1
GATE CE 2023 Set 1
Numerical
+2
-0
A vertical trench is excavated in a clayey soil deposit having a surcharge load of 30 kPa. A fluid of unit weight 12 kN/m3 is poured in the trench to prevent collapse as the excavation proceeds. Assume that the fluid is not seeping through the soil deposit. If the undrained cohesion of the clay deposit is 20 kPa and saturated unit weight is 18 kN/m3 , what is the maximum depth of unsupported excavation (in m, rounded off to two decimal places)? ________________
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2
GATE CE 2023 Set 1
Numerical
+1
-0

The ordinates of a one-hour unit hydrograph for a catchment are given below: 

$$ \begin{array}{|l|l|l|l|l|l|l|l|l|} \hline t(\text { hour }) & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline Q\left(\mathrm{~m}^3 / \mathrm{s}\right) & 0 & 9 & 21 & 18 & 12 & 5 & 2 & 0 \\ \hline \end{array} $$


Using the principle of superposition, a D-hour unit hydrograph for the catchment was derived from this one-hour unit hydrograph. The ordinates of the D-hour unit hydrograph were obtained as 3 m3/s at t = 1 hour and 10 m3/s at t = 2 hour. The value of D (in integer) is _____________.

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3
GATE CE 2023 Set 1
Numerical
+2
-0

A 12-hour storm occurs over a catchment and results in a direct runoff depth of 100 mm. The time-distribution of the rainfall intensity is shown in the figure (not to scale). The 𝜙-index of the storm is (in mm, rounded off to two decimal places) _____________.

GATE CE 2023 Set 1 Hydrology - Infiltration Question 3 English
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4
GATE CE 2023 Set 1
Numerical
+2
-0
In Horton’s equation fitted to the infiltration data for a soil, the initial infiltration capacity is 10 mm/h; final infiltration capacity is 5 mm/h; and the exponential decay constant is 0.5 /h. Assuming that the infiltration takes place at capacity rates, the total infiltration depth (in mm) from a uniform storm of duration 12 h is ____________. (round off to one decimal place) 
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