QUESTION $2$

RETAINING WALLS

$[21]$

The mass retaining wall features a stem height of $1\mathrm{.}10m$ above the base, tapering from $850mm$ to $200mm$ with a backfill projecting $150mm$ below the stem. The backfill is level behind the wall with the surcharge of $0\mathrm{.}4$kPa. Additionally, consider an angle of repose $()$ of $30$ degrees, a coefficient of friction of $0\mathrm{.}35$ and the retained material unit weight of $18\mathrm{.}0k\frac{N}{m^3}.$ The safe working ground pressure is $100$kPa and there is no sliding key. The base measures $0\mathrm{.}85m$ in width, $0\mathrm{.}20m$ in depth, with no heel and toe. All dimensions are in millimetres.

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FO$.$S overturning $=\frac{Ms}{M_n}$;$F0S$ sliding $=\frac{Wtotal}{Fn}$; Fre $=\frac{M_0}{\text{w}\text{t}\text{a}\text{t}\text{a}\text{l}}-\frac{Ms}{\text{W}\text{t}\text{n}\text{t}\text{a}\text{l}}+\frac{B}{2}f=\frac{\text{W}\text{t}\text{n}\text{t}\text{a}\text{l}}{B}\{1+-\frac{6\text{E}\text{c}\text{c}}{B}\}$ and $f=\frac{4W\text{t}\text{o}\text{t}\text{a}\text{l}}{3(B-2\text{E}\text{c}\text{c})}$

Determine the factor of safety against sliding and overturning as well as the pressure below the base for the given retaining wall configuration.