Permeability from Falling Head Test Calculator
Calculate the coefficient of permeability (hydraulic conductivity) k from a falling-head permeameter test. Geotechnical labs use it for fine soils — silts and silty/clayey sands — where a constant-head test would be too slow.
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How to use this calculator
- Enter the standpipe (burette) cross-section area a, the sample length L and the sample cross-section area A.
- Enter the elapsed time t and the initial and final heads h₁ and h₂ (with h₁ > h₂).
- Read k in m/s and mm/s, plus the indicative soil-type band.
How it works
In a falling-head test, water drains through the soil sample from a thin standpipe and the head drops from h₁ to h₂ over time t. Integrating Darcy's law over the falling head gives k = (a·L)/(A·t) · ln(h₁/h₂), where a is the standpipe area, A the sample area and L the sample length. Enter areas in mm² and lengths in mm and k comes out in mm/s, which the tool also converts to m/s (÷1000).
The result is compared against the standard permeability bands: gravel > 1×10⁻², sand 1×10⁻² to 1×10⁻⁵, silt 1×10⁻⁵ to 1×10⁻⁹ and clay < 1×10⁻⁹ m/s. Permeability is temperature-sensitive (through water viscosity), so results are normally reported at 20 °C.
Worked example
Falling-head run. a = 100 mm², L = 100 mm, A = 1000 mm², t = 60 s, head falling from h₁ = 1000 mm to h₂ = 500 mm. ln(1000/500) = 0.693. k = (100 × 100)/(1000 × 60) × 0.693 = 0.1155 mm/s = 1.16×10⁻⁴ m/s — a sand.
Common mistakes
- Mixing units between a, A and the lengths — keep areas in the same unit and lengths in the same unit, or the ratio and k come out wrong.
- Using a falling-head test on clean sands/gravels — they drain too fast to time accurately; use a constant-head test instead.
- Ignoring the temperature correction — report k at 20 °C, especially when test water is much warmer or colder.
Frequently asked questions
What is the falling head permeability formula?
k = (a·L)/(A·t)·ln(h₁/h₂), where a = standpipe area, L = sample length, A = sample area, t = elapsed time, and h₁, h₂ are the initial and final heads.
Falling head or constant head test — which do I use?
Falling head for fine, low-permeability soils (silts, clays, silty sands). Constant head for coarse, high-permeability soils (sands and gravels) that drain too quickly to time a falling head.
What units does k come out in?
If you enter all areas in mm² and all lengths in mm, k is in mm/s. The tool also shows k in m/s (÷1000), the usual reporting unit.
What is a typical permeability for sand or clay?
Roughly: gravel above 1×10⁻² m/s, sand 1×10⁻² to 1×10⁻⁵, silt 1×10⁻⁵ to 1×10⁻⁹ and clay below 1×10⁻⁹ m/s.
Why must h₁ be greater than h₂?
The head falls during the test, so the initial head h₁ must exceed the final head h₂; ln(h₁/h₂) must be positive for a valid k.
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