Quick StudyQuick StudyWhat if the direction of the seepage force was vertically What if the direction of the seepage force was vertically up?up?

θθ = 90° = 90°

So instead of Craig’s vector diagram looking like So instead of Craig’s vector diagram looking like this:this:

the force vector diagram would look something like the force vector diagram would look something like this:this:Instead of Instead of θθ being as shown before: being as shown before:

θθ

θθ = = 90°90°

Effective Weight Effective Weight ’b’b22 : :

Seepage Force Seepage Force iiwwVV : :

Resultant Body Force or Resultant Body Force or Effective StressEffective Stress, , σσ’’

What happens if the upward seepage force is equal in What happens if the upward seepage force is equal in magnitude to the effective weight of the soil?magnitude to the effective weight of the soil?

The effective stress drops to 0 and the soil The effective stress drops to 0 and the soil cannot support anything that won’t float on cannot support anything that won’t float on water!water!

In old English,In old English, quick quick meansmeans alive. alive.This is known asThis is known as aa QUICK QUICK condition.condition.

The soil looks like its boiling and appears to The soil looks like its boiling and appears to bebe “alive”. “alive”.

It’s alive! It’s alive!

IT’S ALIVE!!IT’S ALIVE!!

Quick StudyQuick StudyWhere would you expect to see Where would you expect to see seepage vertically upwards?seepage vertically upwards?

The seepage forces The seepage forces to the right of the to the right of the sheet pile wall sheet pile wall (downstream side) (downstream side) will all have upward will all have upward vertical componentsvertical components

Near the downstream Near the downstream soil surface the soil surface the seepage vectors are seepage vectors are almost completely almost completely vertical (no vertical (no horizontal horizontal component)component)

If a quick condition develops, the If a quick condition develops, the resultant body force = 0 and iresultant body force = 0 and iwwV = V = ’V’V

the hydraulic the hydraulic gradient that gradient that produces a quick produces a quick condition is called condition is called the critical hydraulic the critical hydraulic gradient, igradient, icc::

e11G'

i s

wc

γ

γ

check out eqn. 1.21 on pg 20 in Craig

Quick StudyQuick StudyThe depth of embedment of The depth of embedment of a sheet pile wall extends a sheet pile wall extends from downstream soil from downstream soil surface to the bottom of surface to the bottom of the sheet piling.the sheet piling.

It is designated, d as It is designated, d as shown.shown.

221 d1

2d

dV

dd

Model studies have shown Model studies have shown that the soil mass that the soil mass extending over this depth, extending over this depth, d and half this distance d and half this distance from the piling is most from the piling is most prone to the quick prone to the quick condition.condition.

2d This mass has a volume of:This mass has a volume of:

Quick StudyQuick StudyAt surface DC, the average At surface DC, the average head, hhead, hmm is estimated at is estimated at the midpoint of line DC the midpoint of line DC from the flow net.from the flow net.

At surface AB the excess At surface AB the excess total head has been total head has been dissipated (h = 0).dissipated (h = 0).

dh

i mm dd

Hence, the average Hence, the average hydraulic gradient for hydraulic gradient for seepage from DC to AB is:seepage from DC to AB is:

2d A Factor of Safety against A Factor of Safety against

heaving (quick condition) heaving (quick condition) adjacent to the sheet piling adjacent to the sheet piling is expressed as the is expressed as the average critical hydraulic average critical hydraulic gradient, igradient, icc divided by this divided by this average gradient, iaverage gradient, imm::

hhmm

h = 0h = 0

m

cheave i

iF

For sands, a factor of For sands, a factor of Safety against boiling at Safety against boiling at the surface can be the surface can be expressed using the exit expressed using the exit hydraulic gradient, ihydraulic gradient, iee over over the last element (AEFG):the last element (AEFG):

ΔsΔh

ie

∆∆ss

e

cboil i

iF

Quick StudyQuick StudyConsider the equilibrium of Consider the equilibrium of the forces acting on the soil the forces acting on the soil mass ABCD with unit mass ABCD with unit weight weight satsat. .

The total weight of ABCD is The total weight of ABCD is sat sat xx the Volume of ABCD the Volume of ABCD

2sat2

1 dγ

dd

The elevation head at DC The elevation head at DC is –d if the downstream is –d if the downstream free water surface is at free water surface is at ABAB

2d

The average pore water The average pore water pressure on CD is: pressure on CD is: (h(hmm+d)+d)ww

d- zm

The boundary water force The boundary water force on CD is the area of the on CD is the area of the PWP distribution on CD:PWP distribution on CD:

½d(h(hmm+d)+d)ww wm21 d)d(h γ

Quick StudyQuick StudyTo find the Resultant Body To find the Resultant Body Force of ABCD:Force of ABCD:

2sat2

1 dγ

dd

2d

2w2

1wm2

1 ddh wm21 d)d(h γ

wsatwsat ' then ,-' if γγγγγγ

2212

212

21 dd)d ww γγγγ ''(

1

2

3

221

m212

212

21 ddhdd www γγγγ '' oror

dhd m212

21

wγγ ''

Quick StudyQuick StudyNow, consider the Now, consider the equilibrium of the forces equilibrium of the forces acting on the soil skeleton acting on the soil skeleton ABCD with bouyant unit ABCD with bouyant unit weight weight ’. ’.

The effective weight of The effective weight of ABCD is ABCD is ’’ xx the Volume of the Volume of ABCDABCD

221 d'γ

dd

The average hydraulic The average hydraulic gradient for seepage from gradient for seepage from DC to AB is:DC to AB is:

2d

The seepage force on ABCD The seepage force on ABCD is:is:

dh i m

m

The resultant body force of ABCD The resultant body force of ABCD is:is:

dh2d

dh J wm2

12

wm

m dh J wm2

1m

dhd m212

21

wγγ '' Look familiar?

Quick StudyQuick StudySo, if So, if σσ’ = 0 as with a quick condition, ’ = 0 as with a quick condition, thenthen

A Factor of Safety against heaving (quick A Factor of Safety against heaving (quick condition) can then be expressed.condition) can then be expressed.

dhd0 m212

21

wγγ '

dhd m212

21

wγγ '

Generally, a factor of safety is the ratio of Generally, a factor of safety is the ratio of stabilizing forces over destabilizing forcesstabilizing forces over destabilizing forcesThe stabilizing force is the effective weight The stabilizing force is the effective weight of the soil mass. The seepage force is the of the soil mass. The seepage force is the destabilizing force.destabilizing force.

m

c

m

w

wmwm21

221

ii

dh

'

hd'

dhd'

F γγ

γ

γ

γ

γ

Quick StudyQuick StudyIf the factor of safety is If the factor of safety is making the engineer making the engineer nervous, you could always nervous, you could always redesign the structure and redesign the structure and repeat the process... repeat the process...

Not an option?Not an option?

Well, you could increase Well, you could increase the effective weight of the effective weight of the soil adjacent to the the soil adjacent to the sheet pile wall by adding sheet pile wall by adding a filter material (high a filter material (high density).density).

If the unit weight of the If the unit weight of the filter material is filter material is ’’filt filt and it is and it is placed to a depth of dplaced to a depth of dfiltfilt, , then the extra effective then the extra effective weight is w’ = weight is w’ = ’’filtfilt x ddfiltfilt and and the new factor of safety the new factor of safety would be:would be:

dhw'd'

Fwm2

1

221

γ

γ

’filtdfilt