Highway earthwork for one km length

Given data and assumptions

• Two-lane road: carriageway $7.0$ m with $1.5$ m shoulders on both sides (Nepal Road Standard 2070), so formation width $B = 10.0$ m. The earthwork is taken to subgrade (formation) level.
• Cut slope $1.5:1$, fill slope $2:1$, ground cross slope $9:1$, centre depth of cutting $h = 0.35$ m at every section, so the section is uniform along the 1 km.
• Wearing coat and base course 7.0 m wide; sub-base spread over the full formation width of 10 m.

Earthwork (side-hill section)

At the up-hill edge the ground is $0.35 + 5/9 = 0.906$ m above formation (cutting), and at the down-hill edge it is $0.35 - 5/9 = -0.206$ m (so that side falls below formation and needs filling). The ground cuts the formation level at $9 \times 0.35 = 3.15$ m from the centre line.

• Up-hill toe: $x_u = 6.630$ m from the centre line, ground $1.087$ m above formation
• Down-hill toe (filling slope): $x_d = 5.529$ m, ground $0.264$ m below formation
• Area of cutting $= 4.428$ m²; area of filling $= 0.244$ m² (from the co-ordinates of the section).

$$\begin{aligned} V_{cut} &= 4.428 \times 1000 = 4,428.2\ \text{m}^3\\ V_{fill} &= 0.244 \times 1000 = 244.5\ \text{m}^3 \end{aligned}$$

Pavement quantities for 1 km

Answer: cutting = 4,428.2 m³, filling = 244.5 m³ per km; wearing coat 350 m³, base 1,750 m³, sub-base 3,500 m³. The cost follows by multiplying each quantity by its rate (District Rate) and adding overhead, profit and VAT.