# Dynamic Response Analysis of Asphalt Pavement under Pavement-Unevenness Excitation
## 1 Introduction
[20] further improved the vehicle-road coupling model, simplified the pavement unevenness into a sinusoidal road surface and the vehicle into a seven-degree-of-freedom vehicle model, and studied the thin-plate problem on linear elastic and viscoelastic foundation successively. [PERSON] et al. [21] proposed an iterative solution method for the vehicle-road coupling system based on a quarter vehicle and Timoshenko beam, which can quickly solve the vehicle-road coupling system. In the above sequential decoupling or coupling analysis of vehicle-pavement interaction, the main pavement model used is a beam or plate on an elastic foundation, which is particularly suitable for studying the response of cement pavement. For asphalt pavement, the common pavement model regards it as a multilayer elastic system, which can better reflect the actual structure of asphalt pavement. Although there are many analytical methods for the mechanical response of multilayer elastic asphalt pavement under dynamic load, there are relatively few analytical solutions considering vehicle loads. Most scholars mainly use the finite-element method for simulation analysis to solve the mechanical response of asphalt pavement under vehicle loads. [PERSON] et al. [22] proposed a classification method for road unevenness based on power spectral density, considering the stochastic longitudinal road irregularity classification scheme, the road waviness and vehicle response, and both the vehicle vibration response and the wide-road waviness interval (road elevation, PSD slope). Based on the one-quarter vehicle vibration model, [PERSON] et al. [23] used Simulink software (R2015a) to simulate the maneuverable load of vehicles on the road surface and then established a finite-element analysis model of semi-rigid asphalt pavement to obtain the mechanical response of the road surface under maneuverable load. [PERSON] et al. [24] used ANSYS (R18.0) to build a finite-element model of asphalt pavement. Based on MATLAB (R2018a), the dynamic response of the pavement was obtained when the vehicle load was applied to the model, and the influence of vehicle speed and load amplitude on the pavement was discussed. [PERSON] et al. (2018) established a vehicle model to obtain vehicle dynamic load and then established a three-dimensional finite-element model to evaluate the road response under harmonic excitation. [PERSON] et al. (2018) summarized smoothness specifications in the United States and various countries around the world and provided an overview of the comparison of smoothness measurement. The smoothness measuring devices, indices, limits, and payment schemes vary from country to country. The International Roughness Index is the most used smoothness index in the US and around the world. Inertial profilers are used to measure the pavement profile for smoothness. [PERSON] et al. (2018) used the vehicle model to solve the tire load caused by different roughness of the road surface and used the three-dimensional finite-element (FE) model to simulate the pavement response under dynamic load with non-uniform tire contact stress. The results showed that the position of rougher pavement would cause greater pavement response and accelerate pavement failure. [PERSON] et al. (2018) developed a finite-element model of tire-pavement interaction to study the effect of pavement unevenness on the mechanical response of asphalt pavement. The results show that the pavement irregularity significantly affects the mechanical response of the asphalt pavement, thereby affecting the service life of the asphalt pavement. Although the finite-element method can consider complex mechanical problems and explain the actual vehicle-pavement interaction mechanism, the finite-element method has the disadvantages of large computational cost, long calculation time, and non-convergence of results, and the analytical method is still a favored and efficient method. Recently, based on the exact-integration method and the dual-vector technique, [PERSON] et al.