Lecture 6- Levellinggggggggggggggggg.pptx

LEVELLING

1. Lecture 6 Levelling Isham C. Pelpuo [email protected] Nov 2023 1

2. At the end of this lecture students should be able to: define the terminologies used in levelling procedures; describe field procedures that are used to measure heights or elevations of points; book or record levelling staff readings, and perform all the necessary calculations and checks for determining heights by levelling; assess the quality of levelling results obtained; understand the sources of error in levelling and how they are managed in the field; The objective of the Lecture is to help students to: 2

3. Definition of Levelling Levelling may be defined as: the process of determining the relative elevations (or height differences) of points on the earth’s surface. the operation of determining the difference in elevation between points on the earth’s surface. 3

4. Relevance of Levelling Design of highways, railways, canals, sewers, water supply systems, and other facilities having grade lines that best conform to existing topography; Lay out construction projects according to planned elevations; Calculate volumes of earthworks and other materials; Investigate drainage characteristics of an area; Develop maps showing general ground configurations; and Study earth subsidence and crustal motion. 4

5. Terminologies in levelling operations 5 Level surface : a curved surface which is perpendicular to the plumbline (or direction of gravity) at everywhere. Vertical line : the direction of gravity indicated by a plumbline or a line tangential to the plumbline at a point. Vertical datum : any level surface to which heights are referenced or a point on a level reference surface with an assigned elevation. Horizontal line : a line tangential to a level line (or level surface) or a line perpendicular to a vertical line.

6. Terminologies used in levelling operations Horizontal plane : a plane tangential to a level surface or a plane orthogonal to the plumb line. Mean Sea Level (MSL): the average height of the sea’s surface for all stages of the tide over a Metonic cycle (a period of 19 years or 235 lunar months after which the new and full moons return to the same day of the year). MSL is the commonest reference datum for levelling and is usually assigned an elevation of zero. 6

7. Terminologies used in levelling operations Line of sight : a straight line that joins the centre of the eyepiece to the centre of the objective lens of the telescope. Line of collimation : a horizontal line of sight. Plane of collimation: a horizontal plane obtained by swinging a line of collimation horizontally about the vertical axis of the instrument. Elevation : the vertical distance above or below a reference vertical datum. Reduced level : the height of a point relative to a vertical datum. Reduced level = Elevation Bench mark (BM): a relatively permanent object, natural or artificial, bearing a marked point whose elevation is known. 7

8. Terminologies used in levelling operations Height of Plane of Collimation ( HPC ): the reduced level of the line (or plane) of collimation at an instrument position. Backsight (BS): the first levelling staff reading taken at an instrument position during spirit levelling operations. Intersight (IS): levelling staff reading which is neither a backsight nor a foresight. 8 Foresight (FS): the last levelling staff reading taken before the level instrument is moved from the station.

9. Types of Levelling Operations Levelling operations may be divided into: Spirit (or Differential) levelling: A level instrument and a levelling staff are used to determine the difference in elevation between points on the earth’s surface. Trigonometric levelling: A theodolite or total station and a detailing pole are used to determine the difference in elevation between points on the earth’s surface. Stadia tacheometric levelling: A theodolite or total station and a levelling are used to determine the difference in elevation between points on the earth’s surface Barometric levelling: A barometer or altimeter (an instrument that measures atmospheric pressure, P = mgh ) is used to determine the differences in elevation between points on the earth’s surface. 9

10. Setting up for Levelling The level instrument is mounted on a tripod and levelled, and the staff is held vertically first on a point of known (or assumed) elevation and then at each point where a height is to be measured. A sample tutorial on setting up a level: ...... (7) Surveying 1 - Introduction to leveling - YouTube 10

11. Mode of Operation A Change point (CP) is a common leveling staff position between two instrument setups. A CP has a FS from the previous instrument position and a BS from the next instrument position. 11

12. 12

13. Level Staff Reading 13 0.942 1.000 1.421

14. Differences in staff readings 14

15. Accuracy Assessment To assess the accuracy, the levelling operation must start and close (or end) on a point of known elevation. The difference between the calculated and known values of the closing BM is known as the misclosure of the levelling task and it is the magnitude of this that gives an indication of the accuracy of the levelling. If the misclosure is greater than the allowable misclosure (usually ± 5mm√n , where n is the number of instrument stations) then the levelling must be repeated, but if the misclosure is less than the allowable value then it is distributed throughout the reduced levels. 15

16. Sample Question 16 The following staff readings were taken consecutively during a levelling operation by a team of Civil and Geological Engineering II students during their practical section: 2.356, 1.325, 1.426, 0.843, 1.273, 2.148, 0.532, 0.746, 0.965, 1.294, 2.738, 0.975, 2.346, 2.582, 2.936, 1.642, 1.725, 3.020 (all values recorded in metres). The position of the levelling instrument was changed after the 4 th , 10 th and 15 th staff readings. The first and last staff readings were taken when the staff was placed on bench marks A and B of reduced levels 200.000 m and 199.920 m respectively. Prepare a level field sheet and book the staff readings; Using the Height of Plane of Collimation Method or the Rise and Fall Method, reduce the levels; Perform all arithmetic checks; Determine the levelling misclosure; and Adjust the reduced levels.

17. HPC Method 17 BS IS FS HPC Unadjust . RL Adjusted RL Remarks 2.356 202.356 BM A (200.000 m) 1.325 201.031 201.032 Peg 1 1.426 200.930 200.931 Peg 2 1.273 0.843 202.786 201.513 201.514 Peg 3 (Change Point) 2.148 200.638 200.640 Peg 4 0.532 202.254 202.256 Peg 5 0.746 202.040 202.042 Peg 6 0.965 201.821 201.823 Peg 7 2.738 1.294 204.230 201.492 201.494 Peg 8 (Change Point) 0.975 203.255 203.258 Peg 9 2.346 201.884 201.887 Peg 10 2.582 201.648 201.651 Peg 11 1.642 2.936 202.936 201.294 201.297 Peg 12 (Change Point) 1.725 201.211 201.215 Peg 13 3.020 199.916 199.920 BM B (199.920 m)

18. Notes 18 Each instrument station establishes or creates a new height of plane of collimation. Four (4) instrument stations, four (4) Heights of Planes of Collimation. The first height of plane of collimation, HPC1 = Reduced level of BM A + BS reading to BM A The second height of plane of collimation, HPC2 = HPC1 – 4th Staff reading (FS) + 5th Staff reading (BS) The third height of plane of collimation, HPC3 = HPC2 – 10th Staff reading (FS)+ 11th Staff reading (BS) The fourth height of plane of collimation, HPC4 = HPC3 – 15th Staff reading (FS) + 16th Staff reading (BS) The set of levelling staff readings recorded at an instrument station starts with a BS and ends with a FS. When the Height of Plane of Collimation is established at an instrument station, all staff readings taken from that station are subtracted from that Height of Plane of Collimation to get unadjusted reduced levels of the various points at which the staff was placed. The Number of Backsights = Number of Foresights = Number of Instrument Stations = Number of HPCs . The number of Change Points = Number of Instrument Stations minus 1. Levelling Misclosure = Computed Reduced Level of BM B – Known (or given) Reduced level of BM B = 199.916 – 199.920 = – 0.004 m = – 4 mm. Allowable Misclosure = ± 5mm√n = ± 5mm√4 ="±" 10 𝑚𝑚. Levelling Misclosure is within the Allowable Misclosure, and therefore the accuracy of the levelling is acceptable and the unadjusted reduced levels can be adjusted.

19. Notes 19 ∑ (IS) + ∑ (FS) + ∑( RL’s except first) = ∑(each HPC x number of applications) 14.770 + 8.093 + 2820.927 = 202.356 x 3 + 202.786 x 5 + 204.230 x 4 +202.936 x 2 2843.790 m = 607.068 +1013.930 + 816.920 + 405.872 = 2843.790 m Levelling Misclosure = Computed Reduced Level of BM B – Known (or given) Reduced level of BM B = 199.916 – 199.920 = – 0.004 m = – 4 mm. Allowable Misclosure = ± 5mm n = ± 5mm Levelling Misclosure is within the Allowable Misclosure, and therefore the accuracy of the levelling is acceptable and the unadjusted reduced levels can be adjusted. Correction per station = = 0.001 m Correction C n to be applied to a reduced level obtained from the n th instrument station is given by C n = n x correction per station Reduced levels obtained from the 1 st instrument station will be corrected by C 1 = 1 x 0.001 m = 0.001 m Reduced levels obtained from the 2 nd instrument station will be corrected by C 2 = 2 x 0.001 m = 0.002 m Reduced levels obtained from the 3 rd instrument station will be corrected by C 3 = 3 x 0.001 m = 0.003 m Reduced levels obtained from the 4 th instrument station will be corrected by C 4 = 4 x 0.001 m = 0.004 m  

20. Rise and Fall Method 20 BS IS FS RISE FALL Unadjust . RL Adjusted RL Remarks 2.356 BM A (200.000 m) 1.325 1.031 201.031 201.032 Peg 1 1.426 0.101 200.930 200.931 Peg 2 1.273 0.843 0.583 201.513 201.514 Peg 3 (Change Point) 2.148 0.875 200.638 200.640 Peg 4 0.532 1.616 202.254 202.256 Peg 5 0.746 0.214 202.040 202.042 Peg 6 0.965 0.219 201.821 201.823 Peg 7 2.738 1.294 0.329 201.492 201.494 Peg 8 (Change Point) 0.975 1.763 203.255 203.258 Peg 9 2.346 1.371 201.884 201.887 Peg 10 2.582 0.236 201.648 201.651 Peg 11 1.642 2.936 0.354 201.294 201.297 Peg 12 (Change Point) 1.725 0.083 201.211 201.215 Peg 13 3.020 1.295 199.916 199.920 BM B (199.920 m)

21. Invert levelling 21 Occasionally, it may be necessary to determine the elevations of overhead points such as a ceiling or the underpass of a bridge. Usually, these points will be above the plane of collimation of the level. To obtain the educed levels of these points, the staff is held upside down in an inverted position with its base on the elevated points. When booking an inverted staff reading, it is entered into the levelling table with a minus sign, the calculation proceeding in the normal way taking this sign into account. An inverted staff position must not be used as a change point because it is often difficult to keep the staff vertical and to keep its base in the same position for more than one reading.

22. Trigonometric Levelling 22 A total station is used to determine difference in height between two points A and B which are separated by a short distance. The total station is centred and levelled at A and a reflector is set up at B. Measured Quantities : L = Slope distance α = Vertical angle h i = Height of instrument (using tape) h t = Height of reflector or target Derived/Computed Quantities : V = Vertical distance = L x sin α = Height difference between A and B From: h i + V = h t + = h i + V – h t But = RL B – RL A RL B = RL A + = RL A + h i + V – h t   Note : If α is negative (i.e. angle of depression), V will be negative and RL B = RL A + h i – V – h t . Generally, RL B = RL A + h i ± V – h t

23. END OF LECTURE 6: Levelling 23

24. Assignment 24