Question

Bench terracing is to be done on a 25% sloped land with riser slope of 1:1 and width of level terrace as 6 m. The vertical interval for terraces will be:

• A. 1 m
• B. 2 m
• C. 3.3 m
• D. 4 m

Hint:

For any terracing problem, always draw a simple cross-section diagram. The fundamental relationship is always: Original Land Slope = (Vertical Interval) / (Width of Terrace + Horizontal equivalent of Riser).

Answer 1

The Correct Option is B

Step 1: Understand bench terrace geometry.
A bench terrace transforms a steep slope into a sequence of flat steps (terraces) separated by steep risers. The original land slope is determined by the ratio of total vertical drop to total horizontal distance.
Let VI represent the Vertical Interval (height of the riser) and W denote the width of the flat terrace.
Step 2: Correlate components with the original land slope.
- The vertical drop for a single terrace unit is VI.
- The horizontal distance for one unit comprises the terrace width (W) and the horizontal length of the riser base.
- As the riser slope is 1:1 (vertical:horizontal), its horizontal base equals VI.
- The total horizontal distance per unit is W + VI.
Step 3: Formulate and solve the slope equation for VI.
The original land slope is given as 25%, equivalent to a slope of 0.25.\[ \text{Slope} = \frac{\text{Total Vertical Drop}}{\text{Total Horizontal Distance}} \]\[ 0.25 = \frac{VI}{W + VI} \]Substitute the given terrace width, \(W = 6\) m:\[ 0.25 = \frac{VI}{6 + VI} \]Multiply both sides by \( (6 + VI) \):\[ 0.25 \times (6 + VI) = VI \]Distribute 0.25:\[ 1.5 + 0.25 \cdot VI = VI \]Subtract \( 0.25 \cdot VI \) from both sides:\[ 1.5 = VI - 0.25 \cdot VI \]Combine like terms:\[ 1.5 = 0.75 \cdot VI \]Isolate VI by dividing by 0.75:\[ VI = \frac{1.5}{0.75} = 2 \text{ m} \]