# BlastIQ™ Volume Calculation Release Date:
31th of October 2022
KBA Summary:
This Knowledge Base Article describes how are BlastIQ™ Hole and Blast Volumes calculated.

# Summary

BlastIQ™ calculates hole and blast volumes based on design, drilled and measured information with minimum inputs.

The volume calculations performed by BlastIQ are approximate by nature and they may change as improvements are made to the algorithm to cover more scenarios.

## Objective

Provide automated and consistent volume and powder factor calculations based on minimal D&B information.

# Hole Volume

The volume of a hole considering its relevant position and of other holes in the plan. Volume calculated from the hole area on the collar and toe

Hole Area

Hole Collar and Toe areas are calculated by using a modified Voronoi Tessellation which allows an area of influence for each hole, based on the corresponding coordinates, to be calculated with minimum information without the need for boundaries or theoretical burden and spacing values. This calculation takes in account the hole's collar or toe coordinates and of holes around it.

The Voronoi Tessellation is also used for visualization purposes of blast plans in most of BlastIQ™ Insights dashboards, allowing easy visualisation across different blasthole patterns. Read more here.

Stab holes identification is not considered in this calculation.

Hole Design Volume

The volume of a hole considering the hole design location and Grade Z.

Hole Design Volume = (Hole Collar Area + Hole Toe Area)/2 * h

Where:

• Hole Collar Area = area calculated from design collar coordinates.
• Hole Toe Area= area calculated design toe coordinates.
• h = Collar Z - Grade Z.
• if Grade Z = 'null', then h = Collar Z - Toe Z.

If a hole has no design geometry (collar and toe locations) then is not considered in the Voronoi Tessellation calculation and will have a 'null' hole design volume.

Hole Best Available Viable Volume

Excluded Holes

Holes marked as 'not drilled' or 'abandoned' (read more here) are excluded when calculating the Best Available Viable Area calculation.

The volume of a hole considering the hole best available available information and intended floor surface (Grade Z).

Hole Best Available Viable Volume = (Hole Collar Area + Hole Toe Area)/2 * h

Where:

• Hole Collar Area = area calculated from best available collar coordinates,
• Hole Toe Area = area calculated from best available toe coordinates
• Best available toe coordinates calculated using:
• best available collar coordinates.
• best available angle and bearing.
• the first (from top to bottom) length available out of:
• design length
• drill actual length
• measured actual length
• h = Collar Z - Grade Z.
• if Grade Z = 'null', then h = Collar Z - Toe Z.

Only if complete actual information is available, then Hole Best Available Viable Volume is considered Actual volume.

### Is Actual

Conditions required for Best Available Viable Volume to be Actual Volume

• A hole must have a complete drill actual: collar coordinates + length, angle and bearing.

• A hole must have an adjusted design length.

• A hole must have a Grade Z value

• When all of the above is true, BestAvailableViableIsActual is true.

### Partial Information

To deal with partial data, the following exceptions are in place:

• If a hole has no collar z the average best available collar z is taken.

• if no holes have a collar z then z is taken to be 0.

• if no angle is available assumed to be 0.

• If no bearing is available assumed to be 0.

# Blast Volume

The volume of a blast is calculated by summing the corresponding hole volumes within it. This differs based on what kind of volume is being calculated:

• Blast Design Volume - Only considers holes that have a design geometry.
• Blast Best Available Viable Volume - Only considers holes that are viable. i.e. excludes holes marked as 'not drilled' or 'abandoned'.

Only if complete actual information is available for all holes in the blast, then Blast Best Available Viable Volume is considered Actual volume.

## Exceptions:

Hole and Blast Volume calculations can become invalid where inconsistencies are encountered such as:

• Any of the hole's Grade Z is higher than its Collar Z.
• Holes have duplicate Collar information.

# Calculation Frequency

Hole areas and volumes are calculated on a 20 minute interval. When integrating with API or viewing dashboards, this delay should be considered.