If the height of the hydraulic gradient line above the floor of thickness t is h and the specific gravity of the material of the floor is G, the minimum thickness t of the floor downstream of the crest-wall, is given by the equation A. $${\text{t}} = \frac{{{\text{h}} + 1}}{{{\text{G}} + {\text{t}}}}$$ B. $${\text{t}} = \frac{{{\text{h}} – 1}}{{{\text{G}} + {\text{t}}}}$$ C. $${\text{t}} = \frac{{{\text{h}} – 1}}{{{\text{G}} – {\text{t}}}}$$ D. $${\text{t}} = \frac{{{\text{h}} + 1}}{{\text{G}}}$$

The correct answer is $\boxed{\text{A}}$.

The hydraulic gradient line is a line that represents the direction of flow of water. The specific gravity of a material is the ratio of its density to the density of water. The minimum thickness of the floor downstream of the crest-wall is the thickness of the floor that is required to prevent the water from flowing through the floor.

The equation for the minimum thickness of the floor downstream of the crest-wall is given by:

$$t = \frac{h + 1}{G + t}$$

where:

• $t$ is the minimum thickness of the floor downstream of the crest-wall
• $h$ is the height of the hydraulic gradient line above the floor
• $G$ is the specific gravity of the material of the floor

The equation can be derived by considering the force balance on a small element of the floor. The force due to the weight of the water

is equal to the force due to the pressure of the water. The pressure of the water is equal to the hydraulic head times the specific gravity of the water. The hydraulic head is equal to the height of the hydraulic gradient line above the floor.

Therefore, the equation for the minimum thickness of the floor downstream of the crest-wall is given by:

$$t = \frac{h + 1}{G + t}$$

The other options are incorrect because they do not take into account the specific gravity of the material of the floor.