Draft · 2020-05-06 · Draft Evaluation of recycled asphalt mixture at low temperature using...

Draft

Evaluation of recycled asphalt mixture at low temperature using different analytical solutions

Journal: Canadian Journal of Civil Engineering

Manuscript ID cjce-2019-0303.R1

Manuscript Type: Article

Date Submitted by the Author: 28-Jul-2019

Complete List of Authors: Cannone Falchetto, Augusto; Technische Universität Braunschweig, Civil Engineering - ISBSMoon, Ki Hoon; Korea Expressway Corporation, Corporate strategy and Policy Research Division; Korea Expressway Corporation, Pavement Research DivisionKim, Dong Hyuk; Inha University

Keyword:

Is the invited manuscript for consideration in a Special

Issue? :Not applicable (regular submission)

https://mc06.manuscriptcentral.com//cjce-pubs

Canadian Journal of Civil Engineering

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Evaluation of recycled asphalt mixture at low temperature using different

analytical solutions

Augusto Cannone Falchetto1, Ki Hoon Moon2 and Dong Hyuk Kim3

1Assistant professor, Department of Civil & Environmental Engineering, University of Alaska

Fairbanks, 99775, Alaska, U.S. ([email protected])2Senior Researcher, Korea Expressway Corporation Pavement Research Division (KECPRD),

Dongtan-Myeon, Hwaseong-Si, Gyeonggi-Do, 445-812, Korea (Corresponding Author, email:

[email protected], [email protected])3Ph.D Student, Department of Civil Engineering, Inha University, Incheon 22212, Korea (email:

[email protected])

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mailto:[email protected]

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Abstract

Using Reclaimed Asphalt Pavement (RAP) in road infrastructures is crucial for mitigating the

environmental impact while controlling the construction costs. However, poorer low temperature

performance may be experienced for mixtures containing RAP. In this paper, the effect of RAP on

the material response at low temperature is investigated through mixture creep testing with the

Bending Beam Rheometer. Three different mathematical approaches are selected for further

evaluation in combination with simple statistical analysis. Based on the experimental data, creep

stiffness, m-value, relaxation modulus, thermal stress, and critical cracking temperature are

computed and compared. As a result, no differences are found between the virgin mixture and that

designed with 15% of RAP. Poorer performance is observed when more than 25% of RAP is

incorporated; however, no significant variation was observed for a further increase up to 40%

suggesting that higher amount RAP could be used depending on traffic level and climate.

Keywords: Reclaimed Asphalt Pavement (RAP), Bending Beam Rheometer (BBR), Hopkins and

Hamming’s algorithm, Advanced Power-law function, Advanced Laplace transformation, Low

temperature performance

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1. Introduction

It is well-known that the use of recyclable materials can provide considerable economic and

environmental benefits in the construction of pavement infrastructures (Lee et al. 1999; McDaniel

and Anderson 2001; Moon 2012; Moon et al. 2014; Cannone Falchetto et al. 2017; Cannone

Falchetto et al. 2018; Gu F. et al. 2019; Lyu Z. et al. 2019; Moon et al. 2019; Yan and Roque

2019). During the past decades, various types of recyclable materials, such as Reclaimed Asphalt

Pavement (RAP), iron blast furnace slag, waste tire rubber and reclaimed Portland cement concrete,

were investigated. Among these materials, RAP has found large application in pavement both in

developed and developing countries (McNichol 2005; Cannone Falchetto et al. 2017; Arambula-

Mercado E et al. 2018; Esfandiarpour and Shlaby 2018; Pi A.F. et al. 2018; Yan and Roque 2019).

Approximately 74 and 49 million tons of RAP are annually produced in U.S. and Europe,

respectively (Schimmoller V.E. 2000; Van den Bergh et al. 2009; Hansen et al. 2011; EAPA 2016;

Yan and Roque 2019). Based on different theoretical studies and field observation, pavement

agencies and road authorities proposed specifications and guidelines for designing recycled asphalt

mixture (Li et al. 2008; Hill et al. 2013; Moon et al. 2014; Cannone Falchetto et al. 2018). For

example, mixing RAP up to 55% is allowed based on pavement thickness, traffic level, climate

condition and binder grade in the state of Nebraska (Haghshenas et al. 2016). On the other hand,

in Germany, RAP content is set based on the evaluation of the mixture performance (Moon et al.

2019).

The effect of adding RAP into conventional asphalt mixture was investigated by several

researchers in the past (Lee et al. 1999; Mc Daniel and Anderson 2000; McGraw et al. 2007; Li et

al. 2008; McGraw and Johnson 2010; Hill et al. 2013; Pranshoo et al. 2013). Increase in viscosity

and stiffness was observed at high and intermediate temperature for a higher amount of RAP

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resulting in a better performance against rutting. On the other hand, higher stiffness and increased

brittleness were experienced for recycled mixtures at low temperature leading to an inferior

material response with respect to thermal cracking.

In the recent past, Shirodkar et al. (2011) introduced a method for determining the degree

of partial blending especially for a high percentage of RAP mixture through experimental

evaluations. Two degrees of partial blending, 70%, and 96%, were identified for mixtures prepared

with 25% and 35% RAP and designed with PG 70-28 and PG 58-28 binder, respectively

(AASHTO M 320 2016).

The impact of RAP on fracture properties was recently addressed by the authors of the

present paper (Cannone Falchetto et al. 2018). Finite Element Method (FEM), Indirect Tensile

(IDT) and Semi-Circular Bending (SCB) fracture configurations were adopted, showing a

reasonable correlation between strength and fracture energy for RAP mixtures.

Pi et al. (2018) investigated the effect of RAP on Warm Mix Asphalt (WMA) production

procedure along with material performance against cracking. It was observed that no specific

production means are needed when including up to 15% of RAP in WMA mixture. However,

higher production temperature is recommended when more than 30% of RAP is incorporated in

the mix design. As expected, the addition of RAP led to reduced cracking performance; however,

meeting the volumetric requirements did not translate into improved cracking resistance.

Forensic pavement performance simulation of various RAP mixtures using Mechanical-

Empirical Pavement Design Guide (MEPDG) (AASHTOWare 2018) software was performed by

Esfandiarpour and Shalaby (2018). Dynamic modulus and creep compliance experimental data

were used as Level 1 input parameters in MEPDG analysis. The results indicated an over-

prediction of pavement performance compared to Level 3 analysis, suggesting that more precise

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calibration is needed for further research when introducing RAP mixture in the pavement design

process.

Gu et al. (2019) evaluated the mechanical performance of RAP mixtures through

experimental work, pavement analysis, simulation, and Life Cycle Cost analysis (LCCA). It was

found that bottom-up cracking distress on RAP mixture layers is negligible when compared to

conventional Hot Mix Asphalt (HMA) pavement, while low temperature transverse crack is the

major distress for RAP mixture.

It is well-known that poorer performance can be expected at low temperature when RAP

is used due to the characteristic of the oxidized asphalt binder (Moon et al. 2014; Cannone

Falchetto et al. 2017; Cannone Falchetto et al. 2018; Gu F. et al. 2019; Lyu Z. et al. 2019). Even

though several studies were performed to investigate the effect of RAP on asphalt mixture, most

of them mainly rely on experimentation, while fewer analyzed and evaluated the mechanical

performance of RAP mixture at low temperature based on analytical solutions and a model-

oriented approach (Gibson et al. 2003; Dongre et al. 2005; Orlard and Di Benedetto 2005; Xu and

Solaimanian 2010; Gudmarsson et al. 2015).

2. Objective and research approach

In this paper, the effect of adding a high amount of RAP on the low temperature performance of

asphalt mixture is investigated. Bending Beam Rheometer (BBR) mixture creep test (Marasteanu

et al. 2009; AASHTO T-313 2012) is performed on a set of eight asphalt mixture. Creep stiffness,

m-value, relaxation modulus, thermal stress, and critical cracking temperature are computed and

then visually and statistically compared. Three different mathematical models are considered for

computing, analyzing and evaluating the low temperature characteristics with the goal to provide

upper, intermediate and lower bounds for the calculated parameters. Finally, the feasibility of

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incorporating a high amount of RAP in asphalt mixture is discussed in the view of future research

recommendations. Figure 1 shows the schematic research approach adopted in the present work.

[Insert Figure 1]

Figure 1: Schematic research flow-chart in this paper.

3. Materials and testing

3.1. Asphalt mixture

A total of eight Hot Mix Asphalt (HMA) mixtures designed with two different types of asphalt

binder, PG 64-28 (Plain) and PG 64-34 (1.1% Elvaloy + 0.3% PPA), were prepared and used in

this paper (AASHTO M 320 2016); the binder content was equal to approximately 4.8% to 5.1%

by weight, respectively. The virgin aggregate consisted of screen sand, lime sand, and limestone.

RAP material contained aggregate with a Nominal Maximum Aggregate Size (NMAS) up to

19.0mm and was provided from Korea Expressway Corporation (KEC). The RAP materials were

obtained from three different local county roads in South Korea, constructed approximately 12~15

years ago. Moreover, the original grading of the RAP asphalt binder was PG 64-22 (unmodified).

Three different amounts of RAP were considered in this paper to evaluate the impact of RAP on

the mechanical performance of the mixtures: 15% (low), 25% (medium) and 40% (high). The

HMA mix design followed the current expressway construction specification in South Korea

(MOLIT 2017). All asphalt mixtures were compacted with Superpave Gyratory Compactor (SGC)

and subjected to a short-term aging procedure: conditioned at 135ºC for 4 hours (AASHTO R30

2002; ASTM D 6925-15 2015). Table 1 presents the schematic information on the mixtures

prepared for this paper. It should be mentioned that inclusion of various amount of RAP changed

the NMAS and aggregate gradation curve compared to the control asphalt mixture.

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Table 1: Asphalt Mixtures

[Insert Table 1]

3.2. BBR mixture creep test

Bending Beam Rheometer (BBR) creep testing was performed on thin asphalt mixture beam

(102.0±5mm × 12.7±0.5mm × 6.25±0.5mm) to evaluate the response of the material at low

temperature (Marasteanu et al. 2009; AASHTO T-313 2012; Moon et al. 2014). Similar to the

testing specification for asphalt binder (AASHTO T 313-12 2012), creep stiffness, S(t), and

corresponding m-value, m(t), can be easily computed from the results of the mid-span deflection,

(t), when considering the actual constant load applied to the specimen (4,000mN) (see Eq. (1)).

Due to the higher stiffness of asphalt mixture compared to asphalt binder, testing time was

extended to 1,000 seconds in place of the conventional 240 seconds (Marasteanu et al. 2009; Moon

et al. 2014).

(1)

3

3

2

1(t)(t) (t) 4 (t)

[Log(t)] Log(t)Log (t)(t)Log(t) Log(t)

P lSD b h

d A B Cd Smd d

Where:

S(t) : time-dependent flexural creep stiffness (=MPa);

D(t) : creep compliance (=1/MPa);

σ : bending stress in the beam (=MPa);

ε(t) : time-dependent bending strain in the beam (=mm/mm);

P : applied constant load (=mN);

δ(t) : beam deflection (=mm);

l, b, h : beam dimensions (=mm);

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t : time (=sec);

A, B, C: fitting constants

Thermal stress, (TºC), and corresponding critical cracking temperature, TCR, were

computed with three different mathematical approaches: Hopkins and Hamming’s algorithm

(1967), Power-law function with equivalent time concept (Park and Kim 1999) and advanced

Laplace transformation approach. More detailed information about these three computing

solutions is provided in section 4 of the present manuscript. In this paper, two different testing

temperature conditions, low PG+10ºC and low (PG+10 ºC) + 12ºC, were considered for generating

relaxation modulus, E(t), master curve and computing (TºC) and corresponding TCR (Marasteanu

et al. 2009). Schematic information of BBR mixture creep testing is presented in Table 2 and

Figure 2.

Table 2: BBR mixture testing information

[Insert Table 2]

[Insert Figure 2]

Figure 2: Bending Beam Rheometer (BBR) test specimens (Left) and testing set-up (Right)

4. Mathematical approaches

4.1. Application of advanced Power-law function with equivalent time concept

In this section, a computational solution for determining the thermal stress, (TºC), by using

Gaussian integration approach (Moon et al. 2014) on the approximate inter-converted results of

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relaxation modulus, E(t), derived on the experimental data of creep compliance, D(t), is presented

(Park and Kim 1999).

D(t) and E(t) can be related by simple expression (see Eq. (2)) or through the convolution

integral (see Eq. (3)) as (Findley et al. 1976; Ferry 1980; Park and Kim 1999; Ebrahimi et al.

2014):

(2)( ) ( ) 1E t D t

(3)0 0

0 0

1( ) ( ) ( )( )

1( ) ( ) ( )( )

t t

t t

E t D t d E t d tS t

E t D t d E t d tS t

While Eq. (2) is acceptable only for weak viscoelastic material, Eq. (3) is a more robust solution

but relatively more complex to solve. By taking the Laplace transformation, Eq. (3) can be re-

written as:

(4) 20

1( ) ( ) ( ) ( )t

E t D t d t E s D ss

L L

Finally, thermal stress, (TºC), and critical cracking temperature, TCR, can be computed based on

Eqs. (1) to (4). A brief computation process summary is hereafter presented:

1. Generate approximate mathematical expressions of E(t) and D(t) based on power-law function

fitting of the experimental results as:

(5)1 1 11( ) , ( )n nnE t E E t D t D t

t

In Eq. (5), E1, D1 and n are positive constants (Park and Kim 1999; Ebrahimi et al. 2014).

2. Apply the Laplace transformation and rewrite Eq. (5) as:

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(6)

1 1 1

1 1 11 1

(1 )( ) ( )

! (1 )( ) ( )

nn

nn n

nE t E t E s Es

n nD t D t D s D Ds s

L

L

In Eq. (6), is the Gamma function which can be expressed as:

(7)1

0

( ) n tn t e dt

Based on Eqs. (4) to (7) with the Euler reflection formula, the relationship between D(t) and E(t)

can be expressed as:

(8)

1

2 2 11 1

1

1 1 1

1 1

1 1 1 1 1( )( ) (1 ) (1 )

1( ) ( )(1 ) (1 ) (1 ) (1 ) (1 ) ( )

1 sin( ) 1 sin( ) 1 sin( )( )

sin( )( ) ( )

n

n

n n n

nn

sD ss E s s E n E n s

t t tD s D tE n n E n n E n n n

n n ntE n E t n E t n

nE t D tn

L

In Eq. (8), parameter n can be computed as:

(9)d log ( ) d log ( )

log logt t

D t E tn or n

In previous studies, it was observed that very-good fitting results can be obtained when

experimental data of D(t) (and/or E(t)) are close to a straight line in log-log scale (i.e. time versus

results (Park and Kim 1999).

3. Based on Eqs. (1) to (9) and introducing the concept of equivalent time (t*), E(t) can be derived

as (Park and Kim 1999):

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(10) 1

1

1

sin( )( *) ( ) 1 * 1

sin( ) sin( )* *

nn

nn n

n tE t D t E tn E

n nt t t tn n

4. Then, E(t) master curve can be generated at two different temperature conditions as (i.e.

lowPG+10ºC and low(PG+10)+12ºC):

(11)

( ) ( ) ( )

( ) 1 ( ) 1

1 10 T c

wv vv

g gc c

vLog t Log a Log tg

t w tE t E LogE t LogE Logt v t

wLogE Logv

Where:

Eg = glassy modulus, assumed equal to 30~40GPa for asphalt mixtures (Moon et al., 2014),

tc, v and w = fitting parameters.

aT = horizontal shift factor which can be expressed as:

(12)1 21 210 LogsC C T

T T sa a C C T

C1, C2 = constant parameters, and

Ts = reference temperature (ºC, in this paper lowPG+10ºC).

5. Finally, (TºC) is computed by solving Eq. (13) in the reduced time domain with 24 Gauss

points integration approach at temperature (TºC) ranging from 22ºC(=TiºC) to -40ºC. In this

paper, a cooling rate of 2ºC/hour was considered (Moon et al. 2014).

(13)( ) ( ) ( ') '

( ') ( )( ) ( ') ' ( ( ) '( )) '' '

t

t

t t E t t dt

d d TE d E t t dtd dt

&

where:

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reduced time (14)T

ta

= strain rate which can also be expressed as:( ) ( ') / 't d t dt &

(15)( )t T

= Coefficient of thermal expansion or contraction; in this study, it is assumed =0.00003

(Moon et al. 2014),

= temperature cooling rate.T

4.2. Application of Hopkins and Hamming’s algorithm (1957)

In this section, a numerical approach for computing E(t) from the experimental D(t) by using

Hopkins and Hamming’s algorithm (1957) is shortly summarized (see Eqs. (16), (17), (18) and

(19)).

(16)

01

1 1/2 1 1 1

1

1 1/2 1 1 10

1/21

1

1 1/2 10

1

( ) ( )

( ') ( ') ' ( ) [ ( ) ( )]

( ) [ ( ) ( )]( )

( )

( ) [ ( ) ( )]

( ) (

i

i

t

t

n i n i n it

n

n i n i n ii

nn n

n

n i i ii

n n

E t D t d t

E t D t t dt E t J t t J t t

t E t J t t J t tE t

J t t

t E t J t J t

J t J t

)

Where:

(17) 1 1 10

1( ) ( ) ( ) ( ) ( ) ( ) ( )2

t

n n n n n nJ t D t dt J t J t D t D t t t

t: time interval (i.e. ) expressed as (18)0 1 2 1,0000, 1, 2,... 1,000t t t t )(21

121 iii

ttt

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, , , (19)0)( 0 tf 0)( 0 tE 11

1

( )( )tE t

J t

2 1 2 12

1

( ) ( ) ( )( )

( )t E t J t J t

E tJ t

After the computation of E(t), (TºC) can be computed based on Eqs. (11) to (15) similarly to the

previous section (Section 3.1).

4.3. Application of advanced Laplace transformation approach

Differently from the two previous computation methods (see Section 4.1 and 4.2), a more intuitive

and efficient (TºC) computation approach using the Laplace transformation technique can be

adopted. A schematic thermal stress computation process by using Laplace transformation can be

explained as follows:

1. From the experimental result of LogD(t) versus Log(t) curve (at lowPG+10ºC and

low(PG+10)+12ºC conditions), compute shift factor, aT, along with two parameters: C1 and C2

using Eq. (20) at reference temperature: Ti=22ºC.

(20)(ref 22 ) 1 2iT CLoga C C T

Eq. (20) can be re-written as:

(21)1 2 0 1 2 2 0 3 4 31 2 4 4( ) ( )010 10 10 10 10 10 10i iC C T C t C C T C C t C C t CC C T C t C t

Ta A

2. Generate master curve of in the reduced time domain using D(t) experimental data at ( )D

lowPG+10ºC and low(PG+10)+12ºC based on dual series Power-law function with additional

constants as seen in Eq. (22) differently from the previous study (Moon et al. 2019).

(22)( )B D

B D

T T T

t t tD A C E A C Ea a a

Where:

A, B, C, D, and E are function fitting parameters.

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In this paper, average D() (i.e. average between D(, at lowPG+10ºC) and D(, at

lowPG+10+12ºC)) data was used.

3. Consider Eq. (23) to relate thermal stress and strain assuming an idealized scheme:

(23)0 0

( )( ) ( ) 0tTD d d

By applying the Laplace transformation, Eq. (23) can be rewritten as:

(24)

0 0

0 0

( )( ) ( )

( )( ) ( ) ( ) ( ) ( ) ( ) 0

tTD d d

TD d d s D s s s s T s

L L

= L L

From Eq. (23), thermal stress can be derived as:

(25)( ) ( )( )

( )s T ssD s

Based on Eqs. (15), (20) and (21) parameter and T can be re-expressed as:

(26)

00

00 2

( ) ( ) ( )

( ) ( ) ( )

t t ss

CT t C t T t T ss

L

L

4. Perform inverse Laplace transformation of Eqs. (25), (26) using the Stehfest algorithm (Stehfest

1970; Villinger H. 1985). Then, fit the results of numerically computed () using dual power

law function with constant as:

(27)( ) C EA B D

5. Covert the reduced time domain thermal stress: ( to the actual time domain scale,(TºC),

using Eq. (28):

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(28)4

4 4

4

''

1'0 0 0 40 0 0 0

' ' 1 1 1010 ' 1 10[ ( ')] 10 ln10

tt t t C tC t C t

C tT

dt dt dt Aa T t A A A C

Where:

and (see Eq. (21)).3 1 20 10 10 iC C C TA 4 2 0C C C

By using Eqs. (21) to (28), of (TºC) can be finally computed from 22 to -40ºC with 0.5ºC of

temperature interval.

It must be mentioned that, for the present research, no additional asphalt mixture strength

test was performed therefore TCR was predicted through Single Asymptote Procedure (SAP)

method (Shenoy 2002; Moon et al. 2014). Schematic computation process of TCR with SAP method

is presented in Figure 3.

[Insert Figure 3]

Figure 3: Computation process example of TCR using SAP method (Shenoy, 2002)

5. Data analysis

5.1. Comparison of S(t), m-value and E(t)

Based on Eq. (1), S(t=60sec) and m(t-60sec)-value were computed for the eight different asphalt

mixture prepared in this study. Comparison results of S(t=60sec) and m(t=60sec)-value at

lowPG+10ºC and lowPG+10+6ºC are presented in Figure 4.

[Insert Figure 4]

Figure 4: Results of S(t=60sec) [Left] and m(t=60sec) [Right] results

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Based on the results from Figure 4, a clear difference in S(60) and m(60) between RAP 15% and

25% mixtures was observed. However, no significant variations in S(60) and m(60) were found in

Case 1: control (i.e. RAP 0%) versus RAP 15% mixtures, and Case 2: RAP 25% versus RAP 40%

mixtures, respectively. Overall, similar trends are observed for the two different binders. In South

Korea, RAP 15~25% mixtures are widely used for binder-course construction but also in some

cases they are used for surface-course construction depends on traffic volume. Since 2015, using

RAP 15~25% mixture in to surface layer construction increased due to reduction of environmental

pollution mitigation rather than construction budget rediction by government. Based on the results,

it can be said that the limited impact of a high amount of RAP on S(60) and m(60) may suggest

the possibility of using up to 40% of RAP in asphalt pavement not only for binder-course but also

for surface layer construction.

Similar to S(60) and m(60) comparison, relaxation modulus, E(t), was generated and then

a comparison was performed for each asphalt mixture using Eqs. (10), (11) and (16). First, E(t)

results were computed with two different inter-conversion solutions: advanced power-law function

(Eq. (10)) and Hopkins and Hamming’s algorithm (Eq. (11)). Then, the E(t) was fitted with the

CAM model (Marasteanu and Anderson, 1999: Eq. (16)) over a range between 0.5 to 10,000

seconds and compared. Note that there is no E(t) generation step in Laplace transformation

approach therefore, only the two methods previously mentioned (see Section 4.1 and 4.2), were

considered in this paper.

Statistical analysis (i.e. hypothesis analysis) was performed with a 5% significance level

(i.e. , Cook and Weisberg 1999). Conditions of data normality and constant variance were

assumed together with the following hypotheses as:

Null hypothesis : (29)0 [ ( )] [ ( )]: A E t B E tH

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Alternative hypothesis : (30)0 [ ( )] [ ( )]: A E t B E tH

In Eqs. (29) and (30), indicates the mean (i.e. response) of S(t) (and/or m(t)) obtained from BBR

mixture creep test (Marasteanu et al. 2009). Then the value of pooled standard deviation: P, can

be expressed as (see Eq. (31)):

(31)

2 2,[ ( )] [ ( )]

[ ( )]

2 2,[ ( )] [ ( )]

( ( 10) 1) ( ( 10) 1)( 10) ( 10) 2

918

A A E t B B E tP E t

A B

A E t B E t

n nn n

Where:

: standard deviation of E(t) (Group A);[ ( ) ( )]A S t or m t

: standard deviation of E(t) (Group B);[ ( ) ( )]B S t or m t

nA and nB : number of specimens in Group A and B (n=10).

Based on Eq. (31), the t-static can be computed as:

(32)[ ( )] [ ( )] [ ( )] [ ( )]

[ ( )] [ ( ) ( )]

-static1 1 2

3

A E t B E t A E t B E t

P E t P S t or m tA B

t

n n

In Eq. (32), the degrees of freedom, df, can be expressed as:

(33) 2 10 10 2 18A Bdf n n

Based on Eqs. (32) and (33), the final output of the statistical test, p-value, was computed

and then compared with the adopted threshold value (i.e. =0.05) to verify if the two comparison

groups are statistically equivalent or different. All the comparison results are shown in Figures 5

to 6 and Table 3.

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[Insert Figure 5]

Figure 5: E(t) comparison based on two inter-conversion methods

(Mixtures 1 to 4, PG 64-28)

[Insert Figure 6]

Figure 6: E(t) comparison based on two inter-conversion methods

(Mixtures 5 to 8, PG 64-34)

Table 3: E(t) results: statistical test (t-test) results (p-value)

[Insert Table 3]

When RAP was added into virgin asphalt mixture, no significant differences in relaxation

properties were observed up to 15% addition (i.e. Case 1: control versus RAP 15% mixture). If the

RAP addition was increased up to 25%, a remarkable increase in E(t) was experienced with respect

to control and RAP 15% mixture. However, no significant variation in E(t) could be detected

between mixtures containing 25% and 40% of RAP; this was true for both binders: PG 64-28 and

PG 64-34.

Even though upper and lower bound limits of E(t) value can be derived using two different

computation approaches (i.e. Power-law function (1999) versus Hopkins and Hamming’s

algorithm (1957)), the trend of E(t) comparisons was almost identical. This confirms the idea that

40% of RAP can be potentially used in asphalt mixture for pavement construction not only as

binder course but as surface course depending on the pavement design conditions (e.g. traffic,

climate condition and budget and required performance, among others). Such an opportunity may

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provide not only a remarkable reduction in construction costs but also limits the environmental

impact of the road infrastructure. A more detailed evaluation of thermal stress and the

corresponding critical cracking temperature is provided in the next section.

5.2. Comparisons of thermal stress and corresponding critical cracking temperature

Similarly to the previous section (i.e. Section 5.1), thermal stress, (TºC) and critical cracking

temperature, TCR, were computed based on Eqs. (1) to (28) and then visually and statistically

compared. All the computed results with three different mathematical approaches are shown in

Figures 7 to 9.

[Insert Figure 7]

Fig. 7: (TºC) comparison with Hopkins and Hamming’s algorithm (1957)

(Left: PG 64-28 and Right: PG 64-34)

Mix 1, 5: Control, Mix 2, 6: RAP 15%, Mix 3, 7: RAP 25%, Mix 4, 8: RAP 40%,

[p]: p-value

[Insert Figure 8]

Figure 8: (TºC) comparison with Power law function and equivalent time concept (1999)

[Insert Figure 9]

Figure 9: (TºC) comparison with Laplace transformation

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Based on Figures 7 to 9, no significant differences in (TºC) were found for Case 1 (i.e. control

versus RAP 15% mixture) and Case 2 (i.e. RAP 25% and RAP 40% mixture). It also needs to be

mentioned that approximately 25~33% higher (TºC) was observed for RAP 25% and 40%

mixtures compared to conventional and RAP 15% mixtures; this suggests potentially poorer

performance at low temperature. It must be recalled that the incorporation of 25% RAP in the mix

design is allowed in South Korea and hence a moderate inferior performance at low temperature

is tolerated. In addition, it can be easily expected that higher (TºC) would be computed for stiffer

asphalt binder (PG 64-28) compared to softer asphalt binder (PG 64-34). Based on the results,

approximately 21~33% higher values in (TºC) were estimated from asphalt mixture prepared

with PG 64-28 compared to PG 64-34. Moreover, a steep increase in thermal stress could be

detected for temperatures below -15ºC in most of the tested asphalt mixtures designed with RAP.

Therefore, the in regions experiencing low temperature above -15ºC (e.g. east/south asia), using

recycled mixture up to 40% may not necessarily affect the pavement performance if RAP quality

and construction control are provided. This trend was almost identical for all different three

computation solutions adopted in this paper for estimating (TºC). The comparisons of (TºC)

with respect to the different computation approaches are shown in Figures 10 and 11.

[Insert Figure 10]

Figure 10: (TºC) comparisons based on different computation approaches (Mixtures 1~4)

HH: Hopkins and Hamming’s algorithm (1957), PL: Advanced Power-law function (1999)

La: Advanced Laplace transformation

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21

[Insert Figure 11]


Figures 10 and 11 show that La (Laplace transformation) results in the highest thermal stress

compared to PL (Power law) and HH (Hopkins and Hamming’s algorithm, 1967), which returned

the lowest value of (TºC). The PL computation approach showed intermediate level below 0ºC

in all cases. In this paper, a modified set of equations was considered in the Laplace solution for

providing upper (and/or lower) bounds on (TºC).

Along with (TºC), critical cracking temperature, TCR, was computed based on the Single

Asymptot Procedure (SAP) (Shenoy, 2002; see Figure 3) and compared (Tables 4 and 5). In the

case of statistical analysis, a procedure similar to that previously used in this paper was adopted

(i.e. Eqs. (29) to (33)).

Table 4: Results of TCR [ºC] computation (Mixtures 1 to 8)

[Insert Table 4]

Table 5: Comparison of TCR results [p-value] (statistical analysis, Mixtures 1 to 8)

[Insert Table 5]

Similar to the results of (TºC) comparisons, no significant differences of TCR were found

both in Case 1 (control versus RAP 15% mixture) and Case 2 (RAP 25% and RAP 40% mixture).

Hence, it appears that TCR is not affected by RAP up to 15% in content when compared to

conventional asphalt mixture. When RAP amount is increased to 25%, a remarkable increase in

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22

critical temperature is experienced; however, when further increasing RAP up to 40% no further

significant increase in TCR is observed. Lowest TCR values were computed when using the Hopkins

and Hamming’s algorithm (1957) while the highest TCR was estimated with the Laplace

transformation; power-law function provided an intermediate TCR.

In view of the trends observed in the plots, and the analysis performed, it may be

hypothesized that high proportions of RAP (40%) can be potentially used for highway (and/or

local roads) construction for binder and surface layers in South Korea depending on traffic level,

climate conditions, and construction budget. This appears to be supported as no significant

performance difference at low temperature was found compared to mixtures prepared with 25%

of RAP and considering that the latter design percentage is widely used in asphalt pavement

construction in South Korea.

6. Summary and conclusions

In this paper, the feasibility of designing asphalt mixture with a high amount of RAP up to 40%

was investigated at low temperature. Bending Beam Rheometer (BBR) mixture tests were

performed and creep stiffness, m-value, relaxation modulus, thermal stress, and critical cracking

temperature were computed and next visually and statistically compared. For this purpose, three

different computational solutions were used: Hopkins and Hamming’s algorithm (1957), Power-

law function with equivalent time concept (1999) and a modified Laplace transformation method.

The conclusions derived in the present research effort are as follows:

For the entire set of rheological parameters (creep stiffness, m-value, relaxation modulus,

thermal stress, and critical cracking temperature), poorer low temperature response was

observed only when increasing RAP content to 25%. No significant differences were found

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between control versus 15% RAP mixture (Case 1) and 25% and 40% RAP mixtures (Case

2).

The three computational methods return distinct results with Laplace transformation and

Hopkins and Hamming’s procedure providing upper and lower bounds for thermal stress and

critical cracking temperature.

Based on these findings, higher amount of RAP (40%) should be considered for designing

surface and binder layers depending on materials, traffic conditions, climate, and constriction costs.

Asphalt mixtures containing 25% of RAP have been widely used for highway (and/or local roads)

in South Korea for several decades; however, not many practical studies showed clear feasibility

on incorporating RAP up to 40% especially for low temperature performance evaluation with

various mathematical model approaches in South Korea. Nevertheless, the results obtained in the

present research are limited to low temperature response of the material. Other factors, including

moisture susceptibility may affect the current conclusions. A more in depth evaluation represents

a critical research objective as more extensive experimentation and advanced modeling are needed

to further support the findings in this paper.

Acknowledgments

The support of Korea Expressway Corporation Research Division (KECPRD) and of the Japan

Society for Promotion of Science (JSPS) for international research in Japan is gratefully

acknowledged.

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List of figures

Figure 1. Schematic research flow-chart in this paper.

Figure 2. Bending Beam Rheometer (BBR) test specimens (Left) and testing set-up (Right)

Figure 3. Computation process example of TCR using SAP method (Shenoy, 2002)

Figure 4: Results of S(t=60sec) [Left] and m(t=60sec) [Right] results

Figure 5: E(t) comparison based on two inter-conversion methods (Mixtures 1 to 4, PG 64-

28)

Figure 6: E(t) comparison based on two inter-conversion methods (Mixtures 5 to 8, PG 64-

34)

Figure 7: (TºC) comparison with Hopkins and Hamming’s algorithm (1967)

(Left: PG 64-28 and Right: PG 64-34) , [p]: p-value

Mix 1, 5: Control, Mix 2, 6: RAP 15%, Mix 3, 7: RAP 25%, Mix 4, 8: RAP 40%

Figure 8: (TºC) comparison with Power law function and equivalent time concept (1999)

Figure 9: (TºC) comparison with Laplace transformation


HH: Hopkins and Hamming’s algorithm (1957), PL: Advanced Power-law function (1999)

La: Advanced Laplace transformation


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List of tables

Table 1. Asphalt Mixtures

Table 2. BBR mixture testing information




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Table 1. Asphalt Mixtures

MixID

BinderType

A.V.[%]

B.C.[%]

RAP[%]

VMA[%]

NMAS[mm]

Mixture information[aggregate(mm), passing %]

1 4 4.8 0 16.42 12.5HMA, Wearing Course (WC-1)[13:91%,10:81%,5:52%,2.5:35% 0.6:22%,0.3:15%,0.08:6%]

2 4 4.9 15 16.89 19.0HMA, Wearing Course (WC-3)[19:92%,13:5%,10:63%,5:42%2.5:32% 0.6:23%,0.3:15%,0.08:6%]

3 4 5.0 25 16.91 19.0 Same as Mixture 2 (WC-3)4

PG64-28(Plain)

4 4.9 40 16.55 19.0 Same as Mixture 2 (WC-3)5 4 5.1 0 16.91 12.5 Same as Mixture 1 (WC-1)6 4 5.0 15 17.35 12.5 Same as Mixture 2 (WC-3)7 4 4.9 25 17.41 19.0 Same as Mixture 2 (WC-3)8

PG64-34

(Modified)4 5.0 40 14.23 19.0 Same as Mixture 2 (WC-3)

A.V.: Air Voids (%), B.C.: Binder Content (%), VMA: Voids between Mineral Aggregates (%),

NMAS: Nominal Maximum Aggregate Size (mm)

Table 2. BBR mixture testing information

Test MixtureID

Bindertype

Test temperature [Number of replicates]

Applied load[Testing temperature]

1,2,3,4 PG64-28

lowPG+10ºC: -18ºC [10]low(PG+10)+12ºC:-6ºC [10]

6,000 60mN [-18ºC]±4,000 40mN [-6ºC]±BBR

5,6,7,8 PG64-34

lowPG+10ºC: -24ºC [10]low(PG+10)+12ºC:-12ºC [10]

6,000 60mN [-24ºC]±4,000 40mN [-12ºC]±

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t-test results: p-value (statistically significant if p-value<0.05)Contents 5s 10s 60s 100s 200s 400s 1,000s 2,000s 10,000sApproach 1: Advanced power-law function with equivalent time conceptM1v.M2 0.105 0.112 0.143 0.213 0.151 0.111 0.184 0.195 0.085M2v.M3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000M3v.M4 0.213 0.255 0.233 0.274 0.178 0.123 0.072 0.071 0.064M5v.M6 0.215 0.355 0.318 0.275 0.222 0.158 0.065 0.041 0.058M6v.M7 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000M7v.M8 0.298 0.348 0.345 0.215 0.222 0.158 0.075 0.062 0.051Approach 2: Hopkins and Hamming’s algorithm (1967)M1v.M2 0.223 0.355 0.278 0.178 0.111 0.105 0.071 0.055 0.062M2v.M3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000M3v.M4 0.111 0.085 0.077 0.066 0.115 0.063 0.055 0.048 0.059M5v.M6 0.412 0.355 0.317 0.298 0.222 0.253 0.254 0.154 0.211M6v.M7 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000M7v.M8 0.145 0.111 0.123 0.185 0.098 0.088 0.065 0.055 0.052

M1v.M2: Mixture 1 versus Mixture 2


Asphalt binder: PG 64-28 Asphalt binder: PG 64-34Contents Mix 1

[Control]Mix 2

[R15%]Mix 3

[R25%]Mix 4

[R40%]Mix 5

[Control]Mix 6

[R15%]Mix 7

[R25%]Mix 8

[R40%]HH -27.79 -27.62 -26.99 -26.63 -28.56 -28.29 -27.30 -26.72PL -27.72 -27.48 -26.75 -26.44 -28.46 -28.05 -26.86 -26.57La -27.39 -27.09 -26.34 -26.03 -28.20 -27.99 -26.63 -26.43

HH: Hopkins and Hamming’s algorithm (1967), PL: Power-Law function,

La: Laplace transformation, R: RAP, Mix: Asphalt mixture

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Asphalt binder: PG 64-28 Asphalt binder: PG 64-34Contents M1v.M2 M2v.M3 M3v.M4 M5v.M6 M6v.M7 M7v.M8

HH 0.082[Non-Sig.]

0.032[Sig.]

0.094[Non-Sig.]

0.121[Non-Sig.]

0.012[Sig.]

0.022[Sig.]

PL 0.152[Non-Sig.]

0.012[Sig.]

0.099[Non-Sig.]

0.094[Non-Sig.]

0.024[Sig.]

0.094[Non-Sig.]

La 0.071[Non-Sig.]

0.015[Sig.]

0.088[Non-Sig.]

0.094[Non-Sig.]

0.011[Sig.]

0.094[Non-Sig.]

M1v.M2: Mixture 1 versus Mixture 2, Sig.: Statistically significant,

Non-Sig.: Statistically Non-significant

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