Earthwork and Excavation Volume
Understand the geometric calculations for sloped pits and the 'Swell Factor' which affects disposal costs.
The Geometry of a Pit
When excavating for a footing, we rarely dig a perfectly vertical hole. For safety and accessibility, two factors are usually introduced:
1. Working Space: An extra $300$mm to $600$mm of width around the footing to allow workers to set up formwork and apply waterproofing.
2. Side Slope (Angle of Repose): To prevent the sides from collapsing (cave-in), the pit is often "battered" or sloped outwards. This creates a shape known as a Prismoid or a Frustum of a pyramid.
Prismoidal Formula
Where $A_1$ = Bottom area, $A_2$ = Top area, and $A_m$ = Area at half depth.
What is 'Soil Swell'?
Undisturbed soil in the ground is compacted by the weight of the earth above it. Once excavated, the soil "loosens" and its volume increases by 15% to 30% due to the introduction of air pockets. This is called the Swell Factor ($F_s$).
If your pit is $10$ m³, you might actually need to transport $12$ m³ to the disposal site.
Standard Slope Ratios (H:V)
- Stable Rock: Vertical (0:1)
- Stiff Clay: 0.75 : 1 ($53^\circ$)
- Average Soil: 1 : 1 ($45^\circ$)
- Loose Sand: 1.5 : 1 ($34^\circ$)
Frequently Asked Questions (FAQ)
How many truckloads will I need?
Typical construction dump trucks have a capacity of 5 to 10 cubic meters. When calculating trips, always use the Loose Volume (including swell) to ensure you don't underestimate the hauling costs.