Calculating Elementary Gravity Dam Height

The question asks for the approximate allowable height of a solid gravity dam with an elementary profile, given its base width and the specific gravity of the dam material, and specifically states that uplift pressure should not be considered.

For an elementary profile gravity dam, the profile is a right-angled triangle. The stability of such a dam against overturning and sliding is primarily determined by the relationship between its height, base width, and the specific gravity of the material, considering the hydrostatic pressure from the water.

When the uplift pressure is neglected, the relationship between the base width ($B$), the height ($H$), and the specific gravity of the dam material ($s$) for an elementary profile dam is given by the formula:

\( B = \frac{H}{\sqrt{s}} \)

We are given the following values:

• Base width, \( B = 35 \) m
• Specific gravity of dam material, \( s = 2.45 \)

We need to find the allowable height, \( H \). We can rearrange the formula to solve for \( H \):

\( H = B \times \sqrt{s} \)

Now, substitute the given values into the formula:

\( H = 35 \times \sqrt{2.45} \)

First, calculate the square root of the specific gravity:

\( \sqrt{2.45} \approx 1.565247 \)

Now, multiply the base width by this value:

\( H \approx 35 \times 1.565247 \)

\( H \approx 54.7836 \) m

The calculated approximate height is \( 54.7836 \) m.

Let's compare this value with the given options:

• Option 1: \( 54.80 \) m
• Option 2: \( 64.68 \) m
• Option 3: \( 80 \) m
• Option 4: \( 164 \) m

The calculated height \( 54.7836 \) m is very close to \( 54.80 \) m.

Therefore, the approximate allowable height of the dam having an elementary profile without considering the uplift is approximately 54.80 m.