CIVL2410 Chap.2 Particle size distributions: sieving and sedimentation
Particle size distributions: sieving and sedimentation
Particle size is the cheapest useful measurement in geotechnical engineering, and it correlates with permeability, compressibility and strength. Two quite different experiments produce it, meeting at a boundary of about 75 microns: mechanical separation by sieving above it, and hydraulic separation by settling below it.
This chapter works both, stitches them into one grading curve, and extracts the three characteristic diameters and two coefficients that the classification chapter turns into a symbol.
What this chapter covers
- 01
Why grain size is classified at all, and what it stands in for
- 02
The size bands: clay, silt, sand and gravel, and where the boundaries fall
- 03
The sieve stack, and the closure check that protects the whole curve
- 04
Turning masses retained on trays into percentage passing
- 05
Stokes drag and the terminal velocity of a settling particle
- 06
The hydrometer, what its reading physically means, and the depth correction
- 07
Why the reported fine diameter is an equivalent settling diameter
- 08
Plotting percentage finer against a logarithmic diameter axis
- 09
Reading D10, D30 and D60, and interpolating in the logarithm
- 10
Uniformity and curvature coefficients, and the defect each one detects
- 11
Particle shape: roundness, sphericity, and why they matter for strength
A sieve test worked to a grading verdict
- +1Accumulate the retained masses down the stack: 0, 30, 90, 210, 350, 440, 480, 500 g. The last figure equals the sample mass, so nothing has been lost in the sieves.
- +1Percentage passing is 100 minus cumulative retained over total, giving 100, 94, 82, 58, 30, 12 and 4 per cent at the seven meshes.
- +1Interpolate logarithmically between bracketing points: 60 per cent passing lies between 0.60 mm at 58 per cent and 1.18 mm at 82 per cent, giving D60 = 0.635 mm.
- +130 per cent passing lands exactly on the 0.30 mm mesh, so D30 = 0.30 mm; 10 per cent lies between 0.075 mm at 4 per cent and 0.15 mm at 12 per cent, giving D10 = 0.126 mm.
- +1Cu = 0.635 / 0.126 = 5.0 and Cc = 0.30 squared divided by (0.635 x 0.126) = 1.1.
Key terms
- Grading curve
- Percentage finer plotted against particle diameter on a logarithmic axis. Its shape says how wide a range of sizes the soil contains, and three diameters read off it carry most of the engineering information.
- Uniformity coefficient
- D60 divided by D10, comparing the two ends of the curve. A large value means a wide spread of sizes; a value near one means almost every grain is the same size.
- Curvature coefficient
- D30 squared divided by the product of D60 and D10. It tests whether the curve is smooth between its ends, which is how a gap graded soil is detected.
- Equivalent settling diameter
- The diameter of the sphere that would fall at the same speed as the particle actually measured. Clay particles are plates, so this is a usable engineering quantity rather than a physical width.
- Hydrometer test
- A sedimentation method that infers fine particle sizes from how fast a suspension clears, using Stokes law and a depth correction for the instrument's own length.
Particle size distributions: sieving and sedimentation FAQ
Why are two different tests needed for one curve?
Because mechanical separation stops working at small sizes. A sieve needs an opening that can be manufactured and grains large enough not to clog it, and below about 75 microns neither condition holds. The fine fraction is therefore sized hydraulically instead, by dispersing it in water and reading how fast it settles.
The two halves are stitched into one continuous curve, which is how a grading curve can span four orders of magnitude of diameter, but they carry different uncertainties and the fine end is the one to suspect first.
What does the curvature coefficient add that uniformity does not?
It looks at the middle of the curve rather than its ends. A gap graded soil that is missing a band of intermediate sizes can still span a very wide range overall, so it posts an excellent uniformity coefficient while being a poor engineering material, because the absent sizes cannot fill the voids between the coarse grains.
Curvature is the test that catches exactly that, which is why a soil has to pass both before it is called well graded.
Two laboratories report different clay fractions for the same soil. Who is wrong?
Possibly neither. Clay platelets stick together into flocs that settle like a single much larger particle, so a poorly dispersed suspension hides fine material and under reports the clay fraction. The laboratory using a stronger dispersing agent and longer mixing is closer to the true distribution, which is why dispersion procedure is specified rather than left to the operator.
The wider lesson is that a sedimentation result depends on how the particles behave in suspension, not only on their geometry.
Exam move
Practise the sieve arithmetic until the four column layout is automatic, because it appears in the laboratory report as well as in short assessment items, and the arithmetic is where the marks are lost rather than the concept. Always run the closure check before plotting, since a grading curve built from a broken mass balance looks perfectly plausible.
When reading characteristic diameters, write the logarithms in a spare column and interpolate those; doing it by eye on a logarithmic axis is the single most common source of a wrong coefficient. Finally, learn what each coefficient detects rather than the formulas, because the data sheet supplies the formulas and the examiner is asking which defect you have found.
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