Interaction of Multiple Semi-Cylindrical Gaps and a Shallow-Buried Cavity
In modern municipal construction and earthquake engineering, semi-cylindrical gap and shallow-buried cavity structure are used widely. In this paper, the solution of displacement field for elastic semi-space with multiple semi-cylindrical gaps and a shallow-buried cavity while bearing anti-plane harmonic line source force at any point is studied. 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 multiple semi-cylindrical gaps and a cylindrical cavity 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 gaps and the cylindrical cavity 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. 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 semi-cylindrical gaps , the cylindrical cavity and the location of the line source force. Based on this solution, the problem of interaction of multiple semi-cylindrical gaps , a cylindrical cavity and a linear crack in semi-space can be investigated further.
R. Zhang and H. L. Li, "Interaction of Multiple Semi-Cylindrical Gaps and a Shallow-Buried Cavity", Advanced Materials Research, Vols. 163-167, pp. 3910-3913, 2011