CIVL2410 Chap.6 Measuring permeability in the laboratory and the field
Measuring permeability in the laboratory and the field
Darcy's law is useless without a number, and no single method covers a range spanning nine orders of magnitude. A clean gravel reaches steady flow in seconds while a clay may take weeks to pass a measurable volume, so the apparatus is chosen before the test from the classification.
This chapter covers the two laboratory cells and their derivations, the field methods that sample real ground rather than a remoulded specimen, and the empirical estimates that stand in when no test is available.
What this chapter covers
- 01
Choosing the apparatus from the classification, before the specimen is prepared
- 02
The constant head permeameter, and where its formula comes from
- 03
Saturation, steady state and sidewall leakage as the three practical faults
- 04
The falling head permeameter and the derivation that produces its logarithm
- 05
Why the standpipe area sets the range of the instrument
- 06
Tracer tests, and the four families of tracer
- 07
Pumping and borehole tests, and what a field test sees that a specimen cannot
- 08
Hazen's estimate, and the four conditions it is only claimed within
- 09
Kozeny-Carman, and why permeability responds so steeply to packing
- 10
Reporting a permeability honestly: method, stress level, saturation and direction
A falling head test on a silty sand
- +1Sample area A = pi x 0.075 squared / 4 = 4.418 x 10^-3 square metres.
- +1Standpipe area a = pi x 0.008 squared / 4 = 5.03 x 10^-5 square metres, a ratio of about one to eighty eight.
- +1The leading fraction is a L divided by A t = 5.03 x 10^-5 x 0.180 / (4.418 x 10^-3 x 720) = 2.84 x 10^-6.
- +1The logarithm of the head ratio is ln(1.20 / 0.65) = 0.613, so k = 2.84 x 10^-6 x 0.613 = 1.7 x 10^-6 m/s.
Key terms
- Constant head permeameter
- A cell that holds the driving head fixed with an overflow and measures the volume discharged in a timed interval. It suits coarse soils, which can deliver a measurable volume.
- Falling head permeameter
- A cell supplied from a narrow standpipe whose level is allowed to fall during the test. Because the pipe is narrow, a very small seepage produces a readable change in head, which is what a fine soil can provide.
- Hazen's formula
- An estimate of permeability from the square of the effective size, claimed only for clean uniform sands within a stated range of size, uniformity and porosity.
- Tracer test
- A field method that measures seepage velocity directly by injecting a detectable substance upstream and timing its arrival downstream.
Measuring permeability in the laboratory and the field FAQ
Why not use a constant head test on everything?
Because the volume it would collect from a fine soil is smaller than the measurement error. A clay liner at around 10^-9 m/s in a standard cell under half a metre of head passes something like a third of a millilitre in an eight hour day, which is less than the evaporation and meniscus errors in the measuring cylinder.
The falling head cell measures a different quantity, the fall of a level in a very narrow tube, and that is something a fine soil can supply.
Is an estimate from the grading curve ever acceptable?
As a first pass, provided its conditions are checked and stated. Hazen's estimate is claimed only for clean uniform sands with a uniformity coefficient below five, an effective size between 0.1 and 3 mm and a porosity between 0.25 and 0.5, and it ignores particle shape, packing and pore connectivity entirely. Applied outside that range it produces a confident number with no basis.
Report it as an estimate from grading rather than as a measurement, and state the conditions you checked.
Why does a field test give a different answer from a laboratory one?
Because they measure different volumes of ground. A laboratory specimen is small, remoulded to some degree by sampling, and cut in one direction, so it cannot see the layering, fissures and fabric that actually control flow at the scale of a structure.
Since anisotropy is the rule rather than the exception, a horizontally cut specimen and a vertically cut one from the same deposit can differ by an order of magnitude, and a pumping test that samples an entire aquifer will usually return something larger than either.
Exam move
The examinable skill here is choosing and defending a method, not substituting into a formula, so practise stating the choice before the arithmetic. Learn the falling head derivation as a chain of four steps rather than as a result, because the logarithm makes no sense otherwise and the derivation itself is examinable.
Work in base units from the first line, since these calculations mix millimetres, litres and minutes and every one of those conversions is a chance to lose a factor of a thousand. For the laboratory report, remember that a permeability without its method, stress level, saturation and specimen orientation is close to worthless, because the same soil can return values a factor of two or more apart between specimens.
Working through Measuring permeability in the laboratory and the field in CIVL2410? Sia is AskSia’s AI Engineering tutor — ask any CIVL2410 Measuring permeability in the laboratory and the field question and get a clear, step-by-step explanation grounded in how CIVL2410 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.
