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# Principle of leveling

الكلية كلية الهندسة     القسم  الهندسة المدنية     المرحلة 2
أستاذ المادة كاظم نايف كاظم اليساري       13/11/2018 06:51:06
PRINCIPLE OF LEVELLING
The instrument is set up and correctly levelled in order to make the line of sight through the telescope
horizontal. If the telescope is turned through 360
?
, a horizontal plane of sight is swept out. Vertical
measurements from this plane, using a graduated levelling staff, enable the relative elevations of ground
points to be ascertained. ConsiderFigure 3.19with the instrument set up approximately midway between
ground pointsAandB. If the reduced level (RL) of point Ais known and equal to 100.000 m above OD
(AOD), then the reading of 3.000 m on a vertically held staff atAgives the reduced level of the horizontal
line of sight as 103.000 m AOD. This sight ontoAis termed a backsight (BS) and the reduced level of the
line of sight is called the height of the plane of collimation (HPC). Thus:
RLA+BS=HPC
The reading of 1.000 m onto the staff atBis called a foresight (FS) and shows the ground point Bto be
1.000 m below HPC; therefore its RL=(103.000?1.000)=102.000 m AOD.
An alternative approach is to subtract the FS from the BS. If the result is positive then the difference is
arisefromAtoB, and if negative afall, i.e.
(3.000?1.000)=+2.000 m rise fromAtoB;
therefore, RLB=100.000+2.000=102.000 m AOD
This then is the basic concept of levelling which is further developed inFigure 3.20.
The field data are entered into a field book that is pre-drawn into rows and columns. An example of
levelling observations from a practical project is shown in Figure 3.21. Observations are booked using
either the rise and fall or the HPC method.
It should be clearly noted that, in practice, the staff readings are taken to three places of decimals, that
is, to the nearest millimetre. However, in the following description only one place of decimals is used
and the numbers kept very simple to prevent arithmetic interfering with an understanding of the concepts
outlined.
The field procedure for obtaining elevations at a series of ground points is as follows.
The instrument is set up atA(as inFigure 3.20) from which point a horizontal line of sight is possible
to the TBM at 1A. The first sight to be taken is to the staff held vertically on the TBM and this is called a
Fig. 3.19 Basic principle of levelling
Vertical control 59
Fig. 3.20 A levelling line
Fig. 3.21 Project levelling observations
60 Engineering Surveying
backsight (BS), the value of which (1.5 m) would be entered in the appropriate column of a levelling book.
Sights to points 2Aand 3Awhere further levels relative to the TBM are required are called intermediate
sights (IS) and are again entered in the appropriate column of the levelling book. The final sight from
this instrument is set up at 4Aand is called the foresight (FS). It can be seen from the figure that this is
as far as one can go with this sight. If, for instance, the staff had been placed atX, it would not have
been visible and would have had to be moved down the slope, towards the instrument atA, until it was
visible. As foresight 4Ais as far as one can see fromA, it is also called the change point (CP), signifying a
change of instrument position toB. To achieve continuity in the levelling the staff must remain at exactly
the same point 4Aalthough it must be turned to face the instrument atB. It now becomes the BS for
the new instrument set-up and the whole procedure is repeated as before. Thus, one must remember that
all levelling commences on a BS and finishes on a FS with as many IS in between as are required; and
that CPs are always FS/BS. Also, it must be closed back into a known BM to ascertain the misclosure
error.
3.7.1 Reduction of levels
FromFigure 3.20realizing that the line of sight from the instrument atAis truly horizontal, it can be seen
that the higher reading of 2.5 at point 2Aindicates that the point is lower than the TBM by 1.0, giving 2A
a level therefore of 59.5. This can be written as follows:
1.5?2.5=?1.0, indicating afallof 1.0 from 1Ato 2A
Level of 2A=60.5?1.0=59.5
Similarly between 2Aand 3A, the higher reading on 3Ashows it is 1.5 below 2A, thus:
2.5?4.0=?1.5 (fall from 2Ato 3A)
Level of 3A=level of 2A?1.5=58.0
Finally thelowerreading on 4Ashows it to behigherthan 3Aby 2.0, thus:
4.0?2.0=+2.0, indicating arisefrom 3Ato 4A
Level of 4A=level of 3A+2.0=60.0
Now, knowing thereduced level(RL) of 4A, i.e. 60.0, the process can be repeated for the new instrument
position atB. This method of reduction is called therise-and-fall(R-and-F)method.
3.7.2 Methods of booking
(1) Rise-and-fall
The following extract of booking is largely self-explanatory. Note that:
(a) Each reading is booked on a separate line except for the BS and FS at change points. The BS is booked
on the same line as the FS because it refers to the same point. As each line refers to a specific point it
should be noted in the remarks column.
(b) Each reading is subtracted from the previous one, i.e. 2Afrom 1A, then 3Afrom 2A,4Afrom 3Aand
stop; the procedure recommencing for the next instrument station, 2Bfrom 1Band so on.
Vertical control 61
BS IS FS Rise Fall RL Distance Remarks
1.5 60.5 0 TBM (60.5) 1A
2.5 1.0 59.5 30 2A
4.0 1.5 58.0 50 3A
3.0 2.0 2.0 60.0 70 CP 4A(1B)
5.5 2.5 57.5 95 2B
6.0 1.0 4.5 62.0 120 CP 3B(1C)
3.0 3.0 65.0 160 TBM (65.1) 2C
10.5 6.0 9.5 5.0 65.0 Checks
6.0 5.0 60.5 Misclosure 0.1
4.5 4.5 4.5 Correct
(c) Three very important checks must be applied to the above reductions, namely:
The sum of BS?the sum of FS=sum of rises?sum of falls
=last reduced level?first reduced level
These checks are shown in the above table. It should be emphasized that they are nothing more than
checks on the arithmetic of reducing the levelling results; they are in no way indicative of the accuracy
of fieldwork.
(d) It follows from the above that the first two checks should be carried out and verified before working
out the reduced levels (RL).
(e) Closing error=0.1, and can be assessed only by connecting the levelling into a BM of known and
proved value or connecting back into the starting BM.
(2) Height of collimation
This is the name given to an alternative method of booking. The reduced levels are found simply by
subtracting the staff readings from the reduced level of the line of sight (plane of collimation). InFigure 3.20,
for instance, theheight of the plane of collimation(HPC) atAis obviously (60.5+1.5)=62.0; now 2Ais
2.5 below this plane, so its level must be (62.0?2.5)=59.5; similarly for 3Aand 4Ato give 58.0 and 60.0
respectively. Now the procedure is repeated forB. The tabulated form shows how simple this process is:
BS IS FS HPC RL Remarks
1.5 62.0 60.5 TBM (60.5) 1A
2.5 59.5 2A
4.0 58.0 3A
3.0 2.0 63.0 60.0 Change pt 4A(1B)
5.5 57.5 2B
6.0 1.0 68.0 62.0 Change pt 3B(1C)
3.0 65.0 TBM (65.1) 2C
10.5 12.0 6.0 65.0 Checks
6.0 60.5 Misclosure 0.1
4.5 4.5 Correct
62 Engineering Surveying
Thus it can be seen that:
(a) BS is added to RL to give HPC, i.e. 1.5+60.5=62.0.
(b) Remaining staff readings aresubtractedfrom HPC to give the RL.
(c) Procedure repeated for next instrument set-up atB, i.e. 3.0+60.0=63.0.
(d) Two checks same as R-and-F method, i.e.:
sum of BS?sum of FS=last RL?first RL
(e) The above two checks are not complete; for instance, if when taking 2.5 from 62.0 to get RL of
59.5, one wrote it as 69.5, this error of 10 would remain undetected. Thus theintermediate sights
arenotchecked by those procedures in (d) above and the following cumbersome check must be
carried out:
sum of all the RL except the first=(sum of each HPC multiplied by the number of IS or FS
taken from it)?(sum of IS and FS)

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