written by pro. kiema

1. Prof. Dr.-Ing. John Bosco Kyalo Kiema
University of Nairobi
Email: jbkkiema@uonbi.ac.ke
by
Engineering Surveying
II

2. Course Outline
Introduction. Horizontal Control; traverse
observation, calculation and adjustment. Vertical
control: Levelling and contouring. Applications in
highway drainage and setting out works. Area and
volumes. Mass haul diagram. Practicals: field
surveying.

3. Exam Course
Work
CAT Pass
Mark
Total
70 20 10 50 100
Course Assessment

4. References
1. Awange, J.L., and Kiema, J.B.K. (2013). Environmental
Geoinformatics: Monitoring and Management. Springer Verlag.
2. Bannister, A., Raymond, S., and Baker, R. (1998). Surveying. Pitmans
ELBS. 7th Ed.
3. Irvine and Macclennan (2006). Surveying for Construction. McGraw, C.
5th Ed.,
4. Schofield, W. and Breach, M. (2007). Engineering Surveying.
Butterworth-Heinemann, UK. 6th Ed.
5. Uren and Price. (2010). Surveying for Engineers. Macmillan Press Ltd.
5th Ed.
6. Wolf, P, R., and Ghilani, C.D., (2006). Elementary Surveying: An
Introduction to Geomatics. Pearson Prentice Hall. New Jersey. 11 Ed.

5. Course Assignment/Term Paper
Using suitable examples discuss the role of
Geoinformatics in the monitoring and management of
environmental pollution.

6. Lecture Outline
Part 2: Traversing
 Overview of Control Surveys
 Concept of Traversing
 Traverse Computation
 Accuracy of Traversing
Part 1: Background
 Basic Principle of Surveying
 Datum Concept
 Tenets of Survey Practice
Part 3: Vertical Control
 Introduction and Definitions
 Principle of Levelling
 Sources of Errors
 Applications of Levelling
Part 4: Earthworks
 Computation of Areas and Volumes
 Mass Haul Diagrams

7. Part 1: Background
 Basic Principle of Surveying
 Datum Concept
 Tenets of Survey Practice

8. Basic Principle of Surveying
1) Working from the “whole to the part”. First
provide control using methods with higher
accuracy followed by detail mapping using
lower accuracy and cheaper methods.
2) Always perform independent checks. Make
more observations than the basic minimum
needed.
3) Specifications and accuracy required.

9. Datum Concept
Basic problem in Surveying is to determine the position
(measure) of features on Earth’s curved surface and
map (coordinate) them for diverse purposes often onto
a plane.
Datum refers to a plane or surface to which positions
and elevations of points are referenced.
Ellipsoid is reference surface in geodetic surveys.
Best fitting ellipsoid is selected.
For heighting the most commonly adopted datum is
the Mean Sea Level. This is taken with data from
coastal tide gauges over several years.

10. Datum Concept (2)
Relationship between the Earth’s Surface, Geoid, and Ellipsoid

11. Tenets of Survey Practice
Complete in shortest possible time.
Complete at the least possible cost.
Complete according to client instruction(s) and
survey manual specifications.
Complete using instrumentation of appropriate
accuracy.

12. Part 2: Traversing
 Horizontal Control Surveys
 Concept of Traversing
 Traverse Computation
 Accuracy of Traversing

13. In line with the Principle of Surveying a control
survey provides a framework of survey points,
whose relative positions are known to
prescribed degrees of accuracy.
The areas covered by these points may extend
over a whole country and form the basis for the
national maps of that country.
Alternatively the area may be relatively small,
encompassing a construction site for which a
large-scale plan is required. Although the areas
covered in construction are usually quite small,
the accuracy may be required to a very high
order.
Horizontal Control Surveys

14. Horizontal Control Surveys (2)
Hence control networks provide a reference
framework of points for:
(1) Topographic mapping and large-scale plan
production.
(2) Dimensional control of construction work.
(3) Deformation surveys for all manner of structures,
both new and old.
(4) The extension and densification of existing control
networks.

15. Horizontal Control Surveys (3)
Techniques used in the provision of horizontal control
surveys include:
(1) Traversing
(2) Triangulation Classical methods
(3) Trilateration
(4) Triangulateration Modern approaches
(5) Satellite position fixing (Global Navigation Satellite
Systems)
(6) Inertial position fixing
(7) Continuously Operating Reference Stations (CORS).
Whilst the above systems establish a network of
points, single points may be fixed by intersection
and/or resection.

16. Since the advent of EDM equipment, traversing
has emerged as the most popular method of
establishing control networks not only in
engineering surveying but also in geodetic work.
Traverse networks are, to a large extent, free
of the limitations imposed on the other systems
and have the following advantages:
(1) Much less reconnaissance and organization
required in establishing a single line of easily
accessible stations compared with the laying out
of well-conditioned geometric figures.
(2) The limitations imposed on the other systems by
topographic conditions do not apply to
traversing.
Concept of Traversing

17. Concept of Traversing (2)
(3) The extent of observations to only two stations
at a time is relatively small and flexible
compared with the extensive angular and/or
linear observations at stations in the other
systems. It is thus much easier to organize.
(4) Traverse networks are free of the strength of
figure considerations so characteristic of
triangular systems. Thus once again the
organizational requirements are reduced.
(5) Scale error does not accrue as in triangulation,
whilst the use of longer sides, easily measured
with EDM equipment, reduces azimuth swing
errors.

18. (6) Traverse stations can usually be chosen so as to
be easily accessible, as well as convenient for
the subsequent densification of lower order
control.
(7) Traversing permits the control to closely follow
the route of a highway, pipeline or tunnel, etc.,
with the minimum number of stations.
From the logistical point of view, traversing is
far superior to the other classical horizontal
control methods and offers at least equivalent
accuracy.
Concept of Traversing (3)

19. Definition of Traversing
Traversing is a surveying technique used to
determine the planimetric positions (Easting and
Northing: EB and NB below) of control points or
setting out points using measured angles and
distances (DAB and Q below).
EB=EA+ΔEAB= EA+ DABsin Q
NB=NA+ΔNAB= NA+ DABcosQ

20. In traversing, the relative position of control
points is fixed by measuring the horizontal angle
at each point, subtended by the adjacent
stations, and the horizontal distance between
consecutive pairs of stations.
The liability of a traverse to undetected error
makes it essential that there should be some
external check on its accuracy. Hence, the
traverse needs to commence from and connect
into known points of greater accuracy than the
traverse.
Types of Traverses

21. Types of Traverses (2)
In this way, the error vector of misclosure can
be quantified and distributed throughout the
network, to produce geometric correctness. Such
a traverse is called a ‘link’ traverse.
The link traverse has certain advantages over
the remaining types, in that systematic error in
distance measurement and orientation are clearly
revealed by the error vector.
Alternatively, the error vector can be obtained
by completing the traverse back to its starting
origin. Such a traverse is called a ‘polygonal’ or
‘loop’ traverse.

22. Types of Traverses (3)
a) Link traverse b) Loop traverse (oriented)
d) Open (free) traverse
c) Loop traverse (independent)

23. Both the ‘link’ and ‘polygonal’ traverses are
generally referred to as ‘closed’ traverses.
The third type of traverse is the ‘free’ or
‘open’ traverse, which does not close back onto
any known point and which therefore has no way
of detecting or quantifying the errors.
Open traverses are not recommended due to
the lack of checks. Nevertheless, it is
frequently utilized in mining and tunnelling work
because of the physical restriction on closure.
Types of Traverses (4)

24. Field Procedure
Reconnaissance is a vitally important part of any
survey project. Its purpose here is to decide
the best location for the traverse points.
In the first instance the points should be
intervisible from the point of view of traverse
observations.
If the purpose of the control network is the
location of topographic detail only, then they
should be positioned to afford the best view of
the terrain, thereby ensuring that the maximum
amount of detail can be surveyed from each
point.

25. Field Procedure (2)
If the traverse is to be used for setting out
e.g., the centre-line of a road, then the
stations should be sited to afford the best
positions for setting out the intersection points
(IPs) and tangent points (TPs), to provide
accurate location.
The distance between stations should be kept as
long as possible to minimize effect of centring
errors.
Finally, as cost is always important, the scheme
should be one that can be completed in the
minimum of time, with the minimum of
personnel.

26. Sources of Errors
The sources of error in traversing include:
(1) Errors in the observation of horizontal and vertical
angles (angular error).
(2) Errors in the measurement of distance (linear
error).
(3) Errors in the accurate centring of the instrument
and targets, directly over the survey point
(centring error).

27. Traverse Computation
Using the data given below, compute the
coordinates of various points in the following
traverse.
Apply Bowditch rule to distribute the
misclosure.

28. Station Observations Station Observations
At Tr29 At Tr37
Tr28 97 11 10 Tr36 179 02 59
Tr10 279 15 11 Tr42 2154 58
Tr36 52 15 03
At Tr42
At Tr36 Tr37 201 54 58
Tr29 232 15 03 Tr43 234 55 58
Tr37 359 02 59 Tr41 120 32 05
Traverse Computation (2)

29. Traverse Computation (3)
Traverse Distances: Datum Bearings:
Tr29 – Tr36: 78.959m Tr29 – Tr28: 97 11 10
Tr36 – Tr37: 68.589m Tr10 – Tr29: 99 15 25
Tr37 – Tr42: 62.019m Tr42 – Tr43: 234 56 07
Tr42 – Tr41: 120 31 34
Datum Coordinates:
Station N (Metres) E
Tr29 78 674.77 92 174.20
Tr42 78 849.21 92 258.63

30. Bearing Sheet
Station Observations Orientation
Correction
Provisional
Bearing
Misclosure Final
Bearing
At Tr29
Tr28
Tr10
Tr36
At Tr36
Tr29
Tr37
At Tr37
Tr36
Tr42
At Tr42
Tr37
Tr43
Tr41
97 11 10
279 15 11
52 15 03
232 15 03
359 02 59
179 02 59
21 54 58
201 54 58
234 55 58
120 32 05
00
+14
+07
+07
+07
+07
52 15 10
232 15 10
359 03 06
179 03 06
21 55 05
201 55 05
234 56 05
120 32 12
-05
-09
-14
-18
+02
-38
97 11 10
279 15 25
52 15 05
359 02 57
21 54 51
234 56 07
120 31 34

31. Computation of Coordinates
ΔN (m) ΔE N (metres) E
Tr29 – Tr36 Tr29:+78 674.77 +92 174.20
52 15 05 +48.339 +62.433
78.959m -0.01 -0.01
Tr36 – Tr37 Tr36:+78 723.10 +92 236.62
359 02 57 +68.580 -1.138
68.589m -0.01 0.00
Tr37 – Tr42 Tr37:+78 791.67 +92 235.48
21 54 51 +57.538 +23.147
62.019m 0.00 0.00
Tr42:+78 849.21 +92 258.63

32. ΔN (m) ΔE
By Datum: 174.440 84.430
By Traverse: 174.456 84.442
Misclosure: -0.016 -0.012
Length of Traverse = 209.567m
Accuracy = Sqrt{(-0.016)2+(-0.012)2}/209.567 = 1 in 13,000
(approx)
Computation of Coordinates (2)

33. Accuracy of Traversing
Traversing is generally more accurate than
classical triangulation and trilateration.
Due to the weak geometry of a traverse, it
generally has only three degrees of freedom (that
is three redundant observations), it is difficult to
arrive at an estimate of accuracy.
Although there have been many attempts to
produce equations defining the accuracy of a
traverse, at the present time the best approach is
a strength analysis using variance–covariance
matrices from a least squares adjustment.

34. Blunders in the observed data
Blunders or mistakes in the measurement of the
angles, results in gross angular misclosure.
Provided it is only a single blunder it can easily be
located.
In the case of an angle, the traverse can be computed
forward from X (Figure) and then backwards from Y.
The point which has the same co-ordinates in each
case, is where the blunder occurred and the angle must
be re-observed.
Figure: Detection of
angular traverse blunder

35. Blunders in the observed data (2)
In the case of a blunder in measuring distance,
the incorrect leg is the one whose bearing is
similar to the bearing of the error vector.
If there are several legs with similar bearings the
method fails.
Again the incorrect leg must be re-measured.

36. Part 3: Vertical Control
 Introduction and Definitions
 Principle of Levelling
 Sources of Errors
 Applications of Levelling

37. The process of determining elevations (heights)
of points of interest above or below a reference
datum or differences in elevations.
For most practical applications only the
difference in elevation between points of
interest and not absolute heights is often
required.
Used in all aspects of surveying, particularly for
engineering surveys, route surveys, construction,
etc.
Different methods may be used for estimating
heights or height differences including;
differential levelling, barometric heighting,
trigonometric heighting, gravimetry and
satellite positioning etc.
Overview of Levelling

38. a) Differential levelling: basic idea involves obtaining of height
difference between points by measuring their vertical distance
from a horizontal line of sight.
b) Trigonometric heighting: method is generally used in
determination of elevation differences of lower accuracy than
spirit levelling. It is useful where it is very difficult (or
impossible) for differential levelling to be undertaken (e.g.
towers, spires, mountain ranges etc).
c) Barometric heighting: method consists of reading air pressure
differences from which elevation differences are computed.
d) Gravimetry: by measuring the gravitational potential variation
between different points it is possible to correlate this to
differences in heights.
d) Satellite Positioning: method is poised for extensive use in the
future with its only drawback being the determination of the
separation between the geoid and ellipsoid in areas of interest.
Comparison of Various Heighting Methods

39. a) Differential Levelling b) Trigonometric heighting
c) Barometer d) Gravimeters

40. e) Satellite Heighting

41. A horizontal line is a line that
is tangential to the level line
at a particular point. Hence a
horizontal line is perpendicular
to the direction of gravity.
Levelling Line and Horizontal Line
A level line is a line that is
normal to the direction of
gravity as shown by a plumbline
at any point. A level line is
curved by virtue of the shape
of the Earth. Hence, a level
line is a line in which all points
are the same height.

42. Basic Concept

43. Datum: A level surface to which elevations of points may
be referenced. The most commonly adopted datum is the
Mean Sea Level (MSL).
Reduced level: The elevation (above or below) of a point
in relation to the Datum.
Benchmark (BM): A permanent monument or feature for
which elevation is known. BMs are built on stable rock.
Three (3) types of benchmarks can be distinguished:
1) Fundamental benchmarks (FBMs): Very stable concrete structures
most often built into rock forming part of the primary levelling
network.
2) Ordinary benchmarks: Concrete points or marks on rocks, culverts,
bridges etc constructed between FBMs.
3) Temporary benchmarks (TBMs): Stable points established in the course
of a survey between established benchmarks, which may be some
distance away.
Datums, Reduced Levels and Benchmarks

44. A (curved) surface orthogonal to the plumb line
everywhere.
More correctly an equipotential surface for which
gravitational potential is constant.
A still body of water unaffected by tides is a good
analogy.
They are not equidistant apart, but converge and diverge
due to changes in density.
Level Surface

45. Vertical Line
The direction of gravity
Therefore the direction indicated by a plumb
line
In general it deviates from a line emanating
from the geometric centre of the Earth
In reality it is curved, but this can be
neglected in small plane surveys

46. Horizontal Plane
A plane tangent to a level surface (orthogonal
to the plumb line).
The collimation axis (line of sight) of a levelling
instrument that is in correct adjustment, once
levelled, defines a horizontal plane as the
instrument is rotated.

47. Levelling Instruments
Level, Tripod, staff and tape
Change plate.

48. Level and reading of staff

49. Level and reading of staff
Staffs of a variety of lengths and
graduation styles made from a
variety of materials (wood,
aluminium, fibreglass) exist.
The alternate metre lengths are in
black and red on a white
background.
Majority of staffs are telescopic
or socketed in three sections for
easy carrying.
Graduations can take various forms
with E-pattern type popular. The
smallest graduation on the staff is
0.01 m, with readings estimated to
the nearest millimetre.
As the staff must be held vertical
during observation it should be
fitted with a circular bubble.

50. Types of Levels

51. Examples of Levels

52. Examples of Levels
NA2000 Digital level with
coded levelling staff

53. Two Peg Test
This test is often conducted before using a level for any
levelling exercise.
The purpose of the test is find out to if the line of
collimation is parallel to the bubbles tube axis.
Collimation error occurs if the line of sight is not truly
horizontal when the bubble is centred. The line of sight
may be inclined either upwards or downwards from
the horizontal.

54. Levelling Procedure
A horizontal line of sight is established using some
form of levelling mechanism:
Spirit level tube
Swinging pendulum
A graduated staff is read through the telescope of
the level.
The elevation of points can be established by first
reading the staff on a bench mark.
The staff is then moved to the desired point, the
level is turned and the staff is read again.

55. Levelling Procedure (2)
The reading at the benchmark is called the backsight
(BS)
The reading taken after turning the instrument and
moving the staff is the foresight (FS)

56. Levelling Procedure (3)
To continue levelling, the staff is kept on the point at
A and the instrument moved to the midpoint between
A and the next point, B.
A is called the change point (CP) or turning point (TP).
The staff at A is carefully turned toward the
instrument and a BS reading taken.
Then the staff is moved to B and a FS reading is
made.
The procedure is repeated as many times as needed.
The levelling should always end on a BM as a check!

57. Levelling Procedure (4)
Two note reduction methods for calculating elevations
from the BS and FS observations exist.
Each use only two equations for the computations.
Height of Collimation method HC = Elev + BS
Elev = HC – FS
Rise and Fall method Rise (or Fall) = BS – FS
Elev = Previous Elev + Rise (or Fall)
A Fall is simply a negative Rise

58. Rise and Fall
Check: ∑BS - ∑ FS = ∑ Rise - ∑ Fall = RLlast - RLFirst

59. Height of Collimation
Check: ∑BS - ∑ FS = RLlast - RLFirst
Applied when points of interest can be seen

60. Accuracy in Levelling
Many factors affect accuracy of ordinary levelling:
Reading of staff.
Bubble not being central.
Instrument (level) being out of adjustment. Ensuring
that backsights and foresights are equal in length
lessens effects of maladjustment.
Differential settlement of the tripod.
Tilting and settlement of the staff.
Sensitivity of the bubble or compensator.

61. Acceptable Misclosures
Maximum acceptable misclosure depends on class of
levelling and specifications for the particular survey.
As a guideline the following figures give an indication of
misclosures for various classes:
Precise levelling:  4K
2nd order levelling:  8K
3rd order levelling:  12K.
Ordinary levelling falls into this category. On rough
ground, allowance may be made for misclosures of up to
 30K (Where K is the total distance levelled in
kilometres).

62. Precise Levelling
This class of levelling requires further refinement to
field technique and instrumentation to that applied in
ordinary levelling.
The accuracy requirements for this class of levelling
are more stringent than for ordinary levelling.
Typical rules governing field technique for precise
levelling include:
1) Backsights and foresights are made equal in length,
two staffs being used.
2) Readings are made to one particular staff at each
setup, and there being an even number of set ups.
Readings are made to all three hairs of the reticule
at each set up and a special format for booking of
readings used.

63. Precise Levelling (2)
3) All lines of levels to be run twice in opposite
directions, the runs being made on different days
with different change points.
4) All change points made on special footplates.
5) Staff readings below 0.5m level to be avoided.
6) Special staffs with invar strip and a bubble to be
used.
7) Only levels designed for precise levelling (or
comparable accuracy) should be used (e.g. with
parallel plate micrometer).
8) If the standards in the regulations for allowable
error are not complied with, the work is repeated.

64. Sources of Errors
Equipment errors
(a) Collimation error
(b) Compensator not working
(c) Parallax
(d) Defective staff
(e) Defective Tripod

65. Sources of Errors (2)
Field or on-sight errors (Gross error sources)
(a) Staff reading error.
(b) Unstable change point.
(c) Non‐vertical staff.
(d) Booking error
(e) Instrument not level
(f) Handling the instrument and tripod
Effect of curvature and refraction
(a) Earth curvature.
(b) Vertical collimation error in the instrument.
(c) Temperature relation expansion in the staff.

66. How to Reduce Errors
Levelling should start and finish at known Bench Mark.
Where possible, all sight lengths should be below 50m.
The staff must be held vertically.
BS and FS must be kept equal for each instrument
position.
Rise and Fall method should be used when heighting
controls.
HCM should be used when setting out.
For Automatic levels, staff readings should be booked
immediately they are observed.

67. Establishing vertical control.
To establish heights of points during
constructions – setting out levels.
For contouring purposes.
For road cross‐section, longitudinal
sections/profiles or volumes of
Earthwork in civil engineering works.
For provision of levels of inclined surface
during construction.
Applications of levelling

68. Part 4: Earthworks
 Overview
 Computation of Areas and Volumes
 Mass Haul Diagrams

69. Estimation of areas and volumes is basic to
most engineering schemes such as route
alignment, reservoirs, tunnels, etc.
Excavation and hauling of material is the
most significant and costly aspect of the
work, on which profit or loss may depend.
Areas may be required in connection with
the purchase or sale of land, with the
subdivision of land or with the grading of
land.
Overview

70. Earthwork volumes are estimated to:
i) enable route alignment to be located at such
lines and levels that cut and fill are balanced
as far as practicable;
ii) to enable contract estimates of time and
cost to be made for proposed work;
iii) to form the basis of payment for work
carried out.
Overview (2)

71. Areas
a) Trapezoidal rule
Area (A) = w(h1 + h2
b) Simpson’s rule

72. Many volumes encountered in civil engineering appear, at
first glance, to be rather complex in shape.
Generally, estimation of volumes can be divided into
computation of volumes for prisms, wedges or pyramids.
(1) Prism
The two ends of the prism (Figure 9.17) are equal and
parallel, the resulting sides thus being parallelograms.
Volume = AL
Volumes
(2) Wedge
Volume of wedge (Figure 9.18)
= L/6 (sum of parallel edges × vertical height of base)
= L/6 [(a + b + c) × h] (9.7a)
when a = b = c: V = AL/2

73. Mass-haul diagrams (MHD) are used to compare
the economy of various methods of earthwork
distribution on road or railway construction
schemes.
By the combined use of the MHD plotted directly
below the longitudinal section of the survey centre-
line, one can find:
(1) The distances over which cut and fill will balance.
(2) Quantities of materials to be moved and the
direction of movement.
(3) Areas where earth may have to be borrowed or
wasted and the amounts involved.
(4) The best policy to adopt to obtain the most
economic use of plant.
Mass-Haul Diagrams