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3D and 4D Explosive Energy Models

2DBench incorporates static and dynamic 3D/4D models for calculating and displaying the distribution of explosive energy in space. The static 3D model does not consider timing, while the dynamic 4D model is a 3D analysis that incorporates timing as the fourth dimension using a weighting function. Explosive energy can be expressed in various units including kg/tonne, kg/m3, MJ/tonne, MJ/m3, and MJ/m2. The cooperation time affects the weighting function and represents the time interval where detonating charges will interact before rock movement reduces their effect.

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316 views2 pages

3D and 4D Explosive Energy Models

2DBench incorporates static and dynamic 3D/4D models for calculating and displaying the distribution of explosive energy in space. The static 3D model does not consider timing, while the dynamic 4D model is a 3D analysis that incorporates timing as the fourth dimension using a weighting function. Explosive energy can be expressed in various units including kg/tonne, kg/m3, MJ/tonne, MJ/m3, and MJ/m2. The cooperation time affects the weighting function and represents the time interval where detonating charges will interact before rock movement reduces their effect.

Uploaded by

Jose Rojas
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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08-07-2009 2DBench Help

Explosive Energy Distribution

2DBench incorporates two methods for calculating and displaying the distribution of the energy of explosives in
3D space.

3D static explosive energy distribution.

4D dynamic explosive energy distribution.

Explosive energy distribution may be expressed in several units: kg/tonne, kg/m³, MJ/tonne, MJ/m³ and MJ/m².
The first four unit types (excluding MJ/m²) available in the explosive distribution model are analogous to the
conventional powder factor calculation (kg of explosive divided by tonnes or volume of rock blasted), except
concentrated at a small point; the fifth unit is an energy flux value.

Static 3-D Explosive Distribution


The three dimensional explosive energy distribution of a charge does not take timing into account and is
determined in 2DBench following the approached developed by Kleine et al (1993).

The traditional powder factor calculation was extended by considering a small infinitesimal segment of charge
and writing the equation for the resulting explosive concentration at a point "P" for a sphere centred at the charge
segment, the general form of the equation is as follows (see diagram below).

(1)

Equation (1) can be integrated and


rewritten as:

(2)

Special conditions apply to the


above relationships at the charge
axis (ie. h=0) and at very large
distances (ie. h = infinity). The
explosive concentration at any
point in 3D is determined by
solving the appropriate integrated
form of the equation for each
explosive charge and summing the
values.

Dynamic 4-D Explosive Distribution


The 4D explosive energy distribution differs from a 3D calculation, in that the detonation timing is considered as
the fourth dimension. The model is based in the 3D analysis and incorporates a weighting factor which is a
function of the time a deck detonates and a rock mass specific factor called "cooperation time".

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08-07-2009 2DBench Help
As part of the 4D energy distribution analysis, a timing simulation must be carried out first. The 4D energy
distribution tessellates points on a plane specified by the user just like the 3D energy distribution. For each
calculation point, the nearest charged deck is found. The time at which this deck detonates is used as a
reference time (tnd). A weighting function is determined based on the cooperation time and detonation time of the
charges. For every explosive deck in the timing simulation the 3D explosive energy value is calculated and
multiplied by the term given by the following weighting function:

(3)

where

td is the time the deck detonated,

tnd is the time the nearest deck to the calculation point detonated and

tc is the co-operation time.

The graph of this weighting function is shown below.

The cooperation time affects how steeply the weighting goes to zero and is the time interval within which decks
adjacent to a detonating deck will assist in the fragmentation of the rock mass. After this time interval, the
interaction of decks reduces significantly due to the movement of the rock mass. The time is approximately the
time to first burden movement and is very much a rock mass dependent property.

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