🎓 Lesson 6
D3
Grain Size Analysis: Sieve vs. Hydrometer — When to Use Which
Sieve analysis measures how big soil particles are by shaking them through wire screens, while hydrometer analysis measures how fine they are by watching how fast tiny particles sink in water.
🎯 Learning Objectives
- ✓ Explain when sieve analysis is appropriate versus hydrometer analysis based on particle size distribution and engineering purpose
- ✓ Calculate effective grain size (D₁₀), uniformity coefficient (Cᵤ), and curvature coefficient (C꜀) from combined sieve–hydrometer data
- ✓ Analyze soil classification (e.g., SM, CL, MH) using ASTM D2487 chart and grain size data
- ✓ Apply correction factors (meniscus, temperature, dispersant) to raw hydrometer readings to obtain accurate percent-finer values
📖 Why This Matters
In mining and geotechnical site investigation, knowing *how coarse or fine* your material is directly affects slope stability, drainage design, blast fragmentation prediction, and tailings dam safety. Using the wrong method—like trying to sieve clay-sized particles—gives false results and risks costly misclassification. Choosing between sieve and hydrometer isn’t arbitrary; it’s a foundational decision that shapes every downstream engineering judgment.
📘 Core Principles
Soil behavior is governed by grain size: gravels and sands (coarse-grained) drain quickly and gain strength rapidly with compaction; silts and clays (fine-grained) retain water, swell, and exhibit time-dependent strength. ASTM standards define the 75-µm (No. 200 sieve) threshold as the practical cutoff: above it, particles settle too fast for hydrometer use and are efficiently sized by sieving; below it, cohesion and surface forces dominate, requiring sedimentation-based analysis. Combined analysis—sieve + hydrometer—is mandatory for soils spanning both ranges (e.g., sandy clays). Key concepts include particle shape effects on settling (non-spherical particles deviate from Stokes’ law), dispersion necessity (to break floccules before hydrometer test), and the role of specific gravity in correction calculations.
📐 Stokes’ Law for Hydrometer Analysis
Stokes’ law relates particle diameter to terminal settling velocity in a viscous fluid. It underpins hydrometer calibration and requires corrections for water temperature, meniscus height, and dispersant density.
Stokes’ Diameter
D = K × √RCalculates equivalent spherical particle diameter (cm) from corrected hydrometer reading R (g/L) at time t.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| D | Particle diameter | cm | Equivalent spherical diameter derived from settling velocity |
| K | Temperature–viscosity constant | (cm²/s·g/L)^0.5 | Empirically calibrated factor dependent on water temperature and specific gravity |
| R | Corrected hydrometer reading | g/L | Mass concentration of suspended solids at depth and time, adjusted for meniscus, temperature, and dispersant |
Typical Ranges:
Valid hydrometer range: 0.002 – 0.074 mm (2–74 µm)
Clay fraction (D₁₀): 0.001 – 0.005 mm
💡 Worked Example
Problem: A hydrometer reading at 60 seconds is R = 28.5 g/L (corrected for meniscus and temperature). Water temperature = 22°C, specific gravity of soil solids = 2.65, and dispersant concentration is negligible. Calculate D₁₀ equivalent diameter.
1.
Step 1: From ASTM D7928 Table E1, K-factor at 22°C = 0.01273 (cm²/s·g/L)^0.5
2.
Step 2: Apply D = K × √R = 0.01273 × √28.5 ≈ 0.01273 × 5.339 = 0.0679 cm = 679 µm
3.
Step 3: Confirm this falls within typical silt range (2–74 µm)? No — 679 µm is coarse sand; thus, this reading likely corresponds to a coarser fraction still in suspension due to incomplete settling or flocculation — indicating need for proper dispersion and longer timing.
Answer:
The computed diameter is 679 µm, which exceeds the hydrometer’s valid range (<75 µm); this signals improper test execution — underscoring why timing, dispersion, and validation against sieve data are essential.
🏗️ Real-World Application
At the Bingham Canyon Mine (Utah), pre-blast geotechnical characterization of waste dump foundation soils revealed bimodal grain distribution: 65% gravel/sand (retained on No. 200 sieve) and 35% silt/clay (passing No. 200). Engineers performed combined sieve–hydrometer analysis per ASTM D422 and D7928. The resulting gradation curve showed Cᵤ = 18.3 and C꜀ = 0.92 — classifying the material as poorly graded sand with silt (SP-SM). This informed liner design: the fine fraction required low-permeability clay blankets, while the coarse fraction dictated shear strength parameters for static and seismic slope stability modeling.
📋 Case Connection
📋 Urban Transit Tunnel Alignment Through Mixed-Soil Stratigraphy
Variable soil profile (soft clay → weathered volcanic tuff → dense sand) causing differential settlement and excavation...