## 4 Numerical Results and Discussion
### Comprehensive Influence of the Amplitude, Speed and VCVP on Operation Safety  
At present, the maximum operating speed of high-speed railways in China has reached 350 km/h, and research is undergoing to develop the technology for an operating speed above 350 km/h. Using the method of the impact of infrastructure disruption on the vehicle operating safety based on the stochastic analysis in this paper, taking the example of 10 m as harmonic irregularity wavelength and 2-120 m as stochastic irregularity wavelength, calculating different VCVP and the amplitude of different harmonic irregularity when the operating speed was in the range of 350-450 km/h, we obtained the calculation results of reliability shown in Figure 17.  
Figure 16: Relationship between variation coefficients of the vehicle parameters and wheel load reduction rate. Figure 17: _Cont._  
Figure 15: Overload probability of the reduction rate of wheel load for different variation coefficients. As can be seen in Figure 17, the stochasticity of the vehicle parameters is a factor that must be considered in the stochastic analysis of vehicle-track-bridge coupled dynamics. Figure 17: Reliability of vehicle vertical safety with different deformation amplitudes and different VCVP. The reliability of vehicle vertical safety decreases gradually with the increase of vehicle operation speed, irregularity amplitude, and VCVP. It can be observed in the figures that at the speeds of 400 km/h, 425 km/h, 450 km/h, the degree of influence on the reliability of vehicle vertical safety was higher with respect to the change of track irregularity amplitude than with respect to the change of VCVP. In contrast, when the operation speed was not less than 425 km/h and the amplitude of the foundation settlement was greater than 10 mm, the variation coefficient of the vehicle parameters might increase, as well as the reliability of vehicle vertical safety, which may due to the fact that the vehicle parameters could be optimized at high operation speed. In addition, at an operation speed higher than 375 km/h, when the irregularity amplitude caused by foundation deformation is greater than 6 mm, the attenuation of reliability increased; so, in the construction of high-speed railways and their maintenance and reparation, it is important to ensure that the irregularity amplitude caused by foundation deformation is less than 6 mm. Because of the lack of research on vehicle parameters stochasticity and their distribution, a quantitative analysis per se is still difficulty, and in the case of large variation coefficients, the vehicle needs maintenance; so in this paper, only Table 2 lists the different settlement amplitudes when the VCVP was not considered. Table 3 lists the different settlement amplitudes of the reliability of vehicle vertical safety when the VCVP was 0.1. Considering Figure 17 together with Tables 2 and  
1. The vertical acceleration at the center plate and the dynamic reduction rate of wheel load under the influence of different foundation deformation amplitudes were calculated. Compared with the limit of 0.13 g of the vertical acceleration, the limit of 0.8 of the reduction rate of wheel load is more strict. 2. From the point of view of reliability, settlement is more harmful to vehicle safety than up-arch. In the case of a wavelength of 10 m, the amplitude is 12 mm, VCVP is 0, and the operation speed is 350 km/h; the reliability of operation safety in settlement compared to the up-arch was reduced by 0.0293, corresponding to about 3.02%. With the increase of VCVP, the influence of settlement was more significant. 3. The stochasticity of the vehicle parameters has a non-negligible impact on the vehicle vertical safety, and the increase of the dispersion of vehicle parameters will gradually reduce the safety of vehicle operation. Regardless of the influence of the stochasticity of the vehicle parameters (speed 350 km/h), a deformation amplitude of 10 mm will not affect the reliability of operation safety.