Blasting (KCO)

Description

This article describes the Kuznetsov–Cunningham–Ouchterlony (KCO) model (Ouchterlony, 2005) for predicting rock fragmentation by blasting.

Model theory

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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

• Distributions (Swebrec)