Data Source and Methodology
Authoritative Data Source: US Army Corps of Engineers (USACE), Engineer Manual EM 1110-2-2300 — “Earth and Rock-Fill Dams: General Design and Construction Considerations,” July 2004. Direct PDF. Typical bulking and shrinkage practices for earthwork are documented within USACE earthwork guidance.
Additionally, the volumetric methodology used here aligns with standard civil engineering practice and GIS implementations such as Esri’s Cut/Fill Volume Calculation, which compute volumes by integrating height differences over area.
Statement: All calculations are rigorously based on the formulas and data provided by this source.
The Formula Explained
For each cell i with area A_i and adjusted height difference Δh_i between existing and design grades:
\( \Delta h_i = (E^{\text{existing}}_i - t) - E^{\text{design}}_i \)
\( V_{\text{cut}} = \sum_{i} \max(\Delta h_i, 0)\cdot A_i \quad,\quad V_{\text{fill}} = \sum_{i} \max(-\Delta h_i, 0)\cdot A_i \)
Adjustments for bulking (swell) and compaction (shrinkage):
\( V_{\text{cut, loose}} = V_{\text{cut}} \cdot (1 + s) \quad,\quad V_{\text{borrow, loose}} = \dfrac{V_{\text{fill}}}{1 - c} \)
Where t is topsoil strip thickness, s and c are decimals (e.g., 20% → 0.20).
Glossary of Variables
- Eexisting, Edesign: Existing and design elevations per area or grid cell (m or ft).
- A: Area of the site (Simple mode) or uniform cell area (Grid mode) in m² or ft².
- t: Topsoil strip thickness subtracted from existing elevation (m or ft).
- Δh: Height difference. Positive → cut; negative → fill.
- Vcut, Vfill: In-place volumes before bulking/compaction (m³ or yd³ as applicable).
- s: Bulking (swell) fraction, e.g., 0.20 for 20%.
- c: Compaction fraction, e.g., 0.10 for 10%.
- Vcut, loose: Loose excavated volume after swell (used for haul/export).
- Vborrow, loose: Loose borrow required to achieve compacted fill.
How It Works: A Step-by-Step Example
Scenario: Metric units. Area = 2,000 m². Average existing elevation = 101.2 m. Design elevation = 100.7 m. Topsoil strip t = 0.00 m. Swell s = 20% (0.20). Compaction c = 10% (0.10).
- Compute height difference: Δh = (101.2 − 0.00) − 100.7 = 0.5 m → Cut.
- In-place volumes: Vcut = 0.5 × 2,000 = 1,000 m³; Vfill = 0.
- Loose cut: Vcut, loose = 1,000 × (1 + 0.20) = 1,200 m³.
- Borrow: Vborrow, loose = 0 ÷ (1 − 0.10) = 0 m³.
- Balance: Export 1,200 m³ loose if not reused; import is 0.
Frequently Asked Questions (FAQ)
Do I need to enter negative numbers for fill?
No. Enter actual elevations. The calculator detects whether each cell/area is cut (existing above design) or fill (existing below design).
How accurate are results compared to 3D models?
For conceptual estimates, this 2D height-difference method is standard. For final takeoffs, validate against your project’s digital terrain models (DTMs) or BIM.
What values should I use for bulking and compaction?
They depend on soil type and moisture. Typical ranges: granular soils 10–25% swell; clays 15–40%. Always confirm with geotechnical data and specs.
Can I account for topsoil stripping?
Yes. Enter the strip thickness; the calculator subtracts it from existing elevations before computing volumes.
What unit conversions are shown?
Primary outputs follow your unit setting. A secondary line shows the same volumes converted between m³ and yd³.
How do I know if I need import or export?
If loose cut exceeds borrow required, you have export. If borrow required exceeds loose cut, you need import. The Balance line summarizes this.