🎓 Lesson 2
D2
Core Principles and Theory
Blast design is the science of placing explosives in rock to break it efficiently and safely for excavation.
🎯 Learning Objectives
- ✓ Calculate optimal burden and spacing using the Kuz-Ram fragmentation model
- ✓ Design a delay sequence to minimize ground vibration using time-domain superposition principles
- ✓ Analyze blast-induced airblast and peak particle velocity against USBM and DIN 4150-3 limits
- ✓ Apply powder factor to estimate explosive consumption per unit volume of rock and compare against industry benchmarks
📖 Why This Matters
Every ton of copper, lithium, or rare earths extracted for renewable energy infrastructure—solar panel mounts, wind turbine foundations, battery-grade ore—starts with a precisely engineered blast. Poor blast design causes oversize boulders (increasing crushing costs), excessive ground vibration (damaging nearby infrastructure), or flyrock (endangering personnel). In today’s ESG-driven mining sector, optimized blasting directly reduces diesel consumption in downstream hauling and crushing—cutting CO₂ emissions by up to 15% per ton of ore moved.
📘 Core Principles
Blast design rests on three interdependent pillars: (1) Energy balance—matching explosive energy input to rock strength and fracture energy; (2) Wave interaction—controlling stress wave superposition through precise millisecond delays to enhance rock breakage; and (3) Confinement management—using stemming and burden geometry to maximize energy coupling into the rock mass rather than venting upward. Rock mass rating (RMR), joint orientation, and weathering significantly modulate these principles—e.g., highly jointed rock requires reduced burden and tighter spacing, while massive granite demands higher powder factor and longer delays between rows.
📐 Kuz-Ram Fragmentation Model
The Kuz-Ram model predicts mean fragment size (x₅₀) based on explosive energy, rock properties, and blast geometry. It is widely used for initial design and benchmarking in open-pit operations. The model assumes uniform rock mass and isotropic explosive energy distribution—so field calibration is mandatory.
Kuz-Ram Mean Fragment Size
x₅₀ = A × PF⁻⁰·⁸ × (B/S)⁰·⁴Predicts the 50th percentile fragment size (m) for a given blast design.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| x₅₀ | Mean fragment size | m | Size at which 50% of fragment mass is finer |
| A | Rock factor | dimensionless | Empirical constant based on rock strength and abrasivity |
| PF | Powder factor | kg/m³ | Explosive mass per unit volume of rock broken |
| B | Burden | m | Distance from hole to free face |
| S | Spacing | m | Distance between holes in same row |
Typical Ranges:
Hard rock (UCS > 100 MPa): 0.8 – 1.6 m
Soft rock (UCS < 50 MPa): 0.3 – 0.7 m
💡 Worked Example
Problem: Given: ANFO density = 0.85 g/cm³, detonation velocity = 4,500 m/s, rock density = 2.65 g/cm³, uniaxial compressive strength (UCS) = 120 MPa, burden = 4.2 m, spacing = 5.0 m, subdrill = 1.2 m, bench height = 12 m.
1.
Step 1: Calculate powder factor (PF) = total explosive mass / blasted volume = (π × (0.114/2)² × (12 + 1.2) × 0.85 × 1000) / (4.2 × 5.0 × 12) ≈ 0.32 kg/m³
2.
Step 2: Compute rock factor (A) = 0.17 × UCS⁰·⁴⁵ = 0.17 × 120⁰·⁴⁵ ≈ 0.79
3.
Step 3: Apply Kuz-Ram: x₅₀ = A × (PF)⁻⁰·⁸ × (B/S)⁰·⁴ = 0.79 × (0.32)⁻⁰·⁸ × (4.2/5.0)⁰·⁴ ≈ 0.79 × 1.82 × 0.96 ≈ 1.38 m
Answer:
The predicted mean fragment size is 1.38 m, which falls within the safe and target range of 0.8–1.6 m for primary crusher feed in copper porphyry operations.
🏗️ Real-World Application
At the BHP Olympic Dam expansion (South Australia), blast design was revised to support renewable-powered electric haul trucks. By reducing burden from 5.1 m to 4.3 m, increasing spacing ratio (S/B) from 1.1 to 1.3, and implementing electronic detonators with 25-ms inter-hole delays, fragmentation improved by 22% (measured via digital photogrammetry), enabling 100% electric truck fleet deployment without crusher bottlenecking—reducing site-wide Scope 1 emissions by 11,000 tCO₂e/year.