Impact of different ageing levels on binder rheology

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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: sara.bressi@epfl.ch

International Journal of Pavement Engineering, 2015

http://dx.doi.org/10.1080/10298436.2014.993197

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

S. Bressi et al.2

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

��

ffiffiffiffiffiffiffi

; ð3Þ

where t�a

� 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

International Journal of Pavement Engineering 3

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:

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

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.

S. Bressi et al.4

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

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.

S. Bressi et al.6

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

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

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).

S. Bressi et al.8

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

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.

S. Bressi et al.10

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.

References

ASTM D 2872, 2012. Standard test method for effect of heat andair on a moving film of asphalt (rolling thin-film oven test).American Society for Testing and Materials.

ASTM C670, 2013. Standard practice for preparing precision

and bias statements for test methods for construction

materials. American Society for Testing and Materials.ASTM C802, 2009. Standard practice for conducting an

interlaboratory test program to determine the precision of

test methods for construction materials. American Societyfor Testing and Materials.

Anderson, D.A., et al., 1994. Binder characterization, Vol. 3:

physical properties, SHRP-A-369. Washington, DC: StrategicHighways Research Program, National Research Council.

Box, G.E.P., Hunter, J.S., and Hunter, W.G., 1978. Statistics foeexperiments. Design, innovation and discovery. Wiley series

in probability and statistics. New Jersey: Wiley.Bush, D, 2004. Incorporation of reliability into mechanistic-

empirical pavement design. Washington, DC: University ofWashington. Available from: http://courses.washington.edu/kckapur/526/526projects/DBush.pdf

Collop, A., Armitage, R., and Thom, N. 2001. Assessingvariability of insitu pavement material stiffness moduli.Journal of Transportation Engineer, 127(1): 74–81.

Darter, M.I, McCullough, B.F, and Brown, J.L, 1972. Reliabilityconcepts applied to the Texas flexible pavement system. 51stAnnual Meeting of the Highway Research Board, Washing-ton, Record No. 407.

Kenis, W. and Wang, W., 2004. Pavement variability andreliability. Available from: http://www.ksu.edu/pavements/trb/A2B09/CS13-12.pdf [Accessed January].

Kim, H.B and Buch, N, 2003. Reliability-based pavement designmodel accounting for inherent variability of designparameter. In: 82nd Transportation Research Board annualmeeting, Washington, DC.

Lemer, A.C. and Moavenzadeh, F, 1971. Reliability of highwaypavements. Highway Research Board. 362: 1–8.

Maji, A and Das, A, 2008. Reliability considerations of bituminouspavement design by mechanistic-empirical approach. Inter-national Journal of Pavement Engineering. 9(1), 19–31.

NCHRP 1-37A, 2005. Mechanistic-empirical design of new andrehabilitated pavement structures. Available from: http://www.trb.org/mepdg/guide.htm [Accessed September].

Noureldin, S.A, et al., 1994. Estimation of standard deviation of

predicted performance of flexible pavements using AASHTOmodel. Washington, DC, Transportation Research Record,No. 1449 TRB.

Ott, R.L and Longnecker, M, 2000. An introduction to statisticalmethods and data analysis. 5th ed. Pacific Grove, CA:Duxbury Press.

Petersen J.C., et al., 1994. Binder characterisation, volume 4:testmethods. SHRP-A-370, Strategic Highways ResearchProgram, National Research Council, Washington, DC.

Snedecor, G.W. and Cochran, W.G., 1967. Statistical methods.6th ed. Amos, IA: The Iowa State University Press.

Sprinthall, R.C., 2000. Basic statistical analysis. Boston: Allynand Bacon.

Timm, D.H., Briggison, B, and Newcomb, D.E, 1998. Variabilityof mechanistic-empirical flexible pavement design par-ameters. In: Proceedings of the 5th international conferenceon the bearing capacity of roads and airfields, Norway. Vol. 1.

Welch, BL., 1938. The significance of the difference betweentwo means when the population variances are unequal.Biometrika, 29, 350–362.

Impact of different ageing levels on binder rheology

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