To reflect the characteristics of soil more accurately, an improved two-parameter foundation-plate model is built. A vehicle-road coupled model is modeled as a 2-DOF vehicle moving along a plate with finite length and width on a cubic nonlinear foundation. The variation of depth of elastic layer is modeled using sine wave. The Galerkin truncation method is used to discretize the partial differential equations into ordinary differential control equations. Using product to sum formula and introducing the Dirac delta function, the double integral term resulted from nonlinearity is removed. The effects of parameters from vehicle and foundation-plate on vehicle-road coupled model responses are studied. In addition, in order to analyze the influence of vehicle-road coupled vibration on crack propagation, initial cracks with certain length and width are set on the pavement. Using the J-integral Criterion of crack propagation, the stress intensity factors (SIF) of mode I and mode II cracks for mixed cracks are obtained through the stress on the discrete integral loop, and then the propagation path of surface crack of road is obtained. The propagation of the vehicle-road coupled model considering pavement crack, the vehicle-road coupled model without considering pavement crack and the traditional foundation-plate model are computed and compared. It can be found that the influence of vehicle-road coupled vibration for pavement crack can not be ignored. In short, the results presented in this paper realize the fast and accurate calculation of foundation-plate model described by ultra-high dimensional nonlinear ordinary differential equations, and then can realistically simulate the crack propagation path, which is helpful to better understand the cracking behavior of asphalt pavement.

为更准确地反映土体特性，建立了改进的二参数基础板模型。车辆-道路耦合模型被建模为在三次非线性基础上沿有限长和宽的板移动的 2-DOF 车辆。弹性层深度的变化使用正弦波建模。伽辽金截断法用于将偏微分方程离散为常微分控制方程。用乘积求和公式，引入狄拉克δ函数，去除非线性引起的二重积分项。研究了车辆和底板参数对车路耦合模型响应的影响。此外，为了分析车路耦合振动对裂纹扩展的影响，在路面上设置一定长度和宽度的初始裂缝。利用裂纹扩展的J积分判据，通过离散积分环上的应力得到混合裂纹I型和II型裂纹的应力强度因子（SIF），进而得到路面表面裂纹的扩展路径. 计算比较了考虑路面裂缝的车路耦合模型、不考虑路面裂缝的车路耦合模型和传统的基础板模型的传播情况。可以发现，车路耦合振动对路面裂缝的影响不容忽视。总之，本文提出的结果实现了超高维非线性常微分方程描述的基础板模型的快速准确计算，