## 3 Analysis of Test Results
### Bostwick Rotary Viscosity Test  
The results of the Bostwick rotary viscosity test of asphalt mastic under the action of temperature and humidity coupling cycles at 135 \({}^{\circ}\)C, 145 \({}^{\circ}\)C, 155 \({}^{\circ}\)C, 165 \({}^{\circ}\)C, and 175 \({}^{\circ}\)C are shown in Figure 8.  
The results in Figure 8 show that the viscosity of the mastic increases with the number of cycles at the same test temperature. The increase in viscosity after temperature and humidity coupling cycles is more pronounced at lower test temperatures, and the increase in viscosity is smaller as the test temperature increases. The most significant change in the viscosity of the mastic occurs when cycling within the range of \(-20\)\({}^{\circ}\)C to 60 \({}^{\circ}\)C, and as the temperature difference in the cycling temperature range decreases, the increase in viscosity of the mastic decreases. This is because, after temperature and humidity coupling  
Figure 7: Ductility results of SBS-modified asphalt mastics under different conditions. cycles, the light components of SBS-modified asphalt mastic volatilize or transform into heavy components, increasing the proportion of heavy components, leading to increased intermolecular movement resistance within the mastic and resulting in increased viscosity. In temperature ranges with larger differences, the reaction rate is faster. The Arrhenius equation can be used to characterize the relationship between chemical reaction rates at different temperatures. SBS-modified asphalt mastic undergoes complex chemical reactions during temperature and humidity coupling cycles, causing viscosity changes. The reaction process of SBS-modified asphalt mastic during temperature and humidity coupling cycles can be characterized by establishing an Arrhenius equation with viscosity as a parameter. The Arrhenius equation reflects the relationship between the viscosity and temperature of SBS-modified asphalt mastic. \[\lg(\eta(T))=\lg(K)+\frac{E_{\eta}}{2.303 RT} \tag{2}\]  
In the above formula, \(\eta(T)\) is the viscosity at a temperature of \(T\), Pa-s; \(K\) is the material constant; \(R\) = 8.314 J/(mol-K), \(R\) is the Boltzmann constant; and \(E_{\eta}\) is the activation energy, J/mol. \(E_{\eta}\) refers to the minimum energy required for the flow units (i.e., molecular segments) of polymer materials to overcome barriers and transition from their original positions to nearby \"holes\" during the flow process. According to existing research [30; 31; 32], the activation energy \(E_{\eta}\) of asphalt mastic can characterize the ease of flow and temperature sensitivity of the mastic. By plotting \(\lg(\eta(T))\) and \(1/T\) according to Equation (2) and performing linear regression on the data, the slope of the resulting straight line, which represents \(E_{\eta}\), can be obtained. Refer to Table 4 for the results. Figure 8: Viscosity results of SBS-modified asphalt mastics under different conditions. As shown in the above table, under different temperature and humidity coupling cycle numbers, the relationship between \(lg(\eta(T))\) and \(I/T\) for the SBS-modified asphalt mastic can be expressed as a linear relationship with determination coefficients (R2) all greater than 0.990 and \(p\) values all less than 0.05. In different cycling temperature ranges, with the increase in temperature and humidity coupling cycle numbers, the \(E_{\eta}\) values all show an upward trend, but the magnitudes of such increases vary. The mastic \(E_{\eta}\) shows the largest increase when cycled within the \(-\)20 \({}^{\circ}\)C to 60 \({}^{\circ}\)C range, reaching 77.48 kJ/mol after 12 cycles, followed by a slightly lower increase when cycled within the \(-\)20 \({}^{\circ}\)C to 40 \({}^{\circ}\)C and 0 \({}^{\circ}\)C to 60 \({}^{\circ}\)C ranges, and the smallest increase is observed when cycled within the 0 \({}^{\circ}\)C to 40 \({}^{\circ}\)C range, with \(E_{\eta}\) reaching 76.05 kJ/mol after 12 cycles.