b$)$ A dockside retaining wall $10m$ high retains a non$-$cohesive backfill with a horizontal surface level with the top of the wall. The properties of the backfill material are, $G=2\mathrm{.}65,e=0\mathrm{.}55,$ and $=32.$ An additional superimposed load of $20k\frac{N}{m^2}$ is induced at the surface of the backfill due to construction of warehouses and dockyard traffic. Compute the lateral thrust on the wall when the water table is;

$(10$ Marks$)$

$($i$)2m$ below the level surface,

$($ii$)5m$ below the level surface, and

$($iii$)$ at the bottom of the wall. Neglect wall friction.

Use $=\frac{{}_w(G_s+e{S}_r)}{1+e}$