MAD 256 SURVEYING APRIL 10 Levelling Güneş Ertunç, PhD Assist. Prof gertunc@hacettepe.edu.tr
What is Levelling? A measurement process whereby the difference in height between two or more points can be determined. B Difference in height A
Known height? (e.g DATUM) B A DATUM: Sea Level Difference in height =?
Known height? (e.g DATUM) Difference in height B A DATUM: Sea Level
Definitions Reduced Level (RL) The height of a point above the datum. Benchmark (BM) A stable reference point of known reduced level. Difference in height Benchmark (BM) B A DATUM: Sea Level
Definitions Line of sight Difference in height Benchmark (BM) B A DATUM: Sea Level
Definitions Height of instrument (HI) B Benchmark (BM) ( 364.89 m) A DATUM: Sea Level
Definitions Height of instrument (HI) Backside (BS) (BS) B Benchmark (BM) ( 364.89 m) A DATUM: Sea Level
Definitions Foreside (FS) (FS) B Benchmark (BM) ( 364.89 m) A DATUM: Sea Level
Glossary Backsight (BS): The vertical distance between the line of sight and a point of known or assumed elevation, or the reading taken on such a point. Always the first reading from new instrument station. Foresight (FS): The vertical distance between the line of sight and a point whose elevation is desired, or the reading taken on such a point. Always the last reading from the current instrument station. Benchmark (BM): A reference point with known elevation. Benchmarks are established using precise leveling techniques and instrumentation. Benchmarks are bronze disks or plugs set into (usually) vertical wail faces. Benchmark elevations and locations are published by federal, state or provincial, and municipal agencies and are available to surveyors for a nominal fee.
0.376 m 0.35 m 0.3 m 0.34 m
Levelling procedures FS = 2.80 m HI = 414.97 m BS = 4.71 m B Height Station B = 410.26 + (4.71 2.80) (BS FS) = 412.17 m A BM = 410.26 m
Glossary (cont d) Temporary benchmark (TBM): is a semipermanent point of known elevation. TBMs can be flange bolts on fire hydrants, nails in the roots of trees, top corners of concrete culvert headwails, and so on. Turning point (TP): A point whose elevation has been determined by a FS and whose purpose has been served after a BS has been taken on it. We use turning points if the distance between known and unknown point is too large to have readings on rods. Intermediate foresight (IS) or (IFS): A secondary point having connection only to a benchmark (BM) or to a turning point (TP). It is a rod reading taken at any other point wherethe elevation is required. Height of instrument (HI): is the elevation of the line of sight through the level (i.e., elevation of BM + BS = HI).
Levelling procedures Aim: Finding the elevation of BM 461 from BM 460 BM 461? m Level Location #2 Level Location #1 BM 460 161.273 m
Levelling procedures BM 461 164.596 m Level Location #2 TP #1 FS = 0.982 m 161.273 m - Elev. of BM 460 Level Location #1 BS = 2.868 m + 2.868 m - BS of BM 460 Level @ Location #1 164.141 m - Height of Instrument - 0.982 m - FS of TP#1 163.159 m - Elev. of TP#1 BM 460 161.273 m
Levelling procedures FS = 0.540 m BS = 1.977 m BM 461 164.596 m Level Location #2 TP #1 163.159 m - Elev. of TP#1 + 1.977 m - BS of TP#1 Level @ Location #2 165.136 m - Height of Instrument Level Location #1 BM 460 161.273 m - 0.540 m - FS of BM 461 164.596 m - Elev. of BM 461
Levelling procedures FS = 0.540 m BS = 1.977 m BM 461 164.596 m Level Location #2 TP #1 FS = 0.982 m Level Location #1 BS = 2.868 m BM 460 161.273 m
Height of Instrument = Known Elevation + BS New Elevation = Height of Instrument - FS
A B C D E F
CP32 CP31 CP12 CP11 CP23 CP21 CP22 BM beytepe
CP32 CP31 CP12 CP11 CP23 CP21 CP22 BM beytepe
CP32 CP31 CP12 CP11 CP21 Setup #1 CP23 CP22 BM beytepe
CP32 CP31 Setup #2 CP12 CP11 CP23 CP21 CP22 BM beytepe
CP32 CP31 CP12 Setup #3 CP11 CP23 CP21 CP22 BM beytepe 921.16 m
Backside (BS) Intermediate Station (IS) Foreside (FS) Rise (+) Fall (-) Relative Elevation (m) Station 1.32 921.16 BM beytepe 1.11 0.21 CP11 1.30 CP21 2.54 0.76 CP22 1.62 CP23 3.84 1.58 CP31 3.75 CP32 1.20 CP12 0.26 BM beytepe
Backside (BS) Intermediate Station (IS) Foreside (FS) Rise (+) Fall (-) Relative Elevation Station 1.32 921.16 BM beytepe 1.11 0.21 921.37 CP11 1.30-0.19 921.18 CP21 2.54 0.76 CP22 1.62 CP23 3.84 1.58 CP31 3.75 CP32 1.20 CP12 0.26 BM beytepe
Backside (BS) Intermediate Station (IS) Foreside (FS) Rise (+) Fall (-) Relative Elevation Station 1.32 921.16 BM beytepe 1.11 0.21 921.37 CP11 1.30-0.19 921.18 CP21 2.54 0.76 0.54 921.72 CP22 1.62 CP23 3.84 1.58 CP31 3.75 CP32 1.20 CP12 0.26 BM beytepe
Backside (BS) Intermediate Station (IS) Foreside (FS) Rise (+) Fall (-) Relative Elevation Station 1.32 921.16 BM beytepe 1.11 0.21 921.37 CP11 1.30-0.19 921.18 CP21 2.54 0.76 0.54 921.72 CP22 1.62 0.92 922.64 CP23 3.84 1.58 CP31 3.75 CP32 1.20 CP12 0.26 BM beytepe
Backside (BS) Intermediate Station (IS) Foreside (FS) Rise (+) Fall (-) Relative Elevation Station 1.32 921.16 BM beytepe 1.11 0.21 921.37 CP11 1.30-0.19 921.18 CP21 2.54 0.76 0.54 921.72 CP22 1.62 0.92 922.64 CP23 3.84 1.58 0.04 922.68 CP31 3.75 CP32 1.20 CP12 0.26 BM beytepe
Backside (BS) Intermediate Station (IS) Foreside (FS) Rise (+) Fall (-) Relative Elevation Station 1.32 921.16 BM beytepe 1.11 0.21 921.37 CP11 1.30-0.19 921.18 CP21 2.54 0.76 0.54 921.72 CP22 1.62 0.92 922.64 CP23 3.84 1.58 0.04 922.68 CP31 3.75 0.09 922.77 CP32 1.20 CP12 0.26 BM beytepe
Backside (BS) Intermediate Station (IS) Foreside (FS) Rise (+) Fall (-) Relative Elevation Station 1.32 921.16 BM beytepe 1.11 0.21 921.37 CP11 1.30-0.19 921.18 CP21 2.54 0.76 0.54 921.72 CP22 1.62 0.92 922.64 CP23 3.84 1.58 0.04 922.68 CP31 3.75 0.09 922.77 CP32 1.20 2.55 925.32 CP12 0.26 BM beytepe
Backside (BS) Intermediate Station (IS) Foreside (FS) Rise (+) Fall (-) Relative Elevation Station 1.32 921.16 BM beytepe 1.11 0.21 921.37 CP11 1.30-0.19 921.18 CP21 2.54 0.76 0.54 921.72 CP22 1.62 0.92 922.64 CP23 3.84 1.58 0.04 922.68 CP31 3.75 0.09 922.77 CP32 1.20 2.55 925.32 CP12 0.26 0.94 926.26 BM beytepe
Backside (BS) Intermediate Station (IS) 1.32 921.16 BM beytepe 1.11 0.21 921.37 CP11 1.30-0.19 921.18 CP21 2.54 0.76 0.54 921.72 CP22 1.62 0.92 922.64 CP23 3.84 1.58 0.04 922.68 CP31 3.75 0.09 922.77 CP32 1.20 2.55 925.32 CP12 0.26 0.94 926.26 BM beytepe Σ 7.70 2.60 5.29-0.19 5.10 5.10 5.10 Foreside (FS) Rise (+) Fall (-) Relative Elevation Station
Misclosure (ε) The amount by which the measured height (RLmeasured) differs from the known height (RLknown) of the starting and finishing benchmarks ε = RL measured RL known = 926.26-921.16 = 5.10 m ε = ΣBackside ΣForeside = 7.70 2.60 = 5.10 m ε = ΣRise ΣFall = 5.29 0.19 = 5.10 m
Adjusting the misclosure (ε) Adjustment is carried out to ensure that the measured and known RLs of the closing benchmark agree. The misclosure is linearly distributed according to the number of set-ups The adjustment per set-up for our example is Correction=(-5.10/3)
CP32 CP31 Setup #2 CP12 Setup #3 CP11 CP23 CP21 Setup #1 CP22 BM beytepe
Setup #1 =1*(-5.10/3) Setup #2 =2*(-5.10/3) =3*(-5.10/3) Setup #3
Plotting contours 2.510 B C 2.905 The RL s for points A, B and C have been determined by levelling. 1.100 A
2.510 B Plotting contours LINE AB Horizontal distance D AB = 10 m Elevation difference AB = 2.51-1.10 = 1.41 m B 1.41 m 1.100 A A 10 m
Plotting contours 2.510 2.5 B For the 1.5 m contour: D = 10*(1.5 1.1)/1.41 = 2.84 2 For the 2.0 m contour : D = 10*(2.0-1.1)/1.41 = 6.38 B 1.5 For the 2.5 m contour : D = 10*(2.5-1.1)/1.41 = 9.93 A 0.4 0.9 10 m 1.4 1.41 m 1.100 A 2.84 6.38 9.93
Plotting contours 2.510 2.5 B C 2.905 2 2 2.5 LINE AC DH AC = 2.905-1.100 = 1.805 D AC = 14.14 m 1.5 1.100 A 1.5 For the 1.5 m contour : D = 14.14*(1.5-1.1)/1.805 = 3.13 For the 2.0 m contour : D = 14.14*(2.0-1.1)/1.805 = 7.05 For the 2.5 m contour : D = 14.14*(2.5-1.1)/1.805 = 10.97
Plotting contours 2.510 B C 2.905 1.100 A
Plotting contours