🎓 Lesson 2
D2
Core Principles and Theory
Blast design is the science of placing and timing explosives to break rock efficiently, safely, and predictably.
🎯 Learning Objectives
- ✓ Calculate optimal burden and spacing using the Kuz-Ram fragmentation model
- ✓ Design a delay sequence to minimize ground vibration using the USBM scaled distance equation
- ✓ Analyze powder factor to evaluate blast efficiency against industry benchmarks (e.g., SME Guidelines)
- ✓ Apply rock mass rating (RMR) to adjust burden and spacing for variable geology
- ✓ Explain the relationship between explosive energy partitioning and post-blast muck pile uniformity
📖 Why This Matters
Every ton of ore moved in open-pit mining starts with a well-designed blast. Poor blast design leads to oversized boulders (increasing crushing costs), excessive fines (reducing recovery), high ground vibration (damaging infrastructure), or flyrock (endangering personnel). In fact, 30–40% of total mining cost is tied to blasting efficiency—making precise, physics-informed design not just academic, but economically decisive.
📘 Core Principles
Blast design rests on three interdependent pillars: (1) Energy transfer — how explosive energy couples into rock via shock wave propagation and gas pressure expansion; (2) Rock response — governed by discontinuity density, strength, and confinement (burden); and (3) Timing effects — where millisecond delays control fracture coalescence and stress wave interference. The Kuznetsov-Rammler (Kuz-Ram) model links explosive energy input to fragment size distribution, while the 'burden-spacing triangle' defines geometric limits for effective fracture development. Critically, burden must balance confinement (to prevent blowout) and energy utilization (to avoid over-compaction), while spacing governs lateral fracture propagation and inter-hole interaction.
📐 Kuz-Ram Fragmentation Prediction
The Kuz-Ram model estimates the 80% passing size (X₈₀) of blasted muck based on explosive energy, rock properties, and blast geometry. It is widely used for preliminary design and benchmarking in both open-pit and underground operations.
Kuz-Ram X₈₀
X₈₀ = K × (B × S × PF)^(-0.2)Predicts the 80% passing fragment size (m) based on rock factor K, burden B (m), spacing S (m), and powder factor PF (kg/m³).
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| X₈₀ | 80% passing fragment size | m | Size at which 80% of fragments by weight are smaller |
| K | Rock factor | dimensionless | Function of UCS (MPa) and RQD (%) — typically 0.8–1.8 |
| B | Burden | m | Perpendicular distance from borehole to nearest free face |
| S | Spacing | m | Distance between adjacent holes in same row |
| PF | Powder factor | kg/m³ | Explosive mass per unit volume of rock broken |
Typical Ranges:
Hard rock (copper/gold): 0.8 – 1.4 m
Limestone/quarry: 0.5 – 0.9 m
Soft coal seam: 0.3 – 0.6 m
💡 Worked Example
Problem: Given: ANFO density = 0.85 g/cm³, velocity of detonation = 4,000 m/s, rock density = 2.65 g/cm³, RQD = 72%, unconfined compressive strength (UCS) = 120 MPa, burden = 4.2 m, spacing = 5.0 m, powder factor = 0.32 kg/m³.
1.
Step 1: Compute rock factor K = 0.1 × UCS^(0.5) × (100/RQD)^0.5 = 0.1 × √120 × √(100/72) ≈ 0.1 × 10.95 × 1.18 ≈ 1.29
2.
Step 2: Compute explosive factor A = (ρ_exp × VOD²) / (ρ_rock × g) = (850 × 4000²) / (2650 × 9.81) ≈ 519,000 J/kg (normalized energy factor)
3.
Step 3: Apply Kuz-Ram: X₈₀ = K × (B × S × PF)^(-0.2) = 1.29 × (4.2 × 5.0 × 0.32)^(-0.2) = 1.29 × (6.72)^(-0.2) ≈ 1.29 × 0.85 ≈ 1.10 m
4.
Step 4: Compare to target X₈₀ = 0.8–1.2 m for primary crusher feed — result (1.10 m) meets specification.
Answer:
The predicted X₈₀ is 1.10 m, which falls within the safe and target range of 0.8–1.2 m for this operation.
🏗️ Real-World Application
At BHP’s Escondida copper mine (Chile), engineers redesigned a 15-m bench blast using Kuz-Ram-guided burden reduction (from 5.0 m to 4.3 m) and optimized delay timing (17 ms inter-hole delays). Post-blast analysis showed X₈₀ improved from 1.42 m to 0.98 m, reducing secondary breaking costs by 22% and increasing shovel productivity by 14%. Crucially, peak particle velocity (PPV) remained below 50 mm/s at 300 m — meeting Chilean regulatory limits (DS 132/2018).
✏️ Design Check Exercise
A limestone quarry (UCS = 85 MPa, RQD = 85%) uses ANFO (ρ = 0.85 g/cm³, VOD = 4,200 m/s) in 10-m benches. Current burden = 4.8 m, spacing = 5.6 m, powder factor = 0.28 kg/m³. Using Kuz-Ram, calculate X₈₀. Then determine if adjusting spacing to 5.2 m (keeping burden constant) improves X₈₀ toward the target of 0.75 m — and justify whether the change is geometrically feasible per the burden-to-spacing ratio guideline (S/B ≤ 1.3).