Assignment: Retaining Wall Design

A highway cut necessitates the construction of a retaining wall, which is $15$ feet in height as depicted in Figure $1.$ This wall will be filled behind with densely compacted sand, having a unit weight of $110$ pcf$.$ To assess the backfill soil's properties, direct shear box tests were carried out under normal stresses of $25\mathrm{.}7,62\mathrm{.}2,98\mathrm{.}7,147\mathrm{.}4,$ and $183\mathrm{.}9$kPa. The relationship between horizontal strain and shear stress for these tests is illustrated in Figure $2.$ The foundation soil has a unit weight of $119$ pcf$,$ a cohesion $($c$)$ of $0,$ an internal friction angle $()$ of $30$ degrees, and a friction angle $()$ between the soil and concrete that is two$-$thirds of the foundation soil's internal friction angle. Assume there is no soil in front of the wall.

a$)$ Identify the most cost$-$efficient cantilever retaining wall design that complies with the minimum Factor of Safety $($F$.$S$.)$ criteria of $1\mathrm{.}5$ for sliding and overturning, and $3\mathrm{.}0$ for bearing capacity. Use the standard dimensions outlined in Figure $3$ as a starting point for your preliminary design iteration. Execute at least two design trials and provide scaled drawings of your final wall design on the provided sheets.

b$)$ Repeat part a for a gravity wall.

Figure $1.$ Proposed retaining wall at a highway cut.