Levelling Misclosure on a Water-Supply Alignment
You are the survey assistant on a 0.8 km water-supply alignment from benchmark BM-1, with reduced level 100.000 m, to a proposed overhead tank. The crew closes the level run on BM-2, whose published reduced level is 101.245 m. The booked elevation difference from BM-1 to BM-2 is +1.200 m, giving a misclosure of −0.045 m. Eight instrument setups were used; the longest sight is 85 m and the shortest is 12 m. The staff is a 4 m telescopic staff. One change point was taken on soft ground beside an excavated drain. The foreman wants to distribute the 45 mm error across the eight setups so that the tank invert can be fixed the next morning. The tank invert level is critical because the inlet pipe has only 150 mm clearance above the foundation raft.
1. Calculate the permissible misclosure using a 12 mm times square-root-K criterion, where K is the length in kilometres, and decide whether the run can be adjusted.
Read the worked answer
K = 0.8 km. Permissible misclosure = 12 × √0.8 = 12 × 0.894 = 10.73 mm, say 11 mm.
The observed misclosure is 45 mm, which is more than four times the permissible value. This is not a normal random error that can be spread across the setups. It indicates a blunder or a systematic problem, such as a change point on soft ground, a staff reading error, a booking error, or a collimation error.
Therefore the run must not be adjusted tonight. Distributing 45 mm across eight setups would make the booking look neat but would give a false tank invert level. The correct decision is to stop, recheck, and re-observe the suspect sections before any invert is set.
2. List the likely causes and describe a field recheck that would locate the error without re-surveying the whole line.
Read the worked answer
Likely causes, in order of probability here:
- The change point beside the drain settled or the staff sank into soft ground.
- The staff was not held vertical, especially on the longest 85 m sight.
- A reading was misbooked, for example a 1.235 read as 1.325.
- Parallax or a loose focusing screw caused an incorrect reading.
- The instrument collimation error was not checked.
A targeted recheck would:
- Inspect the suspect change point and take a new reading on a stable peg or rock.
- Re-observe the two setups around that change point, not the whole line.
- Carry out a two-peg or collimation check over a known distance.
- Re-read BM-2 and confirm its published value from the client’s datum sheet.
- Check the booking arithmetic line by line, including rise and fall signs.
This approach finds most blunders in less time than a full re-survey and preserves the original booking for comparison.
3. If the recheck produces an acceptable 10 mm misclosure, show how the adjustment would be made and how you would protect the 150 mm pipe clearance.
Read the worked answer
A 10 mm misclosure is just within the 11 mm limit, so it may be adjusted. The correction is applied in proportion to the distance run, with opposite sign to the misclosure. For a total correction of +0.010 m over 0.8 km, a point 0.4 km from BM-1 receives about +0.005 m. The adjusted BM-2 level should then agree with 101.245 m.
The tank invert must not be set from an unadjusted or rounded level. Compute the invert from the design drawing, apply the adjusted reduced level, and then check the pipe clearance separately. The inlet pipe needs at least 150 mm clear above the raft, so the invert level must be low enough to provide that clearance plus the pipe wall thickness and any bedding. If the adjusted level leaves less than 150 mm, raise the raft locally or revise the pipe alignment rather than shaving the clearance.
Record the adjustment table, the final BM-2 check, and the invert calculation. The foreman should receive a signed setting-out sheet, not a verbal level.