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Behaviour of asphalt mixturescontaining reclaimed asphalt pavementand asphalt shingleNouffou Tapsobaa, Cédric Sauzéata, Hervé Di Benedettoa, HassanBaajb & Mohsen Echb
a University of Lyon/ENTPE, LGCB & LTDS (UMR CNRS 5513), RueMaurice Audin, 69518, Vaulx-en-Velin, Franceb Lafarge Research Center, 95 rue du Montmurier, 38291 Saint-Quentin-Fallavier, FrancePublished online: 02 Jan 2014.
To cite this article: Nouffou Tapsoba, Cédric Sauzéat, Hervé Di Benedetto, Hassan Baaj & MohsenEch (2014) Behaviour of asphalt mixtures containing reclaimed asphalt pavement and asphaltshingle, Road Materials and Pavement Design, 15:2, 330-347, DOI: 10.1080/14680629.2013.871091
To link to this article: http://dx.doi.org/10.1080/14680629.2013.871091
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Road Materials and Pavement Design, 2014Vol. 15, No. 2, 330–347, http://dx.doi.org/10.1080/14680629.2013.871091
Behaviour of asphalt mixtures containing reclaimed asphalt pavement andasphalt shingle
Nouffou Tapsobaa∗, Cédric Sauzéata. Hervé Di Benedettoa, Hassan Baajb and Mohsen Echb
aUniversity of Lyon/ENTPE, LGCB & LTDS (UMR CNRS 5513), Rue Maurice Audin, 69518, Vaulx-en-Velin,France; bLafarge Research Center, 95 rue du Montmurier, 38291 Saint-Quentin-Fallavier, France
(Received 10 December 2012; accepted 20 July 2013 )
This paper presents the results of laboratory research on asphalt mixtures containing reclaimedasphalt pavement (RAP) and asphalt shingle, including the study of their linear viscoelas-tic (LVE) behaviour and fatigue characteristics. Complex modulus measurements usingthe tension-compression test on cylindrical specimens were conducted to determine LVEbehaviour. Sinusoidal cyclic loadings with a strain amplitude of approximately 50 × 10−6
were applied at several temperatures (from −30◦C to +40◦C) and frequencies (from 0.01 to10 Hz). In addition to axial stresses and strains, radial strains were also measured. The complexmodulus E* and complex Poisson’s ratio ν* were then obtained and the three-dimensional(3D) LVE behaviour (with isotropy hypothesis) was then completely described. The time–temperature superposition principle was verified with good approximation in uni-dimensionaland 3D conditions for the same values of shift factor. Experimental results were modelledusing the 2 springs, 2 parabolic creep elements and 1 dashpot model developed at University ofLyon/ENTPE. Fatigue properties were evaluated by tension-compression tests on cylindricalspecimens using the same testing device used for complex modulus. Sinusoidal loading at10 Hz in controlled axial strain mode was applied at 10◦C. The variation of complex modulusE* and complex Poisson’s ratio ν* as a function of the number of cycles was obtained. Thefatigue test results were analysed using six different fatigue life criteria. The analysis of theresults provided a ranking of the tested materials. The influence of RAP and asphalt shinglecontents was quantified.
Keywords: linear viscoelastic; fatigue; RAP; shingles
1. IntroductionEnvironmental matter and sustainable development has become an important stake in the worldeconomy. In this context, different innovative solutions have appeared in the pavements industry.Recycling has spread beyond reclaimed asphalt pavement (RAP) to other bituminous products.Apart from apparent environmental benefits, with the ever-increasing price of oil, savings shouldbe expected in the construction costs. In order to take advantage from recycling, the newly obtainedmaterials must be well characterised to provide an improved pavement design with well-defineddurability properties.
RAP was the main recycled material used in hot mix asphalts. Several authors (McDaniel,Shah, Huber, & Copeland, 2012; Mogawer et al., 2012; Mogawer, Austerman, Mohammad, &Kutay, 2013; Pasetto & Baldo, 2012; Sias Daniel, Gibson, Tarbox, Copeland, & Andriescu, 2013;
∗Corresponding author. Email: [email protected]
© 2013 Taylor & Francis
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Road Materials and Pavement Design 331
Stroup-Gardiner & Wagner, 2007; Visintine, Khosla, & Tayebali, 2013), have studied the useof RAP in road construction. Long-term performances of asphalt mixes and the influence ofhigh ratios of RAP remain important issues. However, according to Al-Qadi et al. (2009), theperformance of pavements using properly prepared RAP was found to be satisfactory in terms offatigue, rutting, thermal resistance and durability.
The use of manufacturer-waste asphalt shingles as recycled material in hot mix asphalt wasanother solution to save non-renewable raw materials. For more than 10 years, several researchstudies were conducted in Canada and other countries addressing the use of manufacturer-wasteasphalt roofing shingles as substitution material in hot mix asphalt (Baaj & Paradis, 2008; Baaj,Ech, Lum, & Forfylow, 2011; Baaj, Ech, Tapsoba, Sauzéat, & Di Benedetto, 2013; Lum, Yonke,& Greco, 2004; Yonke, Lum, Budd, Uzarowski, & Emery, 1999). These studies showed the greatpotential of this recycled material not only as substitution material but also as modifier of themixture behaviour. The fact that the asphalt cement used in the shingles is a high-quality bindertogether with fibreglass or organic (cellulose) fibres seem to play a very positive role in thebehaviour of asphalt mixes incorporating shingles. The roofing asphalt shingles are shredded andprocessed to allow for a good incorporation and a homogeneous dispersion into the final asphaltmixture. Such a material (Asphalt Shingle Modifier ASM®) was used in this study and will bereferred to as asphalt shingle in this paper.
The objective of the present research was to study three-dimensional (3D) viscoelastic linearand fatigue behaviours of asphalt mixes which were modified by adding asphalt shingle and RAPin the mix. Complex modulus tests and fatigue tests were carried out in tension-compressionon cylindrical samples. The experimental test set-up and the tested materials are first described,followed by the obtained results, analysed in the linear viscoelastic (LVE) domain and, finally,the fatigue results will be presented.
2. Experimental research2.1. Test equipmentTension-compression tests were carried out using a hydraulic press with a maximum capacity of±25 kN and ±50 mm axial stroke.
A thermal chamber was used for thermal conditioning of the specimens during the test. Thetemperature was measured using a thermal gauge (PT100 temperature probe) fixed on the surfaceof the specimen.
Three axial extensometers located at 120◦ around the specimen were used to measure the axialstrain (Figure 1). The axial strain was considered to be the average of the three measurements.The radial strain was obtained from two non-contact displacement transducers (range 500 μm)that measured diameter changes at mid-height of the specimen.
A general view of the specimen and the strain measurement devices developed at Universityof Lyon/ENTPE is shown in Figure 1.
2.2. Test procedures2.2.1. Complex modulus testAdvanced complex modulus tests were carried out using the described equipment. Specimenswere loaded at seven frequencies (0.01–10 Hz) and eight temperatures (from −30.0◦C to 40.0◦C)in order to determine the viscoelastic properties of tested materials on a range as wide as possible.The amplitude of axial strain during cyclic loading was 50 μm/m. The number of loading cyclesvaried from 6 cycles at 0.01 Hz up to 100 cycles at 10 Hz. A rest period of 300 s was applied
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332 N. Tapsoba et al.
Specimen
Loading
Upper cap
Lower cap
Axial Extensometer (3)
Target for non contact sensor (2)
Radial non contact sensor (2)
PT100 surface temperature probe
Thermal chamber
System to maintain non-contact sensor
Figure 1. General view of the experiment (left) and strain systems measurement (right) developed atUniversity of Lyon/ENTPE to measure the axial strain and the radial strain.
50µm/m 50µm/m50µm/m 50µm/m
50µm/m
50µm/m
50µm/m 50µm/m 50µm/m
20ºC –30ºC –20ºC –10ºC 0ºC
10°C 20ºC 3ºC 40ºC
4 hours
4 hours
4 hours 4 hours4 hours 4 hours
4 hours 4 hours
Time
Stra
inam
plitu
de (
e A
ax)
~ 47mn ~ 47mn ~ 47mn ~ 47mn
~ 47mn ~ 47mn ~ 47mn ~ 47mn
~ 47mn
= 0= 0 = 0 = 0 = 0
= 0 = 0 = 050µm/m
4 hours ~ 47mn
= 0
20ºC
s ssss
s s s s
Figure 2. Schematic presentation of the complex modulus test chronology.
between two successive cyclic loading periods (i.e. between each frequency change). For eachtemperature, this represents a test’s duration of 47 min approximately. A conditioning period of 4 hwas also considered when the temperature was changed to ensure an homogeneous temperatureinside the specimen. During this period, the load applied on the specimen is equal to 0. Figure 2shows the schematic presentation of complex modulus test chronology.
A sinusoidal axial strain (εax) (average of three extensometers) was applied and the sinusoidalaxial stress (σax) was measured using a load cell. The sinusoidal radial strain (εrad) was obtainedfrom the two non-contact sensors. The following equations were used:
εax(t) = εAax sin(ωt), (1)
σax(t) = σAax sin(ωt + ϕE), (2)
εrad(t) = εArad sin(ωt + π + ϕν) = −εArad sin(ωt + ϕν), (3)
where ϕE is the phase angle between the axial strain and the axial stress, ϕν is the phase anglebetween the axial strain and the opposite radial strain and εAax, εArad and σAax are the axial strainamplitude, the radial strain amplitude and the axial stress amplitude, respectively.
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Road Materials and Pavement Design 333
When applying Equations (1)–(3), the complex modulus (E∗) and complex Poisson’s ratio (ν∗)were calculated as follows:
E∗ = σAax
εAaxejϕE = |E∗|ejϕE , (4)
ν∗ = −εArad
εAaxejϕν = |ν∗|ejϕν , (5)
where |E∗| is the norm of complex modulus, |ν∗| is the norm of Poisson’s ratio and j is the complexnumber defined by j2 = −1.
2.2.2. Fatigue testFatigue tests were also carried out in tension-compression on cylindrical specimens. Sinusoidalcyclic loading was applied at a constant monitored axial strain amplitude. Temperature was setat 10◦C as in the French standard (NF EN 12697-24, 2012) and frequency at 10 Hz (which is thelimit of our experimental device).
At least four different levels of strain amplitude were applied for each tested material. The axialload, axial strain and radial strain were recorded during tests.
Data acquisition frequency was 2500 Hz, giving 250 data per cycle. Because of the great numberof performed cycles, only cycles indicated in Table 1 were recorded.
As for the complex modulus test, during fatigue test, the complex modulus and the complexPoisson’s ratio were calculated (Equations (4) and (5)) and plotted versus the number of cycles,N . The dissipated energy per cycle (WN ) was also calculated. It is the area within the axialstress–strain hysteresis loop, given by Equation (6)
WN = πεAaxσAax sin ϕE. (6)
2.3. Tested materialsFive bituminous mixes with different contents of RAP (from 0% to 40% of the total mass) andasphalt shingle (from 0% to 5% of the total mass) were tested (Table 2). The material M1, notcontaining shingles and RAP, was used as the reference material. The same virgin bitumen wasused for all the materials and its grade was PG58-28. The bitumen content of material M1 was5.18% (of total mix mass). All the mixes have the same aggregates size distribution (Figure 2). Themaximum particle size was 12.5 mm. The slab compactor (LPC type, in French “Laboratoire desPonts et Chaussées”) was used to produce 600 × 400 × 120 mm slabs according to NF EN 12697-33 (2004). Eight cylindrical specimens were cored and sawn from each slab. These cylindricalspecimens were used for complex modulus and fatigue tests. Their diameter was 75 ± 0.5 mm andtheir length was 140 ± 2 mm. The first specimen sp1 was used for the complex modulus test andthe other specimens (sp2–sp5) for fatigue tests (Table 2). Table 2 also provides the compactionlevels of each specimen.
Table 1. Recorded cycles during fatigue test.
Number of cycles (N ) Recording period Number of recorded cycles
Cycle 1–1000 All cycles 1000Cycle 1000–10,000 2 Cycles every 20 cycles 900Cycle 10,000–100,000 2 Cycles every 200 cycles 900Cycle 100,000 to 1,000,000 2 Cycles every 2000 cycles 900After one million 2 Cycles every 5000 cycles —
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Table 2. RAP and asphalt shingle contents of the tested materials andcompaction levels of each tested specimen.
M1 M2 M4 M5 M6
RAP (%) 0 15 15 15 40Asphalt shingle (%) 0 0 3 5 0Compaction levels (%)
Specimen 1 (sp1) 94.7 95.1 94.7 94.6 97.4Specimen 2 (sp2) 94.7 95.1 94.1 94.1 96.8Specimen 3 (sp3) 93.8 94.9 94.3 94.3 96.6Specimen 4 (sp4) 94.1 94.8 93.9 93.9 97.1Specimen 5 (sp5) 94.5 94.9 94.5 94.5 97.3
3. LVE behaviour, in the small strain domain: complex modulus3.1. Experimental resultsSeveral research studies (Delaporte, Di Benedetto, Chaverot, & Gauthier, 2009; Di Benedetto,Delaporte, & Sauzeat, 2007; Di Benedetto, Mondher, Sauzeat, & Olard, 2007; Di Benedetto,Sauzeat, & Sohm, 2009; Ho & Romero, 2011; Mangiafico et al., 2013, in press; Mounier,Di Benedetto, & Sauzeat, 2012; Nguyen, Pouget, Di Benedetto, & Sauzeat, 2009; Nguyen,Sauzéat, Di Benedetto, & Tapsoba, 2013; Nguyen, Di Benedetto, Sauzéat, & Tapsoba, 2013;Olard & Di Benedetto, 2003; Pouget, Sauzeat, Di Benedetto, & Olard, 2010a; Wu, Huang, & Shu,2012; Yin, Buttlar, Paulino, & Di Benedetto, 2008) using unidirectional experiments showed thatthe time–temperature superposition principle (TTSP) is verified for bituminous mixtures in thesmall strain amplitude (up to 10−4 m/m) domain, where the behaviour can be considered as LVE(Figure 3).
The results of the complex modulus (E∗) and the Poisson’s ratio (ν∗), in the Cole–Cole axes andBlack diagram, are presented in Figure 4. Figure 4(a) and 4(b) shows that the TTSP is applicableto the complex modulus measurements (as found in the literature), as expected, as only onecurve could be obtained for each material. The extension of this principle to the Poisson’s ratiomeasurements is also verified but with some scattering in the results at high temperatures and lowfrequencies. Thus, the TTSP may be extended to the 3D behaviour of the tested mixes. |ν∗| variesapproximately from 0.1 for high frequencies and/or low temperatures to 0.5 for low frequenciesand/or high temperatures for all the mixes. It decreases when temperature decreases and whenfrequency increases. Additionally, ϕν ranges between approximately 1◦ and −7.3◦. This is worthmentioning as ν∗ is considered as a constant real number in pavement design in all design methods.As TTSP is verified, master curves for |E∗|, ϕE , |ν∗| and ϕν were plotted for all tested materials.They are presented in Figure 8, with a simulation made using the 2S2P1D model (whose name
0.1 1 10 1000
20
40
60
80
100 M1M2M4M5M6
Pass
ing
(%)
Aggregate size (mm)
Figure 3. Aggregate grading curves of the five tested mixes.
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Road Materials and Pavement Design 335
0 10000 20000 30000 400000
1000
2000
3000
4000(a) (a)
(c) (d)
M1_sp1 M2_sp1 M4_sp1 M5_sp1 M6_sp1
E 2 (
MPa
)
E1 (MPa)
0 10 20 30 40 5010
100
1000
10,000
100,000
M1_sp1 M2_sp1 M4_sp1 M5_sp1 M6_sp1
|E* |
|n|
(M
Pa)
0.0 0.2 0.4 0.6
–0.03
–0.02
–0.01
0.00
0.01 M1_sp1 M2_sp1
M4_sp1 M5_sp1 M6_sp1
n 2
n1
–8 –6 –4 –2 0 20.0
0.2
0.4
0.6 M1_sp1 M2_sp1 M4_sp1 M5_sp1 M6_sp1
jE (º)
jn (º)
Figure 4. Experimental results for tested materials: (a) complex modulus in Cole–Cole axes ; (b) complexmodulus in Black diagram; (c) complex Poisson’s ratio in Cole–Cole axes and (d) complex Poisson’s ratioin Black diagram.
means that this rheological model is composed of 2 springs, 2 parabolic creep elements and 1dashpot) (Section 3.1.2).
Figures 4 and 8 show that the complex modulus of material M1 is lower than that of allother tested materials. The use of RAP and/or asphalt shingle increases the complex modulus ofmaterials M2, M4, M5 and M6. Moreover, at low equivalent frequencies, the complex modulustends to increase with the asphalt shingle content. This observation is not valid for high equivalentfrequencies as M2 and M5 materials (respectively, 0% and 5% asphalt shingle content) showedidentical complex modulus values. The use of asphalt shingle seems also to influence the phaseangle value for lower equivalent frequencies and the peak value tends to decrease with the asphaltshingle content.
In the French pavement design method (NF P 98-082, 1994), the used modulus value is thecomplex modulus at 15◦C and 10 Hz. The values of two parameters (complex modulus |E∗| andcomplex Poisson’s ratio |ν∗|) at 15◦C and 10 Hz are analysed more in detail in the following. Thecomplex modulus norm and the complex Poisson’s ratio norm values (|E∗| and |ν∗|) at 15◦C and10 Hz are presented in Figures 5 and 6, respectively, as a function of RAP content and shinglecontent. For the mixes without asphalt shingles, Figure 5(a) shows clearly that the addition ofRAP increases the stiffness of the mixes. In Figure 6(a), it is observed that the stiffness of asphaltmixes, containing of 15% RAP, increases significantly with the asphalt shingle content. Regardingthe complex Poisson’s ratio, no clear tendency is observed when the content of RAP (Figure 5(b))increases. However, increasing the shingle content (for mixes with 15% of RAP: Figure 6(b))leads to an increase in the complex Poisson’s ratio.
3.2. Simulation using the 2S2P1D modelThe 2S2P1D model, developed at the University of Lyon/ENTPE, is a generalisation of theHuet–Sayegh model (Olard & Di Benedetto, 2003). This 2S2P1D model is based on a simple
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0 10 20 30 405000
6000
7000
8000
9000
10,000
11,000(a) (b)
RAP (%)0 10 20 30 40
0.20
0.25
0.30
0.35
0.40
0.45
0.50
RAP (%)
|E* |
(Mpa
) at
15º
C, 1
0 H
z
|n* |
at 1
5ºC
, 10
Hz
Figure 5. Complex modulus (a) and complex Poisson’s ratio (b) values at 15◦C and 10 Hz for the testedmixes (influence of RAP content).
0 1 2 3 4 55000
6000
7000
8000
9000
10,000
without RAP with 15% of RAP
Shingle (%)0 1 2 3 4 5
0.20
0.25
0.30
0.35
0.40
without RAP with 15% of RAP
Shingle (%)
(a)
|E* |
(Mpa
) at
15º
C, 1
0 H
z
(b)
|n* |
at 1
5ºC
, 10
Hz
Figure 6. Complex modulus (a) and complex Poisson’s ratio (b) values at 15◦C and 10 Hz for the testedmixes (influence of shingle content).
Figure 7. Analogical representation of the 2S2P1D model (Di Benedetto, Delaporte, et al., 2007; Olard& Di Benedetto, 2003).
combination of physical elements (spring, dashpot and parabolic element). The graphical repre-sentation of the 2S2P1D model is shown in Figure 7. The 2S2P1D model is widely used to modelthe LVE uni-dimensional or 3D behaviour of bituminous materials (including binders, masticsand mixes) (Pouget, Sauzéat, Di Benedetto, & Olard, 2010b; Pouget, Sauzeat, Di Benedetto, &Olard, 2012; Tiouajni, Di Benedetto, Sauzeat, & Pouget, 2011).
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The complex modulus and the Poisson’s ratio, at a given temperature, are given by Equations (7)and (8) in the 2S2P1D model
E∗2S2P1D(ω) = E00 + E0 − E00
1 + δ(jωτE)−k + (jωτE)−h + (jωβτE)−1 , (7)
ν∗2S2P1D(ω) = ν00 + ν0 − ν00
1 + δ(jωτν)−k + (jωτν)−h + (jωβτν)−1 , (8)
where j is the complex number defined by j2 = −1, ω is the pulsation, ω = 2π f (f is the fre-quency), k , h constant exponents such as 0 < k < h < 1; δ is the constant, E00 is the staticmodulus when ω → 0; E0 is the glassy modulus when ω → ∞, ν00 is the static Poisson’s ratiowhen ω → 0; ν0 is the glassy Poisson’s ratio when ω → ∞, β is the parameter linked with η,the Newtonian viscosity of the dashpot, η = (E0 − E00)βτE , and τE and τν are characteristic timevalues, which are only parameters depending on temperature and have a similar evolution
τE(T ) = aT (T ).τ0E and τν(T ) = aT (T ).τ0ν , (9)
where aT is the shift factor at temperature T , τE = τ0E and τν = τ0ν at reference temperature Tref .Ten constants (E00, E0, δ, k , h, β, ν00, ν0, τ0E and τ0ν) are required to completely characterisethe 3D LVE properties (with isotropy hypothesis) of the tested material at a given temperature.The evolutions of τE and τν were approximated by the William-Landel-Ferry (WLF) law (Ferry,1980) (WLF law, Equation (10)). τ0E and τ0ν were determined at the chosen reference temperatureTref = 10◦C. When the temperature effect is considered, the number of constants becomes 12,
10-7 10-5 10-3 10-1 101 103 105 107 10910
100
1000
10,000
Tref
= 10ºC
M1_sp1 M2_sp1 M4_sp1 M5_sp1 M6_sp1
M1_sp1 M2_sp1 M4_sp1 M5_sp1 M6_sp1 (
MPa
)
aT ×frequency
aT ×frequency aT ×frequency
aT ×frequency
(a)
(c) (d)
(b)
10-7 10-5 10-3 10-1 101 103 105 107 109
0
10
20
30
40
50
60
Tref
= 10ºC M1_sp1 M2_sp1 M4_sp1 M5_sp1 M6_sp1
M1_sp1 M2_sp1 M4_sp1 M5_sp1 M6_sp1
10-7 10-5 10-3 10-1 101 103 105 107 109
0.1
0.2
0.3
0.4
0.5
0.6T
ref = 10ºC M1_sp1
M2_sp1 M4_sp1 M5_sp1 M6_sp1
M1_sp1 M2_sp1 M4_sp1 M5_sp1 M6_sp1
10-7 10-5 10-3 10-1 101 103 105 107 109
–7.5
–5.0
–2.5
0.0
2.5 M1_sp1 M2_sp1 M4_sp1
M5_sp1 M6_sp1
M1_sp1 M2_sp1 M4_sp1 M5_sp1 M6_sp1
Tref
= 10ºC
|E* |
|n* |
jE (
º)j n
(º)
Figure 8. Master curves of the complex modulus (norm and phase angle) and the Poisson’s ratio (normand phase angle): data and simulations using the 2S2P1D model.
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Table 3. Constants of the 2S2P1D model and WLF parameters for the tested mixes (referencetemperature: 10◦C).
Material E00 (MPa) E0 (MPa) k h δ τ0E(s) B ν00 ν0 τ0ν (s) C1 C2
M1 25 3.50E+04 0.20 0.60 2.5 0.025 800 0.38 0.18 0.002 22.32 157.72M2 28 3.75E+04 0.20 0.60 2.4 0.045 250 0.33 0.08 0.075 20.35 143.14M4 40 4.10E+04 0.18 0.52 2.2 0.070 700 0.47 0.09 0.005 25.98 183.68M5 50 3.80E+04 0.17 0.50 2.0 0.054 800 0.44 0.25 0.004 28.04 184.11M6 38 4.10E+04 0.18 0.56 2.1 0.102 100 0.47 0.23 0.102 35.16 240.13
–30 –20 –10 0 10 20 30 4010–5
10–3
10–1
101
103
105
107
109
a TWLF_M1_sp1
aTWLF_M2_sp1
aTWLF_M4_sp1
aTWLF_M5_sp1
aTWLF_M6_sp1
a TE_M1_sp1
a TE_M2_sp1
a TE_M4_sp1
a TE_M5_sp1
a TE_M6_sp1
Shif
t fac
tor
(aT)
Temperature (ºC)
Tref
=10ºC
Figure 9. Shift factors aT of the tested materials and WLF law fitting (Equation (10)).
including the 2 WLF constants (C1 and C2 calculated at the reference temperature) (Equation (9))
log(aT ) = − C1(T − Tref)
C2 + T − Tref. (10)
Simulations using the 2S2P1D model of the E∗ and ν∗ master curves for the tested asphalt mixes,are presented in Figure 8. The model fits rather well the data on the whole range of temperaturesand frequencies. Used 2S2P1D parameters are reported in Table 3 for the five mixes.
The shift factors obtained from the construction of the master curves of all the tested materialsare presented in Figure 9 as a function of the temperature. This figure shows that the values of aTare close for all the materials. The coefficients C1 and C2, of the WLF law, are given in Table 3.
4. Fatigue behaviourIn order to present fatigue test results, the observed behaviour on an arbitrarily chosen specimen(M4_sp4) is described in detail, before presenting the used fatigue life criterion and the comparisonbetween materials.
4.1. Example of fatigue test results: M4_sp4Results of the M4_sp4 fatigue test (material M4, specimen 4, see Table 2) are presented inFigure 10. The complex modulus (norm |E∗| and phase angle ϕE), obtained for the applied strainamplitude (121 μm/m) is plotted as a function of the number of cycles in Figure 10(a). Aspreviously highlighted by some authors (Baaj, Di Benedetto, & Chaverot, 2005; Di Benedetto &De la Roche, 1998; Di Benedetto, De La Roche, Baaj, Pronk, & Lundström, 2004; Di Benedetto,
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0 100000 200000 3000000
2000
4000
6000
8000
10000
Phase IIIPhase II
Phas
e I
Test: M4_sp4 at 121µm/m
N (cycles)
(a) (b)
(c) (d)
10
15
20
25
30
10 15 20 25 30 350
2000
4000
6000
8000
10000
12000
Direction of test travel
end of test
beginning of test
A(Nfmaxj)Test: M4_sp4_at 121µm/m
Phase III
Phase II
Phase I
0 100,000 200,000 300,0000.00
0.05
0.10
0.15
0.20
0.25
0.30 Test: RAM4_sp4 at 121µm/m
Pha
se I
Phase IIIPhase II
N (cycles)
c)
–30
–25
–20
–15–10
–5
0
5
10
0 100000 200000 3000000
20406080
100120140160
Wn
Tem
pera
ture
(ºC
)
Phase IIIPhase II
Phas
e I
Test: M4_sp4 at 121µm/m
Wn
(J/m
3 )
N (cycles)
9.6
9.8
10.0
10.2
10.4
Temperature
|E* |
(MPa
)
|E* |
(MPa
)
j E (
º)j n
(º)
jE (º)
|n* |
|n*|jE
E *|jE
jEmax
Figure 10. Evolution of certain parameters during the M4_sp4 fatigue test at a strain amplitude of121 μm/m: (a) E∗ versus the number of cycles; (b) E∗ in the Black diagram; (c) ν∗ versus the numberof cycles and (d) dissipated energy and temperature versus the number of cycles.
Nguyen, & Sauzeat 2011; Homsi, Bodin,Yotte, Breysse, & Balay, 2012; Lundström, Di Benedetto,& Isacsson, 2004; Nguyen, Di Benedetto, & Sauzéat, 2012; Shen & Sutharsan, 2011; Tapsoba,Sauzéat, & Di Benedetto, 2013; Van Rompu, Di Benedetto, Buannic, Gallet, & Ruot, 2012), threephases (adaptation phase (phase I), quasi-stationary phase (phase II) and failure phase (phase III))can be observed during fatigue tests. The evolution of E∗ in the Black diagram (|E∗| versus ϕE)is presented in Figure 10(b). Phases I, II and III are also represented in this figure. The end ofphase II, corresponding to the beginning of macro-crack propagation, was close or equal to themaximum of phase angle.
The norm and phase angle of the complex Poisson ratio are presented according to the numberof cycles in Figure 10(c). The three phases determined with the evolution of complex modulus arealso shown in Figure 10(c), and seem to correspond with the evolution of complex Poisson’s ratio.The norm of the complex Poisson ratio increased during phase I. In phase II, it decreased veryslowly (from 0.27 to 0.25). In phase III, a quick decrease in the Poisson’s ratio was observed butthis is not representative because the sample was no longer homogeneous due to macro-cracks.Interpretation of the measured data (in terms of complex modulus or Poisson’s ratio), as made inphases I and II is no longer valid. This output from our fatigue test on the Poisson’s ratio is quitenew and should be further analysed.
The dissipated energy per cycle and temperature are plotted in Figure 10(d) as a function ofthe number of cycles. The three phases are also given in this figure. The boundaries between thethree phases are quite noticeable on the temperature curve. They correspond to rapid changesin the slope of the curve. At the beginning of the test, the surface temperature increased rapidly(more than 0.55◦C for about 35,000 cycles (4000 s)). The temperature of the material reachedits maximum level at approximately 35,000 cycles. This maximum temperature more or lesscorresponded to the boundary between phases I and II. This temperature increase corresponds toabout 500 MPa decrease for |E∗| and then does not explain the whole |E∗| decrease in phase I.Others reversible phenomena, such as thixotropy, should be considered in this phase I.
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4.2. General evolution of damageFigure 11 presents the evolution of classical damage parameter: 1 − |E∗|/|E∗
0 |, versus logarithmof the number of cycles for the five tested mixes. Four tests with different levels of strain amplitudeare carried out for each mixes. The applied axial strain is indicated for each test (after the specimenname). In this figure, the corresponding parameter extended to the Poisson’s ratio is also plotted(1 − |ν∗|/|ν∗
0 |). |E∗0 | and |ν∗
0 | represent, respectively, the value of complex modulus and complexPoisson’s ratio at the beginning of the test. This value is determined by linear fitting of complexmodulus (for |E∗
0 |) and complex Poisson’s ratio (for |ν∗0 |) measurement from cycles 50 to 250,
and extrapolation to cycle 1. This value is indicated for each test in Table 4.For all the tests, after 103 cycles, the complex modulus starts decreasing significantly. This
decrease, which goes on until failure, is a classical observation for fatigue tests. It is usuallyexplained by appearing micro-cracks that damage the material. Before failure, the classical damageparameter (1 − |E∗|/|E∗
0 |) has reached at least 30% for all the tests. In order to better characterisethe material evolution during fatigue tests, it is interesting to look at the complex Poisson’s ratio.On the contrary of the complex modulus, the complex Poisson’s ratio remains rather constantduring the first phase and, in most cases, tends to slightly increase (less than 10%) before thefailure. During the third phase, the sudden evolution should not be considered as the specimenis no more homogeneous, with the apparition of macro-cracks. The evolution of the complexPoisson’s ratio should not be mixed up with a volumetric deformation of the specimen throughoutthe fatigue tests (which could be explained by the apparition of the micro-cracks). It indicatesonly that the cyclic radial strain amplitude remains constant or becomes smaller and smaller ateach cycle. This observation requires more than only common sense to be explained.
4.3. Definition of studied fatigue criteriaSix criteria were considered to determine the fatigue life of the tested mixes (Pronk & Hopman,1990). These criteria may be classified in four categories:
• Criteria based on modulus decrease: The classical fatigue criterion, used in the Frenchpavement design method, is based on a relative arbitrary decrease in the complex modulusof 50%. The fatigue life (Nf50%) is then defined as the number of cycles when the modulusreaches 50% of its initial value (Figure 12(d)). This criterion is investigated in addition toanother corresponding to 30% of stiffness decrease (Nf30%).
• Criterion based on the phase angle of the complex modulus evolution: The fatigue life(Nfmaxϕ) is defined as the number of cycles corresponding to the highest value of phaseangle (Figure 10(a) and 10(b)).
• Criteria obtained from the analysis of the specimen homogeneity: Two criteria are definedas follows:◦ The phase angle criterion: With this criterion, the fatigue life (Nf�ϕ) is defined as the
number of cycles at which the value �ϕi = ϕεiax − ϕE reaches 5◦ for any extensometer(where ϕεiax is the phase angle between the sinusoidal measurement from extensometersi and the axial stress, with i = 1, 2 or 3) (Figure 12(a)).
◦ The axial strain amplitude criterion: With this criterion, the fatigue life (Nf�εax) isdefined as the number of cycles at which the value (�εaxi = (εAaxi − εAax)/εAax × 100%reaches 25% for any extensometer (where εAaxi is the axial strain amplitude of the threeextensometers: i = 1, 2 or 3 ) (Figure 12(b)).
• Viscous dissipated energy criterion: The fatigue life (NfWN) was proposed by Pronk &Hopman (1990). It was obtained from the analyses of the evolution of the dissipated energy
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101 102 103 104 105 106-0.2
0.0
0.2
0.4
0.6
0.8
1.0 M1_sp3_D79 M1_sp5_D99 M1_sp2_D119 M1_sp4_D148
Log N (Cycles)101 102 103 104 105 106
–0.1
0.0
0.1
0.2
0.3
0.4
0.5 M1_sp3_D79 M1_sp5_D99 M1_sp2_D119 M1_sp4_D148
Log N (Cycles)
101 102 103 104 105 106–0.2
0.0
0.2
0.4
0.6
0.8
1.0 M2_sp2_D80 M2_sp3_D100 M2_sp4_D120 M2_sp5_D177
Log N (Cycles)101 102 103 104 105 106
–0.1
0.0
0.1
0.2
0.3
0.4
0.5 M2_sp2_D80 M2_sp3_D100 M2_sp4_D120 M2_sp5_D177
Log N (Cycles)
101 102 103 104 105 106–0.2
0.0
0.2
0.4
0.6
0.8
1.0 M4_sp2_D92 M4_sp3_D100 M4_sp4_D121 M4_sp5_D151
Log N (Cycles)101 102 103 104 105 106
–0.1
0.0
0.1
0.2
0.3
0.4
0.5 M4_sp2_D92 M4_sp3_D100 M4_sp4_D121 M4_sp5_D151
Log N (Cycles)
101 102 103 104 105 106 107–0.2
0.0
0.2
0.4
0.6
0.8
1.0 M5_sp5_D78 M5_sp4_D100 M5_sp3_D125 M5_sp2_D148
Log N (cycles)101 102 103 104 105 106 107
0.0
0.1
0.2
0.3
0.4
0.5 M5_sp5_D78 M5_sp4_D100 M5_sp3_D125 M5_sp2_D148
Log N (cycles)
101 102 103 104 105 106–0.2
0.0
0.2
0.4
0.6
0.8
1.0 M6_sp5_D81 M6_sp4_D103 M6_sp3_D125 M6_sp2_D157
Log N (cycles)101 102 103 104 105 106
–0.1
0.0
0.1
0.2
0.3
0.4
0.5 M6_sp5_D81 M6_sp4_D103 M6_sp3_D125 M6_sp2_D157
Log N (cycles)
1- |
E*
| /| E
* 0 |
1- |
E*
| /| E
* 0 |
1- |
E*
| /| E
* 0 |
1- |
E*
| /| E
* 0 |
1- |n
* | /
| n* 0
|1-
|n*
| /| n
* 0 |
1- |n
* | /
| n* 0
|1-
|n*
| /| n
* 0 |
1- |
E*
| /| E
* 0 |
1- |n
* | /
| n* 0
|
Figure 11. Relative decrease of the norm of complex modulus (classical damage parameter) and the normof complex Poisson’s ratio versus number of cycles (log) for tested mixes.
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0 100,000 200,000 300,000–20
–15
–10
–5
0
5
10
15
20
5ºTest: M4_sp4 at 121µm/m
N (cycles)
N
5º
0 100,000 200,000 300,000–100
–75
–50
–25
0
25
50
75
100(b)(a)
Test: M4_sp4 at 121µm/m
N (cycles)
NfDeAax
fDeAax
fDj
0 100,000 200,000 300,0000.0
2.0x105
4.0x105
6.0x105
8.0x105
1.0x106(c)Test: M4_sp4 at 121µm/m
DE
R
N (cycles)
NfWn
0 100000 200000 3000000
2000
4000
6000
8000
10000
(d)
Nf30%
N
N
N fWN
Nfmaxj
0.7×E0
Test: M4_sp4 at 121µm/m
N (cycles)
E0/2
N f50%
0 100,000 200,000 300,000
Dji (
º)
DeA
ax (%
)
Deax1Djax3Djax2Djax1 Deax1Deax1
fDeAax
|E* |
(MPa
)
Figure 12. Representation of the six considered criteria for test M4_sp4: (a) phase angle versus the numberof cycles and criterion Nf�φ; (b) axial strain amplitude versus the number of cycles and criterion Nf�εax;(c) DER evolution versus the number of cycles and criterion NfWN and (d) complex modulus versus thenumber of cycles and indication of all the criteria.
ratio (DER) given in the following:
DER =N∑
i=1
Wi
WN, (11)
where∑N
i=1 Wi is the cumulated dissipated energy up to cycle N and WN is the dissipatedenergy at cycle N . There are two periods in the evolution of DER (Figure 12(c)). Theevolution appears to be linear in both of the periods but the slope is higher in the secondperiod. Two straight lines could then be drawn to linearise the evolution of each period. Thenumber of cycles NfWN is obtained at the intersection of the two straight lines (Figure 12(c)).
The applied axial strain amplitude (εAax), the complex modulus at the beginning of test |E∗0 |
and the number of cycles at failure considering the six defined criteria is presented in Table 4 fortested specimens. The number of cycles obtained with the criterion Nf30% is much lower comparedwith the other criteria, which show rather close values. These results are used in the followingsection to analyse the fatigue life of the different materials.
4.4. Analysis of fatigue lifeThe classical Wöhler representation was used: number of cycles at failure versus strain amplitudein logarithmic axes. The Wöhler curves for bituminous mixtures are classically straight lines.
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esign343
Table 4. Data of fatigue tests for the five tested materials.
εAax E0 Nf30% Nf50% Nfϕmax Nf�εax Nf�ϕ NfWNMix specimen (μm/m) (GPa) ν0 (×103 cycles) (×103 cycles) (×103 cycles) (×103 cycles) (×103 cycles) (×103 cycles)
M1 sp2 119 8.6 0.3 33 280 244 280 281 280sp3 79 7.5 0.21 300 560 555 520 535 550sp4 148 7.6 0.3 12.8 130 130 126 128 128sp5 99 8.3 0.29 200 430 430 448 448 415
M2 sp2 80 9.9 0.29 520 674 674 670 674 670sp3 100 9.4 0.26 134 486 468 500 452 506sp4 120 10 0.32 47.6 190 190 194 196 196sp5 177 9.6 0.43 3.7 26 36 80 32 60
M4 sp2 92 11 0.33 240 1685 1490 1705 994 1640sp3 100 10.7 0.23 122 482 470 490 460 480sp4 121 9.8 0.26 29 224 220 248 225 240sp5 151 10.4 0.25 9.1 38 38 42 40 40
M5 sp2 148 12.1 0.37 13 99 99 118 110 120sp3 125 12.8 0.31 35 200 114 368 142 250sp4 100 12.5 0.28 350 1355 1355 1360 1190 1350sp5 78 13.1 0.31 1200 5500 4620 5850 2835 6300
M6 sp2 157 12.1 0.25 15 70.2 108 158 118 155sp3 125 14 0.29 32 300 300 354 320 320sp4 103 13.7 0.27 170 650 582 722 580 680sp5 81 14.3 0.37 720 2240 2160 2345 2170 2200
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344 N. Tapsoba et al.
M1 M2 M4 M5 M60
20
40
60
80
100
6575.6
93.6 95.9
e 6 (µ
m/m
)
Nf30% Nf50%
Nfmaxj NfDj
NfDeax NfWN
102
Figure 13. ε6 values for the tested materials with the different fatigue criteria.
60 80 100 120 140 160 180 200104
105
106
107
Lin(Nff-M6)
Lin(Nff-M2)
Lin(Nff-M1)
Lin(Nff-M4)
M1M2M4M5M6
Nff (
cycl
es)
e (µm/m)
Lin(Nff-M5)
Figure 14. Wöhler curves from Nff criterion for the tested materials.
They are defined by the following equation:
Nf
106 =(
ε
ε6
)−β
, (12)
where Nf is the number of cycles at failure, ε is the applied strain amplitude, β is a constant thatdepends on the material and ε6 represents the axial strain amplitude level for which failure isobtained after one million cycles.
The values of β, ε6 and the determination coefficient R2 for each criterion and for the fivemixes are given in Table 5. R2 values are above 0.93 in most cases, which indicates that thedata obtained with the different criteria are well lined up and that the Wöhler curves are welldetermined. A comparison of the ε6 values for the five tested mixes and the six different fatiguecriteria is presented in Figure 13. This figure shows that ε6 values are close (except the Nf 30%criterion) for any fixed mix. Results of M1, M2 and M6 materials (with, respectively, 0%, 15%and 40% RAP content) indicate clearly that this fatigue parameter improves with RAP content.From results of M2, M4 and M5 materials (with, respectively, 0%, 3% and 5% shingles content),it may be concluded that the addition of shingle also improves this fatigue parameter.
In order to give equal importance to each criterion, an average fatigue life, Nff , was considered.In order to calculate Nff , Nf30% criterion, which gives very different values as given in Table 4and which does not provide an adequate fatigue evaluation, as described in Tapsoba et al. (2013)was excluded. Nff is the average value of Nf50%, Nfmaxφ, Nf�φ , Nf�εax and NfWN (Tapsoba et al.,2013).
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Road Materials and Pavement Design 345
Table 5. Values of β and ε6 (parameter of the Wöhler curve defined in Equation (12)) for the tested mixes.
M1 M2 M4 M5 M6
Criteria β R2 ε6 β R2 ε6 β R2 ε6 β R2 ε6 β R2 ε6
Nf30% 5.19 0.880 63.6 6.16 0.999 72.2 6.92 0.991 74.6 6.80 0.971 82.0 6.07 0.976 75.9Nf50% 2.33 0.945 66.7 4.24 0.961 77.5 7.08 0.965 95.2 5.99 0.970 102.0 5.12 0.992 95.6Nfmaxϕ 2.39 0.962 64.7 3.81 0.974 76.0 6.88 0.969 94.5 6.00 0.906 101.0 4.43 0.991 94.6Nf�ϕ 2.39 0.932 63.9 2.80 0.965 74.5 6.86 0.959 95.9 5.59 0.997 106.0 4.04 0.991 97.9Nfεax 2.37 0.934 65.5 3.95 0.972 77.0 6.10 0.986 92.0 5.08 0.916 96.5 4.29 0.987 94.9NfWn 2.34 0.949 65.1 3.17 0.971 75.0 6.91 0.962 95.0 5.83 0.975 104.5 4.00 0.988 96.3Nff 2.33 0.941 65.2 3.47 0.975 74.9 6.80 0.967 94.5 5.71 0.971 102.9 4.32 0.993 96.1
The Wöhler curve obtained with the Nff criterion is plotted in Figure 14 for all the tested mixes.This figure shows that parameter β is rather different for considered materials and this shouldalso be studied for fatigue performance. M1 material seems to have the lower slope parameter β.Adding RAP increases this parameter (as shown with material M2 and M6) and adding shinglesdoes the same (as shown with material M4 and M5), which induces a more important influenceof amplitude strain on the fatigue performance for such materials.
5. ConclusionsThe objective of the research work presented in this paper was to study the LVE and the fatiguebehaviour of asphalt mixtures containing two types of recycled materials RAP and asphalt shingle.Five mixtures with different recycled material contents were studied. The following conclusionscan be drawn from the obtained results:
• The TTSP was verified for the tested asphalt mixtures in the LVE domain.• Master curves were built for the complex modulus and complex Poisson’s ratio. The shift
factors used were close for all the tested mixes, showing that a unique set of shift factorscan describe the 3D behaviour of the material with respect to the TTSP.
• The 2S2P1D model reveals good fitting on the entire range of temperatures and frequenciesfor the complex modulus and complex Poisson’s ratio.
• The addition of RAP (40%) and asphalt shingle (up to 5%) in asphalt mixes increasesstiffness.
• Six criteria were applied to determine the fatigue life of the tested materials. Except forNf30% criterion, the five other used criteria gave similar results for all the tested materials.
• The fatigue performances of tested mixes showed that the addition of RAP (40%) andasphalt shingle (up to 5%) improves the ε6 values.
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