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Sâannibè Ciryle Somé, Vincent Gaudefroy, Alexandre Pavoine
To cite this version:
Sâannibè Ciryle Somé, Vincent Gaudefroy, Alexandre Pavoine. Viscoelastic behavior of fluxed asphalt binders and mixes. 22ème Congrès Français de Mécanique, Aug 2015, Lyon, France. �hal-01986582�
Viscoelastic behavior of fluxed asphalt binders and mixes
Saannibe Ciryle SOMEa, Vincent GAUDEFROYb, Alexandre PAVOINEa,
a. CEREMA Laboratoire d’ ´Eco-Mat´eriaux 120 route de Paris Sourdun 77487 Provins
b. L’UNAM Universit´e IFSTTAR, Route de Bouaye, BP 4129, 44344 Bouguenais
R´
esum´
e :
Cet article traite de l’influence des fluxants v´eg´etaux sur les propri´et´es rh´eologiques des bitumes et des b´etons bitumineux (granulats + bitume). Deux fluxants organiques compos´es d’esther methylique d’acide gras `a base de tournesol (Oleoflux) et de r´esines flux´ees d’esther mono-alkhyle (Greenseal) ont ´
et´e utilis´es. Les r´esultats obtenus montrent une forte influence de la teneur en fluxant (0 % 0.5 % et 5 %) sur les propri´et´es visco´elastiques. Le comportement visco´elastique des bitumes et celui des b´etons bitumineux a ´et´e mod´elis´e `a l’aide de mod`eles existants. Les mod`eles montrent qu’une augmentation de la teneur en fluxant conduit `a une r´eduction consid´erable du temps de relaxation des bitumes et par cons´equent celui des b´etons bitumineux.
Abstract :
The paper deals the effects of vegetable fluxes on the rheological properties of bitumen and asphalt concretes. Two organic fluxes which consist of a methyl ester of fatty acid of sunflower (Oleoflux) and a resin fluxed with esters moalkyl (Greenseal) have been used. The results show that the additives’ content (0 % 0.5 % and 5 %) infuences highly the viscoelastic properties. The viscoelastic behavior of the bitumen and the asphalt concretes has been modeled with existing models. From the models, it has been found that the increase of the fluxes contents reduces the relaxation time of the bitumen and the asphalt concrete accordingly.
Mots clefs :
Bitumen, asphalt concrete, viscoelasticity, complex modulus, phase angle1
Introduction
Asphalt concrete consist of aggregates (≈ 95% by mass) and bitumen (≈ 5%). The aggregates consist of several granular fractions which diameters vary generally from ∼ 0 to 14 mm. Commonly, the asphalt concretes are obtained by heating, mixing and compacting bitumen and aggregates at
tem-pertures above 150◦C. These processes are commonly called ”hot mix asphalt”. At these temperaures
the viscosity of the paving grade bitumen is below 0.2 Pa.s which is suitable to get a good coating ag-gregates. However, for energy consumption reduction and greenhouse gas emission saving reasons, the
manufacturing temperatures have been reduced to 110◦C or below called warm mix asphalt (WMA).
This causes a poor coating of the aggregates or leads to compaction difficulties due to the high viscosity of the binder. The consequence is the loss of performances of the final asphalt concrete. To avoid this, most these WMA processes use additives to reduce the binder viscosity or to improve adhesion with aggregates to achieve performances which comply with the standars. Today, increasingly analyses have been undertaken to highlight the effect of the fluxes on the bitumen behavior. However, the varieties of additives required specific relevant study on each additive.
Because of the bitumen binder, the asphalt concrete behaves as a viscoelastic materials even if the pile of aggregates which constitute about 95% of its mass has non-linear elastic behavior. The proposed study deals with the influence of two additives on the rheological behavior of asphalt binders and the final asphalt concrete and the modeling of their linear viscoelastic properties. The paper is organized as follows : a theoretical background and the existing models are reminded first before experimental principle description. The final part of the paper is devoted to the results analysis.
2
Theoretical background
The study of the rheological properties of bituminous materials requires dynamic (shear or tensile) test at imposed deformation or imposed stress. Due to the viscoelasticity of these materials, the complex modulus E∗ can be written as follows :
E∗(iω) = E0(ω) + iE”(ω) = |E∗|eiδ(ω) (1)
where E0 and E” are respectively the storage and the loss modulus. δ is the phase angle between the
imposed strain and the stress response (tan δ = E”/E0). ω is the pulsation (= 2πf , where f is the
frequency). E0 and E” as well as |E∗| and δ are respectively inter-dependent i.e. the knowledge of one of these parameters allows the determination of the second one. The inter-dependency can be seen
through the Kramers-Kronig relations between E0 and E” and between |E∗| and δ :
E0(ω) = E∗(∞) ± 2ω 2 π Z ∞ 0 u.E”(u) − ω.E”(ω) u2− ω2 du; E”(ω) = ∓ 2ω π Z ∞ 0 E0(u) − E0(ω) u2− ω2 du (2) log |E∗(ω)| = log |E∗(∞)|−2 π Z ∞ 0 u.δ(u) − ω.δ(ω) u2− ω2 du; δ(ω) = 2ω π Z ∞ 0
log |E∗(u)| − log |E∗(ω)|
u2− ω2 du (3)
The creep behavior of bituminous materials fits parabolic function f (t) = A.tα [1]. In this condition, it can proved that δ(ω) relation in Eq. 3 becomes :
δ(ω) = π
2
d log(|E∗(ω)|)
dlog(ω) (4)
For thermo-rheologically simple viscoelastic matrials, time and temperature have equivalent effect on the material behavior : this is called Time-Temperature Superposition Principle (TTSP). For materials
that obey to the TTSP, the complex modulus isothermals in the Black diagram (δ = g(|E∗|)) and in
the Cole-Cole plan (E” = g(E0)) are continuous curves (g is an arbitrary function). Assuming that
the TTSP is valid, the master curves of the complex modulus (|E∗| = g(ω)) and the phase angle
(δ = g(ω)) can be built by shifting the isothermal curves. The shift factor aT which is needed to get the same modulus for different loading conditions is defined as follows :
E∗(Ti, ωi) = E∗(Tj, fj = a(Ti,Tj).ωi); i, j = 1, 2, ..., N (5)
It can be proved that for materials that obey to the TTSP, the shift factor aT can be estimated at a reference temperature Tref by [2] :
log(a(Ti,Tref)) = π 2 j=ref X j=i log(|E∗(Tj, ω)|) − log(|E∗(Tj+1, ω)| δ(Tj,Tj+1) avr (ω) ; i = 1, 2, ..., N (6) where δ(Tj,Tj+1)
avr is the average phase angle estimated between two closing temperatures Tj and Tj+1.
In pratical cases the classical William-Landel-Ferry (WLF) or Arrhenius laws are generaly used to determine the shift factor aT. In this study, one considers the WLF law given by :
log(a(Ti,Tref)) = −C1.(T − Tref) C2+ T − Tref
(7) where C1 and C2 are two constants independent to the choice of Tref. Then, the construction of the master curve implies the determination of these two constants.
3
Modeling of the linear viscoelastic properties of fluxed bituminous
binders and asphalt concretes
The linear viscoelastic behavior of asphalt concretes has been historically modeled by Huet [1]. His model consists of a serial association of a Spring (with stiffness E∞) and two parabolic creep elements (Pkand Ph) which have respectively the creep function fk(t) = Atkand fh(t) = Bth with the condition 0 < k < h < 1 (see Fig 1(a)). A and B are constants and t the time. It comes that the creep compliance of this model is : J∗(iωτ ) = A∞ 1 + (iωτ1)−k+ (iωτ2)−h (8)
i is the complex number defined by i2 = −1, A∞ is a constant which corresponds to the compliance
when → ∞, τi is characteristic time of each creep element i. As there is a proportionality relation
between the τi (see ref [1]) i.e. τ1 = µτ2 = µτ and considering that µ−k = δ and considering the
relation between the compliance and the complex modulus : J∗(iω) · E∗(iω) = 1, it comes that :
E∗(iωτ ) = E∞
1 + δ(iωτ )−k+ (iωτ )−h (9)
This model describes well the linear viscoelastic behavior of asphalt concrete for a wide range of temperatures and frequencies except high temperatures or low frequency. For this reason a weak elastic spring E0 has been added in parallel to this model and the glassy modulus E∞ ajusted accordingly to E∞−E0(see Fig 1(b))[5][6]. The obtained model described successfully the linear viscoelastic behavior of the conventional asphalt concretes. However, it fails to model the bituminous binders behavior due to the higher viscous effect of the binder compared to the asphalt concrete (which containts aggregates ≈ 95%). Then, the 2S2P1D model (2 Springs, 2 Parabolic elements and 1 daspot), represented on Fig fig. 1(c), which consists of an addition of a Newtonian viscosity parameter η represented by a dashpot, has been proposed for binders and mixes [3]. The complex modulus of this model is written as follows :
E∗(iωτ ) = E0+
E∞− E0
1 + δ(iωτ )−k+ (iωτ )−h+ (iωτ β)−1 (10)
E∞ : the glassy modulus when ω → ∞ ; E0 the static modulus when ω → 0 ; η : Newtonian viscosity
of the dashpot, η = (E∞− E0)βτ ; τ : characteristic times, whose value varies only with temperature : τ (T ) = a(T, Tref).τref; aT : is the shift factor at the temperature T.
Only 7 parameters (τ, k, h, E0, E∞, β, δ) are required to model the behavior of the bitumions binder and only 6 of them (except β) are required to model the behavior of the asphalt concrete. This few number of parameters gives more advantages than generalized models such as ganeralized Maxwell model which requires higher number of parameters. These parameters can be obtained by minimization of the objective function J .
J (Xp) =
Z ∞
0
h
E1exp(ω) − E1mod(ω)i2+hE2exp(ω) − Emod2 (ω)i2
dω (11)
Where Xp =t [β, τ, δ, k, h, E0, E∞] is the vector of the parameters to be determined. However, we have to precised for bituminous binders that the 2S2P1D model does not always models well modified bituminous binders behaviors due to the non validity of the TTSP.
4
Experimental setup
— The asphalt concrete complex modulus was carried out on a trapezoidal cantilever beam in
accordance with the standard EN 12697-26. A sinusoidal strain load (50.10−6) is applied to
measure the complex modulus varying the temperature from -10◦C to 40◦C and the frequency
(a) Huet model (b) Huet-Sayegh-Soleimani model (c) 2S2P1D model
Figure 1 – Asphalt concrete and bituminous binder models
— The fluxed bitumen viscoelastic behavior has been investigated with the METRAVIB
appara-tus. Two loading modes have been used : anular shearing for temperatures between 20◦C and
80◦C and tension-compression test for low temperatures between -20◦C and +20◦C. The shear modulus G* given by the annular shearing experiment is converted into tension-compression modulus E* using a poisson ratio equal to 0.5. 1 Hz to 125 Hz frequencies range was considered for an applied strain of (50.10−6). The schematic view of the device is given on Fig. 2(b).
(a) For the asphalt concrete (b) For the bituminous binder
Figure 2 – Experimental test principle
5
Results
5.1
Complex modulus of the binders
The validity of the TTSP has been first verified by representing the experimental results on the Black space and on the Cole-Cole plan. Fig 3(a) and 3(b) show, for each bitumen, a good superposition of the experimental data, which prove the applicability of the TTSP contrary to some of polymers modified bitumen. Then, master curves of the complex modulus and the phase angle can build thank to the shift factor calculated from Eq. 7.
The results represented on Fig 3(d) show a high decrease of the complex modulus when additive content reaches 5%. A high increase of the phase angle δ is accordingly observed. The influence of the Oleoflux additive (noted EM ) is more pronounced than Greenseal additive (noted AG). Furthermore, these results are have been modeled by the 2S2P1D model. The parameters of the model have been evaluated based on Eq. 11 implemented in the viscoanalyse software. The solid curves on the 3(d) correspond to the model and the dots to the measurements. Relatively good agreement is found between the experimental results and the model at high equivalent frequencies. The model parameters are given in the Table 1.
- The constants δ, k and h are slightly sensitive to the additives’ effects whatever theirs percentages. - The relaxation time τ highly decreases for high additives (5 %). τ is linked to the temperature, and
has been computed at a reference temperature Ts=15◦C. It is called primary relaxation time. These
results show that the soft mixes (mixes with 5 % additives) have a faster stress relaxation. For binders
fluxed at 5%, the relaxation time are 7.10−6 s for additive EM and 9.10−9 s for additive AG. This
means better faster stress relaxation for bitumen fluxed with additive AG.
- Constant E∞, which represents the glassy modulus when ω → ∞, is slightly dependent to the
additive content. It seems that the high increase of the additives percentage, increases the complex modulus of the binder.
Then, among the 7 parameters needed to calibrate the model, 5 of them are independent to the additives and theirs contents.
150 200 250 300 E " (M P a) B1 B2(EM 0.5%) 0 50 100 0 500 1000 1500 2000 E " (M P a) E' (MPa) B2(EM 0.5%) B2(EM 5%) B3(AG 0.5%) B3(AG 5%)
(a) In Cole-Cole plan
50 60 70 80 90 100 δ (° ) B1 B2(EM 0.5%) 0 10 20 30 40 0.001 0.1 10 1000 δ |E*| (MPa) B2(EM 0.5%) B2(EM 5%) B3(AG 0.5%) B3(AG 5%) (b) In Black space 1.E+00 1.E+02 1.E+04 C o m p le x m o d u lu s (M P a) B1 B2(EM 0.5%) 1.E-04 1.E-02 1.E+00
1.E-05 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05
C o m p le x m o d u lu s (M P a) Equivalent frequency (Hz) B2(EM 0.5%) B2(EM 5%) B3(AG 0.5%) B3(AG 5%) (c) Master curves of |E∗| at 15◦ C 60 80 100 P h as e an g le ( °) B1 B2(EM 0.5%) B2(EM 5%) B3(AG 0.5%) B3(AG 5%) 0 20 40
1.E-05 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07
P h as e an g le ( Equivalent frequency (Hz) B3(AG 5%) (d) Master curves of δ at 15◦C
Figure 3 – Binder complex modulus |E∗| and phase angle δ representations
5.2
Complex modulus of the asphalt concretes
As for the previous case, the mixes TTSP validity is first verified through the Black and Cole-Cole representations (Figs. 4(a) and 4(b)). The good alignment of the data means the applicability of the TTSP and then allows the building of the master curves. The master curves of E∗and δ are represented on Figs 4(c) and 4(d) respectively.
There is a slight difference between the mixes with 0.5 % of additive and the control WMA without additive. However, for additive content of 5 %, the reduction of the stiffness is more noticeable. At low frequencies, results are scattered and the model does not match very well the phase angle (see Fig. 4(d)). However, one can note the increase of the phase angles with the fluxes content on the asphalt concretes. The model parameters are given in the Table 1.
Mixes E0 E∞ k h δ τ β (MPa) ×103 (MPa) Mixes E1 3.08 34 0.20 0.63 1.9 0.245 E2(0.5%EM ) 19.4 34 0.21 0.66 2.0 0.121 E2(5%EM ) 27.5 39 0.19 0.65 1.9 0.003 E3(0.5%AG) 30.3 34 0.21 0.64 1.9 0.138 E3(5%AG) 30.9 36 0.23 0.67 2.1 0.016 Binders B1 2.10−3 2.28 0.23 0.59 3.02 5.10−4 216 B2(0.5%EM ) 1.10−3 2.14 0.26 0.63 4.10 8.10−4 108 B2(5%EM ) 0.10−3 2.00 0.17 0.53 1.41 7.10−6 398 B3(0.5%AG) 3.10−3 2.22 0.25 0.61 3.81 7.10−4 100 B3(5%AG) 0.1.10−3 2.61 0.24 0.63 4.02 9.10−9 201
Table 1 – Binders and Mixes model parameters at Tref = 15◦C
- The relaxation time τ highly decreases for higher additives content (5 %). The decrease of τ for the mixes is consistent with the decrease of the bitumen relaxation times.
- Constant E∞, increase slightly with the additive content.
Then, among the 6 parameters needed to calibrate the model, 4 of them are independent to the additive and its content.
6
Conclusion
This study showed that the addition of additives (EM and AG) reduces the stiffness of the bitumen and the final manufactured asphalt concrete. It was found that the TTSP applies for the studied binders and mixes. The models used describe relatively well the complex modulus and the phase angles of the binders and mixes. The relaxation time τ and the Newtonian viscosity parameter β are highly modified when increasing additives content.
R´
ef´
erences
[1] Huet, C. 1963 ´Etude par une m´ethode d’imp´edance du comportement visco´elastiques des mat´eriaux hydrocarbon´es. Th`ese de doctorat Universit´e de Paris.
[2] Chailleux, E. Ramond, G. Such, C. de la Roche, C. 2006 A mathematical-based master-curve construction method applied to complex modulus of bituminous materials. Int J. of Road Materials and Pavement Design Vol 7 Special Issue 75-92.
[3] Olard, F. Di Benedetto, H. 2003 General 2S2P1D model and relation between the linear viscoelastic behaviors of bituminous binders and mixes. Int J. of Road Materials and Pavement Design Vol 4 N◦ 2 185-224.
[4] Ferry, J.D. 1960 Viscoelastic properties of polymers. John Wiley and Sons.
[5] Sayegh, G. 1965 Contribution `a l’´etude des propr´et´es visco´elastiques des bitumes purs et b´etons bitumineux. Th`ese de doctorat Universit´e de Paris.
[6] Soleimani, P. 1965 ´Etude sur le comportement visco´elastiques des mat´eriaux bitumineux par la m´ethode de fluage. Th`ese de doctorat Universit´e de Paris.
2000 3000 4000 5000 E " (M P a) E1 E2(EM 0.5%) 0 1000 2000 0 10000 20000 30000 40000 E " (M P a) E'(MPa) E2(EM 5%) E3(AG 0.5%) E3(AG 5%)
(a) Mixes Cole-Cole space curves
40 50 60 70 (° ) E1 10 20 30
1.E+02 1.E+03 1.E+04 1.E+05
δ ( |E*| (MPa) E2(EM 0.5%) E2(EM 5%) E3(AG 0.5%) E3(AG 5%)
(b) Mixes Black space curves
1000 10000 100000 | E * | (M P a) E1E2 (0.5%EM) 10 100
1.E-04 1.E-02 1.E+00 1.E+02 1.E+04 1.E+06
| E * | (M P a) aT*frequency (Hz) E2 (5%EM) E3 (0.5%AG) E3 (5%AG)
(c) Mixes complex modulus master curves at 15◦C
30 40 50 60 70 °) E1 E2(EM 0.5%) E3(AG 0.5%) E2(EM 5%) E3(AG 5%) 0 10 20 30
1.E-04 1.E-02 1.E+00 1.E+02 1.E+04 1.E+06
δ
(°
aT*frequency (Hz)
E3(AG 5%)
(d) Mixes phase angle master curves at 15◦C
