🎓 Lesson 4 D3

Design and Planning Fundamentals

Blast design is the careful planning of where and how much explosive to use so rock breaks efficiently, safely, and predictably.

🎯 Learning Objectives

✓ Calculate optimal burden using rock properties and explosive energy output
✓ Design drill pattern geometry by applying spacing-to-burden ratios for target fragmentation
✓ Analyze powder factor to verify compliance with regulatory limits and cost-efficiency targets
✓ Explain the relationship between stemming length and backbreak/airblast control
✓ Apply blast design principles to adapt a standard pattern for variable rock conditions

📖 Why This Matters

In mining and civil excavation, 60–80% of total production cost originates upstream—from drilling and blasting. A poorly designed blast leads to oversized boulders (increasing secondary breaking costs), excessive fines (reducing crusher efficiency), flyrock (endangering personnel), or ground vibration damage (triggering regulatory penalties). Mastering blast design isn’t just technical—it’s economic, legal, and ethical.

📘 Core Principles

Blast design rests on three interdependent pillars: (1) Energy delivery—matching explosive energy (kJ/kg) to rock strength (MPa) and fracture toughness; (2) Confinement—using burden and stemming to direct energy into rock rather than air; and (3) Timing—controlling stress wave interaction via millisecond delays to enhance fracturing. Burden defines the shortest distance from explosive to free face and governs primary fragmentation; spacing controls secondary breakage between holes; and stemming prevents premature venting of gases. Rock mass rating (RMR), joint spacing, and weathering significantly modify empirical design rules—making site-specific calibration essential.

📐 Burden Calculation (Langefors–Kihlstrom)

The Langefors–Kihlstrom formula estimates optimal burden based on rock strength, explosive energy, and packing density. It balances confinement and energy coupling—critical for minimizing oversize and avoiding cratering. Used widely in surface bench blasting for hard to medium rock.

Langefors–Kihlstrom Burden Formula

B = K × √(ρ × E / σ_c)

Calculates optimal burden (B) in meters based on explosive density (ρ), energy per mass (E), rock uniaxial compressive strength (σ_c), and empirical constant K.

Variables:

Symbol	Name	Unit	Description
B	Burden	m	Shortest distance from charge center to nearest free face
K	Empirical constant	dimensionless	Ranges 1.0–1.4 depending on rock type and explosive; 1.25 typical for ANFO in hard rock
ρ	Explosive density	kg/m³	Mass per unit volume of loaded explosive
E	Explosive energy	J/kg	Total available chemical energy per kilogram of explosive
σ_c	Rock uniaxial compressive strength	Pa	Maximum axial stress rock can withstand before failure

Typical Ranges:

Hard rock (UCS > 150 MPa): 4.0 - 5.5 m

Medium rock (UCS 80–150 MPa): 3.0 - 4.2 m

Soft rock (UCS < 80 MPa): 2.2 - 3.2 m

💡 Worked Example

Problem: Given: Rock uniaxial compressive strength (UCS) = 180 MPa, ANFO density = 0.85 g/cm³, ANFO energy = 3.0 MJ/kg, hole diameter = 250 mm, desired fragmentation index = 0.9.

1. Step 1: Calculate relative weight strength (RWS) = (ANFO energy / 4.184) × 100 = (3.0 / 4.184) × 100 ≈ 71.7%

2. Step 2: Compute burden B = K × √(ρ × E / σ_c), where K = 1.25 (for ANFO in hard rock), ρ = 850 kg/m³, E = 3.0e6 J/kg, σ_c = 180e6 Pa → B = 1.25 × √((850 × 3.0e6) / 180e6) = 1.25 × √14.17 ≈ 1.25 × 3.76 = 4.70 m

3. Step 3: Verify against typical burden range for 12-m bench: 4.0–5.5 m → 4.70 m is acceptable and aligns with industry practice for UCS > 150 MPa.

Answer: The calculated burden is 4.70 m, which falls within the safe and typical range of 4.0–5.5 m for hard rock surface blasting.

🏗️ Real-World Application

At Newmont’s Boddington Mine (Western Australia), engineers redesigned the pit wall blast pattern after observing 22% oversize (>76 cm) and excessive backbreak. Using core logging and RMR mapping, they reduced burden from 5.2 m to 4.5 m, increased spacing from 6.0 m to 6.8 m (maintaining S/B = 1.5), and switched from 100-ms to 25-ms inter-hole delays. Post-implementation fragmentation improved to 92% < 76 cm, flyrock incidents dropped to zero over 18 months, and shovel loading time decreased by 14%—demonstrating how calibrated design directly improves safety, productivity, and cost.