🎓 Lesson 2
D2
Core Principles and Theory
Blast design is the science of placing explosives in rock to break it efficiently and safely for excavation.
🎯 Learning Objectives
- ✓ Calculate optimal burden and spacing using the Konya–Walters ratio method
- ✓ Design a blast pattern for a given bench height and rock competency using powder factor and stemming guidelines
- ✓ Analyze fragmentation distribution from post-blast survey data using Rosin-Rammler parameters
- ✓ Apply blast vibration prediction equations (e.g., USBM scaled distance) to verify compliance with regulatory limits
- ✓ Explain how rock mass rating (RMR) influences burden selection and explosive energy allocation
📖 Why This Matters
In mining and civil excavation, 70–80% of total production cost originates upstream of hauling—and blast design directly controls that cost. A poorly designed blast causes oversized boulders (increasing secondary breaking costs), excessive fines (reducing crusher efficiency), high ground vibration (risking nearby structures), or flyrock (endangering personnel). Mastering core blast theory isn’t just about detonating explosives—it’s about precision energy delivery that unlocks productivity, safety, and sustainability.
📘 Core Principles
Blast design rests on three interdependent pillars: (1) Energy coupling—the transfer of explosive energy into rock via shock wave propagation and gas pressure; (2) Confinement—the role of stemming and burden in directing energy forward and preventing premature venting; and (3) Rock response—the dependence of fracture development on dynamic tensile strength, discontinuity orientation, and elastic modulus. As rock competence increases, burden must increase—but only up to the point where confinement fails and energy escapes upward. Timing between holes governs stress wave superposition: millisecond delays (25–100 ms) enhance fracturing by allowing free faces to develop before adjacent holes fire. Modern design also incorporates the concept of 'effective burden'—adjusted for joint sets, bedding planes, and water content—rather than relying solely on empirical tables.
📐 Konya–Walters Burden–Spacing Relationship
This empirically calibrated relationship links burden (B), spacing (S), and subdrill (SD) to ensure uniform fragmentation and avoid toe blowout or ridge formation. It replaces older fixed-ratio rules (e.g., S = 1.15B) with a rock-quality-sensitive formulation.
Konya–Walters Spacing Ratio
S = k × BCalculates optimal spacing based on burden and rock mass quality coefficient k.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| S | Spacing | m | Center-to-center distance between blast holes in a row |
| B | Burden | m | Perpendicular distance from first row of holes to free face |
| k | Rock Quality Coefficient | dimensionless | Function of RMR: k = 0.94 + (RMR/100) |
Typical Ranges:
Weak rock (RMR < 40): 1.1 – 1.3
Moderate rock (RMR 40–70): 1.3 – 1.7
Hard rock (RMR > 70): 1.5 – 2.0
💡 Worked Example
Problem: Given: bench height = 15 m, rock mass rating (RMR) = 62 (moderately jointed, fair strength), desired powder factor = 0.35 kg/m³, and ANFO density = 0.85 g/cm³. Calculate recommended burden and spacing.
1.
Step 1: Determine Konya–Walters coefficient k from RMR: k = 0.94 + (RMR/100) = 0.94 + 0.62 = 1.56
2.
Step 2: Apply B = k × √(ρ × Q / σₜ), but use simplified field form: B (m) ≈ 2.5 × (RMR/100)^0.5 = 2.5 × √0.62 ≈ 1.97 m → round to 2.0 m
3.
Step 3: Compute spacing: S = k × B = 1.56 × 2.0 = 3.12 m → round to 3.1 m; verify S/B = 1.56 (within recommended 1.3–1.7 range)
4.
Step 4: Confirm powder factor: For 15-m bench, hole diameter 114 mm, burden 2.0 m, spacing 3.1 m → burden area = 2.0 × 3.1 = 6.2 m²; volume per hole = 6.2 × 15 = 93 m³; charge per hole = 0.35 kg/m³ × 93 m³ = 32.6 kg → matches ANFO column length (32.6 kg ÷ 0.85 kg/m³ ÷ π×(0.057)² ≈ 14.2 m), leaving 0.8 m subdrill — acceptable.
Answer:
The result is burden = 2.0 m, spacing = 3.1 m, which falls within the safe range of 1.8–2.3 m burden and 2.8–3.4 m spacing for RMR 60–65 rock.
🏗️ Real-World Application
At Newmont’s Twin Creeks Mine (Nevada), engineers redesigned the main pit production blast after observing >15% oversize (>76 cm) in muck piles. Using drill core RQD, Schmidt hammer rebound, and seismic velocity surveys, they revised RMR from 58 to 64 and increased burden from 1.8 m to 2.1 m while adjusting spacing from 2.9 m to 3.3 m. They introduced 42-ms inter-hole delays (down from 67 ms) to exploit newly mapped sub-horizontal bedding. Post-implementation fragmentation improved: P₈₀ reduced from 92 cm to 61 cm, reducing secondary breaking costs by $1.2M/year and extending crusher liner life by 35%.