Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.

Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.

OCR for page 111

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.

OCR for page 111

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 %.

OCR for page 111

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.

OCR for page 111

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

OCR for page 111

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
11.1.5.1 Equation used for extrapolation and R2 value for equation
11.1.5.2 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.