## 4 Results and Discussion
### Driving Stability Analysis on Multi-Factor  
#### 4.2.1 Analysis on Safety Requirement Based on Various Driving Conditions  
Figure 12 is the bar chart of the simulation results from case 1 to case 32, which presents the maximum LA, SA, LTR, and RA determined from 32 cases. From Figure 12a, it was found that the LAs were less than 0.4 g for all 32 cases, which did not exceed the safety threshold. As shown in Figure 12b, the SAs of cases 4, 11, 13, and 31 far exceeded the threshold value. These results caused the drift of the vehicle, thus leading to steering problems and large sideslips, whereas the SAs of other cases were within the threshold. From Figure 12c, it was found that all the LTRs were smaller than 1.0, presenting a high roll-over stability. However, the RAs in a large number of cases dramatically exceeded the threshold, showing high roll-over risks. Through contrastive analysis, it is known that the results of RAs were not consistent with that of LTRs, and the results of LAs were not in compliance with that of SAs, though they equally characterized the sideslip stability and roll-over stability.  
As mentioned in the results of cases 4, 11, 13, and 31, the SAs were 59.22\({}^{\circ}\), 23.98\({}^{\circ}\), 58.81\({}^{\circ}\), and 15.80\({}^{\circ}\), which far exceeded the threshold, resulting in a vehicle with a great tendency of swaying and slip. The common characteristic of the four cases was the extremely low friction coefficient of the road surface, which was as low as 0.18, regardless of other favorable factors. So, the considerable decrease in the friction coefficient, due to snowy weather, is the leading factor that gives rise to sideslip instability [62]. In terms of RAs, their values in cases 4, 8, 12, 16, 20, 24, 28, and 32 were far beyond the threshold, even reaching over 13\({}^{\circ}\). It was found that the WHRs of these cases were all equal to 5, with a rutting opening width of 1 m and a rutting depth of 4 cm. The loss of instantaneous stability, when driving across the ruts, made the vehicle susceptible to rolling over. So, the rutting condition can be accounted as a dominant factor that leads to the roll-over instability of the vehicle, which verifies the relevant vehicle dynamics simulations concerning pavement rutting [4, 5, 63].  
The worst dynamic response occurred in case 4, with super high SA and RA. In this case, the vehicle was considered to be in a completely unstable state, which showed high susceptibility to traffic accidents. The vehicle crossed a rut with a WHR equal to 5 under the poorest road alignment and weather conditions, even with relative low driving speed. Those conditions made the vehicle have insufficient resistance to lateral slip, so it had difficulties in quickly recovering back to a stable state after encountering a rut impact, resulting in a severe loss of control and continuous slip. So, it reveals that the composite effect of adverse weather and rutting conditions shows a high probability of causing the lateral instability of the vehicle. Limiting driving speed alone is still not an effective way to ensure driving safety. Instead, preventive measures on pavement maintenance are expected to be implemented.  
To determine the safety requirement of various driving conditions, it was demonstrated that dangerous results always occurred when the WHR = 5 or \(f\) = 0.18. However, several instability phenomena still happened, even solely increasing the WHR to 10 or increasing the \(f\) to 0.4. Thus, it can be deduced that multiple factors need to be controlled simultaneously. By comparing 32 cases in this study, the lateral stability of the vehicle is able to be guaranteed when the WHR is greater than 10 and the \(f\) is greater than 0.4, concurrently.