Dams, spillways and reservoir sedimentation

Storage is only as good as the structure that holds it. The Kestrel Lake dam is a 23 ft high earth embankment about 460 ft long, with a concrete overflow spillway 26 ft wide at one abutment and a low-level outlet through the embankment. It was built in 1958 for a pulp company's camp, passed to the municipality in the 1980s, and has never had a full dam safety review. The master plan must answer three questions: how serious would a failure be, how large a flood must the dam pass safely, and how fast is the lake filling with sediment?

Types of dams

Embankment dams are built of earth or rockfill and are by far the most common type, because they use local materials and suit most foundations. An earthfill dam relies on a zone of low-permeability soil, a core or a homogeneous section, to hold water, with filters and drains to control seepage; a rockfill dam uses a central clay core or an upstream membrane of concrete or asphalt. Concrete gravity dams resist the water by their weight and need a rock foundation; arch dams carry the load into the valley walls; buttress dams use a sloping slab supported on ribs. The type follows the site: the valley shape, the foundation, the materials and the spillway arrangement.

The Kestrel Lake dam is a homogeneous embankment of the silty sand and till found nearby, with a riprap facing on the upstream slope, a grassed downstream slope and, according to the 1958 drawings, a toe drain of gravel. The low-level outlet is a 24 in. concrete pipe with a gate at the upstream end.

How dams fail

Embankment dams fail mainly by overtopping, by internal erosion and by slope or foundation instability. Overtopping occurs when the spillway cannot pass a flood; water flowing over an earth crest erodes it quickly, cuts a breach and releases the reservoir. Internal erosion, often called piping, occurs when seepage carries soil particles out of the embankment or foundation, enlarging a pipe that eventually collapses the dam; it is especially likely along conduits through the embankment, at contacts with concrete and where filters are missing. Instability occurs when slopes slide under high pore pressure, after rapid drawdown of the reservoir or during an earthquake. Internationally, overtopping and internal erosion together account for most embankment failures.

Inspection of Kestrel Lake dam in the spring found a wet area on the downstream slope near the outlet pipe and minor erosion of the upstream riprap. Dr. Lena Kowalczyk recommends piezometers on either side of the conduit and a filter diaphragm around it if the conduit is replaced. Those geotechnical measures belong to the dam safety review; this lesson concentrates on the hydrologic and hydraulic adequacy of the spillway.

Consequence classification and the inflow design flood

Dam safety in the United States is mostly a state responsibility, guided by the Federal Guidelines for Dam Safety published through FEMA and the National Dam Safety Program. Federal practice rates a dam's hazard potential as high, significant or low according to the likely consequences of failure: probable loss of life for high, economic, environmental or lifeline losses without probable loss of life for significant, and minor losses for low. Minnesota's dam safety rules, administered by the DNR, place dams in hazard classes I, II and III on similar grounds, and the required spillway design flood rises with the class, approaching or reaching the probable maximum flood (PMF) for the highest-hazard dams. Many owners also use incremental hazard analysis, which asks how much worse a failure makes a flood that would occur anyway.

A dam-break study shows that a breach of Kestrel Lake dam would send a flood wave down the creek that would reach the operations center's yard, overtop Ridgeway Road and flood several houses on the lower creek. The team expects a high hazard potential rating. Pending the DNR's review, it adopts as a working inflow design flood a flood one third of the way between the 1,000-year flood and the PMF, a common incremental value, and tests the PMF as well.

The probable maximum flood is the flood from the probable maximum precipitation, the greatest depth of rain physically possible over the basin for a given duration, combined with the most severe reasonable snowmelt and watershed conditions. It is estimated by storm maximization and transposition of large observed storms, and then routed through a watershed model. For the 1.2 mi² drainage area of Kestrel Lake, the team's hydrologist estimates a PMF peak inflow of about 2,470 cfs, against 850 cfs for the 1-in-1,000-year flood. One third of the way between them is about 1,380 cfs.

Spillways and flood routing

The spillway carries floods past the dam. Overflow spillways, a crest with a chute or stepped face below it, are the most common; side-channel spillways run along a valley wall; labyrinth spillways fold the crest into a zigzag to fit more length into a narrow site; and fuse plugs are erodible embankment sections designed to wash out in a rare flood and open an emergency channel. The discharge over a crest follows the weir equation:

where \(L\) is the crest length and \(H\) the head above the crest. A reservoir with a large surface area attenuates the flood: water rises above the crest, storing part of the inflow, and the peak outflow is less than the peak inflow. The level-pool routing method from CIV-370 applies, with continuity \(dS/dt = I - O\) and the spillway rating relating the outflow to the level. The design check is that the routed maximum level leaves the required freeboard below the dam crest.

# Kestrel Lake dam: sediment trap efficiency and spillway check for the inflow design flood
from math import log10
UNITS = "US"
SI = UNITS == "SI"
C = 420e3                       # total capacity, m3
A = 3.1                         # drainage area, km2
I = 0.88e6                      # mean annual inflow, m3
yield_t = 35.0                  # sediment yield, t/km2/yr (illustrative)
rho = 1.10                      # dry bulk density of deposits, t/m3
CI = C / I
TE = 0.97 ** (0.19 ** log10(CI))          # Dendy's fit to Brune's median curve
loss = yield_t * A * TE / rho             # m3/yr trapped
print(f"C/I = {CI:.2f}; Brune trap efficiency {TE:.0%}; storage lost {loss:.0f} m3/yr" if SI else
      f"C/I = {CI:.2f}; Brune trap efficiency {TE:.0%}; storage lost {loss/1233.5:.2f} acre-ft/yr")
print(f"Years to lose 20 % of capacity: {0.2 * C / loss:.0f}")

# level-pool routing of a triangular inflow hydrograph over a free overflow spillway
area = 9.5e4                    # reservoir surface area, m2 (taken constant)
Cw = 1.70                       # broad-crested weir coefficient, SI
def route(Qp, Tp_h, Lw, dt=60.0):
    tb = 2.67 * Tp_h * 3600
    h, out_max, h_max, t = 0.0, 0.0, 0.0, 0.0
    while t < 4 * tb:
        qin = Qp * t / (Tp_h * 3600) if t < Tp_h * 3600 else max(0.0, Qp * (tb - t) / (tb - Tp_h * 3600))
        qout = Cw * Lw * h ** 1.5
        h = max(0.0, h + (qin - qout) * dt / area)
        out_max, h_max, t = max(out_max, qout), max(h_max, h), t + dt
    return out_max, h_max
crest_to_dam = 2.0              # height of the dam crest above the spillway crest, m
freeboard = 0.6                 # minimum freeboard above the routed level, m
cases = [("1-in-1000-year flood", 24.0), ("1/3 between 1-in-1000 and PMF", 39.0), ("PMF", 70.0)]
for Lw in (8.0, 12.0):
    print(f"\nSpillway crest length {Lw:.0f} m" if SI else f"\nSpillway crest length {Lw/0.3048:.0f} ft")
    for name, Qp in cases:
        qo, hm = route(Qp, 2.0, Lw)
        fb = crest_to_dam - hm
        if SI:
            print(f"  {name:30s} inflow {Qp:5.1f} m3/s  outflow {qo:5.1f}  head {hm:4.2f} m  freeboard {fb:4.2f} m  {'OK' if fb >= freeboard else 'too little'}")
        else:
            print(f"  {name:30s} inflow {Qp*35.315:5.0f} cfs  outflow {qo*35.315:5.0f}  head {hm/0.3048:4.2f} ft  freeboard {fb/0.3048:4.2f} ft  {'OK' if fb >= freeboard else 'too little'}")

C/I = 0.48; Brune trap efficiency 95%; storage lost 0.08 acre-ft/yr
Years to lose 20 % of capacity: 897

Spillway crest length 26 ft
  1-in-1000-year flood           inflow   848 cfs  outflow   521  head 3.46 ft  freeboard 3.10 ft  OK
  1/3 between 1-in-1000 and PMF  inflow  1377 cfs  outflow   916  head 5.05 ft  freeboard 1.52 ft  too little
  PMF                            inflow  2472 cfs  outflow  1783  head 7.87 ft  freeboard -1.30 ft  too little

Spillway crest length 39 ft
  1-in-1000-year flood           inflow   848 cfs  outflow   591  head 2.87 ft  freeboard 3.69 ft  OK
  1/3 between 1-in-1000 and PMF  inflow  1377 cfs  outflow  1021  head 4.14 ft  freeboard 2.42 ft  OK
  PMF                            inflow  2472 cfs  outflow  1953  head 6.38 ft  freeboard 0.18 ft  too little

Reading the results

With the existing 26 ft crest, the 1,000-year flood rises 3.5 ft over the crest and leaves 3.1 ft of freeboard, but the working inflow design flood rises 5.1 ft and leaves only 1.5 ft, below the 2 ft the team requires for wave run-up and settlement. Widening the crest to 39 ft passes it with 2.4 ft of freeboard. Neither crest passes the PMF: it would overtop the embankment by 1.3 ft with the existing spillway, and come within 0.2 ft of the crest with the wider one. If the DNR's rules call for the full PMF for this dam, the plan will need a further step, such as a fuse plug or a modest raise of the embankment crest.

Attenuation by the lake is significant: the peak outflow is about two thirds of the peak inflow in every case, because the lake surface stores the first part of the flood. A lake with a smaller area would need a longer crest for the same safety.

Reservoir sedimentation

Every reservoir traps sediment carried in by its streams, losing storage over time. The fraction trapped, the trap efficiency, depends mainly on the ratio of capacity to mean annual inflow, \(C/I\): large reservoirs that hold the water for months trap nearly everything, while small ones on large rivers pass much of the finer sediment through. Brune's 1953 curves, based on many US reservoirs, remain the standard first estimate. A convenient fit to his median curve is

The annual loss of storage is the sediment yield of the watershed, in metric tons per square mile per year, times the area and the trap efficiency, divided by the dry density of the deposits. Sediment yields vary by orders of magnitude, from a few metric tons per square mile a year in forested shield country to thousands in erodible agricultural or semi-arid basins, and should be measured or estimated from nearby reservoir surveys where possible. Deposits settle first where the stream enters the lake, forming a delta that advances toward the dam, and finer material spreads along the bottom.

Dam safety management

A safe dam needs more than adequate structures. The owner should keep an operation, maintenance and surveillance manual; inspect routinely and after floods and earthquakes; monitor instruments such as piezometers, seepage weirs and survey points; and maintain an emergency preparedness plan with inundation maps, warning procedures and contacts. A formal dam safety review every several years, by qualified engineers, checks the whole dam against current standards. For Kestrel Lake, the master plan recommends the spillway widening, a new outlet conduit with a filter diaphragm, piezometers and a seepage weir at the toe, and an emergency plan coordinated with the city's emergency management office.

Practical points

• Classify the dam by the consequences of failure before choosing the design flood.
• Route the inflow design flood through the reservoir; attenuation can be large.
• Check freeboard for wind, waves and settlement, not just the still-water level.
• Treat conduits through embankments as the most likely path for internal erosion.
• Estimate sediment loss early; it decides whether a reservoir has a life of decades or centuries.