Vibration, Flyrock & Safety Analysis

Ground vibration and flyrock are the two most critical safety parameters in blast design. BlastCAD’s analytics engine computes both, allowing engineers to validate designs against regulatory limits before any explosive is loaded.

Ground Vibration — PPV Prediction
Regulatory Compliance
1. Minimum Safe Distance
Detonation Timing Analysis
1. Timing Chart
2. Scatter Analysis
Flyrock Analysis
1. Risk Zones
2. Reducing Flyrock Risk
Stemming Adequacy Analysis
Critical Radius (Livingston Crater Theory)

Ground Vibration — PPV Prediction

Model: Attewell & Farmer (1976)

BlastCAD predicts Peak Particle Velocity (PPV) using the scaled-distance relationship:

\[PPV = K \times \left(\frac{R}{\sqrt{MIC}}\right)^{-\alpha}\]

The term $\frac{R}{\sqrt{MIC}}$ is the Scaled Distance (SD).

Parameters

Symbol	Parameter	Default	Description
$K$	Site transmission constant	1140	Calibrated from site monitoring data
$\alpha$	Site attenuation exponent	1.6	Rate of vibration decay with distance
$R$	Distance to monitoring point	User input (m)	Distance from the nearest blast hole to the sensitive receptor
$MIC$	Maximum Instantaneous Charge	Auto-calculated (kg)	Maximum charge weight detonating within an 8 ms window

Setting Site Constants

Default values ($K = 1140$, $\alpha = 1.6$) are conservative estimates for hard rock. For accurate predictions, calibrate these values from your site vibration monitoring records:

Open Statistics → Vibration tab.
Click Configure Site Constants.
Enter $K$ and $\alpha$ derived from regression of historical PPV vs. scaled distance data.

Maximum Instantaneous Charge (MIC)

MIC is the total explosive mass detonating within any 8 ms timing window. BlastCAD calculates MIC automatically from the delay sequence:

All hole delays are sorted.
For each timing window [t, t + 8ms], the sum of charges firing in that window is computed.
MIC = the maximum of all window sums.

Minimizing MIC is one of the most effective ways to reduce PPV at a given distance. Strategies:

Increase inter-hole delay intervals (spread the timing window).
Split the blast into multiple decks.
Reduce charge mass per hole.

Regulatory Compliance

BlastCAD checks computed PPV against user-defined regulatory limits:

Receptor Type	Common Limit	Standard
Residential buildings	5 mm/s	AS 2187.2-2006
Heritage structures	2 mm/s	AS 2187.2-2006
Underground structures	25 mm/s	Site-specific
Monitoring instruments	1 mm/s	Site-specific

Set your compliance limit in Project Settings → Vibration Limits. The Vibration tab shows a colour-coded indicator (green = compliant, red = exceedance) against each defined receptor.

Minimum Safe Distance

The inverse PPV formula gives the minimum safe distance $R_{min}$ for a given PPV limit $V_{limit}$:

\[R_{min} = \sqrt{MIC} \times \left(\frac{K}{V_{limit}}\right)^{1/\alpha}\]

BlastCAD displays this as a circle in the 3D viewport when the Vibration overlay is enabled.

Detonation Timing Analysis

The Timing tab visualizes the complete firing sequence across all holes and rings.

Timing Chart

X-axis: Time (ms)
Y-axis: Hole ID (sorted by ring and hole number)
Each hole is represented by a vertical bar spanning its expected detonation window (nominal delay ± scatter).

Scatter Analysis

Detonation scatter is defined per detonator type in the Explosives Database as a percentage of the nominal delay:

\[\text{Scatter window} = \pm \left(\text{Nominal Delay} \times \frac{\text{Scatter \%}}{100}\right) \text{ ms}\]

Detonator type	Typical scatter
Electronic	±0.1% (< 1 ms for typical delays)
Non-electric (shock tube)	±3–5%
Pyrotechnic	±10–15%

The timing chart shows scatter bars for each hole. Timing window collisions (where two holes’ scatter windows overlap) are highlighted in yellow — these indicate a risk that two holes may fire simultaneously, increasing MIC above the intended design value.

Flyrock Analysis

Flyrock is rock ejected beyond the intended blast zone. BlastCAD estimates the maximum theoretical ejection distance using the model:

\[D_{fly} = \frac{V_0^2 \sin(2\theta)}{g}\]

Where:

$V_0$ = Initial ejection velocity (computed from stemming length and charge energy)
$\theta$ = Ejection angle (worst case = 45°)
$g$ = Gravitational acceleration (9.81 m/s²)

The ejection velocity is estimated from the powder factor and stemming adequacy:

\[V_0 = C_{fly} \times \sqrt{\frac{Q}{V_{hole}} \times (1 - L_s / L_{hole})}\]

Where $L_s$ is the stemming length and $C_{fly}$ is an empirical ejection coefficient.

Risk Zones

BlastCAD maps three flyrock risk zones in the 3D viewport:

Zone	Color	Risk Level
Inner (0 – 50% of $D_{fly}$)	Red	High — exclusion zone during blasting
Middle (50 – 80% of $D_{fly}$)	Orange	Medium — personnel must be sheltered
Outer (80 – 100% of $D_{fly}$)	Yellow	Low — observer positions acceptable

Reducing Flyrock Risk

Increase stemming length — the most effective mitigation.
Reduce charge per hole — reduces ejection energy.
Use inert stemming material — crushed stone at 16–19 mm provides the best confinement vs. cuttings or drill chips.

Stemming Adequacy Analysis

The Stemming tab analyses each hole’s collar stemming length relative to industry guidelines.

The minimum recommended stemming length is:

\[L_{stem,min} = 20 \times d\]

Where $d$ is the hole diameter in metres (i.e., 20 diameters of stemming is the industry rule of thumb).

Hole diameter	Min. recommended stemming
76 mm (3”)	1.52 m
89 mm (3.5”)	1.78 m
102 mm (4”)	2.04 m
127 mm (5”)	2.54 m
165 mm (6.5”)	3.30 m

BlastCAD flags any hole where the collar stemming length is less than $20d$ with a warning in the Stemming tab and in the Properties Panel.

Critical Radius (Livingston Crater Theory)

The Critical Radius tab computes per-hole breakage and critical radii using Livingston’s Crater Theory.

\[R_c = C_b \times Q^{1/3}\] \[R_b = C_b \times \Delta^{1/3} \times Q^{1/3}\]