CIVL2410 Chap.8 Reading a flow net: pore pressure, uplift and piping
Reading a flow net: pore pressure, uplift and piping
A discharge is the least interesting thing a flow net gives you. The three quantities that decide whether a structure survives are the pore water pressure at chosen points, the uplift force those pressures exert on a base, and the exit gradient where seepage emerges at the downstream face.
All three are read off the same finished net, which is why the sketch has to be drawn to scale and why the boundary conditions have to be labelled before anything is computed.
What this chapter covers
- 01
The six step construction order, from scale drawing to counting
- 02
The four boundary condition types, and how to recognise each on a section
- 03
The four construction errors that produce a net which is not a solution
- 04
Total head at a point by counting drops from a known boundary
- 05
Turning that head into a pore water pressure, and the datum discipline it needs
- 06
Why a cut off wall lowers uplift as well as seepage
- 07
Uplift as the area under the pressure diagram along a base
- 08
The trapezoidal rule, and why the ordinates are spaced evenly
- 09
The seepage force per unit volume, and the balance it has to lose for piping
- 10
Why the critical gradient is close to one for almost every soil
Pore pressure at a point beneath a dam
- +1Each equipotential drop is 6.0 / 12 = 0.5 m of head.
- +1Four drops from the upstream boundary leave a total head at P of 9.0 - 4 x 0.5 = 7.0 m above the datum.
- +1Subtract the elevation of the point to get the pressure head: 7.0 - 3.2 = 3.9 m of water.
- +1Multiply by the unit weight of water: u = 9.81 x 3.9 = 38.3 kPa.
Key terms
- Uplift
- The upward force produced by pore water pressure acting on the base of a structure. It is the area under the pressure diagram along that base, and it reduces the effective weight holding the structure down.
- Piping
- The failure that occurs when upward seepage cancels the submerged weight of the soil at an exit face, so the effective stress reaches zero and grains are free to move. It accelerates once started, because erosion shortens the seepage path.
- Exit gradient
- The local hydraulic gradient in the last cell of a flow net where seepage emerges. It is the value that has to be checked against the critical gradient, and it is usually several times the average gradient across the section.
- Seepage face
- A boundary where water emerges at atmospheric pressure. It is one of the four boundary types that have to be identified before a net can be drawn.
- Trapezoidal rule
- A numerical integration that sums evenly spaced ordinates as half the two end values plus all the interior ones, multiplied by the spacing. It is how an uplift diagram is converted into a force.
Reading a flow net: pore pressure, uplift and piping FAQ
Why check the gradient at the exit rather than across the whole section?
Because piping is a local failure and the gradient is not uniform. Averaging the head loss over the whole flow path buries the one place that matters, which is where the net's cells are smallest and the flow is most crowded, typically at the downstream toe or immediately behind a wall.
The local gradient there can be several times the average, so an average gradient that looks comfortable can sit alongside a local one that is close to critical. This is exactly why the net has to be drawn to scale.
What does a cut off wall actually achieve?
Two things, and the less obvious one is usually the more valuable. It lengthens the seepage path, which adds equipotential drops and therefore reduces the discharge. More importantly, it forces several of those drops to occur before the water reaches the base of the structure, so the total head at every point on that base is lower, the pressure head is lower, and the uplift diagram shrinks.
Seepage merely costs pumping, while uplift threatens stability.
Exam move
Treat the sketch as the intermediate result and the readings as the answer, because a full seepage question typically asks for the net, then the flow, then a pressure or an uplift, and finally a stability comment, with each part depending on the last. That dependency is why an unlabelled or unscaled net costs marks three times over, and why a coarse net with correct boundary conditions beats a fine net with guessed ones.
Practise the pore pressure procedure until the four steps are automatic, and always finish a piping check with a sentence about what the factor of safety means, since the mechanism accelerates once it starts and a thin margin on a runaway failure is not the same as a thin margin elsewhere.
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