bench terrace is to be constructed in a hilly area with 12% slope.
Considering a vertical interval
of 2 m and a batter slope of 1:1 calculate: Width of terrace Length of bench terrace per hectare
earthwork requirement area lost in percentage.
Here’s how to calculate the dimensions and earthwork requirements for a bench terrace:
1. Calculate the horizontal distance (base) of the batter slope:
* Since the batter slope is 1:1, for every 1 unit of vertical distance, there is 1 unit of horizontal
distance.
* Therefore, the base of the batter slope is equal to the vertical interval: 2 meters.
2. Calculate the slope angle in degrees:
* Slope percentage = 12% = 0.12
* Slope angle = arctangent (slope percentage) = arctangent (0.12) ≈ 6.84 degrees
3. Calculate the width of the terrace:
* Terrace width = (vertical interval / tangent(slope angle)) + base of batter slope
* Terrace width = (2 meters / tangent(6.84 degrees)) + 2 meters
* Terrace width ≈ 16.67 meters + 2 meters ≈ 18.67 meters
4. Calculate the length of the bench terrace per hectare:
* 1 hectare = 10,000 square meters
* Length per hectare = Area per hectare / Terrace width
* Length per hectare = 10,000 square meters / 18.67 meters
* Length per hectare ≈ 535.71 meters
5. Calculate the earthwork requirement (approximate):
* Earthwork per hectare = (vertical interval * terrace width) / 2 * length per hectare
* Earthwork per hectare = (2 meters * 18.67 meters) / 2 * 535.71 meters
* Earthwork per hectare ≈ 10,000 cubic meters
6. Calculate the area lost in percentage:
* Area lost = (vertical interval * length per hectare) / Area per hectare * 100%
* Area lost = (2 meters * 535.71 meters) / 10,000 square meters * 100%
* Area lost ≈ 10.71%
Therefore:
* Width of terrace: Approximately 18.67 meters
* Length of bench terrace per hectare: Approximately 535.71 meters
* Earthwork requirement per hectare: Approximately 10,000 cubic meters
* Area lost in percentage: Approximately 10.71%
To calculate the required parameters for the bench terrace construction, let’s define the given
values:
Slope of the land = 12% (i.e., 12 m rise per 100 m horizontal distance)
Vertical Interval (VI) = 2 m
Batter Slope = 1:1 (45° slope)
Land Area = 1 hectare = 10,000 m²
1. Width of Terrace (W)
The width of the terrace can be determined using the formula:
W = \frac{VI}{S} + VI \times B
Where:
= slope in decimal form = 12% = 0.12
= batter slope = 1
W = \frac{2}{0.12} + (2 \times 1)
W = 16.67 + 2 = 18.67 \text{ m}
2. Length of Bench Terrace per Hectare
The length of the bench terraces per hectare is calculated as:
L = \frac{\text{Total area}}{\text{Width of terrace}}
L = \frac{10,000}{18.67}
L = 535.57 \text{ m}
3. Earthwork Requirement per Hectare
The earthwork volume per hectare can be estimated using the formula:
\text{Earthwork} = \frac{VI^2}{2S} \times L
\text{Earthwork} = \frac{2^2}{2 \times 0.12} \times 535.57
= \frac{4}{0.24} \times 535.57
= 16.67 \times 535.57
= 8,926.5 \text{ m}^3
4. Area Lost Due to Bench Terracing (%)
The percentage of land lost is due to the batter slope area.
\text{Area lost} = \frac{\text{Batter slope width} \times L}{\text{Total area}} \times 100
= \frac{(2 \times 535.57)}{10,000} \times 100
= \frac{1071.14}{10,000} \times 100
= 10.71\%
Final Answers
Width of Terrace = 18.67 m
Length of Bench Terrace per Hectare = 535.57 m
Earthwork per Hectare = 8,926.5 m³
Area Lost Due to Terracing = 10.71%
Where:
= Width of terrace
= Vertical interval (2 m in this case)
= Slope (12% or 0.12 in decimal form)
= Batter slope (1:1)
= Length of bench terrace per hectare
= Total area (1 hectare = 10,000 m²)
= Earthwork requirement
