Highway Geometric Design Earthworks 2014 2015
Highway Geometric Design Earthworks 2014 2015
Highway Geometric Design Earthworks 2014 2015
GEOMETRIC
DESIGN
6.0. EARTHWORK
COMPUTATIONS
6.1. INTRODUCTION
Earthworks
Earthworks
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6.1. INTRODUCTION
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6.1. INTRODUCTION
Applications
of Earthworks :
works
Railways
Irrigation projects (dams, canals, etc)
etc
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Road
Earthworks
a).
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Calculated
Area,
A S S a S b S c
OR:
OR:
1
a b c
2
1
ab Sin C
2
where : C angle between side lengths a & b.
C
b
North
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Standard
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B (E2, N2)
C(E3, N3)
N 1)
,
(E 1
Area
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B (E2, N2)
C(E3, N3)
N 1)
,
(E 1
Area
Area
of
1
ABQP:2 N1 N 2 E 2 - E1
of
1
N 2 N 3 E 3 - E 2
BCRQ:
2
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B (E2, N2)
C(E3, N3)
N 1)
,
(E 1
Area
of ACRP
1
:2 N1 N 3 E 3 - E1
10
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B (E2, N2)
C(E3, N3)
N 1)
,
(E 1
Area
11
Graphical method:
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Squares
Trapezoidal rule
Assumption:
Trapezoidal rule
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Generally,
A
ON
area A:
L
O1 O N 2 O 2 O 3 O 4 .... O N1
2
offsets
13
Simpsons rule
Offsets
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Assumption:
L
O1 4O 2 O 3 ,
3
L
A 3 A 4 O 3 4O 4 O 5
3
A1 A 2
Generally,
area A =L/3(O1+ON+4even
offsets+2 remaining odd offsets), N= number
of offsets.
14
Planimeter
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Mechanical
15
PLANIMETE
R:
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16
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Cross
A1 A 2
2
Average
Volume
If
area:
L A1 A 2
2
of earthworks:
L A 2 A 3 sections,
L A 3 A 4
L A1 A
L A ntotal
2
1 A n volume:
there
are
then
n cross
......
2
2
2
Can be further simplified to :
L
A1 2A 2 2A 3 2A 4 ..... 2A n-1 A n
2
17
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h
a b
2
a 2ft, b 2 (1.5x2) 2 3 5ft
3
A1 2 5 1.5x7 10.5ft 2
2
Similary, A 2 :
A1
h
a b
2
a 2ft, b 2 (1.0x2) 2 2 4ft
2
A 2 2 4 6ft 2
2
A2
18
Thus, Volume, V
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L
A1 A 2 100 10.5 6 825ft 3
2
2
19
Prismoidal formula
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Volume
20
Prismoidal formula
If
3 cross sections:
L
A4, A5 were added then:
V35 A 3 4A 4 A 5
3
Volume
In
L
A1 4A 2 A 3
3
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For
V13
L
for 1 to 5 sections:
V A
15
4A 2 2A 3 4A 4 A 5
L
A1 A n 4 even areas 2 remaining odd areas
3
21
Diagram
gives:
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Bulking
Cut
Fill
Borrow
23
general:
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Cut
24
Cut
Fill
Borrow
25
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26
excess cut:
embankment width
Greater embankment height
Flatter side slopes
If
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Greater
deficit of fill:
Deeper
cutting
Wider cutting
Import/borrow material
However,
EARTHWORK COMPUTATIONSVOLUMES
Homework
Cut area
(cm2)
20
10
Fill area
(cm2)
12
20
30
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Cross
28