Abstract: Considering the physical and mechanical properties change continuously along the depth in non-homogeneous foundation, the linear transformative relationship is analyzed between the phase velocity and group velocity of the inhomogeneous elastic body waves and the solution of corresponding homogeneous elastic foundation. Firstly, based on the basic equations of elastodynamics, the analytical expressions for the phase velocity and group velocity of the planar elastic body waves in any non-uniformly changing foundation are obtained. Compared with the classical solution of the elastic wave phase velocity of the homogeneous foundation, it is found that the solution of the non-homogeneous foundation can be expressed linearly with the solution of the homogeneous foundation, thus the similarity conversion between the two solutions is obtained. At last, as a numerical example, considering the power law relationship of material properties change continuously along the thickness in the non-homogeneous foundation, the influence of foundation non-uniformity, Poisson's ratio and phase angle on the similarity conversion coefficients is analyzed. The calculation results show that, with the help of the classical solution of elastic wave velocity in homogeneous foundation, the solution of wave velocity in non-homogeneous foundation can be converted into the calculation of the similarity conversion coefficients, thereby simplifying the solution process.

Key words: non-homogeneous foundation, phase velocity, group velocity, analogous relationship, analytical solution