$28\mathrm{.}1$ Consider the retaining structure shown and the backfill properties provided.

Calculate and show the following:

a$.$ The earth pressure at rest distribution acting on the wall assuming the soil is not compacted, the resulting force, and where it acts on the wall.

b$.$ The Rankine's active stress distribution acting on the wall, its resultant force, where it acts on the wall, and the failure planes in the soil.

c$.$ The Rankine's passive stress distribution acting on the wall, its resultant, and where it acts on the wall.

For $10$ bonus points, show the planes along which shear failure would be expected in the backfills for cases b and c$.$