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CE5101 Lecture 3
Seepage through Soilsby
Prof Harry Tan
14 AUG 2013
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Outline
• Seepage Theory
• Potential and Stream Functions
• Flow Nets and FEM models
• Seepage through Dams and Embankments
• Seepage in Anisotropic Soils
• Instability due to Seepage
• Seepage and Effective Stress
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Seepage Theory – Continuity Equation
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Seepage Theory – Continuity Equation
dx
dψ−
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Graphical Picture of Two Equations
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Graphical Picture of Two Equations
Similarly, the head difference between any two
adjacent equipotentials is constant.
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Graphical Picture of Two Equations
Comparing the two
equations, equipotentials
must be perpendicular to
flow lines
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Properties of Flow Nets
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Properties of Flow Nets
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Flow Net Construction
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Flow Net Construction
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Example 1 – Sheetpile Wall
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Example 1 – Sheetpile Wall
= 8m= 7m
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Example 1 – Sheetpile Wall
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Example 1 – Sheetpile Wall
= 16.7 m
HQ = 17.5 – 8.4*0.455
= 13.7 m
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EX 1 – Plaxis Result
Closed flow boundaries
H=17.5m H=12.5m
Hp=16.8m Hq=13.6m
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EX 1 Plaxis Results
Total discharge = 15.7e-6 m3/s per m
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EX 1 Plaxis Results
Pp=88 kPaPq=66 kPa
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Example 2 – Gravity Dam
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Example 2 – Gravity Dam
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Example 2 – Gravity Dam
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EX 2 Plaxis Results
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EX 2 Plaxis Results
Discharge = 1.63e-4 m3/s per m
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EX 2 Plaxis Results
90 kPa
33 kPa
Uplift pressures
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Dams and Embankments
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Dam Seepage Entry and Exit Boundary
Conditions
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EX 3 Dam Seepage
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EX 3 Dam Seepage
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EX 3 Plaxis Results
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EX 3 Plaxis Results
Discharge = 17.1e-6 m3/s per m
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Horizontal flow in Stratified Soils
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Vertical flow in Stratified Soils
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Ex 4 Flow in Stratified Soils
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Flow Net in Anisotropic Soil
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Flow Net in Anisotropic Soil
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Flow across Soil Interface
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Piping Instability of Sheetpile Wall
d
hi mavg =
Datum
hm
D=d (same item)
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Piping Instability of Sheetpile Wall
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Piping Instability of Sheetpile Wall
BUT Seepage force = i.γw. volume
=im w
ciγ
γ '=
Critical gradient divide by Applied gradient
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Measures against Piping
Fill w’
wmh γ
d'γ
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Seepage and Effective Stress
Darcy’s law is v=ki (average seepage velocity or Darcy
velocity or apparent or superficial velocity)
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Seepage and Effective Stress
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Seepage and Effective Stress
volumeivolumejFs w... γ==
Seepage force in soils is:
ie Seepage Force = Seepage Pressure x Volume
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Quick condition and critical gradient
wsat γγγ −='Since buoyant unit weight =
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Quick condition and critical gradient
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EX 4 Effective Stress and Seepage
Determine effective stresses at A and B
hs=
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(Total stress at A)
(Pore water pressures at A)
(Effective stress at A)
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Seepage pressures at A=wi γ.
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( )wsA ih γγσ .'' +=i.e.A'σ
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