Fragmentation

Fragment size affects every downstream step — loading, hauling, crushing and grinding. Learn the Kuz-Ram model (mean size from rock factor, powder factor, charge and explosive strength), the Rosin–Rammler size distribution, uniformity index, fragmentation measurement by image analysis, and mine-to-mill optimisation.

A blast that leaves boulders means secondary breaking and slow digging; one that is too fine may cause ore loss and dust. Engineers predict fragmentation before blasting and measure it afterwards to fine-tune designs.

An analogy

Fragmentation is like chopping vegetables for a stew: the right size cooks evenly; big chunks slow everything down.

Why size matters

Shovels dig finer, looser muckpiles faster; trucks fill better; primary crushers choke less; mills grind finer feed with less energy. Oversize (larger than crusher gape) requires rock breakers.

Kuz-Ram model

Mean size decreases with higher powder factor and stronger explosives, and increases with harder, blockier rock (higher A). The uniformity index n (typically 0.8–2.2) depends on pattern geometry — accurate drilling and staggered patterns raise n (more uniform).

Measurement

Photo analysis of muckpiles, truck trays or conveyors (WipFrag, Split, AI camera systems), sieving of samples, and crusher power trends. Measured curves calibrate the model's rock factor.

Mine-to-mill

Studies at many mines show 5–20 % mill throughput increases from finer, more micro-fractured blast products. Advanced models (Swebrec, JKMRC crush-zone) predict fines better than Rosin–Rammler.

Formulas

• Kuznetsov / Kuz-Ram: x₅₀ = A K^(−0.8) Q^(1/6) (115/E)^(19/30) (cm)
• Rosin–Rammler: P(x) = 1 − exp[−0.693 (x/x₅₀)^n]
• Size at percent passing: x_P = x₅₀ [−ln(1 − P)/0.693]^(1/n)

Worked example: Kuz-Ram mean size

Given: A = 7, PF 0.78 kg/m³, Q = 78 kg ANFO (E = 100)

Find: x₅₀.

• K^(−0.8) = 0.78^(−0.8) = 1.22
• Q^(1/6) = 2.07; (115/100)^(0.633) = 1.09
• x₅₀ = 7 × 1.22 × 2.07 × 1.09 = 19.2 cm

Answer: ≈ 19 cm

Worked example: Oversize check

Given: x₅₀ = 19.2 cm, n = 1.5; Oversize limit 50 cm

Find: % passing 50 cm.

• P = 1 − exp(−0.693 × (50/19.2)^1.5) = 94.6 %

Answer: ≈ 5.4 % oversize

Common mistakes

• Wrong: Judging fragmentation by eye alone. — Right: Use image analysis and calibrate the model.
• Wrong: Raising PF without checking vibration. — Right: Balance fragmentation against vibration and flyrock limits.

Applications

• Loading productivity: Finer muck increases dig rates.
• Crusher throughput: Less oversize, fewer blockages.
• Mill energy: Mine-to-mill programmes.

Key takeaways

• x₅₀ = A K^−0.8 Q^(1/6)(115/E)^0.633.
• Rosin–Rammler gives the full curve.
• Measure and calibrate.
• Optimise mine-to-mill.

Going further

• Swebrec function: Better fines prediction than Rosin–Rammler.
• Crush zone model: Predicts fines generated near holes.
• AI fragmentation: Cameras on shovels measure every bucket.