This question asks to calculate the percentage of area lost for cultivation when constructing bench terraces on a hill slope with a given batter slope.
Understanding Bench Terracing Parameters
We are given:
- Hill Slope, $S = 10\% = 0.1$
- Batter Slope notation: $ \frac{1}{2} \text{ H} : 1 \text{ V} $. This is interpreted as the ratio of Vertical (V) to Horizontal (H) components, meaning $V/H = 0.5 / 1 = 0.5$. So, the batter slope $m = 0.5$.
Calculating Area Lost
The percentage area lost for cultivation due to the construction of batters (cut and fill slopes) can be estimated using a formula that considers the hill slope and the batter slope.
A common formula used in this context is:
$ \text{Area Lost (\%)} = \frac{100 \times m \times S}{1 - S} $Where:
- $S$ is the hill slope (as a decimal)
- $m$ is the batter slope (V/H, as a decimal)
Substitute the given values:
$ \text{Area Lost (\%)} = \frac{100 \times 0.5 \times 0.1}{1 - 0.1} $ $ \text{Area Lost (\%)} = \frac{100 \times 0.05}{0.9} $ $ \text{Area Lost (\%)} = \frac{5}{0.9} $ $ \text{Area Lost (\%)} \approx 5.555... \% $Conclusion
The calculated area lost is approximately $5.56\%$. Comparing this to the options provided, the closest value is $5.47\%$.
Important Questions from Terraces
- Bench terraces are planned on $15\%$ hill slope. The vertical interval is $2.5\text{ m}$, and the riser has a slope of $1:1$. The earthwork in cutting is equal to the earthwork in filling. The volume of earthwork per hectare (in $\text{m}^3\text{.ha}^{-1}$) is ________ (Rounded off to the nearest integer)
Hilly areas receiving heavy rainfall, where a major portion of the rainfall is to be drained as surface runoff, are suggested to adopt bench terraces with ____________.
- If the width of bench terrace is W, drop D and existing land slope S; then for 150% batter slope, the drop D will be
- Bench terraces are to be constructed on a 15% hill slope. The batter slope is 1:1 and vertical interval is 2.5 m. The earth work in cutting is equal to filling. The quantum of earthwork in $m^3 ha^{-1}$ will be
- For the eastern Himalayan region having hill slope of 16%, a bench terrace system is to be designed. It is found that the depth of cut for constructing the bench terrace cannot be more than 0.40 m due to the limitation of the soil depth. If a batter slope of $1\frac{1}{2}:1$ is proposed, the maximum possible width of the terrace and the required earthwork per hectare (assuming cut equal to fill) will be
