Excavation and fill
Excavation volume, backfill, haulage and material purchase
How the calculation works
Choose the shape (rectangular pit, trench, circular pit or fill), enter the dimensions and state whether they refer to the structure, the bottom or the top of the excavation, the depth, working space and side slope. For a variable-depth trench enter stations. Add soil layers with bulking and compaction factors, embedded elements and the truck. The calculator works out the excavation by layer, the backfill required, the surplus to haul away, the shortfall of new material and the number of trips.
Formula and assumptions
Pit with side slopes: V = H/6 · (A_bottom + 4·A_middle + A_top). Circular pit: V = πH/3 · (r1² + r1·r2 + r2²). Trench: A = (b + n·h)·h, V = A·L; for variable depth Simpson's rule between stations. Backfill (compacted) = excavation − embedded elements; in-situ material needed = backfill ÷ compaction factor; haulage (loose) = surplus × bulking; trips = max(volume ÷ truck volume, mass ÷ payload).
Worked example
Footing 10 × 8 m, working space 0.6 m, slope 0.5 : 1, depth 1.5 m: bottom 11.2 × 9.2 m, top 12.7 × 10.7 m, excavation 178.64 m³. With an 80 m³ footing the backfill is 98.64 m³ compacted. Topsoil (0.3 m) and the unsuitable part are hauled away: 74.81 m³ in situ, 93.51 m³ loose, about 122.7 t – 10 trips with a 10 m³ / 14 t truck (volume decides).
More worked examples
- Trench with a 0.6 m bottom width, slope 0.5 : 1, depth from 1.0 to 1.6 m over 20 m: A(h) = (0.6 + 0.5·h)·h, by Simpson's rule V = 32.8 m³; the sloped bottom length is 20.009 m.
- Fill of 50 m² with a compacted thickness of 0.3 m = 15 m³; with a factor of 0.8 (1 m³ loose = 0.8 m³ compacted) 18.75 m³ of loose material is needed, at 1600 kg/m³ about 30 t.
Rectangular pit for a 10 × 8 m footing (working space 0.6 m, slope 0.5 : 1)
| Depth (m) | Excavation in situ (m³) | Loose ×1.25 (m³) | Top area (m²) |
|---|---|---|---|
| 1.0 | 113.57 | 141.97 | 124.44 |
| 1.5 | 178.64 | 223.29 | 135.89 |
| 2.0 | 249.55 | 311.93 | 147.84 |
| 2.5 | 326.56 | 408.20 | 160.29 |
| 3.0 | 409.92 | 512.40 | 173.24 |
What affects real consumption
- Soil type and its bulking and compaction factors.
- Side slope and working space required by site conditions.
- Share of excavated material suitable for backfill.
Common mistakes
- Working space added both to the dimensions and as a separate input.
- Comparing backfill with excavation in different states (compacted vs in situ).
- Counting trips by volume only, although the load is too heavy for the truck's payload.
Frequently asked questions
Why is the truncated pyramid formula not used?
For a rectangular pit with equal slopes the cross-section changes quadratically with depth, so the prismoidal formula is exact. The truncated pyramid formula applies only to similar bases, which is generally not the case for a rectangle with an equal offset.
Does the mass of material increase with bulking?
No. Bulking increases the volume while the mass stays the same – it is calculated from the in-situ state and the density in that state.
How is the number of trips calculated?
The number of trips must satisfy both limits: the truck's load volume for loose material and the permitted payload (not the vehicle's gross weight). The larger of the two numbers decides.