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Prof. Dr.-Ing. John Bosco Kyalo Kiema
University of Nairobi
Email: jbkkiema@uonbi.ac.ke
by
Engineering Surveying
II
Course Outline
Introduction. Horizontal Control; traverse
observation, calculation and adjustment. Vertical
control: Level...
Exam Course
Work
CAT Pass
Mark
Total
70 20 10 50 100
Course Assessment
References
1. Awange, J.L., and Kiema, J.B.K. (2013). Environmental
Geoinformatics: Monitoring and Management. Springer Ve...
Course Assignment/Term Paper
Using suitable examples discuss the role of
Geoinformatics in the monitoring and management o...
Lecture Outline
Part 2: Traversing
 Overview of Control Surveys
 Concept of Traversing
 Traverse Computation
 Accuracy...
Part 1: Background
 Basic Principle of Surveying
 Datum Concept
 Tenets of Survey Practice
Basic Principle of Surveying
1) Working from the “whole to the part”. First
provide control using methods with higher
accu...
Datum Concept
Basic problem in Surveying is to determine the position
(measure) of features on Earth’s curved surface and
...
Datum Concept (2)
Relationship between the Earth’s Surface, Geoid, and Ellipsoid
Tenets of Survey Practice
Complete in shortest possible time.
Complete at the least possible cost.
Complete according to c...
Part 2: Traversing
 Horizontal Control Surveys
 Concept of Traversing
 Traverse Computation
 Accuracy of Traversing
In line with the Principle of Surveying a control
survey provides a framework of survey points,
whose relative positions a...
Horizontal Control Surveys (2)
Hence control networks provide a reference
framework of points for:
(1) Topographic mapping...
Horizontal Control Surveys (3)
Techniques used in the provision of horizontal control
surveys include:
(1) Traversing
(2) ...
Since the advent of EDM equipment, traversing
has emerged as the most popular method of
establishing control networks not ...
Concept of Traversing (2)
(3) The extent of observations to only two stations
at a time is relatively small and flexible
c...
(6) Traverse stations can usually be chosen so as to
be easily accessible, as well as convenient for
the subsequent densif...
Definition of Traversing
Traversing is a surveying technique used to
determine the planimetric positions (Easting and
Nort...
In traversing, the relative position of control
points is fixed by measuring the horizontal angle
at each point, subtended...
Types of Traverses (2)
In this way, the error vector of misclosure can
be quantified and distributed throughout the
networ...
Types of Traverses (3)
a) Link traverse b) Loop traverse (oriented)
d) Open (free) traverse
c) Loop traverse (independent)
Both the ‘link’ and ‘polygonal’ traverses are
generally referred to as ‘closed’ traverses.
The third type of traverse is t...
Field Procedure
Reconnaissance is a vitally important part of any
survey project. Its purpose here is to decide
the best l...
Field Procedure (2)
If the traverse is to be used for setting out
e.g., the centre-line of a road, then the
stations shoul...
Sources of Errors
The sources of error in traversing include:
(1) Errors in the observation of horizontal and vertical
ang...
Traverse Computation
Using the data given below, compute the
coordinates of various points in the following
traverse.
Appl...
Station Observations Station Observations
At Tr29 At Tr37
Tr28 97 11 10 Tr36 179 02 59
Tr10 279 15 11 Tr42 2154...
Traverse Computation (3)
Traverse Distances: Datum Bearings:
Tr29 – Tr36: 78.959m Tr29 – Tr28: 97 11 10
Tr36 – Tr37: 68...
Bearing Sheet
Station Observations Orientation
Correction
Provisional
Bearing
Misclosure Final
Bearing
At Tr29
Tr28
Tr10
T...
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
78.95...
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
Acc...
Accuracy of Traversing
Traversing is generally more accurate than
classical triangulation and trilateration.
Due to the we...
Blunders in the observed data
Blunders or mistakes in the measurement of the
angles, results in gross angular misclosure.
...
Blunders in the observed data (2)
In the case of a blunder in measuring distance,
the incorrect leg is the one whose beari...
Part 3: Vertical Control
 Introduction and Definitions
 Principle of Levelling
 Sources of Errors
 Applications of Lev...
The process of determining elevations (heights)
of points of interest above or below a reference
datum or differences in e...
a) Differential levelling: basic idea involves obtaining of height
difference between points by measuring their vertical d...
a) Differential Levelling b) Trigonometric heighting
c) Barometer d) Gravimeters
e) Satellite Heighting
A horizontal line is a line that
is tangential to the level line
at a particular point. Hence a
horizontal line is perpend...
Basic Concept
Datum: A level surface to which elevations of points may
be referenced. The most commonly adopted datum is the
Mean Sea Le...
A (curved) surface orthogonal to the plumb line
everywhere.
More correctly an equipotential surface for which
gravitationa...
Vertical Line
The direction of gravity
Therefore the direction indicated by a plumb
line
In general it deviates from a lin...
Horizontal Plane
A plane tangent to a level surface (orthogonal
to the plumb line).
The collimation axis (line of sight) o...
Levelling Instruments
Level, Tripod, staff and tape
Change plate.
Level and reading of staff
Level and reading of staff
Staffs of a variety of lengths and
graduation styles made from a
variety of materials (wood,
al...
Types of Levels
Examples of Levels
Examples of Levels
NA2000 Digital level with
coded levelling staff
Two Peg Test
This test is often conducted before using a level for any
levelling exercise.
The purpose of the test is find...
Levelling Procedure
A horizontal line of sight is established using some
form of levelling mechanism:
Spirit level tube
Sw...
Levelling Procedure (2)
The reading at the benchmark is called the backsight
(BS)
The reading taken after turning the inst...
Levelling Procedure (3)
To continue levelling, the staff is kept on the point at
A and the instrument moved to the midpoin...
Levelling Procedure (4)
Two note reduction methods for calculating elevations
from the BS and FS observations exist.
Each ...
Rise and Fall
Check: ∑BS - ∑ FS = ∑ Rise - ∑ Fall = RLlast - RLFirst
Height of Collimation
Check: ∑BS - ∑ FS = RLlast - RLFirst
Applied when points of interest can be seen
Accuracy in Levelling
Many factors affect accuracy of ordinary levelling:
Reading of staff.
Bubble not being central.
Inst...
Acceptable Misclosures
Maximum acceptable misclosure depends on class of
levelling and specifications for the particular s...
Precise Levelling
This class of levelling requires further refinement to
field technique and instrumentation to that appli...
Precise Levelling (2)
3) All lines of levels to be run twice in opposite
directions, the runs being made on different days...
Sources of Errors
Equipment errors
(a) Collimation error
(b) Compensator not working
(c) Parallax
(d) Defective staff
(e) ...
Sources of Errors (2)
Field or on-sight errors (Gross error sources)
(a) Staff reading error.
(b) Unstable change point.
(...
How to Reduce Errors
Levelling should start and finish at known Bench Mark.
Where possible, all sight lengths should be be...
Establishing vertical control.
To establish heights of points during
constructions – setting out levels.
For contouring pu...
Part 4: Earthworks
 Overview
 Computation of Areas and Volumes
 Mass Haul Diagrams
Estimation of areas and volumes is basic to
most engineering schemes such as route
alignment, reservoirs, tunnels, etc.
Ex...
Earthwork volumes are estimated to:
i) enable route alignment to be located at such
lines and levels that cut and fill are...
Areas
a) Trapezoidal rule
Area (A) = w(h1 + h2
b) Simpson’s rule
Many volumes encountered in civil engineering appear, at
first glance, to be rather complex in shape.
Generally, estimatio...
Mass-haul diagrams (MHD) are used to compare
the economy of various methods of earthwork
distribution on road or railway c...
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Engineering surveying-ii

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Engineering surveying-ii

  1. 1. Prof. Dr.-Ing. John Bosco Kyalo Kiema University of Nairobi Email: jbkkiema@uonbi.ac.ke by Engineering Surveying II
  2. 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. 3. Exam Course Work CAT Pass Mark Total 70 20 10 50 100 Course Assessment
  4. 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. 5. Course Assignment/Term Paper Using suitable examples discuss the role of Geoinformatics in the monitoring and management of environmental pollution.
  6. 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. 7. Part 1: Background  Basic Principle of Surveying  Datum Concept  Tenets of Survey Practice
  8. 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. 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. 10. Datum Concept (2) Relationship between the Earth’s Surface, Geoid, and Ellipsoid
  11. 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. 12. Part 2: Traversing  Horizontal Control Surveys  Concept of Traversing  Traverse Computation  Accuracy of Traversing
  13. 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. 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. 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. 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. 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. 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. 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. 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. 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. 22. Types of Traverses (3) a) Link traverse b) Loop traverse (oriented) d) Open (free) traverse c) Loop traverse (independent)
  23. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 36. Part 3: Vertical Control  Introduction and Definitions  Principle of Levelling  Sources of Errors  Applications of Levelling
  37. 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. 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. 39. a) Differential Levelling b) Trigonometric heighting c) Barometer d) Gravimeters
  40. 40. e) Satellite Heighting
  41. 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. 42. Basic Concept
  43. 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. 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. 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. 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. 47. Levelling Instruments Level, Tripod, staff and tape Change plate.
  48. 48. Level and reading of staff
  49. 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. 50. Types of Levels
  51. 51. Examples of Levels
  52. 52. Examples of Levels NA2000 Digital level with coded levelling staff
  53. 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. 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. 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. 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. 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. 58. Rise and Fall Check: ∑BS - ∑ FS = ∑ Rise - ∑ Fall = RLlast - RLFirst
  59. 59. Height of Collimation Check: ∑BS - ∑ FS = RLlast - RLFirst Applied when points of interest can be seen
  60. 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. 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. 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. 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. 64. Sources of Errors Equipment errors (a) Collimation error (b) Compensator not working (c) Parallax (d) Defective staff (e) Defective Tripod
  65. 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. 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. 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. 68. Part 4: Earthworks  Overview  Computation of Areas and Volumes  Mass Haul Diagrams
  69. 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. 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. 71. Areas a) Trapezoidal rule Area (A) = w(h1 + h2 b) Simpson’s rule
  72. 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. 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

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