Drill-and-Blast Pattern Design: Fragmentation Calculator & Visualizer

simulator intermediate ~12 min
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PF = 0.52 kg/m³ — moderate blast energy

A 3.5m burden × 4m spacing × 10m bench with 150mm holes yields a powder factor of 0.52 kg/m³ and estimated mean fragment size of 380 mm — well-suited for primary crusher feed.

Formula

PF = ρ_e × π × D² / (4 × B × S) (powder factor)
x50 = A × K^(-0.8) × Q^(0.167) × (V_0/Q)^0.8 (Kuz-Ram mean fragmentation)
S/B ratio = 1.0 to 1.3 for staggered patterns

The Art and Science of Rock Blasting

Drill-and-blast remains the primary method of rock excavation in mining, moving billions of tonnes of rock annually worldwide. The goal is controlled fragmentation — breaking rock into pieces small enough for efficient loading, hauling, and crushing while minimizing flyrock, ground vibration, and explosive waste. The blast pattern geometry (burden, spacing, hole depth) and charge design determine the energy distribution that shatters the rock mass.

Blast Geometry and Powder Factor

Burden (B) is the critical distance from each blasthole to the free face — too small causes cratering and flyrock, too large results in poor breakage. Spacing (S) controls lateral energy distribution between holes. The powder factor PF = explosive mass / rock volume provides a single metric of blast intensity, typically ranging from 0.3 kg/m³ in soft limestone to 1.0+ kg/m³ in hard granite. Staggered patterns improve energy distribution over square patterns.

Fragmentation Prediction

The Kuz-Ram model, introduced by Cunningham in 1983, combines Kuznetsov's equation for mean fragment size with the Rosin-Rammler size distribution. It predicts x50 (the size through which 50% of fragments pass) from explosive energy, rock factor, and blast geometry. While empirical, it remains the industry standard for initial blast design. Finer fragmentation improves crusher throughput, reduces energy consumption downstream, and increases SAG mill performance.

Optimization and Economics

Modern mine-to-mill programs optimize blasting not in isolation but as part of the total value chain. Spending more on explosives (higher powder factor) can dramatically reduce crushing and grinding costs, which dominate energy consumption. This simulation lets you explore how pattern geometry affects fragmentation and powder factor, revealing the tradeoffs between explosive cost and downstream processing efficiency.

FAQ

What is powder factor in blasting?

Powder factor (PF) is the mass of explosive per cubic meter of rock broken, typically 0.3-1.0 kg/m³ for open-pit mining. Higher PF means more energy per unit volume, producing finer fragmentation but at greater cost. It is the single most important parameter linking blast design to downstream processing.

What is the Kuz-Ram fragmentation model?

The Kuz-Ram model, developed by Cunningham (1983) combining the Kuznetsov and Rosin-Rammler equations, predicts mean fragment size x50 from explosive energy, rock factor, and geometry. It remains the most widely used empirical fragmentation model in blast design, despite known limitations for fine fractions.

What is burden and spacing in blasting?

Burden is the distance from the blasthole to the nearest free face (bench edge). Spacing is the distance between adjacent holes in the same row. The ratio S/B typically ranges from 1.0 to 1.3. These two parameters control rock volume per hole and energy distribution throughout the blast.

How does hole diameter affect fragmentation?

Larger diameter holes hold more explosive, producing higher energy concentration and generally finer fragmentation. However, they also require wider burden and spacing, affecting energy distribution. Typical open-pit diameters range from 150 mm to 310 mm; underground operations use 45-100 mm.

Sources

Embed

<iframe src="https://homo-deus.com/lab/mining-engineering/blast-design/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub