Dynamic response of an axisymmetric transversely isotropic medium with its modulus varying with depth subjected to LWD load

In this paper, the dynamic response of an axisymmetric transversely isotropic medium with its modulus varying with depth subjected to the lightweight deflectometer (LWD) load is calculated by an analytical solution method. In this model, the analytical solutions are expressed as power series, and both cases of vertical modulus, increasing and decreasing with depth, are considered. This study can be divided into three key steps. Firstly, the ordinary differential equations are obtained via the Hankel-Laplace transform, and the general solutions of dynamic response are obtained according to the Frobenius method. Secondly, combined with the boundary conditions, the dynamic responses of the subgrade in the time domain are calculated. The accuracy and reliability of this dynamic model are proved by parameter convergence analysis, finite element method and comparison validation. Lastly, the effect of thickness, non-uniform distribution of modulus and transverse isotropy subjected to LWD load are analysed and discussed. The calculation methods and the corresponding results are meaningful for the design and non-destructive monitoring of the subgrade.