Measurements for volume are nothing more than applying basic distance and elevation measurements to determine the locations and elevations of points where the volume is to be determined. It usually is not practical to take the time to collect data everywhere there is a slight change in elevation. Therefore, it must be understood that volume calculations do not give exact answers. Typically, approximations must be made and averages determined. The field engineer will analyze the data and make decisions that result in the best estimate of the volume.
The key to volume calculation is the determination of area. Most volume calculation formulas contain within them the formula for an area, which is simply multiplied by the height to determine the volume. For instance, the area of a circle is pi times the radius squared. The volume of a cylinder is the area of the circle times the height of the cylinder. If an area can be determined, it is generally easy to determine the volume.
2. Counting Squares
Approximation is possible by plotting the figure to scale on cross-sectional paper and counting the squares. Each square represents x number of square feet. Incomplete squares along the edges of the cross section are visually combined and averaged.
The electromechanical digital planimeter is a quick method of determining the area of irregularly shaped figures. The irregular shape is drawn to scale and the planimeter is used to trace the outline of the shape. Inputting a scale factor into the planimeter results in a digital readout of the area.
4. Geometric Formula
Although a shape at first may seem irregular, it is often possible to break it into smaller regular shapes such as squares, rectangles, triangles, trapezoids, etc., that will allow the use of standard geometric formulas to determine the area. This method may be cumbersome because of all the shapes that may need to be calculated.
5. Cross-Section Coordinates
If cross-sectional field data are available, use of this data is the recommended method of calculating volume. Once understood, this process is fast and the most accurate way of determining area. Cross-section data collected on a project represent elevation and location information for points on the ground. These points can be used as coordinates to determine area.
Volume Computations — Road Construction
In road construction the shape of the ground must be changed to remove the ups and downs of the hills and valleys for the planned roadway. Often mountains of dirt must be moved to create a gentle grade for the roadway. Payment for the removal and placement of dirt is typically on a unit cost basis. That is, the contractor will be paid per cubic yard of soil and will receive a separate price per cubic yard of rock.
It can be seen that accurate determination of the volume moved is critical to the owner and to the contractor. Each wants an accurate volume so payment for the work is correct.
For road projects, cross sections of the ground elevations are measured at the beginning of the project, during the project, and at the end of the project. Comparisons between final cross sections and original cross sections are used to determine the volume moved. Areas of the cross sections are most easily determined by using the elevations of the points and their locations from the centerline (coordinates).
The average end area method uses the end areas of adjacent stations along a route and averages them. Refer to fig-1. This average is then multiplied by the distance between the two end areas to obtain the volume between them. In formula form the process is as follows:
Volume = [L/27]*[(Area 1 + Area 2)/2]
where L represents the distance between the cross-sectional end areas being used in the formula, and 27 represents the number of cubic feet in 1 cubic yard. Dividing cubic feet by 27 converts to cubic yards.
Volume Computations — Building Excavation
A method known as borrow-pit leveling can be used effectively to determine volume on building projects.
A grid is established by the field engineer and elevations on the grid points are determined both before the excavation begins and when the work is complete.
The borrow-pit method uses a grid and the average depth of the excavation to determine the volume. Before the excavating begins the field engineer creates a grid over the entire area where the excavation is to occur. Elevation data are collected at each of the grid points and recorded for future reference. At any time during the excavating, the field engineer can reestablish the grid and determine new elevations for each of the field points. Using the average height formula shown below, the volume of soil removed from each grid area can be determined. Refer to fig-2. The smaller the grid interval, the more accurate the volume.