π Lesson 2
D2
Core Principles and Theory
Blast design is the careful planning of where and how much explosive to use so rock breaks efficiently, safely, and predictably.
π― Learning Objectives
- β Calculate optimal burden using the empirical burden formula for a given rock type and explosive
- β Design drill pattern geometry by applying recommended spacing-to-burden ratios for specific fragmentation goals
- β Analyze powder factor against industry benchmarks (e.g., 0.2β0.6 kg/mΒ³ for hard rock) and adjust for geotechnical conditions
- β Explain the relationship between stemming length, confinement, and explosive energy transfer efficiency
- β Apply the Kuz-Ram fragmentation model to estimate fragment size distribution from blast parameters
π Why This Matters
Poor blast design wastes explosives, damages equipment, creates oversized boulders requiring secondary breakage, increases dust and flyrock risk, and violates OSHA 1926.900 and MSHA Part 46 regulations. In mining, a 10% improvement in fragmentation can reduce crushing energy by 15% β directly impacting operational cost and carbon footprint. This lesson equips you to make technically defensible, code-compliant blast decisions from day one.
π Core Principles
Blast design rests on three interdependent pillars: (1) Rock mass characterization β including RMR, Q-system, or uniaxial compressive strength (UCS), which governs resistance to fracture; (2) Explosive energy coupling β how efficiently chemical energy converts to rock breakage (influenced by borehole diameter, confinement, and impedance matching); and (3) Geometric relationships β burden (distance from free face), spacing (inter-hole distance), and stemming β which control stress wave interaction and fragment size. Modern practice blends empirical rules (e.g., LangeforsβKihlstrom) with digital tools like BlastLogic or DFN-based simulations, but foundational theory remains essential for validation and troubleshooting.
π Empirical Burden Formula
The Langefors burden formula estimates minimum burden required for effective breakage based on rock strength and explosive performance. It ensures sufficient confinement for energy transfer while avoiding excessive overbreak or poor fragmentation.
Langefors Burden Formula
B = K Γ E Γ βdCalculates minimum practical burden (B) in meters based on rock strength, explosive properties, and borehole diameter.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| B | Burden | m | Perpendicular distance from free face to first row of holes |
| K | Rock Factor | dimensionless | Empirically derived constant based on rock mass rating or UCS |
| E | Explosive Constant | dimensionless | Function of explosive velocity of detonation (VOD) and density (Ο) |
| d | Hole Diameter | m | Drill hole diameter |
Typical Ranges:
Hard rock (UCS > 100 MPa): 8.0 - 12.0 m
Medium rock (UCS 50β100 MPa): 5.5 - 8.5 m
Soft rock (UCS < 50 MPa): 3.0 - 5.5 m
π‘ Worked Example
Problem: Given: rock UCS = 120 MPa, ANFO density = 0.85 g/cmΒ³, ANFO VOD = 4,000 m/s, hole diameter = 165 mm. Calculate recommended burden.
1.
Step 1: Compute rock factor K = 0.27 Γ UCS^(0.5) = 0.27 Γ β120 β 0.27 Γ 10.95 = 2.96
2.
Step 2: Compute explosive constant E = 0.15 Γ (VOD Γ Ο)^(0.5) = 0.15 Γ β(4000 Γ 0.85) = 0.15 Γ β3400 β 0.15 Γ 58.31 = 8.75
3.
Step 3: Apply B = K Γ E Γ d^(0.5), where d = 0.165 m β βd β 0.406 β B = 2.96 Γ 8.75 Γ 0.406 β 10.5 m
Answer:
The calculated burden is 10.5 m, which falls within the safe range of 8β12 m for this bench height (12 m) and rock type β confirming adequate confinement without excessive throw.
ποΈ Real-World Application
At the BHP Olympic Dam copper mine (South Australia), engineers redesigned the primary blast pattern in the oxide zone after repeated oversize (>75 cm) generation. Using updated RMR-89 data (RMR = 52), they reduced burden from 11.2 m to 9.8 m, increased spacing from 6.2 m to 6.8 m (maintaining S/B = 0.69), and switched from 60/40 emulsion to high-density ANFO (Ο = 0.92 g/cmΒ³). Post-blast analysis showed 22% reduction in >75 cm material and 14% lower crusher energy consumption β validated via digital image analysis (DIA) of muck piles per ASTM D5778.