1. Wes Marshall, P.E. University of Connecticut March 2007
CE 276 Site Design
Chapter 7 – Earthwork
Wes Marshall, P.E University of Connecticut March 2007

2. Chapter 7 Earthwork

3. Definitions

4. Definitions
Subgrade
The top of the material on which the surface material is placed
Top of a fill situation & bottom of a cut
Compacted subgrade must attain a specified density
Undisturbed subgrade has not been changed or excavated

5. Definitions Base / Sub-base
Imported material that is typically placed under pavements
Typically a course or fine aggregate

6. Definitions Finished Grade
Final grade after all landscaping has been completed (i.e. top surface of lawns, pavements, etc.)
Typically designated with contours and spot elevations on a grading plan

7. Definitions Finished Floor Elevation (FFE)
Typically the elevation of the first floor of a structure
However, it can be used for any floor
The relationship of FFE to the exterior grades depends upon the type of construction

8. Cut & Fill
plan
section

9. Other Definitions Cut & Fill Cut The process of removing soil
plan
section
Cut
The process of removing soil
Proposed contours extend across existing contours in the uphill direction
Cut

10. Other Definitions Cut & Fill Fill The process of adding soil
plan
section
Fill
The process of adding soil
Proposed contours extend across existing contours in the downhill direction
Fill
Cut

11. Other Definitions Compaction Topsoil Borrow
The densification of soil under controlled conditions, sometime with a specified moisture content
Topsoil
Typically the top layer of a soil profile that can range from ~ one inch up to ~ one foot
Highly organic & subject to decomposition
Therefore not suitable for structures
Borrow
When fill material needs to be imported to a site, it is sometimes referred to as borrow

12. Cut & Fill Factors that influence your cut & fill grading decisions…
Cost
Nature of the site including size & shape
Aesthetics
Intricacy of the grading plan
Soil types & suitability for use
Surrounding uses & elevations

13. Cut & Fill In situations where you cannot balance cut & fill…
It is generally better to use more cut than fill (unless there are very specific soil requirements such as with an athletic playing field)

14. Cut & Fill
Why?
Importing soil tends to be more expensive than removing soil
A fill condition is usually structurally less stable and more susceptible to erosion & settlement
Buying soil, hauling, compacting

15. Calculating Cut & Fill 3 methods of estimating cut & fill volumes
Average End Area Method
Contour Area Method
Grid Method
Volumes ares

16. Calculating Cut & Fill
Earthwork volumes are typically measured in cubic yards…
Keep in mind that cubic feet (ft3) must be divided by 27 ft3/yd3 to convert to cubic yards (yd3)

17. 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

18. 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

19. Average End Area Method
Keep in mind that the vertical scale is usually exaggerated by 5 or 10 times
This is needed because the vertical change is usually a lot smaller than the horizontal scale
It helps you see what is really going on

20. Average End Area Method
The Average End Area Method is best used in linear situations such as:
Roads
Paths
Utility work

21. Contour Area Method Using the grading plan with existing &
proposed contours:
Establish the “no cut - no fill” limit line
Separate the area of cut from the area of fill
Keeping cut & fill separate… Measure the horizontal area of change for each contour line within limit line

22. V = A1h/3 + (A1+A2)h/2 + … + (An-1+An)h/2 + Anh/3
Contour Area Method
V = A1h/3 + (A1+A2)h/2 + … + (An-1+An)h/2 + Anh/3
V = Volume
A1, A2 , An = Area of horizontal change for each contour
h = Vertical distance between areas

23. Contour Area Method V = i(A1 + A2 + … + An)
If h equals i (the contour interval) Then the equation can be simplified as follows:
V = i(A1 + A2 + … + An)
V = Volume
A1, A2 , An = Area of horizontal change for each contour
i = Contour interval
This form of the equation often overestimates volumes…

24. Contour Area Method

25. Step 1 No Cut - No Fill Line

26. Step 2 Line Between Cut & Fill

27. Step 3 Measure Area of Cut & Fill for each contour line

28. Repeat for Each Contour Line
For the 72’ Contour Line
Approximate area of Cut = 284 ft3
Approximate area of Fill = 1,056 ft3
Repeat for Each Contour Line

29. Total Cut & Fill Approximate Total Cut = 1,280 ft3
Approximate Total Fill = 3,216 ft3
Divide by 27 ft3/yd3 to find square yards
Cut = 47.4 yd3
Fill = yd3

30. Contour Area Method
The Contour Area Method is best used for large, relatively uncomplicated grading plans as well as for calculating the volume of water in lakes or ponds

31. 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

32. Step 1 Create Grid

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

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

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

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

37. Adjusting Cut & Fill Volumes
For estimating purposes
Cut & fill volumes are determined for the volume in between existing & proposed subgrades (not the finished grades)
Since grading plans depict finished grade, we typically make adjustments…

38. Adjustment Principles
The depth of the proposed surfacing material (i.e. pavement, topsoil, etc.)
Increases the amount of Cut needed
Decreases the amount of Fill needed

39. Adjustment Principles
The removal of existing surfacing (i.e. pavement, topsoil, etc.)
Decreases the amount of Cut needed
Increases the amount of Fill needed

40. Adjusting Cut & Fill Volumes
If we remove topsoil…
Multiply the area by the depth
For example…
6” of topsoil over 60,000 ft2 of area
= 30,000 ft3 less cut or more fill
If we are installing a pavement…
6” concrete slab w/ 4” gravel base
= 49,800 ft3 more cut or less fill

41. Adjusting Cut & Fill Volumes
If the depth of the
Removed surface & proposed surface are the same
Then no adjustment is needed...
They cancel each other out

42. Adjusting Cut & Fill Volumes
Another factor affecting cut & fill volumes is compaction
Cut volumes (existing in-place soil) will typically yield less than their full volume when used as fill by 10 to 20%
This means that 100 yd3 of material cut will only result in 80 to 90 yd3 of fill

43. Adjusting Cut & Fill Volumes
Therefore, for estimating purposes, fill volumes should be increased by 10 to 20% (depending on the type of soil)

44. It saves money and is the most energy efficient option
Balancing Cut & Fill
Balancing cut & fill on-site is often a goal of the grading process…
It saves money and is the most energy efficient option

45. On a balanced site, no earth needs to be hauled to or from a site
Balancing Cut & Fill
On a balanced site, no earth needs to be hauled to or from a site

46. Balancing Cut & Fill
Taking into account compaction, we would then require a cut to fill ratio between 1.1 & 1.2
Achieving this is typically a process of trial & error

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

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