8/17/2014
Double-Rodded Leveling
Double-Rodded
Double
Rodded
Leveling
A
method of determining the differences in
elevation between points by employing two level
routes simultaneously
 Two turning points are established such that at
each set up of the leveling instrument, two sets of
independent backsights and foresights are taken
Double-Rodded Leveling
 Advantage: provide a continuous check on the
process of determining ground elevations while the
work is in progress
 Useful when there is an urgent need to undertake
differential leveling in a short period of time where
no established benchmarks are available for
checking results
results.
Illustrative Problem
 Complete the following differential level notes for a double-
rodded line from BM1 to BM2. Show the customary
arithmetic check.
STA
BS
HI
FS
BM1
1.86
1.86
TP1 H
L
2.15
2.52
1.10
1.58
TP2 H
L
1.40
1.76
1.79
2.27
TP3 H
L
0.33
0.74
2.99
3.41
BM2
ELEV
205.60m
2.63
2.63
1
8/17/2014
Illustrative Problem
 Arithmetic Check
 1st Method
• Mean Elev BM2 =
 2nd Method
• Mean Elev BM2 = BM1 + [(ΣBS-ΣFS)/2]
• DE1 = (ΣBS-ΣFS)/2
Three-Wire
Leveling
• DE2 = BM1 – Mean Elev BM2
Three-Wire Leveling
 More p
precise method
 Method of determining the differences in elevation
wherein three horizontal hairs are read and
recorded rather than from a single horizontal hair
 Any level equipped with three horizontal cross
g
hairs can be used for three-wire leveling
Three-Wire Leveling
s = a-b
m = (a
(a+b+c)/3
b c)/3
HD = Ks + C
Elev = HI - m
a = upper stadia hair reading
b = lower stadia hair reading
c = horizontal cross hair reading
s = stadia intercept
- difference
diff
b
between
t
th
the upper
and lower stadia hair reading
m = mean of the three-hair readings
HD = horizontal distance from the level to
the rod
K = stadia interval factor (100)
C = instrument constant (0)
2
8/17/2014
Illustrative Problem
BACKSIGHT
STA
HAIR
RDGS
MEAN
RDG
FORESIGHT
S
HI
HAIR
RDGS
MEAN
RDG
S
ELEV
 Arithmetic Check
 1st Method
• DE1 = (ΣBSm-ΣFSm)/2
BM1
1.15
0.95
0.72
TP1
2.79
2.42
2.06
1.11
0.89
0.68
TP2
1.70
1 44
1.44
1.18
1.90
1 54
1.54
1.17
TP3
2.59
2.10
1.59
1.45
1.18
0.95
BM2
Illustrative Problem
 2nd Method
• Elev BM2 = BM1 + ΣBS - ΣFS
445.20
• DE2 = Elev BM1 – Elev BM2
1.60
1.35
1.25
Profile Leveling
P fil L
Profile
Leveling
li
 The process of determining differences in elevation
along a fixed line at designated short measured
intervals
 Design and construction of roads, railroads, canals,
culverts, bridges, sewer lines (horizontal structures)
 Usually taken along the centerline with the level set up
a convenient distance away from it so that sights of
more uniform lengths can be obtained
3
8/17/2014
Profile Leveling
 Any number of foresights can be taken
 Intermediate
I t
di t foresights
f
i ht are taken
t k where
h
necessary to
t
portray accurately the existing ground surface along the
route surveyed
Profile Leveling
 Profile
 A curved line which graphically portrays the intersection
of a vertical plane with the surface of the earth
 Represent the ground elevations of selected critical
points along a surveyed line and the horizontal distances
between these points
 Stationing
 A numerical designation given in terms of horizontal
distance any point along a profile line is away from the
starting point
Profile Leveling
Illustrative Problem
 Intermediate foresights (ground rod readings)
 Taken along the centerline of the proposed project to
provide an accurate representation of the ground surface
 A schematic arrangement of a profile level route from BM3 to BM4
 Full stations
 Points which are established along the profile level route
at uniformly measured distances
 Plus stations
 Points established along a profile level route which is not
designated as a full station
 Points taken at breaks in the ground surface slope and at
critical points (location of culverts, bridges)
are shown below. The values indicated represent
p
backsight,
g ,
foresight, and intermediate foresight readings taken on stations
along the route. Prepare and complete profile level notes for the
portrayed information. Show the customary arithmetic check and
plot the profile. 2+00
HI
1+00
2
3+00
0+00
BM4
TP1
HI1
4+50
5+50
6+70
6+00
BM3
Elev 300.50m
4
8/17/2014
Illustrative Problem
Illustrative Problem
303
BM3
BS
HI
FS
IFS
2.4
300.50m
0+00
1.5
1+00
2.0
2+00
1.3
3+00
0.7
TP1
2.55
3.2
4+50
2.8
5+50
3.5
6+00
4.5
6+70
3.95
BM4
ELEV
302
ELEVATION (m)
E
STA
301
300
299
3.3
298
0+00
1+00
2+00
STATIONINGS
3+00
4+00
Illustrative Problem
 Arithmetic Check
• Elev BM4 = BM3 + ΣBS - ΣFS
Reciprocal Leveling
5
8/17/2014
Reciprocal Leveling
 Employed to determine the difference in elevation
between two points when it is difficult or impossible
to keep backsights and foresights short and equal
 Such conditions are running a line of levels across
wide rivers, lakes, and rugged terrain (deep
canyons)
 Two sets of rod readings are observed (Method of
Reversion)
Reciprocal Leveling
 Errors due to refraction by the atmosphere,
curvature of the earth and faulty adjustment of the
instrument are significantly reduced if not
eliminated
 One set taken with the instrument set up close to one
point and another instrument on the other
Reciprocal Leveling
Illustrative Problem
 In leveling across a deep and wide river, reciprocal level
DE 1 a  b
DE2  a 'b'
Instrumental errors and the effect
of curvature and refraction
DE1 ≠ DE2, » »
TDE 
*Note:
DE 1 DE2 (a  b)  (a 'b' )

2
2
readings were taken between two points, X and Y as
follows:
a. With instrument set up near X, the rod readings on X
are 1.27 and 1.265 meters; on the distant point Y, the
rod readings are 2.50, 2.52, 2.55, and 2.49 meters.
b. With instrument set up near Y, the rod readings on Y are
3 48 and 3.47
3.48
3 47 meters; on the distant point X
X, the rod
readings are 2.13, 2.14, and 2.145 meters.
Determine the true difference in elevation between the two
points and the elevation of Y if the known elevation of X
is 289.90meters.
If TDE is negative, A is higher than B;
If TDE is positive, B is higher than A.
6
8/17/2014
Illustrative Problem
Elev=289.90m
T i
Trigonometric
t i Leveling
L
li
Instrument Set up near X
STA
BS
X
1.27
FS
Instrument Set up near Y
STA
BS
X’
2.13
1.265
Y
FS
2.14
2.50
2 50
2.52
2.145
Y’
2.55
2.49
SUM
3.48
3.47
SUM
MEAN
MEAN
Trigonometric Leveling
Trigonometric Leveling
 “Indirect Leveling”
 Determine
D t
i th
the diff
difference iin elevation
l
ti ffrom
observed vertical angle and either horizontal or
inclined distances
 Used extensively when undertaking topographic
surveys over rugged or rolling terrain since it
provides a rapid means of determining vertical
distances and elevation of points
V  dTan
V  sSin
DEab  dTan  HI  RR
DEab  sSin  HI  RR
ElevB  ElevA  DEab
7
8/17/2014
Trigonometric Leveling
Illustrative Problem
 For horizontal distance is greater than 300 meters,
 A vertical angle of +13°45’ is read to a target
effects of the earth’s
earth s curvature and refraction must
be considered in the calculation of the vertical
distances.
d 2
DEab  dTan  HI  RR  0.0675(
)
1000
d 2
DEab  sSin  HI  RR  0.0675(
)
1000
1.23m
1
23m above point B.
B the measured inclined
distance, s, is 823.29m and the elevation of A is
123.65m above datum. If the HI at A is 1.35m,
determine the difference in elevation between A
and B and the elevation of B, considering the
p
refraction.
effects of curvature and atmospheric
Illustrative Problem
Cross-Section
Leveling
8
8/17/2014
CROSS-SECTION LEVELING
 Short profiles taken perpendicular to the centerline
of projects such as a highway
highway, railroad
railroad, irrigation
canal, or sewer line
 They may also be taken for borrow pits and
excavations required for buildings, structures, and
quarries.
Roadway Cross-Sections
Borrow-Pit Cross Sections
ROADWAY CROSS-SECTION
 This type of cross-section is
required for most route
projects such as roads and
railroads.
 Elevations of ground points
along the section are taken at
regular intervals on either side
side.
Where significant changes
occur in ground features,
ground elevations are also
taken.
BORROW-PIT CROSS-SECTION
 Employed in the construction of structures and buildings,
and in the excavation of borrow pits.
 Borrow pit is an open area which is usually adjacent to a
construction project where suitable fill material is
excavated.
The base line from which the GL are
referred should be established outside the
immediate project area so that reference
stakes and other markers will not be
obliterated or disturbed during the process
of excavation.
Similarly, any reference bench mark should
also be located outside the work area.
9