José A. Sanchidrián

A Distribution-Free Description of Fragmentation by Blasting Based on Dimensional Analysis

A model for fragmentation in bench blasting is developed from dimensional analysis adapted from asteroid collision theory, to which two factors have been added: one describing the discontinuities spacing and orientation and another the delay between successive contiguous shots. The formulae are calibrated by nonlinear fits to 169 bench blasts in different sites and rock types, bench geometries and delay times, for which the blast design data and the size distributions of the muckpile obtained by sieving were available. Percentile sizes of the fragments distribution are obtained as the product of a rock mass structural factor, a rock strength-to-explosive energy ratio, a bench shape factor, a scale factor or characteristic size and a function of the in-row delay. The rock structure is described by means of the joints’ mean spacing and orientation with respect to the free face. The strength property chosen is the strain energy at rupture that, together with the explosive energy density, forms a combined rock strength/explosive energy factor. The model is applicable from 5 to 100 percentile sizes, with all parameters determined from the fits significant to a 0.05 level. The expected error of the prediction is below 25% at any percentile. These errors are half to one-third of the errors expected with the best prediction models available to date.

Percentile Fragment Size Predictions for Blasted Rock and the Fragmentation–Energy Fan

Abstract It is shown that blast fragmentation data in the form of sets of percentile fragment sizes, xP, as function of specific charge (powder factor, q) often form a set of straight lines in a log(xP) versus log(q) diagram that tend to converge on a common focal point. This is clear for single-hole shots with normal specific charge values in specimens of virgin material, and the phenomenon is called the fragmentation–energy fan. Field data from bench blasting with several holes in single or multiple rows in rock give data that scatter much more, but examples show that the fragmentation data tend to form such fans. The fan behavior implies that the slopes of the straight size versus specific charge lines in log–log space depend only on the percentile level in a given test setup. It is shown that this property can be derived for size distribution functions of the form P[ln(xmax/x)/ln(xmax/x50)]. An example is the Swebrec function; for it to comply with the fragmentation–energy fan properties, the undulation parameter b must be constant. The existence of the fragmentation–energy fan contradicts two basic assumptions of the Kuz-Ram model: (1) that the Rosin–Rammler function reproduces the sieving data well and (2) that the uniformity index n is a constant, independent of q. This favors formulating the prediction formulas instead in terms of the percentile fragment size xP for arbitrary P values, parameters that by definition are independent of any size distribution, be it the Rosin–Rammler, Swebrec or other. A generalization of the fan behavior to include non-dimensional fragment sizes and an energy term with explicit size dependence seems possible to make.

Uncertainty in Measurements of Vibrations From Blasting

Ground vibrations from blasting induce environmental concerns near the blasting sites. National standards and recommendations (AENOR 1993; BSI 1993; DIN 1986; Singh and Roy 2010; SIS 1991; Siskind et al. 1980) define threshold values as function of the characteristics of the structures and also of the predominant frequency of ground vibrations. In order to assess compliance with these regulations, the engineer should monitor the resulting seismic field at the position of interest. For this purpose, monitoring devices (geophones and recording units) must meet some minimum characteristics and must be periodically calibrated (AENOR 1993; ISEE 2010; DIN 1995; Instantel 2011). Other important considerations for measuring vibrations are that the sensor does not lose contact with the ground in the vertical direction nor slip in the horizontal plane, and that it accurately follows ground motion (Adhikari et al. 2005; Drijkoningen et al. 2006; Hutchison et al. 2005; Krohn 1984; Wheeler 2005; Williams and Treleaven 2003). The preferred coupling methods are: for soil, attach the sensor at the top of a mount that is embedded into ground, and for rock, anchor, glue or cement the sensor to the ground surface (Blair 1995a). Other suggested coupling methods of the sensors to rock at low vibration levels, such as sensors freely laid on the ground surface or sensors held with sandbags (ISRM 1992; ISEE 2009), alter the amplitude of vibrations and should be avoided (Blair 1987, 1995b). Once vibrations have been measured, the estimated peak particle velocities and dominant frequencies must be written in a report. In many science and engineering fields, when a result of a measurement is reported, it is obligatory to show together with it, an estimate of its uncertainty (Miller and Miller 1993; Taylor and Kuyatt 1994; JCGM 2008). This is mandatory to qualify a laboratory in accordance with ISO regulations (AENOR 2005) and may have a bearing in lawsuits, but at present it is not made in vibration measurements from blasting. This prevents assessment of how well a reported value represents the value of the magnitude being measured or to study the quantitative effect of poor or good measuring practices. There are, nowadays, few studies that assess uncertainty in vibration measurements from blasting (Segarra et al. 2010). This work tries to fill this void, and reports and analyzes uncertainties for four measuring conditions that are representative of common field monitoring techniques. The implications of these uncertainties in the assessment of compliance with standards are also highlighted.

The influence of some blasting techniques on the probability of ignition of firedamp by permissible explosives

The ignition of firedamp by permissible explosives is assessed by means of gallery testing conducted by the Bruceton up-and-down method. Six test series were made in order to analyze the influence of several blasting practices in long-holes coal blasting, namely: use of slotted PVC pipes, detonating cord, salt cartridges and double (top and bottom) initiation. The parameters of the distributions of the probability of ignition are determined by the maximum likelihood method; normal, logistic, lognormal and Weibull distributions have been used. Confidence bands for the probability points are obtained both from the asymptotic standard errors of the parameters and by a bootstrap-like technique. The four distributions used give similar results in a rather ample probability range; discrepancies in the probability points are within 2% and in the confidence limits within 10% in a range of probability [0.1, 0.9] in most of the cases. The use of detonating cord is found to affect significantly the probability of ignition; the double initiation does also have an influence though not statistically significant at a 95% level; the use of salt cartridges, in the amount tested, has little effect in the ignition probability; the use of PVC pipe shows no effect.

On borehole pressure and spacing in cautious blasting with an extension to water-filled holes

Abstract The evaluation of borehole spacing in presplitting and smooth blasting is closely connected to the evaluation of borehole pressure. Pressures required for splitting the rock, using the classical simple theory of pressurized uncracked holes in an infinite medium, are calculated for the case of granite cutting with detonating cord, and compared with a variety of estimations available. A survey of these approximations evidences a fairly large spread in borehole pressure values. Of them, the classical Calder pressure estimation leads to spacings, from the simple theory, quite consistent with reality. The presence of water as coupling medium between the explosive and the borehole wall affects both the borehole pressure and the spacing required. Blasts in granite with detonating cord of several explosive loads per meter have been conducted to analyze such effect. From the maximum allowable spacings, the borehole pressures are estimated. A correction factor for the calculation of borehole pressure in wa...

Optimization of granite splitting by blasting using notched holes

Abstract It is demonstrated that the technique of borehole notching is effective in ornamental rock quarrying, allowing a significant increase of the borehole spacing or smaller effective borehole pressures for a given spacing, so that the explosive loads and also the risk of damage to the rock can be reduced. The drilling of notches must be performed carefully and efficiently for those to be effective; for this a design of a notching machine prototype with two or four hammers is proposed.

The Fragmentation-Energy Fan Concept and the Swebrec Function in Modeling Drop Weight Testing

A recent concept called the fragmentation-energy fan has been used to analyze drop weight testing (DWT) data and to obtain both the mathematical form of the breakage index equation, i.e., t10 versus impact energy and the parameter values needed for making an actual prediction with it. The fan is visualized by plotting the progeny size corresponding to a set of percent passing values versus scaled drop energy in log–log scale and fitting straight, i.e., linear fan lines with a common focal point to these data. The fan behavior lies inherent in the fact that the DWT sieving data closely follow the Swebrec distribution. A mathematical expression for t10 in closed form follows directly from a functional inversion, and this expression differs from the forms it has been given by the JKMRC. In most cases five fan lines suffice to provide a very accurate t10 equation. When applied to a suite of eight rocks, ores mostly, the coefficient of determination

Bestimmung der Korngrößenverteilung von Sprenghauwerk auf der Grundlage digitaler Bilder: Generelle Vorgehensweise, Grenzen der Anwendung

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