1. Quick Study What if the direction of the seepage force was vertically up? θ = 90° So instead of Craig’s vector diagram looking like this: the force vector diagram would look something like this:Instead of θ being as shown before: θ θ = 90° Effective Weight  ’b2 : :: : Seepage Force iwV : :: : Resultant Body Force or Effective Stress, σ’ What happens if the upward seepage force is equal in magnitude to the effective weight of the soil? The effective stress drops to 0 and the soil cannot support anything that won’t float on water! In old English, quick means alive. This is known as a QUICK condition. The soil looks like its boiling and appears to be “alive”. It’s alive! IT’S ALIVE!!

2. Quick Study Where would you expect to see seepage vertically upwards? The seepage forces to the right of the sheet pile wall (downstream side) will all have upward vertical components Near the downstream soil surface the seepage vectors are almost completely vertical (no horizontal component) If a quick condition develops, the resultant body force = 0 and iwV = ’V the hydraulic gradient that produces a quick condition is called the critical hydraulic gradient, ic: check out eqn. 1.21 on pg 20 in Craig

3. The depth of embedment of a sheet pile wall extends from downstream soil surface to the bottom of the sheet piling. It is designated, d as shown. d Model studies have shown that the soil mass extending over this depth, d and half this distance from the piling is most prone to the quick condition. This mass has a volume of:

4. At surface DC, the average head, hm is estimated at the midpoint of line DC from the flow net. At surface AB the excess total head has been dissipated (h = 0). d Hence, the average hydraulic gradient for seepage from DC to AB is: A Factor of Safety against heaving (quick condition) adjacent to the sheet piling is expressed as the average critical hydraulic gradient, ic divided by this average gradient, im: hm h = 0 For sands, a factor of Safety against boiling at the surface can be expressed using the exit hydraulic gradient, ie over the last element (AEFG): ∆s

5. Consider the equilibrium of the forces acting on the soil mass ABCD with unit weight sat. The total weight of ABCD is sat x the Volume of ABCD d The elevation head at DC is –d if the downstream free water surface is at AB The average pore water pressure on CD is: (hm+d)w The boundary water force on CD is the area of the PWP distribution on CD: ½d(hm+d)w

6. To find the Resultant Body Force of ABCD: d 1 2 3 or

7. Now, consider the equilibrium of the forces acting on the soil skeleton ABCD with bouyant unit weight ’. The effective weight of ABCD is ’ x the Volume of ABCD d The average hydraulic gradient for seepage from DC to AB is: The seepage force on ABCD is: The resultant body force of ABCD is: Look familiar?

8. So, if σ’ = 0 as with a quick condition, then A Factor of Safety against heaving (quick condition) can then be expressed. Generally, a factor of safety is the ratio of stabilizing forces over destabilizing forces The stabilizing force is the effective weight of the soil mass. The seepage force is the destabilizing force.

9. If the factor of safety is making the engineer nervous, you could always redesign the structure and repeat the process... Not an option? Well, you could increase the effective weight of the soil adjacent to the sheet pile wall by adding a filter material (high density). If the unit weight of the filter material is ’filt and it is placed to a depth of dfilt, then the extra effective weight is w’ = ’filt x d dd dfilt a aa and the new factor of safety would be:  ’ filt d filt