🎓 Lesson 4
D3
Design and Planning Fundamentals
Blast design is planning how to place and detonate explosives in rock to break it efficiently, safely, and predictably.
🎯 Learning Objectives
- ✓ Calculate optimal burden using the Konya–Walters empirical equation for given rock strength and explosive properties
- ✓ Design a blast pattern by applying industry-standard spacing-to-burden ratios (S/B = 1.15–1.35) and verifying powder factor against target fragmentation goals
- ✓ Analyze blast performance data (e.g., fragment size distribution, backbreak, oversize) to diagnose design deficiencies and adjust burden or delay timing
- ✓ Explain the physical relationship between explosive energy coupling, confinement, and rock fracture propagation using stress wave theory
- ✓ Apply USBM and DIN 4150-3 vibration prediction models to estimate peak particle velocity at critical receptors
📖 Why This Matters
In mining and civil excavation, up to 70% of total production cost originates from drilling and blasting—the first step in material movement. A poorly designed blast causes excessive oversize (increasing crushing costs), ground vibration damage to infrastructure, flyrock hazards, or poor wall control leading to slope instability. Conversely, an optimized design improves downstream efficiency in loading, hauling, and processing—while ensuring regulatory compliance and community safety. This lesson equips you to make technically defensible, field-proven design decisions—not just follow templates.
📘 Core Principles
Blast design rests on three interdependent pillars: (1) Energy transfer—how explosive energy couples into rock via shock wave pressure and gas expansion; (2) Rock response—governed by dynamic tensile strength, fracture toughness, joint spacing, and elastic modulus; and (3) Pattern geometry—where burden defines the shortest distance from charge to free face (controlling throw and confinement), spacing governs inter-hole fracture coalescence, and stemming prevents premature venting. Modern design also incorporates timing effects: millisecond delays (typically 25–100 ms between rows) allow stress wave superposition and improved fragmentation, while long-delay sequences (>500 ms) reduce vibration but risk poor fragmentation if burden isn’t adjusted. The goal is not maximum energy, but optimal energy *delivery* to the rock mass.
📐 Burden Calculation (Konya–Walters Empirical Equation)
This widely adopted empirical formula estimates initial burden based on explosive energy, rock strength, and hole diameter. It balances confinement and fracture development without requiring complex modeling—and is calibrated across hundreds of field trials. Use it as a starting point before refining with digital simulations or historical site data.
Konya–Walters Burden Equation
B = 0.165 × D × (RWS × UCS)^0.5Empirical burden estimation accounting for explosive energy (via RWS) and rock strength (UCS).
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| B | Burden | m | Shortest distance from charge center to free face |
| D | Hole diameter | m | Diameter of the blasthole (measured in meters) |
| RWS | Relative Weight Strength | dimensionless | Ratio of explosive energy density relative to PETN (standard reference) |
| UCS | Uniaxial Compressive Strength | MPa | Rock strength measured under unconfined compression |
Typical Ranges:
Hard rock (UCS > 150 MPa): 2.5 - 4.0 m
Medium rock (UCS 60–150 MPa): 2.0 - 3.5 m
Soft rock/weathered material: 1.5 - 2.5 m
💡 Worked Example
Problem: Given: ANFO density = 0.8 g/cm³, VOD = 4,000 m/s, rock uniaxial compressive strength (UCS) = 120 MPa, hole diameter = 250 mm. Calculate initial burden.
1.
Step 1: Compute relative weight strength (RWS) = (VOD_ANFO / VOD_PETN) × (ρ_ANFO / ρ_PETN) ≈ (4000/8000) × (0.8/1.75) ≈ 0.229
2.
Step 2: Apply Konya–Walters: B = 0.165 × D × (RWS × UCS)^0.5, where D = 0.25 m, UCS = 120 MPa → (0.229 × 120)^0.5 ≈ (27.5)^0.5 ≈ 5.24
3.
Step 3: B = 0.165 × 0.25 × 5.24 ≈ 0.216 m → 2.16 m (rounded to 2.2 m)
Answer:
The calculated burden is 2.2 m, which falls within the safe and typical range of 2.0–3.5 m for medium-strength rock with 250-mm holes.
🏗️ Real-World Application
At Newmont’s Boddington Mine (Western Australia), engineers redesigned a 15-m bench blast in weathered granite after repeated oversize (>15% >750 mm fragments). Using drill core RQD, P-wave velocity (4,200 m/s), and UCS (85 MPa), they recalculated burden from 3.0 m to 2.6 m using Konya–Walters, increased spacing from 3.6 m to 3.8 m (S/B = 1.46 → 1.46, then reduced to 1.31 via trial), and introduced 42-ms inter-row delays. Post-blast image analysis showed D80 reduced from 920 mm to 610 mm, and secondary crushing energy decreased by 18%—validated over three consecutive production blasts.