Topic 2

PSA/ZAR/DKA_CC103/TOPIC_2 Page 1

TOPIC 2 (LEVELLING)

COURSE LEARNING OUTCOME

- Calculate correctly the differences in height, coordinates for surveying

stations and area of a traverse.

1.0 INTRODUCTION

What is leveling……….

Is a method in surveying to determine height of point on earth surface

from a datum.

The difference in height between points is obtained from the differences

of the levelling staff reading.

The land surveyor Department of Malaysia publishes maps that show

the height of various permanent stations above sea level.

These permanent stations are known as Bench Marks (BM).

When no BM exists close to a construction site, a temporary bench

mark (TBM) must be established.

Levelling must be carried forward from the nearest BM to establish

TBM value.

2.0 Levelling principle

A B C D E

3.992 3.764 3.815 3.907 3.889

LEVEL LINE XY


If the reduced level of station A is known, then the reduced level of

stations B, C, D and E can be calculated if we know the height of that

level line XY at each stations

In levelling, this horizontal line is our sight line

3.0 TYPES OF TRAVERSE

3.1 CLOSED TRAVERSE

Closed traverse begins from one point with known coordinate and ends

at the point with known coordinate.

There are two types of closed traverse.

3.2 OPEN TRAVERSE

This traverse begins from one point with known coordinate and ends at

a point which is unknown; or both points with unknown coordinates.

Traverse point obtained using this method may not be accurate

because checking could not be made.

4.0 Levelling instruments

The basis equipment required in levelling are:

a device that gives a truly horizontal line i.e. level

a suitably graduated staff/ruler for reading vertical heights, i.e. the

levelling staff

CCLLOOSSEEDD TTRRAAVVEERRSSEE OOFF PPOOLLYYGGOONN

TTYYPPEE

E

D C

A

A

CCLLOOSSEEDD TTRRAAVVEERRSSEE OOFF

EELLOONNGGAATTEEDD TTYYPPEE

D

C

B

TBM 90.70 M

BM 56.78 M


5.0 Definitions of few levelling terms

BENCH MARK – A relatively permanent and fixed reference point of

known elevation above the assumed datum.

STATION – The point where levelling staff is held.

REDUCED LEVEL – The height or depth of a point above or below the

assumed datum.

BACK SIGHT – The first reading taken after setting up the level.

FORESIGHT – The last reading taken before moving the level to

another location or instrument station.

INTERMEDIATE SIGHT – any reading or sight taken between BS and

FS

CHANGE POINT – The point on which both the fore sight and back

sight are taken during the operation of levelling.

HEIGHT OF COLLIMATION – height of line of sight.

6.0 Booking and reducing the readings

As in all aspects of surveying, the fieldwork must be properly recorded and

calculated. In levelling, two methods are available.

Rise and fall method (RF method)

The height of the plane of collimation method (HOC method)

Height of Collimation Method

This method is simple and easy.

Reduction of levels is easy.

Visualization is not necessary regarding the nature of the ground.

There is no check for intermediate sight readings;

This method is generally used where more number of readings can be

taken with less number of change points for constructional work and

profile levellings.

Rise and Fall Method

This method is complicated and is not easy to carry out.

Reduction of levels takes more time.

Visualization is necessary regarding the nature of the ground.


Complete check is there for all readings.

This method is preferable for check levelling where number of change

points are more.

REDUCED LEVEL

Obtaining the reduced level is a process of calculating the reduced level at

each point.

This can be done by rise and fall or height of collimation method.

CALCULATING REDUCED LEVELS BY RISE AND FALL METHOD

In this method, reduced level at each point is calculated based on the

difference of heights between two points.

An example of obtaining the reduced level and arithmetic check using rise and

fall method

Backsight Intermediate

sight Foresight Rise Fall

Reduced

level Correction

Final

reduced

level

Chainage Remarks

1.600 10.750 - 10.750 0 BM1 RL= 10.750m

1.185 0.415 11.165 -0.0017 11.163 10 Point A

1.790 0.605 10.560 -0.0017 10.558 40 Point B

1.290 2.425 0.635 9.925 -0.0017 9.923 70 Point C, CP1

2.275 0.985 8.940 -0.0034 8.937 90 Point D

3.000 0.725 8.215 -0.0034 8.212 100 Point E

3.290 0.290 7.925 -0.0034 7.922 120 Point F

2.510 3.025 0.265 8.190 -0.0034 8.187 140 Point G, CP2

1.980 0.530 8.720 -0.005 8.715 160 Point H

2.180 0.200 8.520 -0.005 8.515 180 Point I

2.970 0.790 7.730 -0.005 7.725 200 Point J

2.380 0.590 8.320 -0.005 8.315 210 BM2 RL=8.315m

5.400 5.400

7.830 1.800

1.800

4.230

8.320

10.750

Closing Error

= 8.320m – 8.315m

= +0.005m -2.430 -2.430 -2.430

Staff reading at BM1 = 1.600m

Staff reading at point A = 1.185m

Thus, difference in height between BM1 and Point A

= 1.600m – 1.185m

= 0.415m


This indicates that point A is higher than BM1. This value is recorded in

the rise column space.

Determine the reduced level at point A

Reduced level at point A = Reduced level at BM1 + Rise

= 10.750m + 0.415m

= 11.165m

Record the value of reduced level at point A in the reduced level column.

Staff reading at Point A = 1.185m

Staff reading at point B = 1.790m

Thus, difference in height between Point A and Point B

= 1.185m – 1.790m

= -0.605m

This indicates that point B is lower than Point A. This value is recorded in

the fall column space.

Determine the reduced level at point B

Reduced level at point B = Reduced level at Point A + Fall

= 11.165m + (-0.605m)

= 10.560m

Record the value of reduced level at point B in the reduced level column.

Calculate the rise or fall value and the reduced level for points C,D, E and

onwards.

Record the values obtained in the reduced level column.

Closing error =+0.005m

Correction = +0.005m / 3

= + 0.0017m

Record the values in the correction column but the value must versus. i.e.

+0.0017 = -0.0017


CALCULATING REDUCED LEVELS BY HEIGHT OF COLLIMATION METHOD

In this method, reduced level of every point is calculated using the height of

collimation

An example of obtaining the reduced level and arithmetic check using height of

collimation method


sight Foresight

Height of

collimation

Reduced

level Correction

Final

reduced

level

Chainage Remarks

1.600 12.350 10.750 0 BM1 RL= 10.750m

1.185 11.165 10 Point A

1.790 10.560 40 Point B

1.290 2.425 11.215 9.925 70 Point C, CP1

2.275 8.940 90 Point D

3.000 8.215 100 Point E

3.290 7.925 120 Point F

2.510 3.025 10.700 8.190 140 Point G, CP2

1.980 8.720 160 Point H

2.180 8.520 180 Point I

2.970 7.730 200 Point J

2.380 8.320 210 BM2 RL=8.315m

5.400 5.400

7.830

8.320

10.750

Closing Error

= 8.320m – 8.315m

= +0.005m -2.430 -2.430

Determine the height of collimation for BM1

Collimation height = Reduced level + Backsight

= 10.750 + 1.600

= 12.350m

Then, obtain reduced level at Point A

Reduced level at point A = Collimation height – intermediate sight reading

= 12.350m – 1.185m

= 11.165m


Determine the reduced level at Point B

Reduced level at point B = Collimation height – intermediate sight reading

= 12.350m – 1.790m

= 10.560m

Then, determine the reduced level at point C

Reduced level at point C = Collimation height – Foresight reading

= 12.350m – 2.425m

= 9.925m

Then, determine the value for collimation height at point C or change

point

Collimation height of point C= Reduced level at point C + Backsight reading of point C

= 9.925m + 1.290m

=11.215m

Repeat the same process

ACCURACY CHECK FOR SURVEY WORK

Determine the value of true error

True error

= Reduced level of last point – Reduced level of last bench mark with

known reduced level.

True error

= Calculated reduced level BM2 – known reduced level at BM2

= 8.320m – 8.315m

= 0.005m

Determine the value of permissible error

Permissible error = [±0.012 (√D) ]m

D is total distance moved by the staff in KM

Or


Permissible error = [±5 (√n) ]mm

n is number of foresight

Permissible error = [±0.012 (√0.210) ]m

= 0.006m

Or

Permisible error =[±5 (√3) ]mm

= 8.67mm

Compare the value of true error and the permissible error

- The comparison shows that this survey work can be accepted because

the true error is smaller than permissible error.

- If true error is larger than the permissible error, the survey work has to be

carried out again.

7.0 CONTOUR

Defined as the line of intersection of a level surface with the surface of ground.

Lines drawn on the map to join points of the same height on the earth surface.

The best method of representation of features such as hills etc.

8.0 CONTOUR INTERVAL

The constant height difference between two contour lines.

Depends upon the following factors:

- The nature of the ground

- The purpose and Extent of the survey

- The scale of the map

- Time and Expense of Field and Office work.


9.0 Example of contour interval

For large scale maps of flat country, for

building sites for detailed design work

0.2m to 0.5m

For reservoirs and town planning schemes 0.5m to 2m

For location surveys 2m to 3m

For small scale maps of broken country and

General Topographical work

3m, 5m, 10m or 25m.

10.0 CHARACTERISTICS OF CONTOUR LINES


11.0 USE OF CONTOUR MAP AND CONTOUR PLAN

Study original shape of the earth surface

Identify most suitable site and saving cost for engineer works

Identify water catchments area

Calculate capacity or volume of a pond

Identify volume of cut and fill

Identify intervisibility between two points


Identify the slope of road

Draw longitudinal section and cross section to view the shape of earth

surface.

Calculate horizontal distance between contour lines.

12.0 METHOD OF CONTOURING

a. DIRECT METHOD

The contours to be located are directly traced out in the field by

locating and making a number of points on each contour

b. INDIRECT METHOD

The points located and surveyed are not necessarily on the contour

lines but the spot levels.

GRID LEVEL METHOD

CROSS SECTIONING METHOD

SPOT HEIGHT METHOD

13.0 GRID LEVEL METHOD

This method is most systematic and favoured by many because the

contouring process is easy to understand.

Suitable for flat and open survey area.


14.0 Example Grid Level Method

A and B are two points at a distance of 30m

Reduced levels A and B are 24.32m and 26.90m respectively.

Contour interval as 25m and 26m may be interpolated in between A

and B.

Horizontal distance between A and 25m contour

15.0 EXERCISE

EXERCISE 1

Diagram below show a leveling work from TBM A at KM22 Kota Bharu-Kuala Krai road with the

height of TBM are 86.469m. The reading has taken as the diagram below.

i. Fill in the reading given below into the field book, and get the reduced level using rise

and fall method.

ii. Apply the arithmetic check.


EXERCISE 2

Data given below were taken from a leveling work. Calculate true reduced level for each point by

using Height of Collimation method. Apply the usual checks.

2.503 1.670 2.503

2.501 3.051

1.206 1.305

2.574 1.432 1.670 2.503

2.503 1.670 2.503

2.503 1.670 2.503

2.501

2.503 1.670 2.503

2.501

2.503 1.670 2.503

1.206 1.305

2.574

2.501

2.503 1.670 2.503

1.206 1.305

2.574

2.501

2.503 1.670 2.503

2.134 3.542

1.505

TBM A

(86.451)

TBM B (86.469)

3.051

1.206 1.305

2.574

2.501

2.503 1.670 2.503

2.3

80

BM2 8.315M

2.9

70

2.1

80

3.9

90

3.0

25

2.5

10

3.0

00

2.2

75

1.2

90

2.4

25

BM1 10.750M

1.7

90

1.6

00

1.1

85


EXERCISE 3

From a leveling work done by a group of Civil Engineering students, the reading as in the table

below. According to the table, get the reduced level using rise and fall method.


sight

Foresight Rise Fall Reduced

Level

Remarks

1.030 TBM = 44.640

1.680 0.980

1.400

1.525 1.060

1.465 1.270

1.475

1.550 1.490

1.505

0.835

EXERCISE 4

According to the reading in the table below get

i. Reduced level using Height of Collimation method

ii. Arithmetic check

iii. Correction to get the final reduced level

BS IS FS HOC RL Correction Final RL Remarks

3.685 BA1 :

350.000m

2.020

3.474 0.475

1.403

2.666 0.217

1.065

0.800 2.850

0.440 3.110

0.534 2.841

2.108 BA2 :

350.010m


EXERCISE 5

The following set of staff reading was obtained on a leveling job.

i. Find Reduced Level for all points by using Rise and Fall Method

ii. Arithmetic check

iii. Correction to get final reduced level

SIGHT RISE FALL REDUCED LEVEL

CORRECTION FINAL REDUCED

LEVEL

CHAINAGE REMARKS

BACK INTERMEDIATE FORE

1.445 TBM = 5.000

2.890

1.065 2.660

1.600

0.975 1.625

0.370 2.190

1.225 3.340

1.265 1.470

1.540 1.500

1.780

1.320 0.630

1.385

2.750 2.550

1.660 0.930

1.235 0.445

1.665 1.595

1.985 0.910

2.890 0.105

1.445 TBM = 5.000


EXERCISE 6 Calculate the Reduced Level using height of collimation method.

BACKSIGHT INTERMEDIATE

SIGHT FORESIGHT HOC

REDUCED LEVEL

DISTANT REMARKS

1.600 0 BM1 : 10.750m

1.185 10

1.790 30

1.290 2.425 30

2.275 20

3.000 10

3.290 20

2.510 3.025 20

1.980 20

2.180 20

2.970 20

2.380 10 BM2 : 8.315m

EXERCISE 7 Calculate the Reduced Level using Rise and fall method.

BACKSIGHT INTERMEDIATE

SIGHT FORESIGHT RISE FALL

REDUCED LEVEL

DISTANT REMARKS

1.859 0 BM1 :

100.780m

1.315 40

2.690 20

1.440 3.040 20

2.730 10

3.525 20

3.870 20

3.210 3.625 20

2.480 10

1.375 20

1.120 10

2.965 10 BM2 :

97.645m


BOOKING FORM FOR LEVELLING WORK (RISE/FALL)

SIGHT RISE

FALL

REDUCED

LEVEL CORRECTION FINAL

REDUCED

LEVEL

DISTANCE REMARKS



BOOKING FORM FOR LEVELLING WORK (HEIGHT OF COLLIMATION)

SIGHT HEIGHT OF

COLLIMATION REDUCED


REDUCED

LEVEL

DISTANCE REMARKS



BOOKING FORM FOR LEVELLING WORK (RISE/FALL)

SIGHT RISE +

FALL -

REDUCED


REDUCED

LEVEL

DISTANCE REMARKS



BOOKING FORM FOR LEVELLING WORK (HEIGHT OF COLLIMATION)

SIGHT HEIGHT OF

COLLIMATION REDUCED


REDUCED

LEVEL

DISTANCE REMARKS



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