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

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

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

Garber and Hoel, 2002

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

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

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

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

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

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

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

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

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

Step 1 Create Grid

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

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

Step 2 Find 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…

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 = 15.85 feet cut Multiply by the Area of one Grid Cell 15.85’(100’)(100’) = 158,500 ft3 → 5,870 yd3

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

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

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