1. Calculating Cut and Fill
Norman W. Garrick
CE 4410 Spring Lecture 8

2. Average End Area Method
Typically used for linear projects such as roads, railroads, canals

3. Find area of Fill and Cut separately
for selected cross-sections
Volume of Fill (or cut) between
Two Cross-sections
= [(A1 + A2)/2 ] * L
Where:
A1 is area of fill for Cross-section 1
A2 is area of fill for Cross-section 2
L is distance between 1 and 2

4. A refinement to this approach is used
when A1 or A2 is an end cross-section
(there is not fill or cut)
In this case, (A1+A2)/2 * L
Over estimates the volume since
The shape of the earthwork is more
Like a pyramid.
In this case a more accurate formula Is
[(A1+A2)/3] * L
(Note there is an error in text for this formula)

5. Contour Area Method Calculating Cut and Fill

6. Determine the cut/fill line

7. Find the area between the existing and finished contour for cut and fill separately
Contour Line
Cut Area (sq. ft)
Fill Area (sq. ft) 28 26
10000 24
15000 22
30000 20
35000 18
17500 16

8. Calculate Cut and Fill Volumes
Contour Line
Cut Area (sq. ft)
Fill Area (sq. ft) 28 26
10000 24
15000 22
30000 20
35000 18
17500 16
V = A1*h/3 + (A1+A2)*h/2 + (A2+A3*h/2 +…. (An-1+An)*h/2 + An*h/3

9. Calculate Cut and Fill Volumes
Contour Line
Cut Area (sq. ft)
Fill Area (sq. ft) 28 26
10000 24
15000 22
30000 20
35000 18
17500 16
Cut
V = A1*h/3 + (A1+A2)*h/2 + (A2+A3*h/2 +…. (An-1+An)*h/2 + An*h/3
= 10000*2/3 +( )*2/2+( )*2/2*30000*2/3
= cu. Feet
= 3600 cubic yard
Cut
V = A1*h/3 + (A1+A2)*h/2 + (A2+A3*h/2 +…. (An-1+An)*h/2 + An*h/3
= 35000*2/3 +( )*2/ *2/3
= cu. Feet
= 3200 cubic yard

10. Borrow Pit Method Calculating Cut and Fill

11. Find amount of cut or fill needed to create a terrace at elevation 96 ft
Figure 4.5 Textbook

12. Find amount of cut or fill needed to create a terrace at elevation 96 ft
No.1
No.2
No.3
No.4
Figure 4.5 Textbook

13. Find amount of cut or fill needed to create a terrace at elevation 96 ft
Cell No. 1
Cut/Fill at each Corner
B3 Cut 99.4 – 96.0 = 3.4 ft
B4 Cut 98.4 – 96.0 = 2.4 ft
C3 Cut 98.3 – 96.0 = 2.3 ft
C4 Cut 97.8 – 96.0 = 1.8 ft
Average Cut = ( )/4
= 9.9/4 = ft
Amount of Cut Cell No. 1
= Average Cut * Area
= 2.475*10,000
= 24,750 cu. ft
= 24,750/27
= 917 cubic yard
= 920 cubic yard
No.1
No.2
No.3
No.4
Figure 4.5 Textbook

14. Find amount of cut or fill needed to create a terrace at elevation 96 ft
Cell No. 2
Cut/Fill at each Corner
B4 Cut 98.4 – 96.0 = 2.4 ft
B5 Cut 97.1 – 96.0 = 1.1 ft
C4 Cut 97.8 – 96.0 = 1.8 ft
C5 Cut 96.7 – 96.0 = 0.7 ft
Average Cut = ( )/4
= 6.0/4 = 1.5 ft
Amount of Cut Cell No. 1
= Average Cut * Area
= 1.5*10,000
= 15,000 cu. ft
= 15,000/27
= 556 cubic yard
= 560 cubic yard
No.1
No.2
No.3
No.4
Figure 4.5 Textbook

15. Find amount of cut or fill needed to create a terrace at elevation 96 ft
Cell No. 3
Cut/Fill at each Corner
C3 Cut 98.3 – 96.0 = 2.3 ft
C4 Cut 97.8 – 96.0 = 1.8 ft
B3 Cut 96.7 – 96.0 = 0.7 ft
B4 Cut 96.6 – 96.0 = 0.6 ft
Average Cut = ( )/4
= 5.4/4 = 1.35 ft
Amount of Cut Cell No. 3
= Average Cut * Area
= 1.35*10,000
= 13,500 cu. ft
= 13,500/27
= 500 cubic yard
No.1
No.2
No.3
No.4
Figure 4.5 Textbook

16. Find amount of cut or fill needed to create a terrace at elevation 96 ft
Cell No. 4
Cut/Fill at each Corner
C4 Cut 97.8 – 96.0 = 1.8 ft
C5 Cut 96.7 – 96.0 = 0.7 ft
B4 Cut 96.6 – 96.0 = 0.6 ft
B5 Cut 96.0 – 96.0 = 0.0 ft
Average Cut = ( )/4
= 3.1/4 = 0.78 ft
Amount of Cut Cell No. 1
= Average Cut * Area
= 0.78*10,000
= 7,800 cu. ft
= 7.800/27
= 289 cubic yard
= 290 cubic yard
No.1
No.2
No.3
No.4
Figure 4.5 Textbook

17. Find amount of cut or fill needed to create a terrace at elevation 96 ft
Total Volume
Cut
Cell 1 – 920 cu. yd.
Cell cu. yd.
Cell 3 – 500 cu. yd.
Cell cu. yd.
= 2270 cubic yard
No.1
No.2
No.3
No.4
Figure 4.5 Textbook

18. A Calculation Short-cut
Find amount of cut or fill needed to create a terrace at elevation 96 ft
A Calculation Short-cut
Use
V = (A/4)*(1*h1 + 2*h2 + 3*h3 + 4*h4)
Where
V – volume of cut or fill
A – area of each cell
h1 – sum of cuts (or fill) for all grid corners common to one grid
h2 – sum of cuts (or fill) for all grid corners common to two grids
h3 – sum of cuts (or fill) for all grid corners common to three grid
h4 – sum of cuts (or fill) for all grid corners common to four grids
No.1
No.2
No.3
No.4
Figure 4.5 Textbook

19. A Calculation Short-cut
Find amount of cut or fill needed to create a terrace at elevation 96 ft
A Calculation Short-cut
V = (A/4)*(1*h1 + 2*h2 + 3*h3 + 4*h4)
h1 = ( )+( ) )+( ) =
= 5.2
No.1
No.2
No.3
No.4
Figure 4.5 Textbook

20. A Calculation Short-cut
Find amount of cut or fill needed to create a terrace at elevation 96 ft
A Calculation Short-cut
V = (A/4)*(1*h1 + 2*h2 + 3*h3 + 4*h4)
h2 = ( )+( ) )+( ) =
= 6.0
No.1
No.2
No.3
No.4
Figure 4.5 Textbook

21. A Calculation Short-cut
Find amount of cut or fill needed to create a terrace at elevation 96 ft
A Calculation Short-cut
V = (A/4)*(1*h1 + 2*h2 + 3*h3 + 4*h4)
h3 = 0
No.1
No.2
No.3
No.4
Figure 4.5 Textbook

22. A Calculation Short-cut
Find amount of cut or fill needed to create a terrace at elevation 96 ft
A Calculation Short-cut
V = (A/4)*(1*h1 + 2*h2 + 3*h3 + 4*h4)
h4 = ( )
= 1.8
No.1
No.2
No.3
No.4
Figure 4.5 Textbook

23. A Calculation Short-cut
Find amount of cut or fill needed to create a terrace at elevation 96 ft
A Calculation Short-cut
h1 = 5.2
h2 = 6.0
h3 = 0
h2 = 1.8
V = (A/4)*(1*h1 + 2*h2 + 3*h3 + 4*h4)
= (10,000/4)*(1* * *0 + 4*1.8)
= 2260 cubic yards
No.1
No.2
No.3
No.4
Figure 4.5 Textbook

24. Find amount of cut or fill needed to create a terrace at elevation 97 ft
We need to do separate calculations
for cut and fill
Cut
h1 =
h2 =
h3 = 0
h2 = 0.8
V = (A/4)*(1*h1 + 2*h2 + 3*h3 + 4*h4)
= 1000 cubic yards
No.1
No.2
No.3
No.4
Fill
h1 =
h2 =
h3 = 0
h2 = 0
V = (A/4)*(1*h1 + 2*h2 + 3*h3 + 4*h4)
= 250 cubic yards
Figure 4.5 Textbook