Levelling
Levelling (or Leveling) is
a branch of surveying, the object of which is: i) to find the elevations of
given points with respect to a given or assumed datum, and ii) to establish
points at a given or assumed datum. The first operation is required to enable
the works to be designed while the second operation is required in the setting
out of all kinds of engineering works. Levelling deals with measurements in a
vertical plane.
Level surface: A level surface is defined as a curved
surface which at each point is perpendicular to the direction of gravity at the
point. The surface of a still water is a truly level surface. Any surface
parallel to the mean spheroidal surface of the earth is, therefore, a level
surface.
Level line: A level line is a line lying in a level
surface. It is, therefore, normal to the plumb line at all points.
Horizontal plane: Horizontal plane through a point is a
plane tangential to the level surface at that point. It is, therefore,
perpendicular to the plumb line through the point.
Horizontal line: It is a straight line tangential to the
level line at a point. It is also perpendicular to the plumb line.
Vertical line: It is a line normal to the level line at
a point. It is commonly considered to be the line defined by a plumb line.
Datum: Datum is any surface to which elevation
are referred. The mean sea level affords a convenient datum world over, and
elevations are commonly given as so much above or below sea level. It is often
more convenient, however, to assume some other datum, specially, if only the
relative elevation of points are required.
Elevation: The elevation of a point on or near the
surface of the earth is its vertical distance above or below an arbitrarily
assumed level surface or datum. The difference in elevation between two points
is the vertical distance between the two level surface in which the two points
lie.
Vertical angle: Vertical angle is an angle between two
intersecting lines in a vertical plane. Generally, one of these lines is
horizontal.
Mean sea level: It is the average height of the sea for
all stages of the tides. At any particular place it is derived by averaging the
hourly tide heights over a long period of 19 years.
Bench Mark: It is a relatively permanent point of
reference whose elevation with respect to some assumed datum is known. It is
used either as a starting point for levelling or as a point upon which to close
as a check.
Methods of levelling
Three principle methods are used for determining differences in
elevation, namely, barometric levelling, trigonometric levelling and spirit
levelling.
Barometric levelling
Barometric levelling makes use of the phenomenon that difference
in elevation between two points is proportional to the difference in
atmospheric pressures at these points. A barometer, therefore, may be used and
the readings observed at different points would yield a measure of the relative
elevation of those points.
At a given point, the atmospheric pressure doesn’t remain constant
in the course of the day, even in the course of an hour. The method is,
therefore, relatively inaccurate and is little used in surveying work except on
reconnaissance or exploratory survey.
Trigonometric
Levelling (Indirect Levelling)
Trigonometric or Indirect levelling is the process of levelling in
which the elevations of points are computed from the vertical angles and
horizontal distances measured in the field, just as the length of any side in
any triangle can be computed from proper trigonometric relations. In a modified
form called stadia levelling, commonly used in mapping, both the difference in
elevation and the horizontal distance between the points are directly computed
from the measured vertical angles and staff readings.
Spirit Levelling
(Direct Levelling)
It is that branch of levelling in which the vertical distances
with respect to a horizontal line (perpendicular to the direction of gravity)
may be used to determine the relative difference in elevation between two
adjacent points. A horizontal plane of sight tangent to level surface at any
point is readily established by means of a spirit level or a level vial. In
spirit levelling, a spirit level and a sighting device (telescope) are combined
and vertical distances are measured by observing on graduated rods placed on
the points. The method is also known as direct levelling. It is the most
precise method of determining elevations and the one most commonly used by
engineers.
Levelling Instruments
The instruments commonly used in direct levelling are:
- A level
- A levelling staff
Dumpy Level:
The first type consists of a telescopic sight. Like that of a
transit but usually of slightly higher magnification, to which a long spirit
level (see fig. 11) is attached and adjusted so that the bubble centres when
the line of sight is horizontal. A dumpy level
is also known as builder’s auto level, leveling instrument or automatic level.
It is an optical instrument used in surveying and building to transfer measure
or set horizontal levels.
The level instrument is set up on a tripod and, depending on the
type, either roughly or accurately set on a leveled condition using foot screws
(Leveling screws). The operator looks through the eyepiece of the telescope
while as assistant holds a tape measure or graduated staff vertical at the
point under measurement. The instrument and staff are used to gather and / or
transfer elevation (levels) during site surveys. Measurement generally starts
from the benchmark with known height determined by a pervious survey, or an
arbitrary point with an assumed height. A dumpy level (Fig 10) is an
older-style instrument that requires skilled use to set accurately. The
instrument requires to be set level in each quadrant to ensure it is accurate
through a full 360o traverse.
A variation in the dumpy and one that was often used by surveyors,
where greater accuracy and error checking was required, is a tilting level.
This instrument allows the telescope to be effectively flipped through 180o,
without rotating the head. The telescope is hinged to one side of the
instrument’s axis; flipping it involves lifting to the other side of the
central axis (thereby inverting the telescope). This action effectively cancels
out any errors introduced by poor setting procedure or errors in the
instrument’s adjustment. The tilting level is similar to dumpy but the
telescope with main bubble attached can be separately tilted up and down by
means of a micrometer screw, given it greater accuracy.
Self Level:
The self – leveling level is similar to tilting level except that
it has no micrometer screw. Instead, self –leveling level contains an internal
compensator mechanism (a swinging prism or pendulum) that, when set close to
level, automatically removes any remaining variation from level. This
automatically reduces the need for setting the instrument for leveling as in
the case of dumpy and tilting level. Self leveling instruments are highly
preferred instrument in surveying due to ease of use and minimal rapid set up
time consuming.
Digital Level:
A digital electronic level is another leveling instrument set up
normally on a tripod and it reads a bar – coded staff using electronic laser
methods. The height of the staff where the level beam crosses the staff is
known on a digital display. This type of level removes interpolation of
graduation by a person, thus removing a source of error and increasing
accuracy.
The level rod or level Staff:
A level staff, also called leveling rod, is a graduated wooden or
aluminum rod, the use of which permits the determination of differences in
metric graduation as the left and imperial on the right (see fig. 12) leveling
rods can be one piece, but many are sectional and can be shortened for storage
and transport or lengthened for use. Aluminum rods may adjust length by
telescoping section inside each other, while wooden rod sections are attached
to each other with sliding connections or slip joints. There are many types of
rods, with names that identify the form of the graduations and other
characteristics. Marking can be in imperial or metric units. Some rods are
graduated on only one side while others are marked on both sides. If marked on
both sides, the markings can be identical or, in some cases, can have imperial
units on one side and metric on the other side.
Aneroid
Barometers:
Vertical measurements can be approximately
determined by finding the different in barometric pressure at the two
elevations. Aneroid barometers and hypsometers measure such differences.
Aneroid barometers are devices in which changes in atmospheric pressure cause a
needle to move over a scale. Instruments of this type designed for surveying
are called altimeters. A type that records time along with pressures is usually
placed at the points where measurements of elevation are desired. When the second
instrument is read, the time is recorded, so that the simultaneous reading of
the base instrument can be selected (see fig. 14 (a) and 14 (b)). The
difference of the two readings must be corrected to the unit weight of the air,
which is estimated from the barometric pressure, temperature and humidity.
Fig. 14 (a) An Old Aneroid Barometer Fig. 14 (b) A modern
Aneroid Barometer
More accurate results independent of the
unit weight of the air can be obtained by the two – base method. Recording
aneroid are placed at two bases, preferably one higher and another lower than
the elevations to be determined. Each field reading is adjusted in proportion
to the relative height above and below the two bases, so that the sum of the
two heights equals the known difference in the height between the bases. Within
a radius of ten miles (16 kilometers) this method gives elevations within about
two feet 0.6 meters).
What Is Leveling?
Leveling is a branch
of surveying in civil engineering to measure levels of different points with
respect to a fixed point such as elevation of a building, height of one point
from ground etc.
Types of Leveling in Surveying
1. Direct leveling
2. Trigonometric leveling
3. Barometric leveling
4. Stadia leveling
Direct Leveling
It is the most
commonly used method of leveling. In this method, measurements are observed
directly from leveling instrument.
Based on the
observation points and instrument positions direct leveling is divided into
different types as follows:
·
Simple
leveling
·
Differential
leveling
·
Fly leveling
·
Profile
leveling
·
Precise
leveling
·
Reciprocal
leveling
Simple Leveling
It is a simple and
basic form of leveling in which the leveling instrument is placed between the
points which elevation is to be find. Leveling rods are placed at that points
and sighted them through leveling instrument. It is performed only when the
points are nearer to each other without any obstacles.
Differential Leveling
Differential leveling
is performed when the distance between two points is more. In this process,
number of inter stations are located and instrument is shifted to each station
and observed the elevation of inter station points. Finally difference between
original two points is determined.
Fly Leveling
Fly leveling is
conducted when the benchmark is very far from the work station. In such case, a
temporary bench mark is located at the work station which is located based on
the original benchmark. Even it is not highly precise it is used for
determining approximate level.
Profile Leveling
Profile leveling is
generally adopted to find elevation of points along a line such as for road,
rails or rivers etc. In this case, readings of intermediate stations are taken
and reduced level of each station is found. From this cross section of the
alignment is drawn.
Precise Leveling
Precise leveling is
similar to differential leveling but in this case higher precise is wanted. To
achieve high precise, serious observation procedure is performed. The accuracy
of 1 mm per 1 km is achieved.
Reciprocal Leveling
When it is not possible to locate the leveling instrument in
between the inter visible points, reciprocal leveling is performed. This case
appears in case of ponds or rivers etc. in case of reciprocal leveling,
instrument is set nearer to 1st station and sighted towards 2nd station.
Trigonometric Leveling
The process of
leveling in which the elevation of point or the difference between points is
measured from the observed horizontal distances and vertical angles in the
field is called trigonometric leveling.
In this method,
trigonometric relations are used to find the elevation of a point from angle
and horizontal distance so, it is called as trigonometric leveling. It is also
called as indirect leveling.
Barometric Leveling
Barometer is an
instrument used to measure atmosphere at any altitude. So, in this method of
leveling, atmospheric pressure at two different points is observed, based on
which the vertical difference between two points is determined. It is a rough
estimation and used rarely.
Stadia Leveling
It is a modified form
of trigonometric leveling in which Tacheometer principle is used to determine
the elevation of point. In this case the line of sight is inclined from the
horizontal. It is more accurate and suitable for surveying in hilly terrains.
Carrying out a level traverse
To determine the difference in level between points on the surface
of the ground a 'series' of levels will need to be carried out; this is called
a level traverse or level run.
Leveling or Field Procedures
The leveling or field procedure that should be followed is shown
in Figure 1 below..
Figure 1
- Set up the leveling instrument
at Level position 1.
- Hold the staff on the Datum
(RL+50 m) and take a reading. This will be a backsight, because it is the
first staff reading after the leveling instrument has been set up.
- Move the staff to A and
take a reading. This will be an intermediate sight.
- Move the staff to B and
take a reading. This also will be an intermediate sight.
- Move the staff to C and
take a reading. This will be another intermediate sight.
- Move the staff to D and
take a reading. This will be a foresight; because after this reading the
level will be moved. (A changeplate should be placed on the ground to
maintain the same level.)
- The distance between the
stations should be measured and recorded in the fieldbook (see Table 1)
- Set up the level at Level
position 2 and leave the staff at D on the changeplate.
Turn the staff so that it faces the level and take a reading. This will be
a backsight.
- Move the staff to E and
take a reading. This will be an intermediate sight.
- Move the staff to F and
take a reading. This will be a foresight; because after taking this
reading the level will be moved.
- Now move the level to Leveling
position 3 and leave the staff at F on the changeplate.
Now repeat the steps describe 8 to 10 until you finished at
point J.
Field procedures for leveling
All staff readings should be recorded in the fieldbook. To
eliminate errors resulting from any line of sight (or collimation) backsights
and foresights should be equal in distance. Length of sight should be kept less
than 100 metres. Always commence and finish a level run on a known datum or
benchmark and close the level traverse; this enables the level run to be
checked.
There are two main methods of booking levels:
- rise and fall method
- height of collimation method
Table 1 Rise & Fall Method
Back-
sight |
Inter-
mediate |
Fore-
sight |
Rise
|
Fall
|
Reduced
level |
Distance
|
Remarks
|
2.554
|
50.00
|
0
|
Datum RL+50 m
|
||||
1.783
|
0.771
|
50.771
|
14.990
|
A
|
|||
0.926
|
0.857
|
51.628
|
29.105
|
B
|
|||
1.963
|
1.037
|
50591
|
48.490
|
C
|
|||
1.305
|
3.587
|
1.624
|
48.967
|
63.540
|
D / change point 1
|
||
1.432
|
0.127
|
48.840
|
87.665
|
E
|
|||
3.250
|
0.573
|
0.859
|
49.699
|
102.050
|
F
/ change point 2
|
||
1.925
|
1.325
|
51.024
|
113.285
|
G
|
|||
3.015
|
0.496
|
1.429
|
52.453
|
128.345
|
H / change point 3
|
||
0.780
|
2.235
|
54.688
|
150.460
|
J
|
|||
10.124
|
5.436
|
7.476
|
2.788
|
54.688
|
Sum
of B-sight & F-sight,
Sum of Rise & Fall |
||
-5.436
|
-2.788
|
-50.000
|
Take
smaller from greater
|
||||
4.688
|
4.688
|
4.688
|
Difference
should be equal
|
The millimeter reading may be taken by
estimation to an accuracy of 0.005 metres or even less.
- Backsight, intermediate sight
and forsight readings are entered in the appropriate columns on different
lines. However, as shown in the table above backsights and foresights are
place on the same line if you change the level instrument.
- The first reduced level is the
height of the datum, benchmark or R.L.
- If an intermediate sight or
foresight is smaller than the immediately preceding staff
reading then the difference between the two readings is place in the rise column.
- If an intermediate sight or
foresight is larger than the immediately preceding staff
reading then the difference between the two readings is place in the fall column.
- A rise is added to the
preceding reduced level (RL) and a fall is subtracted from the preceding
RL
While all arithmetic calculations can be checked there is no
assurance that errors in the field procedure will be picked up. The arithmetic
check poves only that the rise and fall is correctly recorded in the approriate
rise & fall columns. To check the field procedure for errors the level
traverse must be closed. It is prudent to let another
student check your reading to avoid a repetition of the level run.
If the arithmetic calculation are correct, the the difference
between the sum of the backsights and the sum of the foresights will equal:
- the difference between the sum
of the rises and the sum of the falls, and
- the difference between the
first and the final R.L. or vice versa.
(there are no arithmetic checks made on the intermediate sight calculations. Make sure you read them carefully)
Table 2 Height of collimation
method (height of instrument)
Back-
sight |
Inter-
mediate |
Fore-
sight |
Height
of
collimation |
Reduced
level |
Distance
|
Remarks
|
2.554
|
52.554
|
50.00
|
0
|
Datum RL+50 m
|
||
1.783
|
50.771
|
14.990
|
A
|
|||
0.926
|
51.628
|
29.105
|
B
|
|||
1.963
|
50591
|
48.490
|
C
|
|||
1.305
|
3.587
|
50.272
|
48.967
|
63.540
|
D / change point 1
|
|
1.432
|
48.840
|
87.665
|
E
|
|||
3.250
|
0.573
|
52.949
|
49.699
|
102.050
|
F
/ change point 2
|
|
1.925
|
51.024
|
113.285
|
G
|
|||
3.015
|
0.496
|
55.468
|
52.453
|
128.345
|
H / change point 3
|
|
0.780
|
54.688
|
150.460
|
J
|
|||
10.124
|
5.436
|
54.688
|
Sum
of B-sight & F-sight,
Difference between RL's |
|||
-5.436
|
-50.000
|
Take
smaller from greater
|
||||
4.688
|
4.688
|
Difference
should be equal
|
- Booking is the same as the rise
and fall method for back-, intermediate- and foresights. There are no rise
or fall columns, but instead a height of collimation column.
- The first backsight reading
(staff on datum, benchmark or RL) is added to the first RL giving the
height of collimation.
- The next staff reading is
entered in the appropriate column but on a new line. The RL for the
station is found by subtracting the staff reading from the height of
collimation
- The height of collimation
changes only when the level is moved to a new position. The new height of
collimation is found by adding the backsight to the RL at the change
point.
- Please note there is no check
on the accuracy of intermediate RL's and errors could go undetected.
The rise and fall method may take a bit longer to complete, but a
check on entries in all columns is carried out. The RL's are easier to
calculate with the height of collimation method, but errors of intermediate
RL's can go undetected. For this reason students should use the rise and fall
method for all leveling exercises.
Always commence and finish a
level run on a datum, benchmark or known RL. This is what is known as a closed
level traverse, and will enable you to check the level run.
Closed level traverse
Series of level runs from a known Datum or RL to a known Datum or RL.
Misclosure in millimeter
24
x √km
Series of level runs from a known Datum or RL to a known Datum or RL.
Misclosure in millimeter
24
x √km
Closed loop level traverse
Series of level runs from a known Datum or RLback to the known Datum or RL.
Misclosure in millimeter
24
x √km
Series of level runs from a known Datum or RLback to the known Datum or RL.
Misclosure in millimeter
24
x √km
Open level traverse
Series of level runs from a known Datum or RL. This must be avoided because there are no checks on misreading
Series of level runs from a known Datum or RL. This must be avoided because there are no checks on misreading
There
are different ways to calculate the area of the opposite figure. Try to
minimise the amount of calculation. The figure could be divided in three
distinct areas
a=10.31x5.63+
b=6.25x5.76+
c=10.39x4.79
or the whole rectangle minus the hole (d)
A =16.67x10.31-6.25x4.55.
a=10.31x5.63+
b=6.25x5.76+
c=10.39x4.79
or the whole rectangle minus the hole (d)
A =16.67x10.31-6.25x4.55.
As you can see the 2nd method is easier. Look at the shape and try
to shorten the calculations.
If you know only the sides of a triangle then use the formula
given in the figure below.
An area can usually be divided it in triangles (rectangles,
parallelograms, trapeziums etc).
Parallelograms
has opposite sides parallel and equal. Diagonals bisect the figure and opposite
angles are equal..
The trapezium has one pair of opposite sides parallel.
(A regular trapezium is symmetrical about the perpendicular bisector of the parallel sides.)
(A regular trapezium is symmetrical about the perpendicular bisector of the parallel sides.)
An arc
is a part of the circumference of a circle; a part propo
If 360° corresponds to the full circumference. i.e. 2
r then
for a central angle of 
(see
opposite figure) the corresponding arc length will be b = /180 x r .
Volume calculations for rectangular prism and pyramid are shown
below:
A
truncated pyramid is a pyramid which top has been cut off.
If the A1+A2 is almost equal in size
then the following formula can be used instead:
V = h × (A1 + A2) / 2
A prismoid is as a solid whose end faces lie in parallel planes
and consist of any two polygons, not necessarily of the same number of sides as
shown opposite, the longitudinal faces may take the form of triangles,
parallelograms, or trapeziums.
Type of Error
|
Correction
|
1. Incorrect setting-up of instrument.
|
|
2. Movement of staff from position when
changing level station.
|
|
3. Staff not held vertically.
|
|
4. Parallax: Instrument knocked or moved during
backsight-foresight reading
|
|
5. Ground heating causes chaotic refraction
of light
|
|
6. Tripod or rod settles between
measurements e.g Bubble off center
|
|
7. Staff not properly extended and locked.
|
Comments
Post a Comment