Gradient: A gradient is the rate of rise or falls along the length of the road with respect to horizontal. It is expressed as ‘1' vertical unit to 'N' horizontal units.
Tan θ =
h
I
h
I
=
1
N
Area of trapezoidal: According to the trapezoid area formula, the area of a trapezoid is equal to half the product of the height and the sum of the two bases. Area =
1
2
× (Sum of parallel sides) × (perpendicular distance between the parallel sides). Calculation:
Road embankment = 10 m Average height = 5 m Difference in elevation(h) = 280 - 220 = 60 m Average gradient =
1
40
h
l
=
1
40
60
1
=
1
40
L = 2400 m
Average cross-sectional area(A) = 12×(10+30)×5 A = 100 m2 Volume of earthwork = A × L Volume of earthwork = 100 × 2400 ∴ Volume of earthwork = 2,40,000 m3