$($b$)$ A $4$ m high retaining wall is constructed as shown in Figure. Q$\mathrm{.}4($b$)$ to support a surcharge of $15k\frac{N}{m^2}.$ The ground water level is $2$ m below the top of the wall. The properties of the soil are given in the figure.

$($i$)$ Determine the coefficient of active lateral earth pressure under Rankine's Theory.

$(2$ marks$)$

$($ii$)$ Calculate the total lateral force per unit length of the wall.

$(8$ marks$)$

$($iii$)$ Find the location of the line of action of the total lateral force.

$(4$ marks$)$