A concrete gravity dam 25 ft high is used to cre. ate a lake in an area where a snall river flow

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A concrete gravity dam 25 ft high is used to cre. ate a lake...

A concrete gravity dam $25 \mathrm{ft}$ high is used to cre. ate a lake in an area where a snall 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 Illastration 5 , with the top width equal to $4 \mathrm{ft}$ and the bottom width equal to $22 \mathrm{fl}$. The downstream face slopes uniformly to intersect the indicated base dimension. The dam is situaled 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 $\mu$ equal to 0.75 . detemine (a) the factor of safety against overturning (b) the factor of safety against sliding (c) the location of the resultant passing through the hase.

A concrete gravity dam $25 \mathrm{ft}$ high is used to cre. ate a lake in an area where a snall 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 Illastration 5 , with the top width equal to $4 \mathrm{ft}$ and the bottom width equal to $22 \mathrm{fl}$. The downstream face slopes uniformly to intersect the indicated base dimension. The dam is situaled 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 $\mu$ equal to 0.75 . detemine
(a) the factor of safety against overturning
(b) the factor of safety against sliding
(c) the location of the resultant passing through the hase.

Key Concepts

Structural Geometry in Gravity Dams

The geometry of a gravity dam, including factors like height, top and base widths, and the slopes of the faces, plays a critical role in its stability. Analyzing the cross-sectional shape is essential as it influences how the dam's weight is distributed and how it resists various loads. Proper geometric design ensures that the resultant forces remain within safe limits, thus providing inherent stability against both overturning and sliding.

Overturning Analysis

Overturning analysis in dam engineering involves calculating and comparing the moments about a selected pivot point, usually at the downstream edge of the dam's base. The objective is to ensure that the resisting moment generated by the dam’s weight and geometry exceeds the overturning moment due to external forces such as hydrostatic pressure and additional loads (e.g., ice loading). This analysis is central to maintaining the stability of concrete gravity dams against tipping failures.

Sliding Analysis

Sliding analysis focuses on the horizontal stability of the dam. This involves comparing the frictional resistance at the dam-foundation interface, determined by factors such as the coefficient of friction and the dam's weight, to the applied horizontal forces like water and ice loads. The factor of safety against sliding is calculated by dividing the resisting frictional force by the driving force, ensuring that the dam remains securely in place under all loading conditions.

Resultant Force and Its Line of Action

Determining the location of the resultant force is crucial in the stability analysis of dams. The resultant force is the vector sum of all forces acting on the dam, including vertical loads from the dam's weight and horizontal loads from water pressure and ice loading. Its line of action must pass within the dam’s base to prevent both overturning and sliding, making it an essential factor in evaluating the overall safety of the structure.

Ice Loading

Ice loading is a specific loading condition where additional force is applied to the dam due to the accumulation and movement of ice. This load can have significant impacts on both the overturning and sliding stability of a dam. It is therefore necessary to include ice loading in structural analyses to ensure that the dam can safely withstand these extra forces, especially when the dam also serves multiple functions such as acting as a spillway.

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