Analytical solution and distribution characteristics of mechanical response for elastic half-space body under hyperbolic paraboloid vertical load

In current asphalt pavement design methods, the wheel load is characterized by a cylindrical load. However, field measurements of the contact pressure of tyres show that the real spatial distribution of the pressure under heavy load could be better described with the hyperbolic paraboloid function. Therefore, based on the general solution of the asymmetric elastic layered theory, the general solution for an elastic half-space body subjected to an asymmetric vertical load was determined. Then considering the hyperbolic paraboloid loading boundary conditions for an elastic half-space body, the Hankel integral transform of load function was solved and the analytical solution presented. Finally, the relevant computer program was compiled and the analytical formula of pavement deflection was obtained. Compared with the mechanical response of an elastic half-space body subjected to a circular uniformly distributed load, significant differences in the field distributions of both stresses and displacements were noted. The first principal stress, first principal strain, and maximum of shear stress and deflection throughout the pavement structure clearly increased. It was also found that an asymmetric vertical load would aggravate the fracture and deformation failure potential of asphalt pavement.