Design and Construction of Gravity Dams

Question 1
A concrete dam holds 10 m of static water as shown in the figure (not drawn to the scale). The uplift assumed to vary linearly from full hydrostatic head at the heel, to zero at the toe of dam. The coefficient of friction between the dam and foundation soil is 0.45. Specific weights of concrete and water are 24 kN/m^3 and 9.81 kN/m^3, respectively.

For NO sliding condition, the required minimum base width B (in m, round off to two decimal places) is __________.
A
12.45
B
18.26
C
14.12
D
15.87
GATE CE 2020 SET-2   Irrigation Engineering
Question 1 Explanation: 


\begin{aligned} \mu &=0.45\\ \gamma_{conc} &=24 kN/m^3\\ B_{min. sliding}&=\frac{10}{0.45(2.4-1)}\\ &=15.873m \end{aligned}
Question 2
A concrete gravity dam section is shown in the figure. Assuming unit weight of water as 10\: kN/m^{3} and unit weight of concrete as 24\: kN/m^{3}, the uplift force per unit length of the dam (expressed in kN/m) at PQ is ____________.
A
10500
B
6000
C
45000
D
15000
GATE CE 2016 SET-1   Irrigation Engineering
Question 2 Explanation: 


\begin{aligned} &\text { Total uplift pressure }\\ &=250 \times 10+40 \times 50+\frac{1}{2} \times 200 \times 40+\frac{1}{2} \times 400 \times 10\\ &=2500+2000+4000+2000\\ &=10500 \mathrm{kN} / \mathrm{m} \end{aligned}
Question 3
The base width of an elementary profile of a gravity dam of height H is b. The specific gravity of the material of the dam is G and uplift pressure coefficient is K. The correct relationship for no tension at the heel is given by
A
\frac{b}{H}=\frac{1}{\sqrt{G-K}}
B
\frac{b}{H}=\sqrt{G-K}
C
\frac{b}{H}=\frac{1}{G-K}
D
\frac{b}{H}=\frac{1}{K\sqrt{G-K}}
GATE CE 2008   Irrigation Engineering
Question 3 Explanation: 
Tension will not be developed at the heel with full resevoir, when,
b \geq \frac{H}{\sqrt{G-K}}
There are 3 questions to complete.

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