This document provides examples and steps for calculating earthwork quantities for roads and canals. It includes sample problems showing how to calculate the cross-sectional area of a canal cutting using the width, depth, and side slopes. It also shows how to calculate earthwork quantities using the mid-sectional area method and mean sectional area method by considering the ground level, formation level, height/depth at different stations, and length between stations. Formulas and tables with chainage, height, depth, areas, and quantities are provided for illustrative examples.

1. EARTHWORK FOR
ROADS AND CANALS
Prepared By:
B.Govinda Rajulu

4. ➔

8. Sl.
No
Chainage
/ Station
Depth /
Height
Mean Depth
/ Height (d)
Width (B) Area of
central portion
(BXd)
Area of sides
(Sd²)
Total sectional
Area
A = (Bd+Sd²)
Length
(L)
Quantity
Q = A X L
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Sl.
No
Chainage
/ Station
Depth /
Height
(d)
Width
(B)
Area of
central
portion (BXd)
Total (A1)
sectional Area
(Bd1 + Sd1²)
Total (A2)
sectional
Area
(Bd2+ Sd2²)
Mean sectional
Area
A = (A1+A2)/2
Length
(L)
Quantity
Q = A X L
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

9. Example – 1:
A canal is in cutting and has a width of 4.00 m at bottom of the depth of cutting is 2.00 m and side slopes are
1 ½ : 1, find the area of cross section?
Solution: Given Data: - Width of canal = 4.00m; Depth of the cutting = 2.00 m; Side slopes = 1 ½ : 1 ( S: 1 / n: 1)
Area of c/s of canal = (b+nd)d (or) Bd + Sd²
(4 + 1.5*2)2 (or) 4x2 + 1.5 x 2²
4+3*2 (or) 8 + 6
= 14.00 Sq.m (or) 14.00 Sq.m

10. Example – 2:
A) Mid sectional area method.
A) Mean sectional area method.
Solution:

11. Mid - Sectional Area Method:
Volume of earth work (V) = Area of Mid point X Length
Area of the Midpoint = (b+nd)xd
Where b= 10 m, n = 1.5, d = 1+2+3/3 = 2 m. Am = (10 + 1.5*2)x2 = 26 sq. m
Therefore Volume of earthwork (V) = 26 X 120m = 3120 cu m.

12. Chainage 0 50 100 150 200
R. L of Ground 97.00 96.50 96.00 97.50 98.00

13. Height of the
Bank / Cutting
3.00 3.50 4.00 2.50 2.00
Formation Level 100.00 100.00 100.00 100.00 100.00
R. L of Ground 97.00 96.50 96.00 97.50 98.00
Chainage 0 50 100 150 200

14. …………

17. ₹
₹
Chainage 10 11 12 13 14 15 16 17 18 19 20
R. L of Ground 105 105.60 105.44 105.90 105.42 104.30 105.00 104.10 104.62 104.00 103.30
R.L of Formation 107 Down gradient 1 in 150 Down gradient 1 in 100

18. Depth of
cutting
- - - - - - - - - - -
Height of bank 2.00 1.20 1.16 0.50 0.78 1.60 0.60 1.20 0.38 0.70 1.10
R. L of
Formation
107 106.80 106.60 106.40 106.20 105.90 105.60 105.30 105 104.70 104.40
R. L of Ground 105 105.60 105.44 105.90 105.42 104.30 105 104.10 104.62 104 103.30
Distance in m 300 330 360 390 420 450 480 510 540 570 600
Chainage 10 11 12 13 14 15 16 17 18 19 20

19. Station/
Chainage
Length Height /
Depth
Mean
Height/
Depth
(d)
Central
Area (Bd)
Side
Area
(Sd²)
Total
Section
Area
(Bd +Sd²)
Length in
b/w
stations
(L)
Quantity (Bd+Sd²) X L
Banking Cutting
10 300 2.00 - - - - - - -
11 330 1.20 1.60 16.00 5.12 21.12 30 633.60 -
12 360 1.16 1.18 11.80 2.78 14.58 30 437.40 -
13 390 0.50 0.83 8.30 1.38 9.68 30 290.40 -
14 420 0.78 0.64 6.40 0.82 7.22 30 216.60 -
15 450 1.60 1.19 11.90 2.83 14.73 30 441.90 -
16 480 0.60 1.10 11.00 2.42 13.42 30 402.60 -
17 510 1.20 0.90 9.00 1.62 10.62 30 318.60 -
18 540 0.38 0.79 7.90 1.25 9.15 30 274.50 -
19 570 0.70 0.54 5.40 0.58 5.98 30 179.40 -
20 600 1.10 0.90 9.00 1.62 10.62 30 318.60 -
TOTAL QUANTITY 3513.60 Cu m

20. Station/Ch
ainage
Length Height/
Depth
Area of
central
portion (Bd)
Area of
sides (Sd²)
Total Sectional
Area
(Bd +Sd²)
Mean
sectional
Area
Length b/w
stations
Quantity (Bd + Sd²) X L
Banking Cutting
10 300 2.00 20.00 8.00 28.00 - - - -
11 330 1.20 12.00 2.88 14.88 21.44 30 643.20 -
12 360 1.16 11.60 2.69 14.29 14.59 30 437.70 -
13 390 0.50 5.00 0.50 5.50 9.90 30 297.00 -
14 420 0.78 7.80 1.22 9.02 7.26 30 217.80 -
15 450 1.60 16.00 5.12 21.12 15.07 30 451.95 -
16 480 0.60 6.00 0.72 6.72 13.92 30 417.60 -
17 510 1.20 12.00 2.88 14.88 10.80 30 324.00 -
18 540 0.38 3.80 0.29 4.09 9.49 30 284.4 -
19 570 0.70 7.00 0.98 7.98 6.03 30 180.90 -
20 600 1.10 11.00 2.42 13.42 10.70 30 321.00 -
TOTAL QUANTITY 3575.10 cu m

21. Station /
Chainage
Length/
Distance
Height / Depth Mean Height /
Depth (d)
Sloping
Breadth of side
slope d√s²+1
Length in
between stations/
chainage
Total Area of both side
slopes (2X L X d√s²+1)
10 300 2.00 - - - -
11 330 1.20 1.60 3.58 30 214.80
12 360 1.16 1.18 2.63 30 157.80
13 390 0.50 0.83 1.85 30 111.00
14 420 0.78 0.64 1.42 30 85.80
15 450 1.60 1.19 2.65 30 159.60
16 480 0.60 1.10 2.45 30 147.60
17 510 1.20 0.90 2.00 30 120.60
18 540 0.38 0.79 1.77 30 106.20
19 570 0.70 0.54 1.20 30 72.60
20 600 1.10 0.90 2.00 30 120.60
TOTAL QUANTITY 1294.80 sq m

22. Item no Particulars of item Quantity Unit Rate Per Amount in
₹.
1 Earth work in Banking 3513.06 Cu m 345 % cu m 12,120.00
2 Turfing/ pitching for Side slopes 1294.80 Sq m 270 % sq m 3495.96
TOTAL COST in Rs. 16,000.00

23. ₹
Chainage / Station / Distance of the point R. L. of Ground Level
420 118.60
450 119.25
480 119.40
510 118.85
540 118.50
570 117.25
600 116.80
630 117.15
660 117.20

24. Chainage 420 450 480 510 540 570 600 630 660
R.L. of G.L 118.60 119.25 119.40 118.85 118.50 117.25 116.80 117.15 117.20
R.L. of F.L 118.60 118.45 118.30 118.15 118.00 117.85 117.70 117.55 117.40
Height of the bank 0 - - - - 0.60 0.90 0.40 0.20
Depth of the Cutting 0 0.80 1.1 0.7 0.50 - - - -

25. Chainage R.L of
Ground
Distance Height /
Depth
Mean
height /
depth
Central
Area (Bd)
Area of
sides
(Sd²)
Total Sectional
Area (Bd+Sd²)
Length b/w
stations
Quantity (Bd+Sd²) X L
Banking Cutting
420 118.60 420 0 - - - - - - -
450 119.25 450 - 0.80 -0.40 4.80 0.24 5.04 30 - 151.20
480 119.40 480 -1.10 -0.95 11.40 1.35 12.75 30 - 382.50
510 118.85 510 -0.70 -0.90 10.80 1.22 12.02 30 - 360.60
540 118.50 540 -0.50 -0.60 7.20 0.54 7.74 30 - 232.20
passes 118.50 0 0 -0.25 3.00 0.09 3.09 14 - 43.26
570 117.25 570 0.60 0.30 3.60 0.18 3.78 16 60.48 -
600 116.80 600 0.90 0.75 9.00 1.23 10.23 30 306.90 -
630 117.15 630 0.40 0.65 7.80 0.85 8.65 30 259.50 -
660 117.20 660 0.20 0.30 3.60 0.18 3.70 30 113.40 -
Total Quantity 740.28
Cu m
1169.76
Cu m

26. Station /
Chainage
Height / Depth Mean Height / Depth
(d)
Sloping Breadth of
side slope d√s²+1
Length in between
stations/ chainage
Total Area of both side slopes
(2X L X d√s²+1)
420 0.00
450 - 0.80
480 -1.1 Being Cutting - No Turfing is to be taken.
510 -0.70
540 -0.50
Passes 0.00
570 0.60 0.30 0.67 16 21.44
600 0.90 0.75 1.68 30 100.80
630 0.40 0.65 1.45 30 87.00
660 0.20 0.30 0.67 30 40.20
TOTAL QUANTITY 249.54 sq .m

27. Item no Description of item Quantity Unit Rate Per Amount in
₹.
1 Earth work in Cutting 1169.76 Cu m 13.00 Cu m 15,206.88
2 Earthwork in banking 740.28 Cu m 13.00 Cu m 9,623.64
3 Turfing/ pitching for Side slopes 294.54 Sq m 9.00 Sq m 2,650.86
Sundries 518.62
TOTAL COST in Rs. 28,000.00

28. Chainage / Distance / Station R.L. of Ground
0 78.10
20 77.74
40 77.80
60 78.20 & 80.40
80 80.75
100 80.20
120 79.98

29. Chainage 0 20 40 60 80 100 120
R.L. of Ground 78.10 77.74 77.80 78.20
&
80.40
80.75 80.20 79.98
Formation Level 78.50 78.70 78.90 79.10 79.30 79.50 79.70
Height of Bank 0.40 0.96 1.10 0.90 - - -
Depth of Cutting - - - 1.30 1.45 0.70 0.28

30. Chainage R.L of
Ground
Distance Height /
Depth
Mean
height /
depth
Central
Area (Bd)
Area of
sides
(Sd²)
Total Sectional
Area (Bd+Sd²)
Length b/w
stations
Quantity (Bd+Sd²) X L
Banking Cutting
0 78.10 0 0.40 - - - - - - -
20 77.74 20 0.96 0.68 8.16 0.92 9.08 20 181.60 -
40 77.80 40 1.10 1.03 12.36 2.12 14.48 20 289.60 -
60 78.20 60 0.90 1.00 12.00 2.00 14.00 20 280.00 -
60 80.40 60 -1.30 - - - - - - -
80 80.75 80 -1.45 -1.375 -16.50 1.89 18.39 20 - 367.80
100 80.20 100 -0.70 -1.075 -12.90 1.16 14.06 20 - 281.20
120 79.98 120 -0.28 -0.49 -5.88 0.24 6.12 20 - 122.40
Total Quantity 751.20
Cu m
771.40
Cu m