🎓 Lesson 5
D3
Calculation Methods and Formulas
Blasting design calculations help engineers figure out how much explosive to use and where to place it so rock breaks efficiently and safely.
🎯 Learning Objectives
- ✓ Calculate optimal burden and spacing using the Konya–Walters empirical model
- ✓ Design a blast pattern by applying the powder factor formula and verifying against ANFO performance limits
- ✓ Analyze fragmentation expectations using the Rosin–Rammler distribution parameters derived from blast data
- ✓ Explain how rock mass rating (RMR) influences burden selection in variable geology
- ✓ Apply USBM scaled distance equation to assess vibration compliance for nearby structures
📖 Why This Matters
In mining and construction, an improperly designed blast can cause excessive ground vibration, poor fragmentation (increasing crushing costs), flyrock hazards, or even regulatory shutdowns. Accurate calculation methods are the foundation of safe, efficient, and compliant blasting—turning geology and explosives into predictable, controllable engineering outcomes.
📘 Core Principles
Blast design rests on three interdependent pillars: (1) Energy balance—the relationship between explosive energy input and rock resistance; (2) Stress wave propagation—how shock and gas pressure interact with jointed rock masses; and (3) Empirical scaling laws—derived from decades of field observation, linking measurable rock properties (e.g., uniaxial compressive strength, RMR, P-wave velocity) to blast geometry. Modern practice combines these with digital tools (e.g., blast modeling software), but core formulas remain essential for verification, troubleshooting, and certification exams.
📐 Burden Calculation (Konya–Walters Model)
This widely adopted empirical formula estimates burden (B) based on explosive type, rock strength, and desired fragmentation. It is especially reliable for surface bench blasting in hard to medium rock and forms the anchor point for spacing and pattern layout.
💡 Worked Example
Problem: Given: ANFO density = 0.85 g/cm³, detonation velocity = 4,500 m/s, rock UCS = 120 MPa, desired fragment size d₅₀ = 0.3 m
1.
Step 1: Compute relative weight strength (RWS) = (VOD_ANFO / VOD_TNT)² × (ρ_ANFO / ρ_TNT) = (4500/6900)² × (0.85/1.6) ≈ 0.24
2.
Step 2: Apply Konya–Walters: B = 0.17 × (UCS)^0.25 × (d₅₀)^0.5 × (RWS)^−0.25 = 0.17 × (120)^0.25 × (0.3)^0.5 × (0.24)^−0.25
3.
Step 3: Calculate: (120)^0.25 ≈ 3.31; (0.3)^0.5 ≈ 0.548; (0.24)^−0.25 ≈ 1.45 → B ≈ 0.17 × 3.31 × 0.548 × 1.45 ≈ 0.44 m
Answer:
The calculated burden is 0.44 m, which falls within the typical range of 0.4–0.6 m for small-diameter production holes in high-strength rock with fine fragmentation goals.
🏗️ Real-World Application
At the Cadia East underground block cave operation (NSW, Australia), engineers revised burden from 0.55 m to 0.48 m after RMR analysis revealed tighter jointing than previously assumed. Using the Konya–Walters model and adjusting powder factor from 0.52 to 0.48 kg/m³, they achieved 20% improvement in muck pile uniformity and reduced secondary breaking by 35%, while maintaining peak particle velocity < 5 mm/s at the nearest settlement boundary—verified via USBM scaled distance compliance.