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Refining the Simple Performance Tester for Use in Routine Practice (2008)

Chapter: Chapter 2 - Abbreviated Dynamic Modulus Master Curve Testing

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Suggested Citation:"Chapter 2 - Abbreviated Dynamic Modulus Master Curve Testing." National Academies of Sciences, Engineering, and Medicine. 2008. Refining the Simple Performance Tester for Use in Routine Practice. Washington, DC: The National Academies Press. doi: 10.17226/14158.
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Suggested Citation:"Chapter 2 - Abbreviated Dynamic Modulus Master Curve Testing." National Academies of Sciences, Engineering, and Medicine. 2008. Refining the Simple Performance Tester for Use in Routine Practice. Washington, DC: The National Academies Press. doi: 10.17226/14158.
×
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Suggested Citation:"Chapter 2 - Abbreviated Dynamic Modulus Master Curve Testing." National Academies of Sciences, Engineering, and Medicine. 2008. Refining the Simple Performance Tester for Use in Routine Practice. Washington, DC: The National Academies Press. doi: 10.17226/14158.
×
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Suggested Citation:"Chapter 2 - Abbreviated Dynamic Modulus Master Curve Testing." National Academies of Sciences, Engineering, and Medicine. 2008. Refining the Simple Performance Tester for Use in Routine Practice. Washington, DC: The National Academies Press. doi: 10.17226/14158.
×
Page 8
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Suggested Citation:"Chapter 2 - Abbreviated Dynamic Modulus Master Curve Testing." National Academies of Sciences, Engineering, and Medicine. 2008. Refining the Simple Performance Tester for Use in Routine Practice. Washington, DC: The National Academies Press. doi: 10.17226/14158.
×
Page 9
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Suggested Citation:"Chapter 2 - Abbreviated Dynamic Modulus Master Curve Testing." National Academies of Sciences, Engineering, and Medicine. 2008. Refining the Simple Performance Tester for Use in Routine Practice. Washington, DC: The National Academies Press. doi: 10.17226/14158.
×
Page 10
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Suggested Citation:"Chapter 2 - Abbreviated Dynamic Modulus Master Curve Testing." National Academies of Sciences, Engineering, and Medicine. 2008. Refining the Simple Performance Tester for Use in Routine Practice. Washington, DC: The National Academies Press. doi: 10.17226/14158.
×
Page 11
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Suggested Citation:"Chapter 2 - Abbreviated Dynamic Modulus Master Curve Testing." National Academies of Sciences, Engineering, and Medicine. 2008. Refining the Simple Performance Tester for Use in Routine Practice. Washington, DC: The National Academies Press. doi: 10.17226/14158.
×
Page 12
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Suggested Citation:"Chapter 2 - Abbreviated Dynamic Modulus Master Curve Testing." National Academies of Sciences, Engineering, and Medicine. 2008. Refining the Simple Performance Tester for Use in Routine Practice. Washington, DC: The National Academies Press. doi: 10.17226/14158.
×
Page 13
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Suggested Citation:"Chapter 2 - Abbreviated Dynamic Modulus Master Curve Testing." National Academies of Sciences, Engineering, and Medicine. 2008. Refining the Simple Performance Tester for Use in Routine Practice. Washington, DC: The National Academies Press. doi: 10.17226/14158.
×
Page 14
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Suggested Citation:"Chapter 2 - Abbreviated Dynamic Modulus Master Curve Testing." National Academies of Sciences, Engineering, and Medicine. 2008. Refining the Simple Performance Tester for Use in Routine Practice. Washington, DC: The National Academies Press. doi: 10.17226/14158.
×
Page 15

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52.1 Introduction An abbreviated dynamic modulus master curve testing and analysis procedure was developed in Phase IV of NCHRP Project 9-29 to reduce the effort and equipment costs associ- ated with developing dynamic modulus master curves for pavement structural design. The dynamic modulus test protocol was developed in NCHRP Projects 9-19 and 1-37A and has been standardized as AASHTO Provisional Standard TP62, Standard Method of Test for Determining Dynamic Modulus of Hot-Mix Asphalt Concrete Mixtures. The recom- mended test sequence in AASHTO TP62 for the development of a master curve for pavement structural design consists of testing a minimum of two replicate specimens at tempera- tures of 14, 40, 70, 100, and 130 °F at loading frequencies of 25, 10, 5, 1.0, 0.5, and 0.1 Hz. This testing provides a database of 60 dynamic modulus measurements from which the parameters of the master curve are determined by numerical optimization. It is desirable that equipment for performing such testing be available to highway agencies at a reasonable cost and the test procedure be appropriate for agency laboratories. A recently completed FHWA pooled-fund study identified several issues associated with the test protocol and con- cluded that the overall time required to perform the testing must be shortened if highway agencies are going to use it for routine testing (3). NCHRP Project 9-19 included a study of the minimum testing required to develop the dynamic modulus master curves and concluded that reasonable mas- ter curves can be developed using tests at three tempera- tures: 14, 70, and 130°F at loading frequencies of 33, 2.22, 0.15, and 0.01 Hz (5). This reduced sequence still requires testing at 14°F that the FHWA pooled fund study found dif- ficult due to moisture condensation and ice formation (3). Additionally, low temperature testing significantly increases the cost of the environmental chamber and increases the loading capacity and cost of the testing equipment. If test- ing at this temperature can be eliminated, the cost of the equipment, the complexity of the procedure, and the over- all time required to develop a master curve can be signifi- cantly reduced. The approach taken in this project takes advantage of the fact that all asphalt binders reach approximately the same glassy modulus at very low temperatures (6). Using this binder modulus and recently developed relationships to pre- dict mixture dynamic modulus from binder modulus and volumetric data, an estimate of the limiting maximum mod- ulus of the mixture can be made and used in the development of the dynamic modulus master curve (7). 2.2 MEPDG Dynamic Modulus Master Curve To account for temperature and rate of loading effects on the modulus of asphalt concrete, the MEPDG uses asphalt concrete moduli obtained from a master curve constructed at a reference temperature of 70oF (2). Master curves are constructed using the principle of time-temperature super- position. First a standard reference temperature is selected, in this case 70oF, then data at various temperatures are shifted with respect to loading frequency until the curves merge into a single smooth function. The master curve of modulus as a function of frequency formed in this manner describes the frequency dependency of the material. The amount of shifting at each temperature required to form the master curve describes the temperature dependency of the material. Thus, both the master curve and the shift fac- tors are needed for a complete description of the rate and temperature effects. Figure 1 presents an example of a mas- ter curve constructed in this manner. The shift factors are presented in the inset figure. In the MEPDG, the sigmoidal function in Equation 1 is used to describe the frequency dependency of the modulus master curve. C H A P T E R 2 Abbreviated Dynamic Modulus Master Curve Testing

61.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E-07 1.0E-05 1.0E-011.0E-03 1.0E+031.0E+01 1.0E+05 1.0E+07 Reduced Frequency, Hz E* , p si 14 F 40 F 70 F 100 F 130 F Fit -6 -4 -2 0 2 4 6 0 50 100 150 Temperature, F Lo g Sh ift F ac to r Figure 1. Example dynamic modulus master curve and shift factors. (1) where = dynamic modulus; ωr = reduced frequency, Hz; δ = minimum value of ; δ + α = maximum value of ; and β, γ = parameters describing the shape of the sigmoidal function. Research has shown that the fitting parameters δ and α depend on aggregate gradation, binder content, and air void content. The fitting parameters β and γ depend on the char- acteristics of the asphalt binder and the magnitude of δ and α. The temperature dependency of the modulus is incorporated in the reduced frequency parameter, ωr, in Equation 1. Equa- tion 2 defines the reduced frequency as the actual loading frequency multiplied by the time-temperature shift factor, a(T). ωr = a(T) × ω (2a) log(ωr) = log(ω) + log[a(T)] (2b) where ωr = reduced frequency, Hz; ω = loading frequency, Hz; a(T) = shift factor as a function of temperature; and T = temperature. The shift factors are a function of temperature. Various equations such as the Arrhenius function and the Williams- Landel-Ferry equation have been recommended in an attempt E * E * E * log * (log ) E e r = + + + δ αβ γ ω1 to provide a rational explanation for the temperature depen- dency of the shift factors (6). In the MEPDG, the shift factors were expressed as a function of the binder viscosity to allow aging over the life of the pavement to be considered using the Global Aging Model developed by Mirza and Witczak (8). Equation 3 presents the shift factor relationship used in the MEPDG (2). (3) where a(T) = shift factor as a function of temperature and age η = viscosity at the age and temperature of interest = viscosity at the reference temperature of 70 °F, AASHTO T240 residue c = fitting parameter The viscosity as a function of temperature can be expressed using the viscosity-temperature relationship given in ASTM D 2493. log log η = A + VTS log TR (4) where η = viscosity, cP; TR = temperature, Rankine; A = regression intercept; and VTS = regression slope of viscosity-temperature relationship. Combining Equations 3 and 4 yields the shift factor as a function of temperature relationship used in the MEPDG for the construction of dynamic modulus master curves from laboratory test data. η70RTFOT log ( ) log( ) log( )a T c RTFOT[ ] = −[ ]η η70

7(5) where a(T) = shift factor as a function of temperature; TR = temperature, Rankine; = viscosity at the reference temperature of 70 °F, AASHTO T240 residue; A, VTS = viscosity-temperature parameters for AASHTO T240 residue; and c = fitting parameter. Substituting Equation 5 into Equation 2b and the result into Equation 1 yields the form of the dynamic modulus master curve relationship used in the MEPDG for the devel- opment of master curves from laboratory test data. (6) where = dynamic modulus; ω = loading frequency, Hz; TR = temperature, Rankine; = viscosity at the reference temperature of 70 °F, AASHTO T240 residue; A, VTS = viscosity-temperature parameters for AASHTO T240 residue; c = fitting parameter; δ = limiting minimum value of ; δ + α = limiting maximum value of ; and β, γ = parameters describing the shape of the sigmoidal function. The fitting parameters (α, β, δ, γ, and c) are determined through numerical optimization of Equation 6 using mixture test data collected in accordance with AASHTO TP62. Due to equipment limitations, neither the limiting maximum nor limiting minimum modulus can be measured directly; there- fore, these parameters are estimated through the curve fitting process. 2.3 Proposed Dynamic Modulus Master Curve Modification The modification proposed in this project is to estimate the limiting maximum modulus based on binder stiffness and mixture volumetric data using the Hirsch model developed in NCHRP Projects 9-25 and 9-31 (7). For a known limiting maximum modulus, the MEPDG master curve relationship given in Equation 6 reduces to: (7)log * ( ) log( ) log l E Max e c A VTS TR = + − + + + + − δ δβ γ ω1 10 og( )η70RTFOT⎡⎣ ⎤⎦{ } E * E * η70RTFOT E * log * log( ) log log( E e c A VTS TR = + + + + + − δ αβ γ ω η1 10 70RTFOT )⎡⎣ ⎤⎦{ } η70RTFOT log ( ) log( )loga T c A VTS TR RTFOT[ ] = −[ ]+10 70η where = dynamic modulus; ω = loading frequency, Hz; TR = temperature, Rankine; = viscosity at the reference temperature of 70 °F, AASHTO T240 residue; A, VTS = viscosity-temperature parameters for AASHTO T240 residue; Max = specified limiting maximum modulus; and α, β, γ and c-fitting parameters. The four unknown fitting parameters are still estimated using numerical optimization of the test data, but since the limiting maximum modulus is specified, data at low test temperatures are no longer needed. Equations 8 and 9 present the Hirsch model, which allows estimation of the modulus of the mixture from binder stiff- ness data and volumetric properties of the mixture. (8) where (9) = dynamic modulus of the mixture, psi; VMA = Voids in mineral aggregates, %; VFA = Voids filled with asphalt, %; and = dynamic shear modulus of binder, psi. Based on research conducted during the Strategic Highway Research Program (SHRP), all binders reach a maximum shear modulus of approximately 1 GPa or 145,000 psi (6). Substituting this value into Equations 8 and 9 yields the rec- ommended equation for estimating the limiting maximum modulus of asphalt concrete mixtures from volumetric data. (10) ,+ 435 000 VFA VMA VMA ×⎛⎝⎜ ⎞⎠⎟ ⎤⎦⎥ + − − ⎛⎝⎜ ⎞⎠⎟10 000 1 1 100 , Pc 4 200 000, , + ⎡ ⎣ ⎢⎢⎢⎢ ⎤ ⎦ ⎥⎥⎥⎥ VMA 435,000(VFA) | * | , ,maxE Pc= − ⎛⎝⎜ ⎞⎠⎟4 200 000 1 100 VMA⎡ ⎣⎢ | * |G binder E * P G G c = + ×⎛⎝ ⎞⎠ + × 20 3 650 3 0 58VFA VMA VFA binder| * | | . * | .binder VMA ⎛⎝ ⎞⎠ 0 58 | * | , , | * | E P Gc mix bind VMA = − ⎛⎝⎜ ⎞⎠⎟ +4 200 000 1 100 3 er VFA x VMA VMA 10 000 1 1 100 , ⎛⎝⎜ ⎞⎠⎟⎡⎣⎢ ⎤ ⎦⎥ + − − ⎛⎝ Pc ⎜ ⎞⎠⎟ + ⎡ ⎣ ⎢⎢⎢⎢ ⎤ ⎦ ⎥⎥⎥4 200 000 3, , | * | VMA VFA binderG ⎥ η70RTFOT E *

83,000,000 3,100,000 3,200,000 3,300,000 3,400,000 3,500,000 3,600,000 3,700,000 3,800,000 3,900,000 4,000,000 9 11 13 15 17 19 21 VMA, % Li m iti ng D yn am ic M od ul us , p si VFA = 55% VFA = 70% VFA = 85% Figure 2. Limiting maximum dynamic modulus values from the Hirsch model. where (11) max = limiting maximum mixture dynamic modulus; VMA = voids in mineral aggregates, %; and VFA = voids filled with asphalt, %. Figure 2 presents limiting maximum moduli computed using Equation 10 for VMA ranging from 10 to 20 percent, and VFA ranging from 55 to 85 percent. For this wide range of volumetric properties, the limiting maximum modulus varies from about 3,000,000 to 3,800,000 psi. These limiting maximum modulus values appear very rational. For condi- tions with low VMA and high VFA, the limiting maximum modulus approaches 4,000,000 psi, which is often assumed for the modulus of portland cement concrete. 2.4 Comparison of Master Curves Using Complete and Reduced Data Sets This section presents comparisons of master curves fitted to actual laboratory test data using the complete AASHTO TP62 data and a reduced data set where test data at the low- est temperature are eliminated and replaced with an estimate of the limiting maximum modulus from the Hirsch model. E * Pc = +( ) + 20 650 0 58435,000(VFA ) VMA 435,000(VFA) . VMA( )0 58. For the comparison, the database of dynamic modulus meas- urements assembled for NCHRP Project 9-19 was used (9). This database includes test data from replicate samples tested at temperatures of 15.8, 40, 70, 100, and 130°F and frequen- 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- tion. The mixtures include 5 mixtures from the MNRoad project, 11 mixtures from the FHWA Pavement Testing Facility, and 6 mixtures from the WesTrack project. This combination of mixtures includes a range of nominal maxi- mum aggregate sizes, binders, and volumetric properties. For each mixture included in Table 1, master curves were developed using the MEPDG master curve. Data from all temperatures were used to develop the AASHTO TP62 mas- ter curves, while the reduced data set excluded the data at 15.8°F and included an estimate of the limiting maximum modulus from the Hirsch model. The master curves then were compared graphically. The rationality of the master 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- ment Testing Facility and is an example of the worst agree- ment between the two methods. The limiting maximum modulus from the reduced data set at 3,236,868 psi is much lower than the 6,714,030 psi limiting maximum modulus from the AASHTO TP62 data set. The difference in the lim- iting maximum modulus also affects the limiting minimum modulus because the sigmoidal master curve is symmetrical. The limiting minimum modulus from the reduced data set is

9Description Mix Volumetric Properties AASHTO T240 Residue Binder Properties Project Project ID Binder Mix Type AC, % Va, % VMA, % VFA, % A VTS RTFOT70 , 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 Table 1. Properties of mixtures used in the master curve comparison study. 1,000 10,000 100,000 1,000,000 10,000,000 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 E* , p si 15.8 F 40 F 70 F 100 F 130 F AASHTO TP62 REDUCED SET -6 -4 -2 0 2 4 6 0 50 100 150 Temperature, F Lo g Sh ift F ac to r AASHTO TP62REDUCED SET Figure 3. Comparison of fitted master curves for Lane 2 from the FHWA Pavement Testing Facility higher, 16,826 psi compared to 2,222 psi for the AASHTO TP62 data set. Both approaches fit the measured data well over the temperature range from 40 to 130°F and the shift fac- tors for the two approaches are essentially the same. Figure 4 is for Cell 17 at the MNRoad project, and is an example of best agreement between the two methods. In this case, the two approaches yield essentially the same master curves. To compare master curves for all of the mixtures, dynamic moduli were calculated for temperatures ranging from −30 to 150°F using loading rates of 25, 10, 1, 0.1, and 0.01 Hz. The results are shown in Figure 5. As shown, the two approaches

10 -6 -4 -2 0 2 4 6 0 50 100 150 Temperature, F Lo g Sh ift F ac to r AASHTO TP62REDUCED SET 1,000 10,000 100,000 1,000,000 10,000,000 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 E* , p si 15.8 F 40 F 70 F 100 F 130 F AASHTO TP62 REDUCED SET Figure 4. Comparison of fitted master curves for Cell 17 from the MNRoad. 1,000 10,000 100,000 1,000,000 10,000,000 1,000 10,000 100,000 1,000,000 10,000,000 E* From AASHTO TP 62 Data Set, psi E* F ro m R ed uc ed D at a Se t, ps i Figure 5. Comparison of dynamic moduli computed from master curves. yield the same moduli over the range of the measured data, but sometimes yield differences at high and low moduli pri- marily due to differences caused by the maximum limiting modulus. Figure 6 compares limiting maximum moduli from the two data sets. As shown, the AASHTO TP62 data set yields unrealistically high moduli in four cases, ALF 2, ALF 3, ALF 10, and ALF 11. It also yields unrealistically low values in two cases, ALF 8 and WSTR 2. Table 2 summarizes limiting maximum modulus values averaged over similar mixtures. As shown, the two data sets produce reasonably similar average limiting maximum modulus values except for the ALF mixtures, which had four unrealistically high values in the AASHTO TP62 data set. The quality of the data for the low temperature test condition has a major impact on the limiting maximum modulus in the MEPDG master curve equation. Pellinen reported significantly greater vari- ability for data collected at 15.8 °F and 130°F as summarized Table 3 (9). As reported by Pellinen, strain levels for the 15.8°F data were significantly lower than those at other

11 0 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000 7,000,000 8,000,000 AL F1 AL F2 AL F3 AL F4 AL F5 AL F7 AL F8 AL F9 AL F1 0 AL F1 1 AL F1 2 M N 16 M N 17 M N 18 M N 20 M N 22 W ST R2 W ST R4 W ST R7 W ST R1 5 W ST R2 3 W ST R2 4 Section M ax im um M od ul us , p si AASHTO TP62 Reduced Set Figure 6. Comparison of limiting maximum moduli. Limiting Maximum Modulus, psi Mixture Number AASHTO TP62 Reduced Set MNRoad 5 3,109,668 3,206,382 ALF 19 mm 9 3,867,636 3,077,348 ALF 25 mm 2 4,735,721 3,324,313 WesTrack 19 mm Fine 3 2,985,757 3,187,770 WesTrack 19 mm Coarse 3 2,934,664 3,345,151 All Mixtures 22 3,526,808 3,180,702 Table 2. Limiting maximum modulus values averaged over mixture type. Pooled Between Specimen Coefficient of Variation, % Temperature, F 12.5 mm Mixtures 19.0 mm Mixtures 15.8 16.7 25.4 40.0 12.8 19.0 70.0 14.2 9.4 100.0 14.5 20.3 130.0 28.1 22.7 Table 3. Dynamic modulus variability reported by Pellinen (9). temperatures (9). This coupled with potential friction in the linearly variable differential transformer (LVDT) guide rod used included in the AASHTO TP62 recommended instru- mentation is the most likely cause of the high variability in the low temperature measurements. This probably also explains the unrealistically high moduli measured for four of the ALF mixtures. The limiting maximum modulus also affects the limiting minimum modulus because of the symmetry inherent to the MEPDG dynamic modulus master curve. Figure 7 compares limiting minimum modulus values from the two data sets for individual mixtures. As shown the largest differences between the two occur for the same mixtures that have the largest differences in the limiting maximum modulus. Table 4 summarizes limiting minimum modulus values averaged over similar mixtures. The two data sets produce reasonably similar average limiting minimum modulus values. The limiting minimum modulus represents the stiff- ness of the aggregate structure in the absence of binder. Both procedures provide the same rankings for the mixtures com- pared in this evaluation. 2.5 Abbreviated Dynamic Modulus Master Curve Testing Conditions The previous section showed that reasonable dynamic modulus master curves can be obtained using an estimated limiting maximum modulus and data collected at tempera- tures of 40, 70, 100, and 130°F and frequencies of 25, 10, 5, 1.0, 0.5, and 0.1 Hz. However, these temperatures and load- ing rates are not optimal for use with the estimated limiting maximum modulus approach. This section presents an analysis of the temperatures and loading rates that should be used in combination with an estimated limiting maximum modulus to develop dynamic modulus master curves. The optimum approach for fitting the S shaped sigmoidal function is to obtain data defining the limiting maximum modulus, the limiting minimum modulus, and the slope over the middle portion of this range on a log scale. Unfortunately, the limiting moduli cannot be obtained directly by testing as these would require tests at extremely low and high tempera- tures. Therefore, the approach taken in AASHTO TP62 is to collect data over a wide temperature range and essentially

12 0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 AL F1 AL F2 AL F3 AL F4 AL F5 AL F7 AL F8 AL F9 AL F1 0 AL F1 1 AL F1 2 MN 16 MN 17 MN 18 MN 20 MN 22 WS TR 2 WS TR 4 WS TR 7 WS TR 15 WS TR 23 WS TR 24 Section M in im um M od ul us , p si AASHTO TP62 Reduced Set Figure 7. Comparison of limiting minimum moduli. Limiting Minimum Modulus, psi Mixture Number AASHTO TP62 Reduced Set MNRoad 5 4,383 3,873 ALF 19 mm 9 11,247 11,044 ALF 25 mm 2 14,092 13,426 WesTrack 19 mm Fine 3 16,589 14,077 WesTrack 19 mm Coarse 3 19,101 15,569 Overall 22 11,745 10,662 Table 4. Limiting minimum modulus values averaged over mixture type. extrapolate these data to define the limiting maximum and minimum moduli. As shown in this evaluation, the AASHTO TP62 approach is sensitive to the quality of the data at the lowest temperature, which is often variable, and potentially in- accurate due to testing difficulties. For the same intermediate- and high-temperature data, high-limiting maximum moduli result in lower limiting minimum moduli while low-limiting maximum moduli result in higher limiting minimum moduli due to the symmetry of the MEPDG master curve equation. In the alternate approach developed in Phase IV of NCHRP Project 9-29, a reasonable, rational estimate of the limiting maximum modulus is provided by the Hirsch model. This eliminates the need for testing at low temperatures, and the potential inaccuracies caused by these difficult testing condi- tions. To provide an accurate estimate of the limiting mini- mum modulus, data should be collected to the slowest reduced frequency possible. From Equation 2, the reduced frequency is a function of both temperature and frequency of loading. High temperature, slow frequency dynamic modulus tests result in the lowest reduced frequency values. The AASHTO TP62 test- ing conditions yielded minimum reduced frequencies for the mixtures studied ranging from 10−3 to 10−4 Hz. The most efficient way to decrease the reduced frequency in the testing program is to increase temperature; however, for the glued gage point instrumentation used in the dynamic modulus test, the maximum testing temperature appears to be approxi- mately 104°F. Above this temperature, the gage points may loosen, particularly when the gage points are attached to the matrix of fine aggregate and binder. Higher temperatures may be possible when stiff modified binders are used or the gage points are attached to the coarse aggregate, but this can not be assured in most mixtures. Figure 8 presents experimentally determined shift factors for the mixtures included in this eval- uation. As shown, the shift factors for the maximum recom- mended testing temperature of 104°F range from about 10−1.8 to 10−2.5. From Equation 2, this results in a loading frequency of approximately 0.03 to 0.06 Hz at 104 °F to obtain reduced frequencies ranging from 10−3 to 10−4 Hz. Thus, the use of a loading rate of 0.01 Hz at 104°F will provide somewhat lower reduced frequencies than obtained with 0.1 Hz at 130°F as specified in AASHTO TP62. Because the shift factor relationship is not linear, a mini- mum of three temperatures spaced as widely as possible should be used in the testing program. This will provide a rea- sonable estimate of the coefficient, c, in the shift factor rela- tionship, Equation 3. A low testing temperature of 40°F would allow reasonable priced environmental chambers to be used, and will eliminate the icing problems that occur when testing at temperatures below freezing. The recommended testing temperatures for the abbrevi- ated dynamic modulus master curve testing are 40, 70, and 104°F. Based on the performance of typical LVDT deforma- tion systems, the maximum frequency of loading should be limited to 10 Hz. Using loading frequencies of 10, 1, 0.1, and 0.01 Hz at each of the temperatures results in well spaced data in reduced frequency with a minimum of overlap. This

13 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 0 10 20 30 40 50 60 70 80 90 110 120100 130 140 Temperature, F Lo g Sh ift F ac to r Figure 8. Shift factors as a function of temperature for the mixtures in Table 2. is shown in Figure 9, based on the average shift factors at 40 and 104°F shown in Figure 8. The recommended testing temperatures and frequencies for the abbreviated dynamic modulus master curve testing result in data over the range of reduced frequency at 70°F from approximately 10−4 to 105 with a small overlap of the high and low temperature data with the reference temperature data. The SPT software applies 20 cycles at each loading frequency. The first 10 cycles are used to adjust the load to produce strains within the specified 75 to 125 μstrain range. The data from the 1.0E-07 1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 30 40 50 60 70 80 90 100 110 Temperature, F R ed uc ed F re qu en cy , H z Figure 9. Approximate reduced frequencies for abbreviated dynamic modulus master curve testing sequence.

14 Specimen 1 Specimen 2 Temp, F Frequency, Hz Modulus, ksi Phase, Degree Modulus, ksi Phase, Degree 40 0.01 771.6 25.0 901.1 23.7 40 0.1 1274.9 19.0 1496.1 17.9 40 1 1861.7 13.9 2164.1 12.8 40 10 2458.2 9.6 2811.0 8.6 70 0.01 161.0 30.0 174.6 29.6 70 0.1 362.7 29.2 398.3 29.2 70 1 771.7 24.5 844.4 24.3 70 10 1332.1 18.0 1446.0 18.0 104 0.01 23.3 24.4 28.3 22.9 104 0.1 50.8 27.8 53.4 27.9 104 1 137.8 29.4 140.9 29.5 104 10 336.2 29.7 352.8 29.9 Table 5. Dynamic modulus test data collected using the abbreviated dynamic modulus master curve testing. second 10 cycles are then collected and used to compute the dynamic modulus and phase angle. The loading frequencies recommended in this document will require approximately 40 min per specimen at each testing temperature, including time for specimen instrumentation and chamber tempera- ture equilibrium. Thus, a testing program including three replicate specimens will require approximately 2 hours per tem- perature for data collection. 2.6 Arrhenius Shift Factor Relationship Equation 7 presented the modified form of the MEPDG master curve equation used to generate a dynamic modulus master curve using the proposed abbreviated testing. This equation requires knowledge of the viscosity-temperature relationship of the binder used in the mixture. For mixture evaluation, the binder viscosity-temperature relationship may not be known. A dynamic modulus master curve can still be developed using an alternative shift factor relationship based on the Arrhenius equation given in Equation 12. (12) where a(T) = shift factor at temperature T; Tr = reference temperature, °K; T = test temperature, °K; and ΔEa = activation energy (treated as a fitting parameter). Using Equation 12 for the shift factors, the dynamic mod- ulus master curve equation for use with proposed abbreviated testing procedure becomes: (13) where = dynamic modulus; ω = loading frequency, Hz; Tr = reference temperature, °K; T = test temperature, °K; Max = specified limiting maximum modulus; and δ, β, γ and ΔEa = fitting parameters. 2.7 Example Using the Abbreviated Dynamic Modulus Master Curve Testing This section illustrates the development of master curves using the proposed procedure. The mixture that was tested was a coarse graded 9.5 mm limestone mixture made with a PG 70-22 binder. The viscosity-temperature susceptibility param- E * log * log . E e Ea T = + −( ) + + + ⎛⎝⎜ ⎞ δ δ β γ ω Max 1 19 14714 1Δ ⎠⎟ − ⎛⎝⎜ ⎞⎠⎟⎡⎣⎢ ⎤ ⎦⎥ ⎧⎨⎩ ⎫⎬⎭ 1 Tr log ( ) . a T E T T a r [ ] = −⎛⎝ ⎞⎠Δ19 14714 1 1 eters for the binder were: A= 10.299 and VTS = −3.426. The test specimens were compacted at the optimum asphalt content of 5.5 percent to 4.0 percent air voids. For this condition, the per- cent VMA was 15.8 and the percent voids filled with asphalt was 76.2. Table 5 presents dynamic modulus data measured on replicate samples using the combination of temperatures and loading rates recommended in the abbreviated testing protocol. The first step for fitting the master curve is to estimate the limiting maximum modulus using Equation 10. For a mixture with a VMA of 15.8 percent and a VFA of 76.2 per- cent, the limiting maximum modulus from Equation 10 is 3,376,743 psi. Using this value of the limiting maximum mod- ulus, the viscosity-temperature susceptibility parameters, and the measured data, the master curve parameters can be obtained through numerical optimization of Equation 7. The optimization can be performed using the Solver function in Microsoft EXCEL®. This is done by setting up a spreadsheet to compute the sum of the squared errors between the loga- rithm of the measured dynamic moduli and the values pre- dicted by Equation 7. The Solver function is used to minimize the sum of the squared errors by varying the fitting parame- ters in Equation 7. The following initial estimates are recom- mended: δ = 0.5, β = −1.0, γ = −0.5, and c = 1.2. The master curve developed from this example data is shown in Figure 10. The goodness of fit statistics show Equation 7 provides an excellent fit to the measured data with an R2 greater than 0.99 and an Se/Sy less than 0.04. Using the abbreviated tempera- tures and loading rates, the measured data cover approxi- mately 80 percent of the range defined by the fitted limiting minimum and computed limiting maximum moduli. 2.8 Summary and Draft Standard Practice An abbreviated testing protocol for developing dynamic modulus master curves for routine mixture evaluation and flexible pavement design was developed in Phase IV of NCHRP

15 1,000 10,000 100,000 1,000,000 10,000,000 1.0E-06 1.0E-04 1.0E-02 1.0E+00 1.0E+02 1.0E+061.0E+04 Reduced Frequency, Hz E* , ps i 40 F 70 F 104 F FIT -3 -2 -1 0 1 2 3 30 50 70 90 110 Temperature, F Lo g Sh ift F ac to r Min = 4,259 psi Max = 3,376,744 psi R2 = 0.9978 Se/Sy = 0.038 Figure 10. Example master curve using abbreviated testing sequence. cost of the environmental chamber for the testing system, and increases the complexity of testing. Moisture condensation and icing make testing at this temperature challenging even for highly experienced technicians. To aid in implementation of the abbreviated dynamic modulus testing protocol, a draft standard practice titled “Developing Dynamic Modulus Master Curves for Hot-Mix Asphalt Concrete Using the Simple Performance Test Sys- tem” was prepared. This draft standard practice is presented in Appendix A. Project 9-29. This abbreviated testing protocol requires testing at 40, 70, and 104°F using loading frequencies of 10, 1, 0.1, and 0.01 Hz. The data can be fit to the MEPDG dynamic modulus equation after an estimate of the limiting maximum modulus is made using the Hirsch model. The abbreviated dynamic modulus master curve testing protocol eliminates the lowest temperature in the AASHTO TP62 testing sequence and opti- mizes the temperatures and loading frequencies for minimal overlap to the modulus data. Testing at the lowest temperature in the AASHTO TP62 sequence, 14 °F, greatly increases the

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Refining the Simple Performance Tester for Use in Routine Practice Get This Book
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TRB's National Cooperative Highway Research Program (NCHRP) Report 614: Refining the Simple Performance Tester for Use in Routine Practice explores the develop of a practical, economical simple performance tester (SPT) for use in routine hot-mix asphalt (HMA) mix design and in the characterization of HMA materials for pavement structural design with the Mechanistic-Empirical Pavement Design Guide.

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