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83 where, In Chapter 3, a practical definition of a long-life or per- FC = fatigue cracking (% of lane area), petual pavement is one able to withstand 500 million axle C1 = 2 C2, repetitions in a 40-year period without failing. A shift fac- C2 = 2.40874 39.748 x (1+hac)2.85609 tor of 10 was assumed, resulting in a laboratory equivalent of hac = thickness of the HMA (in.), 50 million repetitions. Based on the analyses in this section, a D = cumulative theoretical fatigue damage, %. shift factor of 10 appears reasonable. Varying the shift factor when determining the endurance limit is not recommended. Solving Equation 42 for a 5-in.-thick pavement, a cumula- tive damage of 0.294 (29.4%) corresponds to 20% cracking of Sensitivity of Mechanistic-Empirical the lane area. Considering the predicted cracking described Pavement Design Methods above and back-calculating the corresponding cumulative to the Endurance Limit damage, the shift factor would be approximately 1.0 for Sec- tion N1, and approximately 0.73 for Section N2. Four sensitivity analyses were conducted to assess the impact of the endurance limit on pavement design. The first analysis compared pavement design thicknesses using conventional Summary of Observed Shift Factors from and perpetual design procedures. The second analysis looked 2003 NCAT Test Track Structural Sections at the sensitivity of perpetual designs to the measured value of The observed shift factors based on the performance of the the endurance limit. The traffic and materials from the 2003 2003 NCAT Test Track structural sections are summarized in NCAT Test Track were used in the first two analyses. Since Table 7.14. Based on the measured strains and the PerRoad the NCAT Test Track used a limited range of axle weights, the analyses, the shift factor for the PG 67-22 mix at optimum third and fourth analyses were performed using the materials asphalt content exceeds the assumed shift factor of 10.0. The from the 2003 NCAT Test Track but the MEPDG's default shift factors for the PG 76-22 mix at optimum asphalt con- truck traffic classification No. 1 for principal arterials. The tent, represented by Section N1, from both the measured third and fourth analyses repeated the first two analyses with strain and PerRoad analyses, are less than 10.0. The beam a distribution of axle types and weights that are representa- fatigue results for the PG 76-22 mix were variable, with some tive of typical traffic on a principal arterial. long fatigue lives observed at relatively high strain levels (see Table 4.4). This same variability resulted in a reduced 95% NCAT Test Track Traffic prediction limit of the endurance limit. The shift factor for Section N8, the PG 67-22 mix at optimum plus binder content, The 2003 NCAT Test Track pavement section was designed is slightly less than 10.0; however, this analysis was based on using three methodologies: 1993 AASHTO procedure, MEPDG several assumptions regarding the measured strains once slip- Version 1.0, and PerRoad Version 3.3. The 1993 AASHTO page between the layers occurred. design was conducted using a change in pavement service- The fatigue equations developed from the laboratory testing ability index (PSI) = 1.2, design reliability = 95%, and an were not used in the MEPDG, rather the NCHRP 1-37A cal- overall standard deviation = 0.45 for 200 million ESALs, the ibrated fatigue models (64) were used. Based on these analyses, expected traffic over a 40-year period. The structural number the MEPDG fatigue model reasonably predicts the observed was determined from the AASHTO design equation (42) nu- cracking. However, design is based on the predicted cracking merically using the bisection method. Two design subgrade at some level of reliability being less than 25% area cracking. Mr values were used in the analysis, 5,500 psi used in the orig- The 90% reliability cracking in Sections N1 and N2 exceeded inal design of the 2000 Track (72), and 14,000 psi, the value the observed cracking by 91% and 68%, respectively. from Table 7.9 used in the perpetual designs. Layer coefficients Table 7.14. Summary of observed shift factors. Section Measured Strain PerRoad MEPDG N1 4.2 6.7 1.0 N2 75.8 19.2 0.73 N6 38.0 17.6 * N8 8.3 NA NA Notes: *Since the MEPDG bases failure on 20% cracking and this did not occur in Section N6, shift factor could not be calculated. NA = Not applicable; no attempt was made to model debonding as part of this research.

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84 of 0.14 and 0.44 were assigned to the granular base and The results are summarized in Figure 7.8. All three MEPDG HMA, respectively. design thicknesses are less than that determined from the 1993 AASHTO Pavement Design Guide. Although the 20-year and log10W18 = Z R So + 9.36 log10 ( SN + 1) - 20 perpetual MEPDG designs are the same thickness, the impli- cations are significantly different. In the first case, at 90% PSI reliability, bottom-up cracking over 20% of the lane area log10 + 4.2 - 1.5 + 2.32 log M - 8.07 (43) would be expected after 20 years; in the second case, no crack- 10 R 1094 0.40 + ing would be expected after 40 years. This is further illustrated (SN + 1) 5.19 in Table 7.15 where pavement thickness was iterated in the MEPDG without specifying an endurance limit and the result- where, ing damage determined. Thicknesses of 39 in. and 35 in. were W18 = the number of expected 18-kip ESALs in the design required for the PG 67-22 and PG 76-22 mixes at optimum lane over the design life 200 106, asphalt content to achieve predicted cracking performance ZR = the normal deviate associated with the chosen level similar to that achieved when an endurance limit was con- of reliability, 90% = -1.28, sidered (for maximum cracking of 0% to be predicted at the S0 = materials standard deviation, 0.45, end of 40 years). Some damage was predicted in all of the cases SN = structural number, tested, including 1.45% bottom-up cracking at 90% reliabil- PSI = initial minus terminal serviceability, 1.2, and ity, which was predicted to occur in the first month of service. MR = effective soils resilient modulus, psi. It was expected that the PerRoad perpetual thickness would be less than that determined with the MEPDG. This expecta- MEPDG analyses were performed using the inputs described tion was based on the differences in the manner in which both previously. The three scenarios examined included 20-year and programs handle pavement temperatures. For PerRoad, up 40-year designs with 90% reliability of bottom-up cracking of to five seasons can be specified, with corresponding moduli less than 25% of the total lane area, and a 40-year perpetual for each season. Typically, this would be based on grouping analysis where the pavement thickness was selected to provide average monthly temperature data. In this analysis, actual maximum damage and cracking = 0% at the end of 40 years. temperature data from the 2003 NCAT Test Track cycle were The PerRoad analyses were performed using the inputs grouped and used in the analyses. This most likely resulted in described previously. Both the MEPDG and PerRoad perpet- higher temperatures being selected for the warmer season, ual analyses used the respective one-sided 95% lower predic- which results in correspondingly lower design moduli. Dur- tion limits of the endurance limit for the PG 67-22 (151 ms) ing PerRoad's Monte Carlo simulations, modulus is allowed to and PG 76-22 (146 ms) mixes at optimum asphalt content vary within a season based on a log-normal distribution. The determined in Phase I of this study. The design thickness was default coefficient of variation used in this study is 30%. For selected such that approximately 95% of the load applications the MEPDG, temperatures are predicted using the Enhanced were less than the endurance limit (85). Integrated Climatic Model on an hourly basis. They are then 20 18 18 18 PG 67-22 16 16 16 14.5 14.5 PG 76-22 HMA Thickness, in. 14 13 12 11 11 11 10 10 10 8 6 4 2 0 AASHTO 93, AASHTO 93, M-E PDG, 20 M-E PDG, 40 M-E PDG PerRoad Mr = 5,500 psi Mr = 14,000 yr. yr. Perpetual Perpetual psi Figure 7.8. Comparison of pavement thicknesses from empirical, M-E, and perpetual design methodologies.

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85 Table 7.15. Damage as a function of pavement thickness for the MEPDG with no endurance limit. PG 67-22 at Optimum PG 76-22 at Optimum 90% 90% Reliability, Reliability, HMA Maximum Maximum Bottom- Maximum Maximum Bottom- Thickness, Damage, Cracking, Up Damage, Cracking, Up In. % % Cracking % % Cracking 10 11.5 9.07 27.18 11 14.5 11.4 29.51 6.57 5.28 23.29* 12 8.92 7.21 25.31 13 5.67 4.61 22.45* 15 2.47 1.99 6.52 20 0.442 0.34 1.79 0.195 0.14 1.59 22 0.109 0.08 1.53 23 0.0838 0.06 1.51 25 0.112 0.08 1.53 0.0501 0.03 1.48 27 0.031 0.02 1.47 30 0.0352 0.02 1.47 0.0159 0.01 1.46 33 0.0191 0.01 1.46 35 0.0132 0.01 1.46 0.00601 0* 1.45 37 0.00927 0.01 1.45 38 0.00782 0.01 1.45 39 0.00664 0* 1.45 40 0.00564 0 1.45 0.00258 0 1.45 41 0.00481 0 1.45 42 0.00413 0 1.45 45 0.00264 0 1.45 Note: *Indicates minimum thickness with cracking less than 25% of total lane area at the end of the design life. collected into five "bins" on a monthly basis for determination The second set of analyses examined the sensitivity of the of layer moduli. This would be expected to result in higher MEPDG and PerRoad to the measured endurance limit using temperatures occurring at some points during the year and, the NCAT Test Track traffic. Pavement design simulations hence, lower moduli and higher strains. were conducted using both the PG 67-22 and PG 76-22 mixes A second difference that may have affected the MEPDG at optimum asphalt content, the previously described pave- versus the PerRoad results is the way that the layers were sub- ment design parameter, and three levels of the endurance divided for calculation purposes. For the PerRoad analysis, limit: 70 ms, 100 ms, and the measured endurance limits (151 the HMA was treated as a single layer. The pavement temper- and 146 ms, respectively). The results, illustrated graphically ature was calculated according to Equation 44 (86). in Figures 7.9 and 7.10 for the PG 67-22 and PG 76-22 mixes, respectively, indicate that the perpetual pavement design MMPT = 1.05 MMAT + 5 (44) thickness is extremely sensitive to the measured endurance where, MMPT = mean monthly pavement temperature, F and 30 MMAT = mean monthly air temperature, F. HMA Thickness, in. 25 25 20 20 Equation 44 is representative of the average temperature of 19 16.5 the HMA layer for pavement 10 in. thick. By comparison, the 15 15 10 11 10-in.-thick MEPDG section was subdivided (automatically) into seven layers, the top 0.5 in., the next 0.5 in., three 1.0-in. 5 M-E PDG Per Road sublayers, a 4.0-in. sublayer and a bottom 2.0-in. sublayer. 0 Pavement temperatures and corresponding moduli were cal- 50 100 150 200 Endurance Limit, micro-strains culated for each of these layers. The net result of this is that the temperature of the bottom 2-in. layer tends to be lower, result- Figure 7.9. Sensitivity of pavement thickness to ing in a higher layer moduli, and, therefore, lower strains. endurance limit for PG 67-22 mixes.

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86 30 the previously described pavement design parameters, and HMA Thickness, in. 25 24 three levels of the endurance limit: 70 ms, 100 ms, and the 20 20 measured (151 ms) endurance limit. 15 16 16 The MEPDG's Level 3 default truck traffic classification 13 10 10 No. 1 and associated axle weight distributions for principal 5 arterials were used for the load spectra. The MEPDG pro- M-E PDG Per Road duces a file that records the accumulated ESALs on a monthly 0 50 100 150 200 basis throughout the design life of the project. For the NCAT Endurance Limit, micro-strains Test Track traffic, the MEPDG calculated 171,514,458 ESALs at the end of 40 years, assuming no growth. The average annual Figure 7.10. Sensitivity of pavement thickness to endurance limit for PG 76-22 mixes. daily truck traffic (AADTT) was adjusted using the Level 3 default truck traffic classification No. 1 to produce a similar number of ESALs after 40 years (171,561,129). An AADTT of 21,833 with a 50% directional split, two lanes in each direc- limit. The use of polymer modified PG 76-22 has a more sub- tion, and 90% of the trucks in the design lane were used for stantial impact on pavement thickness with the MEPDG, as the calculations. compared to PerRoad with the difference in thickness ranging Traffic can be defined in PerRoad in two manners: FHWA between 1.0 and 3.0 in., depending on the endurance limit. vehicle class using default axle weight distributions or axle Larger differences were observed with lower endurance limits. weight distribution by type (single, tandem, etc.). The MEPDG default truck traffic classification No. 1 was converted to the Typical Principal Arterial format used by PerRoad. The axle load configuration con- Truck Traffic Classification sisted of 9,824 axle groups per day in the design lane, of which The third and fourth set of analyses examined the sensitiv- 45.2% were single axles, 54.3% were tandem axles, and 0.5% ity of the MEPDG and PerRoad to the measured endurance were tridem axles. The load spectra for the three axle types are limit using a normal load spectra that might be expected on shown in Figure 7.11. a principal arterial. Pavement design simulations were con- Figure 7.12 shows the sensitivity of the MEPDG and Per- ducted using the PG 67-22 mix at optimum asphalt content, Road to the measured endurance limit. Both the MEPDG and 30% 25% 20% Frequency, % 15% 10% 5% 0% 0 10 20 30 40 50 60 70 80 90 10 11 , ,0 ,0 ,0 ,0 ,0 ,0 ,0 , 0, 0, 00 00 00 00 00 00 00 00 00 00 00 0 0 0 0 Axle Weight, lbs Single Tandem Tridem Figure 7.11. Axle weight distribution used in PerRoad.

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87 40 35 35 30 HMA Thickness, in. 27 25 20 20 19 15 16 12.5 10 5 ME-PDG Per Road 0 50 100 150 200 Endurance Limit, micro-strains Figure 7.12. Sensitivity of pavement thickness to the endurance limit for typical axle distribution. PerRoad are sensitive to changes in the measured endurance endurance limit. For the MEPDG, the thickness that resulted limit. For the MEPDG, a change in the endurance limit of in at least 90% reliability against both bottom-up and top- 50 ms results in a change in pavement thickness of approxi- down fatigue cracking was determined. Figure 7.13 shows mately 7 to 8 in. For PerRoad, a change in the endurance limit a comparison of the conventional and perpetual design of 50 ms results in a change in pavement thickness of approx- thicknesses. imately 4 in. This sensitivity highlights the need to measure The PerRoad perpetual design using the measured endur- the endurance limit as accurately as possible. ance limit of 151 ms is slightly less thick than the 40-year Finally, design thicknesses were determined using the empirical design using the 1993 AASHTO Design Guide. The MEPDG and 1993 AASHTO Pavement Design Guide using MEPDG thicknesses considering only fatigue cracking are sim- design lives of both 20 and 40 years without considering an ilar to the PerRoad thickness. However, at an 11-in. pavement 20 19 18 16 14 14 13 HMA Thickness, in. 12.5 12 12 11 10 8 6 4 2 0 AASHTO 93, AASHTO 93, M-E PDG, M-E PDG, M-E PDG PerRoad 20-yr. 40-yr. 20-yr. 40-yr. Perpetual Perpetual Figure 7.13. Comparison of pavement thicknesses from empirical, M-E, and perpetual design methodologies for typical axle distribution.