CE 208

Quantity Surveying
(Earthwork Excavation for Roadway)

Md. Sazedul Islam

Lecturer
Department of Civil Engineering
Ahsanullah University of Science and Technology
 Earthwork Embankment

MD. SAZEDUL ISLAM, LECTURER, DEPARTMENT OF CIVIL ENGINEERING, AUST. 23 August 2021 2
 Terms and Abbreviations

EGL (Existing Ground Level) or GL (Ground Level): The existing earth surface

FL (Formation Level): The proposed level of roadway.

RL (Reduced Level): A level stated in relation to a known bench mark or datum.

FL

EGL/GL

Datum

MD. SAZEDUL ISLAM, LECTURER, DEPARTMENT OF CIVIL ENGINEERING, AUST. 23 August 2021 3
 Terms and Abbreviations
Longitudinal Slope/ Gradient: Gradient may be defined as the rate of rise or fall along the length
of highway.
Side Slope: Side slope is defined as the rate of rise or fall of the shoulders of the pavement. It
depends on the soil characteristics and geographic location of the highway.

Longitudinal Slope Side Slope

MD. SAZEDUL ISLAM, LECTURER, DEPARTMENT OF CIVIL ENGINEERING, AUST. 23 August 2021 4
 Calculation of Volume
There are three methods generally adopted for computation of earthwork volume (according to the
formation of the solid). They are:
1. From cross sections: Measurement from cross section is a universally applicable method.
2. From spot levels: measurement from spot levels are applied sometime for large excavation.
3. From contours: Rough estimates of volume may be made by treatment of the contour line and
not much used in practice.

MD. SAZEDUL ISLAM, LECTURER, DEPARTMENT OF CIVIL ENGINEERING, AUST. 23 August 2021 5
 Measurement from Cross Sections
The cross sectional area along the line is first calculated by standard formulae and the volumes of
the prismoids between successive cross-sections are then calculated by following methods:
1. Formulae of Mid-section method/ Average height method.
2. Formulae of Trapezoidal method/ Average end area method/ mean-sectional area method.
3. Formulae of Prismoidal method according to Simpson’s one-third rule.

MD. SAZEDUL ISLAM, LECTURER, DEPARTMENT OF CIVIL ENGINEERING, AUST. 23 August 2021 6
 Mid-section Formula/Average Height Method
Depth section (1) = d1 (note that d1 is the difference between GL & FL) b
Depth section (2) = d2 (note that d2 is the difference between GL & FL)
d1 +d2
Average depth, davg =
2
Width of section = b
Side slope = 1: s (vertical: horizontal)
1
Area of mid-section, Amid = bdavg + 2 × sd2avg
2

Amid = b +sdavg × davg

Length between two consecutive sections (between section (1) & (2)) = L
Volume of earthwork between these two consecutive sections (between section (1) & (2)),
V1-2 = Aavg x L
V1-2 = 𝐛 +𝐬𝐝𝐚𝐯𝐠 × 𝐝𝐚𝐯𝐠 × 𝐋 (may be cut or fill)

MD. SAZEDUL ISLAM, LECTURER, DEPARTMENT OF CIVIL ENGINEERING, AUST. 23 August 2021 7
 Trapezoidal Formula/ Average End Area Method

Depth section (1) = d1 (note that d1 is the difference between GL & FL) b
Depth section (2) = d2 (note that d2 is the difference between GL & FL)
Area at end 1, A1 = b +sd1 × d1
Area at end 2, A2 = b +sd2 × d2
A1 +A2
Mean sectional area, Amean =
2
Width of section = b
Side slope = 1: s (vertical: horizontal)
Length between two consecutive sections (between section (1) & (2)) = L
Volume of earthwork between these two consecutive sections (between section (1) & (2)),
V1-2 = 𝐀𝐦𝐞𝐚𝐧 x L (may be cut or fill)

MD. SAZEDUL ISLAM, LECTURER, DEPARTMENT OF CIVIL ENGINEERING, AUST. 23 August 2021 8
 Prismoidal formula
Depth section (1) = d1 (note that d1 is the difference between GL & FL) b
Depth section (2) = d2 (note that d2 is the difference between GL & FL)
d1 +d2
Average depth, davg =
2
Area at end 1, A1 = b +sd1 × d1
Area at end 2, A2 = b +sd2 × d2
Area of mid-section, Amid = b +sdavg × davg
Length between two consecutive sections (between section (1) & (2)) = L
Volume of earthwork between these two consecutive sections (between section (1) & (2)),

𝐀𝟏 +𝟒 𝐀𝐦𝐢𝐝 +𝐀𝟐
V1-2 = × 𝐋 (may be cut or fill)
𝟔

MD. SAZEDUL ISLAM, LECTURER, DEPARTMENT OF CIVIL ENGINEERING, AUST. 23 August 2021 9
 Worked Out Problem
A 1 km road is to be constructed in existing ground level having reduced levels 54.1, 53.8, 53.5,
53.5, 54.3, 54.6, 54.6, 54.9, 54.5, 54.7 and 54.3 meters at 100 m intervals. A required reduced level
at station 1 is 55 meter and the downward gradient is 1 in 1000. The width of the road at formation
level is 8 meter. Slopes to be maintained at cutting and filling are 1:2 (V: H) and 1:3 (V: H)
respectively. Calculate the volume of Earthwork.

FL

EGL

Figure : Long Section of the Road

MD. SAZEDUL ISLAM, LECTURER, DEPARTMENT OF CIVIL ENGINEERING, AUST. 23 August 2021 10
 Worked Out Problem
A 1 km road is to be constructed in existing ground level having reduced levels 54.1, 53.8, 53.5,
53.5, 54.3, 54.6, 54.6, 54.9, 54.5, 54.7 and 54.3 meters at 100 m intervals. A required reduced level
at station 1 is 55 meter and the downward gradient is 1 in 1000. The width of the road at formation
level is 8 meter. Slopes to be maintained at cutting and filling are 1:2 (V: H) and 1:3 (V: H)
respectively. Calculate the volume of Earthwork.

Figure : Typical Fill Section Figure : Typical Cut Section

MD. SAZEDUL ISLAM, LECTURER, DEPARTMENT OF CIVIL ENGINEERING, AUST. 23 August 2021 11
 Worked Out Problem
FL

EGL

Figure : Long Section of the Road Figure : Length of Cut and Fill between
station 5 & 6.
From figure,

X 100 − X
=
0.3 0.1
=> X= 75 m
MD. SAZEDUL ISLAM, LECTURER, DEPARTMENT OF CIVIL ENGINEERING, AUST. 23 August 2021 12
 Earthwork Computation Table (Mid-section/Average height method)
Depth
FL EGL Average depth Area Length Volume, V = A x L
Station d = EGL ~ FL Remark
(m) (m) davg (m) A = (b + sdavg)davg (m2) L (m) (m3)
(m)
1 55 54.1 0.9
1 (8 + 3 X 1) X 1 = 11 100 1100 Fill
2 54.9 53.8 1.1
1.2 (8 + 3 X 1.2) X 1.2 = 13.92 100 1392 Fill
3 54.8 53.5 1.3
1.25 (8 + 3 X 1.25) X 1.25 = 14.68 100 1468 Fill
4 54.7 53.5 1.2
0.75 (8 + 3 X 0.75) X 0.75 = 7.68 100 768 Fill
5 54.6 54.3 0.3
0.15 (8 + 3 X 0.15) X 0.15 = 1.26 75* 95.06 Fill
0 X X 0
0.05 (8 + 2 X 0.05) X 0.05 = 0.4 25* 10.18 Cut
6 54.5 54.6 0.1
0.15 (8 + 2 X 0.15) X 0.15 = 1.245 100 124.5 Cut
7 54.4 54.6 0.2
0.4 (8 + 2 X 0.4) X 0.4 = 3.52 100 352 Cut
8 54.3 54.9 0.6
0.45 (8 + 2 X 0.45) X 0.45 = 4.01 100 400.5 Cut
9 54.2 54.5 0.3
0.45 (8 + 2 X 0.45) X 0.45 = 4.01 100 400.5 Cut
10 54.1 54.7 0.6
0.45 (8 + 2 X 0.45) X 0.45 = 4.01 100 400.5 Cut
11 54 54.3 0.3

MD. SAZEDUL ISLAM, LECTURER, DEPARTMENT OF CIVIL ENGINEERING, AUST. 23 August 2021 13
 Earthwork Computation (Mid-section/Average height method)

Volume of total cutting = 1688.18 m3

Volume of total filling = 4824.56 m3

FL

Cut EGL
Fill

MD. SAZEDUL ISLAM, LECTURER, DEPARTMENT OF CIVIL ENGINEERING, AUST. 23 August 2021 14
 Earthwork Computation Table (Trapezoidal formula/Average End Area Method)
Depth
FL EGL Area Mean Area Length
Station d = EGL ~ FL Volume, V = A x L (m3) Remark
(m) (m) A = (b+sd)d Amean (m2) L (m)
(m)
1 55 54.1 0.9

2 54.9 53.8 1.1

3 54.8 53.5 1.3

4 54.7 53.5 1.2

5 54.6 54.3 0.3

0 X X 0

6 54.5 54.6 0.1

7 54.4 54.6 0.2

8 54.3 54.9 0.6

9 54.2 54.5 0.3

10 54.1 54.7 0.6

11 54 54.3 0.3

MD. SAZEDUL ISLAM, LECTURER, DEPARTMENT OF CIVIL ENGINEERING, AUST. 23 August 2021 15
 Earthwork Computation Table (Prismoidal formula)
Depth Area Volume, V =
FL EGL Area Average depth Length
Station d = EGL ~ FL Amid = (b + sdavg)davg 𝐀𝟏 +𝟒 𝐀𝐦𝐢𝐝 +𝐀𝟐 Remark
(m) (m)
(m)
A = (b+sd)d davg (m)
(m2)
L (m) × 𝐋 (m3)
𝟔
1 55 54.1 0.9

2 54.9 53.8 1.1

3 54.8 53.5 1.3

4 54.7 53.5 1.2

5 54.6 54.3 0.3

0 X X 0

6 54.5 54.6 0.1

7 54.4 54.6 0.2

8 54.3 54.9 0.6

9 54.2 54.5 0.3

10 54.1 54.7 0.6

11 54 54.3 0.3

MD. SAZEDUL ISLAM, LECTURER, DEPARTMENT OF CIVIL ENGINEERING, AUST. 23 August 2021 16
MD. SAZEDUL ISLAM, LECTURER, DEPARTMENT OF CIVIL ENGINEERING, AUST. 23 August 2021 17