Burden is calculated according to the following expression:

 $$ B=\frac{0.17 \cdot P_{h} \cdot r_{h}}{k\cdot \sigma_{t}} $$

Where:

   $ \sigma_{t} $ - Tensile strength of the monolith rock (MPa)

   $P_{h} $ - Detonation pressure (GPa)

   $r_{h} $ - Borehole radius (m)

   $$ k=\frac{(1-\nu )}{(1+\nu )(1-2\nu )} $$

   $\nu - $Poisson's ratio

 

According Chapman-Jouguet detonation theory, Chapman [1] and Jouguet [2], pressure on the blasthole walls for explosives with density above 1 g/cm3 can be calculated as:

 

 

$$ {{P}_{d}}=\frac{{{\rho }_{e}}\cdot {{D}^{2}}}{8} \label{eqn:1} \tag{1}$$

Where:

            ρe – density of explosive (g/cm3)

            D – detonation velocity of explosive (km/s)

 

 

For explosive with density below 1 g/cm3 pressure on the blasthole walls is calculated by:

 $$ {{P}_{d}}=\frac{{{\rho }_{e}}\cdot {{D}^{2}}}{4.5} \label{eqn:2} \tag{2}$$

 

Equations \ref{eqn:1} and \ref{eqn:2} assume that blasthole if fully filled with explosive, if blasthole radius and radius of explosive charge differ or blasthole is not fully filled with explosive, pressure on the blasthole walls is calculated by:

 

$$ {{P}_{h}}={{P}_{d}}\cdot {{\left( \frac{{{d}_{e}}}{{{d}_{h}}} \right)}^{3}} $$

Where:

            Ph – Pressure on the blasthole walls (GPa)

            Pd – Detonation pressure (GPa)

            de – Diameter of explosive charge

            dh – Blasthole diameter

 

 

Burden calculator provides simple form that is it be used for burden calculation by above explained procedure.

    

 

References

[1] Chapman, D. L. "On the rate of explosion in gases". Philosophical Magazine Series 5 47 (284): 90–104. 1899.  DOI:10.1080/14786449908621243

[2] Jouguet, Emile. “Sur la propagation des réactions chimiques dans les gaz" [On the propagation of chemical reactions in gases], Journal de Mathématiques Pures et Appliquées, series 6 (in French) 347–425 pp. 1905.


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