Blasting (KCO): Difference between revisions
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== Model theory == | == Model theory == | ||
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=== Swebrec distribution === | === Swebrec distribution === | ||
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[[File:BlastingKCO4.png|thumb|425px|Figure 1. Schematic of blast design geometry (after Bergman, 2005).{{Bergman (2005)}}]] | [[File:BlastingKCO4.png|thumb|425px|Figure 1. Schematic of blast design geometry (after Bergman, 2005).{{Bergman (2005)}}]] | ||
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Figure 1 outlines the primary blast design dimensions relevant to the KCO model. | Figure 1 outlines the primary blast design dimensions relevant to the KCO model. | ||
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=== Maximum block size, ''x''<sub>max</sub> === | === Maximum block size, ''x''<sub>max</sub> === | ||
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The maximum block size is the smallest value of the ''in situ'' block size, the blast-hole burden, <math>B</math>, and the spacing, <math>S</math>, (m), i.e.: | The maximum block size is the smallest value of the ''in situ'' block size, the blast-hole burden, <math>B</math>, and the spacing, <math>S</math>, (m), i.e.: | ||
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:<math>x_{\rm max} = \min \{ \textit{in}\text{ }\textit{situ}\text{ block size}, S, B \}</math> | :<math>x_{\rm max} = \min \{ \textit{in}\text{ }\textit{situ}\text{ block size}, S, B \}</math> | ||
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=== Mean size parameter, ''x''<sub>50</sub> === | === Mean size parameter, ''x''<sub>50</sub> === | ||
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The mean size of the distribution, <math>x_{50}</math> (mm), is estimated by: | The mean size of the distribution, <math>x_{50}</math> (mm), is estimated by: | ||
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* <math>q</math> is the specific charge (kg/m<sup>3</sup>) | * <math>q</math> is the specific charge (kg/m<sup>3</sup>) | ||
* <math>g(n) = 1</math> is assumed | * <math>g(n) = 1</math> is assumed | ||
* The 10 factor converts Ouchterlony's '' | * The 10 factor converts Ouchterlony's ''centimeter'' units to ''millimeters''. | ||
The rock mass factor, <math>A</math> is: | The rock mass factor, <math>A</math> is: | ||
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:<math>\mathit{JF} = \mathit{JPS} + \mathit{JPA}</math> | :<math>\mathit{JF} = \mathit{JPS} + \mathit{JPA}</math> | ||
where the joint plane spacing, <math>\mathit{JF}</math>, is related to the | where the joint plane spacing, <math>\mathit{JF}</math>, is related to the average joint spacing, <math>S_{\rm J}</math> (m), by: | ||
:<math>\mathit{JPS} = | :<math>\mathit{JPS} = | ||
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where <math>E</math> is Young's Modulus (GPa) and <math>\sigma_{\rm c}</math> is the compressive strength of the rock (MPa). | where <math>E</math> is Young's Modulus (GPa) and <math>\sigma_{\rm c}</math> is the compressive strength of the rock (MPa). | ||
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=== Curve-undulation exponent, ''b'' === | === Curve-undulation exponent, ''b'' === | ||
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The curve-undulation exponent <math>b</math> is determined from: | The curve-undulation exponent <math>b</math> is determined from: | ||
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* <math>H</math> is the bench height or hole depth (m) | * <math>H</math> is the bench height or hole depth (m) | ||
* <math>\mathit{SD}</math> is the standard deviation of drilling accuracy (m). | * <math>\mathit{SD}</math> is the standard deviation of drilling accuracy (m). | ||
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== Excel == | == Excel == | ||
Latest revision as of 08:34, 1 May 2025
Description
This article describes the Kuznetsov–Cunningham–Ouchterlony (KCO) model (Ouchterlony, 2005) for predicting rock fragmentation by blasting.[1]
Model theory
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Swebrec distribution
Maximum block size, xmax
Mean size parameter, x50
Curve-undulation exponent, b
Excel
The KCO blasting model may be invoked from the Excel formula bar with the following function call:
=mdUnit_Blasting_KCO(Parameters as Range, Size as Range)
Invoking the function with no arguments will print Help text associated with the model, including a link to this page.
Inputs
The required inputs are defined below in matrix notation with elements corresponding to cells in Excel row ([math]\displaystyle{ i }[/math]) x column ([math]\displaystyle{ j }[/math]) format:
- [math]\displaystyle{ Parameters= \begin{bmatrix} H\text{ (m)}\\ B\text{ (m)}\\ S\text{ (m)}\\ \varnothing_{\rm h}\text{ (m)}\\ L_{\rm b}\text{ (m)}\\ L_{\rm c}\text{ (m)}\\ L_{\rm Tot}\text{ (m)}\\ \mathit{SD}\text{ (m)}\\ Q\text{ (kg)}\\ q\text{ (kg/m}^3\text{)}\\ s_{\rm ANFO}\text{ (}%\text{)}\\ \rho\text{ (t/m}^3\text{)}\\ \sigma_{\rm c}\text{ (MPa)}\\ E\text{ (GPa)}\\ \textit{In}\text{ }\textit{situ}\text{ block size (m)}\\ \mathit{RMD}\\ \end{bmatrix},\;\;\;\;\;\; Size = \begin{bmatrix} d_{1}\text{ (mm)}\\ \vdots\\ d_p\text{ (mm)}\\ \end{bmatrix} }[/math]
Results
The results are displayed in Excel as an array corresponding to the matrix notation below:
- [math]\displaystyle{ \mathit{mdUnit\_Blasting\_KCO} = \begin{bmatrix} \begin{bmatrix} \mathit{RMD}\\ \mathit{RDI}\\ \mathit{HF}\\ x_{\rm max}\text{ (mm)}\\ n\\ g(n)\\ x_{50}\text{ (mm)}\\ b\\ \end{bmatrix} & \begin{array}{c} \begin{bmatrix} \mathit{P}_1\text{ (w/w)}\\ \vdots\\ \mathit{P}_p\text{ (w/w)} \end{bmatrix} \\ \\ \\ \\ \end{array} \end{bmatrix} }[/math]
Example
The images below show the selection of input arrays and output results in the Excel interface.
 Figure 1. Example showing the selection of the Parameters (blue frame) array in Excel. |
 Figure 2. Example showing the selection of the Size (red frame) array in Excel. |
 Figure 3. Example showing the selection of the Results (light blue frame) array in Excel. |
See also
References
- ↑ Ouchterlony, F., 2005. The Swebrec© function: linking fragmentation by blasting and crushing. Mining Technology, 114(1), pp.29-44.