Asymmetric blasting: a rock mass dependent blast design method

Blasting has been the most frequently used method for rock breakage since black powder was first used to fragment rocks, more than two hundred years ago. This paper is an attempt to reassess standard design techniques used in blasting by providing an alternative approach to blast design. The new approach has been termed asymmetric blasting. Based on providing real time rock recognition through the capacity of measurement while drilling (MWD) techniques, asymmetric blasting is an approach to deal with rock properties as they occur in nature, i.e., randomly and asymmetrically spatially distributed. It is well accepted that performance of basic mining operations, such as excavation and crushing rely on a broken rock mass which has been pre conditioned by the blast. By pre-conditioned we mean well fragmented, sufficiently loose and with adequate muckpile profile. These muckpile characteristics affect loading and hauling [1]. The influence of blasting does not end there. Under the Mine to Mill paradigm, blasting has a significant leverage on downstream operations such as crushing and milling. There is a body of evidence that blasting affects mineral liberation [2]. Thus, the importance of blasting has increased from simply fragmenting and loosing the rock mass, to a broader role that encompasses many aspects of mining, which affects the cost of the end product. A new approach is proposed in this paper which facilitates this trend 'to treat non-homogeneous media (rock mass) in a non-homogeneous manner (an asymmetrical pattern) in order to achieve an optimal result (in terms of muckpile size distribution).' It is postulated there are no logical reasons (besides the current lack of means to infer rock mass properties in the blind zones of the bench and onsite precedents) for drilling a regular blast pattern over a rock mass that is inherently heterogeneous. Real and theoretical examples of such a method are presented.

Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods

There has been a resurgence of interest in the mean trace length estimator of Pahl for window sampling of traces. The estimator has been dealt with by Mauldon and Zhang and Einstein in recent publications. The estimator is a very useful one in that it is non-parametric. However, despite some discussion regarding the statistical distribution of the estimator, none of the recent works or the original work by Pahl provide a rigorous basis for the determination a confidence interval for the estimator or a confidence region for the estimator and the corresponding estimator of trace spatial intensity in the sampling window. This paper shows, by consideration of a simplified version of the problem but without loss of generality, that the estimator is in fact the maximum likelihood estimator (MLE) and that it can be considered essentially unbiased. As the MLE, it possesses the least variance of all estimators and confidence intervals or regions should therefore be available through application of classical ML theory. It is shown that valid confidence intervals can in fact be determined. The results of the work and the calculations of the confidence intervals are illustrated by example. (C) 2003 Elsevier Science Ltd. All rights reserved.

Stereological and other methods applied to rock joint size estimation - Does Crofton's theorem apply?

A number of authors concerned with the analysis of rock jointing have used the idea that the joint areal or diametral distribution can be linked to the trace length distribution through a theorem attributed to Crofton. This brief paper seeks to demonstrate why Crofton's theorem need not be used to link moments of the trace length distribution captured by scan line or areal mapping to the moments of the diametral distribution of joints represented as disks and that it is incorrect to do so. The valid relationships for areal or scan line mapping between all the moments of the trace length distribution and those of the joint size distribution for joints modeled as disks are recalled and compared with those that might be applied were Crofton's theorem assumed to apply. For areal mapping, the relationship is fortuitously correct but incorrect for scan line mapping.