Numerical modelling of resonance mechanisms in jointed rocks using transfer functions

Abstract

Resonance effects in parallel jointed rocks subject to stress waves are investigated using transfer functions, derived from signals generated through numerical modelling. Resonance is important for a range of engineering situations as it identifies the frequency of waves which will be favourably transmitted. Two different numerical methods are used for this study, adopting the finite difference method and the combined discrete element-finite difference method. The numerical models are validated by replicating results from previous studies. The two methods are found to behave similarly and show the same resonance effects; one operating at low frequency and the other operating at relatively high frequency. These resonance effects are interpreted in terms of simple physical systems and analytical equations are derived to predict the resonant frequencies of complex rock masses. Low frequency resonance is shown to be generated by a system synonymous with masses between springs, described as spring resonance, with an equal number of resonant frequencies as the number of blocks. High frequency resonance is generated through superposition of multiple reflected waves developing standing waves within intact blocks, described as superposition resonance. While resonance through superposition has previously been identified, resonance based on masses between springs has not been previously identified in jointed rocks. The findings of this study have implications for future analysis of multiple jointed rock masses, showing that a wave travelling through such materials can induce other modes of propagation of waves, i.e. spring resonance.

Keywords

• Resonance
• Jointed rocks
• Finite difference method
• Discrete element
• Transfer functions
• Wave propagation