Green's Function Solution of the Semi-Space with Double Shallow-Buried Cavities

Abstract

In mechanical engineering and modern municipal construction, shallow-buried cavity structure is used widely. In this paper, Green's Function is studied, which is the solution of displacement field for elastic semi-space with double shallow-buried cavities while bearing anti-plane harmonic line source force at any point. In the complex plane, considering the symmetry of SH-wave scattering , the displacement field aroused by the anti-plane harmonic line source force and the scattering displacement field impacted by the circle cavities comprised of Fourier-Bessel series with undetermined coefficients which satisfies the stress-free condition on the ground surface are constructed. Through applying the method of multi-polar coordinate system, the equations with unknown coefficients can be obtained by using the stress-free condition of the circle cavities in the radial direction. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. Green's function, that is, the total wave displacement field is the superposition of the displacement field aroused by the anti-plane harmonic line source force and the scattering displacement field. By using the expressions, an example is provided to show the effect of the change of relative location of the circle cavities and the location of the line source force. Based on this solution, the problem of interaction of double circular cavities and a linear crack in semi-space can be investigated further.