Illustrations%20of%20flow%20nets

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Illustrations of flow nets

• 3D6 Environmental Engineering II
• Dr Gopal Madabhushi

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• Trench supported by sheet piles

5m
6m
6m
Uniform sand
6m
Impermeable clay
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• Trench supported by sheet piles

5m
6m
6m
Uniform sand
6m
Impermeable clay
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• Trench supported by sheet piles

5m
6m
?h6m Nh10 Nf2.52.5
6m
Uniform sand
6m
Impermeable clay
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• Excavation supported by a sheet pile

Steel sheet
Water pumped away
Uniform sand
Shale
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• Excavation supported by a sheet pile

Steel sheet
Water pumped away
Uniform sand
Shale
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• Reduced sheet penetration possible liquefaction
  ??v 0

Steel sheet
Uniform sand
Shale
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• Reduced sheet penetration possible liquefaction
  ??v 0

Reservoir
Tail water
Uniform sand
Shale
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• Concrete dam or weir

Reservoir
Tail water
Uniform sand
Shale
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• Concrete dam with cut-off reduces uplift pressure

Reservoir
Uniform sand
Shale
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• Concrete dam with cut-off reduces uplift pressure

Reservoir
Uniform sand
Shale
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• Pumped well in confined aquifer

Observation well
Elevation Aquifer heads
pumped well
H
Radial flow
aquifer
D
Impermeable stratum
Plan
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• Pumped well in confined aquifer

Observation well
Elevation Aquifer heads
pumped well
H
Radial flow
aquifer
D
Impermeable stratum
Plan
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• Clay dam, no air entry

atmospheric line
reservoir
drain
clay
Shale
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• Clay dam, no air entry

atmospheric line
reservoir
drain
clay
Shale
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• Clay dam, no air entry

Observation well
atmospheric line
reservoir
drain
clay
Shale
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• Clay dam, no air entry, reduced drain seepage
  out of downstream face

atmospheric line Not possible
reservoir
clay
Shale
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• Clay dam, with air entry

reservoir
drain
clay
Shale
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• Clay dam, with air entry

reservoir
drain
clay
Shale
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• Clay dam, no capillary, reduced drain seepage
  out of downstream face

reservoir
clay
Shale
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• Clay dam, no capillary, reduced drain seepage
  out of downstream face

reservoir
clay
Shale
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Flow of water in earth dams

• The drain in a rolled clay dam will be made of
  gravel, which has an effectively infinite
  hydraulic conductivity compared to that of the
  clay, so far a finite quantity of flow in the
  drain and a finite area of drain the hydraulic
  gradient is effectively zero, i.e. the drain is
  an equipotential

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Flow of water in earth dams

• The phreatic surface connects points at which the
  pressure head is zero. Above the phreatic surface
  the soil is in suction, so we can see how much
  capillarity is needed for the material to be
  saturated. If there is insufficient capillarity,
  we might discard the solution and try again.
  Alternatively assume there is zero capillarity,
  the top water boundary is now atmospheric so
  along it and the flow net has to be adjusted
  within an unknown top boundary as the phreatic
  surface is a flow line if there is no
  capillarity.

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Flow of water in earth dams

• If then in the flow net, so once
  we have the phreatic surface we can put on the
  starting points of the equipotentials on the
  phreatic surface directly

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Unsteady flow effects

• Consolidation of matrix
• Change in pressure head within the soil due to
  changes in the boundary water levels may cause
  soil to deform, especially in compressible clays.
  The soil may undergo consolidation, a process in
  which the voids ratio changes over time at a rate
  determined by the pressure variation and the
  hydraulic conductivity, which may in turn depend
  on the voids ratio.

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Breakdown of rigid matrix

• Liquefaction (tensile failure)
• The total stress ? normal to a plane in the soil
  can be separated into two components, the pore
  pressure p and the effective inter-granular
  stress ?
• By convention in soils compressive stresses are
  ve.
• Tensile failure occurs when the effective stress
  is less than the fracture strength ?fracture,
  and by definition for soil ?fracture0. When the
  effective stress falls to zero the soil particles
  are no longer in contact with each other and the
  soil acts like a heavy liquid. This phenomenon is
  called liquefaction, and is responsible to quick
  sands.

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Large upward hydraulic gradients
Uniform soil of unit weight ?
Upward flow of water
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standpipe
Water table and datum
Critical potential Head
Critical head Pressure hcrit
Uniform soil of unit weight ?
Plug of Base area A
z
Gap opening as plug rises
Upward flow of water
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At the base of the rising plug, if there is no
side friction
So if ?v?0 then ?v p and
, icrit0.81.0
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where icrit is the critical hydraulic gradient
for the quick sand Condition. As ? ? 1820 kN/m3
for many soils (especially sands and silts) and
?w ? 10 kN/m3
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Frictional (shear failure)

• Sliding failure of a gravity concrete dam due to
  insufficient friction along the base

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Reservoir
Tail water
W
H1
H2
W
Uniform sand
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Limiting condition on shear force T is
where tan?max is the co-efficient of friction,
so considering the base of the dam we are looking
for
where W W-U is the effective weight of the
dam, U is the total uplift due to the pore
pressure distribution p along the base of the
dam, and F H1- H2 is the shear force along the
Dam base