Hydraulic Gradient Calculator
Calculates the hydraulic gradient i = Δh / L — the head loss driving groundwater seepage divided by the length of the flow path. Optionally it also returns the critical (quick/boiling) gradient and the factor of safety against piping. Used by geotechnical engineers and hydrogeologists analysing seepage, dewatering, cofferdams and excavations.
Enter Values
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How to use this calculator
- Enter the head loss Δh (m) and the flow-path length L (m) over which it occurs.
- Optionally add the specific gravity of solids Gs and the void ratio e to get the critical gradient and piping factor of safety.
- Read i (dimensionless); if a warning appears, the acting gradient exceeds the critical gradient (quick condition).
How it works
The hydraulic gradient is simply the head loss divided by the flow path length, i = Δh / L. It is dimensionless — metres of head lost per metre travelled — and is the gradient term in Darcy's law for seepage.
When upward seepage occurs, effective stress reduces. At the critical hydraulic gradient ic = (Gs − 1)/(1 + e) the effective stress reaches zero and the soil boils (a quick condition / piping). The factor of safety against piping is ic / i; values below 1 indicate the acting gradient exceeds the critical value.
Worked example
Seepage under a sheet pile wall. With a head loss Δh = 3 m over a flow path L = 10 m, i = 3 / 10 = 0.30. For a sand with Gs = 2.65 and void ratio e = 0.7, the critical gradient ic = (2.65 − 1)/(1 + 0.7) = 0.971, so the factor of safety against piping = 0.971 / 0.30 ≈ 3.2 — safe.
Common mistakes
- Using the straight-line distance instead of the actual flow-path length L along the seepage path (e.g. down and under a wall).
- Confusing the critical gradient (≈ 1 for typical soils) with a factor of safety — ic itself is a gradient, not a safety factor.
- Forgetting that i is dimensionless; both Δh and L must be in the same length units.
Frequently asked questions
What is a hydraulic gradient?
It is the loss of hydraulic head divided by the distance over which it occurs, i = Δh / L. It drives groundwater flow and is dimensionless.
What is the critical hydraulic gradient?
ic = (Gs − 1)/(1 + e) is the upward gradient at which effective stress falls to zero and the soil boils (a quick condition). For common soils it is close to 1.
How do I get the factor of safety against piping?
Divide the critical gradient by the acting gradient: FoS = ic / i. A value below 1 means piping/boiling is likely.
Is the hydraulic gradient the same as the slope of the water table?
For mostly horizontal flow it approximates the water-table slope, but strictly it is the loss of total head along the actual flow path, which can be steeper (e.g. under a cutoff wall).
Why is the answer dimensionless?
Both the head loss and the path length are lengths, so their ratio has no units — it is metres of head per metre of path.
Related tools
- Seepage Flow Calculator
- Permeability from Falling Head Test Calculator
- Pore Pressure Calculator
- Void Ratio Calculator
- Piezometric Level Calculator
- Degree of Saturation Calculator
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