1. Wes Marshall, P.E. University of Connecticut March 2007
CE 276 Site Design
Prismoidal Cut/Fill Analysis
Wes Marshall, P.E University of Connecticut March 2007

2. Average End Area Method
Take cross sections at regular intervals indicating both existing & proposed contours
Calculate the amount of cut & fill at each cross-section based upon existing & proposed grades
Multiply average of two adjacent cross-sections by the length between them

3. Average End Area Method
V = [(A1 + A2) / 2] x L
V = Volume
A1, A2 = Cut/Fill area of cross sections
L = Distance between A1 & A2

4. Garber and Hoel, 2002

5. Estimating End Area Cut Fill Ground line

6. Estimating End Area Fill Area = ∑Shapes Cut Fill Ground line

7. Computing Volume Station 1: Cut Area = 6 ft2 Fill Area = 29 ft2 Cut
Ground line

8. Computing Volume Station 2: Cut Area = 29 ft2 Fill Area = 5 ft2 Cut
Ground line

9. Volume Errors
Average End Area technique leads to volume errors when cross-sections taper between cut and fill sections
Due to these “prisms,” computer-aided calculations often use the Prismoidal Formula

10. V = (A1+ 4Am + A2)/6 x L Prismoidal Formula
Where V is Volume and A1 and A2 are end areas at ends of section
Am = cross sectional area in middle of section, and Am is based on linear measurements at the middle
L = length from A1 to A2

11. http://www. ctre. iastate

12. Consider cone as a prism
Radius = R, height = H
End Area 1 = πR2
End Area 2 = 0
Radius at midpoint = R/2
Volume =((π R2+4π(R/2)2+ 0)/ 6) * H
= (π R2/3) * H

13. Grid Method Also known as the Borrow Pit Method
Create a grid over the area to be graded
Smaller cells → More accurate
For each grid cell
Find the average change in elevation by determining the elevation difference for all four corners of the grid cell
The volume is calculated by
Adding the averaged cut & fill volumes separately
Then multiplying by the area of one grid cell

14. Step 1 Create Grid

15. Step 2 Find Avg. Change in Elevation
(existing spot)
proposed spot

16. Grid Method
Lay a grid over a drawing and determine existing/proposed grades at each node
Calculate Cut and Fill at each node
Calculate average Cut and Fill for each grid cell
Sum Cuts and Fills separately and multiply by the area of one grid

17. Step 2 Find Avg. Change in Elevation
Vavg = (h1 + h2 + h3 + h4) / 4
Vavg =
Vavg = 3.45 feet of cut
Repeat for each grid cell…

18. Step 3 Add Cuts/Fill Separately & Multiply by Grid Cell Area
Grid Cell #1 = 3.45 feet cut Grid Cell #4 = 2.30 feet cut
Grid Cell #2 = 3.48 feet cut Grid Cell #5 = 2.35 feet cut
Grid Cell #3 = 2.50 feet cut Grid Cell #6 = 1.78 feet cut
Add cuts & fills separately
In this case, the site is all cut
Total of Grid Cells = feet cut
Multiply by the Area of one Grid Cell
15.85’(100’)(100’) = 158,500 ft3 → 5,870 yd3

19. Grid Method
The Grid Method is best used for complex grading projects and urban conditions

20. Use the Average End Area Method to find the volumes of cut & fill Stations 0+00 & 2+35 have no cut or fill

21. Use the Contour Area Method to find the volumes of cut & fill