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Chapter 2

2 .1 THEORITICAL BACKGROUND OF LEVELLING
Leveling is the major part of the surveying as well as civil engineering activities to measure the level difference of different points with respect to the fixed point by using direct or indirect method. Such as elevation of building, height of one point from the ground. it provides geodetic height measurement using optical leveling instrument and level rods aiming obtain the elevation of a point with respect to the datum and establishment a point for a given elevation with respect to the assumed or given datum. There are many methods to determine the heights or height differences.
They are classified into three categories according to the surveying instruments and procedures which applied. They are;
• Geometric Leveling (Direct Leveling)
• Trigonometric Leveling(Indirect Leveling)
• GPS/Leveling

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2.1.1 Geometric Leveling
Geometric method appears as a very simple and best resulting method. It is the method of determination of height differences between points by using level and holding vertical rod. But in practically to carrying out this method is difficult on the rough ground (Ceylan, 1988).So taking equal backward and forward observation the error can be eliminated.

? Direct Leveling
This method is the most common method of leveling. In here the measurements are observed directly from the instrument. This method is divided into different types based on instrument positions and observation points.
They are;
• Simple Leveling
• Differential Leveling
• Fly Leveling
• Profile Leveling
• Precise Leveling
• Reciprocal Leveling

2.1.2 Trigonometric Leveling
Trigonometric leveling is used where the difficult terrain. Such as tall buildings mountainous areas. This method can be used when height difference between two points is large and horizontal distance is short. Such as a tall building. And also in this cases if the observation distance is not short, the displaying height values by the total station are useless. Total Station is used to take the measurement. Because of Total Station consist with both Electronic Distance Measurement (EDM) to measure slope distance and Theodolite to measure vertical angle or zenith angle. In this procedure the slope distance and vertical angle are measured between two points.
Total Station has algorithms to provide capability of calculating and displaying horizontal distance and vertical height and also it consist algorithms to do the correction for refraction and the curvature. Because of these facilities, trigonometric leveling is used in various heightening procedures and contouring. When the observation distances are not relatively short the displaying height values of the total station are useless because of effect of the refraction and the curvature. But total station contains algorithms to apply corrections. (Bedada and Reda, 2012)

Figure 2.1.2 : Trigonometric Leveling
According to the figure ;
When measuring the angle v = s sin ?
When measuring Zenith angle v = s cos z
When using horizontal distance v = d tan ? = d cot z
The difference of elevation between point A and B
e = hi+ v – hr
e = v + hi- hr

For long distance effect of the curvature and refraction are “c” and “r” respectively.
Therefore;
e = v + hi- hr+ (c-r) { (c-r) = 0.067d2 _ distance in km} (Geofrey, no date)

2.1.3 GPS/Leveling
GPS /Leveling method is an advance method and the most recent method for height determinations. In this method three dimensional coordinates and coordinate differences can be obtained by GPS Geocentric coordinate system. This Cartesian coordinates are transformed into geodetic latitude geodetic longitude and ellipsoidal height according to the reference ellipsoid .But this ellipsoidal heights are not used for surveying practical directly. Because the ellipsoidal height should be transformed into the orthometric height that is the distance between geoid and point on the earth surface measured along the plumb line and taken positive upward from the geoid (National Geodetic Survey, 1986).

The common leveling instruments are spirit level, dumpy level, Digital Level and Automatic Level.

? Spirit level.

This consists of rigidly fixed telescope with a cross hair and a level tube. When the bubble of the level tube is centered it is considered that the line of sight of the Telescope is horizontal.
When taking observation, the spirit level is set up on the tripod with sight to the points which is to be measured the height difference and the graduated leveling rods or staff are held vertically on both points. Then the focusing to the sights, readings are taken by the observer. By subtracting from back sight to fore sight the height difference can be obtained. And also placing the instrument in equidistant between two point which is going to be taken height difference, It’s adjustment errors and errors effecting earth curvature can be eliminated. (Geofrey, no date)

? Dumpy Level
Hence it is easier to transport and robust it is considered as the dumpy level is less accurate when comparing with other leveling.

? Digital Level

Digital level is a kind of modern electronic level instrument which is mostly uses in civil engineering applications replacing spirit levels. It is similar to the automatic level. By centering circular bubble using foot screws, horizontal line is established. The staff reading can be taken as electronically bar coded readings and it is recorded data automatically and displayed the measurement. It also displays the horizontal distance to the staff. In this method hence it is not need to read staff and write the readings by the observer , the most common errors such as blunders writing wrong data and reading wrong values can be reduced. And hence calculates heights by using on board computer the mistakes making are removed and also it applies and computes the curvature and refraction correction.

It provides many advantages than the other leveling instrument. they are;
• It provides digital readings of distance clearly.
• It is displaying precise numeric angles within 360′

.
This instrument is capable of leveling to required orientation and precisely aligning the steel beam under the construction , which are ensure the steel stricture’s rigidity, stability and strength in the sites.

2.2 Automatic level
Automatic level ensures that the line of sight is horizontal after operator leveled the instrument. This instrument can be quickly and easily leveled by the surveyor and no need to re-level after sighting to the each point. Three level screws are used to level this instrument.

Figure 2.2 Automatic Level

There are many feature of the automatic level. They are;

Figure A: Features of the Auto Level

2.3 Leveling Staff
The leveling staff is graduated in centimeter .it is started from zero and numbered by every 10 centimeters. When the person holding the staff vertically, it can be seen easily and can take reading of the staff. To take accurate reading the staff should be slowly swing towards to the observer an away from the observer. In here the value is varying between minimum and maximum value. So lowest value is taken as correct reading.

Figure 2.3 Leveling Staff

2.4 Collimation error of the Spirit Level

2.4.1 Determination of Collimation Error

This is known as “Two peg adjustment” .The purpose of this is to make line of collimation or line of sight horizontal when the bubble is center.
The two points (A ; B) are placed 45m distance apart on fairly leveled ground.

Stage 1: Instrument is set up at the midpoint between them and leveled up. Staves are hold on point A and point B . Then staff readings are taken. Height difference of the two points is calculated. (Geofrey, no date)

Height difference = b1 – a1 = H1

Figure 2.4.1.1 Stage 1

Stage 2: Instrument is set up at the point near to the point A. Then staff readings are taken again. Then height difference is calculated again.

Height Difference = b1 – a1 = H2

Figure 2.4.1.2 Stage 2

Stage 3: Instrument is set up at the point near to the point B. Then staff readings are taken again. Then height difference is calculated again.

Height Difference = b1 – a1 = H3

Figure 2.4.1.3 Stage 3

Then if the height difference is same for the three stages, it can be considered as there is no collimation error of the instrument.

H1 = H2 = H3

2.5 Total Station

At present Total Station is used in various construction sites. But due to the lack of knowledge of principle of total station leveling and techniques ,sometimes it is not used in construction activity for height determination. It is used as a level since development of the total station (Reda and Bedada,2012)
The main advantage of adapting the total station for height measurement, it is sighting for longer distances that are not possible to the spirit leveling and not only vertical position reading but also horizontal distance reading also taken. hence This instrument has multiple abilities, it provides more benefits to the construction. Due to the total station instrument consist with dual axis compensation; it can be ensure the horizontal and vertical angles errors minimum.
The minimum conditions should be satisfied to the total station leveling. If the conditions are satisfied the earth curvature effects and refraction effects are cancelled,
They are ,

-Maintain the back sight distance to the foresight distance.
-Maintain instrument height to the target height.

It is same as the spirit level when subtracting back sight from foresight.
Even though the back sight subtracts from the foresight like spirit leveling working, hence exist an inclination, both horizontal location and elevation can be obtained while collecting data for horizontal positioning. Using Total Station for leveling is called as indirect leveling method. This method can be maintained the considerable accuracy. Mostly this is used in road construction, air port construction and cities construction. Hence the Total Station comprises with EDM (Electronic Distance Measurement) device to measure the distance and Telescope to measure the vertical angle, can more simply and quickly find elevation.(Reda and Bedada,2012)

Figure 2.5 Total Station

There are some studies had done regarding leveling using Total Station and Automatic Level. Jongchool LEE and Taeho RHO had done a study about leveling using Total Station. It describes the measurement principle and errors of EDM.
LEE and RHO states (no date) the measurement principle of EDM. It shows the distance is calculated by measuring phase difference of the light wave between radiated from EDM and returns from the reflector. This frequency can be considered as portion of the frequency as the unit of length or time under the conditions.
The elevation can be found by using EDM measurements .as;
When the reference point is A
Slope distance = S
Measured slope angle= ?
Elevation of the specific point = Elevation of point A+HI ± S sin? – HR
HI – Height of instrument
HR – Height of reflector

According to the their study the measured distance can be formulated as
L=V+Nµ/2
Here V: Phase difference of reflected light wave
N: Number if transmitted wavelength
µ: Wavelength
When the velocity and the wave length of the electric wave are “u” and “f” respectively.
Therefore
µ= u/f. According to the speed of the light wave under the vacuum “c”
u=c/n – “n” = refractive index
Therefore ;
µ = c/nf

2.5.1 Source of errors in the process of Total Station leveling.

The major errors of the total station instrumentation are;
• Horizontal collimation error.
• Vertical collimation error.
• Tilting axis error
• Compensator Index error

2.5.1.1. Horizontal Collimation (Line of Sight ) Error
A kind of error which happens in Total Station When the optical axis (Line of collimation) is not exactly perpendicular to the telescopic axis. To check the horizontal error, first the telescope point to a target in face one and then the telescope point to the same target in face two. Then check whether the difference in horizontal angle is 180′ or not. Horizontal Collimation error can be corrected by taking mean value of face left and face right reading of the instrument.

Figure 2.5.1.1

2.5.1.2. Vertical Collimation (Vertical Index) error
In the Total Station When the 0′ to 180′ line of the vertical axis does not coincide with the vertical axis there exist a vertical collimation error. It can be eliminated by taking reading of face left and face right readings and determining i.

Figure 2.5.1.2

2.5.1.3 Tilting axis error
This error occurs in the Total Station when the tilting axis is not perpendicular to the vertical axis. As this error happens with horizontal collimation error this error can be eliminated by measuring error of the tilting axis in procedure of the calibration and measurements are taken from two face.When corrections applied to the horizontal circle readings if the angle between tilting axis and the instrumental axis is too large the instrument must be returned to the manufacturer.

Figure 2.5.1.3

2.5.1.4 Compensator Index error
This kind of errors is happened when the total station or theodolite is not leveling; the error cannot be eliminated by taking two faces readings.
In here the residuals tilts are measured of the instrument when the Total Station is fitted with the compensator and the corrections apply to the horizontal and vertical angles. The compensators have traverse error and longitudinal error . The both errors are called as Zero point errors. These errors are averaged by using face left reading and face right readings .But for single face reading must be determined by calibration function of the total station.

Figure 2.5.1.4

2.6 Calibration of the Total Station
Calibration is a comparison between measurements which one of known magnitude set by the one device and another measurement which set by the second device as similar way. The device which consists of assigned or known correctness is called as standard. At present to maintain the accuracy of the total station monitoring the instrumental error is the most important thing. Some instrumental errors can be eliminated observing two faces of the total station and averaging. So it is very important to determine the magnitude of the error in the construction sites. In the Total Station, the collimation error, tilting axis error and compensator error are measured and corrected by using electronic calibration procedures. It is important to do the electronic calibration when;

• After long storage periods.
• Before using the instrument for the first time.
• After long period of work.
• After big changes in temperature.(Reda and Bedada,2012)

There are two method of calibrating a Total Station. They are;

? Field Method
? Laboratory Method

2.6.1 Field Calibration Method:-
Total Station is calibrated over a base line which consist series of distances representing the range of instrument. The baseline is the distance with known the length marked distance permanently.Atleast there should be four marked monuments in uniformly sloping terrain in straight line.(Staiger,2007).
To determine statistically error of a total station, the base line is designed. It is ranging from 500-1400 meters. This method is most suitable for determine scale error.

? 2.6.1.1 Scale error
It can be arisen from internal source and external source and it proportional to the measured distance.
I. Internal Source:- Temperature effect, Drift, Aging
II. External Source:- Variation of standard value of refractive index due to the atmospheric changes along a measured distance.

2.6.2 Laboratory Calibration Method
The calibration measurement is done over the short distance ranging from 5-100 meter distance series of segments. It assists to determine the additive constant and while larger distance helps to determination of scale error. (Reda and Bedada,2012)

? Additive Constant (Prism Constant)
It is a function of geometrical and physical properties of the prism. It is a system constant which depend on reflector and instrument being used. It is only valid for both of combination. The additive constant (index correction/zero correction) is an algebraic constant to be applied directly to every measured distance. (Reda and Bedada,2012)

2.7 Usages of Leveling ;
? For building construction
? For bridge and tunnel construction
? To design water distribution and drainage systems
? For volume calculation
? To get cross sections and longitudinal sections along roads, railways, canals etc
? To identify topography and drainage

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