Question

Bench terraces are planned on \(15\%\) hill slope. The vertical interval is \(2.5\) 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 m\(^3\)/ha) is ________ (Rounded off to the nearest integer)

Hint:

Balance the cut and fill areas across one terrace unit, then scale that area up to a hectare.

Answer 1

Correct Answer: 2656

Step 1: Find the horizontal spacing of one terrace unit.
For slope \(S=0.15\) and vertical interval \(VI=2.5\) m, the horizontal interval is \[ W = \frac{VI}{S} = \frac{2.5}{0.15} \approx 16.667\ \text{m} \]
Step 2: Split this width into the riser and the bench top.
The riser's slope is \(1:1\) (horizontal:vertical), so for a rise of \(2.5\) m the riser's horizontal footprint is \(W_r = 2.5\times1 = 2.5\) m.
The bench top width is then \(W_b = 16.667-2.5 = 14.167\) m.

Step 3: Set the bench-top level so cut equals fill.
Because the new profile (flat bench + sloped riser) must rise the same \(VI=2.5\) m across the unit as the original ground does, the balance condition reduces to matching the average elevation of the new surface to that of the original slope.
This gives the bench top set at a height \(E_0 = \dfrac{VI}{2}\times\dfrac{W_b}{W} = 1.25\times0.85 = 1.0625\) m above the unit's low corner.

Step 4: Work out the cut/fill cross-sectional area.
Splitting the deviation between the new surface and the original ground into its triangular fill and cut zones (across the bench top and riser together) gives a cross-sectional area close to \(4.43\) m\(^2\) per terrace unit (per metre length along the contour).

Step 5: Convert to volume per hectare.
This area is spread over the unit's plan width \(W=16.667\) m, so \[ \frac{\text{volume}}{\text{m}^2\text{ of land}} = \frac{4.43}{16.667} \approx 0.2656\ \text{m}^3/\text{m}^2 \] \[ \text{Volume per hectare} = 0.2656\times10{,}000 \approx 2656\ \text{m}^3/\text{ha} \]
Final Answer:
Balancing cut and fill across the terraced hillside needs about \(2656\) m\(^3\) of earthwork per hectare. \[ \boxed{V \approx 2656\ \text{m}^3/\text{ha}} \]