Excavation, Sloped Pit and Backfill Volume Calculator

How is excavation volume calculated?

A pit with vertical sides has a volume of bottom area times depth. If working space is left around the structure for formwork and waterproofing, it is added on both sides: the bottom becomes a + 2w by b + 2w.

Sloped excavation

Where the ground cannot stand vertically, the sides are cut to a slope. The slope is usually given as horizontal to vertical: at 1 to 1 the edge moves back one metre for every metre of depth. The top opening is wider than the bottom by m × h on each side.

The volume of this shape is slightly less than the average of the bottom and top areas times the depth. The prismoidal formula gives the exact value:

V = h / 6 × [a·b + (a + a′)·(b + b′) + a′·b′]

Averaging the two end areas counts the corners too generously.

Trench

A sloped trench has a trapezoidal section: V = (b + m × h) × h × L.

Example

A pit with a 10 m × 8 m bottom, 2 m deep with 1 to 1 slopes has a 14 m × 12 m top opening. The volume is 2 / 6 × (80 + 24 × 20 + 168) = 242.7 m³. Cut vertically it would be 160 m³, so the slopes add 82.7 m³.

Backfill

Backfill is the excavated volume less the volume of the structure left below ground. The remaining soil is hauled away.

Limits

Results are bank volumes. Excavated soil swells, so apply a swell factor separately for truck counts. The tool does not suggest a slope angle. Excavation safety depends on the ground investigation and the safety rules.