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Illustrations of flow nets. 3D6 Environmental Engineering II Dr Gopal Madabhushi. 5m. Trench supported by sheet piles. 6m. 6m. Uniform sand. 6m. Impermeable clay. 5m. Trench supported by sheet piles. 6m. 6m. Uniform sand. 6m. Impermeable clay. 5m. Trench supported by sheet piles.

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illustrations of flow nets

Illustrations of flow nets

3D6 Environmental Engineering II

Dr Gopal Madabhushi

slide2

5m

  • Trench supported by sheet piles

6m

6m

Uniform sand

6m

Impermeable clay

slide3

5m

  • Trench supported by sheet piles

6m

6m

Uniform sand

6m

Impermeable clay

slide4

5m

  • Trench supported by sheet piles

6m

h=6m

Nh=10

Nf=2.5+2.5

6m

Uniform sand

6m

Impermeable clay

slide5

Steel sheet

Water pumped away

  • Excavation supported by a sheet pile

Uniform sand

Shale

slide6

Steel sheet

Water pumped away

  • Excavation supported by a sheet pile

Uniform sand

Shale

slide7

Steel sheet

  • Reduced sheet penetration; possible liquefaction v = 0

Uniform sand

Shale

slide8

Reservoir

  • Reduced sheet penetration; possible liquefaction v = 0

Tail water

Uniform sand

Shale

slide9

Reservoir

  • Concrete dam or weir

Tail water

Uniform sand

Shale

slide10

Reservoir

  • Concrete dam with cut-off; reduces uplift pressure

Uniform sand

Shale

slide11

Reservoir

  • Concrete dam with cut-off; reduces uplift pressure

Uniform sand

Shale

slide12

Elevation

Aquifer heads

Observation well

pumped well

  • Pumped well in confined aquifer

H

Radial

flow

aquifer

D

Impermeable stratum

Plan

slide13

Elevation

Aquifer heads

Observation well

pumped well

  • Pumped well in confined aquifer

H

Radial

flow

aquifer

D

Impermeable stratum

Plan

slide14
Clay dam, no air entry

atmospheric line

reservoir

drain

clay

Shale

slide15
Clay dam, no air entry

atmospheric line

reservoir

drain

clay

Shale

slide16

Observation well

  • Clay dam, no air entry

atmospheric line

reservoir

drain

clay

Shale

slide17
Clay dam, no air entry, reduced drain; seepage out of downstream face

atmospheric line

Not possible

reservoir

clay

Shale

slide18
Clay dam, with air entry

reservoir

drain

clay

Shale

slide19
Clay dam, with air entry

reservoir

drain

clay

Shale

flow of water in earth dams
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
flow of water in earth dams1
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.
flow of water in earth dams2
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
unsteady flow effects
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.

breakdown of rigid matrix
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 ’fracture=0. 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.

slide27

Large upward hydraulic gradients:

Uniform soil of unit

weight 

Upward flow of water

slide28

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

slide29

At the base of the rising plug, if there is no side friction:

So if v=0 then v = p and :

, icrit=0.8~1.0

slide30

where icrit is the critical hydraulic gradient for the quick sand

Condition. As   18~20 kN/m3 for many soils (especially sands

and silts) and w  10 kN/m3 :

frictional shear failure
Frictional (shear failure)
  • Sliding failure of a gravity concrete dam due to insufficient friction along the base:
slide32

Reservoir

Tail water

W

H1

H2

Uniform sand

slide33

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