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2/28/2015
1
Seepage
Chapter 7
Laplace’s Equation
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Laplace’s Equation
A
Laplace’s EquationNostorageNodrainage
Darcy’sLaw
AnisotropicSoil
IsotropicSoil
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Solution of Laplace’s Equation
Flow Line
Equipotential Line
h=constant
Sincewatercanonlyflowduetoachangeinhead,andequipotentiallinesarelinesofconstanthead,theflowlinesmustbeperpendiculartotheequipotentiallineseverywhere.
Flow Nets
h=H2h=H1
Upstream and downstream surfaces are equipotential lines
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Flow Nets
q=0
q=0
All impervious boundaries are flow lines
Flow Nets
Flow lines and equipotential lines are orthogonal
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Flow Nets
“Square”
Ideally, the “cells” in the flow net should be “square”
Flow Net Example
Flow lines are to upstream ground surfaceFlow lines are to face of toe filter faces
Equipotential lines are to impervious boundariesFlow lines are to equipotential lines everywhere“Cells in the flow net are “square” everywhere
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Common Flow Net Mistakes
NotSquare
Flow Lines NotPerpendicular
Extraneous Equipotential Lines
Common Flow Net Mistakes
DisappearingFlow Lines
Equipotential LinesNot Perpendicular
Not arightangle
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Correctly Drawn Flow Net
Seepage Calculations
∆ 1
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Seepage Calculations
Seepage Calculations
∆ ⋯
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Seepage Calculations
∆Totalheadloss
#ofheaddrops
Seepage Calculations
① ② ③ ④ ⑤ ⑥ ⑦
⑧
❶
❷
❸
H
3flowchannels
8headdrops∆
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Flow Nets
Flow Nets
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Example
16m
3 10 /
1.Whatistheheadatpointsa,b,c,dande?2.Whatistheseepageratebeneaththedam?
b
c
e
d
a
Partial Flow Channels
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Partial Flow Channels
∆ ⋯
Partial Flow Channels
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Partial Flow Channels
2.38flowchannels
6 headdrops
1
1
0.38
2.38flowchannels
