Calculation of End Area Method in Earthwork

End Area Method, also known as Average End Areas method, is a popular method to estimate the earthwork volume. Like grid method, it is also easy to use, easy to understand and can be carried out by someone even with minimum mathematical training.

The procedure to compute cut and fill volume from End Area Method is simple.

The Procedure #

1. Define cut sections separated by a fix interval, say 25 m. Make sure that your cut sections adequately cover your project area in both latitude and longitude direction, as shown below.

2. For each section, calculate the respective cut and fill area. In MiTS, the cut and fill area for each of the end area section are stated in the cut section view. You can double check the value by measuring the area of the cut and fill by using the CAD command.

3. Compute each section volume by using the formula V_i = \frac{A_{i-1} + A_i}{2} \times L, where:

Example:

Let’s say we are calculating the volume for the End Area 1-8. Considering A_{i-1} ​ is the End Area 1-7, the area is computed in the table below based on the cut section (Image 1.2 & Image 1.3).

	End Area 1-7	End Area 1-8
Measured Cut Area ($\mathrm{m}^2$)	4.13	0.00
Measured Fill Area ($\mathrm{m}^2$)	770.52	1060.46

Using the formula, we compute the volume for cut and fill respectively as below.

Cut Volume	Fill Volume
V = \frac{A_{i-1} + A_i}{2} \times L V = \frac{4.13 + 0.00}{2} \times 25 V = 51.62\,\mathrm{m}^3	V = \frac{A_{i-1} + A_i}{2} \times L V = \frac{770.52 + 1060.46}{2} \times 25 V = 22887.25\,\mathrm{m}^3

4. Tabulate the cut section area and then sum up the volume for both cut and fill in an excel spreadsheet. Then you can already get your end area cut and fill volume.
   Notice the calculated cut and fill volume example in step 3 coincide with the value in the table below. The slight difference is due to the decimal places used in the calculation.

Discussion #

1. Although End Area Method is a popular cut and fill method, but it is by no means the most accurate method. This title goes to DTM ( Digital terrain method)
2. The reason being, like grid method, it depends on the cut section interval. You will have to use extremely small interval to capture accurate earthwork results, if your cross section varies a lot over short interval of space.
3. Also, the cut section is generated from the interpolation of the ground level, which itself is an approximation. So when you are taking the volume as a function of the two subsequent cut section areas, then it is a double approximation, which further reduces the accuracies.
4. Read also on how pavement thickness affect the cut/ fill area and how to ensure cut section tally with the report for more information.