A heuristic methodology for economic and geomechanical optimization in sublevel open stoping mining method

The top-down extraction sequence in the sublevel open stope method relies on rib pillars to support excavations, making pillar and stope stability crucial for controlling dilution. This study introduces an integrated methodology using a genetic algorithm to optimize the layout of open stopes and rib pillars while considering both economic and geomechanical performance. The methodology incorporates user-defined parameters such as the minimum size of stopes and pillars, maximum accepted dilution and acceptable percentage of pillar failure. A profit function that attributes economic value to the geometric configurations, including geomechanical performance, is employed. The geomechanical performance, assessed using numerical models in FLAC3D, includes the average percentage of pillar failure and potential dilution. The study was tested on a mining panel from an underground gold mine using a top-down mining sequence. The optimization achieved an 8 percent increase in net profit compared to the traditional engineer’s design when 70 percent hangingwall support efficiency was assumed, and a threefold reduction in pillar failure percentage. When no hangingwall support was considered, the net profit increase reached 22 percent. These results demonstrate that the proposed methodology enables integrated optimization, balancing mining costs with geomechanical performance and reducing the need for secondary support compared to traditional methods. Background In traditional mining operations, the generalization of stope and pillar sizes often leads to inefficiencies. Rock mass characteristics, such as dip angles and thickness variations, can influence the overall geomechanical stability and economic outcome. To address these variations, this study suggests that designing an irregular arrangement of stopes and pillars, considering the specific geomechanical and economic conditions of the mining panel, can result in a more optimized and profitable layout. Pillars are ideally placed in areas with low-grade ore or waste material, where the geomechanical requirements are higher, which helps reduce the potential for dilution in the stopes. Previous optimization methods have limitations as they often reach local maximum points, failing to account for the geomechanical performance of the layout. (An overview of cited authors’ methodologies for sublevel stoping optimization is provided in the full paper.) In mining projects, a balance between safety and economic return is essential. The optimization process must include the cost of geomechanical performance, addressing both ore dilution and pillar failure, to maximize the overall profitability. The goal of this study is to propose an integrated methodology for the joint economic and geomechanical optimization of open stopes and rib pillars. The proposed methodology incorporates an evolutionary algorithm that considers key user-defined criteria, such as minimum stope and pillar sizes, maximum expected dilution, and acceptable pillar failure percentage. Methods The proposed algorithm was developed using Python for the genetic algorithm and profit function, along with FLAC3D’s internal programming language, FISH, to enable automated numerical modeling. Initially, the case study files were imported into Micromine, a mining software that optimized the economic boundary of the stopes. These boundaries were divided into one-meter-thick vertical slices along the strike of the mineralized body, forming closed wireframe volumes. The algorithm generates potential solutions (individuals) by arranging stopes and pillars based on the agglomeration of selected slices, while adhering to size restrictions. Each individual is then sent to FLAC3D, where its geomechanical performance is evaluated. The fitness function assigns a net profit to each individual based on its economic and geomechanical characteristics. The genetic algorithm then proceeds by selecting individuals from the population to reproduce, creating offspring that inherit genetic traits from their parents. Mutations may occur, ensuring genetic diversity in the population. This process continues through iterations until the user-defined maximum is reached. Pillar performance is evaluated using the strength-stress ratio (SSR) obtained from the FLAC3D numerical analysis. The volume of failed pillar elements and the stress relaxation zone in the hangingwall of the stopes are used to assess the geomechanical performance of the designs. The FISH programming language is used to automate this evaluation (Fig. 1). Results The results of the proposed optimization algorithm were compared to the traditional design method used by the engineer in the case study. The optimized scenario provided significant improvements in both economic and geomechanical performance. The genetic algorithm parameters included an initial population of 20 individuals, a maximum of 1,000 iterations and a mutation probability of 0.5. The algorithm showed the highest rate of evolution up to 200 generations, with gradual improvement up to 750 generations. Table 1 shows the economic and operational input parameters entered by the user in the program’s graphical interface. The optimized design resulted in an ore production of 263 kt with an average grade of 1.55 g/t, yielding 13,000 ounces of gold and a global recovery of 70.4 percent. The potential dilution in the optimized design was 24.4 percent, but with 70 percent hangingwall support efficiency, the actual dilution was reduced to 14.3 percent, which was similar to the engineer’s design. The optimized design also achieved a pillar failure rate of 3.4 percent, three times lower than the engineer’s design. The gross income from the optimized design was estimated at $18.7 million, with costs totaling $14.8 million, resulting in a net profit of $3.9 million. Without hangingwall support, the actual dilution reached 24.4 percent, lowering the net profit to $2.6 million. The optimized design provided a 22 percent increase in net profit when no hangingwall support was considered and an 8 percent increase when 70 percent support efficiency was applied. The final layout of the stopes and pillars, as analyzed in FLAC3D, was relatively irregular, with larger stopes in the central portion of the panel and smaller stopes in the upper levels (Fig. 2). The total number of stopes was 34, with an average length of 12.7 m, while the number of pillars was 37, with an average length of 8.2 m. Fig. 2 Algorithm result of stopes and pillars layout:(a) isovolume of pillar failures (red) and (b) isovolumeof potential hangingwall dilution (red). Conclusions An integrated methodology was developed in this study to optimize the economic arrangement of stopes and pillars. This methodology incorporates an evolutionary algorithm and specific mutation operations, with user-defined criteria such as minimum stope and pillar sizes, maximum expected dilution and maximum acceptable failure percentage in pillars. This work emphasizes the need for integrated economic and geomechanical optimization. This need becomes apparent when the proposed methodology shows an 8 percent higher net profit in the optimized scenario. The results indicate a reduced need for secondary support compared to the engineer’s design methodology. This conclusion is supported by a decrease in hangingwall instability volume (dilution) and a threefold reduction in pillar failure volumes. References A list of all references is available in the full paper.

A heuristic methodology for economic and geomechanical optimization in sublevel open stoping mining method

Authored by: Diogo Peixoto Cordova, Andre Cezar Zingano and Italo Gomes Gonçalves

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