横观各向同性黏弹性沥青路面动力响应解析解

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.