Equivalent material modelling of fractured rock mass resonance effects

• Published in: Expanding Underground - Knowledge and Passion to Make a Positive Impact on the World pp. 268 - 276
• Main Authors: Holmes, H.T., Paraskevopoulou, C., Hildyard, M., Neaupane, K., Connolly, D.P.
• Format: Book Chapter
• Language: English
• Published: United Kingdom CRC Press 2023; Taylor & Francis Group
• Edition: 1
• Subjects: Homogenous Equivalent Medium; Equivalent Medium; Equivalent Material; Geological Strength Index; FDM; Overburden; Finite Difference Mesh; Spring Resonance; Resonance Mechanisms; Velocity Time Series; Crack Density Parameter; BIM Model; Train Vibrations; Homogenous Equivalent Material; Discrete Fractured; Homogenous Equivalent; Resonance Effects; Crack Density; Higher Dimensional Scenario; Stress Waves; SEM; Discrete Fractured Model; SCL; Fractured Rock Masses; Vibrations Incident
• DOI: 10.1201/9781003348030-33

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. Resonance effects in parallel fractured rock masses are investigated using equivalent material models. Vibrations propagating through fractured rock masses are a subject area with a rich history. A numerical model is used to evaluate the effect of different equivalent material models on resonance effects. There is a model size related effect in the homogenous equivalent material model in its current form, as used by E. Parastatidis. Holmes et al. investigated resonance effects within parallel fractured rock masses, finding that there are two mechanisms which allow high transmission. These are superposition resonance and spring resonance. Transfer functions have been derived which show how the amplitude of different frequencies of waves transmitted through the model change. A localised equivalent material model has been shown to match closely with the response of a discrete fracture model, which gives scope to use more diverse models to predict such vibrations.