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

Numerical modelling of resonance mechanisms in jointed rocks using transfer functions

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

Landslide susceptibility mapping at VAZ watershed (Iran) using an artificial neural network model: a comparison between multilayer perceptron (MLP) and radial basic function (RBF) algorithms

Landslide susceptibility and hazard assessments are the most important steps in landslide risk mapping. The main objective of this study was to investigate and compare the results of two artificial neural network (ANN) algorithms, i.e., multilayer perceptron (MLP) and radial basic function (RBF) for spatial prediction of landslide susceptibility in Vaz Watershed, Iran. At first, landslide locations were identified by aerial photographs and field surveys, and a total of 136 landside locations were constructed from various sources. Then the landslide inventory map was randomly split into a training dataset 70 % (95 landslide locations) for training the ANN model and the remaining 30 % (41 landslides locations) was used for validation purpose. Nine landslide conditioning factors such as slope, slope aspect, altitude, land use, lithology, distance from rivers, distance from roads, distance from faults, and rainfall were constructed in geographical information system. In this study, both MLP and RBF algorithms were used in artificial neural network model. The results showed that MLP with Broyden–Fletcher–Goldfarb–Shanno learning algorithm is more efficient than RBF in landslide susceptibility mapping for the study area. Finally the landslide susceptibility maps were validated using the validation data (i.e., 30 % landslide location data that was not used during the model construction) using area under the curve (AUC) method. The success rate curve showed that the area under the curve for RBF and MLP was 0.9085 (90.85 %) and 0.9193 (91.93 %) accuracy, respectively. Similarly, the validation result showed that the area under the curve for MLP and RBF models were 0.881 (88.1 %) and 0.8724 (87.24 %), respectively. The results of this study showed that landslide susceptibility mapping in the Vaz Watershed of Iran using the ANN approach is viable and can be used for land use planning

Jointed rock masses as metamaterials – Implications for railway tunnel vibrations

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