## 3 Results and Discussion
### Permanent Deformation Analysis of BRT Asphalt Pavement Structure  
The deformation of asphalt pavement includes creep deformation and elastic deformation. Permanent deformation is severe road distress that is mainly caused by creep deformation [49]. In this analysis, the strain hardening creep model as shown in Equations (1) and (2) was applied to simulate permanent deformation. The high-temperature season of Lanzhou was considered to last 100 days, and the atmospheric temperatures during one day being listed in Table 3. The transient temperature field for each day, as shown in Figure 6, was introduced into the model to calculate the permanent deformation of the asphalt pavement structure under the influence of BRT vehicles. Repeated loading of BRT vehicles was simulated by replacing moving loads with static loads [43], in which the vertical load was 0.733 MPa and the horizontal coefficient was 0.5. Figure 16 shows the number of times the BRT vehicles passed a certain station in a day. Assuming that repeated and single loading processes, which have the same cumulative time, are equivalent, the cumulative action time of the load at the various vehicle speeds can be calculated with Equation (9):  
\[t=\frac{0.36 NP}{n_{w}pBv} \tag{9}\]  
where \(t\) denotes the cumulative action time of wheel load (s), \(N\) denotes the number of wheel load actions, \(P\) denotes the axle load of the vehicle (kN), \(n_{w}\) denotes the number of wheels on the axle, \(p\) denotes the tire-ground stress (MPa), \(B\) denotes the tire grounding width (cm), and \(v\) denotes the speed of the vehicle (km/h). The permanent vertical deformations of the road surface after repeated loading at the different vehicle speeds are shown in Figure 17.  
Figure 17 shows that the surface of the road was deformed, including depression and uplift deformation, under the combined action of vertical and horizontal loads. The maximum depression deformation appeared in the center of the wheel stamp. Uplift deformation occurred on both sides of the wheel stamp, with the maximum value occurring at 0.135 m outside the wheel stamp. By adding the maximum values of depression and uplift deformation, the rut depth of the BRT asphalt pavement after 100 days of loading  
Figure 16: Number of times BRT vehicles pass analysis station in 1 day. during the high-temperature season could be obtained. After repeated loads at 10, 20, 30 and 40 km/h, the calculated rut depth was 7.5, 6.2, 5.5 and 5.1 mm, respectively. With the speed increased from 10 km/h to 40 km/h, the rut depth decreased by 32%. The range of calculated rut value is basically consistent with the rut depth of the Lanzhou BRT asphalt pavement structure after one year of repaving. The points in the pavement structure with the same horizontal position as the maximum values of depression and uplift deformation were defined as A and B, respectively. Figure 18 shows the variation in the permanent deformation at points A and B over time at different depths of the pavement. As shown in Figure 18, the development of permanent deformation was similar for different BRT speeds. Permanent deformation mainly occurred in the surface layers, and the deformation value below the base layer was close to 0. The development of permanent deformation during one day could be divided into 4 phases. Phase I was from 6:00 to 11:00. During this period, although the frequency of BRT vehicles gradually increased, the pavement temperature did not rise, and thus the deformation at each depth of the pavement increased slowly; compact depression deformation occurred. Phase II was from 11:00 to 14:00, with a rapid increase in asphalt pavement temperature as shown in Figure 6. The depression deformation at each depth of pavement obviously accelerated, and uplift deformation of the road surface began to appear. This showed that the asphalt mixture began to flow and rearrange under the comprehensive action of compressive stress and shear stress.