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Consider a random element of a flow net:. Each side has the same length, b. SEEPAGE FORCES. A. b. B. b. θ. D. C. the direction of flow is inclined at an angle of θ to the horizontal. lines AB and DC define the elemental flow channel.

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seepage forces

Consider a random element of a flow net:

Each side has the same length, b

SEEPAGE FORCES

A

b

B

b

θ

D

C

the direction of flow is inclined at an angle of θ to the horizontal

lines AB and DC define the elemental flow channel

lines AD and BC are equipotentials, with a drop in head of ∆h when water seeps from AD to BC

seepage forces2

Geometrically:

SEEPAGE FORCES

A

B

θ

θ

θ

D

θ

θ

C

Four congruent right angle triangles are formed from vertical and horizontal lines projected inwards from the four corners of the flow net element

The difference in elevation between A and D is the same as between B and C and is equal to bcosθ.

The difference in elevation between A and B is the same as between D and C and is equal to bsinθ.

Each has an angle θ as shown

seepage forces3

The pore pressure distributions acting on each side of the element are shown below:

If the pore water pressure at point A is uA, and u = w(h-z), and

The change in pore water pressure from point A to point B is due to a loss in total head -∆h and the elevation drop, bsinθ

The change in pore water pressure between point B and point C is due only to the elevation drop, bcosθ,

SEEPAGE FORCES

bsinθ

-∆h

bcosθ

the change in pore water pressure between point A and point D is due only to the elevation drop, bcosθ,

bcosθ

uD = uA + w bcosθ

uB = uA + w(bsinθ-∆h)

uC = uB + wbcosθ or

uC = uA + w(bsinθ-∆h) +wbcosθ or

uC = uA + w(bsinθ+bcosθ-∆h)

seepage forces4

The pore pressure distribution acting on AD will be cancelled by that acting on BC, leaving:

The pore pressure distribution acting on AB will be cancelled by that acting on DC leaving:

The equivalent point load (net boundary water force) acting on DC is: b x wbcosθor wb2cosθ

The net boundary water force acting on BC is: b x w(bsinθ-∆h)or wb2sinθ - ∆hwb

uD-uA = uC-uB = w bcosθ

w(bsinθ-∆h)

SEEPAGE FORCES

uB-uA = uC-uD = w(bsinθ-∆h)

b

b

wb2sinθ - ∆hwb

w bcosθ

uD = uA + w bcosθ

uB = uA + w(bsinθ-∆h)

w b2cosθ

uC = uA + w(bsinθ+bcosθ-∆h)

seepage forces5

What would the boundary water forces be if seepage stopped? (i.e., the static case)

∆h would be 0, and

the forces on DC and BC would be wb2cosθand wb2sinθrespectively, orthogonal vectors with a resultant of wb2 , (acting vertically)

The only difference between the static and seepage cases is the force ∆hwb called the seepage force, J

SEEPAGE FORCES

If the average hydraulic gradient, i across the element is:

wb2sinθ - ∆hwb

Then:

If b2 x 1 m is the volume of the element, V then the seepage pressure, j is defined as the seepage force per unit volume:

j = iw

w b2cosθ

seepage forces6

the total weight of the element = satb2 = vector ab

How will seepage affect the effective stress at any point in the soil mass?

If the effective stress is reduced too much by upward seepage, then the soil will lose its ability to support loads.

In the extremes: if the seepage direction is downward, the effective stress will be increased or if upward the effective stress will be decreased

Therefore, let’s consider all the gravitational and seepage forces acting on the soil element à la a vector diagram. First, the SEEPAGE case:

The concern is with the support conditions of the soil.

Boundary water force on CD = wb2cosθ = vector bd

Boundary water force on BC = wb2sinθ-∆hwb = vector de

Resultant boundary water force = vector be

SEEPAGE FORCES

Resultant body force = vector ae = Effective Stress, σ’

wb2sinθ - ∆hwb

w b2cosθ

SEEPAGE CASE

seepage forces7

Now consider the STATIC case:

the total weight of the element = satb2 = vector ab

Boundary water force on CD = wb2cosθ = vector bd

Boundary water force on BC = wb2sinθ= vector dc

Resultant boundary water force = wb2 = vector bc

SEEPAGE FORCES

Resultant body force =  ’b2vector ac = Effective Stress, σ’

wb2sinθ - ∆hwb

w b2cosθ

STATIC CASE

seepage forces8

This brings up an alternative solution to the seepage case:

Effective weight of the element =  ’b2 = vector ac

Seepage force = ∆hwb = vector ce

SEEPAGE FORCES

Resultant body force vector ac = Effective Stress, σ’

To summarize, the resultant body force (effective stress) can be obtained by considering:

B) the equilibrium of the soil skeleton,

add the effective weight of the soil mass (ac)

to the seepage force (be)

to find effective stress (ae)

  • the equilibrium of the whole soil mass,
  • add the total saturated weight of the soil mass (ab)
  • to the resultant boundary water force (ce)
  • to find effective stress (ae)

OR

SEEPAGE CASE (reprise)

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