CE5101 Lecture 3 - Seepage Theory and Flow Nets (14 AUG 2013)

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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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