R.J. Fowell

THE USE OF THE CRACKED BRAZILIAN DISC GEOMETRY FOR ROCK FRACTURE INVESTIGATIONS

Abstract The cracked Brazilian disc geometry is receiving attention for rock fracture mechanics research due to its many advantages over other conventional geometrical configurations. A thorough study of the geometry is vitally important at this stage. A superimposition technique is presented to accurately solve the general cracked straight through Brazilian disc (CSTBD) fracture problem using the dislocation method and also the complex stress function method. The solution is valid for any crack inclination angle and any crack length. The solution for the cracked chevron notched Brazilian disc (CCNBD) is then discussed. The theoretical evaluation for the Mode I cracked Brazilian disc fracture problem, a special case of the general problem, has been numerically calibrated by both finite element and boundary element methods, and a simple and accurate method to calculate the Mode I critical (minimum) dimensionless stress intensity factor for the CCNBD specimen is given. The valid geometrical range and valid minimum specimen size for the CCNBD geometry is presented to allow a valid Mode I fracture toughness value to be determined. The theoretical and numerical solutions for the stress intensity factor and the valid geometrical range are also substantiated by extensive experimental validation by comparing the results with those obtained by the ISRM-suggested CB and SR methods.

The cracked chevron notched Brazilian disc test- geometrical considerations for practical rock fracture toughness measurement

The two chevron notched rock fracture specimens, CB and SR, recommended by the ISRM to determine rock Mode I fracture toughness have several disadvantages, such as low loads required to initiate failure, relatively large amounts of intact rock core are required at the correct orientation, complicated loading fixtures and complex sample preparation for SR specimens. The Cracked Chevron Notched Brazilian Disc (CCNBD, Fig. 1.c) and the Cracked Straight Through Brazilian Disc (CSTBD, Fig.l.b) specimen geometries overcome these problems and are suitable for mixed fracture mode testing at the same time. The general case for the cracked Brazilian disc problem is when the sample is loaded diametrically with the crack inclined at an angle 0 to the loading direction (Fig. 1.a). Different combinations of mode I and mode II fracture intensities can be obtained simply by changing this angle.

A flexible true plurigaussian code for spatial facies simulations

The current forms of plurigaussian simulation have serious limitations for applications to large numbers of geological facies, or units, which have complex contact relations. In this paper the authors present a true plurigaussian simulation (PGS) method, which can be applied in a simple way to any number of geological facies by using any number of Gaussians. A recursive technique is used for multi-dimensional integration of the Gaussian functions, which forms the major part of the PGS computation. A binary, dynamic contact matrix (DCM) is used to specify the contact relations among the facies; this method has proved to be simple, flexible and capable of dealing with general, complex contact relations. A method for incorporating into PGS multivariate correlations among any number of random variables is also included. A simulated example is used to demonstrate the application of the generalised PGS. This example shows that PGS is more robust to under-sampling than traditional direct indicator simulation.

Lerchs–Grossmann algorithm with variable slope angles

Abstract One of the most important design factors in open-pit mining is determination of the optimal pit. Pits may be redesigned many times during the life of a mine in response to changes in design parameters as more information is obtained and to changes in the values of technical and economic parameters. Over the past 35 years the determination of optimum open-pits has been one of the most active areas of operational research in the mining industry and many algorithms have been published. The most common optimizing criterion in these algorithms is maximization of the overall profit within the designed pit limits subject to mining (access) constraints. Almost all algorithms use a block model of the orebody, i.e. a three-dimensional array of identically sized blocks that covers the entire orebody and sufficient surrounding waste to allow access to the deepest ore blocks. Of these, the Lerchs-Grossmann algorithm, based on graph theory, is the only method that is guaranteed always to yield the true optimum pit. However, the original algorithm assumes fixed slope angles that are governed by the block dimensions. None of the subsequent attempts to incorporate variable slope angles provides an adequate solution in cases where there are variable slopes controlled by complex structures and geology. A general method of incorporating variable slope angles in the Lerchs-Grossman algorithm is presented. It is assumed that the orebody and the surrounding waste are divided into regions or domain sectors within which the rock characteristics are the same and that each region is specified by four principal slope angles—north, south, east and west face slope angles. Slope angles can vary throughout the deposit to follow the rock characteristics and are independent of the block dimensions.

FACTORS GOVERNING THE ONSET OF SEVERE DRAG TOOL WEAR IN ROCK CUTTING

Laboratory cutting tests have been performed in hard rock utilising an instrumented SO tonne capacity rock planer. The experiment involved intermittent cutting of felsic gneiss up to a maximum of 20 m or until tool failure, Each cutting tool was fitted with a thermocouple in the tungsten carbide insert to monitor the insert tip temperature. The cutting forces and tool wear were also monitored. Cutting was conducted with and without high pressure water jet assistance (HPWJA). The results show that a dependence exists between the tool temperature and the tool normal force component. HPWJA enhances the tool life and acts as a heat sink during cutting. An elementary model is proposed to explain the findings and provide a theoretical basis for anticipating high tool wear.

Simulating Correlated Marked-point Processes

Abstract The area of marked-point processes is well developed but simulation is still a challenging problem when mark correlations are to be included. In this paper we propose the use of simulated annealing to incorporate the spatial mark correlation into the simulations of correlated marked-point processes. Such a simulation has wide applications in areas such as inference and goodness-of-fit investigations of proposed models. The technique is applied to a forest dataset for which the results are extremely encouraging.

Incorporation of slope design into optimal pit design algorithms

Abstract The design of an optimum open-pit requires an estimate of a set of average and safe slope angles. Pit slope angles may vary throughout a deposit to accommodate varying rock characteristics and ore/waste ratios. If insufficient geotechnical information is available, the pit slopes may be found from other mines of similar size and geological conditions. If the mine is in operation, predefined or existing pit slopes can be used in the design of the optimum pit. Two approaches are described and associated computer programs for the estimation of a set of safe average pit slopes for use in an optimal pit design program are presented. The first approach determines the steepest safe angle by kinematic analysis; the second includes methods for the design of slopes by limit equilibrium analysis in terms of the safety factor or the probability of failure determined by application of the Monte Carlo simulation technique.

A Windows program for optimal open pit design with variable slope angles

ABSTRACT This paper describes the structure and operation of an interactive Windows software package for determining optimum open pits with variable slope angles. It is based on the Lerchs-Grossmann algorithm and is capable of taking advantage of all available computer memory thus allowing the design of optimum pits for large, complex, deposits. The software provides for interactive slope design and includes graphical and numerical displays of the input data and the results of optimisation.