Coupled integral equations for sound propagation above a hard ground surface with trench cuttings

A set of coupled integral equations is formulated for the investigation of sound propagation from an infinitesimal harmonic line source above a hard ground surface corrugated with cuttings. Two half-space Green's functions are employed in the formulation. The first one defined for the upper half space is used to reduce the problem size and eliminate the edge effect resulting from the boundary truncation; the other one for the lower half space is to simplify the representation of the Neumann-Dirichlet map. As a result, the unknowns are only distributed over the corrugated part of the surface, which leads to substantial reduction in the size of the final linear system. The computational complexity of the Neumann-Dirichlet map is also reduced. The method is used to analyze the behavior of sound propagation above textured surfaces the impedance of which is expectedly altered. The effects of number and opening of trench cuttings, and the effect of source height are investigated. The conclusions drawn can be used for reference in a practical problem of mitigating gun blast noise.