Question $,$ a: $4\%,$ b:$12\%,$ c:$8\%,$ d:$10\%)$

A rectangular individual footing with dimensions $BL,$ shown below, is to be designed to support a gross foundation load of $3000kN.$ The Mohr$-$Coulomb shear strength parameters of the silty sand layer are given $c^{\text{'}}=0$ and ${}^{\text{'}}=30.$ The depths of foundation and the ground water table are given as $1\mathrm{.}2$ meters and the unit weights of silty sand below and above the ground water table can be assumed as $19k\frac{N}{m^3}$ and $21k\frac{N}{m^3},$ respectively. Answer the following questions:

a$)$ List at least four assumptions of the Terzaghi's bearing capacity equation for global shear failure.

b$)$ If the length $L,$ is given as $5$ meters, determine the width, $B,$ of the footing for a factor of safety of $FS=3\mathrm{.}0$ against global shear failure.

Hint: You may use Terzaghi's bearing capacity equation. Bearing capacity factors for a particular value of ${}^{\text{'}}$ can be found in the form of tables in various sources.

$($e$.$g$.$ from Bowles, $1988,$ Table $4\mathrm{.}2$ or from your lecture notes.$)$