**2. Experimental**

### *2.1. Temperature Scanning Test by Dynamic Shear Rheometer*

The DSR (Dynamic Shear Rheometer) can be used to measure the complex shear modulus (*G\**) and phase angle (*δ*) of the asphalt binder at multiple temperatures to characterize the viscoelastic characteristics of the asphalt materials. At the same time, the rutting factor ( *G*∗/*sinδ*) is calculated and used as the main index to evaluate the high temperature performance of asphalt. The complex shear modulus (*G\**) can be considered to measure the total resistance to deformation of the asphalt when it is repeatedly sheared [18]. The higher the temperature, the smaller the complex shear modulus (*G\**) and the worse the anti-deforming capability of the asphalt. The phase angle (*δ*) is defined as the ratio of the time of strain hysteresis stress to the corresponding stress cycle in a loading cycle. It can be used to characterize the sensitivity of asphalt binders under certain temperature as environmental conditions change. The smaller the phase angle (*δ*), the more elastic the material. When *δ* = 0 ◦ , the material is purely elastic; and When *δ* = 90◦ , the material is purely viscous [18].

### *2.2. Bending Beam Rheometer Test*

A BBR test was employed to characterize the low-temperature performance of SBS modified asphalt in all combinations according to ASTM D6648. The test temperature was −12, −18 ◦C and the average results of three replicates were used as the testing results. Creep stiffness modulus (*S*) and creep rate (m-value) was employed to characterize the low temperature performance. The greater the creep stiffness modulus *S* value, the more elastic, less viscous and more brittle the asphalt, and the worse the low temperature resistance to deformation. The larger the creep slope *m* value, the stronger the anti-deformation ability of the asphalt and the better the low temperature performance [19,20].

### *2.3. Infrared Spectroscopic Analysis*

The content of SBS in modified asphalt is quantitatively detected by infrared spectroscopy. As literature indicates, when continuous infrared light is irradiated on the material, the energy level transition occurs in the material molecules, and the substance absorbs infrared light of a specific wavelength to obtain a graph showing changes in absorbance at different wavelengths, which is an infrared spectrum. Its molecular structure is reflected by the infrared spectrum, thereby identifying heteroatom compounds in the asphalt and functional groups of SBS [17,21].

Generally, in the SBS modified asphalt, the base asphalt and the SBS modifier are physically mixed without chemical reaction, so the functional groups of the two do not disappear or add. In the modified asphalt, the vibration frequency of the SBS polymer molecules and the matrix asphalt molecules after infrared light irradiation is different, and the wavelengths of the infrared light absorption are also different, so the positions of the absorption peaks displayed on the infrared spectrum differ. For the modified asphalt with different SBS content, although the absorption peaks positions of the SBS polymer molecules and the matrix asphalt molecules are roughly the same in the infrared spectrum, their absorbance is not the same. Therefore, by comparing the absorption peaks of matrix asphalt and modified asphalt in the infrared spectrum, the existence of SBS modifier can be qualitatively identified and the content of modifier can be quantitatively analyzed [22].

Fourier infrared spectroscopy is based on Lambert-Beer law to achieve quantitative analysis of SBS modifier in modified asphalt as shown in Equation (1). Lambert-Beer law is that when a beam of light penetrates a sample of material, the absorbance at a certain wavenumber (*v*) is related to the concentration and the optical path length of the material sample, i.e.,

$$A(v) = \lg\left(\frac{1}{T(v)}\right) = a(v)bc\tag{1}$$

where: *<sup>A</sup>*(*v*) is the absorption intensity (absorbance) at wavenumber *v*, *<sup>T</sup>*(*v*) is the transmittance at wavenumber *v*, *a*(*v*) is the absorbance coefficient at wavenumber *v*, is the optical path length (the thickness of the sample, mm), is the concentration of the material sample (%).

Therefore, under the same test conditions, the characteristic absorption peak area ratio of SBS has linear relation with its content. The absorption peak area is selected as the characterization of absorption intensity in the infrared test. Infrared spectroscopy tests are carried out on a series of modified asphalt samples with known SBS content to establish a calibration curve of characteristic absorption peak area ratio and SBS content. By measuring the ratio of characteristic peak areas of SBS modified asphalt under the same test conditions the SBS content can be determined according to this calibration curve.

In order to establish the calibration curve of different SBS content, the matrix asphalt, SBS modifier and different modified asphalt samples with the SBS content of 2%, 4%, 6% are completely dissolved in tetrahydrofuran and titrated to KBr tablets. These tablets are placed in an oven at 60 ◦C for 20 min, and the infrared spectrum samples are prepared after the solvent is completely evaporated. By scanning each sample with an infrared spectrometer, the infrared spectrum is obtained. The spectral acquisition interval is 366~4000 cm<sup>−</sup><sup>1</sup> and the resolution is 2 cm<sup>−</sup>1.

### *2.4. Orthogonal Experimental Design*

Three factors including SBS, rubber oil and sulfur, which could influence the testing index of infrared spectroscopy, are considered in this paper. Each factor includes three levels of content, which are listed in Table 1. The properties of SBS-modified asphalt and base asphalt are listed in Table 2. Orthogonal tests can be used for multi-factor and multilevel tests. The orthogonal test is based on the orthogonality to select some representative points from the comprehensive test. These representative points have the characteristics of uniformity, dispersion and comparability, which can analyze the comprehensive influence of multiple factors with a small amount of test. It can reduce the number of tests, shorten the test period, and then improve the test efficiency. Therefore, for the case where there are many influencing factors and levels in this subject, the orthogonal test can not only reduce the number of tests, but also make the testing results intuitive and easy to analyze, which is of high rationality.

**Table 1.** Levels of different factors.


**Table 2.** Properties of Asphalt.


Three factors and three levels are involved in this study. Due to the repeated tests, the L9 (33) orthogonality table without blank columns can be used for the sake of simplicity. If the three-factor and three-level tests are carried out in accordance with the requirements of comprehensive test, 33 = 27 combinations of tests must be carried out, and the parallel tests of each combination have not been considered. However, if the test is arranged according to the L9 (33) orthogonality table, only 9 rounds of tests need to be carried out, obviously reducing the workload. The factor level table is listed in Table 1.
