🎓 Lesson 5
D3
Calculation Methods and Formulas
Blast design formulas help engineers figure out how far apart to place explosive holes and how much explosive to use, so rock breaks efficiently and safely.
🎯 Learning Objectives
- ✓ Calculate optimal burden using the Konya–Hill empirical formula for given rock density and explosive strength
- ✓ Design spacing-to-burden ratio (S/B) to achieve target fragmentation index (F20) within ±15% accuracy
- ✓ Analyze powder factor against site-specific production goals and regulatory limits (e.g., OSHA 1926.900, MSHA Part 47)
- ✓ Apply stemming length formulas to prevent premature venting and ensure adequate confinement
📖 Why This Matters
Getting blast design wrong can cost millions: over-breaking wastes energy and damages equipment; under-breaking creates oversized boulders that stall loading, increase secondary breakage costs, and delay haulage schedules. In transportation mode selection—especially for mine-to-port conveyor or truck-haul systems—consistent, predictable fragmentation directly impacts fleet utilization, fuel consumption, and maintenance cycles. Accurate calculations aren’t just theory—they’re the difference between a profitable 18-month haul road life and a $2.3M premature reconstruction.
📘 Core Principles
Blast design rests on three interdependent pillars: (1) Energy transfer—how explosive energy couples into rock via confinement and borehole pressure; (2) Stress wave propagation—governed by rock elastic modulus, P-wave velocity, and discontinuity spacing; and (3) Fragmentation mechanics—where crack coalescence, tensile failure, and gas expansion dictate final fragment size distribution. Empirical methods (e.g., Konya–Hill, Langefors–Kihlström) simplify this complexity by correlating measurable field parameters—like unconfined compressive strength (UCS), rock density, and explosive relative weight strength (RWS)—to geometric ratios. Modern practice combines these with digital modeling (e.g., DFN-based fragmentation simulators), but field-calibrated formulas remain the industry’s first-line design tool due to speed, transparency, and auditability.
📐 Optimal Burden Calculation (Konya–Hill Method)
The Konya–Hill burden formula is widely adopted for surface bench blasting because it explicitly accounts for explosive energy density and rock resistance. It replaces outdated 'rule-of-thumb' burden = 25–30× hole diameter with physics-informed scaling based on rock density and explosive strength.
Konya–Hill Burden
B = 2.5 × (RWS × 1000 / ρ)⁰·⁵Calculates optimal burden (m) based on explosive relative weight strength and rock density.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| B | Burden | m | Shortest distance from hole center to free face |
| RWS | Relative Weight Strength | dimensionless | Explosive energy relative to TNT (e.g., ANFO = 0.80–0.85) |
| ρ | Rock Density | kg/m³ | Bulk density of intact rock measured from core or geophysical logs |
Typical Ranges:
Hard rock (granite, quartzite): 1.2 – 1.8 m
Medium rock (sandstone, limestone): 1.0 – 1.4 m
Soft rock (shale, weathered basalt): 0.8 – 1.2 m
💡 Worked Example
Problem: Given: ANFO with RWS = 0.82 (relative to TNT), rock density = 2.65 g/cm³ (2650 kg/m³), bench height = 12 m, desired stemming = 3.5 m. Calculate optimal burden.
1.
Step 1: Identify knowns — RWS = 0.82, ρ = 2650 kg/m³
2.
Step 2: Apply Konya–Hill formula: B = 2.5 × (RWS × 1000 / ρ)⁰·⁵ → B = 2.5 × (0.82 × 1000 / 2650)⁰·⁵
3.
Step 3: Compute: (820 / 2650) = 0.3094 → √0.3094 ≈ 0.556 → B = 2.5 × 0.556 = 1.39 m
4.
Step 4: Verify: For hard rock (UCS > 120 MPa), typical burden range is 1.2–1.8 m → 1.39 m is valid. Also check B ≤ 0.7 × bench height (0.7 × 12 = 8.4 m) → OK.
Answer:
The calculated burden is 1.39 m, which falls within the safe and typical range of 1.2–1.8 m for competent granite at this scale.
🏗️ Real-World Application
At the Boddington Gold Mine (Western Australia), engineers redesigned the primary blast for the North Pit ore zone after fragmentation analysis showed 22% oversize (>75 cm) in haul trucks, causing crusher jamming and 14% downtime. Using Konya–Hill burden recalibration (RWS adjusted for emulsion blend, ρ updated from core logging), they reduced burden from 1.65 m to 1.42 m and increased spacing from 2.1 m to 2.3 m (S/B = 1.62). Post-blast F20 improved from 68% to 89%, reducing secondary breaking costs by AU$1.1M/year and extending conveyor belt life by 22% through lower impact loading.