| Recent research has lead to a new method of stope design. The method discretizes the ore zone into three-dimensional blocks having volumes, tonnages, and economic value. Block geometries are developed to be consistent with mining parameters. Each row of blocks is a panel, with panel direction defined by the mining direction. By determining the optimal starting and ending locations for mining within each panel, an optimal stoping boundary is developed. To determine the starting and ending locations, two cumulative functions are used for each panel. The first function sums block values along the panel for inclusion within the stope. The second function sums values for exclusion. The difference between the two functions is the sum of block values lying between the starting and ending locations within each panel. These locations are defined by boundary location variables. Functions containing boundary variables are used to constrain stope spans, based on design criteria. The model is optimized by a mixed integer approach known as "type two special ordered sets". This approach establishes a discrete variable at each value on the cumulative functions. The discrete variables create an interval in which the boundary locations must reside during each solution iteration. Restrictions are placed on the system so no more than two discrete variables for any function can be active in any solution, and if two are active, they must be adjacent. These restrictions force an efficient-solution for the boundary location variables. Practical investigations of the design method are conducted on data from the Pea Ridge Iron Ore Company. A block model containing 160 blocks {dollar}(60spprime times 60spprime times 100spprime){dollar} is used to discretize an ore zone for stope layout optimization. The optimization objective is to maximize profit, with restrictions placed on stope length, total layout tonnage produced, and adjacency of stope end faces in each panel. Models are optimized for production from 400,000-1,500,000 tons. Various cost structures are also investigated. Mining, milling, and fixed cost components are investigated to determine their effect on stope layouts and the overall objective. The results of optimization are graphed to show sensitivity to various tonnages and costs. |
