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OCR for page 8
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where For the comparison, the database of dynamic modulus meas-
)
urements assembled for NCHRP Project 9-19 was used (9).
Pc =
( 435,000(VFA ) 0.58
20 +
VMA (11)
This database includes test data from replicate samples tested
at temperatures of 15.8, 40, 70, 100, and 130°F and frequen-
650 + (
435,000(VFA) 0.58
VMA ) cies of 25, 10, 5, 1.0, 0.5, and 0.1 Hz. Table 1 summarizes
pertinent properties of the mixtures included in the evalua-
E * max = limiting maximum mixture dynamic modulus; tion. The mixtures include 5 mixtures from the MNRoad
VMA = voids in mineral aggregates, %; and project, 11 mixtures from the FHWA Pavement Testing
VFA = voids filled with asphalt, %. Facility, and 6 mixtures from the WesTrack project. This
combination of mixtures includes a range of nominal maxi-
Figure 2 presents limiting maximum moduli computed mum aggregate sizes, binders, and volumetric properties.
using Equation 10 for VMA ranging from 10 to 20 percent, For each mixture included in Table 1, master curves were
and VFA ranging from 55 to 85 percent. For this wide range developed using the MEPDG master curve. Data from all
of volumetric properties, the limiting maximum modulus temperatures were used to develop the AASHTO TP62 mas-
varies from about 3,000,000 to 3,800,000 psi. These limiting ter curves, while the reduced data set excluded the data at
maximum modulus values appear very rational. For condi- 15.8°F and included an estimate of the limiting maximum
tions with low VMA and high VFA, the limiting maximum modulus from the Hirsch model. The master curves then
modulus approaches 4,000,000 psi, which is often assumed were compared graphically. The rationality of the master
for the modulus of portland cement concrete. curve parameters also was considered.
Figure 3 and Figure 4 present examples of the master
curves generated. Figure 3 is for Lane 2 at the FHWA Pave-
2.4 Comparison of Master Curves
ment Testing Facility and is an example of the worst agree-
Using Complete and Reduced
ment between the two methods. The limiting maximum
Data Sets
modulus from the reduced data set at 3,236,868 psi is much
This section presents comparisons of master curves fitted lower than the 6,714,030 psi limiting maximum modulus
to actual laboratory test data using the complete AASHTO from the AASHTO TP62 data set. The difference in the lim-
TP62 data and a reduced data set where test data at the low- iting maximum modulus also affects the limiting minimum
est temperature are eliminated and replaced with an estimate modulus because the sigmoidal master curve is symmetrical.
of the limiting maximum modulus from the Hirsch model. The limiting minimum modulus from the reduced data set is
4,000,000
3,900,000
3,800,000
Limiting Dynamic Modulus, psi
3,700,000
3,600,000
VFA = 55%
3,500,000 VFA = 70%
VFA = 85%
3,400,000
3,300,000
3,200,000
3,100,000
3,000,000
9 11 13 15 17 19 21
VMA, %
Figure 2. Limiting maximum dynamic modulus values from the Hirsch model.
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Table 1. Properties of mixtures used in the master curve comparison study.
Description Mix Volumetric Properties AASHTO T240 Residue Binder
Properties
Project Project ID Binder Mix Type AC, % Va, % VMA, % VFA, % A VTS 70 RTFOT , cP
MNRoad Cell 16 AC-20 Fine 9.5 mm 5.08 8.2 18.0 54.4 10.7826 -3.6065 1.22E+09
MNRoad Cell 17 AC-20 Fine 9.5 mm 5.45 7.7 18.2 57.6 10.7826 -3.6065 1.22E+09
MNRoad Cell 18 AC-20 Fine 9.5 mm 5.83 5.6 17.1 67.2 10.7826 -3.6065 1.22E+09
MNRoad Cell 20 120/150 Pen Fine 9.5 mm 6.06 6.3 18.3 65.6 10.8101 -3.6254 3.96E+08
MNRoad Cell 22 120/150 Pen Fine 9.5 mm 5.35 6.5 16.9 61.5 10.8101 -3.6254 3.96E+08
ALF Lane 1 AC-5 Fine 19 mm 4.75 6.1 16.9 63.9 10.6766 -3.5740 5.35E+08
ALF Lane 2 AC-20 Fine 19 mm 4.85 6.5 17.3 62.5 10.6569 -3.5594 1.38E+09
ALF Lane 3 AC-5 Fine 19 mm 4.75 7.7 18.3 57.9 10.6766 -3.5740 5.35E+08
ALF Lane 4 AC-20 Fine 19 mm 4.9 9.7 20.3 52.1 10.6569 -3.5594 1.38E+09
ALF Lane 5 AC-10 Fine 19 mm 4.8 8.6 19.0 54.7 10.7805 -3.6116 5.72E+08
ALF Lane 7 Styrelf Fine 19 mm 4.9 11.9 22.1 46.2 8.9064 -2.9089 4.02E+09
ALF Lane 8 Novophalt Fine 19 mm 4.7 11.9 21.6 45.0 8.8136 -2.8817 1.58E+09
ALF Lane 9 AC-5 Fine 19 mm 4.9 7.7 18.4 58.1 10.6766 -3.5740 5.35E+08
ALF Lane 10 AC-20 Fine 19 mm 4.9 9.3 19.8 53.0 10.6569 -3.5594 1.38E+09
ALF Lane 11 AC-5 Fine 37.5 mm 4.05 6 14.2 57.9 10.6766 -3.5740 5.35E+08
ALF Lane 12 AC-20 Fine 37.5 mm 4.05 7.4 15.5 52.3 10.6569 -3.5594 1.38E+09
WesTrack Sec 2 PG 64-22 Fine 19 mm 5.02 10.4 17.3 39.9 11.0757 -3.7119 1.63E+09
WesTrack Sec 4 PG 64-22 Fine 19 mm 5.24 6.6 14.3 53.8 11.0757 -3.7119 1.63E+09
WesTrack Sec 7 PG 64-22 Coarse 19 mm 6.28 6.9 15.9 56.6 11.0757 -3.7119 1.63E+09
WesTrack Sec 15 PG 64-22 Fine 19 mm 5.55 8.7 16.9 48.4 11.0757 -3.7119 1.63E+09
WesTrack Sec 23 PG 64-22 Coarse 19 mm 5.78 4.9 13.0 62.3 11.0757 -3.7119 1.63E+09
WesTrack Sec 24 PG 64-22 Coarse 19 mm 5.91 7.2 15.4 53.2 11.0757 -3.7119 1.63E+09
higher, 16,826 psi compared to 2,222 psi for the AASHTO case, the two approaches yield essentially the same master
TP62 data set. Both approaches fit the measured data well curves.
over the temperature range from 40 to 130°F and the shift fac- To compare master curves for all of the mixtures, dynamic
tors for the two approaches are essentially the same. moduli were calculated for temperatures ranging from -30 to
Figure 4 is for Cell 17 at the MNRoad project, and is an 150°F using loading rates of 25, 10, 1, 0.1, and 0.01 Hz. The
example of best agreement between the two methods. In this results are shown in Figure 5. As shown, the two approaches
10,000,000
1,000,000
15.8 F
40 F
E* , psi
70 F
100,000 100 F
130 F
6 AASHTO TP62 AASHTO TP62
4
Log Shift Factor
REDUCED SET REDUCED SET
2
0
10,000 -2
-4
-6
0 50 100 150
Temperature, F
1,000
1.0E-07 1.0E-05 1.0E-03 1.0E-01 1.0E+01 1.0E+03 1.0E+05 1.0E+07
Reduced Frequency, Hz
Figure 3. Comparison of fitted master curves for Lane 2 from the FHWA Pavement
Testing Facility
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10,000,000
1,000,000
15.8 F
40 F
E* , psi
70 F
100,000 100 F
130 F
6 AASHTO TP62 AASHTO TP62
4
Log Shift Factor
REDUCED SET REDUCED SET
2
0
10,000 -2
-4
-6
0 50 100 150
Temperature, F
1,000
1.0E-07 1.0E-05 1.0E-03 1.0E-01 1.0E+01 1.0E+03 1.0E+05 1.0E+07
Reduced Frequency, Hz
Figure 4. Comparison of fitted master curves for Cell 17 from the MNRoad.
yield the same moduli over the range of the measured data, As shown, the two data sets produce reasonably similar
but sometimes yield differences at high and low moduli pri- average limiting maximum modulus values except for the
marily due to differences caused by the maximum limiting ALF mixtures, which had four unrealistically high values
modulus. in the AASHTO TP62 data set. The quality of the data for
Figure 6 compares limiting maximum moduli from the the low temperature test condition has a major impact on
two data sets. As shown, the AASHTO TP62 data set yields the limiting maximum modulus in the MEPDG master
unrealistically high moduli in four cases, ALF 2, ALF 3, ALF curve equation. Pellinen reported significantly greater vari-
10, and ALF 11. It also yields unrealistically low values in ability for data collected at 15.8 °F and 130°F as summarized
two cases, ALF 8 and WSTR 2. Table 2 summarizes limiting Table 3 (9). As reported by Pellinen, strain levels for the
maximum modulus values averaged over similar mixtures. 15.8°F data were significantly lower than those at other
10,000,000
E* From Reduced Data Set, psi
1,000,000
100,000
10,000
1,000
1,000 10,000 100,000 1,000,000 10,000,000
E* From AASHTO TP 62 Data Set, psi
Figure 5. Comparison of dynamic moduli computed from
master curves.
