Question

Derive an equation for quicksand condition.

Answer 1

If the side friction  with the tube is neglected, the process of quick sand can be avoided if the following condition is satisfied:  

AL gsub >  hAgw                       (3.12)

where gsub and gw are  respectively the submerged specific weight of the soil and the specific weight of water.

The critical hydraulic gradient ic is defined as that which corresponds to the case in which both sides of relation (3.12) are equal, or

ic = gsub/gw                   (3.13)

This means that if the hydraulic gradient  in granular soil exceeds the ratio between the submerged  specific weight of soil and that of water, quick sand condition is expected to occur.  

The  gsub  is defined in terms of the specific gravity of the solid particles G and the void ratio  e by the relation:

gsub = gw(G-1)/(1+e)            (3.14)  

The substitution from (3.14) into (3.13) leads to equation (3.15)

ic =  (G-1)/(1+e)                      (3.15)

The later is the more common relation used for ic.