kirra-docs

PPV & Vibration Models

Kirra provides 6 vibration prediction models ranging from simple empirical site laws to full time-domain waveform synthesis. This page summarises each model and its key parameters.

Screenshot coming soon – PPV overlay on blast pattern

1. PPV Site Law

The simplest model. Computes Peak Particle Velocity using the empirical scaled-distance law.

Formula: PPV = K x (D / Q^n)^(-b)

Parameter	Default	Description
K	1140	Site constant (calibrated from blast monitoring)
b	1.6	Site exponent (attenuation slope, typical 1.5-2.0)
n	0.5	Charge weight exponent (0.5 = square-root scaling)
Cutoff Distance	1.0 m	Minimum distance to avoid singularity
Target PPV	0 mm/s	Black contour line at this value (0 = disabled)

MIC Bin Mode: When the Time Window parameter is set to a value greater than 0, the model switches to Maximum Instantaneous Charge bin mode. Fixed-width bins group holes by firing time, and each bin’s combined charge mass is used instead of individual hole masses. Essential for accurate near-field PPV prediction.

2. PPV Per-Deck

Per-deck variant of the site law. Instead of treating each hole as a single point charge, this model evaluates PPV separately for each charged deck using that deck’s own mass and position.

Advantages over PPV Site Law:

Multi-deck holes show per-deck influence zones
Air gaps between decks are naturally excluded
Each deck uses its own mass, not the total hole mass

Same parameters as PPV Site Law, with an additional max display distance setting.

3. Heelan Original

Physics-based model implementing Heelan’s (1953) analytical solution for radiation from a cylindrical charge. Divides each charge column into discrete elements and computes P-wave and SV-wave contributions with directional radiation patterns.

Parameter	Default	Description
Rock Density	2700 kg/m3	Rock mass density
P-Wave Velocity	4500 m/s	From seismic testing
S-Wave Velocity	2600 m/s	From seismic testing
VOD	5500 m/s	Fallback when no product VOD assigned
Elements	20	Charge discretisation count (max 64)
Q_p	50	P-wave attenuation factor (0 = elastic)
Q_s	30	S-wave attenuation factor (0 = elastic)

Features:

Supports angled holes (uses collar-to-toe axis)
Reads actual charge column bounds from charging data
Per-hole VOD from assigned explosive products
Viscoelastic attenuation

4. Scaled Heelan

Bridges the empirical site law with Heelan’s directional radiation patterns. Each element’s waveform peak is given by the site law constants K and b, while retaining directional behaviour from the Heelan model. Developed by Blair & Minchinton (2006).

Same parameters as PPV Site Law plus rock velocity parameters from Heelan Original.

Best for: Compliance prediction with directional accuracy at sites with calibrated K and b values.

5. Blair Lite (Scaled Heelan 90%)

Same energy summation approach as Scaled Heelan but uses Blair’s (2015) improved radiation patterns:

P-wave radiation is non-zero on the hole axis (unlike pure Heelan)
S-wave velocity is derived from P-wave velocity and Poisson’s ratio (instead of separate input)
Primer-aware element ordering
Near-axial regularisation

Parameter	Default	Description
K	1140	Site constant
B	1.6	Site exponent
P-Wave Velocity	4500 m/s
Poisson’s Ratio	0.25	S-wave velocity derived from this
VOD	5500 m/s	Fallback

6. Blair Heavy (Time-Domain)

Full time-domain waveform superposition model. Runs on CPU via Web Workers (not GPU), computing PPV on a 3D voxel grid for truly volumetric output. Uses multiple workers based on your computer’s processor count.

Parameter	Default	Description
K	700	Site constant (gamma x SITEK)
B	1.5	Site exponent
Charge Exponent	0.7
Gamma	0.0455	Waveform scaling factor
Poisson’s Ratio	0.25
Rock Density	2500 kg/m3
P-Wave Velocity	6000 m/s
VOD	5279 m/s	Fallback
Bandwidth	10000	Hz-like waveform parameter
Pulse Order	6	Waveform shape parameter
Elements per Deck	12

Key differences from other models:

Time-domain waveform synthesis with P/S arrival times
Primer location controls detonation front direction
Results are exported to GLB for safe persistence in IndexedDB
Does not support time interaction or real-time updates

Damage and Energy Models

7. Non-Linear Damage (Holmberg-Persson)

Computes cumulative damage index based on PPV threshold for crack initiation.

Parameter	Default	Description
Rock UCS	120 MPa	Unconfined Compressive Strength
Rock Tensile	12 MPa	Typically UCS/10
PPV Critical	700 mm/s	Threshold for new crack initiation
K_hp	700	Holmberg-Persson site constant
Alpha	0.8	Charge length exponent
Beta	1.4	Distance exponent

Output: Damage Index (0-1). Values approaching 1.0 indicate significant damage.

8. Jointed Rock Damage

Combines intact rock fracture with joint-controlled failure. Evaluates both dynamic stress against tensile strength and Mohr-Coulomb failure on joints.

Additional parameters: joint set angle, joint cohesion, joint friction angle.

Output: Damage Ratio (values > 1.0 = failure).

9. Borehole Pressure

Computes borehole wall pressure and its attenuation with distance from each charged deck.

Formula: P(R) = Pb x (a / R)^alpha

Where Pb = rho_e x VOD^2 / 8 (borehole wall pressure).

Output: MPa. Best for near-field wall damage assessment and presplit design.

10. Volumetric Powder Factor

Per-deck powder factor analysis. Each charged deck contributes its mass within a spherical volume at the observation distance.

Output: kg/m3 on a log scale.