Design and optimization for bench blast based on Voronoi diagram

• An efficient method of bench blast design and optimization.
• Determining positions of boreholes automatically.
• Identifying initiation sequence based on Voronoi diagram.
• Convenience and reliability for engineering applications.

A method is proposed for bench blasting in open pit mines that can automatically determine the blastholes positions, calculate the explosive charge mass, and identifies the initiation sequence in the case of the hole-by-hole initiation. An analytical solution of the blasthole and row spacing is first deduced based on the concept of the explosive charge maximization. Then for a specified blast area, the coordinates of the blastholes are determined by a cluster of reference polylines. A Voronoi diagram of the blast area is constructed by means of the reference points of the blasthole coordinates. Based on the Voronoi diagram, the explosive charge mass of a blasthole can be easily calculated by the volume formula of charge calculation. An algorithm that can identify the initiation sequence for the hole-by-hole blast is developed from the Voronoi diagram. A code for the bench blast design is developed in C++. The proposed method can automatically complete the whole bench blast design according to the blast area configuration and several parameters required by this method. The results of practical application show that the proposed method can greatly reduce the amount of the design work and validly improve the blast results.