- 2082 Baisakh · 6 marks
Road earthwork with RL of GL and FL (0-600)
Short answer
Cutting = 2410.45 m³, filling = 1875.00 m³. Level-gound areas (B+sh)h; volumes averaged between sections; filling-to-cutting transition split by depth ratio.
Calculate earthwork for the following section of road from the given data. i) Formation width = 8 m, ii) Side slope in filling and cutting = 2:1 and 1½:1 respectively.
| Distance (m) | 0 | 100 | 200 | 300 | 400 | 500 | 600 |
|---|---|---|---|---|---|---|---|
| RL of GL | 99.5 | 100 | 99.8 | 101.6 | 102.3 | 101.1 | 103 |
| RL of FL | 100 | 1:200 (upward) | 1:400 (downward) |
Given data and assumptions
- Formation width m; side slope in filling , in cutting (H:V). Ground is taken as level across the road (no cross slope given).
- Formation level at 0 m is 100.00 m. The gradient is read as 1 in 200 upward from 0 to 300 m and 1 in 400 downward from 300 m to 600 m (the printed table shows only the two gradients).
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+000 | 99.500 | 100.000 | filling 0.500 |
| 0+100 | 100.000 | 100.500 | filling 0.500 |
| 0+200 | 99.800 | 101.000 | filling 1.200 |
| 0+300 | 101.600 | 101.500 | cutting 0.100 |
| 0+400 | 102.300 | 101.250 | cutting 1.050 |
| 0+500 | 101.100 | 101.000 | cutting 0.100 |
| 0+600 | 103.000 | 100.750 | cutting 2.250 |
Sectional areas
| Chainage | Centre ht. (m) | Cutting area (m²) | Filling area (m²) |
|---|---|---|---|
| 0+000 | fill 0.50 | 0.000 | 4.500 |
| 0+100 | fill 0.50 | 0.000 | 4.500 |
| 0+200 | fill 1.20 | 0.000 | 12.480 |
| 0+300 | cut 0.10 | 0.815 | 0.000 |
| 0+400 | cut 1.05 | 10.054 | 0.000 |
| 0+500 | cut 0.10 | 0.815 | 0.000 |
| 0+600 | cut 2.25 | 25.594 | 0.000 |
Volumes
| Between | Distance (m) | Cutting (m³) | Filling (m³) |
|---|---|---|---|
| 0+000 – 0+100 | 100.0 | 0.00 | 450.00 |
| 0+100 – 0+200 | 100.0 | 0.00 | 849.00 |
| 0+200 – 0+300 | 100.0 | 3.13 | 576.00 |
| 0+300 – 0+400 | 100.0 | 543.44 | 0.00 |
| 0+400 – 0+500 | 100.0 | 543.44 | 0.00 |
| 0+500 – 0+600 | 100.0 | 1,320.44 | 0.00 |
| Total | 600.0 | 2,410.45 | 1,875.00 |
Answer: Earthwork in cutting = 2,410.45 m³; earthwork in filling = 1,875.00 m³.
✓ Answer checked by Claude Opus 5.5 (high effort)
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