Question $3$

$($a$)$

$($i$)$ A concrete dam, shown in Figure Q$3$a below, rests on a solid foundation which prevents uplift pressure from acting on the base of the dam. Determine the minimum coefficient of friction needed between the dam and the foundation to prevent the dam from sliding. Base your analysis on a unit width of dam.

Also, check if the dam is likely to overturn about its toe, O $.$

$[8]$

$($ii$)$ Consider the dam below again where a constant uplift pressure acts along the base of the dam. The uplift pressure is equal to $50\%$ of the hydrostatic pressure acting on the upstream face of the dam.

What is the minimum coefficient of friction now required to prevent the dam from sliding.

$[2]$