8.5 Earthwork Volumes, Contours, and Mass Diagrams

Earthwork Quantity Methods

Earthwork volume is listed in the FS Survey Computations and Computer Applications area because surveyors often support grading, roadway, site, and construction quantity work. Volumes can be estimated from cross sections, grids, contours, or surfaces. The exam usually provides the needed dimensions and asks for the correct formula, sign, or interpretation.

The average end area method is common for route work. If the cross-section area at station 10+00 is 120 square ft and the area at station 11+00 is 180 square ft, the volume between them over 100 ft is (120 + 180)/2 x 100 = 15000 cubic ft. Divide by 27 to convert cubic ft to cubic yards. The method is simple and works best when area changes approximately linearly between sections.

Cut and fill signs should be consistent. Some tables use cut as positive and fill as negative. Others reverse that. The FS problem should define or imply the convention. A net positive number only means surplus if positive has been assigned to cut. Do not assume a sign convention without reading the table headings.

Shrink and swell may appear in practical scenarios. Excavated material may occupy a different volume after removal, compaction, or placement. If a problem gives a shrinkage or swell factor, apply it to the appropriate state of material. Bank cubic yards, loose cubic yards, and compacted cubic yards are not automatically equal.

Mass diagrams plot cumulative earthwork along an alignment. When the curve rises, cumulative cut is increasing under a cut-positive convention. When it falls, fill is consuming material. Peaks and valleys can mark balance points. The slope of the mass curve relates to rate of earthwork, and horizontal distance between balance points can support haul analysis. The FS level is usually conceptual or arithmetic, not full construction estimating software operation.

A grid method divides a site into cells. If a square cell is 50 ft by 50 ft and the average fill depth at its corners is 1.2 ft, the approximate fill volume is 50 x 50 x 1.2 = 3000 cubic ft, or 111.1 cubic yd. If corner depths include both cut and fill, the cell may need subdivision or a method that accounts for the zero-depth line.

A reliable volume workflow is:

1. Identify the data type: sections, grid depths, contours, or surfaces.
2. Confirm units for length, area, and volume.
3. Compute volume in cubic length units first.
4. Convert cubic ft to cubic yd by dividing by 27 when needed.
5. Track cut and fill signs separately before netting.
6. Apply shrink, swell, or compaction factors only when provided.
7. Interpret mass diagrams as cumulative quantity, not ground profile.

Volume questions can look like route surveying, construction surveying, or spreadsheet problems. The arithmetic is manageable if the method matches the data. The best answer keeps quantity basis, units, and sign convention visible.