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SeepageSeepage

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Seepage: Earth dams

One-dimensional flow

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Discharge = Q = v. A = k . i . A= k (h/L). A

Laplace equation of Continuity In reality, the flow of water through soil is not in one direction

only, nor is it uniform over the entire area perpendicular to the flow.

The flow of water in two dimensional is described using Laplace equation.

Laplace equation is the combination of the equation of continuity and Darcy’s law.

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Laplace equation of ContinuityFlow in:

Flow out:

Flow in = Flow out (Continuity equation)

By simplification, we get

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dxdydzz

vvdydzdx

x

vv z

zx

x

dxdyvdydzv zx

dxdyvdydzvdxdydzz

vvdydzdx

x

vv zx

zz

xx

0

dxdydzz

vdxdydz

x

v zx

0

z

v

x

v zx

Laplace equation of ContinuityFrom Darcy’s Law:

Replace in the continuity equation

If soil is isotropic (i.e. kx = kz = k)

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0 2

2

2

2

z

hk

x

hk zx

dz

dhkv

dx

dhkv zzxx

0 2

2

2

2

z

h

x

h

Laplace equationThis equation governs the steady

flow condition for a given point in the soil mass

Flow nets• Flow nets are the combination of flow lines and equipotential

lines.• To complete the graphic construction of a flow net, one must

draw the flow and equipotential lines in such away that:

1. The equipotential lines intersect the flow lines at right angles.

2. The flow elements formed are approximate squares.

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Flow channel

Flow line

Equipotential line

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Piping failure Fontenelle Dam , UAS (1965)

Example of Dam Failure

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Around 7:00 am on June 5, 1976 a leak about 30 m from the top of Teton dam was observed.

Example of Dam Failure

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The Dam Broke at 11:59 AM

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Good compaction around antiseep collars was difficult to achieve

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