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Validating the Fatigue Endurance Limit for Hot Mix Asphalt (2010)

Chapter: Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit

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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
×
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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
×
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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
×
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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
×
Page 77
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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
×
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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
×
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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
×
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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
×
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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
×
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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
×
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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
×
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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
×
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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
×
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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
×
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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
×
Page 88
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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
×
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Suggested Citation:"Chapter 7 - Sensitivity of Pavement Thickness to the Endurance Limit." National Academies of Sciences, Engineering, and Medicine. 2010. Validating the Fatigue Endurance Limit for Hot Mix Asphalt. Washington, DC: The National Academies Press. doi: 10.17226/14360.
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73 Summary of Predicted Endurance Limits Estimates of the endurance limit were obtained from beam fatigue tests, uniaxial tension tests, and analysis of field per- formance. Table 7.1 summarizes the endurance limit predic- tions from the beam fatigue and uniaxial tension tests. An analysis of LTPP data, presented in Chapter 6, indicated an endurance limit of 65 ms. There appears to be good corre- lation between the beam fatigue estimates of the endurance limit determined in Phase I and those determined during the mini round-robin analysis. Based on the predicted val- ues determined from testing at NCAT and the Asphalt Insti- tute, stiffer high-temperature binder grades and optimum plus asphalt contents produce higher endurance limit values. The 95% lower prediction limit samples follow the same gen- eral trend. The prediction of the endurance limit from the round-robin data shows small differences based on binder grade and asphalt content. The rankings from the uniaxial tension tests are the reverse of those determined from the beam fatigue tests. For the uniaxial tension tests, the PG 76-22 mixes generally result in lower estimates of the endurance limit. This appears to be the opposite of field experience with polymer modified binders, illustrated in Figures 6.21 and 6.22. There are a number of potential reasons for the differences observed between beam fatigue and uniaxial tension testing. There were very few uni- axial replicates tested, especially compared with the number of beams tested. In some cases, the trends are based on results from only one or two samples. Early in the uniaxial testing, there were a number of problems with end failures. Speci- men fabrication was altered to reduce this problem. Finally, the modes of loading uniaxial and beam fatigue samples are different. To date, the basic research has not been completed to understand the differences between the modes of loading or how the stress state changes with damage. The state of stress in pavements is not completely understood either. More effort is needed prior to considering this approach. Estimate of Shift Factors between Laboratory Tests and Field Performance In Chapter 3, calculations were provided to show that the maximum expected load repetitions in a 40-year period is approximately 500 million. Then, using a shift factor of 10 between laboratory and field performance, a limit of 50 mil- lion cycles was determined for the laboratory beam fatigue testing. The selection of a shift factor of 10 was based on rec- ommendations from SHRP (46). The structural sections from the 2003 NCAT Test Track provide an opportunity to verify the shift factors. Three methodologies were used to as- sess the shift factors for the 2003 NCAT Test Track structural sections: measured strains from in-place instrumentation, PerRoad, and the MEPDG. The NCAT Test Track was initially constructed in 2000. All of the sections of the 2000 track consisted of 19 in. of HMA (15 in. of which were the same dense-graded mixes for all of the sections and the remaining 4 in. that were the experi- mental mixes that varied between sections), 5 in. of perme- able asphalt-treated drainage layer, 6 in. of crushed aggregate base, and 12 in. of improved (AASHTO A-2) subgrade. The 2003 NCAT Test Track cycle included eight struc- tural sections. Three pavement sections were designed using the 1993 AASHTO Pavement Design Guide to carry approx- imately 1⁄3, 2⁄3, and the full 10 million ESAL loading (for that cycle). The design reliabilities are summarized in Table 7.2. The input parameters are summarized in Von Quintus (72). The eight structural sections were selected to evaluate pave- ment sections designed for varying levels of traffic, polymer modified and unmodified or neat asphalt binders, stone matrix asphalt (SMA), and rich bottom layer. All eight sec- tions were placed on 6 in. of granular base. The section lay- out is shown in Figure 7.1. The thin, medium, and thick pave- ment sections were constructed using both a neat PG 67-22 binder and a styrene-butadiene-styrene (SBS) polymer mod- ified PG 76-22. The 19.0-mm NMAS base course was used for C H A P T E R 7 Sensitivity of Pavement Thickness to the Endurance Limit

74 Beam Fatigue Beam Fatigue Round-Robin Uniaxial C versus S Uniaxial Increasing Amplitude Mix Predicted 95% Lower Confidenc e Limit Predicted 1 95% Lower Confidence Limit 2 Average 95% Lower Confidence Limit 2 Power Model Exponential Model Average for Loop Formation 3 Average Lowest for Loop Formation 3 PG 58-22 107 82 NA NA NA NA NA NA NA PG 64-22 89 75 NA NA NA NA NA NA NA PG 67-22 172 151 182 130 103 261 96 195 133 PG 67-22 Opt. + 184 158 176 141 121 194 64 223 150 PG 76-22 220 146 195 148 126 197 70 NA NA PG 76-22 Opt. + 303 200 NA NA NA 164 47 189 124 Notes: 1Calculated using the pooled data from the round-robin. 2Average of the 95% lower confidence limit calculated by each individual lab. 3Averages calculated based on individual specimen data not presented in Chapter 5. Table 7.1. Summary of estimates of the endurance limit (ms). Traffic HMA, In. Granular Base, In. Fill1, In. Structural Number Reliability at 10 Million ESALs Full 9 6 15 6.2 92% 2/3 7 6 17 5.4 68% 1/3 5 6 19 4.6 30% Note: 1Fill was placed from the top of the original improved subgrade to the bottom of the granular base to maintain the surface elevation of the structural sections with respect to the 2000 track. Table 7.2. 2003 NCAT Test Track structural section design reliabilities (72). 1 1 1 1 1 1 1 1 4 8 6 6 44 8 6 2 6 6 6 6 6 6 6 6 0 2 4 6 8 10 12 14 16 N1 N2 N3 N4 N5 N6 N7 N8 Th ic kn es s, in . Aggregate Base PG 67-22, 19.0 mm Opt+ PG 67-22, 19.0 mm NMAS PG 76-22 , 19.0 mm NMAS PG 76-22 SMA PG 67-22, 9.5 mm NMAS PG 76-22, 9.5 mm NMAS Figure 7.1. Layout of 2003 NCAT Test Track structural sections. the fatigue testing in this study with the same binders. For the seventh section, the 1-in. thick wearing course of the medium thickness design was replaced with SMA. SMA was also used as the wearing surface of the eighth section; in addition, the bottom 2 in. of the 19.0-mm base were replaced with a rich bottom layer containing an additional 0.5% asphalt (medium total thickness). For the 2003 track, loading was provided by five triple- trailer trucks and one five-axle single trailer (FHWA Class 9 vehicle). A typical triple trailer is shown in Figure 7.2. For the triple trailer, the average steer axle weight was 10,680 lbs, the average weight of the tandem drive axles was 40,610 lbs, and the average weight of the single-axle trailer ranged from 20,550 to 21,010 lbs. For the five-axle single trailer, the steer axle weighed 11,550 lbs, the tandem drive axles weighed 33,850 lbs, and the tandem rear axles weighed 32,900 lbs (73). Hot tire inflation pressures were typically 105 psi.

Six of the eight structural sections developed some degree of fatigue cracking during the 2003 test track cycle (all but the 9-in. thick HMA sections N3 and N4). Three of the sections failed, with failure defined as fatigue cracking exceeding 20% of the total lane area (73). The MEPDG assumes cracking of 50% of the total lane area when damage equals 100% (74). The cracking data at failure and failure dates for Sections N1, N2, and N8 are shown in Table 7.3. The evolution, monitor- ing, and calculation of the crack areas are documented by Priest and Timm (73). The degree of cracking in Section N8, with the rich bottom layer, was unexpected, particularly when compared with the performance of Section N7. Willis and Timm (75) conducted a forensic evaluation that indicated slippage or debonding between the rich bottom layer and the overlying base layer. Cracking apparently began in the over- lying layer. Shift Factors Based on Measured Strain The eight structural sections from the 2003 NCAT Test Track were instrumented to measure in situ strain in the asphalt, com- pressive stresses in the unbound layers, and moisture and tem- perature as a function of depth in the pavement structure (72). Temperature and moisture data were collected on an hourly basis throughout the two-year loading cycle. High-speed data (2,000 samples per second) from the asphalt strain gauges and unbound layer pressure cells were collected at least once a month for at least three truck passes for each section and weekly after cracking was initially observed. The layout of the instrumentation for each section is shown in Figure 7.3. Based on the high-speed data acquisition, Priest and Timm (73) developed strain prediction models for each of the sec- tions and the two loading configurations (triple trailer and five-axle single trailer). The regression model used a power relationship (Equation 36). where, εt = horizontal tensile strain (ms), T = mid-depth HMA temperature, °F, and β1 and β2 = regression constants. The regression constants are summarized in Tables 7.4 and 7.5. For Section N8, the data exhibited three different performance periods. Prior to April 20, 2004, the strain re- sponse appears to indicate that the layers were bonded. From April 20 to September 1, 2004, the strain response shifts, but maintains a power model relationship with temperature. After September 1, 2004, increasing strains, even with low mid-depth HMA temperatures, appear to indicate that cracks are propagating through the upper layers. Two separate mod- els are shown in Table 7.4 with coefficients for traffic before and after the point when the bond appears to have failed. A generic relationship for both the triple trailer and five- axle single trailer was developed for the sections as a function of thickness (73). The generic equation (37) was used to cal- culate the strains resulting from the five-axle single trailer for Section N1. Insufficient data were collected before N1 cracked to develop a specific model for Section N1. The surveyed HMA thickness of Section N1 was 4.8 in. A thickness of 5 in. was used for Section N8 after September 1, 2004 to represent debonding between the base and rich bottom layer. where, εt = horizontal tensile strain (ms), T = mid-depth HMA temperature, °F, and t = HMA thickness (in.). The low-speed data acquisition system collected the average mid-depth HMA temperature for each section on an hourly basis. The numbers of laps by each triple trailer and five-axle single trailer truck were recorded for each hour. Both Priest (76) and Willis (77) developed spreadsheets to calculate the εt T t= −2 1228 26 448 371 190. . ( ). ε β βt T= 1 2 36( ) 75 Figure 7.2. Typical triple-trailer weight distribution for 2003 NCAT Test Track (73). Section Failure Date Cracking, % of Total Lane Cracking, % of Wheel Path N1 6/14/2004 20.2 58.3 N2 7/19/2004 19.5 56.3 N8 8/15/2005 18.5 53.5 Table 7.3. 2003 NCAT Test Track structural section failure data (73).

76 Figure 7.3. Typical gauge array for 2003 NCAT Test Track structural sections (72). Section 1 2 R2 N11 4.0439 1.066 0.76 N2 0.0005 3.081 0.88 N3 0.0508 1.899 0.91 N4 0.0211 2.086 0.82 N5 0.0109 2.291 0.88 N6 0.0132 2.293 0.81 N7 0.0022 2.652 0.71 N8 (prior 4/20/2004) 0.1487 1.556 0.90 N8 (4/20/2004 and after) 0.0926 1.824 0.81 1Limited data were available. Table 7.4. Triple-trailer regression analyses for strain-temperature relationship (73 [not N8]). Section 1 2 R2 N1 Insufficient data to perform regression N2 3.922E-05 3.579 0.871 N3 5.501E-03 2.332 0.773 N4 1.304E-03 2.632 0.773 N5 1.440E-04 3.185 0.887 N6 1.852E-02 2.155 0.881 N7 8.310E-04 2.796 0.821 N8 (prior to 9/1/2004) 1.170E-04 3.157 0.850 Table 7.5. Five-axle single-trailer regression analyses for strain-temperature relationship (73 [not N8]).

number of axle repetitions and respective strain for each hour of the 2003 NCAT Test Track loading cycles. Transfer func- tions were developed from the laboratory beam fatigue tests in the form of Equation 38, as follows: where, Nf = number of load repetitions (cycles) to failure, εt = tensile strain at the bottom of the HMA layer, k1 and k2 = regression constants, and β1 = shift factor between laboratory and field per- formance (initially set at 1.0). The regression constants for the 2003 NCAT Test Track 19.0-mm NMAS base mixes, based on the beam fatigue tests conducted as part of this study are shown in Table 7.6. The incremental damage was calculated for each hour of loading by truck type (triple trailer or five-axle single trailer) using Miner’s Hypothesis, shown in Equation 39, where fail- ure is approached when the cumulative damage approaches 1.0 (78). The failure criterion was defined as fatigue cracking equal to 20% of the total lane area. where, D = cumulative damage, Di = incremental damage for condition (in this case, repeti- tions of a given axle’s load at a given HMA temperature over a given hour), D D n N i i f ii n i n = = == ∑∑ 11 39( ) N kf t k = × ⎛⎝⎜ ⎞⎠⎟β ε1 1 21 38( ) ni = number of load applications at condition i, and Nfi = allowable load applications to failure for condition i (in this case, determined using the laboratory fatigue transfer function shown in Equation 38 and Table 7.6). Based on the observed level of cracking, Section N6 was assigned a cumulative damage factor of 0.7 after the applica- tion of 10 million ESALs at the end of the 2003 NCAT Test Track cycle (73). Willis (77) calculated strain for each hour based on the loading conditions using Equation 36 and the coefficients in Tables 7.4 and 7.5 based on the recorded mid- depth HMA temperature. The spreadsheets were modified to calculate Ni for each section, hour, and loading condition using Equation 38 and the coefficients in Table 7.6. The num- ber of load repetitions of a given truck in each hour was divided by their respective Ni to determine the incremental damage. The cumulative damage, D, was determined by summing all the incremental damage according to Equation 39 until the date when failure occurred as identified in Table 7.3. For Sec- tion N6, the damage was summed until the end of the 2003 loading cycle (application of 10 million ESALs). The shift fac- tor for each section, β1, in Equation 38 was solved for using Microsoft Excel’s Solver Function such that the cumulative damage, D, = 1.0 on the failure date. For Section N6, the shift factor was determined for D = 0.7 at the end of the loading cycles. The shift factors were determined with and without the inclusion of an endurance limit. The endurance limit represented by the lower limit of the 95% confidence inter- val was used in the calculations. The calculated shift factors between laboratory and field performance are summarized in Table 7.7. Based on the data in Table 7.7, the use of an endurance limit does not affect the shift factor for pavement sections likely to fail in fatigue. 77 Mix k1 k2 R2 PG 67-22 Optimum 7.189E-15 5.782 0.99 PG 67-22 Optimum+ 4.420E-09 4.107 0.98 PG 76-22 Optimum 4.663E-12 5.052 0.92 Section 19.0-mm NMAS Base Mix Shift Factor Shift Factor with Endurance Limit N1 PG 76-22 Optimum 4.24 4.24 N2 PG 67-22 Optimum 75.77 75.77 N6 PG 67-22 Optimum 38.00 38.00 N8 PG 67-22 Optimum+1 8.33 8.33 Note: 1Until debonding occurred, then PG 67-22 optimum. Table 7.6. Fatigue transfer function coefficients for 2003 NCAT Test Track 19.0-mm NMAS base mixes. Table 7.7. Calculated shift factors between laboratory and field performance based on measured strains.

Shift Factors Based on Calculated Strains Using M-E Design Programs In Chapter 6, three classes of M-E pavement design programs were described, as follows: 1. Those that use equivalent axle loads and equivalent tem- peratures; 2. Those that use equivalent temperatures in the form of seasons and axle load distributions for each axle type; and 3. Those that use detailed temperature, load, and incremen- tal damage calculations. PerRoad is an example of the second type and the MEPDG is an example of the third type of pavement design program. Both programs were used to estimate shift factors between predicted and field performance. The inputs used in the M-E design programs are described below. Where possible, the same inputs were used in both Per- Road and the MEPDG. Resilient modulus (Mr) values were cal- culated for both the subgrade and the granular base. Labora- tory triaxial resilient modulus tests were performed on samples of both unbound materials according to the NCHRP 1-28A protocol by Burns, Cooley, Dennis, Inc. The multivariable, non-linear stress sensitivity model (Equation 40) recom- mended by the MEPDG was fit to the test data (79, 80). The model coefficients are shown in Table 7.8 for the subgrade and unbound granular base materials. where, Mr = resilient modulus, pa = atmospheric pressure (14.696 psi), θ = bulk stress = σ1 + σ2 + σ3 = σ1 + 2σx,y, σ1 = major principal stress = σz + po, σ2 = intermediate principal stress = σ3 for Mr test on cylindrical specimen, σ3 = minor principal stress/confining pressure = σx,y + ko (po), σz = vertical stress from wheel load(s) calcu- lated using layered-elastic theory, σx,y = horizontal stress from wheel load(s) calcu- lated using layered-elastic theory, po = at-rest vertical pressure from overburden of paving layers above unbound layer or subgrade, M k p p p r a a k a k = × ⎛ ⎝⎜ ⎞ ⎠⎟ × ⎛ ⎝⎜ ⎞ ⎠⎟ + ⎡ ⎣⎢ ⎤ ⎦⎥1 2 3 1 θ τoct (40) ko = at-rest earth pressure coefficient, τoct = octahedral shear stress = 1⁄3((σ1 − σ2)2 + (σ1− σ3)2 + (σ2-σ3)2)1/2, and k1, k2, k3 = regression coefficients. A design resilient modulus was calculated using Equation 40 for the pavement structures shown in Figure 7.1. Addi- tional values were calculated for a 12-in. thick HMA section for use in sensitivity analyses to be described later in this chapter. The design values were calculated using an iterative process as described in the MEPDG (80). The wheel-load stresses were calculated for a 20,000-lb, single-axle load using WESLEA for Windows. Dynamic modulus values for the PG 67-22 and PG 76-22 mixes were calculated at a mean annual temperature of 74.3°F and 10 Hz frequency. The design resilient modulus values are summarized in Table 7.9. All of the design values matched the calculated values within 5%. The lower Mr values for the granular base were unexpected; however, they were consistent with previous laboratory testing conducted by the Alabama Department of Transportation (81) and back- calculated values from falling-weight deflectometer tests (79). Also, the subgrade consisted of a very angular material with good compactibility and strength. Dynamic modulus testing was conducted on lab-compacted, field mixed material sampled from the 2003 NCAT Test Track by Purdue University. For the MEPDG, the dynamic modu- lus (E∗) results were used as Level 1 inputs. For PerRoad, a sig- moidal function, in the form recommended by the MEPDG (82), was fit to the experimental data. The E∗ data are pre- sented in Table 7.10 for the PG 67-22 and PG 76-22 19.0-mm NMAS base mixtures. The E∗ master curves for the PG 67-22 and PG 76-22 mixtures are shown graphically in Figure 7.4. Observation of the data in Table 7.10 and Figure 7.4 suggests that the E∗ values for the PG 67-22 and PG 76-22 mixtures are approximately equal. The temperature data from the 2003 cycle of the NCAT Test Track were used for the PerRoad analysis. Figure 7.5 shows a frequency distribution of the air temperature data. The temperature corresponding to the 10th, 30th, 50th, 70th, and 90th percentiles of the frequency distribution were used to identify five “seasons” for the analysis. The air tempera- tures were converted to pavement temperatures at 1⁄3 of the HMA depth using Equation 41 (7). Dynamic modulus values were then calculated at 10 Hz for five temperatures determined from a frequency distribution of the pavement temperatures 78 Material k1 k2 k3 R2 Granite Base 716.28 0.8468 -0.4632 0.93 Subgrade 1878.97 0.4067 -0.7897 0.42 Table 7.8. Unbound materials stress-sensitivity model coefficients (79).

79 Section Binder Grade Total HMA Thickness, in. Granular Base Mr, psi Subgrade Mr, psi N1 PG 76-22 5 17,500 26,000 N2 PG 67-22 5 17,500 26,000 N3 PG 67-22 9 12,000 18,000 N4 PG 76-22 9 12,000 18,000 N5 PG 76-22 7 14,000 21,000 N6 PG 67-22 7 14,000 21,000 Perpetual PG 67-22 12 9,000 14,000 Perpetual PG 76-22 12 9,000 14,000 Table 7.9. Design resilient modulus values for 2003 NCAT Test Track. PG 76-22 Mixture PG 67-22 Mixture Temperature, °F Frequency, Hz Avg. E*, psi Std. Dev. E*, psi COV, % Avg. E*, psi Std. Dev. E*, psi COV, % 0.1 2,277,563 301,583 13.2% 2,298,485 192,823 8.4% 0.5 2,725,367 337,116 12.4% 2,724,243 255,820 9.4% 1 2,907,715 357,532 12.3% 2,897,164 276,114 9.5% 5 3,304,176 410,690 12.4% 3,289,201 315,239 9.6% 10 3,502,587 421,351 12.0% 3,421,801 320,689 9.4% 14 25 3,689,759 450,429 12.2% 3,617,276 355,717 9.8% 0.1 1,153,195 203,310 17.6% 1,072,481 131,115 12.2% 0.5 1,474,779 268,533 18.2% 1,395,625 157,677 11.3% 1 1,623,189 300,838 18.5% 1,543,418 168,029 10.9% 5 1,988,503 376,758 18.9% 1,920,335 188,822 9.8% 10 2,148,479 421,027 19.6% 2,087,564 198,544 9.5% 40 25 2,404,942 474,083 19.7% 2,327,093 210,715 9.1% 0.1 394,829 44,604 11.3% 378,875 67,659 17.9% 0.5 565,357 71,916 12.7% 547,046 83,215 15.2% 1 653,141 84,367 12.9% 643,423 88,274 13.7% 5 913,955 125,840 13.8% 930,961 106,425 11.4% 10 1,061,821 150,939 14.2% 1,064,722 116,677 11.0% 70 25 1,243,734 184,064 14.8% 1,310,597 148,638 11.3% 0.1 151,383 15,348 10.1% 139,490 29,780 21.3% 0.5 214,801 16,759 7.8% 197,650 38,716 19.6% 1 254,106 17,495 6.9% 233,293 42,084 18.0% 5 404,945 28,959 7.2% 359,657 57,351 15.9% 10 507,342 34,227 6.7% 445,592 64,055 14.4% 100 25 614,706 47,519 7.7% 574,095 105,440 18.4% 0.1 65,267 3,879 5.9% 63,055 6,364 10.1% 0.5 83,832 5,467 6.5% 79,553 7,576 9.5% 1 95,036 6,564 6.9% 89,815 9,182 10.2% 5 142,898 4,857 3.4% 135,103 19,120 14.2% 10 174,009 4,556 2.6% 167,845 25,931 15.4% 130 25 218,137 16,623 7.6% 215,345 40,140 18.6% Table 7.10. Dynamic modulus data of 2003 NCAT Test Track base mixtures (after 81). experienced by the structural sections of the 2003 NCAT Test Track. The modulus values used for determining shift factors for the test track sections and subsequent sensitivity analyses are presented in Table 7.11. where, MMPT = mean monthly pavement temperature, °F, MMAT = mean monthly air temperature, °F, and MMPT MMAT Z Z = + + ⎛⎝⎜ ⎞⎠⎟ − + +1 1 4 34 4 6 41( ) Z = depth below surface at the upper third point of the layer, in. For PerRoad, the load spectra were determined from the 2003 NCAT Test Track records. The average daily truck traffic in the design lane was 1,237 trucks. The triple trailers made up 88.5% of the truck traffic and the five-axle, single trailer com- prised the remaining 11.5%. This results in 8,091 axle groups (or repetitions of an axle configuration) per day. The axle configurations had the following distribution: 15.3% steer axles (10,000–12,000 lbs); 67.7% single axles (20,000–22,000 lbs); and

80 10 100 1000 10000 -6.00 -4.00 -2.00 0.00 2.00 4.00 |E* |, k si Log Reduced Frequency, Hz PG 67-22 PG 76-22 0% 20% 40% 60% 80% 100% 120% 0 1000 10 20 30 40 50 60 70 80 90 10 0 11 0 Mo re 2000 3000 4000 5000 6000 7000 Fr eq ue nc y Air Temperature, ˚F Frequency Cumulative % Sections N1 and N2, 5 in. thick Sections N3 and N4, 9 in. thick Sections N5 and N6, 7 in. thick PG 67-22 PG 76-22 PG 67-22 PG 76-22 MMPT, °F PG 67-22 PG 76-22 PG 67-22 PG 76-22 Su mmer 9 80.6 94.8 158,401 168,421 93.3 166,643 177,089 94.0 162,895 173,149 89.6 187,724 199,180 Fall 12 72.2 84.9 219,579 232,367 83.7 229,303 242,454 84.2 224,897 237,886 80.8 252,532 266,478 Winter 10 37.1 43.6 770,325 798,342 43.5 772,034 800,051 43.6 771,269 799,286 44.0 765,289 793,302 Spring 11 53.2 62.6 501,586 526,939 61.9 509,352 534,864 62.2 505,866 531,307 60.9 522,602 548,371 Spring 2 10 65.5 77.1 286,911 301,854 76.0 297,443 312,652 76.5 292,685 307,775 73.8 320,829 336,568 MMPT, °FSeason Length, Weeks 20th Percentile Air Temperature, °F Perpetual Section E*, psi E*, psi E*, psi E*, psi MMPT, °FMMPT, °F Figure 7.4. Master curves for PG 67-22 and PG 76-22 19.0-mm NMAS base mixtures at optimum asphalt content. Figure 7.5. Frequency distribution of air temperature data for the 2003 NCAT Test Track. Table 7.11. Summary of PerRoad E* inputs.

17.0% tandem axles (20.6% of which were 32,000–34,000 lbs and 79.4% of which were 40,000–42,000 lbs). For the MEPDG, the triple-trailer trucks were modeled as FHWA Class 13 vehi- cles, neglecting the steer axle, and the five-axle single trailer truck was modeled as a Class 9 vehicle. Shift factors were calculated using PerRoad for three sec- tions: N1, N2, and N6. It was not felt that Section N8, with debonding occurring part way through the loading cycle, could be modeled with PerRoad. PerRoad runs a 5,000-cycle Monte Carlo simulation. The default variability was used for the modulus and thickness of the HMA and granular layers. Monte Carlo runs are distributed over the five seasons based on the number of weeks for each season and based on the dis- tribution of axle loads. A resulting strain at the bottom of the HMA layer is output for each iteration of the Monte Carlo simulation. The strain was converted to damage per axle repetition using Equations 38 and 39 and the coefficients in Table 7.6 corresponding to the mixture used in a particular section. The average damage per axle repetition was calcu- lated and multiplied by the total number of axle repetitions when the section failed or, in the case of Section N6, reached the end of the 2003 loading cycle. A shift factor was determined for the transfer function for a given section using Microsoft Excel Solver by minimizing the difference squared between the observed and calculated total damage. The shift factors are summarized in Table 7.12. Because Sections N1 and N2 did not go through a summer before they failed, the summer season data were removed and a new average damage and fatigue transfer function shift factor calculated. This shift factor is lower since higher strains (and hence more damage) were observed during the summer season. An estimate of predicted cracking for the 2003 Test Track Sections was determined using the MEPDG (Version 1.0) and the nationally calibrated fatigue model (not the fatigue transfer functions developed as part of this research). The climate data were determined from the Enhanced Integrated Climatic Model using the test track’s coordinates: latitude 32.36, longitude −85.18, elevation 630 ft, and depth to water table (on north tangent) of 12.5 ft. Three weather stations’ data were used in the analysis: Columbus, GA; Troy, AL; and Montgomery, AL. The subgrade and granular base were mod- eled as Level 2 inputs. The Mr values are summarized in Table 7.9. The remaining granular base and subgrade inputs were taken from Taylor and Timm (79). Level 1 inputs were used for the HMA. The entire HMA layer was modeled as the base material for simplicity (recall the surface layer is only 1-in. thick). The dynamic modulus results are summarized in Table 7.10. The binder proper- ties are summarized in Table 7.13. The volumetric proper- ties for specific sections were taken from Taylor and Timm (79). For the sensitivity analyses, described in the next section, the average volumetric properties were used, as follows: • Air voids = 6%, • Volume of effective binder = 10.5%, and • Unit weight = 150.5 pcf. Unless otherwise stated, the MEPDG default values were used for uncommon items, such as thermal properties. Unlike PerRoad, the MEPDG does not output its raw layered elastic calculations. Therefore, a shift factor could not be calculated directly in the same manner as was done with PerRoad. The predicted cracking as a function of time is shown in Figure 7.6 for Section N1 and in Figure 7.7 for Sections N2 and N6. The MEPDG provides the predicted (50% reliability) bottom-up fatigue cracking, termed maximum cracking, and the predicted cracking at some level of reliability, in this case, 81 Section Shift Factor Based on All Seasons Shift Factor Neglecting Summer Season N1 13.4 6.7 N2 45.0 19.2 N6 17.6 NA NA = Not applicable because Section N6 went through two summer seasons. PG 67-22 PG 76-22 Test Temperature, °F G*, Pa Delta, ° G*, Pa Delta, ° 136.4 13.610 73.2 -- -- 147.2 6.125 76.7 6.597 65.9 158.0 2.832 80.0 3.683 67.3 168.8 -- -- 2.057 69.1 Table 7.13. 2003 NCAT Test Track binder properties for MEPDG. Table 7.12. Shift factors from PerRoad analyses.

90%, termed bottom-up reliability in Figures 7.6 and 7.7 (and in the MEPDG output). The MEPDG recommends reliabilities between 85% and 97% for urban interstate-type pavements and between 80 and 95% for rural interstate-type pave- ments (83). Observation of Figure 7.6 suggests that the max- imum cracking (20.1%) closely approximates the observed cracking (20.2%) for Section N1 at the 2003 NCAT Test Track. However, the 90% reliability bottom-up cracking is signif- icantly higher (38.2%). For Section N2, the observed crack- ing (19.5%) exceeded the maximum cracking (14.4%), but was again less than the 90% reliability cracking (32.5%). In the MEPDG, damage is related to predicted cracking according to Equation 42 (84). Note that the minus sign between C1 and C2 in the equation in El-Basyouny and Witczak (74) is incorrect, and should be a plus sign as shown below. FC eC C D = + ⎛⎝⎜ ⎞⎠⎟ × ⎛⎝⎜ ⎞⎠⎟+ × 6 000 1 1 60 42 1 2 , ( ) Log 82 0 10 20 30 40 50 60 70 80 90 100 0 6 12 18 24 A lli ga to r C ra ck in g (% ) Pavement Age (month) Bottom-Up Cracking - Alligator Maximum Cracking Bottom-Up Reliability Maximum Cracking Limit 20.2% Cracking Observed , 20.1% Predicted, Section N1 N2 Maximum Cracking N2 Bottom-Up Reliability Maximum Cracking Limit N6 Maximum Cracking N6 Bottom-Up Reliability 19.5% Cracking Observed, 14.4% Predicted Section N2 0 10 20 30 40 50 60 70 80 90 100 0 6 12 18 24 A lli ga to r C ra ck in g (% ) Pavement Age (month) Bottom-Up Cracking - Alligator Figure 7.6. MEPDG predicted cracking for Section N1 (PG 76-22), 2003 NCAT Test Track. Figure 7.7. MEPDG predicted cracking for Sections N2 and N6 (PG 67-22), 2003 NCAT Test Track.

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

of 0.14 and 0.44 were assigned to the granular base and HMA, respectively. where, W18 = the number of expected 18-kip ESALs in the design lane over the design life 200 × 106, ZR = the normal deviate associated with the chosen level of reliability, 90% = −1.28, S0 = materials standard deviation, 0.45, SN = structural number, ΔPSI = initial minus terminal serviceability, 1.2, and MR = effective soils resilient modulus, psi. MEPDG analyses were performed using the inputs described previously. The three scenarios examined included 20-year and 40-year designs with 90% reliability of bottom-up cracking of less than 25% of the total lane area, and a 40-year perpetual analysis where the pavement thickness was selected to provide maximum damage and cracking = 0% at the end of 40 years. The PerRoad analyses were performed using the inputs described previously. Both the MEPDG and PerRoad perpet- ual analyses used the respective one-sided 95% lower predic- tion limits of the endurance limit for the PG 67-22 (151 ms) and PG 76-22 (146 ms) mixes at optimum asphalt content determined in Phase I of this study. The design thickness was selected such that approximately 95% of the load applications were less than the endurance limit (85). log . log log 10 18 10 10 9 36 1 20W Z S SN PS R o= × + × +( )− + Δ I SN 4 2 1 5 0 40 1094 1 2 32 5 19 . . . . log . − ⎡ ⎣⎢ ⎤ ⎦⎥ + +( ) + × 10 8 07 43MR − . ( ) The results are summarized in Figure 7.8. All three MEPDG design thicknesses are less than that determined from the 1993 AASHTO Pavement Design Guide. Although the 20-year and perpetual MEPDG designs are the same thickness, the impli- cations are significantly different. In the first case, at 90% reliability, bottom-up cracking over 20% of the lane area would be expected after 20 years; in the second case, no crack- ing would be expected after 40 years. This is further illustrated in Table 7.15 where pavement thickness was iterated in the MEPDG without specifying an endurance limit and the result- ing damage determined. Thicknesses of 39 in. and 35 in. were required for the PG 67-22 and PG 76-22 mixes at optimum asphalt content to achieve predicted cracking performance similar to that achieved when an endurance limit was con- sidered (for maximum cracking of 0% to be predicted at the end of 40 years). Some damage was predicted in all of the cases tested, including 1.45% bottom-up cracking at 90% reliabil- ity, which was predicted to occur in the first month of service. It was expected that the PerRoad perpetual thickness would be less than that determined with the MEPDG. This expecta- tion was based on the differences in the manner in which both programs handle pavement temperatures. For PerRoad, up to five seasons can be specified, with corresponding moduli for each season. Typically, this would be based on grouping average monthly temperature data. In this analysis, actual temperature data from the 2003 NCAT Test Track cycle were grouped and used in the analyses. This most likely resulted in higher temperatures being selected for the warmer season, which results in correspondingly lower design moduli. Dur- ing PerRoad’s Monte Carlo simulations, modulus is allowed to vary within a season based on a log-normal distribution. The default coefficient of variation used in this study is 30%. For the MEPDG, temperatures are predicted using the Enhanced Integrated Climatic Model on an hourly basis. They are then 84 18 14.5 11 13 11 16 18 14.5 10 11 10 16 0 2 4 6 8 10 12 14 16 18 20 AASHTO 93, Mr = 5,500 psi AASHTO 93, Mr = 14,000 psi M-E PDG, 20 yr. M-E PDG, 40 yr. M-E PDG Perpetual PerRoad Perpetual H M A T hi ck ne ss , i n. PG 67-22 PG 76-22 Figure 7.8. Comparison of pavement thicknesses from empirical, M-E, and perpetual design methodologies.

collected into five “bins” on a monthly basis for determination of layer moduli. This would be expected to result in higher temperatures occurring at some points during the year and, hence, lower moduli and higher strains. A second difference that may have affected the MEPDG versus the PerRoad results is the way that the layers were sub- divided for calculation purposes. For the PerRoad analysis, the HMA was treated as a single layer. The pavement temper- ature was calculated according to Equation 44 (86). where, MMPT = mean monthly pavement temperature, °F and MMAT = mean monthly air temperature, °F. Equation 44 is representative of the average temperature of the HMA layer for pavement ≥ 10 in. thick. By comparison, the 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. sublayers, a 4.0-in. sublayer and a bottom 2.0-in. sublayer. Pavement temperatures and corresponding moduli were cal- 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- ing in a higher layer moduli, and, therefore, lower strains. MMPT MMAT= × +1 05 5 44. ( ) The second set of analyses examined the sensitivity of the MEPDG and PerRoad to the measured endurance limit using the NCAT Test Track traffic. Pavement design simulations were conducted using both the PG 67-22 and PG 76-22 mixes at optimum asphalt content, the previously described pave- ment design parameter, and three levels of the endurance limit: 70 ms, 100 ms, and the measured endurance limits (151 and 146 ms, respectively). The results, illustrated graphically in Figures 7.9 and 7.10 for the PG 67-22 and PG 76-22 mixes, respectively, indicate that the perpetual pavement design thickness is extremely sensitive to the measured endurance 85 PG 67-22 at Optimum PG 76-22 at Optimum HMA Thickness, In. Maximum Damage, % Maximum Cracking, % 90% Reliability, Bottom- Up Cracking Maximum Damage, % Maximum Cracking, % 90% Reliability, Bottom- Up 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. Table 7.15. Damage as a function of pavement thickness for the MEPDG with no endurance limit. 19 15 11 25 20 16.5 0 5 10 15 20 25 30 50 100 150 200 H M A T hi ck ne ss , i n. Endurance Limit, micro-strains M-E PDG Per Road Figure 7.9. Sensitivity of pavement thickness to endurance limit for PG 67-22 mixes.

limit. The use of polymer modified PG 76-22 has a more sub- stantial impact on pavement thickness with the MEPDG, as compared to PerRoad with the difference in thickness ranging between 1.0 and 3.0 in., depending on the endurance limit. Larger differences were observed with lower endurance limits. Typical Principal Arterial Truck Traffic Classification The third and fourth set of analyses examined the sensitiv- ity of the MEPDG and PerRoad to the measured endurance limit using a normal load spectra that might be expected on a principal arterial. Pavement design simulations were con- ducted using the PG 67-22 mix at optimum asphalt content, the previously described pavement design parameters, and three levels of the endurance limit: 70 ms, 100 ms, and the measured (151 ms) endurance limit. The MEPDG’s Level 3 default truck traffic classification No. 1 and associated axle weight distributions for principal arterials were used for the load spectra. The MEPDG pro- duces a file that records the accumulated ESALs on a monthly basis throughout the design life of the project. For the NCAT Test Track traffic, the MEPDG calculated 171,514,458 ESALs at the end of 40 years, assuming no growth. The average annual 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- tion, and 90% of the trucks in the design lane were used for the calculations. Traffic can be defined in PerRoad in two manners: FHWA vehicle class using default axle weight distributions or axle weight distribution by type (single, tandem, etc.). The MEPDG default truck traffic classification No. 1 was converted to the format used by PerRoad. The axle load configuration con- sisted of 9,824 axle groups per day in the design lane, of which 45.2% were single axles, 54.3% were tandem axles, and 0.5% were tridem axles. The load spectra for the three axle types are shown in Figure 7.11. Figure 7.12 shows the sensitivity of the MEPDG and Per- Road to the measured endurance limit. Both the MEPDG and 86 16 13 10 24 20 16 M-E PDG Per Road 0 5 10 15 20 25 30 50 100 150 200 H M A T hi ck ne ss , i n. Endurance Limit, micro-strains Figure 7.10. Sensitivity of pavement thickness to endurance limit for PG 76-22 mixes. 0% 5% 10% 15% 20% 10,000 0 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000 110,000 25% 30% Fr eq ue nc y, % Axle Weight, lbs Single Tandem Tridem Figure 7.11. Axle weight distribution used in PerRoad.

PerRoad are sensitive to changes in the measured endurance limit. For the MEPDG, a change in the endurance limit of 50 ms results in a change in pavement thickness of approxi- mately 7 to 8 in. For PerRoad, a change in the endurance limit of 50 ms results in a change in pavement thickness of approx- imately 4 in. This sensitivity highlights the need to measure the endurance limit as accurately as possible. Finally, design thicknesses were determined using the MEPDG and 1993 AASHTO Pavement Design Guide using design lives of both 20 and 40 years without considering an endurance limit. For the MEPDG, the thickness that resulted in at least 90% reliability against both bottom-up and top- down fatigue cracking was determined. Figure 7.13 shows a comparison of the conventional and perpetual design thicknesses. The PerRoad perpetual design using the measured endur- ance limit of 151 ms is slightly less thick than the 40-year empirical design using the 1993 AASHTO Design Guide. The MEPDG thicknesses considering only fatigue cracking are sim- ilar to the PerRoad thickness. However, at an 11-in. pavement 87 35 27 1920 16 12.5 0 5 10 15 20 25 30 35 40 50 100 150 200 H M A T hi ck ne ss , i n. Endurance Limit, micro-strains ME-PDG Per Road Figure 7.12. Sensitivity of pavement thickness to the endurance limit for typical axle distribution. 13 14 11 12 19 12.5 0 2 4 6 8 10 12 14 16 18 20 AASHTO 93, 20-yr. AASHTO 93, 40-yr. M-E PDG, 20-yr. M-E PDG, 40-yr. M-E PDG Perpetual PerRoad Perpetual H M A T hi ck ne ss , i n. Figure 7.13. Comparison of pavement thicknesses from empirical, M-E, and perpetual design methodologies for typical axle distribution.

thickness, the 20-year MEPDG design fails the reliability criteria for terminal international roughness index (IRI), total pavement rutting, and HMA rutting. The HMA thick- ness must be increased to 14 in. to produce an acceptable reliability for terminal IRI. The HMA thickness must be increased to 30 in. to produce an acceptable reliability against total pavement rutting. The reliability for HMA rutting can not be achieved for this level of traffic in the NCAT Test Track’s climate using a PG 67-22 binder. The perpetual thickness determined using the MEPDG is significantly thicker than that determined using PerRoad when considering a typical axle distribution. Although the pavement thicknesses appear similar between conventional empirical or mechanistic designs and the per- petual pavement thickness determined using PerRoad, again the implications are very different. Based on the conven- tional MEPDG results, the 11-in. HMA pavement would be expected to have maximum cracking of 4.8% of the lane area after 20 years. The 90% reliability for bottom-up crack- ing is 22.72% of the lane area. Similarly, for the 12-in. pavement after 40 years, maximum bottom-up cracking was predicted at 5.9% with a 90% reliability of 23.99% of the lane area. Based on the conventional analysis, the pavement will have failed and be in need of reconstruction, whereas the perpetual analysis suggests that at a similar thickness there should be no bottom-up fatigue cracking after 40 years. This difference would have a significant effect on life-cycle cost analysis. Summary of Sensitivity Analyses The design thickness for a perpetual pavement is very sensitive to the measured endurance limit using both the MEPDG and PerRoad. Considering a typical traffic stream, a 50-ms change in the endurance limit resulted in a 7- to 8-in. or 4-in. change in HMA thickness, respectively, with the MEPDG and PerRoad. This sensitivity highlights the need for accurate determination of the endurance limit. To improve accuracy, the number of strain levels used to predict the endurance limit in Appendix A was increased from two to three with three replicates at each level from that used in Phase II of the study. Additional samples should reduce the standard error of the log-log regression and result in a smaller t-value when calculating the lower, one-sided prediction limit (endurance limit). Again considering a normal traffic stream, the PerRoad perpetual design thickness was slightly less than that deter- mined using the 1993 AASHTO Pavement Design Guide, and approximately the same as that required to satisfy the fatigue requirements of a 20- or 40-year MEPDG design (not consid- ering the endurance limit). However, the predicted conditions of the pavement at the end of the design life are significantly different. At 90% reliability, the MEPDG would predict over 20% of the lane area to be cracked at the end of the design life whereas the perpetual pavements would not be expected to have any cracking. This significantly changes the required maintenance and rehabilitation requirements in a life-cycle cost analysis. Considerations for Incorporating the Endurance Limit into M-E Design Procedures In the preceding section, sensitivity analyses were presented demonstrating the affect of incorporating the endurance limit into two M-E programs, the MEPDG and PerRoad. Certainly the predicted performance from the MEPDG in terms of bottom-up cracking was improved compared to a conven- tional 20-year design. Using the experimentally determined endurance limits from this study, there was no increase in the design thickness determined using the MEPDG for a 20-year or perpetual design. The thicknesses determined, 11.0- and 10.0-in., respectively, for the PG 67-22 and PG 76-22 mixes at optimum asphalt content are consistent with Nunn’s (10) recommendations that long-life pavements should range between 7.9 and 15.4 in. Further, Section N3 and N4 of the 2003 NCAT Test Track have now gone through two test track loading cycles without any observed fatigue cracking (77). This indicates that pavement thicknesses close to those designed as perpetual pavements (N3 and N4 are 9 in. thick) with the MEPDG are performing well after a fairly high number (20 million ESALs) of load applications. However, the sen- sitivity of the required pavement thickness to the measured endurance limit also has been demonstrated, as well as the apparent sensitivity to temperature as evidenced by the increased pavement thicknesses determined using PerRoad. Therefore, consideration should be given as to whether the endurance limit is really best represented by a single value, determined at a single temperature. One hypothesis is that the fatigue endurance limit is driven, in part, by the ability of asphalt mixtures to heal. Healing occurs more readily at higher temperatures. Therefore, a mixture’s fatigue capacity or endurance limit may be higher at higher temperatures. Testing was only conducted at a single temperature, 20°C, as part of this study. Tsai et al. (87) tested mixes at three temperatures, 10°C, 20°C, and 30°C, as part of a reflective-cracking study. A total of six samples was tested at each temperature, three each at two strain levels. The sam- ples were compacted to 6% air voids (target). Five binders were tested: AR-4000, type G asphalt rubber (RAC-G), and three modified binders termed MB4, MB15, and MAC16. The endurance limit was predicted from published data included in Tsai et al. (87) using the procedure described in Appendix A. The results are shown in Table 7.16. Varia- tions in the predicted endurance limit were observed both 88

with changes in test temperature and binder. Three of the binders generally followed the expected trend of increasing endurance limit with increasing test temperature. In two of the cases, the predicted endurance followed the expected trend, while the 95% lower prediction limit was more vari- able, due to variability in the beam fatigue test results. For the RAC-G, the 95% lower prediction limit showed a trend of increasing endurance limit with increasing temperature. The MB15 binder indicated decreasing endurance limit with increasing temperature. The AR-4000 binder indicated its lowest endurance limit at 20°C. Based on measured strains from the NCAT Test Track from sections that have not experienced fatigue cracking, Willis (77), proposed designing perpetual pavements based on a cumula- tive frequency distribution of allowable strains. A similar con- cept was initially proposed by Priest (76). The proposed upper bound for a cumulative frequency distribution of endurance limit strain is shown in Table 7.17 for Sections N3 and N4 of the NCAT Test Track. A cumulative frequency distribution defines the percentage of observed data below a given value. Based on Table 7.17, 50% of the in-service strain values should be less than 181 ms to prevent fatigue cracking. It should be 89 Binder Test Temperature, °C Predicted Endurance Limit, ms Lower 95% Prediction Limit, ms 10.2 101 39 19.9 52 12 AR-4000 30.4 105 80 10.3 130 91 20.2 190 106 RAC-G 30.0 183 124 10.0 176 127 20.0 255 178 MAC15 30.3 461 100 9.9 377 284 20.5 394 230 MB4 29.8 555 247 10.1 348 261 20.0 215 135 MB15 30.4 171 82 Table 7.16. Predicted endurance limit as a function of test temperature. Percentile Upper Bound Fatigue Limit Maximum Fatigue Ratio 394 2.83 346 2.45 310 2.18 282 1.98 263 1.85 247 1.74 232 1.63 218 1.53 205 1.44 193 1.35 181 1.27 168 155 143 132 122 112 101 90 72 99 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 1 49 Table 7.17. Cumulative distribution of strain criteria for long-life pavements (77).

noted that the mean annual air temperature measured during the 2003 NCAT Test Track cycle was 65.5°F, which corre- sponds to a pavement temperature (based on Equation 44) of 73.8°F. This is greater than the 20°C (68.8°F) test temperature used for the beam fatigue tests. Hence, the fact that the 50% strain values are greater than the endurance limits measured for this study is not unexpected. Table 7.17 also presents strain ratios, which are ratios of the upper bound for the allowable strain at a given percentile to the measured endurance limits (151 ms and 146 ms for the PG 67-22 and PG 76-22 mixes, respectively) determined as part of this study. This offers an opportunity to adjust the distribution based on measured material properties. Both concepts were developed based on observations that the cumulative frequency distribution of measured strains of sections that did and did not crack differed above the 55th percentile. It should be reiterated that these distri- butions are based on two sections for which bottom-up fatigue cracking has not been observed after the application of approx- imately 20 million ESALs. It is possible that fatigue cracking could occur with additional loading. The last concept that needs to be considered in long-life pavement design is how different rates of loading may be accommodated. In addition to designing against damage from expected axle loads, frequency of application needs to be considered. Low volume roads may, in some cases, experi- ence the same distribution of axle loads over time, but differ- ent frequencies of application. Infrequent load applications may offer more time for healing to occur and hence less accu- mulated damage. If load frequency is not considered, all per- petual pavements designed for the same distribution of axles on the same subgrade will have the same thickness. 90

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Validating the Fatigue Endurance Limit for Hot Mix Asphalt Get This Book
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TRB’s National Cooperative Highway Research Program (NCHRP) Report 646: Validating the Fatigue Endurance Limit for Hot Mix Asphalt explores the existence of a fatigue endurance limit for hot mix asphalt (HMA) mixtures, the effect of HMA mixture characteristics on the endurance limit, and the potential for the limit’s incorporation in structural design methods for flexible pavements.

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