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International Journal of Pavement EngineeringPublicat ion det ails, including inst ruct ions for aut hors and subscript ion informat ion:ht t p: / / www. t andfonl ine.com/ loi/ gpav20
Impact of different ageing levels on binder rheologySara Bressia, Alan Cart erb, Nicolas Buechec & André-Gil les Dumont a
a Traf f ic Facil i t ies Laborat ory LAVOC-EPFL, St at ion 18, Rout e Cant onale, 1015 Lausanne,Swit zerlandb Départ ement de Génie de la Const ruct ion ETS, 1100 Rue Not re-Dame Ouest , Mont real QCH3C 1K3 Mont real, Canadac NibuXs, Rue de Bassenges 4, 1024 Ecublens, Swit zerlandPubl ished onl ine: 02 Jan 2015.
To cite this article: Sara Bressi, Alan Cart er, Nicolas Bueche & André-Gil les Dumont (2015): Impact of dif ferent ageing levelson binder rheology, Int ernat ional Journal of Pavement Engineering, DOI: 10.1080/ 10298436.2014.993197
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Impact of different ageing levels on binder rheology
Sara Bressia*, Alan Carterb, Nicolas Buechec and Andre-Gilles Dumonta
aTraffic Facilities Laboratory LAVOC-EPFL, Station 18, Route Cantonale, 1015 Lausanne, Switzerland; bDepartement de Genie de la
Construction ETS, 1100 Rue Notre-Dame Ouest, Montreal QC H3C 1K3 Montreal, Canada; cNibuXs, Rue de Bassenges 4,
1024 Ecublens, Switzerland
(Received 4 December 2013; accepted 23 November 2014)
This paper evaluates the variability of binder rheology for different ageing levels and the influence of ageing at different testingtemperatures. Three different ageing levels were applied on a single type of bitumen with a penetration grade of 70/100.Theartificial ageing of the binder was performed using the rolling thin-film oven test and the pressure ageing vessel. Therheological behaviour was investigated at low temperatures with the bending beam rheometer (BBR) and at medium and hightemperatures with the dynamic shear rheometer (DSR). Several experiments were conducted to determine the range ofstiffness and complexmodulus results, the type of distribution comparing real and theoreticalmodels, and the effects of ageingon the variability of the rheological behaviour. It was shown that not only the mean results from BBR and DSR tests changewith ageing, but also the variability of the results changes with ageing. This would have an impact on mechanistic-empiricalpavement design because it would influence the calculated stresses and strains as well as the calculated reliability.
Keywords: binder; ageing; probability distribution; variability; stiffness; complex modulus; bending beam rheometer;dynamic shear rheometer; reliability; mechanistic-empirical; pavement design
Introduction
Although most agencies throughout the world use
empirical pavement design methods, the use of mechan-
istic-empirical (M-E) pavement design methods is clearly
on the increase. With M-E pavement design methods,
rheological properties of the materials composing the
pavement structure are used to evaluate the pavement
behaviour under loads and estimate degradations.
However, the variability of these properties should be
more precisely taken into account.
One of the main criteria for obtaining accurate results
concerning M-E pavement design methods is taking into
account the degradation of material properties. In this
framework, the evaluation of the variability that affects the
rheology of materials during their service life becomes the
starting point for more reliable design. Because the input
parameters on which the pavement design system is based
exhibit significant variability (Darter et al. 1972,
Noureldin et al. 1994, Timm et al. 1998, Bush 2004,
Kenis and Wang 2004), this variability must be properly
defined before any calculations are undertaken in the
pavement design method. The variability regarding
material properties affecting pavement performance can
be divided into the following two categories:
(1) Spatial variability that includes a real difference in
the basic properties of materials from one point to
another in what are assumed to be homogeneous
layers and a fluctuation in the material and cross-
sectional properties due to construction quality
(Kim and Buch 2003). For example, the back-
calculated asphaltic material stiffness modulus
distribution over a given pavement surface
generally fits a Gaussian (normal) frequency
curve (Collop et al. 2001).
(2) Input parameter variability that originates from
the inherent variability of the mechanical proper-
ties of the materials and the variability of tests
used to measure those properties.
Variability is the core of the reliability considerations
in pavement design. Reliability issues have been addressed
since as early as the 1970s (Lemer and Moavenzadeh
1971). The AASHTO (1986, 1993) pavement design
approach incorporated the reliability concept in the design
equations, and the latest M-E design procedure in the USA
(NCHRP 2005) suggests independent failure probability
models for rutting, fatigue and thermal cracking based on
field performance data (NCHRP 1-37A 2005). Never-
theless, this approach does not predict the change in
reliability when the variability of one (or more) of the
parameters changes with time. Indeed, nowadays, the
variability used to determine reliability remains constant
throughout the service life (Maji and Das 2008). Moreover,
limited studies are available in the literature which deal
with the variability of all the possible input parameters
affecting the reliability of a pavement design.
q 2015 Taylor & Francis
*Corresponding author. Email: [email protected]
International Journal of Pavement Engineering, 2015
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Variability is directly linked with the distribution of
the results of a given test around the mean. It is common to
assume that results follow a normal or log-normal
distribution when insufficient information is available.
However, there are many different types of distribution
that can fit the experimental results (Box et al. 1978). The
study of the distribution of the results is very important
because it is one of the basic assumptions for the analysis
of variance (ANOVA) (Sprinthall 2000).
The aimof this paperwas to provide a complete study of
the inherent variability of the rheological properties of the
binder, analysing different ageing levels that represent
different steps of pavement service life. Inherent variability
takes into account the measurement uncertainties and
dispersion of results around the average value, providing
information concerning the evolution of binder character-
istics during ageing and the random error for values
considered representative. For more accurate pavement
design, the change in variability and change in the mean
value of the characteristic of the parameter itself should not
be neglected. The spatial variability is not studied here.
Materials and tests
For this study, a 70/100 non-polymer-modified asphalt
binder was used. The ageing of the binder was performed
using two different methods. First, the rolling thin-film oven
test (RTFOT, ASTM D 2872), which simulates the changes
in the properties of binders during the hot mixing at the plant
and lay-down process, was used. The secondmethod used is
the pressure ageing vessel (PAV), which is representative of
the long-term ageing due to in situ field ageing (Strategic
Highway Research Program Petersen et al. (1994).
For each ageing level – virgin (no ageing), short-term
(RTFOT) and long-term(RTFOT þ PAV) – several samples
were made to test stiffness at low temperatures with the
bending beam rheometer (BBR) and complex modulus at
high temperatures with a dynamic shear rheometer (DSR) as
explained in Table 1 for a total of 252 experiments.
DSR complex modulus tests at medium temperature
were also performed. Because the results at high and
medium temperatures exhibit the same trend, it was
decided not to show the results at medium temperature in
order to simplify the content of this paper.
In this last case, the aim was not to test extreme
temperatures but investigate useful domains for pavement
design methods and temperatures also suitable for bitumen
with narrow performance grade.
Bending beam rheometer
The BBR test provides a measure of the low-temperature
stiffness and relaxation properties of asphalt binders.
These parameters give an indication of an asphalt binder’s
ability to resist low-temperature cracking. The stiffness is
calculated with the following equation:
SðtÞ ¼pL3
4bh3dðtÞ; ð1Þ
where S(t) is the time-dependent flexural creep stiffness,
MPa; P is the constant load, N; L is the span length, mm; b
is the width of beam, mm; h is the depth of beam, mm; and
d(t) is the deflection of beam, mm.
The maximum stiffness registered during the test was
considered in this study and 12 samples for each ageing
level were tested at three temperatures: 210, 220 and
2308C.
Dynamic shear rheometer
The DSR is used to characterise the viscous and elastic
behaviour of asphalt binders at medium to high
temperatures. In this study, several frequency sweeps (21
frequencies tested) were conducted at 20, 40 and 508C
measuring the complex modulus. Among these frequen-
cies, three were selected to be compared and be
representative of low, medium and high frequencies,
respectively, 0.4, 1.0 and 10.3Hz.
Methodology
Before undertaking a more complex statistical study,
certain criteria have to be met to assess the repeatability of
the measurements (i.e. statement on a single-operator
precision). According to Equation (2), the acceptable
range r (acceptable difference between the highest and
Table 1. Summary of the experiments.
Ageing levelType oftest
Testing temperature(8C)
No. ofexperiments
Virgin BBR 230 12Virgin BBR 220 12Virgin BBR 210 12Virgin DSR 20 16Virgin DSR 40 16Virgin DSR 50 16RTFOT BBR 230 12RTFOT BBR 220 12RTFOT BBR 210 12RTFOT DSR 20 16RTFOT DSR 40 16RTFOT DSR 50 16RTFOT þ PAV BBR 230 12RTFOT þ PAV BBR 220 12RTFOT þ PAV BBR 210 12RTFOT þ PAV DSR 20 16RTFOT þ PAV DSR 40 16RTFOT þ PAV DSR 50 16
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lowest values for each point) was defined. The real range
was not expected to exceed the acceptable range with a
probability of 5% in the normal and correct operation of
the test method (ASTM C670).
r ¼ s�f ; ð2Þ
where r is the acceptable range, s is the single-operator
standard deviation for single test determination and f is the
coefficient depending on the number of repetitions for
each determination (ASTM C670).
In this study, the reproducibility, the statement on
multi-laboratory precision, was not evaluated, because all
the measurements were provided by a single operator in a
single laboratory (ASTM C802). Nevertheless, for the
purpose of the paper, it was really important to go a step
further in the statistical analysis to determine the
probability distribution of the results and the evolution
of their differences with the ageing of the materials.
Indeed, the second important step of this analysis was
to determine the probability distribution of the DSR and
BBR results in order to evaluate which theoretical models
best represent real data. In the literature, there is limited
information on this subject. The goodness of fit was also
determined by computing a probability plot.
An F-test (Fisher test) is used to ascertain whether the
variances of two populations are equal (Snedecor and
Cochran 1967). For the third step, the F-test was computed
based on results for different ageing levels and
temperatures. For this study, a 95% confidence was used.
In this case, the temperature was first kept constant and the
ageing levels were varied, and subsequently the ageing
level was kept constant and the temperature varied.
Moreover using the DSR results, a comparison was made
among different frequencies to evaluate whether ageing
has any effect on the variance of the response at different
frequencies. Where the F-test demonstrated that the
hypothesis of the same variance was acceptable, the
ANOVA was performed. Where the F-test demonstrated
that this hypothesis was not verified, a Welch test was
performed instead of the ANOVA. The Welch test is a
more robust method that accepts samples exhibiting
possibly unequal variances (Welch 1938).
The fourth step consists of the comparison of the
means. Once it has been verified that all the results follow
a normal distribution (Step 2) and the variance is equal
among the groups (Step 3), it is possible to compute an
ANOVA to determine significant differences between the
mean of rheological properties for different ageing levels.
In the ANOVA, the variation in the response measure-
ments is partitioned into components that correspond to
different sources of variation. The goal of this procedure is
to split the total variation of the data into a portion due to
random error and a portion due to changes in the values of
the independent variable. Assessing that the results were
normally distributed was fundamental in order to satisfy
one of the main hypotheses of the ANOVA test.
Indeed, the hypotheses underlying the use of the
ANOVA are (Box et al. 1978) as follows:
. Data normally distributed.
. Independent values.
. Homoscedasticity (i.e. the variance of the groups is
the same for the population). The group variances
for each treatment are equal to each other and,
together, are equal to the variance of the population.
Where the last hypothesis was not verified, a more
robust model was used – the Welch test that compares the
means, admitting unequal variance among the groups
(Welch 1938).
If the means vary, the next step is to define which
means change. For this purpose, a least significance
difference (LSD) test is performed (Ott and Longnecker
2000) using the following equation:
LSD ¼ t�a
2;df
��
ffiffiffiffiffiffiffi
2S2en
s
; ð3Þ
where t�a
2;df
� is the value of t-student related to the level of
confidence (a ¼ 0.05) and the degrees of freedom of the
residual variance, Se is the residual variance and n is the
number of experiments for each group.
At this point, the differences between the means of all
groups are calculated. If the difference (in absolute value)
is greater than LSD, the means are significantly different.
If it is less, then the means are equal.
Results analysis
For all the measurements, an acceptable repeatability was
found. An example of calculation is reported in Table 2
that provides information (acceptance range) concerning
the precision of the measurement of the virgin binder with
the BBR at2308C. The difference between the largest and
smallest of the 12 determinations is less than the difference
Table 2. Example of acceptance and real range for BBR results at 2308C for virgin binder.
Stiffness measurement (MPa) 1050 1010 988 964 930 922 922 910 884 881 787 750Stiffness mean (MPa) 916.50STD 85.83Real range (MPa) 300Acceptance range (MPa) 386.2
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between the limits of the acceptable range, thus the
repeatability is verified (ASTM C670).
Stiffness at low temperatures
The main results of the BBR are shown in Table 3, which
gives the mean, standard variation (STD) and coefficient
of variation (COV) for each group.
At all the testing temperatures, and for all the ageing
levels, it can be said that the normal distribution accurately
fits the results. In Figures 1 and 2, the example of the virgin
binder at 2108C is shown. The cumulative probability
function is comparedwith the theoreticalmodel in Figure 1,
as well as the Gaussian distribution of the experimental
data. In Figure 2, the normal probability plot is used to
evaluate the goodness of fit, which verifies that the points
are distributed along the straight line.
Even with this limited set of experimental points, the
results shown in Figures 1 and 2 clearly demonstrate that the
results of the stiffnessmeasuredwith the BBR at2108C for
this binder follow a normal distribution. The same
distribution was observed for the results at the other test
temperatures (220 and2308C). As mentioned earlier, the
data follow a normal distribution, which is one of the
hypotheses required to conduct an ANOVA.
The next step was to verify the other hypothesis that
deals with the equality of variance among the groups.
Table 4 shows the results of the F-test and it can be seen
that only in one case (2208C RTFOT þ PAV–virgin)
is the null hypothesis (Hypothesis 1) rejected because the
p-value is ,0.05 (a) (see italicised part in Table 4). In all
other cases, Hypothesis 1 is verified.
H0 : s21 ¼ s
22 ðHypothesis 1Þ;
Ha : s21 – s
22 ðHypothesis 2Þ:
ð4Þ
In the majority of cases, the variance does not change
with ageing (Table 4). The variance of the binder stiffness
at low temperatures, independent of the temperature
chosen, does not change with short- and long-term ageing.
Even if, according to Table 4, the ageing has no effect
on the variance of the BBR results at constant temperature,
the artificial ageing used in this study makes stiffness
variance more sensitive to temperature change, as shown
in Table 5. Indeed, if the same test is computed for
comparing the variance for different temperatures at the
same ageing level, different results are obtained.
As can be seen, both short- and long-term ageing have
an effect on the variance. Table 5 shows that, for most
cases, the null hypothesis is not verified, which means that
the variance differs according to temperature. For the rest
of this study, the data were analysed at constant
temperature, for which the null hypothesis is respected.
Because the F-test has shown that the variance does not
change with ageing, it is now possible to carry out an
ANOVA. In all cases (Table 6), the null hypotheses in the
ANOVA were rejected ( p-value , 0.05) and it is thus
possible to conclude that there is a highly significant
difference between the means of groups, which is not only
due to random errors.
Once it is clear that the mean varies, our interest now is
to define which means change. The LSD test was
Table 3. Mean, STD and COV of stiffness values obtained withBBR at different temperatures and for different ageing levels.
Levelofageing
Testingtemperature
(8C)
Stiffnessmean(MPa) STD
COV(%)
Virgin 230 916.50 85.83 9.4Virgin 220 414.33 21.46 5.2Virgin 210 109.22 15.76 14.4RTFOT 230 1029.82 91.18 8.9RTFOT 220 486.25 38.06 7.8RTFOT 210 152.83 12.67 8.3RTFOT þ PAV 230 1039.33 71.61 6.9RTFOT þ PAV 220 522.25 56.81 10.9RTFOT þ PAV 210 205.67 20.34 9.9
Figure 1. (a) Cumulative probability function and (b) probability mass function for virgin binder at 2108C.
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performed and the results are shown in Table 7. As can be
seen, the only case in which the means between two groups
does not change is at 2308C between the RTFOT and
RTFOT þ PAV results.
Because of the ANOVA and LSD test results, it is not
possible to keep the binder stiffness constant during the
pavement service life and implement an incremental
pavement design process that does not change material
Figure 2. Goodness of fit using normal probability plot for virgin binder at 2108C.
Table 4. F-test that compares variances of different ageing levels with temperature kept constant.
RTFOT Virgin RTFOT RTFOT þ PAV Virgin RTFOT þ PAV
2308CMean 1029.818 916.500 1029.818 1039.333 916.500 1039.333Variance 8313.164 7633.091 8313.164 5127.515 5127.515 5127.515Observations 11 12 11 12 12 12df 10 11 10 11 11 11F 1.129 1.621 1.437a 0.05 0.05 0.05p-Value 0.841 0.440 0.558F-critic 3.526 3.526 3.474Significance No No No
2208CMean 486.25 414.333 522.250 486.250 522.250 414.333
Variance 1448.386 460.424 3227.477 1448.386 3227.477 460.424
Observations 12 12 12 12 12 12df 11 11 11 11 11 11
F 3.146 2.228 7.010
a 0.05 0.05 0.05
p-Value 0.070 0.200 0.003F-critic 3.474 3.474 3.474
Significance No No Yes
2108CMean 109.217 152.833 205.667 152.833 205.667 109.217Variance 248.234 160.515 413.697 160.515 413.697 248.234Observations 12 12 12 12 12 12df 11 11 11 11 11 11F 1.546 2.577 1.667a 0.05 0.05 0.05p-Value 0.481 0.132 0.410F-critic 3.474 3.474 3.474Significance No No No
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characteristics with time. In the pavement design process,
there is a need for a model that shows significant changes
in the binder characteristics with time.
Complex modulus at medium and high temperatures
Before undertaking the complex modulus test, it is
necessary to do a stress sweep at the test temperature in
order to establish the limit of the linear visco-elastic region
of the behaviour of the binder. The Linear Visco-Elastic
(LVE) limit was defined as the point where the storage
modulus (G0) decreased to 95% of its initial value as
prescribed by the SHRP specification (Anderson et al.
1994). An example of the graphical representation of the
LVE limit obtained at 508C is provided in Figure 3.
Table 5. F-test that compares variances of different temperatures with ageing level kept constant.
2308C 2208C 2208C 2108C 2308C 2108C
Virgin binderMean 916.5 414.333 414.333 109.217 916.500 109.217Variance 7366.091 460.424 460.424 248.234 5127.515 248.234Observations 12 12 12 12 12 12df 11 11 11 11 11 11F 0.063 1.855 29.674a 0.05 0.05 0.05p-Value 2.000 0.320 0.000F-critic 3.474 3.474 3.474Significance No No Yes
RTFOTMean 1029.818 486.25 486.25 152.833 1029.818 152.833Variance 8313.164 1448.386 1448.386 160.515 8313.164 160.515Observations 11 12 12 12 11 12df 10 11 11 11 10 11F 0.174 9.023 51.791a 0.05 0.05 0.05p-Value 1.992 0.001 1.71E-07F-critic 3.665 3.474 3.526Significance No Yes Yes
RTFOT þ PAVMean 1039.333 522.25 522.25 205.667 1039.333 205.667Variance 5127.515 3227.477 3227.477 413.697 5127.515 413.697Observations 12 12 12 12 12 12df 11 11 11 11 11 11F 0.629 27.802 12.394a 0.05 0.05 0.05p-Value 1.545 0.002 2.28E-4F-critic 3.474 3.474 3.474Significance No Yes Yes
Table 6. ANOVA for comparison of mean of stiffness for different ageing levels.
SS df MS F p-Value
2308CBetween groups 110,846.9 3 55,423.43 8.04 0.0004Within groups 220,561.3 32 6892.541Total 331,408.2 35
2208CBetween groups 72,456.06 3 36,228.03 21.16 7.9167E-08Within groups 56,499.17 33 1712.096Total 128,955.2 36
2108CBetween groups 55,985.51 3 27,992.75 102.11 8.9193E-17Within groups 9046.91 33 274.149Total 65,032.42 36
Notes: SS, sum of the square; df, degree of freedom; MS, mean square; F-statistic ¼ MS between/MS within.
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Subsequently, a complex modulus test can be
performed. A frequency sweep conducted at 40 and 508C
registered 21 points corresponding to different frequen-
cies. From those points, three representatives of low,
medium and high frequencies were selected, 0.4, 1.01 and
10.3 Hz, to represent different traffic speeds. In Tables 8
and 9, a summary of the mean, variance and COV obtained
at 20 and 508C is shown.
The probability distribution at 508C is also represented
in this case by a normal distribution as shown in Figures 4
and 5. The same tendency was observed at 20 and 408C.
Similarly to the case for cold temperatures, anF-test was
performed. The F-test in this framework gave completely
different results. In all cases (Table 10), the null hypothesis is
rejected. The variance of the complex modulus at high
temperatures, independently of the frequency chosen,
changes with short- and long-term ageing, and thus probably
changes during pavement service life.
Because the variances did changewith ageing, it was not
possible to use the ANOVA and the comparison between the
averages was thus done using a more robust method, the
Welch test. This test admits inequality between the
variances. The results in Table 11 show (all
p-value, 0.05) that there is a significant difference between
the means of complex modulus, considering any frequency,
Table 7. Summary of LSD test performed at each temperature between different ageing levels.
T (8C)ta
2df
LSDDifference meanvirgin–RTFOT
Difference meanRTFOT–RTFOT þ PAV
Difference meanvirgin–RTFOT þ PAV
230 2.036933 69.04 113.32 9.52 122.83220 2.034515 34.37 71.92 36 107.92210 2.034515 13.75 43.62 52.83 96.45
Figure 3. Stress sweep at 508C at different ageing levels.
Table 8. Mean, variance and COV of complex modulusobtained at different frequencies and for different ageing levels at208C.
Levelofageing
Frequency(Hz)
Complexmodulusmean(Pa) STD
COV(%)
Virgin 0.4 549,380 5946.42 1.1Virgin 1.01 1,012,811 140,460.7 13.9Virgin 10.3 3,076,900 572,850.1 18.6RTFOT 0.4 1,322,500 36,747.99 2.8RTFOT 1.01 2,067,729 39,633.39 1.9RTFOT 10.3 3,813,011 505,864.9 13.3RTFOT þ PAV 0.4 3,198,757 307,130.4 9.6RTFOT þ PAV 1.01 3,674,042 370,083.7 10.1RTFOT þ PAV 10.3 4,773,753 350,038.6 7.3
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with only one exception, RTFOT–RTFOT þ
PAV at 10.3Hz. It is therefore possible to assert that the
complex modulus changes significantly for different levels
of ageing.
Evolution of binder rheological properties in M-E
pavement design methods
The results obtained earlier can be projected on an M-E
pavement design method. It is possible, for instance, to see
graphically (Figures 6 and 7), how the mean and variance
change over the pavement service life. First, it is assumed
that the RTFOT results correspond to time 0, just after the
mixing process in the plant, and RTFOT þ PAV results
correspond to a certain point in the pavement service life.
Moreover, it will be assumed that the evolution model is
linear. It is possible to see that the stiffness and complex
modulus results show that means are significantly different
for different ageing levels. Concerning the variance, while
in the case of stiffness at low temperatures measured with
the BBR, it is not significantly different, in the case of the
complex modulus at medium and high temperatures
measured with the DSR, the variance is different.
In Figures 6 and 7, it is important to note that the slopes
of the evolution of the variances are different from the
slope of the evolution of the mean.
Table 9. Mean, variance and COV of complex modulusobtained at different frequencies and for different ageing levels at508C.
Levelofageing
Frequency(Hz)
Complexmodulusmean(Pa) STD
COV(%)
Virgin 0.4 1213 127.67 10.5Virgin 1.01 2800 379.01 13.5Virgin 10.3 20,940 3501.38 16.7RTFOT 0.4 3743 467.36 12.5RTFOT 1.01 8030 1343.36 16.7RTFOT 10.3 60,022 9942.06 16.6RTFOT þ PAV 0.4 33,539 4450.78 13.3RTFOT þ PAV 1.01 63,940 9,985.58 15.6RTFOT þ PAV 10.3 332,202 46,768.84 14.1
Figure 5. Goodness of fit using normal probability plot.
Figure 4. (a) Cumulative probability function and (b) probability mass function for virgin binder at 508C at high frequency (10.3Hz).
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In an M-E pavement design method, such as PAVE-
MENT-ME, the input parameters are affected by
variability and that the variability is reflected in the
results of the pavement design. For example, the
modelling of the evolution of fatigue cracking over time
takes into account different percentages of reliability that
results from the variability of the inputs. With the results
obtained in this study, it is obvious that there is a need to
include the change of the mean and of the variability in
models used for calculation of the stresses and strains
existing in the pavement structure. These changes will
have an effect on the degradation models subsequently
used in M-E pavement design methods. Furthermore, to
calculate the reliability, the method does not incorporate
the evolution of the variability over time.
Conclusions
For the estimation of reliability for a given bituminous
pavement structure, it is fundamental to consider the
variability of input parameters. Limited and fragmented
information is available in the literature regarding the
probability distribution and variability used for the
implementation of a reliable method and incremental
process (Timm et al. 1998, Bush 2004, Kenis and Wang
2004).
This paper provides a statistical study, based on more
than 200 tests, of the variability of binder rheology for
different ageing levels, determining the probability
distribution that represents the results, validated with a
goodness of fit. The authors then proceeded with a rigorous
statistical methodology for the evaluation of the effects of
different ageing levels on the variance of stiffness at low
temperatures and complex modulus at medium and high
Table 10. F-test that compares variances of different ageing levels with frequency kept constant at 508C.
RTFOT Virgin RTFOT þ PAV RTFOT RTFOT þ PAV Virgin
0.4HzMean 3744 1213 33,539 3744 33,539 1213Variance 2.184E þ 05 1.630E þ 04 1.981E þ 07 2.184E þ 05 1.981E þ 07 1.630E þ 04Observations 16 16 16 16 16 16df 15 15 15 15 15 15F 13.40 90.69 1215.32a 0.05 0.05 0.05p-Value 9.041E-06 1.195E-11 4.811E-20F-critic 2.862 2.862 2.862Significance Yes Yes Yes
1.01HzMean 8.030E þ 03 2.801E þ 03 6.394E þ 04 8.030E þ 03 6.394E þ 04 2.801E þ 03Variance 1.805E þ 03 1.436E þ 05 9.971E þ 07 1.805E þ 06 9.971E þ 07 1.436E þ 05Observations 16 16 16 16 16 16df 15 15 15 15 15 15F 12.563 55.254 694.152a 0.05 0.05 0.05p-Value 1.381E-05 4.481E-10 3.184E-18F-critic 2.862 2.862 2.862Significance Yes Yes Yes
10.3HzMean 6.002E þ 04 2.094E þ 04 3.322E þ 05 6.002E þ 04 3.322E þ 05 2.094E þ 04Variance 9.884E þ 07 1.266E þ 07 2.187E þ 09 9.884E þ 07 2.187E þ 09 1.226E þ 07Observations 16 16 16 16 16 16Df 15 15 15 15 15 15F 8.063 22.129 178.416a 0.05 0.05 0.05p-Value 2.264E-04 3.029E-07 8.021E-14F-critic 2.862 2.862 2.862Significance Yes Yes Yes
Table 11. Results of Welch test for comparison of means.
Frequency Compared groups p-Value
0.4Hz Virgin–RTFOT 1.12E-13RTFOT–RTFOT þ PAV 4.15E-03Virgin–RTFOT þ PAV 2.73E-03
1.01Hz Virgin–RTFOT 1.41E-07RTFOT–RTFOT þ PAV 2.80E-10Virgin–RTFOT þ PAV 1.12E-10
10.3Hz Virgin–RTFOT 3.71E-09RTFOT–RTFOT þ PAV 6.07E-02Virgin–RTFOT þ PAV 4.88E-02
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temperatures of binder (F-test). TheANOVAand theWelch
test were used to determine whether the differences
between means were significant or due to random error.
From the results obtained, it is possible to conclude
that the following:
. The normal probability distribution fits the trend of
stiffness results at low temperatures. Also in the case
of the complex modulus at medium and high
temperatures, the results for the virgin binder and
the binder artificially aged at each level are well
represented by a normal probability distribution. The
goodness of fit in every case verified this assumption.
. At low temperatures, the stiffness changes signifi-
cantly for different ageing levels and thus the
differences are not due only to random error.
Figure 7. Evolution of complex modulus mean and variance over pavement service life using DSR results at 508C at 1.01Hz.
Figure 6. Evolution of stiffness mean and variance over pavement service life using BBR results at 2108C.
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Material properties change with time and also after
the fabrication process, while the variability remains
constant. This means that the ageing does not
produce an increase in the inherent variability of the
binder at low temperatures, but the increase in the
variability results from external factors such as
humidity, exposure, in what is termed spatial
variability.. In the low-temperature domain, by analysing every
single ageing level separately, it is possible to assess
that the stiffness variance becomes more sensitive to
the temperature change (Table 5).
. At medium and high temperatures, the complex
modulus results are significantly different, consider-
ing different ageing levels for all the frequencies
chosen. The response of the binder under different
traffic speeds changes significantly during the
pavement service life and is also subjected to an
increasing variability, not only due to external factors
but also due to an inherent variability of the material
itself. The variability is increased by not only spatial
variability but also an intrinsic variability to the
material that changes with ageing.
The consequences of these conclusions bring the
author to other considerations in terms of pavement
design. When the variability of one or more of the input
parameters changes, this must be reflected in a change of
the predicted reliability of a certain pavement structure.
All methods currently base the calculation of reliability on
the variability and values of parameters established at the
beginning of the design process and maintained through-
out the life cycle. This paper underlines the absolute need
to implement an incremental process that takes into
account the changes that occur in material properties
during pavement service life.
The next step in this research programme includes
the study of the variability of the phase angle of the binder
over time. Also, more tests are neededwith different binders
to ascertain whether the evolution of the variability follows
the same trend as was seen here. Moreover, it would be
particularly interesting to analyse the variability of in situ
binders to evaluate the difference between the inherent
variability and spatial variability due to all the external
factors that play an important role in reality.
In recent years, great efforts have been deployed in the
development of new materials, such as polymer-modified
binders or additives for warm or cold mixes, but little work
has been done to correctly characterise their behaviour to
fit the theory used in M-E pavement design. For example,
it is known that the addition of reclaimed asphalt pavement
changes the stiffness of the mix, but there is no
information on how stiffness variability is affected by
that addition.
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