Equivalent material modelling of fractured rock mass resonance effects

Resonance effects in parallel fractured rock masses are investigated using equivalent material models. The mechanisms of spring resonance and superposition resonance are considered. Both of these resonance mechanisms give rise to resonant frequencies, which represent bands of high transmission. Three different representations of a fractured rock mass are adopted: discrete fractures using special elements in the finite difference mesh; a homogenous equivalent medium representing the weakening to the material caused by the fractures; and a localised equivalent medium applied in the vicinity of fractures. The models are excited by a wide-band source, the response measured and a transfer function generated from the results. Results are compared to the prediction of spring and superposition resonant frequencies calculated using analytical equations. It is found that the discrete and localised equivalent materials give similar results, which match the predictions from the analytical equations for both resonance mechanisms, while the equivalent homogenous medium does not show any resonance effects. Showing that this effect occurs in the appropriate equivalent material model helps future prediction of ground borne vibrations from underground sources, such as railway tunnels, as it gives a greater scope of models which can accurately model the propagation of stress waves through fractured rock masses.