. The air-void level was 7.0 percent. The test normally ends at 6,000 wheel passes. In this study, the test was continued to 20,000 wheel passes to provide supplementary information. The French PRT is shown in figures 17 and 18.

Table 13 gives the rankings from Fisher's LSD for the average rut depths at 6,000 wheel passes. Only the mixture with the PG 64-28 asphalt binder had a significantly different average rut depth. The rut depths at 20,000 wheel passes provided the same ranking. The analysis indicated that the rut depths at 6,000 wheel passes need to differ by at least 2.1 mm for them to be different at a 5-percent level of significance.

The replicate data are given in table 14. Only one mixture, SBS Radial Grafted, had a high coefficient of variation. The coefficients are remarkably low for testing only two specimens per mixture.

For the 11 materials, figure 19 shows that the correlation between the rut depth at 6,000 wheel passes and G*/sind at 0.9 rad/s was poor. The r2 was 0.52. A DSR frequency of 0.9 rad/s was used because it accounts for the slow speed of the French PRT.(1) The r2 increased from 0.52 to 0.70 using a log-log transformation, which indicates that there is a general trend of decreasing rut depth with increasing G*/sind. The log-log relationship is shown in figure 20. Without EVA, the r2 would be 0.88.

Figure 21 shows that the correlation using the data from all asphalt binders and mixtures was poor. However, the relationship is curvilinear. Figure 22 shows the same data using a log-log transformation. The r2 increased from a poor value of 0.52 to a high value of 0.88. Without EVA, the r2 would be 0.93.

The high-temperature PG's provided fair to good correlations with the rut depths. Figure 23 shows that the r2 for the 11 asphalt binders and mixtures was 0.80. After excluding the data for the PG 64-28 materials, the r2 dropped to 0.71 and the range in the rut depths at 6,000 passes was only 6.5 to 8.5 mm.

Figure 24 shows that the r2 using all asphalt binders and mixtures was 0.80. The data for Styrelf was eliminated to determined if this would decrease the r2. The r2 increased to 0.85. Based on the relationship given in figure 24, an increase of one high-temperature PG, from 70 to 76, would decrease the rut depth from 9.1 to 7.2 mm at 70°C, which is a 21-percent reduction. This is less than the 37-percent reduction provided by the cumulative permanent shear strains at 50°C. This may be due to the difference in test temperature or stress level. It is desirable that an increase of one PG be beneficial. However, a large difference in rutting performance would mean that the performances of asphalt binders within a grade could be significantly different. A decrease in rut depth of 20 to 40 percent with a change in PG seems reasonable.

In the Superpave Validation Study, Novophalt had the highest resistance to rutting according to the French PRT and ALF pavement tests.(1) The French PRT data in table 13 shows that Styrelf is ranked above Novophalt, although the rut depths for these two mixtures are not different at a 5-percent level of significance. No conclusion concerning the possible effect of hydrated lime could be made based on these results because both the test temperature and slab thickness were changed. A test temperature of 60°C and a slab thickness of 100 mm were used in the Superpave Validation Study, compared to 70°C and 50 mm in this study.

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United States Department of Transportation - Federal Highway Administration