Module 14 · Lesson 14.3

Exit gradient, piping and heave

Where seepage emerges, and how it can lift or wash away the ground.

Why this matters

The most dangerous place in a seepage field is where water emerges at the downstream ground surface. There the upward seepage force can lift the soil — heave — or start washing grains out to form a channel that eats back towards the source — piping. Both have destroyed dams and excavations, and both are assessed from the flow net.

Where flow exits upward, the seepage drags the grains up. The upward hydraulic gradient at the exit is the head drop in the last field divided by its length:

i_{e x i t} = \frac{Δ h}{l} = \frac{h / N _{d}}{l},

with $l$ the flow length of the exit square. This is compared with the critical hydraulic gradient at which the upward seepage force just cancels the soil's submerged weight and the effective stress falls to zero — the quick condition of Module 8:

Critical gradient and factor of safety against piping

i_{cr} = \frac{γ ^{'}}{γ _{w}} = \frac{G _{s} - 1}{1 + e}, F = \frac{i _{cr}}{i _{e x i t}}

What it calculates: the gradient at which the ground is lifted, and the margin against it

$i_{cr}$: critical (quick-condition) hydraulic gradient (—)
$i_{e x i t}$: exit hydraulic gradient from the flow net (—)
F: factor of safety against piping/heave

In plain terms: i_cr is typically about 1.0 (for Gs ≈ 2.65, e ≈ 0.65). When i_exit approaches i_cr the ground is on the point of piping; a comfortable factor of safety (commonly 3 or more) is required because piping is sudden and catastrophic.

Worked example

Factor of safety against piping at an excavation

Given

Total head loss h = 6 m, Nd = 12 (so Δh = 0.5 m)
The exit square has flow length l = 1.5 m
Soil Gs = 2.65, e = 0.65, so i_cr = (2.65 − 1)/(1 + 0.65) = 1.0

Find

The exit gradient and the factor of safety against piping.

Assumptions

The critical gradient is taken from the quick condition; the exit square length is read from the net.

Practice

At an excavation the exit gradient from the flow net is i_exit = 0.25 and the critical gradient is i_cr = 1.0. What is the factor of safety against piping?

Summary

Seepage is most dangerous where it emerges upward at the downstream surface.
Exit gradient i_exit = (h/Nd)/l, with l the exit-square length.
The critical gradient i_cr = (Gs − 1)/(1 + e) ≈ 1 is where effective stress reaches zero (quick condition).
Factor of safety F = i_cr/i_exit (commonly ≥ 3); lengthen the seepage path or add a filter to raise it.

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This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint