Jointed rock masses as metamaterials – Implications for railway tunnel vibrations

Abstract

Vibrations from underground railways are known to affect receptors located close to the tunnel. Understanding the transmission pathway between these tunnels and receptors is important in determining the magnitude of vibrations which can be transmitted. Rail tunnels can be excavated in a range of geological conditions, including jointed rock masses. Jointed rock masses have been found to display certain resonant characteristics, namely spring resonance. Therefore, this paper studies the resonant characteristics of jointed rock masses using a series of models solved using the combined discrete element-finite difference method and the finite difference method. Modelling assumptions are tested as well as different equivalent material models. It is found that spring resonances occur at the same frequencies as predicted by analytical functions when different modelling assumptions are used. This indicates that the spring resonance effect will prevail in complex rock masses under a range of geological settings. The spring resonance mechanism is found to cause jointed rock masses to behave like periodic metamaterials in respect to the transmission of stress waves, which can operate as a band-pass or low pass filter, depending on the number of joints within the material. New evidence is presented showing that periodic metamaterials exhibit spring resonance. Results for metamaterials in laboratory scale frequency sweep tests are shown to feature high transmission zones occurring at the predicted spring resonant frequency for that material. Finally, the effects of the spring resonance mechanism operating within the jointed rock masses are appraised in the context of vibrations from railway tunnels.