π Lesson 2
D2
Core Principles and Theory
Blast design is the science of placing and timing explosives to break rock efficiently, safely, and predictably.
π― Learning Objectives
- β Calculate optimal burden and spacing using the Kuz-Ram fragmentation model
- β Design a delay sequence to minimize ground vibration using the USBM scaled distance equation
- β Analyze powder factor to evaluate blast efficiency against industry benchmarks (e.g., SME Guidelines)
- β Apply rock mass rating (RMR) to adjust burden and spacing for variable geology
- β Explain the relationship between explosive energy partitioning and post-blast muck pile uniformity
π 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, 30β40% of total mining cost is tied to blasting efficiencyβmaking precise, physics-informed design not just academic, but economically decisive.
π Core Principles
Blast design rests on three interdependent pillars: (1) Energy transfer β how explosive energy couples into rock via shock wave propagation and gas pressure expansion; (2) Rock response β governed by discontinuity density, strength, and confinement (burden); and (3) Timing effects β 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.
π Kuz-Ram Fragmentation Prediction
The Kuz-Ram model estimates the 80% passing size (Xββ) 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 Xββ
Xββ = K Γ (B Γ S Γ 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/mΒ³).
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| Xββ | 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 (%) β typically 0.8β1.8 |
| 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/mΒ³ | Explosive mass per unit volume of rock broken |
Typical Ranges:
Hard rock (copper/gold): 0.8 β 1.4 m
Limestone/quarry: 0.5 β 0.9 m
Soft coal seam: 0.3 β 0.6 m
π‘ Worked Example
Problem: Given: ANFO density = 0.85 g/cmΒ³, velocity of detonation = 4,000 m/s, rock density = 2.65 g/cmΒ³, RQD = 72%, unconfined compressive strength (UCS) = 120 MPa, burden = 4.2 m, spacing = 5.0 m, powder factor = 0.32 kg/mΒ³.
1.
Step 1: Compute rock factor K = 0.1 Γ UCS^(0.5) Γ (100/RQD)^0.5 = 0.1 Γ β120 Γ β(100/72) β 0.1 Γ 10.95 Γ 1.18 β 1.29
2.
Step 2: Compute explosive factor A = (Ο_exp Γ VODΒ²) / (Ο_rock Γ g) = (850 Γ 4000Β²) / (2650 Γ 9.81) β 519,000 J/kg (normalized energy factor)
3.
Step 3: Apply Kuz-Ram: Xββ = K Γ (B Γ S Γ PF)^(-0.2) = 1.29 Γ (4.2 Γ 5.0 Γ 0.32)^(-0.2) = 1.29 Γ (6.72)^(-0.2) β 1.29 Γ 0.85 β 1.10 m
4.
Step 4: Compare to target Xββ = 0.8β1.2 m for primary crusher feed β result (1.10 m) meets specification.
Answer:
The predicted Xββ is 1.10 m, which falls within the safe and target range of 0.8β1.2 m for this operation.
ποΈ Real-World Application
At BHPβs 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 Xββ 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 β meeting Chilean regulatory limits (DS 132/2018).
βοΈ Design Check Exercise
A limestone quarry (UCS = 85 MPa, RQD = 85%) uses ANFO (Ο = 0.85 g/cmΒ³, VOD = 4,200 m/s) in 10-m benches. Current burden = 4.8 m, spacing = 5.6 m, powder factor = 0.28 kg/mΒ³. Using Kuz-Ram, calculate Xββ. Then determine if adjusting spacing to 5.2 m (keeping burden constant) improves Xββ toward the target of 0.75 m β and justify whether the change is geometrically feasible per the burden-to-spacing ratio guideline (S/B β€ 1.3).