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A road embankment with cross-sectional area of 100 m 2 is constructed with an average gradient of 1 in 50 from contour 200 m to 250 m. Find the volume of the earth work.
22500 m┬│
1250000 m┬│
5000 m┬│
250000 m┬│
250000 m┬│
The volume of earthwork for a road embankment is determined by calculating the horizontal length of the road based on the vertical rise and the gradient, then multiplying by the cross-sectional area. The vertical rise is 250mтИТ200m=50m, and with a gradient of 1:50, the horizontal length L is 50├Ч50=2500m.
The volume of earthwork for a road embankment is determined by calculating the horizontal length of the road based on the vertical rise and the gradient, then multiplying by the cross-sectional area. The vertical rise is 250mтИТ200m=50m, and with a gradient of 1:50, the horizontal length L is 50├Ч50=2500m.
H=H2тАЛтИТH1тАЛ тАФ Vertical rise
L=H├ЧGradient┬аScale тАФ Horizontal length
V=A├ЧL тАФ Volume of earthwork
The principle of uniform gradient states that the length of the road is the vertical height change divided by the gradient slope (s=LHтАЛ). Once the horizontal distance L is determined, assuming a constant cross-sectional area A, the volume V is given by V=A├ЧL.
Gradient 1:50 implies 1 unit of vertical rise for every 50 units of horizontal distance.
Cross-sectional area is considered uniform throughout the length for this calculation.
The total horizontal length calculated is 2500m.
Simple calculation method for uniform sections.
Useful for preliminary estimation of earthwork.
Assumes a constant cross-sectional area which is rarely true in actual terrain.
Does not account for side slopes or varying terrain elevation changes.
Preliminary highway engineering design.
Initial cost estimation of road construction projects.
Calculation: V=100m2├Ч(50m├Ч50)=100├Ч2500=250,000m3.
Option A, B, and C are incorrect due to miscalculation of length or multiplication errors.
D is correct тАФ the total volume is computed as the product of the constant cross-sectional area and the total horizontal length derived from the gradient.
Always ensure the gradient scale is correctly interpreted (1:n means n units of horizontal run for 1 unit of rise) before multiplying by the area.
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