Analysis of fractal characteristics of mine working geometry for assessing quality of perimeter blasting

Abstract

Methods of assessing quality of perimeter blasting when driving mine workings are considered. One of the main criteria is achieving “smooth” working contour. It is shown that a working contour line is a fractal object, geometry of which is adequately estimated by the fractional fractal dimensionality. Determining fractal dimensionality is based on Richardson’s law, connecting the length of an infinitely broken line with a measurement step. An algorithm for calculating the fractal dimensionality in computer software program is presented. Analysis of actual contours of underground workings produced using drilling and blasting operations allowed identifying statistically valid relationship between working surface roughness factor and the value of its fractal dimensionality. A criterion for assessing quality of perimeter blasting is proposed — fractal factor of a working shape. Its value is the ratio of the area of the working equivalent section to its squared perimeter, determined by fractal dimensionality of the contour line. The obtained relationships allow reliable assessing quality of perimeter blasting when driving mine workings.

Keywords

• perimeter blasting technique
• underground workings
• fractal dimensionality
• fractal form factor
• stress concentration factor