Spillway Adequacy on a High-Hazard Earth Dam
A 45 m high homogeneous earth dam impounds a reservoir with a surface area of about 9 km² at full reservoir level (FRL). The gated ogee spillway has a published rating: at El 142.00 (FRL) it passes 900 m³/s, at El 142.50 about 1380 m³/s, and at El 143.00 about 1930 m³/s. The dam crest is at El 143.20. Storage between FRL and crest level is 11 Mm³. The spillway was sized in the 1970s for the 100-year flood, with a peak inflow of 2000 m³/s and a flood volume of 95 Mm³. A level-pool routing of that flood, using the current storage–elevation curve, gives a peak reservoir level of El 142.90. A revised hydrology study now estimates the probable maximum flood at a peak of 4800 m³/s with a volume of 610 Mm³. A town of 40,000 people lies 6 km downstream. The owner argues that the dam has performed for 45 years and that no works are needed.
1. Compute the freeboard available for the routed 100-year flood and judge whether it is adequate.
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Freeboard calculation.
- Dam crest: El 143.20
- Routed peak reservoir level: El 142.90
- Still-water freeboard = 0.30 m
What that 0.30 m has to cover. Freeboard on an earth dam is not measured against still water. It must accommodate:
- Wind setup and wave run-up - for a fetch of roughly 3–4 km and design wind of 40 m/s, a combined allowance of the order of 0.75 m is normal.
- Earthquake-induced seiche and slope slumping - typically another 0.3–0.5 m for a dam of this height.
- Post-construction and long-term settlement of the crest - commonly 0.2–0.3 m.
Adding the first two alone gives a requirement close to 1.0–1.3 m against an available 0.30 m. Even a generous reading of the design basis (1.5 m above maximum water level) is missed by about 1.2 m.
Verdict. The dam does not have adequate freeboard even for the flood it was designed for, on today's storage curve. The practical consequence is that during the design flood, wave run-up will reach and pass over the crest, initiating erosion of the downstream shoulder - the classic mechanism of earth dam failure.
Note also that the routed peak level of 142.90 m corresponds to a spillway discharge of roughly 1750 m³/s, i.e. about 12–13% attenuation of the 2000 m³/s inflow peak, consistent with the 8–9 Mm³ of storage used out of a 95 Mm³ flood volume.
2. Explain why comparing peak inflow with spillway capacity is the wrong test, and what the correct test is.
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The wrong test. 'Peak inflow 2000 m³/s exceeds spillway capacity 900 m³/s at FRL, therefore the dam overtops' is both quantitatively wrong and conceptually wrong. The spillway does not have to pass the peak inflow at FRL; it has to pass the peak outflow at whatever level the reservoir rises to. Between inflow and outflow sit the reservoir's storage and the rising spillway rating.
The correct test is a level-pool routing:
dS/dt = I(t) − Q(h), with Q(h) from the rating curve and S(h) from the storage–elevation curve.
The reservoir absorbs part of the flood volume, so the outflow hydrograph is flatter and later than the inflow. The magnitude of the attenuation depends on the ratio of available storage to flood volume. Here storage above FRL is 11 Mm³ against a 95 Mm³ flood - about 12% - so attenuation is modest but not negligible, which is exactly what the routing shows: 2000 m³/s in, about 1750 m³/s out, with the level rising 0.9 m above FRL.
The corollary. If the storage were large relative to the flood (a big reservoir with a small catchment), a spillway far smaller than the peak inflow would be perfectly safe. Conversely, a small reservoir on a flashy catchment gets almost no attenuation and behaves nearly like a weir. This is why the same 900 m³/s spillway can be adequate on one dam and grossly inadequate on another.
Practical point. The routing must be run with the gates assumed in their most unfavourable credible position (jammed, or power failure preventing opening) as well as fully open, because gate reliability, not hydrology, may govern.
3. Advise the owner on the PMF result and on what to do, given the downstream population.
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Scale of the problem. PMF peak 4800 m³/s against a maximum spillway capacity of about 1930 m³/s at crest level, with a PMF volume of 610 Mm³ against 11 Mm³ of storage above FRL. The reservoir will fill the 1.2 m of freeboard long before the PMF peak arrives, and with only ~2% attenuation available from storage, the dam will be overtopped. Overtopping of a homogeneous earth fill means breach, and a breach releasing a reservoir of this size onto a town 6 km downstream is a potential catastrophe.
Classification. A dam with 40,000 people at risk is a high-hazard structure. For high-hazard dams the design and check flood is the PMF (or an approved standard project flood where PMF is not practicable), not the 100-year flood. The 100-year basis is a 1970s legacy and is no longer defensible for this consequence category.
What to do, in order.
- Interim risk reduction now: lower the maximum operating level by an operating rule, keep gates fully operable with backup power, install/verify early warning sirens and a downstream evacuation plan, and carry out a full inspection of the crest and downstream slope.
- Confirm the hydrology with an independent review - PMF estimates vary widely and the fix must be sized against a defensible number.
- Upgrade the spillway to pass the PMF without overtopping: additional bays, a lowered crest, or a fuse-plug/auxiliary spillway in a saddle, with the stilling basin and downstream channel checked for the higher discharge.
- Raise the crest only as a complement; raising freeboard without increasing discharge capacity simply moves the overtopping point.
- Re-route with gates assumed failed to define the residual risk after the upgrade.
'The dam has performed for 45 years' is not evidence of safety - it is evidence that the design flood has not yet occurred.