Transcript Analysis of Parking & Street Connectivity in Terms of Town

CE 276
Site Design
Prismoidal Cut/Fill Analysis
Wes Marshall, P.E.
University of Connecticut
March 2007
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 crosssections 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
http://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppt
Ground line
Estimating End Area
Fill Area = ∑Shapes
Cut
Fill
http://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppt
Ground line
Computing Volume
Station 1:
Cut Area = 6 ft2
Fill Area = 29 ft2
Cut
Fill
http://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppt
Ground line
Computing Volume
Station 2:
Cut Area = 29 ft2
Fill Area = 5 ft2
Cut
Fill
http://www.ctre.iastate.edu/educweb/ce453/lectures/24%20Mass%20diagram.ppt
Ground line
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 A2
http://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 = 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
1. 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 1
Create Grid
Step 2
Find Avg. Change in Elevation
(existing spot)
proposed spot
Grid Method
1) Lay a grid over a drawing and determine existing/proposed grades at
each node
2) Calculate Cut and Fill at each node
3) Calculate average Cut and Fill
for each grid cell
4) 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 #2 = 3.48 feet cut
Grid Cell #3 = 2.50 feet cut
Grid Cell #4 = 2.30 feet cut
Grid Cell #5 = 2.35 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