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CHAPTER 6
Examination of LTPP Database for Indications
of an Endurance Limit
Introduction 2. Design procedures that use the equivalent temperature
concept but the axle load distribution for each axle type--
Flexible pavements have traditionally been designed to These procedures also use the cumulative damage con-
limit load-related cracking. The more traffic, the thicker the cept to determine the amount of fracture damage for each
HMA layer to limit the load-related cracks to some design structure. The PerRoad Program would fall within this
limit. As noted, however, industry has been proposing the category (63).
use of an endurance limit as a mixture property for HMA 3. Design procedures that calculate and use pavement tem-
layers. The endurance limit is defined as the tensile strain peratures at specific depths over some time interval, gener-
below which no fracture or fatigue damage occurs and applies ally less than a month--These procedures typically use the
to cracks that initiate at the bottom of the HMA layer. Almost incremental damage concept to determine the amount of
all design and analysis procedures that use the endurance fracture damage within specific time intervals and at spe-
limit concept assume that one value applies to all HMA mix- cific depths within the pavement structure. The MEPDG
tures and temperatures. Values that have been used vary from would fall within this category (64).
65 to 120 ms.
This section of the report has three objectives: discuss the The equivalent temperature concept simply defines one
incorporation of the endurance limit design premise into temperature for which the annual or seasonal damage equals
mechanistic-empirical based pavement design procedures, the cumulative damage determined at monthly or more fre-
confirm the reality and values suggested for the endurance quent intervals. The equivalent temperature is used to estimate
limit, and recommend field studies to support use of this con- the dynamic modulus for calculating the tensile strain at the
cept in the MEPDG software. bottom of the HMA layer on an annual or seasonal basis.
All M-E based design procedures, regardless of the group,
use Miner's hypothesis to calculate fracture damage, and
Including the Endurance
assume that wheel-load-related alligator cracks initiate at the
Limit Design Premise into
bottom of the HMA layer and propagate to the surface with
Mechanistic-Empirical-Based
continued truck loadings, with the exception of the MEPDG.
Pavement Design Procedures
In addition, all M-E based design procedures use the max-
All mechanistic-empirical pavement design procedures can imum tensile strain at the bottom of the HMA layer as the
be grouped into three types relative to wheel-load-induced pavement response parameter for calculating fracture damage
cracking. These are as follows: and predicting the amount of alligator cracks. Those design
procedures apply the endurance limit design premise in one
1. Design procedures that use the equivalent axle load and of three methods, which are summarized as follows:
equivalent temperature concepts--The equivalent tem-
perature is determined based on an annual or monthly 1. The introduction of the endurance limit design premise
basis. These procedures typically use the cumulative dam- into those design procedures that use the equivalent tem-
age concept to determine the amount of fracture damage perature and equivalent axle load concepts is straight for-
over the design period for each structure. The DAMA Pro- ward. Stated simply, the maximum tensile strain is cal-
gram would fall within this category (62). culated at the equivalent temperature and axle load and
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Standard Mix; Conv. Low Modulus, Conv. High Modulus, Conv.
Standard Mix, Full-Depth Endurance Limit
180
Tensile Strain, Bottom of HMA,
160
140
120
micro-strains
100
80
60
40
20
0
7 8 9 10 11 12 13 14 15 16 17 18 19
HMA Thickness, inches
Figure 6.1. Tensile strains calculated for an 18-kip single-axle load
for the equivalent annual temperature for different HMA mixtures.
compared to the endurance limit. The HMA layer thickness with this method is that the higher loads result in signifi-
is simply determined for which the maximum tensile strain cantly higher damage indices; an increase in axle load will
equals or is less than the endurance limit. Figure 6.1 illus- result in an increase in damage to a power of about four.
trates the use of the endurance limit within this method. Thus, the probability of cracking is much higher than the
2. The introduction of the endurance limit into those design probability of a specific tensile strain being exceeded.
procedures that use the equivalent temperature concept 3. Those design procedures that use the incremental dam-
but use the actual axle load distribution is also fairly age concept establish a threshold value for the tensile
straight forward. The maximum tensile strain is calculated strain, below which the fracture damage is assumed to
at the equivalent temperature for each axle load within the be zero. In other words, the procedure simply ignores
axle load distribution. The axle load distribution for each calculated tensile strains that are equal to or less than the
axle type is used to determine the probability of the tensile value set as the endurance limit for determining the incre-
strain exceeding the endurance limit. The designer then mental damage within a specific time period and depth.
considers that probability of exceeding that critical value Successive runs have been made with the MEPDG to deter-
in designing an HMA layer for which no fatigue damage mine the difference in calculated fracture damage with and
would accumulate over time. Figure 6.2 illustrates the use without using the endurance limit as an HMA mixture
of the endurance limit within this method. One concern property. Figures 6.3 and 6.4 illustrate the increasing
Standard Mix, Conv. Low Modulus, Conv.
High Modulus, Conv. Standard Mix, Full-Depth
105
Endurance Limit (65 micro-
Probability of Exceeding
100
95
strains), %
90
85
80
75
70
7 8 9 10 11 12 13 14 15 16 17 18 19
HMA Thickness, inches
Figure 6.2. Probability of exceeding the endurance limit for
different HMA mixtures using typical axle load distributions and
seasonal temperatures.
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Summer, 250 ksi E=450 ksi E=650 ksi Winter, 900 ksi Endurance Limit
160
Tensile Strain, Bottom of HMA
140
Layer, micro-strains
120
100
80
60
40
20
0
6 16 26 36
Single Axle Load, kips
Figure 6.3. Increasing tensile strains for varying single-axle loads
for different seasons or dynamic modulus within those seasons
(HMA thickness equals 15 in.).
maximum tensile strains for varying single-axle loads for ing in the wheel paths is assumed to initiate at the surface and
different dynamic modulus values and HMA thicknesses, propagate downward. The MEPDG assumes that both types
respectively. of cracking are caused by load-induced tensile strains. That
hypothesis, however, has yet to be confirmed.
Version 0.9 of the MEPDG did not include the endurance As noted above, the new MEPDG uses an incremental dam-
limit design premise in the recalibration process of the design age index. Fracture damage is computed on a grid basis with
methodology or software. In other words, Version 0.9 assumes depth for each month within the analysis or design period.
that any tensile strain in the HMA layer induces some fac- Temperatures are computed with the Integrated Climatic
ture damage. Two types of load-related cracking are pre- Model at specific depth intervals for each hour of the day.
dicted for designing flexible pavements in accordance with These temperatures are then grouped into five averages at
the MEPDG--alligator cracking and longitudinal cracking in each depth interval for each month. The fatigue cracking
the wheel path. Alligator cracking, the more common crack- (alligator cracking) equation is used to calculate the amount
ing distress used in design, is assumed to initiate at the bottom of fracture damage for each depth interval and month. The
of the HMA layer. These cracks propagate to the surface with monthly damage indices are then summed over time to predict
continued fracture damage accumulation. Longitudinal crack- the area of fatigue cracking at each depth interval.
8-kip Load 14-kip Load 18-kip Load
22-kip Load 28-kip Load 34-kip Load
Endurance Limit
300
Maximum Tensile Strain,
250
micro-strain
200
150
100
50
0
6 8 10 12 14 16 18 20
HMA Thickness, inches
Figure 6.4. Increasing maximum tensile strains for varying single-
axle loads for different HMA thicknesses (HMA dynamic modulus
equals 450 ksi; equivalent annual modulus).
