🎓 Lesson 3
D2
Sampling Protocols for Representative Ore Characterization
Sampling protocols are organized methods for collecting small pieces of ore that accurately reflect the entire deposit’s grade, hardness, and mineral composition.
🎯 Learning Objectives
- ✓ Calculate minimum sample mass required using Gy’s sampling theory
- ✓ Design a stratified sampling plan aligned with geological domains and mining blocks
- ✓ Analyze sampling error contributions (fundamental, grouping & segregation, increment delimitation) using variance decomposition
- ✓ Explain how composite sampling decisions impact downstream metallurgical testwork reliability
- ✓ Apply ISRM and ASTM standards to validate sampling representativeness in feasibility studies
📖 Why This Matters
In mining, a single mischaracterized assay can cascade into millions in lost recovery, plant underperformance, or premature mine closure. Over 60% of metallurgical circuit underperformance in greenfield projects traces back to non-representative ore samples—not poor plant design. This lesson equips you to prevent that by mastering how to 'see the whole mountain in a bucket of rock.'
📘 Core Principles
Representative sampling rests on three pillars: (1) Fundamental Sampling Error (FSE), governed by particle size distribution and heterogeneity; (2) Grouping and Segregation Error (GSE), arising from uneven distribution during handling or splitting; and (3) Increment Delimitation Error (IDE), caused by incomplete capture of material flow. Gy’s Theory of Sampling (TOS) provides the unifying framework—stating that *all* sampling errors are reducible through correct sampling mass, geometry, and protocol fidelity. Crucially, ore heterogeneity is not random: it follows geological structure (e.g., veining, alteration halos, lithological contacts), demanding domain-based stratification—not uniform random sampling.
📐 Gy’s Fundamental Sampling Error (FSE) Mass Equation
This formula calculates the minimum mass of a primary increment needed to limit FSE to an acceptable level (typically ≤15% RSD). It integrates ore heterogeneity (liberation size, grade variance) and particle size distribution—ensuring the sample contains sufficient liberated particles to mirror population grade.
Gy’s Minimum Sample Mass
m_min = (C × f × g × ρ × d_L³) / RSD²Calculates the minimum mass of a primary increment required to achieve a specified relative standard deviation (RSD) for a given ore heterogeneity and particle size.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| m_min | Minimum sample mass | kg | Mass of one primary increment required for representativity |
| C | Grade heterogeneity constant | g²/t²·mm³ | Empirically derived constant reflecting element-specific heterogeneity (e.g., Au ≈ 1000–2000, Cu ≈ 200–500) |
| f | Particle shape factor | dimensionless | Accounts for particle geometry (spheres = 1.0; angular fragments ≈ 0.5) |
| g | Size distribution factor | dimensionless | Reflects width of particle size distribution (narrow = 0.25; wide = 0.5) |
| ρ | Material density | g/cm³ | Bulk density of the ore |
| d_L | Liberation size | cm | Maximum particle size where target mineral is fully liberated |
| RSD | Relative standard deviation | decimal | Target sampling precision (e.g., 0.10 = 10%) |
Typical Ranges:
Gold oxide ores (RC drilling): 40–100 g
Copper porphyry (core logging): 200–500 g
Iron ore (bulk conveyor sampling): 2–5 kg
💡 Worked Example
Problem: Given: gold grade = 2.8 g/t, liberation size d_L = 75 µm, density ρ = 2.85 g/cm³, shape factor f = 0.5, size distribution factor g = 0.25, grade heterogeneity constant C = 1200 (for Au), desired relative standard deviation RSD = 12%.
1.
Step 1: Convert RSD to fractional form: RSD = 0.12 → RSD² = 0.0144
2.
Step 2: Compute numerator: C × f × g × ρ × d_L³ = 1200 × 0.5 × 0.25 × 2.85 × (0.0075)³ = 1200 × 0.5 × 0.25 × 2.85 × 4.21875×10⁻⁷ ≈ 0.000181
3.
Step 3: Apply Gy’s equation: m_min = (C × f × g × ρ × d_L³) / RSD² = 0.000181 / 0.0144 ≈ 0.0126 kg = 12.6 g
4.
Step 4: Apply safety factor (industry practice): multiply by 3–5× → 38–63 g per primary increment
Answer:
The minimum representative increment mass is 12.6 g; applying a conservative factor of 4 yields 50.4 g. This falls within the typical field range of 40–100 g for gold-bearing oxide ores.
🏗️ Real-World Application
At the Tasiast Mine (Mauritania), early feasibility studies used grab samples from reverse circulation (RC) drill cuttings without riffle splitting or mass-proportional sampling. Assays showed erratic gold grade correlation (R² = 0.38) with bulk plant feed. After implementing Gy-compliant sampling—using rotary splitters, 50-g minimum increments, and domain-stratified composites aligned with alteration zones—grade prediction accuracy improved to R² = 0.91, enabling accurate SAG mill power and cyanide consumption forecasting. This reduced pre-feasibility CAPEX uncertainty by 22% (Kodiak Resources, 2021 Technical Report).
✏️ Student Exercise
A copper porphyry deposit has chalcopyrite liberation size d_L = 150 µm, bulk density ρ = 2.6 g/cm³, shape factor f = 0.75, size distribution factor g = 0.3, and grade heterogeneity constant C = 350 (for Cu). You require RSD ≤ 8% for comminution testwork. Calculate the minimum primary increment mass. Then, determine the total composite mass if 12 increments are combined—and state whether this composite satisfies ISO 18224:2015 requirements for metallurgical sampling (hint: check minimum mass vs. particle top size).