Question 1

What is the critical hydraulic gradient?

Accepted Answer

The upward gradient at which seepage force exactly balances the buoyant weight of the soil, so effective stress goes to zero: ic = γ'/γw = (Gs − 1)/(1 + e). For typical sands (Gs ≈ 2.65, e ≈ 0.6–0.7), ic ≈ 1.0 — a convenient and famous coincidence. At i ≥ ic the soil boils: quicksand at the exit face.

Question 2

How do I get the exit gradient from a flow net?

Accepted Answer

The head drop per equipotential drop is Δh = H/Nd, where H is total head loss and Nd the number of drops. The exit gradient is that drop divided by the length of the last flow-net element at the exit face: ie = Δh/L. In finite-element seepage output, read the gradient directly at the exit elements. The exit face — where flow leaves upward through the toe or a ditch bottom — is where heave initiates.

Question 3

What factor of safety is required against heave?

Accepted Answer

FoS = ic/ie. Terzaghi's classical recommendation for heave at the toe of hydraulic structures is 4–5; values as low as 2.5–3 are accepted by some agencies for well-characterized, monitored conditions. The scatter reflects how badly wrong things go past the threshold — heave is brittle, not gradual. Confirm the minimum with the governing agency (state dam safety, USACE) for your structure class.

Question 4

What's the difference between heave and piping?

Accepted Answer

Heave (blowout) is bulk liquefaction of the exit-face soil block when the average upward gradient exceeds critical. Piping is progressive backward erosion — particles detach at the exit and a pipe eats backward toward the reservoir, and it can initiate at gradients well below ic if the soil is internally unstable and unfiltered. A satisfactory heave FoS does not by itself demonstrate piping safety; filter protection does (see the filter criteria tool).

Question 5

How do I lower the exit gradient?

Accepted Answer

Lengthen the seepage path or relieve the head: extend the upstream blanket or cutoff (raises Nd, cuts Δh), add a downstream weighted filter berm over the exit face (adds resisting weight and filter protection), or install relief wells/toe drains to intercept the flow and discharge it under control. A weighted filter berm raises the effective FoS by W/Ws in the Terzaghi block analysis.

Question 6

Does this apply to cofferdams and excavations too?

Accepted Answer

Yes — the classical application is heave at the bottom of a sheeted excavation: Terzaghi's analysis takes a soil block D/2 wide by D deep at the sheet-pile toe and compares its buoyant weight to the uplift from average excess head. The same ic/ie framework governs; only the geometry for extracting ie differs.

Soil state	e	i_c
Dense sand	0.45	1.14–1.17
Medium sand	0.60	1.03–1.06
Loose sand	0.85	0.89–0.92
Silty sand	0.65–0.90	0.87–1.03

Seepage Exit Gradient Calculator

Critical gradient for common soils

Worked example

Example — levee landside toe during high water

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Seepage Exit Gradient Calculator

Critical gradient for common soils

Worked example

Example — levee landside toe during high water

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