A pressure distribution exists under a concrete dam$($specific gravity of $2\mathrm{.}4)$ and resisting body of water as shown. Assume that the hydrostatic uplift at the base foundation is linearly varying from full uplift pressure at the heel to zero at the toe.

$($a$)$ Will the dam topple if $H=6m$ and $h=4m?$ Determine the factor of safeties against overturning and sliding if the coefficient of friction between the base and the foundation is $0\mathrm{.}75.$

$($b$)$ Determine the maximum and minimum stresses along the base of the foundation.

Ans.

$($a$)F{S}_0=2\mathrm{.}4353F{S}_S=2\mathrm{.}1375$

$($b$)$ Max. ${}_{\text{h}\text{e}\text{e}\text{l}}=85\mathrm{.}46$kPa$(C)$ Min. ${}_{\text{t}\text{o}\text{e}}=63\mathrm{.}66$kPa$(C)$