The Swebrec© function: linking fragmentation by blasting and crushing

Ouchterlony, Finn

doi:10.1179/037178405x44539

Cited by 114 publications

(69 citation statements)

References 11 publications

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“…6a, 6b is recognizable as the argument of the basic Swebrec function (Ouchterlony 2003(Ouchterlony , 2005. The basic Swebrec function is consistent with the fragmentation-energy fan behavior of blasting provided that b is independent of q, see below.…”

Section: Relationships For Swebrec Functionmentioning

confidence: 80%

“…The test rounds lay directly behind each other, with a shrunken pattern behind an expanded one and vice versa to minimize Fig. 15 Percentile fragment sizes x P for Vändle benches versus specific charge q, data from Ouchterlony et al (2005) the influence of geology. From the muck piles, four test piles of about 500 tonne were extracted.…”

Section: Full-scale Bench Blastingmentioning

confidence: 99%

“…In Ouchterlony (2015a, b), it was pointed out that the RR function is consistent with the special case that a(P) = constant, i.e., with parallel percentile size lines x P at spacings given by n that have no focal point or alternatively expressed, consistent with lines that have a focal point at infinity. The CDF of the basic Swebrec distribution reads (Ouchterlony 2005(Ouchterlony , 2009a)…”

Section: Relationships For Swebrec Functionmentioning

confidence: 99%

“…The Swebrec function was introduced by Ouchterlony (2005). It is capable of reproducing sieving data really well from the fines range to large boulders, say from 0.5 to 500 mm or three orders of magnitude in fragment size.…”

mentioning

confidence: 99%

“…Recent work by Sanchidrián et al (2014) shows that the Swebrec function is the overall best fitting three-parameter function to sieving data for blasted or crushed rock. Ouchterlony (2005) suggested that the RR function in the Kuz-Ram model be replaced by the Swebrec function to create the KCO (Kuznetsov-Cunningham-Ouchterlony) model. The x 50 prediction equation was retained, and new prediction equations for x max , the largest stone size, and b were sketched.…”

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confidence: 99%

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

2016

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It is shown that blast fragmentation data in the form of sets of percentile fragment sizes, x P , as function of specific charge (powder factor, q) often form a set of straight lines in a log(x P ) 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 fragmentationenergy 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(x max /x)/ln(x max /x 50 )]. 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 fragmentationenergy fan contradicts two basic assumptions of the KuzRam 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 x P 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.

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Section: Relationships For Swebrec Functionmentioning

confidence: 80%

Section: Full-scale Bench Blastingmentioning

confidence: 99%

Section: Relationships For Swebrec Functionmentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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

2016

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Performance evaluation of rock fragmentation prediction based on RF‐BOA, AdaBoost‐BOA, GBoost‐BOA, and ERT‐BOA hybrid models

Zhao,

Li,

Zhou

et al. 2024

Deep Underground Science and Engineering

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Rock fragmentation is an important indicator for assessing the quality of blasting operations. However, accurate prediction of rock fragmentation after blasting is challenging due to the complicated blasting parameters and rock properties. For this reason, optimized by the Bayesian optimization algorithm (BOA), four hybrid machine learning models, including random forest, adaptive boosting, gradient boosting, and extremely randomized trees, were developed in this study. A total of 102 data sets with seven input parameters (spacing‐to‐burden ratio, hole depth‐to‐burden ratio, burden‐to‐hole diameter ratio, stemming length‐to‐burden ratio, powder factor, in situ block size, and elastic modulus) and one output parameter (rock fragment mean size, X50) were adopted to train and validate the predictive models. The root mean square error (RMSE), the mean absolute error (MAE), and the coefficient of determination () were used as the evaluation metrics. The evaluation results demonstrated that the hybrid models showed superior performance than the standalone models. The hybrid model consisting of gradient boosting and BOA (GBoost‐BOA) achieved the best prediction results compared with the other hybrid models, with the highest R2 value of 0.96 and the smallest values of RMSE and MAE of 0.03 and 0.02, respectively. Furthermore, sensitivity analysis was carried out to study the effects of input variables on rock fragmentation. In situ block size (XB), elastic modulus (E), and stemming length‐to‐burden ratio (T/B) were set as the main influencing factors. The proposed hybrid model provided a reliable prediction result and thus could be considered an alternative approach for rock fragment prediction in mining engineering.

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Advanced Analytics for Drilling and Blasting

Siamaki¹

2022

Advanced Analytics in Mining Engineering

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The Swebrec© function: linking fragmentation by blasting and crushing

Cited by 114 publications

References 11 publications

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

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

Performance evaluation of rock fragmentation prediction based on RF‐BOA, AdaBoost‐BOA, GBoost‐BOA, and ERT‐BOA hybrid models

Advanced Analytics for Drilling and Blasting

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