Fractal characteristics analysis of mine workings geometry for the estimation of smooth wall blasting quality

The work examines the ways of estimating the smooth wall blasting quality when excavating mine workings. One of the main criteria is to achieve “smooth” mine working contour. It is shown that the mine working contour line represents a fractal object; its geometry is properly estimated by fractional fractal dimension. The definition of fractal dimension is based on the Richardson’s law, which connects the length of infinitely broken line and measurement interval. The calculation algorithm of fractal dimension in computer program is introduced. The analysis of real mine working contours which are formed in the process of drilling and blasting operations, allowed to determine statistically reliable connection of roughness coefficient of the mine working surface and the value of its fractal dimension. Quality criterion for smooth wall blasting is suggested - fractal coefficient of mine working shape. Its value represents the relation of equivalent cross-section area of a mine working to its perimeter, which is determined by fractal dimension of a contour. Obtained ratios allow to reliably estimate the quality of smooth wall blasting when excavating mine workings.