🎓 Lesson 21
D5
Quiz: Case Study Diagnosis & Recommendation
Blast design is planning how to place and detonate explosives to break rock efficiently and safely for mining.
🎯 Learning Objectives
- ✓ Calculate optimal burden and spacing using rock factor and explosive energy metrics
- ✓ Analyze blast pattern efficiency using powder factor and fragmentation index (RMS) data
- ✓ Design a delay sequence to minimize ground vibration (PPV) below 50 mm/s per USBM standards
- ✓ Explain the trade-off between fragmentation quality and backbreak in high-wall stability contexts
- ✓ Apply the Konya–Walters energy balance model to select appropriate ANFO vs. emulsion for a given rock mass rating (RMR)
📖 Why This Matters
Poor blast design causes 30–40% of downstream material handling failures—such as crusher jamming, conveyor belt wear, and shovel loading inefficiencies—because oversized or poorly sorted muck increases maintenance costs by up to 22% (CIM, 2021). In Module 12, diagnosing blast-related reliability issues isn’t just about explosives—it’s about tracing root causes from fragmented rock all the way to stockpile reclaimers and primary crushers.
📘 Core Principles
Blast design rests on three interdependent pillars: (1) Energy delivery—how much explosive energy reaches the rock versus losses to air, stemming, or misfires; (2) Stress wave interaction—how compressive and tensile waves propagate, reflect, and fracture rock along natural discontinuities; and (3) Fragmentation dynamics—governed by the ratio of explosive energy to rock strength (measured via UCS or point load index) and confinement (burden, stemming, geology). Modern practice treats blasting not as isolated detonation but as the first stage of the materials handling system—where poor fragmentation directly degrades crusher throughput, increases fines generation, and accelerates wear on haul trucks and shovels.
📐 Optimal Burden Calculation (Konya–Walters Empirical Model)
This formula estimates minimum practical burden (B) based on rock strength and explosive energy density, balancing fragmentation and confinement. Used when rock properties (UCS, density) and explosive performance (RE factor) are known.
Konya–Walters Burden Equation
B = 0.17 × (UCS)^0.25 × (ρ)^0.5 × (RE)^−0.25 × (P80)^0.5Empirical burden estimation accounting for rock strength, density, explosive relative effectiveness, and target fragment size.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| B | Burden | m | Shortest distance from charge center to free face |
| UCS | Unconfined Compressive Strength | kPa | Rock strength measured in uniaxial compression test |
| ρ | Rock Density | kg/m³ | Bulk density of intact rock |
| RE | Relative Effectiveness Factor | dimensionless | Energy output ratio of explosive vs. ANFO (ANFO = 1.0) |
| P80 | Target Fragment Size | m | 80% of fragments pass this sieve size |
Typical Ranges:
Hard rock (UCS > 100 MPa): 7.5 – 10.5 m
Medium rock (UCS 50–100 MPa): 5.0 – 7.5 m
Weathered/weak rock (UCS < 50 MPa): 3.0 – 5.0 m
💡 Worked Example
Problem: Given: Rock UCS = 120 MPa, density = 2.65 g/cm³, ANFO RE factor = 0.80, desired fragment size P80 = 300 mm.
1.
Step 1: Convert UCS to kg/m³-equivalent strength: UCS_kg_m3 = UCS × 10^5 / g ≈ 120 × 10^6 Pa → use as-is in kPa scale (120,000 kPa).
2.
Step 2: Apply Konya–Walters: B = 0.17 × (UCS)^0.25 × (ρ)^0.5 × (RE)^−0.25 × (P80)^0.5 → B = 0.17 × (120000)^0.25 × (2650)^0.5 × (0.80)^−0.25 × (0.3)^0.5
3.
Step 3: Compute: (120000)^0.25 ≈ 18.6, (2650)^0.5 ≈ 51.5, (0.80)^−0.25 ≈ 1.057, (0.3)^0.5 ≈ 0.548 → B ≈ 0.17 × 18.6 × 51.5 × 1.057 × 0.548 ≈ 9.2 m
Answer:
The calculated burden is 9.2 m, which falls within the safe range of 7.5–10.5 m for hard massive granite at 12-m bench height per SME Blasting Handbook (2020).
🏗️ Real-World Application
At Newmont’s Boddington Mine (Western Australia), excessive crusher liner wear was traced to inconsistent fragmentation. Blast diagnostics revealed 28% of holes had >15% deviation from designed burden due to drill rig calibration drift and uncorrected topography. After implementing real-time borehole surveying (using HoleScope™) and adjusting burden by ±0.8 m per row, P80 improved from 420 mm to 295 mm, reducing crusher downtime by 37% and extending liner life from 1,200 to 1,850 operating hours—directly improving materials handling system reliability.
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