Wes Marshall, P.E. University of ConnecticutMarch 2007

CE 276Site Design

Prismoidal Cut/Fill Analysis

Average End Area Method

1. Take cross sections at regular intervals indicating both existing & proposed contours

2. Calculate the amount of cut & fill at each cross-section based upon existing & proposed grades

3. 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

Ground line

Cut

Fill

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

Estimating End Area

Ground line

Cut

Fill

Fill Area = ∑Shapes

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

Computing Volume

Station 1:

Ground lineCut

Fill

Cut Area = 6 ft2

Fill Area = 29 ft2

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

Computing Volume

Station 2:

Ground line

Cut Area = 29 ft2

Fill Area = 5 ft2

Cut Fill

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

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 A2http://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppt

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

Consider cone as a prism

Radius = R, height = HEnd Area 1 = πR2

End Area 2 = 0Radius at midpoint = R/2Volume =((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 Method1. Create a grid over the area to be graded

Smaller cells → More accurate

2. For each grid cell Find the average change in elevation by determining the

elevation difference for all four corners of the grid cell

3. The volume is calculated by Adding the averaged cut & fill volumes separately Then multiplying by the area of one grid cell

Step 1Create Grid

Step 2Find Avg. Change in Elevation

(existing spot)

proposed spot

Grid Method

1) Lay a grid over a drawing and determine existing/proposed grades at each node2) Calculate Cut and Fill at each node3) Calculate average Cut and Fill

for each grid cell4) 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 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…

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

Grid Method

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