# Dynamic Response Analysis of Asphalt Pavement under Pavement-Unevenness Excitation
## 4 Numerical Results  
### Example Verification  
Since the mechanical response of asphalt pavement under pavement-unevenness excitation is solved from two independent systems, the accuracy of the results in this paper will be verified from the vehicle system and the road-surface system. In order to verify the correctness of the results of the vehicle load with maneuvering, the random load of the left-front wheel of the vehicle-simulation model established in the literature [34] was selected as a reference in this section, and the dynamic load coefficient was used as an analysis index to evaluate the vehicle load with maneuvering. The expression of the dynamic load coefficient \(DLC\) is as follows:  
\[DLC=1+\frac{\sigma_{F}}{G} \tag{57}\]  
In the above formula, \(F\) is the vehicle load with mobility, \(G\) is the vehicle static load, and \(\sigma_{F}\) is the root mean square of \((F-G)\); i.e.,  
\[\sigma_{F}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(F-G\right)_{i}^{2}} \tag{58}\]  
According to the vehicle parameters in the literature, the dynamic load coefficient of the vehicle driving at 16.7 m/s on the A-D grade road surface was calculated; the dynamic load coefficient results were compared with those calculated in the literature [34] and the simulation model, and the calculation results are shown in Figure 3.  
As can be seen from Figure 3, the vehicle dynamic load coefficient solved by the simulation model established in this paper can achieve good consistency with the simulation results in the literature, and there is a small error, but the error of both is within the allowable range. Therefore, the correctness of the simulated vehicle loading method adopted in this chapter is verified. In order to verify the correctness of the pavement response under dynamic load in this paper, firstly, the load is degraded into static load (\(\omega_{l}\) approaches 0), and then the three-layer pavement structure layer is calculated. Each layer of the pavement is composed of isotropic materials, the contact condition between the layers is completely continuous, and the bottom soil foundation is an elastic half-space. The pavement parameters are selected from the reference [30]. The calculated results are compared with BISAR, a pavement structure design software. It can be clearly seen from Figure 4 that the results of displacement \(u_{z}\), stress \(\sigma_{zz}\), and BISAR in this paper are in good agreement with slight errors, but the errors of both are within the allowable range, which verifies the correctness of the method in this paper. After comparing the proposed method with the calculated results of BISAR, the pavement structure is compared with the analytical results of [PERSON] et al. [30] to calculate the displacements of multiple horizontal positions on the road surface, and the results are shown in Figure 5.  
Figure 4: Comparison of results between this paper and BISAR. (**a**) surface \(u_{z}\); (**b**) surface \(\sigma\)zz. Figure 3: Comparison of the simulation model in this paper with simulation results in the literature. As can be seen from Figure 5, the results obtained in this paper are basically consistent with those obtained by [PERSON] et al. The error is less than 4%, and with the increase in horizontal distance, the error becomes smaller, which verifies the correctness of the proposed method. The second example is selected below to further illustrate the correctness of the calculated results of this method. The random load of the vehicle is degraded into a single harmonic load, and the pavement is composed of four layers. The basic parameters of the pavement structure reference [35] are shown in Table 1. The applied load on the surface of the asphalt pavement is 0.7 MPa circular load, the applied radius \(R\) = 0.15 m, the frequency range is 5 to 65 Hz, and the increment is 5 Hz.