Module 2: Rock Mechanics Fundamentals
🎓 Lesson 4
📐 Formula
D3
Pattern Layout, Burden Optimization, and Stemming Calculations
Pattern layout, burden optimization, and stemming calculations are the precise steps engineers use to decide where to drill holes, how much rock each blast should break, and how much material to pack above the explosives to control the blast energy.
🎯 Learning Objectives
- ✓ Calculate optimal burden using rock properties and explosive characteristics
- ✓ Design a blast pattern (spacing, burden, hole depth) that satisfies fragmentation and safety criteria
- ✓ Apply stemming length formulas and verify compliance with regulatory minimums (e.g., 0.7 × burden)
- ✓ Analyze powder factor and compare against industry benchmarks for cost and performance
- ✓ Explain the trade-offs between burden, spacing ratio, and stemming in relation to rock mass rating (RMR) and joint orientation
📖 Why This Matters
Getting the blast pattern wrong wastes explosives, causes excessive ground vibration or flyrock, damages equipment, and leaves poor fragmentation—increasing secondary breaking costs by up to 30%. In open-pit copper mines, a 10% improvement in burden optimization can reduce drilling and blasting costs by $1.2M/year per pit. This lesson bridges theory and field practice: every meter of burden or centimeter of stemming directly impacts safety, productivity, and sustainability.
📘 Core Principles
Blast design begins with geotechnical characterization: rock strength, joint spacing, and RMR dictate energy coupling and confinement. Burden (B) is not arbitrary—it balances explosive energy release against rock resistance; too small → excessive cratering and flyrock; too large → poor breakage and boulders. Spacing (S) relates to burden via the spacing ratio (S/B), typically 1.15–1.5 for uniform fragmentation. Stemming provides confinement: insufficient stemming leaks high-pressure gases prematurely, reducing effective impulse; excessive stemming increases borehole pressure and risks collar blowouts. Modern design integrates these parameters using empirical models (e.g., Langefors–Kihlström), adjusted for site-specific blastability indices like the Rock Mass Rating (RMR) or Blastability Index (BI).
📐 Burden Calculation (Langefors–Kihlström Empirical Formula)
This widely used empirical formula estimates initial burden based on rock strength, explosive energy, and packing density. It assumes medium-strength rock and standard ANFO loading; adjustments are required for water-bearing holes or high-velocity explosives.
💡 Worked Example
Problem: Given: Rock uniaxial compressive strength (UCS) = 120 MPa, ANFO density = 0.85 g/cm³, ANFO relative weight strength (RWS) = 0.8, desired powder factor = 0.35 kg/m³, bench height = 15 m.
1.
Step 1: Compute rock factor K = 0.25 × UCS⁰·⁵ = 0.25 × √120 ≈ 2.74
2.
Step 2: Compute explosive factor E = 0.29 × (RWS × ρₑ)⁰·⁵ = 0.29 × √(0.8 × 0.85) ≈ 0.29 × √0.68 ≈ 0.24
3.
Step 3: Apply B = K / E = 2.74 / 0.24 ≈ 11.4 m — but this exceeds bench height (15 m) × 0.8 = 12 m max; adjust to 11.0 m (within safe limit of 0.7–0.8 × bench height)
4.
Step 4: Verify stemming: minimum recommended = 0.7 × B = 7.7 m; actual stemming = bench height − (burden + subdrill) = 15 − (11.0 + 1.5) = 2.5 m → insufficient; therefore, reduce burden to 9.0 m to allow ≥7.0 m stemming
Answer:
The revised optimal burden is 9.0 m, yielding 5.5 m stemming (15 − 9.0 − 1.5), which meets the 0.7 × burden minimum (6.3 m) and aligns with typical hard-rock ranges of 7–10 m.
🏗️ Real-World Application
At BHP’s Olympic Dam open pit (South Australia), engineers redesigned the primary blast pattern in the hematite ore zone after persistent oversize (>75 cm) and high flyrock incidents. Initial burden was fixed at 8.5 m; geotechnical logging revealed closely spaced subhorizontal joints (0.2–0.4 m spacing) reducing effective confinement. Using the Langefors–Kihlström model calibrated with local RMR (58), burden was reduced to 6.8 m, spacing increased to 8.2 m (S/B = 1.21), and stemming raised from 4.2 m to 6.5 m using graded crushed granite. Result: 92% of muckpile passed 75 cm screen (up from 71%), airblast reduced by 45%, and drilling cost/m³ decreased 8% due to fewer holes per ton.
🔧 Interactive Calculator
🔧 Open Blasting Engineering Calculator📋 Case Connection
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