CE 276 Site Design
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Transcript of CE 276 Site Design
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Wes Marshall, P.E. University of ConnecticutMarch 2007
CE 276Site Design
Prismoidal Cut/Fill Analysis
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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
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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
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Garber and Hoel, 2002
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Estimating End Area
Ground line
Cut
Fill
http://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppt
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Estimating End Area
Ground line
Cut
Fill
Fill Area = ∑Shapes
http://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppt
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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
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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
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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
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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
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http://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppt
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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
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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
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Step 1Create Grid
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Step 2Find Avg. Change in Elevation
(existing spot)
proposed spot
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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
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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…
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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
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Grid Method
The Grid Method is best used for complex grading projects and urban conditions