Fragmentation Analysis
BlastCAD predicts rock fragmentation using the Kuz-Ram model — the most widely applied empirical fragmentation model in the mining industry, validated across a broad range of rock types and explosive products.
Table of contents
- The Kuz-Ram Model
- Step 1 — Mean Fragment Size (Kuznetsov Equation)
- Step 2 — Uniformity Index
- Step 3 — Rosin-Rammler Distribution
- Fragmentation Curve Visualization
- Energy Analysis
- Tuning Fragmentation Results
The Kuz-Ram Model
Kuz-Ram combines three equations:
- Kuznetsov (1973) — predicts mean fragment size.
- Cunningham (1983) — adjusts for explosive strength (RWS).
- Rosin-Rammler (1933) — models the full fragment size distribution.
Step 1 — Mean Fragment Size (Kuznetsov Equation)
The mean fragment size $x_{mean}$ (cm) is:
\[x_{mean} = A \times \left(\frac{V_0}{Q}\right)^{0.8} \times \left(Q \times \frac{RWS}{115}\right)^{\frac{1}{6}}\]Parameters
| Symbol | Name | Source | Typical Range |
|---|---|---|---|
| $A$ | Rock Factor | Geotechnical input | 5–13 |
| $V_0$ | Breakage volume per hole (m³) | Computed via Voronoi tessellation | |
| $Q$ | Charge mass per hole (kg) | From charge design | |
| $RWS$ | Relative Weight Strength | From Explosives Database | ANFO = 100; Emulsion ≈ 120 |
Rock Factor A
The Rock Factor encapsulates rock mass characteristics. BlastCAD uses these reference values; engineers can override it in the Statistics settings:
| Rock Type | A value |
|---|---|
| Soft rock (weak shale, soft limestone) | 5 – 7 |
| Medium rock (competent limestone, mudstone) | 7 – 9 |
| Hard rock (granite, basalt) | 9 – 11 |
| Very hard, blocky rock | 11 – 13+ |
Volume Calculation (Voronoi Method)
The breakage volume per hole is computed using a Voronoi tessellation of all hole collars projected onto the ring plane. Each hole’s Voronoi cell defines its area of influence; multiplied by the ring burden, this gives $V_0$.
For rings where Voronoi computation is not applicable (e.g., single-hole rings), BlastCAD falls back to the nearest-neighbour averaging method.
Step 2 — Uniformity Index
The uniformity index $n$ describes how spread out the fragment size distribution is:
\[n = \left(2.2 - 14\frac{B}{d}\right) \times \left(1 - \frac{W}{B}\right)^{0.5} \times \left(\frac{1 + S/B}{2}\right)^{0.1} \times \left(\frac{L_c}{H}\right)^{0.1}\]Where:
| Symbol | Parameter | Unit |
|---|---|---|
| $B$ | Burden | m |
| $d$ | Hole diameter | mm |
| $W$ | Standard deviation of drilling accuracy | m |
| $S$ | Spacing | m |
| $L_c$ | Charge length | m |
| $H$ | Hole length | m |
A higher uniformity index ($n$ > 1.5) produces a more uniform fragment distribution — less oversize and less fines. A lower index ($n$ < 1.0) indicates a wider spread.
Step 3 — Rosin-Rammler Distribution
The cumulative passing percentage for any screen size $x$ is:
\[P(x) = \left[1 - e^{-\left(\frac{x}{x_c}\right)^n}\right] \times 100\]The characteristic size $x_c$ is derived from $x_{mean}$ and $n$:
\[x_c = \frac{x_{mean}}{0.693^{1/n}}\]Key Performance Indicators
BlastCAD automatically reports:
| Metric | Meaning |
|---|---|
| P80 | Screen size that 80% of the rock passes through |
| P50 | Median fragment size (50% passing) |
| P20 | Screen size that 20% of the rock passes through |
| Oversize (%) | Percentage of material exceeding the crusher feed size |
The P80 is the most commonly used metric for blast-crusher interfacing. The typical target for underground primary crushing is P80 < 400 mm.
Fragmentation Curve Visualization
The Statistics dashboard plots the full Rosin-Rammler curve as a cumulative passing percentage chart:
- X-axis: Fragment size (mm or cm, logarithmic scale)
- Y-axis: Cumulative passing (%)
- Markers: P20, P50, P80 annotated on the curve
- Reference line: Crusher feed limit (configurable)
The curve updates automatically when blast parameters change (charge mass, burden, hole diameter).
Energy Analysis
Alongside fragmentation, the Energy tab in the Statistics dashboard shows:
| Metric | Formula | Description |
|---|---|---|
| Total explosive energy (MJ) | $E_{total} = \Sigma (m_i \times e_i)$ | Sum of energy across all explosive segments, where $e_i$ = energy per kg (MJ/kg) |
| Energy density (MJ/m³) | $E_{density} = E_{total} / V_{total}$ | Explosive energy relative to total blasted volume |
| Powder factor (kg/t) | $PF = m_{total} / T_{total}$ | Explosive mass per tonne of rock |
| Specific drilling (m/t) | $SD = D_{total} / T_{total}$ | Total drilled metres per tonne of rock |
Energy Values by Explosive Type
| Explosive | Density (kg/m³) | Energy (MJ/kg) | RWS |
|---|---|---|---|
| ANFO | 800 | 3.85 | 100 |
| Emulsion 1.0 | 1000 | 3.18 | 90 |
| Emulsion 1.2 | 1200 | 3.60 | 105 |
| Heavy ANFO (70/30) | 1050 | 4.00 | 115 |
| Dynamite (NG-based) | 1300 | 4.60 | 120 |
Custom explosives: If you have product-specific energy data from the manufacturer, enter it directly into the Explosives Database to override the defaults.
Tuning Fragmentation Results
If the predicted fragmentation does not match observed results on site:
- Adjust Rock Factor A — calibrate against back-analysis of historical blasts.
- Check $W$ (drilling accuracy) — poor drilling accuracy increases scatter and lowers $n$.
- Review burden and spacing — the most impactful parameters. Even 0.2 m of extra burden significantly coarsens the P80.
- Review charge design — a higher powder factor generally reduces P80, but with diminishing returns above the optimal specific charge.
References:
- Kuznetsov, A. (1973). The mean diameter of the fragments formed by blasting rock.
- Cunningham, C.V.B. (1983). The Kuz-Ram model for prediction of fragmentation from blasting.
- Rosin, P. & Rammler, E. (1933). The laws governing the fineness of powdered coal.