Q$1(4$ marks$)$

A retaining wall is shown in the following figure. Determine the Rankine active force $P_a$ per unit length of the wall and the location of the resultant force.

Q$2(6$ marks$)$ A retaining wall with vertical back face is $8\mathrm{.}5m$ high and retains a homogeneous saturated soft clay. The saturated unit weight of the clay is $19\mathrm{.}6k\frac{N}{m^3},$ and laboratory tests indicate an undrained shear strength $c_u$ of $22$kPa. Assume undrained loading condition:

a$)$ Calculate and plot the variation of Rankine's active pressure on the wall with depth

b$)$ Determine the depth up to which tensile cracks can occur

c$)$ Calculate the total active force per unit length of the wall before the tensile crack occurs

d$)$ Determine the total active force per unit length of the wall after the tensile crack occurs, and find the location of the resultant