The two basic failure mechanisms for failure of a Gravity Dam are sliding and overturning at the downstream toe.

Do all exercises per metre length of the dam. Examine the failure criteria for the dam.

First $($Exercise A$)$ work out the minimum values of widths D and W in terms of beight $H,$ freeboard $h,=\frac{h}{H},$ the angle $,=$ the coefficient of friction between the dam and its foundation, the density of water ${}_w,$ the density of the dam material ${}_c$ and with a factor of safety $F.$

Set up equations of overturning moment and righting moment about the downstream toe of the dam, point A$.$ Remember: water pressure can be represented as a force $P$ acting at a height of $\frac{1}{3^{rd}}$ of the depth of the water above the base. Use the average ground pressure for the sliding calculation.

Your expressions should be in the form:

$\frac{D}{H}>$ expression $)"-($sliding$)$; $($use the average ground pressure for this calculation.$)$