A concrete gravity dam 25 ft high is used to create a lake in an area where a small river flows. The dam will also function as a spillway, and the design height for the water behind the dam can be...

A concrete gravity dam 25 ft high is used to create a lake in an area where a small river flows. The dam will also function as a spillway, and the design height for the water behind the dam can be assumed level with the crest. The dam has a cross-sectional shape similar to that shown in Illustration 5, with the top width equal to 4 ft and the bottom width equal to 22 ft. The downstream face slopes uniformly to intersect the indicated base dimension. The dam is situated on a rock foundation, with the downstream water level considered to be at the rock surface. Applying a 5-kip-per-lineal-foot ice loading at the crest of the dam and using µ equal to 0.75, determine

(a) the factor of safety against overturning

(b) the factor of safety against sliding

(c) the location of the resultant passing through the base.