The Application Of Fractal Analysis To Mine Airways

Friction factors or coefficients of friction used to estimate the resistances of mine airways are, in the main, estimated from empirical measurements made in other airways considered to be of a similar geometry and type of lining. A somewhat more analytical approach, although still based on empiricism, is to estimate the ratio of the average height of the asperities to the hydraulic mean diameter of the airway (e/D ratio) and then to employ the Moody Chart or one of the equations that have long been established to represent the [coefficient of friction v Reynolds number curves] on that chart. Unfortunately, the Moody Chart and corresponding equations are based on pipes of uniformly distributed (sand grain) roughness whereas the asperities that exist on the surfaces of mine openings are frequently highly irregular both in their size and distribution. This is considered to be a major cause of discrepancies that have been found between coefficients of friction by the Moody Chart and those actually measured in mine airways. The work described in this paper examines an alternative method of estimating coefficients of friction for rough natural surfaces with uneven sizes and distribution of surface asperities. The technique utilizes the relatively recent developments in fractal analysis. A fractal dimension is determined from the topography of the surface. This has been correlated to coefficient of friction for a scale model of a mine airway. Further work is being carried out in actual mine airways. However, at this time, it appears promising that the fractal method may allow coefficient of friction to be predicted for given types of strata and method of roadway drivage.