Ultimate Pit And Mining Schedule Optimization Method For Open-pit Coal Mines And Its Application

The ultimate pit and long term mining schedule are two of the most important aspects of an open-pit coal mine design, having substantial effects on the overall economic outcome. Therefore, the optimization of ultimate pit and long term mining schedule has been a subject of intensive research in the field of mining production engineering.Based on a systematic literature review into the existing research work in this field and the special geological features of near-level coal deposits, a theorem on "obtaining the optimum mining schedule from a series of geologically optimum push-backs" is given and proven, mathematical optimization models are formulated, and a set of algorithms are developed for deposit modeling and the optimization of ultimate pit and long term mining schedule. The theory, method and models are realized by developing a software package.Based on the feature that most of coal deposits mined by open-pit are composed of near-level coal seams, a coal deposit is modeled using a regular column model which is apt for computer execution and convenient for application. The modeling algorithm and data structure give full consideration to dealing with real-life geological conditions and features of exploration drill hole data. This modeling technique is capable of dealing with faults, seam boundary control, and cluster effect and, therefore, is highly practical.A topographic model of the ground surface is needed for the optimization of ultimate pit and mining schedule. A method for topography modeling using contour lines is proposed, which can effectively deal with various topographic features. An algorithm for this method is also devised.Based on the column model of coal seams and the topographic model of the ground surface, the ultimate pit for a coal mine is optimized using a method of "cone elimination" with an objective function of maximizing the total profit. In this method, a largest possible pit is first generated and, then, starting from this pit an iterating cone scanning process is used to eliminate the non-profit cones or cones with strip ratios greater than the break-even strip ratio. The optimum pit is obtained when no such cones can be found in a round of scanning. This method is simple to apply and fast in execution. It can accommodate different slope angles in different directions (or zones) in real life applications. The problem of overlapping cones is largely overcome in this method through positioning the cone vertex at the bottom of each coal layer. Algorithms for delineating the largest possible pit, cone elimination, and cone-template formation are designed for this optimization method together with the corresponding dada structures.In the context of this study, mining schedule for an open-pit coal mine is defined to include three aspects:the mining sequence (location to be mined each year), production capacity (the amounts of coal, unconsolidated overburden, and hard rock to be mined each year), and the mine life. Existing methods for mining schedule optimization generally solve for the optimum mining sequence under a given production capacity (mine life is also given). However, the mining sequence and production capacity are not independent and the solution obtained by fixing one of them is only partially optimum. The global optimum solution can only be obtained by simultaneous optimization.In this study, a mining schedule optimization theorem,"from geological optimum to economical optimum", is given and proven, which states that the series of push-backs corresponding to the end-of-year pit configurations (location, shape and size) in the optimum mining schedule must be a sub-series of a series of geologically optimum push-backs. For a given total size V, the "geologically optimum push-back" is the one containing the maximum coal quantity of all the push-backs of the same size V, given that the working slope constraint is satisfied. Based on this theorem, a series of geologically optimum push-backs is first generated in the ultimate pit according to the working slope. These push-backs are then dynamically sequenced to find the sub-series which produce the maximum Net Present Value (NPV), i.e. the optimum mining schedule. The optimum mining schedule thus obtained simultaneously gives the best mining sequence, production capacity, and mine life. Based this optimization method, a general model and a dynamic programming model are formulated for dynamically sequencing the geologically optimum push-backs, algorithms for generating a series of geologically optimum push-backs and dynamic push-back sequencing are devised.A software package, CoalDesign, has been developed based on the theory, models and algorithms presented herein. CoalDesign was applied to a real coal deposit to model the deposit using drill hole data, and to optimize the ultimate pit and mining schedule. The case study shows that the theory, models and algorithms are highly efficient and practical, being capable of accommodating constraints in real life applications such as the maximum strip ratio, maximum and minimum mining and striping capacities, variation in slope angles. Using CoalDesign, it is not only possible to get quick optimization results for given geological, coal market and cost conditions, it is also convenient to analyze the effects of coal market changes and cost variations on the optimization results. Therefore, it is a valuable tool for arriving at a sound and detailed final design.