🎓 Lesson 22
D5
Comprehensive Knowledge Quiz
Blast design is the careful planning of where and how much explosive to place in a rock face to break it safely and efficiently.
🎯 Learning Objectives
- ✓ Calculate optimal burden and spacing using rock properties and explosive energy metrics
- ✓ Design a delay-initiated blast pattern to control throw and reduce vibration using wave interference principles
- ✓ Analyze fragmentation distribution (Kuz-Ram model) from drone-derived muck pile imagery and correlate with powder factor
- ✓ Explain the trade-offs between drilling cost, explosives cost, and secondary breaking requirements in economic blast optimization
- ✓ Apply ISEE blast vibration limits and flyrock prediction models to validate design safety margins
📖 Why This Matters
In drone-based mine surveying, high-resolution pre- and post-blast 3D models are now standard—but without rigorous blast design, those data reveal only consequences, not causes. A poorly designed blast wastes energy, damages equipment, violates regulatory vibration limits, and creates hazardous oversized boulders requiring costly secondary breaking. For drone inspectors, understanding blast design means you can diagnose root causes from orthomosaic anomalies, prioritize inspection zones, and collaborate effectively with blasting engineers—turning visual data into actionable engineering insight.
📘 Core Principles
Blast design rests on three interdependent pillars: (1) Energy coupling—how efficiently explosive energy transfers to rock via confinement, stemming, and borehole diameter; (2) Stress wave interaction—timing delays so compressive waves reinforce fragmentation while tensile waves cancel to reduce vibration; and (3) Fragmentation mechanics—governed by rock strength, discontinuity orientation, and energy per unit volume (powder factor). Modern drone surveys feed this theory by quantifying actual burden consistency, backbreak extent, and muck pile gradation—enabling closed-loop design refinement. Critical dependencies include RMR or Q-system rock mass rating, P-wave velocity (measured via seismic refraction or drone-mounted geophones), and explosive detonation velocity (VoD) matching to rock impedance.
📐 Burden Calculation (Langefors–Kihlstrom Empirical Formula)
This widely adopted empirical formula estimates initial burden based on rock strength and explosive energy. It balances confinement pressure against rock resistance to avoid excessive cratering or poor breakage. Used early in design before numerical modeling, it provides a field-validated starting point for drone-assisted pattern verification.
Langefors Burden
B = K × √E × (1 + 0.1 × PF)Empirical estimation of burden (m) based on rock strength, explosive energy coupling, and desired powder factor.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| B | Burden | m | Perpendicular distance from free face to first row of holes |
| K | Rock Factor | dimensionless | UCS (MPa) divided by 10; correlates rock strength to burden capacity |
| E | Explosive Coupling Factor | dimensionless | (Detonation velocity × explosive density) / (Rock density × 1000) |
| PF | Powder Factor | kg/m³ | Mass of explosive per unit volume of rock broken |
Typical Ranges:
Hard rock (UCS > 100 MPa): 3.0 - 9.5 m
Medium rock (UCS 50–100 MPa): 2.5 - 6.0 m
Soft rock (UCS < 50 MPa): 1.8 - 4.0 m
💡 Worked Example
Problem: Given: Rock uniaxial compressive strength (UCS) = 120 MPa, ANFO density = 0.85 g/cm³, VoD = 4,500 m/s, specific gravity of rock = 2.65, desired powder factor = 0.35 kg/m³.
1.
Step 1: Calculate rock factor K = UCS / 10 = 120 / 10 = 12 MPa (dimensionless scale used in Langefors tables)
2.
Step 2: Determine explosive constant E = (VoD × ρ_explosive) / (ρ_rock × 1000) = (4500 × 850) / (2650 × 1000) ≈ 1.44
3.
Step 3: Apply Langefors formula: B = K × √E × (1 + 0.1 × PF) = 12 × √1.44 × (1 + 0.1 × 0.35) = 12 × 1.2 × 1.035 ≈ 14.9 m — but adjust for bench height (12 m): limit B ≤ 0.8 × H = 9.6 m → select B = 9.5 m
4.
Step 4: Verify against typical range: For hard rock (UCS > 100 MPa), burden typically falls between 3.0–9.5 m — 9.5 m is acceptable but requires high-quality stemming and precise drilling.
Answer:
The calculated burden is 9.5 m, which falls within the safe and typical range of 3.0–9.5 m for hard rock at 12 m bench height.
🏗️ Real-World Application
At Newmont’s Boddington Mine (Western Australia), drone-based photogrammetry revealed consistent over-break along the toe of a 15-m bench in the oxide ore zone. Analysis showed burden values averaged 10.2 m—exceeding the Langefors-recommended 8.7 m for UCS = 95 MPa rock. Engineers revised the pattern: reduced burden to 8.5 m, increased spacing to maintain burden/spacing ratio (B/S) at 0.82, and introduced electronic delays (25-ms intervals) to improve wall control. Post-blast drone surveys confirmed 32% reduction in backbreak area and 27% improvement in fragment uniformity (D80 reduced from 1.42 m to 1.04 m), directly reducing loader cycle time and secondary breaking costs.