*2.5. MANOVA*

The results of the orthogonal test are usually analyzed in two ways: direct-viewing analysis and analysis of variance (ANOVA). The direct-viewing analysis method is also called the range analysis method, which determines the primary and secondary relationships among the influencing factors by calculating the range of data and comparing its size. However, when the test results corresponding to different levels of a certain factor are different, the direct-viewing analysis method cannot distinguish whether this difference is caused by different levels of the factor or experimental errors. ANOVA can make up for the limitations of direct-viewing analysis and provide reliable analysis results [23]. ANOVA is usually used in the significance test for differences between two or more sample data, which is also known as *F* test or analysis of variability [24]. Generally, due to the influence of various factors, the data obtained from the test will fluctuate. ANOVA can be used to evaluate the volatility of the test data and the influence of various factors on the test results to find certain regularity. ANOVA for orthogonal test can be carried out by SPSS (Statistical Program for Social Sciences) data analysis tool.

Therefore, this paper uses ANOVA to analyze the results of orthogonal tests. The orthogonal test is a multi-factor and single-index test. The influencing factors are SBS content, sulfur content and rubber oil content. It is assumed that the effects of the three are independent of each other and there is no correlation. Thus, the multi-factor univariate ANOVA model with no interaction in SPSS is used to compare and analyze the test results of three factors and three levels. Multivariate analysis of variance (MANOVA) uses the *F* test, whose null hypothesis is H0: the observed variable values at different levels of each factor have no significant difference. SPSS will automatically calculate the F value and provide the corresponding probability *p* value according to the *F* distribution table. It can be judged whether the different levels of each factor have a significant influence on the observed variables by comparing the *p* value with the magnitude of the significance level *α*.

### **3. Results and Discussion**

### *3.1. Rheological Test Results*

### 3.1.1. Temperature Scanning Test Results

The temperature sweep test is carried out on different virgin SBS modified asphalt samples by DSR. The complex shear modulus *G\** and phase angle *δ* of three modified asphalt at multiple temperatures are measured to calculate the rutting factor *G*<sup>∗</sup>/*sinδ*. According to the test results, the curves of rutting factor *G*∗/*sinδ* with temperature under different SBS content are plotted, as shown in Figure 1.

**Figure 1.** Curves of rutting factor with temperature under different SBS content.

Figure 2 reflects the temperature curves of rutting factor *G*∗/*sinδ* of the three modified asphalt. With the increase of the modifier content, the *G*∗/*sinδ* value of the modified asphalt increases; and as the test temperature increases, the *G*∗/*sinδ* value tends to decrease. This means that the higher the SBS content, the lower the temperature, and the larger the value of *G*<sup>∗</sup>/*sinδ*, indicating that the asphalt is more elastic, the high-temperature flow deformation is smaller, the high-temperature performance is better, and the anti-rutting ability is stronger.

The high temperature performance index of modified asphalt increases with the increase of SBS content, indicating that the higher the SBS content, the better the high temperature performance of the modified asphalt. This is because SBS polymer and matrix asphalt are two completely different materials. SBS is dispersed as particulates in the matrix asphalt under mechanical force. With a different SBS content, SBS has a different distribution in the asphalt. When the SBS content is small, SBS is scattered as a dispersed phase in the continuous asphalt phase. When the SBS content is high, the SBS dispersed phase forms a network structure in the asphalt. If the SBS content is continuously increased, the asphalt will change phase. Therefore, the larger the content of SBS, the more uniform it is distributed in the asphalt. The formation of a three-dimensional network structure can well limit the movement of the entire molecular system of the modified asphalt at high temperature, thereby improving the high temperature performance of the asphalt.

**Figure 2.** Calibration curves of SBS content based on rutting factor.

According to the SBS content and the calculation results of rutting factor, the fitting curves of *G*∗/*sinδ* value and SBS content at different test temperatures can be drawn, taking 73 ◦C, 76 ◦C and 79 ◦C as examples, as shown in Figure 2. It is obvious that the rutting factor has a good linear relation with the SBS content at different temperatures, which can be used for the calibration of SBS content in modified asphalt. However, the good linear relation is related to temperature. The rutting factor increases linearly with the increase of SBS content at different temperatures, but its growth slope is significantly different. When using this result to determine the SBS content in the modified asphalt, the specific calibration curve at the actual temperature of the asphalt needs to be found. So, this method is not simple. In addition, there is another problem with the determination of SBS content in modified asphalt using a calibration curve based on the rutting factor: this method is susceptible to other modifiers in the asphalt. Due to the high market price of SBS, some modified asphalt manufacturers privately reduce the SBS content and add some cheap modifiers to reduce the cost for personal gain. This makes the rutting factor value of the produced SBS modified asphalt can also meet the requirements of the specification, but its road performance is unknown. In this case, the SBS content measured by the calibration curve based on the rutting factor is qualified with a quite different truth.

### 3.1.2. Bend Beam Rheometer Test Results

The creep stiffness modulus *S*, creep rate *m* of the matrix asphalt and the three modified asphalts in long-term aging were determined by bending beam rheometer at different test temperatures. The test results are recorded in Table 3.

According to the above test results, the linear fitting curves of the stiffness modulus *S* and the creep slope *m* with the SBS content at different test temperatures are plotted respectively, as shown in Figure 3. It is obvious that at −18 ◦C, the creep stiffness *S* of modified asphalt decreases with the increase of the SBS content, which indicates that as the SBS content increases, the asphalt becomes more elastic, more viscous and less brittle, and the resistance to deformation increases. At −12 ◦C, although the *S* value of modified asphalt is smaller than that of matrix asphalt, its variation with the SBS content is not stable. At the same time, the creep stiffness *m* value of modified asphalt is lower than that of matrix asphalt at both test temperatures, both decreasing with the increase of SBS content. Moreover, when the SBS content is the same, the lower the test temperature, the lower the *m* value, which means that with the decrease of temperature, the anti-deformation ability of the asphalt decreases, and the low temperature performance becomes worse.

**Table 3.** BBR test results.


**Figure 3.** Calibration curves of SBS content based on (**a**) stiffness modulus *S* and (**b**) creep slope *m*.

It can be seen from the figures that the linear fitting results of creep slope *m* with SBS content at both test temperatures are more precise. The stiffness modulus *S* and SBS content also have a good linear relation at −18 ◦C, but the linear fitting results at −12 ◦C are not accurate. This is because, as can be seen from Table 3 the stiffness modulus of the matrix asphalt has reached 125 MPa at −12 ◦C, which is not much different from that of the modified asphalt after the addition of 2% modifier. Therefore, the change of *S* value with the increase of the amount at −12 ◦C is not obvious. The fitting result of creep slope *m* with SBS content can be used to calibrate the SBS content in modified asphalt, but the good linear relation of the result is also related to temperature, which means the calibration curves differ at different temperatures. The problem with this method is also the same as the calibration method based on the rutting factor.

### *3.2. FTIR Test Results*

### 3.2.1. Analysis of FTIR Test Results

The infrared spectrum of each sample is obtained by scanning it with an infrared spectrometer. Figure 4 shows the infrared spectrum of matrix asphalt, SBS, rubber oil and SBS-modified asphalt in the wave number region between 500–1400 cm<sup>−</sup>1. Comparing the infrared spectrum of matrix asphalt and SBS modifier, it can be found that the methyl and methylene groups in matrix asphalt produce a characteristic absorption peak near 1377 cm<sup>−</sup>1, which is not affected by SBS modifier because SBS does not have this peak. The infrared spectrum of SBS has two strong absorption peaks, one is formed by the out-ofplane rocking vibration of C-H (polystyrene) in benzene ring at 699 cm<sup>−</sup>1, and the other is formed by the out-of-plane rocking vibration of trans-butadiene = CHC2 (polybutadiene) at 966 cm<sup>−</sup><sup>1</sup> [25].

**Figure 4.** Infrared spectrum of SBS, base asphalt, rubber oil and SBS modified asphalt.

Since the SBS modifier is physically compatible with matrix asphalt, the infrared spectrum of SBS-modified asphalt is a simple superposition of that of SBS and base asphalt, where no new peaks appear, or existing peaks disappear [13]. It can be seen from Figure 4 that the modified asphalt retains the SBS characteristic absorption peaks at 699 cm<sup>−</sup><sup>1</sup> and 966 cm<sup>−</sup>1, as well as a characteristic absorption peak of matrix asphalt at 1377 cm<sup>−</sup>1. The absorption peaks of modified asphalt at 699 cm<sup>−</sup><sup>1</sup> and 966 cm<sup>−</sup><sup>1</sup> can be used to judge the existence of SBS modifier, and the SBS content can be quantitatively analyzed according to the intensity of the absorption peak.

Figure 5 is the infrared spectrum of the modified asphalt with different SBS content. The peak area of the absorption peak at 699 cm<sup>−</sup><sup>1</sup> and 966 cm<sup>−</sup><sup>1</sup> has a certain relationship with SBS modifier content, and the intensity of the three absorption peaks does not affect each other. Therefore, the content of SBS modifier can be quantitatively analyzed based on the ratio of the absorption peak area at 699 cm<sup>−</sup>1, 966 cm<sup>−</sup><sup>1</sup> and 1377 cm<sup>−</sup><sup>1</sup> in the infrared spectrum of the modified asphalt.

The absorbance *A* is measured by spectral peak area. In this paper, the ratio of characteristic peak area at 699 cm<sup>−</sup><sup>1</sup> to that at 1377 cm<sup>−</sup><sup>1</sup> is *A*1, and the ratio of the peak area at 966 cm<sup>−</sup><sup>1</sup> to that at 1377 cm<sup>−</sup><sup>1</sup> is *A*2, i.e.,

$$A\_1 = \frac{peak\,\,area\,\,(intensity)\,\,at\,699\,\,\text{cm}^{-1}}{peak\,\,area\,\,(intensity)\,\,at\,1377\,\,\text{cm}^{-1}}$$

$$A\_2 = \frac{peak\,\,area\,\,(intensity)\,\,at\,966\,\,\text{cm}^{-1}}{peak\,\,area\,\,(intensity)\,\,at\,1377\,\,\text{cm}^{-1}}$$

Without any other additives, two kinds of base asphalt (SK70# and Zhongshiyou asphalt) are used to respectively prepare SBS-modified asphalt with the SBS content of 2%, 4% and 6%. Five sets of parallel tests were conducted for each content. By using the OMNIC software reading tool to read the absorbance value the infrared spectrum of these two modified asphalt groups and the two kinds of matrix asphalt is determined. The standard curves of characteristic absorption peak area ratio *A*1, *A*2 and SBS content are drawn, as shown in Figure 6.

**Figure 5.** Infrared spectrum of SBS modified asphalt with different SBS content.

**Figure 6.** Standard curves of *A* value with SBS content at different absorbance (**a**) 699 cm<sup>−</sup><sup>1</sup> and (**b**) 966 cm<sup>−</sup>1.

Regardless of the type of matrix asphalt, the *A*1 and *A*2 values at 699 cm<sup>−</sup><sup>1</sup> and 966 cm<sup>−</sup><sup>1</sup> also increase with the increase of SBS content. The *A* value has a good linear relation with the SBS content, and the correlation coefficient is very close to 1, it is consistent with the results of existing studies [16,17]. Both the *A*1 and *A*2 values can be used as the basis for determining the SBS content in modified asphalt with the correlation not being affected by the type of matrix asphalt. However, the standard equations of the two kinds of base asphalt are quite different, so the original matrix asphalt must be obtained when using this method to determine SBS content, and it cannot be replaced by matrix asphalt of different sources.

#### 3.2.2. Analysis Impact of Additives Based on Orthogonal Test

According to the orthogonality table, nine kinds of modified asphalt are prepared by 0.0%, 0.1%, 0.2% sulfur combined with 0%, 2%, 4% rubber oil. Five parallel samples are prepared for each kind of modified asphalt. FTIR test is carried out on each sample, reading the corresponding absorption peak areas and calculating the infrared spectrum *A* value as a test index. The test plan is listed in Table 4.



Taking *A*1 and *A*2 values as the test indexes, MANOVA is conducted on the orthogonal test results respectively using SPSS21.0, which adopts the system default significance level α = 0.05. The results of MANOVA are listed in Tables 5 and 6, which show the calibration model test in ANOVA. The original hypothesis is that the SBS content, sulfur content and rubber oil content in the model have no effect on *A* value that is the test index. If the probability *p* value is less than the significance level α, it means that the variance model is statistically significant, that is, at least one of the three influencing factors has a significant influence on the *A* value.

**Table 5.** Inter-subject effect test of three factors.


a. R<sup>2</sup> = 0.956 (Adjusted R<sup>2</sup> = 0.949), Dependent Variable: *A*1 Value (699 cm<sup>−</sup>1).

**Table 6.** Inter-subject effect test of three factors.


a. R<sup>2</sup> = 0.964 (Adjusted R<sup>2</sup> = 0.959), Dependent Variable: *A*2 Value (966 cm<sup>−</sup>1).

### 1. *A*1 value as the test index

Comparing the *p* value with the significance level α = 0.05, it can be known whether each factor has a significant influence on the observation results, while the comparison of *F* value shows the influencing degree of each factor. It can be seen from Table 5 that the *p* values of SBS content, sulfur content and rubber oil content are much smaller than the significance level α, indicating that these three factors have significant influence on the infrared spectrum absorbance *A*1 value. However, it's quite different from the influencing

degree of the three factors. Table 5 showed *F*B > *F*C > *<sup>F</sup>*D, the *F* value of SBS content is 376.333, which is much larger than that of sulfur and rubber oil content, and the *F* value of sulfur content is also larger than that of rubber oil content. It indicates that the most influential factor for the absorbance *A*1 value is the SBS content, followed by sulfur content and rubber oil content.

### 2. *A*2 value as the test index

Similarly, as can be seen from the results of MANOVA in Table 6, for the absorbance *A*2 value, the probability *p* values of SBS content, sulfur content and rubber oil content are all close to 0, all significantly less than the significance level α = 0.05, which means all these three factors have significant influence on the *A*2 value. According to the critical value of the 3-factor significance level α = 0.05 for the 2 degrees of freedom is *<sup>F</sup>*(2,3)0.05 = 19.164, Table showed *F*sbs = 441.598 > *<sup>F</sup>*(2,3)0.05, *F*sulfur = 33.542 > *<sup>F</sup>*(2,3)0.05, *F*rubber oil = 9.867 < *<sup>F</sup>*(2,3)0.05. Moreover, comparing the *F* values of the three factors, it is found that the *F* value of SBS content is much larger than that of sulfur content and rubber oil content, and the *F* value of sulfur content is also larger than that of rubber oil content. This means that the influence of these three factors on the absorbance *A*2 value is different, which is the same as the case where the *A*1 value is the test index. In order of their effect, SBS content is the largest, sulfur content followed, and rubber oil content is the smallest. Furthermore, Using SPSS to remove the effects of other variables, the marginal mean was estimated at different levels of each factor and was shown in Figure 7. Figure 7 illustrated that the A2 increased when the content of SBS and rubber oil increased, but reduced when the content of sulfur increased. Therefore, at the significance level α = 0.05, the three factors of SBS content, sulfur content and rubber oil content have significant influence on the *A*1 and *A*2 values, which are the characteristic peak area ratios of SBS-modified asphalt at 669 cm<sup>−</sup><sup>1</sup> and 966 cm<sup>−</sup><sup>1</sup> in the infrared spectrum. The influencing degree is both: SBS content > sulfur content > rubber oil content. This means under different SBS content, the addition of sulfur and rubber oil will have a significant effect on the accuracy of FTIR test results, and the influencing degree of sulfur is greater than that of rubber oil. The reason may be that the rubber oil added to the modified asphalt promotes the cross-linking of SBS polymer without changing the characteristic functional groups in SBS. However, after the addition of sulfur, the double bond of polybutadiene block in the SBS polymer reacts with the hetero atom in asphalt to form SBS-asphalt grafts, which changes the characteristic functional groups in SBS, thereby affecting the magnitude of *A* value. Therefore, the method of rapidly determining the SBS content in modified asphalt by infrared spectroscopy needs to be further improved.

**Figure 7.** Marginal mean of all three factors.
