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112 APPENDIX C Proposed Standard Practice for Extrapolating Long-Life Beam Fatigue Tests Using the Ratio of Dissipated Energy Change (RDEC) AASHTO Designation: PP XX-XX 1. Scope 1.1 This practice describes methodology for extrapolating long-life Beam Fatigue Tests Using the RDEC 1.2 This standard may involve hazardous materials, operations, and equipment. This standard does not purport to address all of the safety problems associated with its use. It is the responsibility of the user of this procedure to establish appropriate safety and health practices and to determine the applicability of regulatory limitations prior to its use. 2. Referenced Documents 2.1 AASHTO Standards · T 321, Determining the Fatigue Life of Compacted Hot-Mix Asphalt (HMA) Sub- jected to Repeated Flexural Bending. 2.2 Other Publications · NCHRP 9-38, "Endurance Limit of Hot Mix Asphalt Mixtures to Prevent Fatigue Cracking in Flexible Pavements," Draft Final Report. 3. Terminology 3.1 Normal strain levels strain levels where failure (50 percent of initial stiffness) occurs in less than 12 million cycles. For tests conducted at 20 °C, strain levels of 300 micro- strain or greater generally meet this requirement. 3.2 Low Strain levels strain levels where failure (50 percent of initial stiffness) does not occur by 12 million cycles. The failure point of low strain tests generally needs to be extrapolated by one of the methods described in this document.
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113 4. Summary of Practice 4.1 This practice describes the analysis needed to extrapolate the failure point of long-life beam fatigue tests that are not tested to failure (50 percent reduction in initial stiffness). 5. Significance and Use 5.1 The extrapolation procedure can be used to estimate the failure point of fatigue tests which do not fail in a reasonable amount of loading cycles (<12,000,000). 6. Apparatus 6.1 Specimen Fabrication Equipment Equipment for fabricating beam fatigue test speci- mens as described in AASHTO T 321, Determining the Fatigue Life of Compacted Hot- Mix Asphalt (HMA) Subjected to Repeated Flexural Bending. 6.2 Beam Fatigue Test System Equipment for testing beam fatigue samples as described in AASHTO T 321, Determining the Fatigue Life of Compacted Hot-Mix Asphalt (HMA) Subjected to Repeated Flexural Bending. 6.3 Analysis Software Data is collected during the test using a data acquisition system described in section 6.2. Data analysis can be conducted using a spreadsheet program or variety of statistical packages. 7. Hazards 7.1 This practice and associated standards involve handling of hot asphalt binder, aggregates and asphalt mixtures. It also includes the use of sawing and coring machinery and servo-hydraulic or pneumatic testing equipment. Use standard safety precautions, equipment, and clothing when handling hot materials and operating machinery. 8. Standardization 8.1 Items associated with this practice that require calibration are included in the documents referenced in Section 2. Refer to the pertinent section of the referenced documents for information concerning calibration. 9. Beam Fatigue Test Data 9.1 Test Specimen Fabrication 9.1.1 Prepare test specimens to the target air void content and aging condition in accordance with AASHTO T 321. The target air void content should be representative of that expected to be obtained in the field. A target air void content of 7 percent was used for mixes produced at optimum asphalt content in the NCHRP 9-38 research. A reduced air void content would be expected for optimum plus or so-called rich-bottom type mixes. Note 1 A reasonable air void tolerance for test specimen fabrication is ± 0.5 %.
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114 9.2 Testing Conditions 9.2.1 Samples tested to a minimum of 10 million cycles, which have not reached 50 percent of initial stiffness, may be extrapolated to determine a failure point as described in the following section. 10. Data Analysis to Extrapolate Long-life Fatigue Test Using RDEC Beam fatigue tests conducted at low strain levels are unlikely to fail in a reasonable number of cycles. 10.1 Ratio of Dissipated Energy Change (RDEC) 10.1.1 PV calculation for normal strain testing 10.1.1.1 Determine the number of loading cycles, Nf , to failure from testing. 10.1.1.2 Obtain a dissipated energy (kPa) vs. loading cycle (DE-LC) relationship. Obtain a best fit equation for the DE-LC data, using a power law relationship. From the best fit equation, record the slope, f, of the curve, that can best represent the original curve. Figure 1 illus- trates a DE-LC fitted curve. 10.1.1.3 Calculate RDEC. By definition, RDEC is the ratio of dissipated energy change between two loading cycles by the number between the cycles, that is, the average ratio of dissi- pated energy change per loading cycles, as seen in Equation 1. DE a - DEb RDEC a = (1) DE a (b - a ) where, RDECa = the average ratio of dissipated energy change at cycle a, comparing to next cycle b ; a, b = load cycle a and b, respectively. The typical cycle count between cycle a and b for RDEC calculation is 100, i.e., b - a = 100; DEa, DEb = the dissipated energy (kPa) produced in load cycle a, and b, respectively. IDOT03 mix 3N704B DE vs. Loading cycles 800 microstrain 1.4 DE (kPa) 1.2 1 0.8 Slope f = - 0.1638 0.6 y = 3.4255x-0.1638 0.4 R2 = 0.9512 0.2 Nf50 0 0 1000 2000 3000 4000 5000 Loading cycles Figure 1. DE vs. LC chart with fitted curve.
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115 10.1.1.4 The average RDEC for an arbitrary 100 cycles at cycle `a' can be simply calculated using Equation 2. f 100 1- 1+ a RDEC a = (2) 100 where, f = the slope from the regressed DE-LC curve 10.1.1.5 Calculate the plateau value (PV). The PV is defined as the RDEC value at the number of cycles equal to the failure point (Nf50). Failure is defined as a 50 percent reduction in initial stiffness, with the initial stiffness being determined at the 50th loading cycle. The PV is determined using Equation 3. f 100 1- 1+ Nf50 PV = (3) 100 where, f = the slope from the regressed DE-LC curve (kPa/cycle) Nf50 = 50% stiffness reduction failure point 10.1.2 PV calculation for low strain testing 10.1.2.1 Plot the DE-LC data and fit the DE-LC curve using the power law relationship. Obtain the f factor of the curve. 10.1.2.2 To achieve the best curve fit, it is recommended to eliminate the initial segment of the DE-LC curve, but use the later part to ensure the fitted curve visually best represents the curve's outspread trend. The fitted segment should not be less than 1/4 of the total testing length to avoid being misleading. 10.1.2.3 Calculate RDEC at each loading cycle using Equation 2, where f is given by the fitted DE-LC curve. Plot the RDEC-LC curve (log-log). 10.1.2.4 Plot the unique PV-Nf curve as shown by Equation 4 on the same chart PV = 0.4428 Nf50 -1.1102 (4) 10.1.2.5 Extend the RDEC-LC curve until it crosses the unique PV-Nf curve. The intersection point of these two curves produces: y = PV, x = Nf50 10.1.2.6 For |f| < 0.25 (which is the case for most fitted DE-LC curves from fatigue testing), calculate PV and Nf50 using equations 5 and 6, respectively. Note: Figure 2 illustrates the fatigue life prediction using the RDEC approach at low strain testing. f 100 1- 1+ Nf50 f PV = - (5) 100 Nf50
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116 0.01 0.001 0.0001 800 microstrain 1E-05 500 microstrain 1E-06 RDEC, log 300 microstrain 1E-07 Nf PV-Nf Unique Line Nf 1E-08 Nf 1E-09 FEL Tests 3N904A(Nf, PV) 300 microstrain 1E-10 5N90P2A(Nf,PV) 100 microstrain 1E-11 Nf Nf 1E-12 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10 1.E+11 1.E+12 loading cycles, log 5N90P3B-800ms 5N90P4A-500ms 5N90P4B-300ms 5N90P2A-100ms 3N904A-300 ms Power (5N90P2A-100ms) Power (3N904A-300 ms) Figure 2. Fatigue life prediction using RDEC approach. -9.0744 -f Nf50 = 0.4428 (6) 11. Report 11.1 For each sample, report the following: 11.1.1 Sample air voids 11.1.2 Test Temperature 11.1.3 Initial flexural stiffness (measured at 50 cycles) 11.1.4 Method of Extrapolation 18.104.22.168 Equation used for extrapolation and R2 value for equation 22.214.171.124 Extrapolated fatigue life Nf for 50 percent of initial stiffness 12. Keywords 12.1 Beam fatigue, long-life 13. References 13.1 Shen, S. and S. H. Carpenter. "Application of Dissipated Energy Concept in Fatigue Endurance Limit Testing" In Transportation Research Record 1929, Transportation Research Board, Washington, DC, 2005, Pp 165-173.