LEC10 Volume Calculation Methods in Construction Surveying

Volume

Used for determining the quantity of earth, gravel, rock, or other material excavated or filled, especially in projects that are not long linear route constructions.
The calculated quantities serve as the basis for payment to the contractor or material supplier.
Applicable for finding the volume of coal or other loose materials in stockpiles.

Area Layout:
- Lay out the area using a total station instrument and tape, or just a tape measure.
Benchmark Establishment:
- Establish a benchmark with a known or assumed elevation outside the area, in a location unlikely to be disturbed.
Elevation Determination:
- Determine elevations at all grid intersection points.
- Designate points with letters and numbers.
Cut or Fill Calculation:
- Calculate the amount of cut or fill at each grid square corner by subtracting the desired leveled elevation from the existing elevation.
Volume Calculation:
- For each square, calculate the average height of the four corners of each prism of cut or fill.
- Multiply the average height by the base area of the square.
Total Volume Calculation:
- Sum the individual volumes for each block.
- Divide the total volume by 27 to convert the result to cubic yards.
- \text{Volume (cubic yards)} = \frac{\text{Total volume (cubic feet)}}{27}

The task is to grade an area to an elevation of 358.0 ft for a building site.
Field notes containing elevation information from borrow-pit leveling are provided.
The area is staked in squares of 20 ft.
The goal is to calculate the volume of material to be excavated from the area.

Field measurements and calculations are recorded in a table.
Benchmark (BM) Road has a backsight (BS) of 4.22, resulting in a Height of Instrument (HI) of 364.70, and an elevation of 360.48.
Cut values are calculated at grid points (A,0 through D,3).
The average height ($\Sigma h_n$) is calculated by summing the cut values at each grid corner.
The table includes point identifiers, backsight readings, HI, foresight readings, elevations, and cut values.
To calculate the total volume that needs to be excavated use the following formula
- \text{Volume} = \frac{\text{area of base} \times \Sigma h_n}{4} Where: area of base is 20 \times 20 = 400 ft^2
- \text{Volume} = \frac{400 \times 22.8}{4} = 2280 ft^3
- \text{Volume in Cubic Yards} = \frac{2280}{27} \approx 84.4 cu.yd

Volumes based on contours can be determined from contour maps using a planimeter to measure the area enclosed by each contour.
Alternatively, CAD software can be used to determine these areas.
The average area of adjacent contours is calculated using the average end area method or coordinate formula.
The volume is obtained by multiplying the average area by the contour spacing (i.e., contour interval).
The prismoidal formula is used only if required for precise calculation.

The volume is calculated based on contour areas.
The contour intervals are at 10 ft increments (910 ft, 920 ft, 930 ft, 940 ft).
Areas within each contour are measured in square inches and converted to acres.
The volume between contours is calculated in acre-feet.
- \text{Volume} = \text{Contour Interval} \times \frac{(\text{Area}1 + \text{Area}2)}{2}
The total volume is the sum of the individual volumes between contours.
Example:
- Contour 910: Area = 1.683 in$^2$ = 9.659 acres
- Contour 920: Area = 5.208 in$^2$ = 29.889 acres
- Contour 930: Area = 11.256 in$^2$ = 64.598 acres
- Contour 940: Area = 19.210 in$^2$ = 110.246 acres
Volume between 910 and 920:
- \text{Volume} = 10 \times \frac{(9.659 + 29.889)}{2} = 197.7 \text{ acre-ft}
Volume between 920 and 930:
- \text{Volume} = 10 \times \frac{(29.889 + 64.598)}{2} = 472.4 \text{ acre-ft}
Volume between 930 and 940:
- \text{Volume} = 10 \times \frac{(64.598 + 110.246)}{2} = 874.2 \text{ acre-ft}
Total Volume = 197.7 + 472.4 + 874.2 = 1544.3 acre-ft

Charles D. Ghilani, Elementary Surveying: An Introduction to Geomatics, 16th edition, Pearson, 2022.
Planimeter, mathematical instrument, Britannica 2025