Computer-aided optimal open pit design with variable slope angles
The use of open pit mining has increased to extract large and low grade deposits with the growth in demand for raw materials, with the advances in mining technology and with the depletion of high grade and readily accessible orebodies. Development and extraction of minerals by this method is a complex operation that may extend over several decades and require very large investments. Before starting the operation, it is necessary to design the size and final shape of the pit in order to determine minable reserves and amount of waste to be removed. It is also needed to locate the waste dump, processing plant, access roads and to develop a production program. The ultimate pit limit depends upon many factors. One of the most important factors is the pit slopes which affect the stripping ratio and amounts of waste to be removed. When dealing with complex deposits in which the pit slopes may vary in different parts of the orebody due to slope stability requirements, it is necessary to take into account variable pit slopes in the designing of the pit limit. Determination of the pit limit 'in open pit mining is one of the ' most important design factors which may be considered many times during the life of the mine as the design parameters change in the future or more information is obtained during the operation. Therefore the use of a computer is essential in order to design the pit as rapidly as possible. As a result, a number of algorithms such as the various versions of the moving cone method, Lerchs-Grossmann algorithm, network or maximal flow techniques, Korobov algorithm, dynamic programming and parameterization techniques have been developed to determine the optimum ultimate pit limit since the advent and wide spread use of computers. The main objective of these algorithms is to determine the optimum pit limit in order to maximise the overall mining profit within the designed pit limit subject to the mining constraints. Of these, the Lerchs-Grossmann algorithm is well known for being the only method which always yields the true optimum pit limit. However, the algorithm which utilises graph theory was based on fixed slope angles that are governed by the block dimensions when it was introduced. In spite of the fact that many attempts have been made to incorporate variable slope angles, none of them provide an adequate solution where there are, variable slopes controlled by complex structures and geology. This algorithm is reconsidered and modified to deal with variable slope angles. 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 each region is specified by four principal slope angles including North, South, East and West face slope angles. Consequently slope angles can vary through the deposit to follow the rock characteristics and are independent of the block dimensions. In addition, two methods were also developed to estimate the four principal slope angles from geotechnical information to use as input parameters in the optimal pit, design algorithm. A general PC software was also developed to determine the optimum pit limit with variable slope angles for an open pit mine. The software is a Windows application that'can be implemented under 32-bit operating systems such as. Windows 95, Windows NT and. Windows 98. It is capable of taking advantage of all the computer memory and designing the optimum pit limit for complex, large and low grade deposits due to solving the memory limitation. The software includes both graphical and numerical presentation of the, input data and the results of optimisation. Two case studies have been used to validate the software developed.