🎓 Lesson 5
D3
Calculation Methods and Formulas
Blast design formulas help engineers figure out how far apart to place explosive holes and how much explosive to use so rock breaks efficiently and safely.
🎯 Learning Objectives
- ✓ Calculate optimal burden using the Konya–Walters empirical formula for a given rock type and explosive
- ✓ Design spacing-to-burden ratio (S/B) to achieve uniform fragmentation in bench blasting
- ✓ Analyze powder factor against industry benchmarks to assess blast economy and overbreak risk
- ✓ Apply stemming length formulas to ensure adequate confinement and energy transfer
📖 Why This Matters
In mining and civil excavation, a poorly designed blast wastes explosives, damages equipment, creates hazardous flyrock, and fails to meet fragmentation targets—leading to costly secondary breaking and delays. Accurate calculation of blast geometry isn’t guesswork; it’s the engineering foundation that links geology, explosives science, and operational safety. Getting these numbers right directly impacts productivity, cost per ton, regulatory compliance, and worker safety.
📘 Core Principles
Blast design rests on three interdependent pillars: (1) Energy delivery—how much explosive energy is needed to fracture rock, governed by rock strength and density; (2) Geometry control—how burden (distance from free face), spacing (hole-to-hole distance), and stemming govern energy distribution and confinement; and (3) Coupling & confinement—how explosive diameter, borehole diameter, and stemming length affect pressure buildup and shockwave transmission. Empirical models (e.g., Konya–Walters, Langefors) bridge laboratory rock properties with field-scale performance, while modern approaches incorporate P-wave velocity and RMR for calibration.
📐 Burden Calculation (Konya–Walters)
The Konya–Walters burden formula is widely adopted for surface and bench blasting because it accounts for both explosive energy and rock resistance. It replaces outdated 'rule-of-thumb' burden estimates with a physics-informed, scalable relationship validated across diverse rock types and explosives.
💡 Worked Example
Problem: Given: ANFO with relative weight strength (RWS) = 0.82, rock uniaxial compressive strength (UCS) = 120 MPa, specific gravity = 2.65, desired burden B (m).
1.
Step 1: Compute rock factor K = 0.27 × UCS^0.5 = 0.27 × √120 ≈ 0.27 × 10.95 = 2.96
2.
Step 2: Apply Konya–Walters: B = K × (RWS × ρ_explosive / ρ_rock)^0.33. Assume ρ_explosive = 0.85 g/cm³, ρ_rock = 2.65 g/cm³ → ratio = 0.85/2.65 ≈ 0.321 → 0.321^0.33 ≈ 0.68
3.
Step 3: B = 2.96 × 0.68 ≈ 2.01 m
Answer:
The calculated burden is 2.01 m, which falls within the safe range of 1.8–2.4 m for medium-strength sedimentary rock with ANFO.
🏗️ Real-World Application
At the Eagle Mountain open-pit copper mine (USA), engineers recalibrated burden and spacing after seismic monitoring revealed excessive back-break and poor muck pile uniformity. Using Konya–Walters with updated P-wave velocity (4,200 m/s) and RQD (78%), they increased burden from 2.1 m to 2.35 m and adjusted spacing to maintain S/B = 1.15. Post-blast image analysis confirmed 85% of fragments were <300 mm—meeting crusher feed specification—and reduced oversize by 42%, cutting secondary breaking costs by $1.2M/year.