A gravity dam is a structure that relies only on the weight of the wall structure to support the hydrostatic forces

and moments caused from the water pushing on the dam wall. A gravity dam structure is proposed to retain

water to a depth h $=4$ m$.$ The dam wall is made from material with specific gravity S $=2\mathrm{.}4$ and has a rectangular

cross section with wall dimensions: wall height H $=5$ m $($vertical$),$ wall depth $($horizontal$)$ D $=2$ m and into

the page wall width W $=1$ m$.$ Assume water to be at T $=20\backslash$deg C$,$ and neglect seepage of water under the dam

wall.

$($a$)$ Provide a schematic of the dam, including necessary variables for the analysis. $(5$ marks$)$

$($b$)$ Will the dam wall overturn with the current water depth h $=4$ m$?$ Justify. $(6$ marks$)$

$($c$)$ To save on construction costs, is it possible to use a less dense dam wall construction material? Make a

recommendation on the required specific gravity $($S$)$ for the wall to just begin to tip over. $(4$ marks$)$

$($Total: $15$ Marks$)$