A 3D brute-force algorithm for the optimum cutting pattern of dimension stone quarries

Abstract

This paper presents a 3D algorithm for finding the optimum cutting direction in ornamental stone quarries aiming at maximizing the recovery ratio of blocks through tackling the fracture problem that causes material and economic loses. The presented algorithm is based on 3D deterministic fracture modeling or mapping data and considers new parameters: i) displacement of the cutting grid; (ii) material lost by quarrying; (iii) irregularity of the tested area; (iv) and subdivision of large quarrying area. The algorithm searches for the optimum cutting direction and displacement of the cutting grid that maximizes the number of non-fractured blocks. The algorithm was coded in a software package named BlockCutOpt. This paper presents BlockCutOpt results applied in two case studies of different characteristics. The first case study was a limestone bench where fractures were modeled deterministically using Ground Penetrating Radar (GPR) survey. The second case study was in a very large area of granite deposit where the regional fractures were mapped using the aerial photogrammetry method (literature data). BlockCutOpt was found a fast tool for finding the optimum cutting pattern in the presented case studies. The results showed that the optimum cutting direction of blocks can vertically (within different strata) and horizontally (within very large scale area) vary, giving geometric information about the cutting grid design that optimizes the number of non-fractured blocks.