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Civil Engineering
3. Minimising Errors in Levelling
Module Notes 3. Minimising Errors in Levelling
Some of the main errors associated with levelling are listed below. The list is not exhaustive.
- Stability of the instrument/tripod: if they move, the results are corrupted.
- Levelling up of instrument: incorrect instrument setting results in a non-horizontal line of sight.
- Focusing: incorrect focusing results in blurred vision and parallax effects.
- Verticality of the staff: non-vertical staff leads to incorrect height reading.
- Collimation error: see later; potentially incorrect results unless IS and FS distances = BS distance.
- Observing: reading the wrong cross-hair, or simply mis-reading the value.
- Booking: untidy, illegible or simply incorrect.
- Change point: unstable, causing errors between readings.
- Weather conditions: poor visibility; atmospheric refraction causes shimmer; high winds make holding of the staff vertical very difficult.
- Lack of checking: not taking time or care in the work. Full consideration of the above whilst carrying out field observations should lead to good accurate results. Levelling Misclosure In the notes 'Levelling – the basics', it was stated that levelling must always start and close on points of known height value, since otherwise there is no check on the correctness of the observations. The difference in value between the known height difference and the observed height difference between starting and closing points, is termed the levelling misclosure. Initially you must determine if the misclosure is within the acceptable tolerance. For the levelling you carry out during practical work within this module, the acceptable tolerance is 3√n (where n is the number of instrument set-ups). In practice, you must check the tolerance requirements of the survey specification as it could be greater than or less than 3√n. In the example on the next page there is a misclosure of + 5 mm which is deemed to be within the acceptable tolerance of 3√n; this misclosure is then distributed through the results in proportion to the number of instrument set-ups used.
Civil Engineering
3. Minimising Errors in Levelling BS IS FS Rise Fall Reduced Level Adj. Adjusted RL Remarks
1.84 5
0.6 75
15.23 5
15.0 05
A (TBM) B C change point change point change point D E change point A (TBM)
- 8.1 40 0.0 05 8.1 40 3.
- 3.45 5 0.0 05 3.4 55 1 5.0 05
0.00 5 Checks All the checks have been carried out and this survey is showing a +5mm misclosure. The acceptable misclosure = 3√n = 3 x 2 = 6 mm, therefore the survey is within tolerance, so the 5mm misclosure can be distributed to determine Adjusted Reduced Levels. From the number of backsights taken it can be seen that 5 instrument set-ups have been used, therefore the + 5 mm misclosure is distributed through the reduced levels by: (- 5 /5) = - 1 mm per instrument set-up The actual changes in reduced level values are built up cumulatively through the circuit such that the final result for TBM A comes back to the known value of 15.000 m. Fill in the adjustments, followed by the adjusted RL’s as shown during the lecture. Note that the original survey data is not altered -- only the final quoted reduced levels.
Civil Engineering
3. Minimising Errors in Levelling Until the observer is proficient, it is often better to observe a line in many small sections rather than one long line. In fact, long line levelling is generally done in this fashion, with each section being observed as a closed loop (i.e. observed in both directions) as the levelling proceeds, so that any errors are detected as the line is observed. Something For You To Do No. 1 A line of levelling has opened on a benchmark of reduced level 36.750 m AOD. Levels have then been taken at 20 m intervals along a proposed drainage line from chainage 0 m to chainage 160 m, with chainages 0 m, 40 m and 100 m being used as change points before closing onto a second bench mark of reduced level 39.22 2 m AOD. Reduce the data, check and adjust accordingly, given that the allowed misclosure for this particular survey must not be greater than 5 n mm (Note: at NTU your tolerance is always 3√n, this example is a more lenient specification of 5√n because the survey specification for this particular project is not as precise and has only required levelling staff observations to the nearest 10mm). BS IS FS Rise Fall Reduced Level Adj Adjusted RL Remarks 1.950 36.750 36.750 OBM 36.750 m 1.400 1.650 Ch 00 CP 1.100 Ch 20 1.500 0.840 Ch 40 CP 1.220 Ch 60 1.000 Ch 80 1.270 0.800 Ch 100 CP 1.050 Ch 120 0.780 Ch 140 0.590 Ch 160 0.350 OBM 39.222 m Checks
Civil Engineering
3. Minimising Errors in Levelling Instrumental errors Automatic level When setting-up an automatic level, the circular bubble is first centred using the footscrews. The circular bubble is not sensitive or accurate enough to ensure that the line of collimation of the instrument will be perfectly horizontal, so the “automatic” prism mechanism inside the instrument ensures the line of sight is horizontal, making sure that the instrument will define a horizontal plane_._ However, if the lenses within the instrument are slightly out of alignment, then the horizontal line of sight may not be truly horizontal and the line of collimation will not be horizontal but inclined either up or down. In that case, all staff readings will be in error, with the size of the error being directly proportional to the distance between instrument and staff. The reading to staff R in the figure below will contain twice as much error as the reading to staff Q. It should be apparent that the readings to any two staffs which are the same distance away from the instrument will be in error by the same amount. Therefore, provided that the backsight and foresight distances are the same, the difference in the readings (BS – FS) will give the correct height difference even though the instrument has a collimation error. This is the basis for the first part of the Two-peg test (which is the test which determines the sign and size of error in the level instrument prior to the instrument being adjusted), and is shown diagrammatically in figure (a) of the Two-peg test section following. It is also the reason that, during all observations and regardless of the fact that a Two-peg test might have shown the instrument to have an acceptably small collimation error, backsight and foresight distances are always kept as close to being equal as possible. True horizontal plane α Line of collimation 2x x D 2D Q^ R
Civil Engineering
3. Minimising Errors in Levelling Two peg test s 1 , s 2 , s 3 , s 4 = observed staff readings s 1 ', s 2 ', s 3 ', s 4 ' = true readings if instrument is in adjustment a) True difference in height A-B = s 1 ' – s 2 ' Observed difference in height = s 1 – s 2 = (s 1 ' + x) – (s 2 ' + x) = s 1 ' + x – s 2 ' – x = s 1 ' – s 2 ' = true height difference b) Apparent height difference = s 3 - s 4 If instrument is adjusted correctly, (s 3 – s 4 ) = (s 3 ' – s 4 ') = (s 1 ' – s 2 ') = true height difference Otherwise, (s 1 – s 2 ) – (s 3 – s 4 ) = error ‘ e’ in instrument over the length of the baseline. To adjust the instrument, it is necessary to calculate what the correct reading at B should be when the instrument is at D, e.g. if L = 50m, L/10 = 5m so distance BD = 55m required reading s 4 ' = s 4 – e.55/ If AD << L/10, e.g. ≈ 1m, then error at A ≈ 0 and required reading at B ≈ s 4 – e A C B S 1 ' S 1 L/ x α S 2 S 2 ' x L/ α Line of collimation True horizontal plane a) A B L/10^ L D α S 3 ' S^3 S 4 ' b)^ S 4
Civil Engineering
3. Minimising Errors in Levelling Principle 1 Place two pegs or select two stable, clearly identifiable existing points, around 50m apart, and name them A and B. It helps if A and B are distinctly different in height, i.e. there is a clear rise or fall from A to B (but well within the range of the levelling staff!). 2 Set up at the mid-point of the line. 3 Observe a Backsight (s1) to A, then Foresight (s2) to B. 4 Calculate the Rise or Fall from A to B. 5 Repeat steps 3 and 4 twice more, varying the height of instrument slightly each time, in order to produce three independent measures of the height difference between A and B. 6 If the three measures agree with each other to within sensible limits, calculate the mean and note this as the TRUE H A-B (true difference in height between A and B). 7 Move the instrument to a measured distance beyond A. 8 Observe a Backsight (s3) to A, then Foresight (s4) to B. Ensure that s3 and s4 are to A and B respectively, not to B and A, i.e. observe the pegs in the same order as in step 3. 9 Calculate the observed Rise or Fall from A to B. 10 If this differs from the TRUE H, repeat steps 8 and 9 twice more, varying the height of instrument slightly each time, in order to produce three independent measures of the height difference between A and B. 11 If the three measures agree with each other to within sensible limits, calculate the mean and note this as the APPARENT H A-B (apparent difference in height between A and B). 12 Compute TRUE - APPARENT, which gives the collimation error in the instrument over the distance AB. If you follow rigorously the sign convention of positive for Rise and negative for Fall, the sign of TRUE - APPARENT shows the inclination of the line of sight to the horizontal: positive for a rising line, negative for a failing line. See the worked example. 13 Generally, error in the instrument of 3mm or less over 50m would not be adjusted. If it is wished to adjust the level instrument, calculate the magnitude of the correction required to reading s4, e.g. error x (55/50) if distance AB is 50m and the instrument is 5m beyond A (i.e. 55m from B). 14 The correction must obviously be of opposite sign to that of the error determined in 10 above. Taking care over the sign, apply the value computed in 1 3 to the observed staff reading s4 at B, to determine what that staff reading should be when the error in the instrument is removed. 15 Adjust the instrument by the appropriate method (which depends on the type of level being used). 16 RECHECK the level by changing its height and re-observing the APPARENT height difference. It should agree with the TRUE height difference determined previously (to within a millimetre or two). 17 Note that there is no need to re-observe the true height difference provided that the pegs have not been disturbed and provided that it was well observed initially (hence the need for steps 5 & 6 above). 18 When booking a two peg test, be sure to record that the error in the instrument was "±x mm over y m" (the magnitude of the error is of little significance unless the length over which it was determined is stated), along with the instrument serial number and the date of the test. Note: If, in step 7, the level is moved to the side of A rather than beyond it, and set-up at the closest possible focusing distance (generally about 1m in modern instruments), the effect of collimation error on the staff reading at A will be negligible, and no multiplication factor will be required in determining the correction to the staff reading s4, the correction being simply equal to the error determined in step 12 and of opposite sign.
Civil Engineering
3. Minimising Errors in Levelling Note that alternative methods of booking the observations for a Two-peg test can be used: BS A
IS FS
B Rise Fall Reduced Level Remarks 0.826 1.328 0. 0.804 1.307 0. 0.785 1.286 0. Mean (^) True H A-B = - 0. 1.265 1.792 0. 1.248 1.775 0. 1.235 1.764 0. Mean Apparent H A-B = - 0. Collimation error = TRUE – APPARENT = - 0.502 – (- 0.528) = + 0.026 m over 50m Correction to s 4 is – 0.026 x 55/50 = - 0.029m required reading at B = 1.764 – 0.029 = 1. Recheck after adjustment: 1.259 1.760 0. Collimation error is now – 0.502 – (- 0.501) = - 0.001m over 50m = OK Or: BS IS FS Rise Fall Reduced Level Remarks A 0.826 0.804 0. B 1.328 1.307 1. dH - 0.502 - 0.503 - 0.501 (^) Mean True H A-B = - 0. After adjustment: A 1.265 1.248 1.235 1. B 1.792 1.775 1.764 1. dH - 0.527 - 0.527 - 0.529 - 0. Mean Apparent H A-B = - 0. Collimation error = TRUE – APPARENT = - 0.502 – (- 0.528) = + 0.026 m over 50m Correction to s 4 is – 0.026 x 55/50 = - 0.029m (^) required reading at B = 1.764 – 0.029 = 1. After adjustment, collimation error is now – 0.502 – (- 0.501) = - 0.001m over 50m = OK It does not matter which layout is used for the observations provided that each item is clearly and unambiguously identified and explained.
Civil Engineering
3. Minimising Errors in Levelling Something For You To Do No. 2 From a two peg test the following results were obtained over a 40 m bay AB. With the instrument placed mid-way between points A and B the reading at A was 1.975 m and at B 1.700 m. When the level was moved to a point 5 m beyond A on the line AB produced, the reading to A was recorded as 2.014 m and to B was recorded as 1.719 m. Determine the collimation error per 4 0 m sight length for this instrument and also determine the readings that should be taken to the staffs at A and B if the instrument was correctly adjusted from the position 5 m from A. Other Checks on Instrumentation The preceding notes have focused on errors in the main level instrument; do not forget to check the ancillary equipment such as the staff and the tripod. The staff is often fitted with a circular pond bubble to assist in holding the staff vertical: check the accuracy of this bubble by aligning the edge and front face of the staff with the vertical crosshair of the level. Check that the staff is extended correctly and that the sections interlock correctly. Also check the baseplate of the staff for signs of irregularity: it should be a flat plane -- if not, work off the front edge of the baseplate to minimise the zero error. With the tripod, check for general wear and tear – are all the nuts and bolts present, do the legs slip on the catches? An unstable tripod will lead to poor results. Recommended Reading Surveying for Construction: 5th^ Edition, William Irvine, McGraw-Hill Elementary Surveying: 8th^ Edition, Elphick, Fryer, Brinker, Wolf, Harper Collins Surveying for Engineers: 4th^ Edition, J Uren and W F Price, Macmillan
Civil Engineering
3. Minimising Errors in Levelling
- A level and staff are used to determine the height of a hill. From the reduction of the readings the crest of the hill is found to be 123.625 m above the starting benchmark. The readings, however, were subject to two sources of error: a) The staff divisions are two small by 1% b) The bubble used to place the staff 'upright' has an error such that the staff actually slopes by 2o^ towards the instrument. Assuming that the level was in correct adjustment, and that no reading / booking errors were made, by how much does the crest of the hill stand above the benchmark? Ans. 122.314 m
- A surveyor is using a level in which the line of sight is depressed by 58" below the horizontal when the bubble is central. In levelling up a slope, he makes his backsights 30 m long but his foresights average only 20 m. What error will be accumulated in a kilometre of levelling? Ans. 56 mm
- Two manholes A and B 50 m apart are to be connected by a 300 mm diameter sewer. Sight rails have been erected based upon a 2.75 m traveller using the levelling data below. BS IS FS Sight Length (m) Remarks 1.730 25 TBM RL 51.435 m 1.005 37 Sight Rail A 1.630 20 Sight Rail B 1.730 25 TBM RL 51.435 m Determine the invert levels at the manholes and the design gradient of the sewer. On a check survey it was found that the level used to set out the sewer was out of adjustment and the actual as built gradient was 1 in 78. Determine: i) The collimation error in the line of sight of the level when it was used to set out the sewer between A and B; ii) The true invert levels at A and B. Ans. Design values ILA = 49.410 m ILB = 48.785 m Gradient 1 in 80 Collimation error + 0o^ 03’ 14” or 0.028m/ True values ILA = 49.421 m ILB = 48.780 m
