$2.($a$)$ A retaining wall $6$ m high with a vertical back supports a cohesionless soil with a dry unit weight of $16$ kN$/$m$3,$ a saturated unit weight of $19\mathrm{.}62$ kN$/$m$3$ and an angle of friction of $350.$ The surface of the soil is horizontal and at level with the top of the wall. Neglecting wall friction, determine the total active earth thrust of the wall per lineal metre, and the height above the base of the wall at which the thrust acts.

Use the following equations to answer both questions:

$(50$ marks$)$

Chp

$1$ sin$+1+$ sin$+$

$1+$ sin$+1$ sin$+$