Problem $1(40$ pts$)$

An Engineer at the Soaring Eagles firm has encountered a steep slope as part of a design project and would like to ensure long$-$term stability of a planned adjacent sidewalk by implementing a gravity wall in the orientation depicted below. The angle of internal friction is $30$ degrees, and the unit density of the soil is $115$ pounds per cubic foot.

The location consists of clean sands that are largely cohesionless with a water table well below the planned installation.

Determine the factor of safety against sliding.

Part $2(15$ pts$)$

Determine the factor of safety against overturning.

Part $3(5$ pts$)$

If the water table was to rise all the way to planned ground surface, would that add more force to the active or passive side of the wall?

Part $4(5$ pts$)$

If instead of clean sands at the site, the Engineer noticed organic peat at a depth of $1$ foot below the planned gravity wall, which mode of failure would you be most concerned about $-$ overturning, sliding, or bearing capacity?