- Asked 2/22
- 2067 Poush (old course) · 10 marks
Road earthwork, formation level at 150 m
Short answer
Earthwork in cutting = 1,786.15 m³; earthwork in filling = 187.07 m³.
Find out the quantity of earth work of a portion of road to be constructed with the following data: Formation width of the road = 10 m. Side slopes in banking and cutting = (2:1) and (1:1). Downward grade 1 in 120 from distance 90 to 120 m while it remains in level from distance 120 to 180 m and again upward grade 1 in 90 from distance 180 to 210 m. The formation level at distance 150 m = 1197.50.
| R.L. of ground | 1198.65 | 1196.40 | 1199.30 | 1200.40 | 1198.10 |
|---|---|---|---|---|---|
| Distance (m) | 90 | 120 | 150 | 190 | 210 |
Given data and assumptions
- Formation width m; banking slope , cutting slope . Ground is level across the road. Stations are at 90, 120, 150, 190 and 210 m (spacing 30, 30, 40, 20 m).
- Formation level at 150 m is 1197.50 m; level from 120 m to 180 m; falling 1 in 120 from 90 to 120 m, so level at 90 m = 1197.75 m; rising 1 in 90 from 180 m, so level at 190 m = 1197.50 + 10/90 = 1197.611 m and at 210 m = 1197.833 m.
Method
Level (plain-ground) sections are used. With centre height , formation width and side slope :
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.
| Chainage | GL (m) | FL (m) | Depth of cutting / height of filling (m) |
|---|---|---|---|
| 0+090 | 1,198.650 | 1,197.750 | cutting 0.900 |
| 0+120 | 1,196.400 | 1,197.500 | filling 1.100 |
| 0+150 | 1,199.300 | 1,197.500 | cutting 1.800 |
| 0+190 | 1,200.400 | 1,197.611 | cutting 2.789 |
| 0+210 | 1,198.100 | 1,197.833 | cutting 0.267 |
Sectional areas
| Chainage | Centre ht. (m) | Cutting area (m²) | Filling area (m²) |
|---|---|---|---|
| 0+090 | cut 0.90 | 9.810 | 0.000 |
| 0+120 | fill 1.10 | 0.000 | 13.420 |
| 0+150 | cut 1.80 | 21.240 | 0.000 |
| 0+190 | cut 2.79 | 35.667 | 0.000 |
| 0+210 | cut 0.27 | 2.738 | 0.000 |
Volumes
| Between | Distance (m) | Cutting (m³) | Filling (m³) |
|---|---|---|---|
| 0+090 – 0+120 | 30.0 | 66.22 | 110.71 |
| 0+120 – 0+150 | 30.0 | 197.75 | 76.36 |
| 0+150 – 0+190 | 40.0 | 1,138.14 | 0.00 |
| 0+190 – 0+210 | 20.0 | 384.05 | 0.00 |
| Total | 120.0 | 1,786.15 | 187.07 |
Answer: Earthwork in cutting = 1,786.15 m³; earthwork in filling = 187.07 m³.
✓ Answer checked by Claude Opus 5.5 (high effort)
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