Modelling high-speed rail induced vibrations around tunnels (jointed rock masses)

This research studies the role of joints within rock masses on the transmission of stress waves. The motivation for this comes from vibrations generated by high speed trains running in tunnels, excavated in jointed rock masses. This will allow industrial partners to better understand how vibrations from high speed rail can impact receptors located close to a railway line. Based on this mitigation measures can be engineered to reduce their impact in the design phase of new railway lines or buildings close to railway lines. The combined discrete element – finite difference code in the software UDEC and the finite difference code in the software WAVE2D are used throughout this research to study jointed materials. Both software’s are modelled with explicitly jointed models as well as equivalent continuum models in order to understand how their effect on the transmission of stress waves through 1D and 2D models. In particular resonance effects in parallel jointed rocks subject to stress waves are investigated. This is undertaken using transfer functions, derived from signals generated by numerical modelling. Resonance is important for a range of engineering situations as it identifies the frequency of waves which are favourably transmitted through a material. The different numerical codes used are shown to be able to model jointed rock masses in similar ways showing two distinct resonance mechanisms, spring resonance and superposition resonance. Spring resonance implies that jointed materials oscillate like masses between springs, with joints acting as springs and blocks acting like masses. This occurs are relatively low frequency and is unrelated to the wave speed of a material. The superposition resonance shows that constructive interference can occur between reflected waves within jointed bounded blocks. This effect operates at higher frequencies that the spring resonance effects, typically allowing the two effects to be distinct within transfer functions. Equations are developed which can accurately predict the two resonance mechanisms identified in jointed materials. Using increasingly complex models, including 2D models and moving loads, the continuity of the resonance mechanisms are proved, showing that the resonance mechanisms first identified in highly simplified 1D models are not a consequence of the modelling assumptions. This indicates that the spring resonance effect will prevail in complex rock masses under a range of geological settings. The effects of the spring resonance mechanism operating within a range of realistic jointed rock masses are appraised in the context of vibrations from railway tunnels. It is shown that vibrations generated from train excitations are likely to be transmitted through all jointed rock masses, while sources from the track are less likely. The similarity of the spring resonance mechanism to the resonance characteristics of periodic metamaterials is appraised. It is shown that jointed materials can operate as a band-pass or low-pass filter, depending on the number of joints within the material. Evidence is presented showing that periodic metamaterials exhibit spring resonance with results from a laboratory scale frequency sweep test on a periodic metamaterial are shown to feature high transmission zones occurring at the predicted spring resonant frequency for that material. The outcomes of this work, especially the resonance mechanisms and associated analytical equations, can be used in industry to inform scoping studies as to the vibrations which will be preferentially transmitted from vibrational sources embedded in jointed rock masses. This is not limited to vibrations from high speed rail but it also applicable to vibrations from any manmade or natural source. With knowledge of the resonant frequencies of a rock mass, prior to operation of new vibrational source or construction of a new building which could be subject to vibrations, designs can be modified to limit the impact of such preferentially transmitted frequencies.