Simulate the constant-head permeability test used to measure the coefficient of permeability of coarse, free-draining soils such as sands and gravels. Adjust the sample dimensions, head difference, collected volume and elapsed time to see the flow rate, hydraulic gradient, Darcy velocity and permeability update in real time through Darcy's law.
Parameters
Sample cross-sectional area A
cm²
Cross-section of the cylindrical sample the water passes through
Sample length L
cm
Length of the sample in the direction of flow
Constant head difference h
cm
Difference between inlet and outlet levels (held fixed)
Collected volume Q
cm³
Volume of water discharged during the elapsed time
Elapsed time t
s
Time over which the collected volume is measured
Results
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Flow rate Q/t (cm³/s)
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Hydraulic gradient i
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Darcy velocity v (cm/s)
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Permeability k (cm/s)
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Permeability k (m/s)
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Permeability rating
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Constant-head apparatus — steady flow animation
An inlet reservoir kept at a constant level by an overflow feeds water steadily through the sample to a constant-level outlet, and a measuring cylinder collects the discharge. The fixed head difference h and the flow direction are labelled.
Collected volume Q vs elapsed time t
Flow rate vs hydraulic gradient i (Darcy's law)
Theory & Key Formulas
$$k=\frac{Q\,L}{A\,h\,t},\qquad i=\frac{h}{L}$$
Coefficient of permeability k and hydraulic gradient i. Q: collected volume, L: sample length, A: cross-sectional area, h: head difference, t: elapsed time. The constant-head test holds a fixed head and measures the steady flow, and suits coarse, permeable soils such as sands and gravels.
$$\frac{Q}{t}=k\,i\,A,\qquad v=k\,i$$
Darcy's law. The flow rate Q/t equals the product of permeability k, hydraulic gradient i and area A, and the Darcy (discharge) velocity v is k·i.
What is the Constant-Head Permeability Test?
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The name "constant-head permeability test" sounds complicated. What does the test actually measure?
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In plain terms, it measures how fast water can travel through a soil. The number that captures that speed is the "coefficient of permeability k". Sand lets water through easily, so its k is large; clay barely lets water through, so its k is tiny. Whenever you deal with water moving in the ground, k is the single most important property — it shows up in almost every calculation.
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So what does the "constant-head" part mean?
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It means the head difference between the inlet and outlet levels is kept constant throughout the test. The inlet reservoir holds its level using an overflow, which keeps spilling the excess. With a fixed head difference, the flow through the soil is also steady and unchanging. Then you just collect the water that emerges in a measuring cylinder — say, how much fills up over two minutes. That gives you the flow rate directly, so the maths becomes very simple.
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How do you get the permeability from the volume of water you collected?
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This is where Darcy's law comes in. It is the basic law of groundwater flow: flow rate equals permeability times hydraulic gradient times cross-sectional area. The hydraulic gradient is the head difference divided by the sample length. Rearrange the law for k and you get k = Q·L/(A·h·t). Try moving the collected-volume or head-difference sliders on the left — k updates instantly.
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Can this test be used for any kind of soil?
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No — and that is the key point. The constant-head test is for coarse, free-draining soils like sand and gravel, because a good measurable volume of water flows in a short time. For silt or clay the flow is so slow that only a few drops emerge in two minutes — lost in measurement error. So fine soils need the falling-head test, which tracks the drop of water in a thin standpipe over time. You choose the test method by the soil's permeability.
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I see. What is k actually used for in practice?
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For example, how much water seeps beneath a dam or levee, how much water flows into an excavation, how to design a drainage or filter layer. None of those numbers can be found without k. A common field problem is "we dug and got far more water than expected" — usually caused by underestimating the k of a sand layer.
Frequently Asked Questions
In a constant-head permeability test a fixed head difference h is held across the sample, and the water that emerges is collected as a volume Q over a time t. The coefficient of permeability follows from k = Q·L / (A·h·t), where L is the sample length and A its cross-sectional area. This is simply Darcy's law Q/t = k·i·A (with i = h/L the hydraulic gradient) solved for k, and it assumes steady flow. This tool reports k in both cm/s and m/s.
The choice depends on how permeable the soil is. For coarse, free-draining soils such as sands and gravels, water flows readily and a good measurable volume is collected in a short time, so the constant-head test is ideal. For fine soils such as silts and clays, the flow is so slow that the collected volume would be negligible and lost in measurement error, so the falling-head test — which tracks the drop of water in a thin standpipe over time — is used instead. As a rough guide, use the constant-head test above about 1×10⁻⁴ cm/s and the falling-head test below it.
The hydraulic gradient i is the head loss per unit length, defined as the dimensionless ratio i = h/L (h is the head difference, L the flow distance). In Darcy's law v = k·i the discharge velocity is proportional to the gradient. So for the same soil, water flows faster when the head difference is larger or when the flow path is shorter. In the seepage analysis of dams and levees, locations of high i carry the greatest risk of seepage pressure and piping, which makes the gradient central to safe design.
The most common cause is air trapped inside the sample. Bubbles block flow paths, so the apparent permeability comes out lower than the true value; the sample must be fully saturated with de-aired water before testing. Other sources of error are side leakage, where water short-circuits along the gap between the sample and the cell wall; turbulence at hydraulic gradients too high for the laminar-flow assumption; and the temperature dependence of water viscosity (results are usually corrected to 15°C). In coarse soils, even small differences in grading or compaction can change k by an order of magnitude.
Real-World Applications
Seepage design of dams and levees: The leakage flowing beneath an embankment dam or river levee, the position of the phreatic line in the seepage flow, and the risk of uplift and piping are all calculated from the soil's coefficient of permeability k. For a permeable sand-and-gravel foundation, the constant-head test fixes k, and the effect of cut-off walls and blankets is then verified by seepage analysis. Miss k by an order of magnitude and the predicted leakage is off by an order of magnitude.
Excavation works and dewatering plans: When excavating for underground structures and foundations, the inflow from the excavation base and side slopes must be predicted in advance. Once the k of the sand layer is known, the required capacity of dewatering methods — sump pumping, wellpoints, deep wells — can be estimated. Many excavation failures in sandy ground stem from dewatering capacity being too small because k was underestimated.
Design of drainage and filter layers: Drainage behind roads and retaining walls, the filter zones of dams, and stormwater infiltration facilities all deliberately place gravel layers that pass water freely. For these materials a high coefficient of permeability is the required performance itself, and the constant-head test verifies k to decide pass or fail. It is also used for the quality control of graded crushed stone.
Evaluating consolidation settlement and ground improvement: The time for consolidation settlement of a clay ground to complete is governed by how fast water can drain through the soil — that is, by its permeability. In ground improvement with sand drains or prefabricated drains, the k of the drainage sand is verified by the constant-head test to predict how much consolidation is accelerated. The fine-grained native soil side is handled together with the falling-head test.
Common Misconceptions and Pitfalls
The biggest pitfall is treating the Darcy velocity as the real speed of the water. The Darcy velocity v = k·i that this tool reports is an "apparent velocity", the flow rate divided by the full cross-sectional area of the sample. In reality water can only travel through the pores between the soil grains. Accounting for the porosity, the true speed at which water weaves between the grains (the seepage velocity) is several times the Darcy velocity. When estimating the travel time of a contaminant or the arrival time of groundwater, you must use the seepage velocity, not the Darcy velocity, or you will be badly wrong.
Next, the misconception that a higher hydraulic gradient lets you test faster and more accurately. Darcy's law is only valid where flow stays laminar. In gravel or coarse sand, pushing the head difference to extreme values makes the flow in the pores turbulent, and the flow rate and hydraulic gradient stop being proportional. When that happens, the value computed from k = Q·L/(A·h·t) comes out smaller than the true permeability. The coarser the soil, the more modest the hydraulic gradient should be; if needed, test at several head differences and check that the proportional relationship has not broken down.
Finally, assuming the measured value can be used directly for design. The k obtained in a laboratory test is only the value of a small sample a few centimetres across. Real ground is layered, and it is not unusual for a single thin sand seam to govern the overall permeability. The k also changes by orders of magnitude with the degree of compaction or sample disturbance during preparation. The laboratory value is an important clue, but it should always be checked against an in-situ permeability test (such as a field pumping test), and the design value set with allowance for the heterogeneity of the ground.
How to Use
Enter the cross-sectional area of your soil sample in cm² (typical range 50–500 cm² for laboratory specimens)
Input the length of soil column in cm (commonly 10–50 cm for permeability testing)
Set the constant head difference in cm (maintain 5–100 cm depending on soil permeability)
Record the volume of water collected in cm³ and the time interval in seconds
Click simulate to compute flow rate, hydraulic gradient, Darcy velocity, and permeability coefficient k
Worked Example
For a sand sample: Area = 100 cm², Length = 20 cm, Head difference = 50 cm, Collected volume = 240 cm³ in 60 seconds. Flow rate Q/t = 4 cm³/s. Hydraulic gradient i = 50/20 = 2.5. Darcy velocity v = 4/100 = 0.04 cm/s. Permeability k = v/i = 0.04/2.5 = 0.016 cm/s or 1.6 × 10⁻⁴ m/s, classified as medium sand with moderate drainage.
Practical Notes
Maintain truly constant head by using overflow standpipes in both inlet and outlet chambers; water level fluctuation above ±2 mm invalidates results
For fine sands and silts (k < 10⁻⁶ m/s), switch to falling-head apparatus; constant-head suits gravels and coarse sands only
Temperature affects viscosity: record water temperature and reference k to 20°C using correction factor (viscosity ratio) if testing outside 18–22°C range
Saturate sample completely before testing; trapped air voids cause erroneously low k values up to 30% underestimation
Run minimum three replicate tests and discard outliers exceeding ±15% of median before reporting design permeability value