🎓 Lesson 5
D3
Calculation Methods and Formulas
Burden is the distance from a blast hole to the nearest free face—the space that lets rock break outward instead of being crushed inward.
🎯 Learning Objectives
- ✓ Calculate optimal burden using empirical formulas for given rock mass properties and explosive type
- ✓ Analyze the effect of burden-to-spacing ratio on fragmentation uniformity and muck pile profile
- ✓ Design a blast pattern by iteratively adjusting burden to meet target powder factor and fragment size distribution
- ✓ Explain how changes in rock strength, jointing, and stemming length influence burden selection
📖 Why This Matters
Getting burden wrong is the #1 cause of poor fragmentation, excessive ground vibration, and costly rehandling. Too small a burden wastes explosive energy and causes cratering; too large leads to boulders, high oversize, and dangerous unexploded material. In pump system design for dewatering blast areas, accurate burden prediction directly informs required sump capacity, inflow estimation, and pump duty cycle—making it foundational for integrated mine planning.
📘 Core Principles
Burden originates from explosive energy confinement: when detonated, the shockwave travels radially until it meets the free face, where reflection creates tensile stress that initiates radial cracking. Rock mass properties—including uniaxial compressive strength (UCS), P-wave velocity, and joint spacing—dictate how far this energy can effectively fracture. Empirical models (e.g., Langefors–Kihlström) link burden to rock resistance and explosive energy density. Modern practice combines these with digital modeling (e.g., DFN-based simulations) to account for anisotropy and geological uncertainty—especially critical when designing dewatering systems near blast zones where water inflow may surge post-blast due to newly opened fractures.
📐 Langefors–Kihlström Burden Formula
This widely accepted empirical formula estimates burden based on rock strength and explosive energy. It accounts for rock resistance via the 'rock factor' K and explosive power via relative weight strength (RWS). Used globally in surface mining for initial pattern layout before refinement with field trials.
Langefors–Kihlström Burden
B = K × √(d × RWS)Estimates optimal burden (m) for surface drilling based on rock factor, hole diameter (cm), and relative weight strength.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| B | Burden | m | Perpendicular distance from blasthole center to nearest free face |
| K | Rock Factor | dimensionless | Empirically derived constant based on rock strength and structure; K = 1.3 + 0.002 × UCS (MPa) |
| d | Hole Diameter | cm | Drill bit diameter converted to centimeters for unit consistency |
| RWS | Relative Weight Strength | dimensionless | Energy ratio of explosive vs. ideal ANFO (RWS = 1.0); e.g., ANFO = 0.82, Emulsion = 1.05 |
Typical Ranges:
Hard rock (UCS > 100 MPa): 6.0 – 8.5 m
Medium rock (UCS 50–100 MPa): 4.5 – 6.5 m
Soft rock / weathered material: 3.0 – 4.5 m
💡 Worked Example
Problem: Given: Rock UCS = 120 MPa, drill diameter = 250 mm, ANFO with RWS = 0.82, desired powder factor = 0.55 kg/m³, bench height = 15 m.
1.
Step 1: Calculate rock factor K = 1.3 + 0.002 × UCS (MPa) = 1.3 + 0.002 × 120 = 1.54
2.
Step 2: Apply Langefors formula: B = K × √(d × RWS) where d = hole diameter in cm → d = 25 cm → B = 1.54 × √(25 × 0.82) = 1.54 × √20.5 ≈ 1.54 × 4.53 = 7.0 m
3.
Step 3: Verify against bench height constraint: B ≤ 0.8 × H = 0.8 × 15 = 12.0 m → 7.0 m is acceptable. Check powder factor: For spacing S = 1.15 × B = 8.05 m, burden B = 7.0 m, subdrill = 1.5 m → burden volume per hole = B × S × (H + subdrill) = 7.0 × 8.05 × 16.5 ≈ 927 m³ → charge per hole = 0.55 kg/m³ × 927 m³ ≈ 510 kg → matches typical ANFO loading for 250 mm holes.
Answer:
The calculated burden is 7.0 m, which falls within the safe range of 5.5–8.5 m for hard rock benches 12–18 m high.
🏗️ Real-World Application
At Rio Tinto’s Pilbara iron ore operation (Yandicoogina Mine), engineers revised burden from 6.2 m to 7.4 m after geotechnical logging revealed tighter joint spacing than assumed. This reduced oversize >75 mm from 18% to 9%, cutting secondary crushing costs by AUD $2.3M/year. Crucially, the change also lowered post-blast groundwater influx into the muck pile sump by 35%—enabling downsizing of the primary dewatering pump station from 3 × 1,200 m³/h units to 2 × 1,000 m³/h units, validated via coupled blast-hydrogeology modeling in RS2 and BlastLogic.
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