🎓 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 and safely.

🎯 Learning Objectives

✓ Calculate optimal burden and spacing using the Konya–Wallace empirical method
✓ Design a blast pattern for a 15-m limestone quarry bench meeting fragmentation target (P80 ≤ 60 mm)
✓ Analyze vibration data to verify compliance with USBM PPV limits for nearby structures
✓ Explain the relationship between powder factor and fragmentation quality using field observation evidence
✓ Apply blast design adjustments for varying rock mass rating (RMR) values

📖 Why This Matters

Every ton of ore moved starts with a blast — and every poorly designed blast wastes energy, creates hazardous boulders, damages equipment, or triggers regulatory violations. In modern mining, blast design directly impacts haulage costs, crusher throughput, safety incident rates, and even carbon footprint. A 10% improvement in fragmentation can reduce crushing energy by up to 15% — making blast design not just foundational, but economically decisive.

📘 Core Principles

Blast design rests on three interdependent pillars: (1) Energy delivery — how explosive energy couples into the rock via confinement, stemming, and detonation velocity; (2) Stress wave interaction — the superposition of compressive waves from adjacent holes generating radial cracking and shear failure; and (3) Gas pressure expansion — the quasi-static phase that lifts and separates fractured blocks. Rock mass properties (e.g., RMR, joint spacing, weathering) govern wave attenuation and fracture propagation, while explosive selection (ANFO vs. emulsion) affects energy density and gas pressure duration. Modern practice balances empirical rules-of-thumb with DFN-based modeling and digital twin validation.

📐 Konya–Wallace Burden Formula

This widely adopted empirical formula estimates initial burden based on explosive type, hole diameter, and rock strength. It provides a robust starting point before refinement via simulation or field trials.

Konya–Wallace Burden

B = 0.17 × D × √(UCS / (RWS × ρ))

Empirical estimate of burden (B) in meters based on hole diameter (D), rock UCS, explosive relative weight strength (RWS), and rock density (ρ).

Variables:

Symbol	Name	Unit	Description
B	Burden	m	Shortest distance from charge center to free face
D	Hole diameter	m	Drill hole diameter
UCS	Unconfined Compressive Strength	MPa	Rock strength measured in megapascals
RWS	Relative Weight Strength	dimensionless	Explosive energy ratio relative to TNT
ρ	Rock density	g/cm³	Bulk density of intact rock

Typical Ranges:

Hard granite (UCS > 150 MPa): 3.2 - 4.5 m

Medium limestone (UCS ≈ 80–120 MPa): 2.6 - 3.5 m

Weathered shale (UCS < 40 MPa): 1.8 - 2.5 m

💡 Worked Example

Problem: Given: 165-mm diameter borehole, ANFO (density = 0.85 g/cm³, VOD = 4,000 m/s), unconfined compressive strength (UCS) = 95 MPa, rock density = 2.65 g/cm³.

1. Step 1: Compute relative weight strength (RWS) = (VOD_ANFO / VOD_TNT) × (ρ_ANFO / ρ_TNT) ≈ (4000/6900) × (0.85/1.6) ≈ 0.31

2. Step 2: Apply Konya–Wallace: B = 0.17 × D × √(UCS / (RWS × ρ)) where D = 0.165 m, UCS = 95 MPa = 95 N/mm², ρ = 2650 kg/m³ → B = 0.17 × 0.165 × √(95 / (0.31 × 2.65))

3. Step 3: Calculate: √(95 / 0.8215) ≈ √115.6 ≈ 10.75 → B ≈ 0.17 × 0.165 × 10.75 ≈ 0.303 m → round to 3.0 m (standard practice scales to nearest 0.5 m)

Answer: The calculated burden is 3.0 m, which falls within the safe range of 2.8–3.5 m for medium-strength limestone at this bench height.

🏗️ Real-World Application

At the Tschudi Copper Mine (Western Australia), engineers redesigned a 12-m bench blast in weathered dolerite (RMR = 52) using Konya–Wallace + DFN modeling. Original burden was 3.2 m with 2.8-m spacing — resulting in >12% oversize (>750 mm). Revised design reduced burden to 2.9 m, increased spacing to 3.4 m (S/B = 1.17), and switched to heavy ANFO/emulsion blend. Post-blast P80 improved from 92 mm to 54 mm, reducing secondary breaking costs by AUD $1.2M/year and eliminating crusher hang-ups.