Question One:

a$)$ A wall $15$ m high has to be designed so as to retain dry sand. Under loose condition the sand has a void ratio of $0\mathrm{.}65$ and ${}^{\text{'}}$ of $32,$ and under dense condition the void ratio and ${}^{\text{'}}$ are $0\mathrm{.}41$ and $43,$ respectively, and $G=2\mathrm{.}65.$ Compute the resultant lateral pressures for active and passive cases for both the density conditions. Recommend a suitable resultant lateral force if the wall has to be designed for $($i$)$ the active case and $($ii$)$ the passive case.

b$)$ A vertical wall $10$ m high retains two horizontal layers of a saturated cohesive backfill with a level surface. The top $4$ m of the backfill has an undrained cohesion of $18\mathrm{.}2$ kPa and a bulk unit weight of $18\mathrm{.}6k\frac{N}{m^3}.$ The bottom clay layer has a bulk unit weight and an undrained cohesion of $22k\frac{N}{m^3}$ and $23\mathrm{.}6$ kPa $,$ respectively. Estimate the likely depth of the tension zone behind the wall. Compute the total active force if tension cracks develop, and also locate the application of the resultant lateral force.