Marc Elmouttie

A Method to Estimate In Situ Block Size Distribution

This paper presents a new technique for estimating the in situ block size distribution in a jointed rock mass. The technique is based on Monte Carlo simulations using more realistic fracture geometry as its input compared to other block size estimation methods described in the literature. This geometry represents fractures as either polygons or triangulated surfaces and therefore models persistence and truncation of fractures accurately. Persistence has been shown to be critically important for the accurate prediction of block size and shape. We show that for rock masses with relatively small discontinuities, the results of our predictions differ markedly from previous methods which over-predict fragmentation.

Stochastic Representation of Sedimentary Geology

Discrete fracture network representations of discontinuities in rock masses have been shown to be useful in capturing heterogeneity in rock mass properties. Providing computational efficiency in the resulting simulations and analyses is attained, these fracture representations can be combined with structural modelling and sampling algorithms. Multiple fracture network realisations can be generated and the resulting rock mass properties interrogated. Statistical analyses based on fracture connectivity, block size distribution and slope stability can be performed and provide results defined in terms of confidence intervals. For sedimentary geology consisting of dense bedding, equivalent medium continuum methods have traditionally been used in preference to discrete fracture representations due to the large numbers of structures involved and resulting computational complexity. In this paper, it is shown that stochastic representation of these layers can be employed. An analytical solution to accommodate bedding given an assumed block size distribution has been derived. Using this formulation, polyhedral modelling has been used to investigate the influence of bedding on block formation and block size distributions using field data. It is shown that the analysis is both computationally efficient and can capture truncation of size distribution by such layers without numerical methods.

Quasi-Stochastic Analysis of Uncertainty for Modelling Structurally Controlled Failures

In one approach to predicting the behaviour of rock masses, effort is being devoted to the use of probabilistic methods to model structures interior to a rock mass (sometimes referred to as ‘inferred’ or ‘stochastic’ structures). The physical properties of these structures (e.g. position, orientation, size) are modelled as random parameters, the statistical properties of which are derived from the measurements of a sample of the population (sometimes referred to as ‘deterministic’ structures). Relatively little attention has been devoted to the uncertainty associated with the deterministic structures. Typical geotechnical analyses rely on either an entirely stochastic analysis, or deterministic analyses representing the structures with a fixed shape (i.e. disc), position, size, and orientation. The simplifications assumed for this model introduce both epistemic and stochastic uncertainties. In this paper, it is shown that these uncertainties should be quantified and propagated to the predictions of behaviour derived from subsequent analyses. We demonstrate a methodology which we have termed quasi-stochastic analysis to perform this propagation. It is shown that relatively small levels of uncertainty can have large influence on the uncertainties associated with geotechnical analyses, such as predictions of block size and block stability, and therefore this methodology can provide the practitioner with a method for better interpretation of these results.

Effect of loading rate on sand pile failure: 2D DEM Simulation

Discrete element method (DEM) is a widely used simulation tool to model physical behaviour of granular materials. In this study 2D DEM simulation has been used to simulate the failure of a sand pile loaded at the crest. The model has been calibrated and validated using experimental force-displacement behaviour, angle of repose and particle velocity profile. The effects of numerical loading rates on simulation results have been investigated. The calibrated DEM model showed that the selection of loading rate is crucial in simulating particle assembly behaviour. In the quasi-static state a small change in loading rate does not change the force-displacement behaviour of the model. However, the system becomes unstable and force-displacement behaviour of the granular assembly diverges from the quasi-static state when the loading rate is higher than the quasi-static loading rate.

A new feature based algorithm for image analysis of deformable materials for laboratory investigations of slope stability

Physical modelling of slope stability scenarios can provide new insights into failure mechanisms as well as assistance with interpretation of numerical modelling investigations. To increase the value of such experiments, algorithms that support rapid analysis and quantification of the slope deformation occurring in the experiment are needed. Feature based image analysis has advantages in this respect over area or patch based approaches but suffers from robustness issues. To this end, a new image processing algorithm for measurement of deformation of granular media in laboratory experiments is presented. Our novel algorithm combines a feature detector with model based constraints and outlier detection to achieve fast and robust particle tracking. Comparison with a high precision particle image velocimetry algorithm shows excellent results with much improved processing times. Application of the algorithm for analysis of a laboratory simulation of slope stability is demonstrated and comparison with numerical modelling confirms the algorithm’s flexibility and robustness.

Rapid characterisation of fracture network realisations for hydrogeological, slope stability and geomechanical modelling

For fractured rock masses, Monte Carlo simulation can be used to generate a multitude of fracture network realisations to support the estimation of the uncertainties in the fracture network properties and behaviour. However, the approach is limited by the computation time associated with performing fluid flow, slope stability or geomechanical analysis on each realisation, where it is often only feasible to analyse a small subset of these. The work presented in this paper facilitates the selection of fracture network realisations, representing conservative and aggressive scenarios, by using fast-to-compute geometry-based metrics. For hydrogeological analyses, we find that the success of such metrics depends on the complexity of the fracture network and we present an analysis of multiple scenarios to demonstrate this. Finally, we propose a similar approach for slope stability analyses and rock mass strength characterisation.