Skip to main content

Road earthwork, upward grade 1:100

Short answer

Earthwork in cutting = 15,610.65 m³; earthwork in filling = 0.00 m³.

Estimate the quantity of earth work for a portion of road, when formation width is 10 m. Side slope in cutting and filling are 1:1 and 2:1 respectively.

Distance0 m30 m60 m90 m
R.L.G100 m110 m111 m112 m
R.L.F100 m, upward grade (1:100)
(as printed; the ground level row is hard to read)

Given data and assumptions

  • Formation width B=10B = 10 m; side slopes: cutting 1:11:1, filling 2:12:1. Ground is level across the road.
  • Ground levels are read as printed (100, 110, 111, 112 m at 0, 30, 60, 90 m, the scan is hard to read) and formation level starts at 100.00 m, rising 1 in 100.

Method

Level (plain-ground) sections are used. With centre height hh, formation width BB and side slope s:1s:1:

A=(B+s h) hA = (B + s\,h)\,h

Volume between two sections = mean area × distance; where a section changes from cutting to filling, the length of each part is found by proportion of the depths and the volume of each part = ½ × end area × length.

ChainageGL (m)FL (m)Depth of cutting / height of filling (m)
0+000100.000100.0000.000
0+030110.000100.300cutting 9.700
0+060111.000100.600cutting 10.400
0+090112.000100.900cutting 11.100

Sectional areas

ChainageCentre ht. hh (m)Cutting area (m²)Filling area (m²)
0+0000.000.0000.000
0+030cut 9.70191.0900.000
0+060cut 10.40212.1600.000
0+090cut 11.10234.2100.000

Volumes

BetweenDistance (m)Cutting (m³)Filling (m³)
0+000 – 0+03030.02,866.350.00
0+030 – 0+06030.06,048.750.00
0+060 – 0+09030.06,695.550.00
Total90.015,610.650.00

Answer: Earthwork in cutting = 15,610.65 m³; earthwork in filling = 0.00 m³.

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Estimating and Costing chapter 6 questions →