横观各向同性黏弹性沥青路面动力响应解析解

主要推导三向移动荷载作用下考虑复杂层间接触状态的横观各向同性黏弹性沥青路面动力响应解析解。首先，从直角坐标系下横观各向同性黏弹性多层体系动力学问题的基本方程出发，借助相对坐标变换和Fourier变换，推导单层沿深度方向的波数域状态向量传递矩阵；其次，基于波传递方法，构造层顶下行波和层底上行波向量，以消除传递矩阵中的正指数项，保证数值计算的稳定性；而后，基于Goodman模型表征的层间接触条件，建立相邻层上、下行波向量的递归关系，并结合荷载和边界条件，对多层体系各层上、下行波向量进行求解；最后，通过Fourier逆变换和相对坐标逆变换，得到沥青路面任意坐标和时刻下的动力响应解析解，并编制数值计算程序。通过ABAQUS有限元模拟，验证了解析解的准确性，且证明了解析解的计算效率远优于有限元模拟；综合分析荷载、材料、层间接触对沥青路面动力响应的影响，可以发现：水平向荷载与路表剪应力关联性强，是导致路面Top-down开裂的重要因素；层间接触条件和横观各向同性均对面层底部水平向应变影响显著，且这2个因素之间存在耦合效应，建议在路面疲劳寿命分析中予以充分考虑。研究得到的解析解可为真实沥青路面力学行为研究提供高效准确的分析工具。

Analytical Solution for Dynamic Response of Transversely Isotropic Viscoelastic Asphalt Pavement

This study derives an analytical solution for the dynamic response of transversely isotropic viscoelastic asphalt pavement with complex interlayer bonding conditions subjected to three-directional moving loads. First, the basic equations for the dynamic problem of a transversely isotropic viscoelastic multilayer medium in the Cartesian coordinate system were considered, and the transfer matrix of the state vector in the wavenumber domain along the depth direction for a given layer was derived using the relative-coordinate and Fourier transforms. Second, according to the wave propagation approach, the positive exponential terms in the transfer matrix were eliminated by constructing down-going wave vector at the top of the layer and up-coming wave vector at the bottom of the layer. This process could guarantee stability of the numerical calculation. Then, the interlayer bonding conditions were characterized using the Goodman model, and the recursive relationship between the up-coming and down-going wave vectors of the adjacent layers was established. By combining the load and boundary conditions, the up-coming and down-going wave vectors in each layer could be solved. Finally, using the inverse Fourier and relative-coordinate transforms, the analytical solution for the dynamic response of the asphalt pavement at arbitrary coordinates and time could be obtained. A numerical calculation program was compiled. The accuracy of the analytical solution was verified by finite-element simulation based on the ABAQUS platform. The computational efficiency of the analytical solution is proven to be significantly better than that of the finite-element simulation. By analyzing the effects of the load, material, and interlayer bonding condition on the dynamic response of the asphalt pavement, the horizontal load is determined to be significantly related to the surface shear stress, which is a key factor that leads to the top-down cracking of the pavement. Both the interlayer bonding conditions and transverse isotropy significantly affect the horizontal strains at the bottom of the surface course, and a coupling effect exists between these two factors. Thus, they should be fully considered in the analysis of pavement fatigue life. The analytical solution proposed in this study can provide an efficient and accurate analysis tool for the study of realistic asphalt pavement mechanical behavior.