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Effect of styrene-butadiene-styrene (SBS) on the rheological behavior of asphalt binders
Construction and Building Materials 231 (2020) 117076
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Effect of styrene-butadiene-styrene (SBS) on the rheological behavior of asphalt binders Liyan Shan ⇑, Xiaofei Qi, Xianglei Duan, Shuang Liu, Jian Chen School of Transportation Science and Engineering, Harbin Institute of Technology, Harbin 150090, Heilongjiang, China
h i g h l i g h t s Use of FT-rheology and strain decomposition to study the nonlinearity of binders. Nonlinearity of binders increases with increase in stress and decrease in frequency. Nonlinearity of SBS modified asphalt binder is more obvious than neat asphalt binder. Nonlinearity of SBS modified asphalt binder increases with increase in SBS content. All binders exhibit stress softening and stress thinning under studied conditions.
a r t i c l e
i n f o
Article history: Received 19 May 2019 Received in revised form 19 September 2019 Accepted 24 September 2019
Keywords: Asphalt binder SBS polymer Rheological behavior Linear Nonlinear LAOS stress
a b s t r a c t The binders in pavement could support the loading in either linear or nonlinear regime. The linear viscoelasticity of asphalt binders was well established, however, a few of researches focused on the nonlinear viscoelasticity of asphalt binders. Here, this paper deals with the effects that SBS exerts on the linear and nonlinear rheological behavior of asphalt binders. The nonlinear rheological behavior of one kind of neat asphalt binder and the corresponding SBS modified asphalt binders under large amplitude oscillatory shear stress (LAOS stress) is analyzed by Fourier Transform (FT)-rheology and strain decomposition methods. The linear viscoelastic measurements show that the elastic proportion and the complexity of rheological behavior of the asphalt binder increases with increase in SBS content. The nonlinear viscoelastic measurements reveal that the relative nonlinearity of asphalt binders increases with increase in stress and decrease in frequency; the relationship between I3/I1 and stress amplitude can obey the sigmoidal function; the intrinsic nonlinearity Q0 decreases with increase in frequency and increases with the increase of SBS content. Both the FT analysis and decomposition results show that the nonlinearity of SBS modified asphalt binder is more obvious than neat asphalt binder and increases with the increase of SBS content. SBS could increase the nonlinearity and the elastic proportion of asphalt binder and decrease its fluidity. All the studied binders exhibit stress softening and stress thinning under all the studied test conditions. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction As an important component of asphalt pavement, asphalt binder has always been the research focus in road engineering regime. Asphalt binder is a complex high molecular weight hydrocarbon, which can be divided into four main compositions, asphaltene, resins, saturates and aromatic. It behaves viscoelastic behavior under specific conditions. However, the neat asphalt binder cannot perform satisfactorily with increasing traffic level, heavier loading, and harsh climate. Thus, modified asphalt binders attract many ⇑ Corresponding author. E-mail address: [email protected] (L. Shan). https://doi.org/10.1016/j.conbuildmat.2019.117076 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
researchers’ attention recently. Among the available asphalt modifiers, the polymers have been used widely in the past few years. It can increase the elasticity of the binders and reduce the stress and temperature susceptibility, which contributes to improve the rutting resistance and anti-fatigue of asphalt binders [1,2]. Styrene-butadiene-styrene (SBS) is one of the most frequently used polymer additives as it forms high interaction with maltene components [3]. SBS is swollen and dispersed throughout the bulk and behaves as cross linker when blended with neat asphalt binder [4]. Additionally, the concentrationon of SBS is one of main factors on this swollen process, which significantly influences the properties of neat asphalt binder [5]. Considering that the rheological properties of asphalt binders can significantly
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affect the performance of asphalt mixtures [6], it is very important to understand the effect of SBS concentrationon on rheological behavior of asphalt binders. The linear rheological characterization of SBS modified asphalt binders have been analyzed thoroughly by researchers from the angle of dynamic modulus, phase angle, and etc [7–12]. Airey et al. investigated the rheological behavior of SBS polymer modified bitumens at three polymer contents by the modulus master curve, phase angle master curve, Han plots or isochronal plots [7,8]. Xia et al. studied morphology evolution and viscoelasticity change of SBS polymer modified binders at different weight fraction of SBS [9]. Rossi et al. evaluated the effect of SBS polymer modifiers on the bitumen phase transition by the temperature sweep test from 30 °C to 150 °C, and the curves of modulus/tand versus temperature could show both the a- and b-relaxation [10]. And different models were used to describe the above rheological behaviors. Stastna et al. used the generalization of the Maxwell model to describe the modulus and phase angle of different kinds of modified (SBS, PE and EVA) asphalt binders and the discrete spectrum was shown to be related to the interface interaction of the neat asphalt and the polymers [11]. Lesueur et al. used the Palierne model to estimate the rheological properties of SBS modified asphalt and the fitting results showed that the Palierne model could describe the modulus and phase angle data fairly well [12]. However, various failure mechanisms of the pavements occur at different strain or stress levels, asphalt binders can undergo loading out of linear regime during ‘‘in life” service. And the linear rheological properties of binders have limited capability for correlating the structure with mechanical properties, therefore, the nonlinear rheological properties of SBS modified asphalt binder should not be ignored. The steady shear viscosity is probably the simplest traditional nonlinear functions that can reveal the anomalous behavior of blends of asphalts with polymers. Jasso et al. also used the viscosity to study the rheological properties of SBS modified asphalt besides the above curves [13]. Vlachovicova et al. showed that the viscosity function was better than the master curves to show difference between neat and polymer-modified asphalts [14]. Polacco et al. found the two step shear thinning regime in the polymer viscosity-shear rate curves as others did, and showed that the phenomenological equation derived from the Wagner model could well fit the test data [15]. Polacco et al. summarized researches about the nonlinear rheological behavior of polymer modified asphalt binders using the shear viscosity [16]. One disadvantage of this test method is that when processing at high rates of deformation for short time, the material does not reach steady state. And steady simple shear rate experiments also have inherent limitations: little information is provided about microstructure since the measurement is made at steady state [17]. LAOS (Large amplitude oscillatory shear) is another method to investigate and quantify nonlinear viscoelastic properties of complex fluids or soft matter. For the LAOS stress tests, when the stress increases beyond the linear regime, the strain output is not purely sinusoidal and the behavior can no longer be fully described in terms of complex modulus (G*) due to the presence of higher harmonic contributions. It does not involve any sudden imposed jumps in speed or position, and consequently it is a relatively easy flow to generate and control [18]. Nevertheless, there is a few of literatures related to nonlinear rheological behavior of asphalt binder including SBS modified asphalt binder under LAOS. The Lissajous plots have been used to study the nonlinear behavior of unmodified, modified asphalt binders [19,20]. Others compared the higher harmonic moduli of neat, SBS modified and EVA modified asphalt binders [21,22]. González et al. tested the rheological characterization of neat bitumen and EVA, HDPE polymer modified bitumen with the LAOS-FTR (Fourier transform rheology) method, and showed that this method could quantitatively differentiate
between the tested binders [23]. The author proposed protocol to obtain the nonlinear rheological properties of asphalt binders under LAOS stress and compared the nonlinear rheological behaviors of neat asphalt and SBS/crumb rubber modified asphalt binder using FT-rheology and strain decomposition methods [24]. While the above works showed that the linear rheological behavior of SBS modified asphalt binder was well studied, but a few of researches focused on its nonlinear rheological behavior. The references also proved that the nonlinear rheological behavior is important to investigate the effect of additives on asphalt binders, study the modified mechanism and differentiate the binders. However, there is no too much attention to the responses of this material under both small and large stresses. Therefore, the rheological behaviors of SBS modified asphalt binder should be understood in depth for a wide range of stress levels to characterize the linear and nonlinear regimes of the asphalt material. The main objective of this paper is to study the effect of SBS concentrations on the linear and nonlinear rheological behavior of asphalt binders. Three SBS contents were blend with neat asphalt binder. The stress sweep test was performed to determine the linear and nonlinear regime and select the stress levels for frequency sweep test and LAOS test. The frequency sweep test was to study the linear rheological behavior by the modulus master curve and phase angle master curve. The LAOS stress test was used to study the nonlinear rheological behavior of the SBS modified asphalt binders by FT-rheology and strain decomposition methods. This study can better understand the responses of this material under both small and large stresses and the effect of SBS contents on its rheological behavior. 2. Material and methods 2.1. Materials A neat asphalt binder with penetration grade of 73.6 1/10-mm and softening point of 48.6 °C (ring and ball) was used for polymer modification. The asphalt binder modified with 3 wt% SBS, 5 wt% SBS and 7 wt% SBS were manufactured to study the effect of SBS content level on the properties of asphalt binders. Blends of asphalt and SBS were prepared by mechanical stirring using the highspeed mixer. The neat asphalt binder was firstly heated at 180 ± 5 °C until it flowed fully, then slowly add (5 g/min) the calculated amount of SBS (3 wt%, 5 wt% or 7 wt%) to the melted asphalt under low shear rate of 500 r/min. Secondly, increase the speed to 4000 r/min and shear for 120 min. Furthermore, the modified binder was kept in the oven at 180 ± 5 °C for 2 h so that the blends became essentially homogenous. The basic information of the SBS modified asphalt binders are summarized in Table 1. It can be seen that the penetration decreases and softening point increases with the SBS content increasing. This can be credited to the continuous three-dimensional network which polymer additives forms in the neat asphalt binder during blending process. 2.2. Test methods Rheological properties test was performed using a TA Instruments AR-G2 Rheometer. Three types of test were conducted: Table 1 The basic information of the studied binders. Binders
Penetration (1/10-mm at 25 °C)
Softening point (°C)
Neat asphalt 3% SBS modified asphalt 5% SBS modified asphalt 7% SBS modified asphalt
73.6 50.2 45.3 40.8
48.6 61.8 78.5 81.2
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The stress sweep test also shows that the loss modulus is greater than the storage modulus, which illustrates that the asphalt binder behaves as a viscous suspension. This result is consistent with the results we have obtained in the previous study. Besides, it can be found that the modulus increases with increase in SBS content, which means that the binder becomes stiffer with increase in SBS content. This is consistent with the penetration and softening point results.
stress sweep, frequency sweep and LAOS stress test. These tests were conducted with an 8-mm-diameter parallel plate geometry and 2-mm gap setting when the temperature was lower than 30 °C, otherwise, a 25-mm-diameter parallel plate geometry and 1-mm gap setting were used. At least, two replicates were performed for each test condition; if the deviation was greater than 10 percent, a third replicate was required. In the linear regime, modulus and phase angle master curves were used to study the linear rheological behavior of SBS modified asphalt binders. In the nonlinear regime, about ten different stress levels were selected as the control stress to do the LAOS stress test. Then, FT-rheology and strain decomposition methods were used to study the nonlinear rheological behavior of SBS modified asphalt binders.
2.2.2. Frequency sweep test Frequency sweep tests were conducted for frequencies from 0.01 Hz to 60 Hz and for temperatures of 20 °C, 30 °C, 40 °C, 50 °C, and 60 °C. This combination of temperatures and frequencies ensure sufficient overlap in the material responses so that the data could be horizontally shifted to obtain master curves of the key properties. The horizontal shift factors for all samples were fitted with the WLF functions. The CAM model can be used to describe the dynamic modulus and phase angle master curves over a wide range of reduced frequencies at a reference temperature. The stress levels for the frequency tests were chosen to be in the linear range. 2.2.3. LAOS stress test The LAOS stress test is used to study the nonlinear rheological behavior of the asphalt binders. The stresses used for the LAOS stress test were chosen in the rectangle regime as shown in Fig. 1. The sample was sheared under the selected stress level until more than ten strain cycles in the time-stable regime were obtained. If the stress level is very large and it is difficult to obtain ten stable cycles, the test was stopped after the stable regime
1E+6
1E+6
1E+5
1E+5
G', G"(Pa)
G', G"(Pa)
2.2.1. Stress sweep test The stress sweep test was performed to determine the linear and nonlinear regime and select the stress levels for frequency sweep test and LAOS test. All the tests were carried out at 30 °C. In this test, the stress was started from a very small value, and increased incrementally until the specimen was broken. Meanwhile, the stress values were collected by the rheometer at a constant frequency. According to the Strategic Highway Research Program (SHRP), if the decrease in the dynamic modulus value is less than 10% of the initial modulus value, the binder is believed to be in the linear region [25]. Otherwise, the regime where the decrease modulus is more than 10% of the initial dynamic modulus is believed to be the nonlinear regime. Based on that, the stress levels used in the following test were chosen as show in Fig. 1.
1E+4
1E+3 1E+2
1rad/s,G' 5rad/s,G' 10rad/s,G'
1rad/s,G'' 5rad/s,G'' 10rad/s,G''
1E+3 1E+4 1E+5 Stress (Pa)
1E+3 1E+2
1E+6
(a) Neat asphalt binder 1E+6
1E+6
1E+5
1E+5
1E+4
1E+3 1E+2
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1rad/s,G'' 5rad/s,G'' 10rad/s,G''
1E+4 1E+5 Stress (Pa)
1rad/s,G' 5rad/s,G' 10rad/s,G'
1rad/s,G'' 5rad/s,G'' 10rad/s,G''
1E+3 1E+4 1E+5 Stress (Pa)
1E+6
(b) 3%SBS modified asphalt binder
G', G"(Pa)
G', G"(Pa)
1E+4
1E+6
(c) 5%SBS modified asphalt binder
1E+4
1E+3 1E+2
1rad/s,G' 5rad/s,G' 10rad/s,G' 1E+3
1rad/s,G'' 5rad/s,G'' 10rad/s,G''
1E+4 1E+5 Stress (Pa)
1E+6
(d) 7%SBS modified asphalt binder
Fig. 1. Stress sweep test results of the studied binders.
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100 80
1E+3 neat,G' neat,G'' 3%SBS modified,G' 3%SBS modified,G'' 5%SBS modified,G' 5%SBS modified,G'' 7%SBS modified,G' 7%SBS modified,G''
1E+0 1E-3 1E-6 1E-5
1E-3 1E-1 1E+1 1E+3 Reduced frequency (rad/s)
(a) Modulus master curve
60 δ( )
G',G"(Pa)
1E+6
40 neat 3%SBS modified 5%SBS modified 7%SBS modified
20 0 1E-5
1E-3 1E-1 1E+1 1E+3 Reduced frequenvy (rad/s)
(b) Phase angle master curve
Fig. 2. Master curves of the studied binders.
obtained. Then, the cycles used for later analysis were selected (three to eight cycles based on the stress level) and the curves were shifted to zero average strain. Details of used methods to select the data and shift the curve can be found in reference [24].
3.1. Linear rheological behavior of SBS modified asphalt binders The master curve is one of the most popular methods to study the linear rheological behavior of asphalt binders. The master curves of the four kinds of asphalt binders are shown in Fig. 2. As shown in Fig. 2(a), the modulus increases with increase in frequency, and the loss modulus is larger than the storage modulus. The difference between the storage modulus and the loss modulus decreases with increase in frequency. Comparing the modulus curves of neat binder with that of SBS modified binders, it can be found that the difference between storage modulus and loss modulus decreases with increase in SBS content. It means that the elastic proportion of the binders increases with adding SBS. This is the reason that the high temperature performance of SBS modified binder is better than the neat asphalt binder. Fig. 2(b) shows the phase angle master curve of the studied binders. It shows that the phase angle decreases with increase in SBS content, which also means that the elastic proportion of the asphalt binder increases. Besides, it also shows that the complexity of rheological behavior increases with increase in SBS content. Because the phase angle decreases with frequency before adding SBS, and it decreases first then increases a little bit and finally decreases again with frequency after adding SBS. 3.2. Nonlinear rheological behavior of SBS modified asphalt binders 3.2.1. FT-rheology As described in references [24], the FT-rheology method is to express the nonlinear shear strain using a Fourier series expansion with either strain amplitude or stress amplitude with odd higher terms as shown in Eqs. (1) and (2) [26], and calculate the relative intensity of higher-harmonics [IðnxÞ=IðxÞ ¼ In =I1 , where x is the excitation frequency] as shown in Eq. (3).
cðtÞ ¼
cn cos ðnxt dn Þ
ð1Þ
n¼1;odd
cðtÞ ¼
X 0 J n ðx; r0 Þcos nxt þ J 00n ðx; r0 Þsin nxt n odd
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 ðc5 cos d5 Þ2 þ ðc5 sin d5 Þ c I5 =I1 ¼ 5 ¼ 2 2 c1 ðc1 cos d1 Þ þ ðc1 sin d1 Þ
3. Results and discussions
X
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 ðc3 cos d3 Þ2 þ ðc3 sin d3 Þ c I3 =I1 ¼ 3 ¼ 2 c1 ðc1 cos d1 Þ2 þ ðc1 sin d1 Þ
ð2Þ
ð3Þ
Any measured response from the tested system at frequencies other than x is associated with nonlinearity in the system response. Therefore, the relative intensity In/I1 is usually used to evaluate the degree of non-linearity of the material’s response. The strain is no longer sinusoidal if the stress amplitude is out of the linear regime. So the Fourier series expansion will have higher harmonics In/I1. As shown in Fig. 3, both I3/I1 and I5/I1 can be measured for 3%SBS modified asphalt, and besides that I7/I1 can be measured for 5%SBS and 7%SBS modified asphalt binders. Because, only I3/I1can be measured for neat asphalt binder, the results are not shown in Fig. 3. It also shows that I3/I1 increases with increase in stress and decrease in frequency, and the changing trend of I5/I1 and I7/I1 versus the stress level is similar to that of I3/ I1. However, the I5/I1 and I7/I1 increase with decrease in frequency at lower stress levels, the changing trend of I5/I1 and I7/I1 versus frequency is unregular at higher stress level, which is inconsistent with that of I3/I1. These phenomenon will be further verified by studying more styles of asphalt binders in the futher research. Besides, I7/I1 only occurs in 5%SBS and 7%SBS modified asphalt binders with frequencies of 1 rad/s and 5 rad/s and higher stress, which shows that with the increase of SBS content and stress amplitude as well as the decrease of frequency, the degree of nonlinearity becomes stronger. As I3/I1 is the most commonly used index to study the nonlinear rheological behavior of materials, the curves of I3/I1 versus stress amplitude for the studied binders were analyzed further and shown in Fig. 4. As shown in Fig. 4, I3/I1 increases with the increase of stress amplitude and the decrease of frequency, which is consistent with the previous results [26]. Eq. (4) was used to fit the I3/I1 data and the results are also shown in Fig. 4.
I3 =I1 ðr0 Þ ¼ A 1
1 1 þ BrC0
ð4Þ
where the parameter A reflects the maximum intensity of I3/I1 at high stress amplitude, B is approximately the point of inflection, and the parameter C is the scaling exponent. It can be seen from Fig. 4 that the equation can well describe the relationship between I3/I1 and stress amplitude.
5
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1E-1
1E-2
1E-2
1E-3
1E-3 In/I1
In/I1
L. Shan et al. / Construction and Building Materials 231 (2020) 117076
1E-4 1E-5 1E-6
1rad/s- I3/I1
1rad/s- I5/I1
5rad/s- I3/I1
5rad/s- I5/I1
1E-5 1E-6
10rad/s- I3/I1 10rad/s- I5/I1
1E-7 20
40
80 Stress(kPa)
1E-4 1rad/s- I3/I1
1rad/s- I5/I1
1rad/s- I7/I1
5rad/s- I3/I1
5rad/s- I5/I1
5rad/s-I7/I1
10rad/s-I3/I1 10rad/s-I5/I1
1E-7 20
160
(a) 3%SBS modified asphalt binder
40
80 Stress(kPa)
160
320
(b) 5%SBS modified asphalt binder
1E-1 1E-2
In/I1
1E-3 1E-4 1E-5 1E-6
1rad/s- I3/I1
1rad/s-I5/I1
1rad/s-I7/I1
5rad/s- I3/I1
5rad/s-I5/I1
5rad/s-I7/I1
10rad/s-I3/I1 10rad/s-I5/I1
1E-7 20
40
80 160 Stress(kPa)
320
(c) 7%SBS modified asphalt binder Fig. 3. In/I1 of the modified asphalt binders.
Q is another parameter that can be used to describe the nonlinear characteristics. The Q parameter under LAOS stress can be described by Eq. (5). The relationships between Q and stress amplitude at various conditions are plotted in Fig. 5. The dotted lines in each figure are the fitting curves by Eq. (5). It can be seen that Q values decrease with increase in frequency and stress amplitude.
Q¼
I3 =I1 ðr0 Þ
ð5Þ
r20
Q 0 lim Q 0 ¼ lim r0 !0
r0 !0
I3 =I1 ðr0 Þ
r20
ð6Þ
It can also be seen from Fig. 5 that, at relatively small stress amplitude, Q had a constant value (Q0) that changes with frequency. The Q0 values for the binders are calculated using Eq. (6) and shown in Fig. 6 (C = 2 was used for each condition in order to calculate Q0 value, Q0 = AB). It shows the trend of Q0 decreasing with frequency. The Q0 value of neat asphalt binder is less than that of modified asphalt at the same frequency, which means that the nonlinearity of neat asphalt binder is less obvious than that of modified asphalt binders. Besides, the nonlinearity of modified asphalt binders also increases with the increase of SBS content. 3.2.2. Strain decomposition Strain decomposition is another important method to study the nonlinear rheological behavior of viscoelastic materials. The strain decomposition method is to decompose the nonlinear strain into 0 an apparent elastic strain, c , and an apparent plastic strain, c} [27]:
c0 ðtÞ ¼ r0
X
J 0n ðx; r0 Þcos nxt
ð7Þ
J 00n ðx; r0 Þsin nxt
ð8Þ
n odd
c00 ðtÞ ¼ r0
X n odd
The elastic [cðtÞ vs sðtÞ] and viscous Lissajous loops [c_ ðtÞ vs sðtÞ] are commonly used to analyze the nonlinear rheological behavior. Besides, some measures in the Lissajous loop can also be used to analyze the nonlinearity, as shown in Fig. 7. The first of these measures is the minimum-stress elastic compliance, denoted hereJ 0M as shown in Eq. (9). Another complementary nonlinear measure that can be defined is the elastic compliance J 0L at large stress, as shown in Eq. (10) [27]. Both J 0M and J 0L are nonlinear elastic measures in the sense that they describe local intra-cycle elastic behavior for the nonlinear materials.
J 0M J 0L
X dc j ¼ ð1Þðn1Þ=2 nJ0n dr r¼0 nodd
X 0 c j ¼ J r r¼r0 nodd n
ð9Þ
ð10Þ
The corresponding nonlinear viscous measures can also be defined for LAOS stress. These are based on the measure fluidities instead of compliances. The first of these is /0M , which is the minimum stress fluidity and is defined as shown in Eq. (11). The second is /0L , which is the fluidity at large stress and is defined as shown in Eq. (12) [27].
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1E-1
1E-2
1E-2
I3/I1
I3/I1
1E-1
1E-3
1E-3 1rad/s 5rad/s 10rad/s
1E-4
1E-5
1E-5 10
20
40 80 Stress (kPa)
20
160
(a) Neat asphalt binder
40
80 Stress (kPa)
160
(b) 3%SBS modified asphalt binder
1E-1
1E-1
1E-2
1E-2 I3/I1
I3/I1
1rad/s 5rad/s 10rad/s
1E-4
1E-3
1E-3 1rad/s 5rad/s 10rad/s
1E-4
1rad/s 5rad/s 10rad/s
1E-4
1E-5
1E-5 20
40
80 160 Stress (kPa)
320
(c) 5%SBS modified asphalt binder
20
40
80 160 Stress (kPa)
320
(d) 7%SBS modified asphalt binder
Fig. 4. The I3/I1 as a function of stress amplitude of the studied binders at various frequencies.
/0M
X dc j ¼ ð1Þðn1Þ=2 n2 J 00n dr r¼0 n odd
ð11Þ
/0L
X c jr¼r0 ¼ nxJ 00n r n odd
ð12Þ
For the studied binders, both the elastic [cðtÞ vs sðtÞ] and viscous representation [c_ ðtÞ vs sðtÞ] are shown together with the Lissajous curves as shown in Fig. 8. For the elastic Lissajous loop, the values in the upper left stand for the maximum strain under this test condition; for the viscous Lissajous loop, the values in the upper left stand for the maximum strain rate under this test conditions. The shapes of the Lissajous curves are similar at different stress levels. Both the elastic Lissajous loop and the viscous Lissajous loop are ellipse, the viscous loop is thinner than the elastic loop. It means that all the studied binders show viscoelastic behavior under the test conditions. Comparing the dotted line between neat asphalt binder and SBS modified asphalt binders, it shows that the dotted lines for the neat asphalt binder are all linear under the studied conditions, but the nonlinearity of the dotted line becomes more and more obvious with increase in stress level and SBS contents for the modified asphalt binders. It proves that the nonlinearity of binders can be increased by adding SBS polymers and the nonlinearity of modified asphalt binders also increases with the increase of SBS contents. The elastic compliance and fluidity for the binders under the conditions shown in Fig. 8 were calculated and shown in Table 2. It is clear that both the small stress and the large stress compliances J 0M and J 0L increase as the stress amplitude increases and the
binder softens. Both the minimum stress fluidity /0M and large stress fluidity /0L also increase with stress amplitude, and the binder is easy to flow. Comparing the compliance and fluidity before and after adding different SBS contents, it can be found that the elastic compliance deccreases with the increase of SBS contents, that is, the elastic proportion increases with the increase of SBS content. The fluidity decreases after adding SBS, which means that it is not easy to flow. In a word, the elastic compliance and fluidity can well reflect the effect of SBS content on binder viscoelastic properties. The elastic and plastic strain can also be represented as a series of orthogonal Chebyshev polynomials Tn ðxÞ [27,28], where x is the scaled stress, x ¼ rðtÞ=r0 :
c0 ðtÞ ¼ r0
X
odd J 0n ðx; r0 Þcos nxt
n
¼ r0
X n
c00 ðtÞ ¼ r0
odd J 0n ðx; r0 Þ T n ðxÞ |fflfflfflfflfflffl{zfflfflfflfflfflffl}
X
ð13Þ
cn
odd nxJ 00n ðx; r0 Þcos nxt
n
¼ r0
X n
odd nx J 00n ðx; r0 Þ T n ðxÞ |fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl}
ð14Þ
fn
The physical interpretation of the higher harmonics can be revealed by considering the Chebyshev coefficients in the orthogonal space formed by the input stress/stain and strain-rate. Due to the convexity of the third Chebyshev polynomial positive values of c3 result in stress softening of the apparent elastic stress-strain curve, while positive values of f3 result in stress thinning of the
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L. Shan et al. / Construction and Building Materials 231 (2020) 117076
1E-6 1rad/s
1E-7
1E-6 1rad/s
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5rad/s
5rad/s 10rad/s
10rad/s
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1E-8 10
20
40 80 Stress (kPa)
160
20
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1E-7
80 Stress(kPa)
160
(b) 3%SBS modified asphalt binder
Q(1/(kPa)2)
Q(1/(kPa)2)
(a) Neat asphalt binder
40
1E-6 1rad/s
1E-7
5rad/s
5rad/s
10rad/s
10rad/s
1E-8
1E-8 20
40
80 160 Stress (kPa)
320
(c) 5%SBS modified asphalt binder
20
40
80 160 Stress (kPa)
320
(d) 7%SBS modified asphalt binder
Fig. 5. Q ¼ I3 =I1 =r20 as a function of stress amplitude of the studied binders at various frequencies.
ening response of the material. Based on the convenxity of the third Chebyshev polynomial theory, all the studied binders will reveal stress softening and stress thinning under all the studied test conditions because both c3 and f3 are positive, as shown in Fig. 9. Besides, with increasing stress, both c3/c1 and f3/f1 increase from the overall trend.
Q0(1/(kPa)2)
1E-05
1E-06
1E-07
4. Conclusions
0
neat 3%SBS modified 5%SBS modified 7%SBS modified 5
10
Frequency (rad/s) Fig. 6. Q0 of the studied binders at various frequencies.
apparent plastic strain-rate vs shear stress curve. Conversely, negative values of c3 imply stress stiffening, while negative values of f3 imply stress thickening. By decomposing the elastic and viscous strain signal into the orthogonal set of Chebyshev polynomial, we may determine quantitatively the stress softening/stiffening and shear thinning/thick-
The effect of SBS concentration on rheological behaviors of asphalt binder was analyzed in depth for a wide range of stress levels to characterize the linear and nonlinear regimes of the bituminous material. The linear rheological behavior of neat asphalt binder and the corresponding SBS modified asphalt binders was studied by the master curves. And the nonlinear rheological behaviors of them were studied by FT-rheology method and strain decomposition method. The results show that the difference between storage modulus and loss modulus decreases with increase in SBS contents. And the phase angle also decreases with increase in SBS contents. For the nonlinear rheological bahaviour, the relative intensity of the nonlinear parameter of asphalt binder increases with the increase of stress and the decrease of frequency. The nonlinearity of the SBS modified asphalt binder is more obvious than that of the neat asphalt binder and increases with the increase of SBS contents. The relationship between I3/I1 and stress amplitude obeys a sig-
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L. Shan et al. / Construction and Building Materials 231 (2020) 117076
1.5
1.5
JM'
1
JL'
0.5
Strain rate(s-1)
Strain(%)
1
0 -0.5 -1
ФM'
0.5 0
ФL'
-0.5 -1
-1.5 -1.5
-1
-0.5 0 0.5 Stress(kPa)
1
1.5
-1.5 -1.5
-1
-0.5
0
0.5
1
1.5
Stress(kPa)
Fig. 7. Schematic of the compliance and fluidity.
Fig. 8. Decomposition of shear strain into elastic and viscous part for the binders at 1 rad/s.
Table 2 The material parameters of the studied binders show in Fig. 8. Binder type
Stress level (kPa)
JM0 (Pa1)
JL0 (Pa1)
UM0 (Pas)1
UL0 (Pas)1
Neat asphalt
30 80 100 30 100 210 30 100 320 30 100 320
4.50E04 4.62E04 4.82E04 4.40E04 4.38E04 5.51E04 4.28E04 5.30E04 9.14E04 3.90E04 4.26E04 1.07E03
4.94E04 5.20E04 5.75E04 4.54E04 4.94E04 6.42E04 4.36E04 5.88E04 1.18E03 4.15E04 5.24E04 1.31E03
2.37E03 2.53E03 2.75E03 1.12E03 1.43E03 2.06E03 7.45E04 0.61E03 1.52E03 7.31E04 0.54E03 1.36E03
2.38E03 2.65E03 2.82E03 1.14E03 1.53E03 2.16E03 7.96E04 0.73E03 1.85E03 7.74E04 0.66E03 1.82E03
3%SBS modified asphalt
5%SBS modified asphalt
7%SBS modified asphalt
L. Shan et al. / Construction and Building Materials 231 (2020) 117076
9
Fig. 9. Relative third order elastic, c3/c1, and viscous, f3/f1 Chebyshev coefficients as a function of stress for the studied binders at different frequencies.
moidal function. The intrinsic nonlinearity Q0 decreases with the increase of frequency. The Q0 value of neat asphalt binder is less than that of SBS modified asphalt binder and increases with
increase in SBS contents at the same frequency, which also shows that the nonlinearity of modified asphalt binder is relatively more obvious than neat asphalt binder and increases with increase in
10
L. Shan et al. / Construction and Building Materials 231 (2020) 117076
SBS contents. The strain decomposition results show that all the studied binders present viscoelastic behavior under all the test conditions, and the nonlinearity increases with stress amplitude and SBS contents. The elastic compliance and fluidity results show that the binders soften with increase in stress level. After adding SBS polymer, it is hard for the binder to flow and the elastic proportion of binders increases. Analysis of the Chebyshev polynomial shows that all the studied binders exhibit stress softening and stress thinning under all the studied test conditions. In a word, the SBS could increase the nonlinearity and the elastic proportion of asphalt binder and decrease its fluidity. The nonlinear and linear measures of asphalt binder show similar results, but the nonlinear results could provide more and unique information compared with the linear results. This study has already showed that LAOS stress measurements can provide useful information to analyze the nonlinearity of modified asphalt binders. In the future study, more test conditions and different types of modified asphalt binders such as crumb rubber, EVA, graphene, etc. will be studied for futher figuring out the practical meaning of LAOS. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement This study was sponsored by the National Natural Science Foundation of China (51778195, 51978218, 51478153 and U1633201). References [1] B. Sengoz, G. Isikyakar, Evaluation of the properties and microstructure of SBS and EVA polymer modified bitumen, Constr. Build. Mater. 22 (2008) 1897– 1905. [2] A. Behnood, J. Olek, Rheological properties of asphalt binders modified with styrene-butadiene-styrene (SBS), ground tire rubber (GTR), or polyphosphoric acid (PPA), Constr. Build. Mater. 151 (2017) 464–478. [3] V. Selvavathi, V.A. Sekar, V. Sriram, et al., Modifications of bitumen by elastomer and reactive polymer- a comparative study, Petrol. Sci. Tech. 20 (5– 6) (2002) 535–547. [4] G. Polacco, S. Berlincioni, D. Biondi, J. Stastna, L. Zanzotto, Asphalt modification with different polyethylene-based polymers, Eur. Polym. J. 41 (2005) 2831– 2844. [5] A. Topal, M. Yilmaz, B.V. Kok, N. Kuloglu, B. Sengoz, Evaluation of Rheological and Image Properties of Styrene-Butadiene-Styrene and Ethylene-Vinyl Acetate Polymer Modified Bitumens, J. Appl. Polym. Sci. 122 (2011) 3122– 3132.
[6] H.U. Bahia, D.A. Anderson, The new proposed rheological properties of asphalt binders: why are they required and how do they compare to conventional properties, Phys. Prop. Asphalt Cem. Binders (1995) 27. [7] G.D. Airey, Rheological properties of styrene butadiene styrene polymer modified road bitumens, Fuel 82 (2003) 1709–1719. [8] G.D. Airey, Styrene butadiene styrene polymer modification of road bitumens, J. Mater. Sci. 39 (2004) 951–959. [9] T. Xia, J. Xu, T. Huang, J. He, Y. Zhang, J. Guo, Y. Li, Viscoelastic phase behavior in SBS modified bitumen studied by morphology evolution and viscoelasticity change, Constr. Build. Mater. 105 (2016) 589–594. [10] C.O. Rossi, A. Spadafora, B. Teltayev, G. Izmailova, Y. Amerbayev, V. Bortolotti, Polymer modified bitumen: rheological properties and structural characterization, Colloids Surf. A: Physicochem. Eng. Aspects 480 (2015) 390–397. [11] J. Stastna, L. Zanzotto, G. Kennepohl, Dynamic materials functions and the structure of asphalts, Transp. Res. Rec. 1535 (1996) 3–9. [12] D. Lesueur, J.F. Gérard, P. Claudy, J.M. Létoffé, D. Martin, J.P. Planche, Polymer modified asphalts as viscoelastic emulsions, J. Rheol. 42 (1998) 1059–1074. [13] M. Jasso, R. Hampl, O. Vacin, D. Bakos, J. Stastna, L. Zanzotto, Rheology of conventional asphalt modified with SBS, Elvaloy and polyphosphoric acid, Fuel Process. Technol. 140 (2015) 172–179. [14] Z. Vlachovicova, J. Stastna, D. MacLeod, L. Zanzotto, Shear deformation and material properties of polymer-modified asphalt, Petroleum. Coal 47 (2005) 38–48. [15] G. Polacco, J. Stastna, D. Biondi, Z. Vlachovicova, L. Zanzotto, P. Magagnini, Time scales in polymer modified asphalts, Macromol. Symp. 228 (2010) 41–50. [16] G. Polacco, J. Stastna, D. Biondi, L. Zanzotto, Relation between polymer architecture and nonlinear viscoelastic behavior of modified asphalts, Curr. Opin. Colloid In. 11 (2006) 230–245. [17] K. Hyun, M. Wilhelm, C.O. Klein, et al., A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS), Prog. Polym. Sci. 36 (12) (2011) 1697–1753. [18] A.J. Giacomin, J.M. Dealy, Large-amplitude oscillatory shear, in: A.A. Collyer (Ed.), Techniques in rheological measurements, Chapman & Hall, London, 1993, pp. 99–121. [19] A. Padmarekha, K. Chockalingam, U. Saravanan, A.P. Deshpande, J.M. Krishnan, Large amplitude oscillatory shear of unmodified and modified bitumen, Road Mater. Pave. 14 (2013) 12–24. [20] M.J. Farrar, J.P. Planche, A.O. Cookman, S. Salmans. Asphalt binder large amplitude oscillatory shear. Western Research Institute Binder ETG meeting, Baton Rouge, LA, Sept.16, 2014. [21] K. Jorshari, J. Stastna, L. Zanzotto, Large amplitude oscillations in asphalt, J. Appl. Asphalt Binder Technol. 1 (2001) 51–71. [22] J. Stastna, K. Jorshari, L. Zanzotto, Nonlinear dynamic moduli in asphalt, Mater. Struct. 35 (2002) 59–63. [23] E. González, L.M.B. Costa, H.M.R.D. Silva, L. Hilliou, Rheological characterization of eva and hdpe polymer modified bitumens under large deformation at 20 °C, Constr. Build. Mater. 112 (2016) 756–764. [24] L.Y. Shan, H.S. He, N.J. Wagner, Z. Li, Nonlinear rheological behavior of bitumen under LAOS stress, J. Rheol. 62 (4) (2018) 975–989. [25] D.A. Anderson, D.W. Christensen, H.U. Bahia, R. Dongre, M.G. Sharma, C.E. Antle, et al., Binder characterization and evaluation. volume 3: physical characterization, Asphalt Cement (1994) 3. [26] K. Hyun, E.S. Baik, K.H. Ahn, S.J. Lee, M. Koyama, Fourier-transform rheology under medium amplitude oscillatory shear for linear and branched polymer melts, J. Rheol. 51 (2007) 1319–1342. [27] C.J. Dimitriou, R.H. Ewoldt, G.H. McKinley, Describing and prescribing the constitutive response of yield stress fluids using large amplitude oscillatory shear stress (LAOStress), J. Rheol. 57 (2013) 27–70. [28] R.H. Ewoldt, A.E. Hosoi, G.H. McKinley, New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear, J. Rheol. 52 (2008) 1427–1458.
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Effect of styrene-butadiene-styrene (SBS) on the rheological behavior of asphalt binders Liyan Shan ⇑, Xiaofei Qi, Xianglei Duan, Shuang Liu, Jian Chen School of Transportation Science and Engineering, Harbin Institute of Technology, Harbin 150090, Heilongjiang, China
h i g h l i g h t s Use of FT-rheology and strain decomposition to study the nonlinearity of binders. Nonlinearity of binders increases with increase in stress and decrease in frequency. Nonlinearity of SBS modified asphalt binder is more obvious than neat asphalt binder. Nonlinearity of SBS modified asphalt binder increases with increase in SBS content. All binders exhibit stress softening and stress thinning under studied conditions.
a r t i c l e
i n f o
Article history: Received 19 May 2019 Received in revised form 19 September 2019 Accepted 24 September 2019
Keywords: Asphalt binder SBS polymer Rheological behavior Linear Nonlinear LAOS stress
a b s t r a c t The binders in pavement could support the loading in either linear or nonlinear regime. The linear viscoelasticity of asphalt binders was well established, however, a few of researches focused on the nonlinear viscoelasticity of asphalt binders. Here, this paper deals with the effects that SBS exerts on the linear and nonlinear rheological behavior of asphalt binders. The nonlinear rheological behavior of one kind of neat asphalt binder and the corresponding SBS modified asphalt binders under large amplitude oscillatory shear stress (LAOS stress) is analyzed by Fourier Transform (FT)-rheology and strain decomposition methods. The linear viscoelastic measurements show that the elastic proportion and the complexity of rheological behavior of the asphalt binder increases with increase in SBS content. The nonlinear viscoelastic measurements reveal that the relative nonlinearity of asphalt binders increases with increase in stress and decrease in frequency; the relationship between I3/I1 and stress amplitude can obey the sigmoidal function; the intrinsic nonlinearity Q0 decreases with increase in frequency and increases with the increase of SBS content. Both the FT analysis and decomposition results show that the nonlinearity of SBS modified asphalt binder is more obvious than neat asphalt binder and increases with the increase of SBS content. SBS could increase the nonlinearity and the elastic proportion of asphalt binder and decrease its fluidity. All the studied binders exhibit stress softening and stress thinning under all the studied test conditions. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction As an important component of asphalt pavement, asphalt binder has always been the research focus in road engineering regime. Asphalt binder is a complex high molecular weight hydrocarbon, which can be divided into four main compositions, asphaltene, resins, saturates and aromatic. It behaves viscoelastic behavior under specific conditions. However, the neat asphalt binder cannot perform satisfactorily with increasing traffic level, heavier loading, and harsh climate. Thus, modified asphalt binders attract many ⇑ Corresponding author. E-mail address: [email protected] (L. Shan). https://doi.org/10.1016/j.conbuildmat.2019.117076 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
researchers’ attention recently. Among the available asphalt modifiers, the polymers have been used widely in the past few years. It can increase the elasticity of the binders and reduce the stress and temperature susceptibility, which contributes to improve the rutting resistance and anti-fatigue of asphalt binders [1,2]. Styrene-butadiene-styrene (SBS) is one of the most frequently used polymer additives as it forms high interaction with maltene components [3]. SBS is swollen and dispersed throughout the bulk and behaves as cross linker when blended with neat asphalt binder [4]. Additionally, the concentrationon of SBS is one of main factors on this swollen process, which significantly influences the properties of neat asphalt binder [5]. Considering that the rheological properties of asphalt binders can significantly
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L. Shan et al. / Construction and Building Materials 231 (2020) 117076
affect the performance of asphalt mixtures [6], it is very important to understand the effect of SBS concentrationon on rheological behavior of asphalt binders. The linear rheological characterization of SBS modified asphalt binders have been analyzed thoroughly by researchers from the angle of dynamic modulus, phase angle, and etc [7–12]. Airey et al. investigated the rheological behavior of SBS polymer modified bitumens at three polymer contents by the modulus master curve, phase angle master curve, Han plots or isochronal plots [7,8]. Xia et al. studied morphology evolution and viscoelasticity change of SBS polymer modified binders at different weight fraction of SBS [9]. Rossi et al. evaluated the effect of SBS polymer modifiers on the bitumen phase transition by the temperature sweep test from 30 °C to 150 °C, and the curves of modulus/tand versus temperature could show both the a- and b-relaxation [10]. And different models were used to describe the above rheological behaviors. Stastna et al. used the generalization of the Maxwell model to describe the modulus and phase angle of different kinds of modified (SBS, PE and EVA) asphalt binders and the discrete spectrum was shown to be related to the interface interaction of the neat asphalt and the polymers [11]. Lesueur et al. used the Palierne model to estimate the rheological properties of SBS modified asphalt and the fitting results showed that the Palierne model could describe the modulus and phase angle data fairly well [12]. However, various failure mechanisms of the pavements occur at different strain or stress levels, asphalt binders can undergo loading out of linear regime during ‘‘in life” service. And the linear rheological properties of binders have limited capability for correlating the structure with mechanical properties, therefore, the nonlinear rheological properties of SBS modified asphalt binder should not be ignored. The steady shear viscosity is probably the simplest traditional nonlinear functions that can reveal the anomalous behavior of blends of asphalts with polymers. Jasso et al. also used the viscosity to study the rheological properties of SBS modified asphalt besides the above curves [13]. Vlachovicova et al. showed that the viscosity function was better than the master curves to show difference between neat and polymer-modified asphalts [14]. Polacco et al. found the two step shear thinning regime in the polymer viscosity-shear rate curves as others did, and showed that the phenomenological equation derived from the Wagner model could well fit the test data [15]. Polacco et al. summarized researches about the nonlinear rheological behavior of polymer modified asphalt binders using the shear viscosity [16]. One disadvantage of this test method is that when processing at high rates of deformation for short time, the material does not reach steady state. And steady simple shear rate experiments also have inherent limitations: little information is provided about microstructure since the measurement is made at steady state [17]. LAOS (Large amplitude oscillatory shear) is another method to investigate and quantify nonlinear viscoelastic properties of complex fluids or soft matter. For the LAOS stress tests, when the stress increases beyond the linear regime, the strain output is not purely sinusoidal and the behavior can no longer be fully described in terms of complex modulus (G*) due to the presence of higher harmonic contributions. It does not involve any sudden imposed jumps in speed or position, and consequently it is a relatively easy flow to generate and control [18]. Nevertheless, there is a few of literatures related to nonlinear rheological behavior of asphalt binder including SBS modified asphalt binder under LAOS. The Lissajous plots have been used to study the nonlinear behavior of unmodified, modified asphalt binders [19,20]. Others compared the higher harmonic moduli of neat, SBS modified and EVA modified asphalt binders [21,22]. González et al. tested the rheological characterization of neat bitumen and EVA, HDPE polymer modified bitumen with the LAOS-FTR (Fourier transform rheology) method, and showed that this method could quantitatively differentiate
between the tested binders [23]. The author proposed protocol to obtain the nonlinear rheological properties of asphalt binders under LAOS stress and compared the nonlinear rheological behaviors of neat asphalt and SBS/crumb rubber modified asphalt binder using FT-rheology and strain decomposition methods [24]. While the above works showed that the linear rheological behavior of SBS modified asphalt binder was well studied, but a few of researches focused on its nonlinear rheological behavior. The references also proved that the nonlinear rheological behavior is important to investigate the effect of additives on asphalt binders, study the modified mechanism and differentiate the binders. However, there is no too much attention to the responses of this material under both small and large stresses. Therefore, the rheological behaviors of SBS modified asphalt binder should be understood in depth for a wide range of stress levels to characterize the linear and nonlinear regimes of the asphalt material. The main objective of this paper is to study the effect of SBS concentrations on the linear and nonlinear rheological behavior of asphalt binders. Three SBS contents were blend with neat asphalt binder. The stress sweep test was performed to determine the linear and nonlinear regime and select the stress levels for frequency sweep test and LAOS test. The frequency sweep test was to study the linear rheological behavior by the modulus master curve and phase angle master curve. The LAOS stress test was used to study the nonlinear rheological behavior of the SBS modified asphalt binders by FT-rheology and strain decomposition methods. This study can better understand the responses of this material under both small and large stresses and the effect of SBS contents on its rheological behavior. 2. Material and methods 2.1. Materials A neat asphalt binder with penetration grade of 73.6 1/10-mm and softening point of 48.6 °C (ring and ball) was used for polymer modification. The asphalt binder modified with 3 wt% SBS, 5 wt% SBS and 7 wt% SBS were manufactured to study the effect of SBS content level on the properties of asphalt binders. Blends of asphalt and SBS were prepared by mechanical stirring using the highspeed mixer. The neat asphalt binder was firstly heated at 180 ± 5 °C until it flowed fully, then slowly add (5 g/min) the calculated amount of SBS (3 wt%, 5 wt% or 7 wt%) to the melted asphalt under low shear rate of 500 r/min. Secondly, increase the speed to 4000 r/min and shear for 120 min. Furthermore, the modified binder was kept in the oven at 180 ± 5 °C for 2 h so that the blends became essentially homogenous. The basic information of the SBS modified asphalt binders are summarized in Table 1. It can be seen that the penetration decreases and softening point increases with the SBS content increasing. This can be credited to the continuous three-dimensional network which polymer additives forms in the neat asphalt binder during blending process. 2.2. Test methods Rheological properties test was performed using a TA Instruments AR-G2 Rheometer. Three types of test were conducted: Table 1 The basic information of the studied binders. Binders
Penetration (1/10-mm at 25 °C)
Softening point (°C)
Neat asphalt 3% SBS modified asphalt 5% SBS modified asphalt 7% SBS modified asphalt
73.6 50.2 45.3 40.8
48.6 61.8 78.5 81.2
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The stress sweep test also shows that the loss modulus is greater than the storage modulus, which illustrates that the asphalt binder behaves as a viscous suspension. This result is consistent with the results we have obtained in the previous study. Besides, it can be found that the modulus increases with increase in SBS content, which means that the binder becomes stiffer with increase in SBS content. This is consistent with the penetration and softening point results.
stress sweep, frequency sweep and LAOS stress test. These tests were conducted with an 8-mm-diameter parallel plate geometry and 2-mm gap setting when the temperature was lower than 30 °C, otherwise, a 25-mm-diameter parallel plate geometry and 1-mm gap setting were used. At least, two replicates were performed for each test condition; if the deviation was greater than 10 percent, a third replicate was required. In the linear regime, modulus and phase angle master curves were used to study the linear rheological behavior of SBS modified asphalt binders. In the nonlinear regime, about ten different stress levels were selected as the control stress to do the LAOS stress test. Then, FT-rheology and strain decomposition methods were used to study the nonlinear rheological behavior of SBS modified asphalt binders.
2.2.2. Frequency sweep test Frequency sweep tests were conducted for frequencies from 0.01 Hz to 60 Hz and for temperatures of 20 °C, 30 °C, 40 °C, 50 °C, and 60 °C. This combination of temperatures and frequencies ensure sufficient overlap in the material responses so that the data could be horizontally shifted to obtain master curves of the key properties. The horizontal shift factors for all samples were fitted with the WLF functions. The CAM model can be used to describe the dynamic modulus and phase angle master curves over a wide range of reduced frequencies at a reference temperature. The stress levels for the frequency tests were chosen to be in the linear range. 2.2.3. LAOS stress test The LAOS stress test is used to study the nonlinear rheological behavior of the asphalt binders. The stresses used for the LAOS stress test were chosen in the rectangle regime as shown in Fig. 1. The sample was sheared under the selected stress level until more than ten strain cycles in the time-stable regime were obtained. If the stress level is very large and it is difficult to obtain ten stable cycles, the test was stopped after the stable regime
1E+6
1E+6
1E+5
1E+5
G', G"(Pa)
G', G"(Pa)
2.2.1. Stress sweep test The stress sweep test was performed to determine the linear and nonlinear regime and select the stress levels for frequency sweep test and LAOS test. All the tests were carried out at 30 °C. In this test, the stress was started from a very small value, and increased incrementally until the specimen was broken. Meanwhile, the stress values were collected by the rheometer at a constant frequency. According to the Strategic Highway Research Program (SHRP), if the decrease in the dynamic modulus value is less than 10% of the initial modulus value, the binder is believed to be in the linear region [25]. Otherwise, the regime where the decrease modulus is more than 10% of the initial dynamic modulus is believed to be the nonlinear regime. Based on that, the stress levels used in the following test were chosen as show in Fig. 1.
1E+4
1E+3 1E+2
1rad/s,G' 5rad/s,G' 10rad/s,G'
1rad/s,G'' 5rad/s,G'' 10rad/s,G''
1E+3 1E+4 1E+5 Stress (Pa)
1E+3 1E+2
1E+6
(a) Neat asphalt binder 1E+6
1E+6
1E+5
1E+5
1E+4
1E+3 1E+2
1rad/s,G' 5rad/s,G' 10rad/s,G' 1E+3
1rad/s,G'' 5rad/s,G'' 10rad/s,G''
1E+4 1E+5 Stress (Pa)
1rad/s,G' 5rad/s,G' 10rad/s,G'
1rad/s,G'' 5rad/s,G'' 10rad/s,G''
1E+3 1E+4 1E+5 Stress (Pa)
1E+6
(b) 3%SBS modified asphalt binder
G', G"(Pa)
G', G"(Pa)
1E+4
1E+6
(c) 5%SBS modified asphalt binder
1E+4
1E+3 1E+2
1rad/s,G' 5rad/s,G' 10rad/s,G' 1E+3
1rad/s,G'' 5rad/s,G'' 10rad/s,G''
1E+4 1E+5 Stress (Pa)
1E+6
(d) 7%SBS modified asphalt binder
Fig. 1. Stress sweep test results of the studied binders.
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L. Shan et al. / Construction and Building Materials 231 (2020) 117076
100 80
1E+3 neat,G' neat,G'' 3%SBS modified,G' 3%SBS modified,G'' 5%SBS modified,G' 5%SBS modified,G'' 7%SBS modified,G' 7%SBS modified,G''
1E+0 1E-3 1E-6 1E-5
1E-3 1E-1 1E+1 1E+3 Reduced frequency (rad/s)
(a) Modulus master curve
60 δ( )
G',G"(Pa)
1E+6
40 neat 3%SBS modified 5%SBS modified 7%SBS modified
20 0 1E-5
1E-3 1E-1 1E+1 1E+3 Reduced frequenvy (rad/s)
(b) Phase angle master curve
Fig. 2. Master curves of the studied binders.
obtained. Then, the cycles used for later analysis were selected (three to eight cycles based on the stress level) and the curves were shifted to zero average strain. Details of used methods to select the data and shift the curve can be found in reference [24].
3.1. Linear rheological behavior of SBS modified asphalt binders The master curve is one of the most popular methods to study the linear rheological behavior of asphalt binders. The master curves of the four kinds of asphalt binders are shown in Fig. 2. As shown in Fig. 2(a), the modulus increases with increase in frequency, and the loss modulus is larger than the storage modulus. The difference between the storage modulus and the loss modulus decreases with increase in frequency. Comparing the modulus curves of neat binder with that of SBS modified binders, it can be found that the difference between storage modulus and loss modulus decreases with increase in SBS content. It means that the elastic proportion of the binders increases with adding SBS. This is the reason that the high temperature performance of SBS modified binder is better than the neat asphalt binder. Fig. 2(b) shows the phase angle master curve of the studied binders. It shows that the phase angle decreases with increase in SBS content, which also means that the elastic proportion of the asphalt binder increases. Besides, it also shows that the complexity of rheological behavior increases with increase in SBS content. Because the phase angle decreases with frequency before adding SBS, and it decreases first then increases a little bit and finally decreases again with frequency after adding SBS. 3.2. Nonlinear rheological behavior of SBS modified asphalt binders 3.2.1. FT-rheology As described in references [24], the FT-rheology method is to express the nonlinear shear strain using a Fourier series expansion with either strain amplitude or stress amplitude with odd higher terms as shown in Eqs. (1) and (2) [26], and calculate the relative intensity of higher-harmonics [IðnxÞ=IðxÞ ¼ In =I1 , where x is the excitation frequency] as shown in Eq. (3).
cðtÞ ¼
cn cos ðnxt dn Þ
ð1Þ
n¼1;odd
cðtÞ ¼
X 0 J n ðx; r0 Þcos nxt þ J 00n ðx; r0 Þsin nxt n odd
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 ðc5 cos d5 Þ2 þ ðc5 sin d5 Þ c I5 =I1 ¼ 5 ¼ 2 2 c1 ðc1 cos d1 Þ þ ðc1 sin d1 Þ
3. Results and discussions
X
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 ðc3 cos d3 Þ2 þ ðc3 sin d3 Þ c I3 =I1 ¼ 3 ¼ 2 c1 ðc1 cos d1 Þ2 þ ðc1 sin d1 Þ
ð2Þ
ð3Þ
Any measured response from the tested system at frequencies other than x is associated with nonlinearity in the system response. Therefore, the relative intensity In/I1 is usually used to evaluate the degree of non-linearity of the material’s response. The strain is no longer sinusoidal if the stress amplitude is out of the linear regime. So the Fourier series expansion will have higher harmonics In/I1. As shown in Fig. 3, both I3/I1 and I5/I1 can be measured for 3%SBS modified asphalt, and besides that I7/I1 can be measured for 5%SBS and 7%SBS modified asphalt binders. Because, only I3/I1can be measured for neat asphalt binder, the results are not shown in Fig. 3. It also shows that I3/I1 increases with increase in stress and decrease in frequency, and the changing trend of I5/I1 and I7/I1 versus the stress level is similar to that of I3/ I1. However, the I5/I1 and I7/I1 increase with decrease in frequency at lower stress levels, the changing trend of I5/I1 and I7/I1 versus frequency is unregular at higher stress level, which is inconsistent with that of I3/I1. These phenomenon will be further verified by studying more styles of asphalt binders in the futher research. Besides, I7/I1 only occurs in 5%SBS and 7%SBS modified asphalt binders with frequencies of 1 rad/s and 5 rad/s and higher stress, which shows that with the increase of SBS content and stress amplitude as well as the decrease of frequency, the degree of nonlinearity becomes stronger. As I3/I1 is the most commonly used index to study the nonlinear rheological behavior of materials, the curves of I3/I1 versus stress amplitude for the studied binders were analyzed further and shown in Fig. 4. As shown in Fig. 4, I3/I1 increases with the increase of stress amplitude and the decrease of frequency, which is consistent with the previous results [26]. Eq. (4) was used to fit the I3/I1 data and the results are also shown in Fig. 4.
I3 =I1 ðr0 Þ ¼ A 1
1 1 þ BrC0
ð4Þ
where the parameter A reflects the maximum intensity of I3/I1 at high stress amplitude, B is approximately the point of inflection, and the parameter C is the scaling exponent. It can be seen from Fig. 4 that the equation can well describe the relationship between I3/I1 and stress amplitude.
5
1E-1
1E-1
1E-2
1E-2
1E-3
1E-3 In/I1
In/I1
L. Shan et al. / Construction and Building Materials 231 (2020) 117076
1E-4 1E-5 1E-6
1rad/s- I3/I1
1rad/s- I5/I1
5rad/s- I3/I1
5rad/s- I5/I1
1E-5 1E-6
10rad/s- I3/I1 10rad/s- I5/I1
1E-7 20
40
80 Stress(kPa)
1E-4 1rad/s- I3/I1
1rad/s- I5/I1
1rad/s- I7/I1
5rad/s- I3/I1
5rad/s- I5/I1
5rad/s-I7/I1
10rad/s-I3/I1 10rad/s-I5/I1
1E-7 20
160
(a) 3%SBS modified asphalt binder
40
80 Stress(kPa)
160
320
(b) 5%SBS modified asphalt binder
1E-1 1E-2
In/I1
1E-3 1E-4 1E-5 1E-6
1rad/s- I3/I1
1rad/s-I5/I1
1rad/s-I7/I1
5rad/s- I3/I1
5rad/s-I5/I1
5rad/s-I7/I1
10rad/s-I3/I1 10rad/s-I5/I1
1E-7 20
40
80 160 Stress(kPa)
320
(c) 7%SBS modified asphalt binder Fig. 3. In/I1 of the modified asphalt binders.
Q is another parameter that can be used to describe the nonlinear characteristics. The Q parameter under LAOS stress can be described by Eq. (5). The relationships between Q and stress amplitude at various conditions are plotted in Fig. 5. The dotted lines in each figure are the fitting curves by Eq. (5). It can be seen that Q values decrease with increase in frequency and stress amplitude.
Q¼
I3 =I1 ðr0 Þ
ð5Þ
r20
Q 0 lim Q 0 ¼ lim r0 !0
r0 !0
I3 =I1 ðr0 Þ
r20
ð6Þ
It can also be seen from Fig. 5 that, at relatively small stress amplitude, Q had a constant value (Q0) that changes with frequency. The Q0 values for the binders are calculated using Eq. (6) and shown in Fig. 6 (C = 2 was used for each condition in order to calculate Q0 value, Q0 = AB). It shows the trend of Q0 decreasing with frequency. The Q0 value of neat asphalt binder is less than that of modified asphalt at the same frequency, which means that the nonlinearity of neat asphalt binder is less obvious than that of modified asphalt binders. Besides, the nonlinearity of modified asphalt binders also increases with the increase of SBS content. 3.2.2. Strain decomposition Strain decomposition is another important method to study the nonlinear rheological behavior of viscoelastic materials. The strain decomposition method is to decompose the nonlinear strain into 0 an apparent elastic strain, c , and an apparent plastic strain, c} [27]:
c0 ðtÞ ¼ r0
X
J 0n ðx; r0 Þcos nxt
ð7Þ
J 00n ðx; r0 Þsin nxt
ð8Þ
n odd
c00 ðtÞ ¼ r0
X n odd
The elastic [cðtÞ vs sðtÞ] and viscous Lissajous loops [c_ ðtÞ vs sðtÞ] are commonly used to analyze the nonlinear rheological behavior. Besides, some measures in the Lissajous loop can also be used to analyze the nonlinearity, as shown in Fig. 7. The first of these measures is the minimum-stress elastic compliance, denoted hereJ 0M as shown in Eq. (9). Another complementary nonlinear measure that can be defined is the elastic compliance J 0L at large stress, as shown in Eq. (10) [27]. Both J 0M and J 0L are nonlinear elastic measures in the sense that they describe local intra-cycle elastic behavior for the nonlinear materials.
J 0M J 0L
X dc j ¼ ð1Þðn1Þ=2 nJ0n dr r¼0 nodd
X 0 c j ¼ J r r¼r0 nodd n
ð9Þ
ð10Þ
The corresponding nonlinear viscous measures can also be defined for LAOS stress. These are based on the measure fluidities instead of compliances. The first of these is /0M , which is the minimum stress fluidity and is defined as shown in Eq. (11). The second is /0L , which is the fluidity at large stress and is defined as shown in Eq. (12) [27].
6
L. Shan et al. / Construction and Building Materials 231 (2020) 117076
1E-1
1E-2
1E-2
I3/I1
I3/I1
1E-1
1E-3
1E-3 1rad/s 5rad/s 10rad/s
1E-4
1E-5
1E-5 10
20
40 80 Stress (kPa)
20
160
(a) Neat asphalt binder
40
80 Stress (kPa)
160
(b) 3%SBS modified asphalt binder
1E-1
1E-1
1E-2
1E-2 I3/I1
I3/I1
1rad/s 5rad/s 10rad/s
1E-4
1E-3
1E-3 1rad/s 5rad/s 10rad/s
1E-4
1rad/s 5rad/s 10rad/s
1E-4
1E-5
1E-5 20
40
80 160 Stress (kPa)
320
(c) 5%SBS modified asphalt binder
20
40
80 160 Stress (kPa)
320
(d) 7%SBS modified asphalt binder
Fig. 4. The I3/I1 as a function of stress amplitude of the studied binders at various frequencies.
/0M
X dc j ¼ ð1Þðn1Þ=2 n2 J 00n dr r¼0 n odd
ð11Þ
/0L
X c jr¼r0 ¼ nxJ 00n r n odd
ð12Þ
For the studied binders, both the elastic [cðtÞ vs sðtÞ] and viscous representation [c_ ðtÞ vs sðtÞ] are shown together with the Lissajous curves as shown in Fig. 8. For the elastic Lissajous loop, the values in the upper left stand for the maximum strain under this test condition; for the viscous Lissajous loop, the values in the upper left stand for the maximum strain rate under this test conditions. The shapes of the Lissajous curves are similar at different stress levels. Both the elastic Lissajous loop and the viscous Lissajous loop are ellipse, the viscous loop is thinner than the elastic loop. It means that all the studied binders show viscoelastic behavior under the test conditions. Comparing the dotted line between neat asphalt binder and SBS modified asphalt binders, it shows that the dotted lines for the neat asphalt binder are all linear under the studied conditions, but the nonlinearity of the dotted line becomes more and more obvious with increase in stress level and SBS contents for the modified asphalt binders. It proves that the nonlinearity of binders can be increased by adding SBS polymers and the nonlinearity of modified asphalt binders also increases with the increase of SBS contents. The elastic compliance and fluidity for the binders under the conditions shown in Fig. 8 were calculated and shown in Table 2. It is clear that both the small stress and the large stress compliances J 0M and J 0L increase as the stress amplitude increases and the
binder softens. Both the minimum stress fluidity /0M and large stress fluidity /0L also increase with stress amplitude, and the binder is easy to flow. Comparing the compliance and fluidity before and after adding different SBS contents, it can be found that the elastic compliance deccreases with the increase of SBS contents, that is, the elastic proportion increases with the increase of SBS content. The fluidity decreases after adding SBS, which means that it is not easy to flow. In a word, the elastic compliance and fluidity can well reflect the effect of SBS content on binder viscoelastic properties. The elastic and plastic strain can also be represented as a series of orthogonal Chebyshev polynomials Tn ðxÞ [27,28], where x is the scaled stress, x ¼ rðtÞ=r0 :
c0 ðtÞ ¼ r0
X
odd J 0n ðx; r0 Þcos nxt
n
¼ r0
X n
c00 ðtÞ ¼ r0
odd J 0n ðx; r0 Þ T n ðxÞ |fflfflfflfflfflffl{zfflfflfflfflfflffl}
X
ð13Þ
cn
odd nxJ 00n ðx; r0 Þcos nxt
n
¼ r0
X n
odd nx J 00n ðx; r0 Þ T n ðxÞ |fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl}
ð14Þ
fn
The physical interpretation of the higher harmonics can be revealed by considering the Chebyshev coefficients in the orthogonal space formed by the input stress/stain and strain-rate. Due to the convexity of the third Chebyshev polynomial positive values of c3 result in stress softening of the apparent elastic stress-strain curve, while positive values of f3 result in stress thinning of the
7
1E-4
1E-4
1E-5
1E-5 Q(1/(kPa)2)
Q(1/(kPa)2)
L. Shan et al. / Construction and Building Materials 231 (2020) 117076
1E-6 1rad/s
1E-7
1E-6 1rad/s
1E-7
5rad/s
5rad/s 10rad/s
10rad/s
1E-8
1E-8 10
20
40 80 Stress (kPa)
160
20
1E-4
1E-4
1E-5
1E-5
1E-6 1rad/s
1E-7
80 Stress(kPa)
160
(b) 3%SBS modified asphalt binder
Q(1/(kPa)2)
Q(1/(kPa)2)
(a) Neat asphalt binder
40
1E-6 1rad/s
1E-7
5rad/s
5rad/s
10rad/s
10rad/s
1E-8
1E-8 20
40
80 160 Stress (kPa)
320
(c) 5%SBS modified asphalt binder
20
40
80 160 Stress (kPa)
320
(d) 7%SBS modified asphalt binder
Fig. 5. Q ¼ I3 =I1 =r20 as a function of stress amplitude of the studied binders at various frequencies.
ening response of the material. Based on the convenxity of the third Chebyshev polynomial theory, all the studied binders will reveal stress softening and stress thinning under all the studied test conditions because both c3 and f3 are positive, as shown in Fig. 9. Besides, with increasing stress, both c3/c1 and f3/f1 increase from the overall trend.
Q0(1/(kPa)2)
1E-05
1E-06
1E-07
4. Conclusions
0
neat 3%SBS modified 5%SBS modified 7%SBS modified 5
10
Frequency (rad/s) Fig. 6. Q0 of the studied binders at various frequencies.
apparent plastic strain-rate vs shear stress curve. Conversely, negative values of c3 imply stress stiffening, while negative values of f3 imply stress thickening. By decomposing the elastic and viscous strain signal into the orthogonal set of Chebyshev polynomial, we may determine quantitatively the stress softening/stiffening and shear thinning/thick-
The effect of SBS concentration on rheological behaviors of asphalt binder was analyzed in depth for a wide range of stress levels to characterize the linear and nonlinear regimes of the bituminous material. The linear rheological behavior of neat asphalt binder and the corresponding SBS modified asphalt binders was studied by the master curves. And the nonlinear rheological behaviors of them were studied by FT-rheology method and strain decomposition method. The results show that the difference between storage modulus and loss modulus decreases with increase in SBS contents. And the phase angle also decreases with increase in SBS contents. For the nonlinear rheological bahaviour, the relative intensity of the nonlinear parameter of asphalt binder increases with the increase of stress and the decrease of frequency. The nonlinearity of the SBS modified asphalt binder is more obvious than that of the neat asphalt binder and increases with the increase of SBS contents. The relationship between I3/I1 and stress amplitude obeys a sig-
8
L. Shan et al. / Construction and Building Materials 231 (2020) 117076
1.5
1.5
JM'
1
JL'
0.5
Strain rate(s-1)
Strain(%)
1
0 -0.5 -1
ФM'
0.5 0
ФL'
-0.5 -1
-1.5 -1.5
-1
-0.5 0 0.5 Stress(kPa)
1
1.5
-1.5 -1.5
-1
-0.5
0
0.5
1
1.5
Stress(kPa)
Fig. 7. Schematic of the compliance and fluidity.
Fig. 8. Decomposition of shear strain into elastic and viscous part for the binders at 1 rad/s.
Table 2 The material parameters of the studied binders show in Fig. 8. Binder type
Stress level (kPa)
JM0 (Pa1)
JL0 (Pa1)
UM0 (Pas)1
UL0 (Pas)1
Neat asphalt
30 80 100 30 100 210 30 100 320 30 100 320
4.50E04 4.62E04 4.82E04 4.40E04 4.38E04 5.51E04 4.28E04 5.30E04 9.14E04 3.90E04 4.26E04 1.07E03
4.94E04 5.20E04 5.75E04 4.54E04 4.94E04 6.42E04 4.36E04 5.88E04 1.18E03 4.15E04 5.24E04 1.31E03
2.37E03 2.53E03 2.75E03 1.12E03 1.43E03 2.06E03 7.45E04 0.61E03 1.52E03 7.31E04 0.54E03 1.36E03
2.38E03 2.65E03 2.82E03 1.14E03 1.53E03 2.16E03 7.96E04 0.73E03 1.85E03 7.74E04 0.66E03 1.82E03
3%SBS modified asphalt
5%SBS modified asphalt
7%SBS modified asphalt
L. Shan et al. / Construction and Building Materials 231 (2020) 117076
9
Fig. 9. Relative third order elastic, c3/c1, and viscous, f3/f1 Chebyshev coefficients as a function of stress for the studied binders at different frequencies.
moidal function. The intrinsic nonlinearity Q0 decreases with the increase of frequency. The Q0 value of neat asphalt binder is less than that of SBS modified asphalt binder and increases with
increase in SBS contents at the same frequency, which also shows that the nonlinearity of modified asphalt binder is relatively more obvious than neat asphalt binder and increases with increase in
10
L. Shan et al. / Construction and Building Materials 231 (2020) 117076
SBS contents. The strain decomposition results show that all the studied binders present viscoelastic behavior under all the test conditions, and the nonlinearity increases with stress amplitude and SBS contents. The elastic compliance and fluidity results show that the binders soften with increase in stress level. After adding SBS polymer, it is hard for the binder to flow and the elastic proportion of binders increases. Analysis of the Chebyshev polynomial shows that all the studied binders exhibit stress softening and stress thinning under all the studied test conditions. In a word, the SBS could increase the nonlinearity and the elastic proportion of asphalt binder and decrease its fluidity. The nonlinear and linear measures of asphalt binder show similar results, but the nonlinear results could provide more and unique information compared with the linear results. This study has already showed that LAOS stress measurements can provide useful information to analyze the nonlinearity of modified asphalt binders. In the future study, more test conditions and different types of modified asphalt binders such as crumb rubber, EVA, graphene, etc. will be studied for futher figuring out the practical meaning of LAOS. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement This study was sponsored by the National Natural Science Foundation of China (51778195, 51978218, 51478153 and U1633201). References [1] B. Sengoz, G. Isikyakar, Evaluation of the properties and microstructure of SBS and EVA polymer modified bitumen, Constr. Build. Mater. 22 (2008) 1897– 1905. [2] A. Behnood, J. Olek, Rheological properties of asphalt binders modified with styrene-butadiene-styrene (SBS), ground tire rubber (GTR), or polyphosphoric acid (PPA), Constr. Build. Mater. 151 (2017) 464–478. [3] V. Selvavathi, V.A. Sekar, V. Sriram, et al., Modifications of bitumen by elastomer and reactive polymer- a comparative study, Petrol. Sci. Tech. 20 (5– 6) (2002) 535–547. [4] G. Polacco, S. Berlincioni, D. Biondi, J. Stastna, L. Zanzotto, Asphalt modification with different polyethylene-based polymers, Eur. Polym. J. 41 (2005) 2831– 2844. [5] A. Topal, M. Yilmaz, B.V. Kok, N. Kuloglu, B. Sengoz, Evaluation of Rheological and Image Properties of Styrene-Butadiene-Styrene and Ethylene-Vinyl Acetate Polymer Modified Bitumens, J. Appl. Polym. Sci. 122 (2011) 3122– 3132.
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