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73 CHAPTER 7 Sensitivity of Pavement Thickness to the Endurance Limit Summary of Predicted Estimate of Shift Factors Endurance Limits between Laboratory Tests and Field Performance Estimates of the endurance limit were obtained from beam fatigue tests, uniaxial tension tests, and analysis of field per- In Chapter 3, calculations were provided to show that the formance. Table 7.1 summarizes the endurance limit predic- maximum expected load repetitions in a 40-year period is tions from the beam fatigue and uniaxial tension tests. An approximately 500 million. Then, using a shift factor of 10 analysis of LTPP data, presented in Chapter 6, indicated an between laboratory and field performance, a limit of 50 mil- endurance limit of 65 ms. There appears to be good corre- lion cycles was determined for the laboratory beam fatigue lation between the beam fatigue estimates of the endurance testing. The selection of a shift factor of 10 was based on rec- limit determined in Phase I and those determined during ommendations from SHRP (46). The structural sections the mini round-robin analysis. Based on the predicted val- from the 2003 NCAT Test Track provide an opportunity to ues determined from testing at NCAT and the Asphalt Insti- verify the shift factors. Three methodologies were used to as- tute, stiffer high-temperature binder grades and optimum sess the shift factors for the 2003 NCAT Test Track structural plus asphalt contents produce higher endurance limit values. sections: measured strains from in-place instrumentation, The 95% lower prediction limit samples follow the same gen- PerRoad, and the MEPDG. eral trend. The prediction of the endurance limit from the The NCAT Test Track was initially constructed in 2000. All round-robin data shows small differences based on binder of the sections of the 2000 track consisted of 19 in. of HMA grade and asphalt content. (15 in. of which were the same dense-graded mixes for all of The rankings from the uniaxial tension tests are the reverse the sections and the remaining 4 in. that were the experi- of those determined from the beam fatigue tests. For the mental mixes that varied between sections), 5 in. of perme- uniaxial tension tests, the PG 76-22 mixes generally result in able asphalt-treated drainage layer, 6 in. of crushed aggregate lower estimates of the endurance limit. This appears to be the base, and 12 in. of improved (AASHTO A-2) subgrade. opposite of field experience with polymer modified binders, The 2003 NCAT Test Track cycle included eight struc- illustrated in Figures 6.21 and 6.22. There are a number of tural sections. Three pavement sections were designed using potential reasons for the differences observed between beam the 1993 AASHTO Pavement Design Guide to carry approx- fatigue and uniaxial tension testing. There were very few uni- imately 1/3, 2/3, and the full 10 million ESAL loading (for that axial replicates tested, especially compared with the number cycle). The design reliabilities are summarized in Table 7.2. of beams tested. In some cases, the trends are based on results The input parameters are summarized in Von Quintus (72). from only one or two samples. Early in the uniaxial testing, The eight structural sections were selected to evaluate pave- there were a number of problems with end failures. Speci- ment sections designed for varying levels of traffic, polymer men fabrication was altered to reduce this problem. Finally, modified and unmodified or neat asphalt binders, stone the modes of loading uniaxial and beam fatigue samples are matrix asphalt (SMA), and rich bottom layer. All eight sec- different. To date, the basic research has not been completed tions were placed on 6 in. of granular base. The section lay- to understand the differences between the modes of loading out is shown in Figure 7.1. The thin, medium, and thick pave- or how the stress state changes with damage. The state of stress ment sections were constructed using both a neat PG 67-22 in pavements is not completely understood either. More effort binder and a styrene-butadiene-styrene (SBS) polymer mod- is needed prior to considering this approach. ified PG 76-22. The 19.0-mm NMAS base course was used for
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74 Table 7.1. Summary of estimates of the endurance limit (ms). Mix Beam Fatigue Beam Fatigue Round-Robin Uniaxial C versus S Uniaxial Increasing Amplitude Predicted 95% Predicted1 95% Average Power Exponential Average Average Lower Lower 95% Model Model for Loop Lowest for Confidence Confidence Lower Formation3 Loop 2 Limit Limit Confidence Formation3 Limit2 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: 1 Calculated using the pooled data from the round-robin. 2 Average of the 95% lower confidence limit calculated by each individual lab. 3 Averages calculated based on individual specimen data not presented in Chapter 5. Table 7.2. 2003 NCAT Test Track structural section design reliabilities (72). Traffic HMA, In. Granular Fill1, In. Structural Reliability Base, In. Number 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: 1 Fill 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. the fatigue testing in this study with the same binders. For the 9 vehicle). A typical triple trailer is shown in Figure 7.2. For seventh section, the 1-in. thick wearing course of the medium the triple trailer, the average steer axle weight was 10,680 thickness design was replaced with SMA. SMA was also used lbs, the average weight of the tandem drive axles was 40,610 as the wearing surface of the eighth section; in addition, the lbs, and the average weight of the single-axle trailer ranged bottom 2 in. of the 19.0-mm base were replaced with a rich from 20,550 to 21,010 lbs. For the five-axle single trailer, bottom layer containing an additional 0.5% asphalt (medium the steer axle weighed 11,550 lbs, the tandem drive axles total thickness). weighed 33,850 lbs, and the tandem rear axles weighed For the 2003 track, loading was provided by five triple- 32,900 lbs (73). Hot tire inflation pressures were typically trailer trucks and one five-axle single trailer (FHWA Class 105 psi. N1 N2 N3 N4 N5 N6 N7 N8 0 Aggregate Base 1 1 1 1 1 1 1 1 2 PG 67-22, 19.0 mm Opt+ 4 4 4 4 6 6 6 PG 67-22, 19.0 mm NMAS Thickness, in. 8 8 6 2 PG 76-22 , 19.0 mm NMAS 8 6 6 PG 76-22 SMA 10 6 6 6 6 12 6 6 PG 67-22, 9.5 mm NMAS 14 PG 76-22, 9.5 mm NMAS 16 Figure 7.1. Layout of 2003 NCAT Test Track structural sections.
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75 tions and the two loading configurations (triple trailer and five-axle single trailer). The regression model used a power relationship (Equation 36). t = 1T 2 (36) where, t = horizontal tensile strain (ms), Figure 7.2. Typical triple-trailer weight distribution T = mid-depth HMA temperature, °F, and for 2003 NCAT Test Track ( 73). 1 and 2 = regression constants. The regression constants are summarized in Tables 7.4 Six of the eight structural sections developed some degree and 7.5. For Section N8, the data exhibited three different of fatigue cracking during the 2003 test track cycle (all but the performance periods. Prior to April 20, 2004, the strain re- 9-in. thick HMA sections N3 and N4). Three of the sections sponse appears to indicate that the layers were bonded. From failed, with failure defined as fatigue cracking exceeding 20% April 20 to September 1, 2004, the strain response shifts, but of the total lane area (73). The MEPDG assumes cracking of maintains a power model relationship with temperature. 50% of the total lane area when damage equals 100% (74). After September 1, 2004, increasing strains, even with low The cracking data at failure and failure dates for Sections N1, mid-depth HMA temperatures, appear to indicate that cracks N2, and N8 are shown in Table 7.3. The evolution, monitor- are propagating through the upper layers. Two separate mod- ing, and calculation of the crack areas are documented by els are shown in Table 7.4 with coefficients for traffic before Priest and Timm (73). The degree of cracking in Section N8, and after the point when the bond appears to have failed. with the rich bottom layer, was unexpected, particularly when A generic relationship for both the triple trailer and five- compared with the performance of Section N7. Willis and axle single trailer was developed for the sections as a function Timm (75) conducted a forensic evaluation that indicated of thickness (73). The generic equation (37) was used to cal- slippage or debonding between the rich bottom layer and the culate the strains resulting from the five-axle single trailer for overlying base layer. Cracking apparently began in the over- Section N1. Insufficient data were collected before N1 cracked lying layer. 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 Shift Factors Based on Measured Strain debonding between the base and rich bottom layer. The eight structural sections from the 2003 NCAT Test Track were instrumented to measure in situ strain in the asphalt, com- t = 2.1228T 1.190 - 26.448t (37) pressive stresses in the unbound layers, and moisture and tem- perature as a function of depth in the pavement structure (72). where, Temperature and moisture data were collected on an hourly t = horizontal tensile strain (ms), basis throughout the two-year loading cycle. High-speed data T = mid-depth HMA temperature, °F, and (2,000 samples per second) from the asphalt strain gauges t = HMA thickness (in.). and unbound layer pressure cells were collected at least once a month for at least three truck passes for each section and The low-speed data acquisition system collected the average weekly after cracking was initially observed. The layout of the mid-depth HMA temperature for each section on an hourly instrumentation for each section is shown in Figure 7.3. basis. The numbers of laps by each triple trailer and five-axle Based on the high-speed data acquisition, Priest and Timm single trailer truck were recorded for each hour. Both Priest (73) developed strain prediction models for each of the sec- (76) and Willis (77) developed spreadsheets to calculate the Table 7.3. 2003 NCAT Test Track structural section failure data (73). Section Failure Date Cracking, % of Cracking, % of Total Lane 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
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76 Figure 7.3. Typical gauge array for 2003 NCAT Test Track structural sections ( 72). Table 7.4. Triple-trailer regression analyses for strain-temperature relationship (73 [not N8]). 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 1 Limited data were available. Table 7.5. Five-axle single-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 1.170E-04 3.157 0.850 9/1/2004)
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77 Table 7.6. Fatigue transfer function coefficients for 2003 NCAT Test Track 19.0-mm NMAS base mixes. 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 number of axle repetitions and respective strain for each hour ni = number of load applications at condition i, and of the 2003 NCAT Test Track loading cycles. Transfer func- Nfi = allowable load applications to failure for condition i tions were developed from the laboratory beam fatigue tests (in this case, determined using the laboratory fatigue in the form of Equation 38, as follows: transfer function shown in Equation 38 and Table 7.6). k2 1 Based on the observed level of cracking, Section N6 was N f = 1 × k1 (38) t assigned a cumulative damage factor of 0.7 after the applica- tion of 10 million ESALs at the end of the 2003 NCAT Test where, Track cycle (73). Willis (77) calculated strain for each hour Nf = number of load repetitions (cycles) to failure, based on the loading conditions using Equation 36 and the t = tensile strain at the bottom of the HMA layer, coefficients in Tables 7.4 and 7.5 based on the recorded mid- k1 and k2 = regression constants, and depth HMA temperature. The spreadsheets were modified to 1 = shift factor between laboratory and field per- calculate Ni for each section, hour, and loading condition formance (initially set at 1.0). 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 The regression constants for the 2003 NCAT Test Track by their respective Ni to determine the incremental damage. 19.0-mm NMAS base mixes, based on the beam fatigue tests The cumulative damage, D, was determined by summing all conducted as part of this study are shown in Table 7.6. the incremental damage according to Equation 39 until the The incremental damage was calculated for each hour of date when failure occurred as identified in Table 7.3. For Sec- loading by truck type (triple trailer or five-axle single trailer) tion N6, the damage was summed until the end of the 2003 using Miner's Hypothesis, shown in Equation 39, where fail- loading cycle (application of 10 million ESALs). The shift fac- ure is approached when the cumulative damage approaches tor for each section, 1, in Equation 38 was solved for using 1.0 (78). The failure criterion was defined as fatigue cracking Microsoft Excel's Solver Function such that the cumulative equal to 20% of the total lane area. 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 n n ni cycles. The shift factors were determined with and without D = Di = (39) i =1 i =1 N f i the inclusion of an endurance limit. The endurance limit represented by the lower limit of the 95% confidence inter- where, val was used in the calculations. The calculated shift factors D = cumulative damage, between laboratory and field performance are summarized Di = incremental damage for condition (in this case, repeti- in Table 7.7. Based on the data in Table 7.7, the use of an tions of a given axle's load at a given HMA temperature endurance limit does not affect the shift factor for pavement over a given hour), sections likely to fail in fatigue. Table 7.7. Calculated shift factors between laboratory and field performance based on measured strains. Section 19.0-mm NMAS Base Shift Factor Shift Factor with Mix 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: 1 Until debonding occurred, then PG 67-22 optimum.
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78 Shift Factors Based on Calculated Strains ko = at-rest earth pressure coefficient, Using M-E Design Programs oct = octahedral shear stress = 1/3((1 - 2)2 + (1- 3)2 + (2-3)2)1/2, and In Chapter 6, three classes of M-E pavement design programs k1, k2, k3 = regression coefficients. were described, as follows: 1. Those that use equivalent axle loads and equivalent tem- A design resilient modulus was calculated using Equation peratures; 40 for the pavement structures shown in Figure 7.1. Addi- 2. Those that use equivalent temperatures in the form of tional values were calculated for a 12-in. thick HMA section seasons and axle load distributions for each axle type; and for use in sensitivity analyses to be described later in this 3. Those that use detailed temperature, load, and incremen- chapter. The design values were calculated using an iterative tal damage calculations. process as described in the MEPDG (80). The wheel-load stresses were calculated for a 20,000-lb, single-axle load using PerRoad is an example of the second type and the MEPDG WESLEA for Windows. Dynamic modulus values for the PG is an example of the third type of pavement design program. 67-22 and PG 76-22 mixes were calculated at a mean annual Both programs were used to estimate shift factors between temperature of 74.3°F and 10 Hz frequency. The design resilient predicted and field performance. modulus values are summarized in Table 7.9. All of the design The inputs used in the M-E design programs are described values matched the calculated values within 5%. The lower Mr below. Where possible, the same inputs were used in both Per- values for the granular base were unexpected; however, they Road and the MEPDG. Resilient modulus (Mr) values were cal- were consistent with previous laboratory testing conducted by culated for both the subgrade and the granular base. Labora- the Alabama Department of Transportation (81) and back- tory triaxial resilient modulus tests were performed on samples calculated values from falling-weight deflectometer tests (79). of both unbound materials according to the NCHRP 1-28A Also, the subgrade consisted of a very angular material with protocol by Burns, Cooley, Dennis, Inc. The multivariable, good compactibility and strength. non-linear stress sensitivity model (Equation 40) recom- Dynamic modulus testing was conducted on lab-compacted, mended by the MEPDG was fit to the test data (79, 80). The field mixed material sampled from the 2003 NCAT Test Track model coefficients are shown in Table 7.8 for the subgrade by Purdue University. For the MEPDG, the dynamic modu- and unbound granular base materials. lus (E) results were used as Level 1 inputs. For PerRoad, a sig- k2 k3 moidal function, in the form recommended by the MEPDG M r = k1 pa × × oct + 1 (4 40) pa pa (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 where, NMAS base mixtures. The E master curves for the PG 67-22 Mr = resilient modulus, pa = atmospheric pressure (14.696 psi), and PG 76-22 mixtures are shown graphically in Figure 7.4. = bulk stress = 1 + 2 + 3 = 1 + 2x,y, Observation of the data in Table 7.10 and Figure 7.4 suggests 1 = major principal stress = z + po, that the E values for the PG 67-22 and PG 76-22 mixtures are 2 = intermediate principal stress = 3 for Mr approximately equal. test on cylindrical specimen, The temperature data from the 2003 cycle of the NCAT 3 = minor principal stress/confining pressure Test Track were used for the PerRoad analysis. Figure 7.5 = x,y + ko (po), shows a frequency distribution of the air temperature data. z = vertical stress from wheel load(s) calcu- The temperature corresponding to the 10th, 30th, 50th, 70th, lated using layered-elastic theory, and 90th percentiles of the frequency distribution were used x,y = horizontal stress from wheel load(s) calcu- to identify five "seasons" for the analysis. The air tempera- lated using layered-elastic theory, tures were converted to pavement temperatures at 1/3 of the po = at-rest vertical pressure from overburden HMA depth using Equation 41 (7). Dynamic modulus values of paving layers above unbound layer or were then calculated at 10 Hz for five temperatures determined subgrade, from a frequency distribution of the pavement temperatures Table 7.8. Unbound materials stress-sensitivity model coefficients (79). Material k1 k2 k3 R2 Granite Base 716.28 0.8468 -0.4632 0.93 Subgrade 1878.97 0.4067 -0.7897 0.42
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79 Table 7.9. Design resilient modulus values for 2003 NCAT Test Track. Section Binder Grade Total HMA Granular Base Subgrade Mr, Thickness, in. Mr, psi 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 experienced by the structural sections of the 2003 NCAT Test Z = depth below surface at the upper third point of Track. The modulus values used for determining shift factors the layer, in. for the test track sections and subsequent sensitivity analyses are presented in Table 7.11. For PerRoad, the load spectra were determined from the 2003 NCAT Test Track records. The average daily truck traffic 1 34 in the design lane was 1,237 trucks. The triple trailers made up MMPT = MMAT 1 + - +6 Z +4 (41) Z +4 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 where, (or repetitions of an axle configuration) per day. The axle MMPT = mean monthly pavement temperature, °F, configurations had the following distribution: 15.3% steer axles MMAT = mean monthly air temperature, °F, and (10,00012,000 lbs); 67.7% single axles (20,00022,000 lbs); and Table 7.10. Dynamic modulus data of 2003 NCAT Test Track base mixtures (after 81). Temperature, Frequency, PG 76-22 Mixture PG 67-22 Mixture °F Hz Avg. E*, Std. COV, Avg. E*, Std. COV, psi Dev. % psi Dev. % E*, psi E*, psi 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% 14 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% 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% 40 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% 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% 70 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% 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% 100 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% 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% 130 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% 25 218,137 16,623 7.6% 215,345 40,140 18.6%
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80 10000 1000 |E*|, ksi 100 PG 67-22 PG 76-22 10 -6.00 -4.00 -2.00 0.00 2.00 4.00 Log Reduced Frequency, Hz Figure 7.4. Master curves for PG 67-22 and PG 76-22 19.0-mm NMAS base mixtures at optimum asphalt content. 7000 120% 6000 100% 5000 80% Frequency 4000 60% 3000 Frequency 40% 2000 Cumulative % 1000 20% 0 0% 10 20 30 40 50 60 70 80 90 0 0 e 10 11 or M Air Temperature, °F Figure 7.5. Frequency distribution of air temperature data for the 2003 NCAT Test Track. Table 7.11. Summary of PerRoad E* inputs. Sections N1 and N2, 5 in. thick Sections N3 and N4, 9 in. thick Sections N5 and N6, 7 in. thick Perpetual Section E*, psi E*, psi E*, psi E*, psi 20th Percentile Length, Air Season Weeks Temperature, °F MMPT, °F PG 67-22 PG 76-22 MMPT, °F PG 67-22 PG 76-22 MMPT, °F PG 67-22 PG 76-22 MMPT, °F PG 67-22 PG 76-22 Summer 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
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81 Table 7.12. Shift factors from PerRoad analyses. Section Shift Factor Based on All Shift Factor Neglecting Seasons 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. 17.0% tandem axles (20.6% of which were 32,00034,000 lbs transfer functions developed as part of this research). The and 79.4% of which were 40,00042,000 lbs). For the MEPDG, climate data were determined from the Enhanced Integrated the triple-trailer trucks were modeled as FHWA Class 13 vehi- Climatic Model using the test track's coordinates: latitude cles, neglecting the steer axle, and the five-axle single trailer 32.36, longitude -85.18, elevation 630 ft, and depth to water truck was modeled as a Class 9 vehicle. table (on north tangent) of 12.5 ft. Three weather stations' Shift factors were calculated using PerRoad for three sec- data were used in the analysis: Columbus, GA; Troy, AL; and tions: N1, N2, and N6. It was not felt that Section N8, with Montgomery, AL. The subgrade and granular base were mod- debonding occurring part way through the loading cycle, eled as Level 2 inputs. The Mr values are summarized in Table could be modeled with PerRoad. PerRoad runs a 5,000-cycle 7.9. The remaining granular base and subgrade inputs were Monte Carlo simulation. The default variability was used for taken from Taylor and Timm (79). the modulus and thickness of the HMA and granular layers. Level 1 inputs were used for the HMA. The entire HMA Monte Carlo runs are distributed over the five seasons based layer was modeled as the base material for simplicity (recall on the number of weeks for each season and based on the dis- the surface layer is only 1-in. thick). The dynamic modulus tribution of axle loads. A resulting strain at the bottom of results are summarized in Table 7.10. The binder proper- the HMA layer is output for each iteration of the Monte Carlo ties are summarized in Table 7.13. The volumetric proper- simulation. The strain was converted to damage per axle ties for specific sections were taken from Taylor and Timm repetition using Equations 38 and 39 and the coefficients in (79). For the sensitivity analyses, described in the next Table 7.6 corresponding to the mixture used in a particular section, the average volumetric properties were used, as section. The average damage per axle repetition was calcu- follows: lated and multiplied by the total number of axle repetitions when the section failed or, in the case of Section N6, reached · Air voids = 6%, the end of the 2003 loading cycle. A shift factor was determined · Volume of effective binder = 10.5%, and for the transfer function for a given section using Microsoft · Unit weight = 150.5 pcf. Excel Solver by minimizing the difference squared between the observed and calculated total damage. The shift factors Unless otherwise stated, the MEPDG default values were are summarized in Table 7.12. Because Sections N1 and N2 used for uncommon items, such as thermal properties. did not go through a summer before they failed, the summer Unlike PerRoad, the MEPDG does not output its raw season data were removed and a new average damage and layered elastic calculations. Therefore, a shift factor could not fatigue transfer function shift factor calculated. This shift be calculated directly in the same manner as was done with factor is lower since higher strains (and hence more damage) PerRoad. The predicted cracking as a function of time is shown were observed during the summer season. in Figure 7.6 for Section N1 and in Figure 7.7 for Sections N2 An estimate of predicted cracking for the 2003 Test Track and N6. The MEPDG provides the predicted (50% reliability) Sections was determined using the MEPDG (Version 1.0) bottom-up fatigue cracking, termed maximum cracking, and and the nationally calibrated fatigue model (not the fatigue the predicted cracking at some level of reliability, in this case, Table 7.13. 2003 NCAT Test Track binder properties for MEPDG. Test PG 67-22 PG 76-22 Temperature, G*, Pa Delta, ° G*, Pa Delta, ° °F 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
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82 Bottom-Up Cracking - Alligator 100 Maximum Cracking 90 Bottom-Up Reliability 80 Maximum Cracking Limit Alligator Cracking (%) 70 60 50 40 30 20 20.2% Cracking Observed , 20.1% Predicted, Section N1 10 0 0 6 12 18 24 Pavement Age (month) Figure 7.6. MEPDG predicted cracking for Section N1 (PG 76-22), 2003 NCAT Test Track. 90%, termed bottom-up reliability in Figures 7.6 and 7.7 (and ing (19.5%) exceeded the maximum cracking (14.4%), but in the MEPDG output). The MEPDG recommends reliabilities was again less than the 90% reliability cracking (32.5%). between 85% and 97% for urban interstate-type pavements In the MEPDG, damage is related to predicted cracking and between 80 and 95% for rural interstate-type pave- according to Equation 42 (84). Note that the minus sign ments (83). Observation of Figure 7.6 suggests that the max- between C1 and C2 in the equation in El-Basyouny and Witczak imum cracking (20.1%) closely approximates the observed (74) is incorrect, and should be a plus sign as shown below. cracking (20.2%) for Section N1 at the 2003 NCAT Test Track. However, the 90% reliability bottom-up cracking is signif- 6, 000 1 FC = × 60 (42) icantly higher (38.2%). For Section N2, the observed crack- 1+ e C1 + C 2 × Log D Bottom-Up Cracking - Alligator 100 N2 Maximum Cracking 90 N2 Bottom-Up Reliability Maximum Cracking Limit 80 N6 Maximum Cracking Alligator Cracking (%) 70 N6 Bottom-Up Reliability 60 50 19.5% Cracking Observed, 14.4% Predicted Section N2 40 30 20 10 0 0 6 12 18 24 Pavement Age (month) Figure 7.7. MEPDG predicted cracking for Sections N2 and N6 (PG 67-22), 2003 NCAT Test Track.