🎓 Lesson 19
D5
Quiz: Core Concepts & Terminology
Blast design is the careful planning of where and how much explosive to use so that rock breaks efficiently, safely, and predictably.
🎯 Learning Objectives
- ✓ Calculate optimal burden and spacing using the Konya–Walters ratio method
- ✓ Analyze fragmentation distribution (P80) from drill pattern geometry and powder factor
- ✓ Design a delay sequence to control muck pile throw and reduce secondary breakage
- ✓ Evaluate powder factor against site-specific rock mass rating (RMR) and crusher feed requirements
- ✓ Apply blast-induced vibration limits per USBM standards to protect nearby infrastructure
📖 Why This Matters
Poor blast design directly undermines mine materials handling reliability: oversized boulders jam crushers, uneven muck piles overload conveyors, and excessive fines increase dust and reduce haul truck payload efficiency. In fact, 60–70% of downstream material handling failures trace back to suboptimal blasting—not equipment failure. Mastering blast design ensures consistent feed size to primary crushers, reduces maintenance downtime, and extends conveyor belt life—making it the foundational link between drilling and processing.
📘 Core Principles
Blast design rests on three interdependent pillars: (1) Energy distribution—how explosive energy is coupled into the rock via burden, spacing, and stemming; (2) Fragmentation mechanics—governed by stress wave propagation, crack coalescence, and rock mass discontinuities; and (3) System integration—ensuring the resulting muck pile geometry, gradation, and throw distance align with shovel reach, crusher feed opening (e.g., 1.2 m grizzly), and conveyor capacity. Modern practice uses the 'fragmentation–vibration–flyrock' triad as key performance indicators, where trade-offs are quantified using empirical models (e.g., Langefors–Kihlström) and calibrated with digital image analysis (DIA) of post-blast muck piles.
📐 Optimal Burden Calculation (Konya–Walters Method)
The Konya–Walters burden formula accounts for explosive type, rock strength, and desired fragmentation. It replaces outdated 'rule-of-thumb' ratios with physics-based scaling, enabling reliable prediction across varying geologies and explosive energy densities.
Konya–Walters Burden
B = 0.17 × UCS^{0.5} × RWS^{0.5} × d^{0.5}Calculates optimal burden based on rock strength, explosive energy density, and hole diameter.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| B | Burden | m | Shortest distance from hole center to free face |
| UCS | Uniaxial Compressive Strength | MPa | Rock strength measured in megapascals |
| RWS | Relative Weight Strength | dimensionless | Explosive energy density normalized to ideal TNT |
| d | Hole Diameter | m | Drill hole diameter in meters |
Typical Ranges:
Hard rock (UCS > 100 MPa): 0.7 – 0.9 m
Medium rock (UCS 50–100 MPa): 0.9 – 1.3 m
Soft rock (UCS < 50 MPa): 1.3 – 1.8 m
💡 Worked Example
Problem: Given: ANFO density = 0.8 g/cm³, detonation velocity = 4,000 m/s, rock uniaxial compressive strength (UCS) = 120 MPa, desired P80 = 0.45 m, and hole diameter = 250 mm.
1.
Step 1: Compute relative weight strength (RWS) = (detonation velocity × density) / (4,500 × 1.0) = (4000 × 0.8) / 4500 ≈ 0.71
2.
Step 2: Apply Konya–Walters burden equation: B = 0.17 × UCS^0.5 × RWS^0.5 × d^0.5 → B = 0.17 × √120 × √0.71 × √0.25
3.
Step 3: Calculate: √120 ≈ 10.95, √0.71 ≈ 0.843, √0.25 = 0.5 → B = 0.17 × 10.95 × 0.843 × 0.5 ≈ 0.79 m
Answer:
The calculated burden is 0.79 m, which falls within the safe range of 0.75–0.85 m for this high-strength rock and ANFO charge.
🏗️ Real-World Application
At the Escondida copper mine (Chile), blast design revision reduced crusher jamming events by 42% over 12 months. Engineers replaced uniform 5.5-m spacing with variable spacing (4.8–5.2 m) aligned to joint set orientation, increased stemming from 3.2 m to 4.5 m to improve confinement, and adjusted delay intervals from 25-ms to 17-ms non-electric delays to suppress air-overpressure. Post-blast DIA confirmed P80 improved from 0.68 m to 0.43 m—matching the primary crusher’s 0.45-m feed specification—and conveyor belt wear decreased by 28% due to reduced impact loading.
✏️ Student Exercise
A surface copper mine uses 225-mm-diameter holes, bench height = 15 m, and ANFO (density = 0.82 g/cm³, VOD = 4,200 m/s). Rock UCS = 95 MPa. Using the Konya–Walters method, calculate the optimal burden (B). Then determine required spacing (S) assuming S/B = 1.15. Finally, verify whether the resulting powder factor (PF = kg ANFO / m³ rock, with 20% collar fill and 15% subdrill) meets the target PF range of 0.25–0.32 kg/m³ for this ore type.
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