Permeability and seepage
Permeability measures how easily water flows through soil. It ranges over many orders of magnitude: clean gravel lets water through almost freely, while clay may take years to pass the same amount. That range governs drainage, dewatering, seepage under dams and how fast a clay layer settles.
Darcy's law states that, for slow laminar flow, the flow velocity is proportional to the hydraulic gradient, the head loss per unit length of flow path. The constant is the coefficient of permeability k.
In the laboratory, the constant-head test suits coarse soils and the falling-head test suits fine soils. In the field, pumping tests from wells give a more representative value because they sample a large volume of ground including its layers and fissures.
For two-dimensional seepage under a dam or around a sheet pile, a flow net of flow lines and equipotential lines gives the seepage quantity and the pore pressures. The exit gradient at the downstream toe must stay well below the critical gradient to prevent piping.
Darcy: v = k i, Q = k i AConstant head: k = Q L / (A h t)Falling head: k = (a L / (A t)) ln(h₁ / h₂)Flow net: q = k H (N_f / N_d) per unit width
Problem. A constant-head test: sample length 150 mm, area 5 000 mm², head 300 mm, 450 ml collected in 120 s. Find k.
- Q per second = 450 000 mm³ / 120 s = 3 750 mm³/s.
- i = 300 / 150 = 2.
- k = Q / (i A) = 3 750 / (2 × 5 000) = 0.375 mm/s = 3.75 × 10⁻⁴ m/s.
Answer. k ≈ 3.8 × 10⁻⁴ m/s
Quick quiz
1Which test suits clay?
Falling-head test.
2What is hydraulic gradient?
Head loss divided by flow path length.
3Why check exit gradient below a dam?
To prevent piping.
- IS 2720 (series) (India): Methods of test for soils: water content, limits, compaction, shear and others, each in its own part.
Clauses and documents to read
- IS 2720 (Part 17): laboratory determination of permeability
Cited by number and clause only. We do not reproduce clause text, tables or figures (BIS Act 2016, s.10(5) and s.11). Check the current edition and amendments before use.
References and further reading
Standard texts, listed in no order of merit. We do not copy text, figures, tables or solved problems from any book; our explanations and examples are original.
- Gopal Ranjan, A. S. R. Rao, Basic and Applied Soil Mechanics, New Age International, latest edition.
- B. M. Das, Principles of Geotechnical Engineering, Cengage, latest edition.
- K. Terzaghi, R. B. Peck, G. Mesri, Soil Mechanics in Engineering Practice, Wiley, 3rd edition.
- J. A. Knappett, R. F. Craig, Craig's Soil Mechanics, CRC Press, latest edition.
Free and official sources
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