Modeling of random ground roughness effects by an effective impedance and application to time-domain methods

Natural grounds can exhibit small scale geometric irregularities, compared to the acoustic wavelength, known as ground roughness. This roughness has a noticeable effect on sound pressure levels and produces a surface wave. In the context of prediction methods improvement for outdoor sound propagation, using an effective impedance appears to be an useful approach to model the effects of surface roughness. Two time-domain numerical methods are considered: finite difference schemes (FDTD), and the transmission line modeling (TLM) method. An effective impedance model for random ground roughness defined by a roughness spectrum, called the SPM model, is exposed. The efficiency of this model for taking into account the mean effects of random roughness on sound pressure levels and for modeling the roughness-induced surface wave is shown, by comparing with results of TLM simulations of propagation above random rough grounds. The direct implementation of the SPM model as a boundary condition in both TLM and FDTD methods is then studied. This approach allows the modeling of ground roughness effects in numerical methods without having to mesh finely the ground roughness profile, allowing easier and faster computations, and more accurate predictions for future impact studies in environmental acoustics.