Reproduce the falling-head permeability test used to measure the coefficient of permeability (hydraulic conductivity) of a fine-grained soil. Adjust the standpipe area, sample dimensions, initial and final head difference and elapsed time to see the permeability and its class update in real time.
Parameters
Standpipe area a
cm²
A thinner pipe makes the level drop easier to read and more sensitive
Sample area A
cm²
Sample length L
cm
Initial head difference h₁
cm
Head difference between the standpipe level and the outlet at the start
Final head difference h₂
cm
Head after the elapsed time. Must be smaller than h₁
Elapsed time t
s
Time taken for the level to fall from h₁ to h₂
Results
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Permeability k (cm/s)
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Permeability k (m/s)
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Head ratio log ln(h₁/h₂)
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Average hydraulic gradient i
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Water volume passed (cm³)
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Permeability class
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Falling-head apparatus — water-level animation
The water level in the thin standpipe falls as water seeps down through the soil sample. The head difference shrinks from h₁ to h₂ and water drains from the bottom of the cell.
Head difference vs time h(t)
Permeability vs standpipe area
Theory & Key Formulas
$$k=\frac{a\,L}{A\,t}\ln\!\frac{h_1}{h_2}$$
Coefficient of permeability k from the falling-head test. a is the standpipe area, A and L the sample area and length, t the elapsed time, h₁ and h₂ the initial and final head differences. The falling-head method suits fine-grained, low-permeability soils.
Average hydraulic gradient i (a representative head-loss gradient during the test) and the volume of water V that passed from the standpipe into the sample.
What is the Falling-Head Permeability Test?
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A "permeability test" measures how much water a soil lets through, right? Why bother watching the level in a thin pipe?
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Good question. A soil's permeability — properly the coefficient of permeability, or hydraulic conductivity — tells you how readily water flows through it, and it is one of the most important properties in soil mechanics. The tricky part is that it has a huge range: from gravel that drains like a sieve to clay that, for practical purposes, lets nothing through. That is more than ten orders of magnitude — gravel and clay can differ by ten billion times.
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Ten orders of magnitude! With a range that wide, one test method surely isn't enough.
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Exactly. There are two main laboratory permeability tests. One is the "constant-head test", which holds a fixed head difference and simply measures the steady flow rate. That works well for coarse soils like gravel and coarse sand, where water flows freely and the volume is easy to collect. But for fine-grained soils — silts and silty sands — it falls apart. The flow is so slow that the volume passing in a reasonable time is tiny and hard to measure accurately.
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So how do you measure the fine soils?
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That is where the "falling-head test" — the one this tool models — comes in. The idea is clever. Instead of trying to measure a tiny flow volume, you connect the sample to a thin standpipe, fill the standpipe with water, and simply watch the water level fall as the water seeps down through the soil. Because the pipe is narrow, even a very small flow makes the level drop a clearly visible amount. You just time how long the level takes to fall from a higher reading to a lower one with a stopwatch.
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I see — you measure how fast the level drops, not the flow rate. What does the formula look like?
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The permeability is k = (a·L)/(A·t)·ln(h₁/h₂). Here a is the pipe area, A and L the sample area and length, t the elapsed time, and h₁ and h₂ the initial and final head differences. The natural logarithm appears because as the level drops the head difference also shrinks and the flow slows — it is an exponential decay. Try making a smaller with the slider on the left: the same drop takes longer, meaning the measurement is more sensitive. That is exactly why the least permeable soils are tested with a deliberately thin standpipe.
Frequently Asked Questions
Because permeability spans more than ten orders of magnitude between soils, the test method is chosen to suit the soil. The constant-head test holds a fixed head difference and measures the steady flow rate directly; it works well for coarse, highly permeable soils such as gravel and coarse sand, where the flow is fast and easily collected. The falling-head test derives permeability from how fast the water level falls in a thin standpipe; it suits fine-grained soils such as silt and silty sand, where the flow is too small to measure directly. This tool models the falling-head test.
The coefficient of permeability is k = (a·L)/(A·t)·ln(h₁/h₂), where a is the standpipe area, A and L are the sample area and length, t is the elapsed time, and h₁ and h₂ are the initial and final head differences. ln is the natural logarithm. The narrower the standpipe, the more the level drops for a given flow, so the least permeable soils are tested with a thin standpipe to gain sensitivity. This tool reports the result in both cm/s and m/s.
As a guide, k ≥ 1×10⁻² cm/s is high permeability (gravel, coarse sand); 1×10⁻⁴ to 1×10⁻² cm/s is medium (sandy soil); 1×10⁻⁷ to 1×10⁻⁴ cm/s is low (silt, fine-grained soil); and below 1×10⁻⁷ cm/s is very low (clay, barrier layer). This is why clay is treated as practically watertight, and the reason clay is used for landfill liners and dam cores.
The most common error source is trapped air in the sample (incomplete saturation). Trapped air makes the apparent permeability lower than the true value, so thorough saturation and de-airing before the test are essential. Other sources are side leakage where water bypasses the soil along the mould wall, the change in water viscosity with temperature (results are corrected to a standard 15°C or 20°C), and clogging by migrating fine particles. Careful specimen preparation and a temperature correction are required.
Real-World Applications
Seepage analysis for dams and levees: The permeability of the core of a fill dam or the embankment of a river levee directly governs its safety. Only when the permeability is known can you compute the phreatic line within the body, the seepage through the foundation, and the safety factor against piping. The core is built from a low-permeability cohesive soil verified by a falling-head test, keeping the dam body practically watertight.
Landfill barrier liners: The clay liner or compacted clay layer (CCL) at the base of a landfill must have an extremely low permeability so contaminated leachate does not escape to the groundwater. Many standards set a target of k ≤ 1×10⁻⁷ cm/s, and the falling-head test is one of the few methods able to measure such a low value directly. It is also essential for post-construction quality control.
Excavation and dewatering design: For an excavation, the permeability of the surrounding ground sets the pumping rate needed for groundwater drawdown (dewatering) and the seepage that flows around a cut-off wall. In a low-permeability cohesive layer the water level barely drops even with pumping, while a sand layer in between can demand large-scale drainage. Knowing k for each stratum is the starting point of the design.
Rate of consolidation settlement: For a soft clay deposit, what matters about consolidation settlement is not only how much it settles but when it finishes settling, and that rate is governed by the clay's permeability. The lower the permeability, the longer the pore water takes to drain, so settlement creeps on slowly over years. The k from a falling-head test is used to verify the coefficient of consolidation and to select ground-improvement methods.
Common Misconceptions and Pitfalls
The biggest pitfall is assuming the sample is fully saturated. The falling-head formula assumes the soil voids are filled with water and no air remains. Trapped air blocks the flow paths and makes the apparent permeability lower than the true value — sometimes by an order of magnitude. Cohesive soils and silts are hard to de-air, and may not saturate fully without vacuum de-airing or back-pressure saturation. When k comes out "strangely low", suspect the degree of saturation first.
Next, ignoring side leakage along the mould wall. If there is even a slight gap between the sample and the inner wall of the mould, water slips along that edge instead of flowing through the soil. The truly low permeability is then overestimated, an unconservative result. Prepare the specimen so it presses tightly against the wall, and where necessary seal it with bentonite or switch to a triaxial-cell permeability test. The lower the permeability, the larger the relative impact of side leakage.
Finally, not correcting for the effect of temperature on viscosity. Permeability is inversely proportional to water viscosity, and viscosity varies strongly with temperature. Water at 10°C is roughly twice as viscous as water at 30°C, so without a correction the same soil can give a k that varies by a factor of two with the season or room temperature. In practice you measure the water temperature during the test and convert k to a standard temperature (15°C in Japan, 20°C internationally) using the viscosity ratio. This tool reports the raw, uncorrected k, so remember this conversion when comparing with field values.
How to Use
Enter the cross-sectional area of the standpipe (a) in cm², typically 0.5–2.0 cm² for fine-grained soils.
Set the cross-sectional area of the soil specimen (A) in cm², commonly 50–100 cm² for laboratory permeameters.
Input the length of the soil specimen (L) in cm; standard values range from 5–10 cm for consolidation cells.
Specify initial head (h₁) in cm and final head (h₂); the simulator calculates the time elapsed and resulting permeability coefficient k.
Review output values: k in cm/s and m/s, head ratio ln(h₁/h₂), hydraulic gradient, water volume drained, and soil classification (clay, silt, sand, gravel).
Worked Example
A silty clay specimen: standpipe area a = 1.0 cm², specimen area A = 60 cm², length L = 8 cm, initial head h₁ = 50 cm, final head h₂ = 12 cm, elapsed time t = 480 minutes. The simulator computes k = 2.1 × 10⁻⁶ cm/s (2.1 × 10⁻⁸ m/s), head ratio ln(50/12) = 1.427, average gradient i = (50+12)/(2×8) = 3.875, and water volume drained = 28.4 cm³. Classification: low-permeability silt, suitable for landfill liners.
Practical Notes
Use falling-head method for k < 10⁻⁵ cm/s (clay, silt); constant-head apparatus suits coarser soils (sand, gravel) with k > 10⁻⁴ cm/s.
Ensure standpipe diameter is small relative to specimen area (typical ratio a/A < 0.05) to achieve measurable head drop over reasonable test duration.
Account for temperature effects: water viscosity changes ~2% per °C; standardize tests at 20°C or apply viscosity correction factor.
Saturation is critical; trapped air bubbles artificially reduce measured k; apply back-pressure or vacuum saturation before testing.