Drain invert set out 230 mm below design at chainage 300 m
You are the junior engineer in charge of a 600 m long RCC storm-water drain for a new township. The invert at chainage 0.000 m is fixed at RL 100.250 m and the design bed gradient is 1 in 400 falling towards the outfall at chainage 600 m. After the first 300 m was laid, you level from a benchmark of RL 100.000 m: backsight 1.450 m on the BM, foresight 2.180 m on the freshly laid invert at chainage 300 m. The contractor's supervisor says the drain is 'practically correct' because the staff reading difference is small. The outfall invert at chainage 600 m must not be lower than RL 98.750 m because of the receiving nala. The next 300 m is still open trench, and the contractor wants to proceed immediately with the same method, using a 3 m staff and a dumpy level whose bubble was last checked six months ago.
1. Reduce the level readings, compute the design invert at chainage 300 m, and quantify the error.
Read the worked answer
Height of instrument = 100.000 + 1.450 = 101.450 m.
Invert at ch 300 = 101.450 − 2.180 = 99.270 m.
Design invert at ch 300 = 100.250 − (300 / 400) = 100.250 − 0.750 = 99.500 m.
Error = 99.270 − 99.500 = −0.230 m, i.e. the drain is 230 mm too low.
Arithmetic check: ΣBS − ΣFS = 1.450 − 2.180 = −0.730 m; last RL − BM = 99.270 − 100.000 = −0.730 m. The level book is internally consistent, so the 230 mm is a setting-out or construction error, not a booking error. It is also far outside any plausible levelling misclosure for 0.6 km (about 12√0.6 ≈ 9 mm), which confirms a gross error. The first reach has actually fallen at 1 in 306, consuming 0.980 m of fall instead of the designed 0.750 m.
2. Can the remaining 300 m still reach the fixed outfall level, and what are your options?
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From 99.270 m at ch 300 to the fixed 98.750 m at ch 600, only 0.520 m of fall remains over 300 m, i.e. a gradient of 1 in 577, flatter than the design 1 in 400.
A drop structure cannot help: a drop would lower the downstream invert further and would push the outfall below 98.750 m, which the nala does not permit. The error can only be absorbed by a flatter downstream reach or by re-laying.
Options:
- Re-lay the first 300 m to the design gradient (or to a compromise gradient) so that ch 300 sits at 99.500 m and the downstream reach can run at 1 in 400 to exactly 98.750 m. Costly because the reach is backfilled.
- Accept 1 in 577 downstream only after a hydraulic check showing that peak-flow velocity still exceeds the self-cleansing value (about 0.6 m/s) and that siltation can be managed; confirm the outfall is above the nala's high-flood level.
- Adjust the alignment or add a de-silting chamber, not a fall, to manage the flatter reach.
Recommend option 1 if the programme allows; otherwise option 2 with a written hydraulic justification.
3. What levelling and setting-out controls would you impose on the remaining reach?
Read the worked answer
The method, not just the arithmetic, is at fault. The 3 m staff on a dumpy level cannot see a 230 mm error unless the invert is checked against a calculated design level at every set-out point.
Controls:
- Compute a sight rail or design-level table for every 20 m before starting, and check the invert against it at each joint, not just at the end of the reach.
- Take a fresh backsight on the BM at the start of each day's work and close the loop back to the BM at the end; compare misclosure with 12√K mm (K in km).
- Service and adjust the dumpy level; check the bubble, parallax and staff zero error, and use a staff with a proper foot plate on the invert.
- Record all readings in a bound level book with the arithmetic check (ΣBS − ΣFS = last RL − first RL).
- Photograph and sign off each invert before any concrete is placed, and stop work if the deviation exceeds about 10 mm.