CE 276 Site Design

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

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 http://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppt

6. Estimating End Area Fill Area = ∑Shapes Cut Fill Ground line http://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppt

7. Computing Volume Station 1: Cut Area = 6 ft2 Fill Area = 29 ft2 Cut Fill Ground line http://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppt

8. Computing Volume Station 2: Cut Area = 29 ft2 Fill Area = 5 ft2 Cut Fill Ground line http://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppt

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 http://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppt

10. Prismoidal Formula V = (A1+ 4Am + A2)/6 x L 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 http://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppt

11. http://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppthttp://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppt

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 http://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppt

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 1Create Grid

15. Step 2Find 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 http://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppt

17. Step 2Find Avg. Change in Elevation Vavg = (h1 + h2 + h3 + h4) / 4 Vavg = 3.5+4.4+2.6+3.3 4 Vavg = 3.45 feet of cut Repeat for each grid cell…

18. Step 3Add 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 = 15.85 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