$($a$)$ Determine the average consolidation settlement $(S_e)$ at mid$-$clay beneath the center of the foundation. $(15\%)$

$($b$)$ Determine the total allowable settlement $({}_a)$ with the following data: The project is a rigid commercial building on sand, with $S=8\mathrm{.}0m,$ which is the span between columns carrying the lowest and highest loads. $(15\%)$

$($c$)$ Determine total settlement $(8)$ which is addition of $S_0($elastic settlement of sand$)$ and $S_0($consolidation settlement of clay$)$ and check with the ${}_a$ determined in Question $5$ and state if the allowable total settlement $({}_a)$ is exceeded or not. $(10\%)$