kirra-docs

Flyrock Modelling

Kirra generates 3D flyrock shroud surfaces representing the ballistic envelope of flyrock hazards around blast holes. Three empirical models are available to predict maximum throw distances and launch velocities.

Screenshot coming soon – 3D flyrock shroud dome over blast pattern

Available Models

1. Richards & Moore (2004)

Empirical model with three distinct flyrock mechanisms:

Mechanism Governed By Description
Face Burst Burden Horizontal projection of rock from the free face
Cratering Stemming length Vertical projection from the collar area
Stem Eject Stemming + angle Angled projection of stemming material

Formula (clearance distances):

Face Burst = (K^2 / g) x (sqrt(W) / B)^2.6 x FoS
Cratering  = (K^2 / g) x (sqrt(W) / St)^2.6 x FoS
Stem Eject = Cratering_base x sin(2 x theta) x FoS

Where W = mass per metre (kg/m), B = burden, St = stemming, K = flyrock constant, FoS = factor of safety.

Parameter Default Description
Flyrock Constant (K) 20 Empirical coefficient (typical range 14-30)
Factor of Safety (FoS) 2 Safety multiplier (1-5)
Stem Eject Angle 80 deg Launch angle for stemming material (30-90 deg)

Note (v1.0.11 fix): A bug was corrected where the Factor of Safety was being applied twice – once in the base distance calculation and again in the clearance distance. FoS is now applied exactly once at the clearance stage.

2. Lundborg (1975/1981)

Simple diameter-based upper-bound estimate:

Lmax = 260 x d^(2/3)    (d in inches)

Conservative, requires only hole diameter. Useful as a quick sanity check.

3. McKenzie (2009/2022)

Scaled Depth of Burial (SDoB) based prediction with contributing charge mass:

Range = 9.74 x (diameter_mm / SDoB^2.167)^(2/3)

Most sophisticated model – accounts for stemming, charge confinement, and contributing charge length.

3D Shroud Generation

The flyrock shroud is generated using the Chernigovskii ballistic envelope – the maximum altitude a projectile can reach at any horizontal distance for any launch angle:

altitude(d) = (V^4 - g^2 x d^2) / (2 x g x V^2)

This creates a parabolic dome above each hole. The shroud surface is built by:

  1. Computing per-hole flyrock parameters from charging data
  2. Creating a regular XY grid over the blast extent plus padding
  3. Computing maximum envelope altitude at each grid point
  4. Triangulating the grid and culling triangles outside the envelope

Configuration

Parameter Default Description
Algorithm Richards & Moore Flyrock calculation method
Rock Density 2600 kg/m3 Rock mass density (1500-4000)
Grid Resolution 40 XY grid cell count (10-100, higher = smoother)
End Angle 85 deg Face steepness culling threshold
Transparency 0.5 Shroud opacity (0-1)

How to Use

  1. Load blast holes with charging data assigned
  2. Click the Flyrock Shroud button in the Surface toolbar
  3. Select your algorithm and adjust parameters
  4. Click Generate to create the 3D shroud
  5. The semi-transparent dome appears over the blast pattern

The shroud is visible from both sides, rendered after the terrain for correct layering, and can be toggled on/off.

Example Calculation (Richards & Moore)

For a 115mm hole, 12m bench height, 2m stemming, 3.6m burden, 1m subdrill, 1.2 kg/L explosive density, K=20, FoS=2: