The Oroville Dam Disaster
The Oroville Dam is one of the largest in the U.S.A., existing in California between Lake
Oroville and Feather River (Figure 1). In February 2017, a combination of heavy rainfall and
snowmelt threatened to overflow this dam. The water level, normally well below the maximum
level of the dam, rose to 900 ft at the height of the storm.
To deal with the overflow, the main spillway was employed to reduce the water level in the
reservoir. A sudden, unexpected erosion of the bed of the main spillway significantly reduced its
flow capacity and prompted use of the emergency spillway. The emergency spillway, however,
was unable to manage the high flows necessary to keep the reservoir level stable. As engineers
scrambled to figure out how to repair the main spillway and prevent dam failure, the more than
180,000 people living downstream from the structure and Lake Oroville were evacuated.
You are coming in after the event to figure out what happened. Answer the following questions
and think hard about how you would fix the original dam design.
Figure 1: Schematic of the Oroville Dam, 770 ft tall and set between Lake Oroville and Feather River.
The main spillway is clearly marked, used as an emergency outlet for lake water if it threatens to overtop
Assuming a uniform dam depth, draw the (qualitative) shape of the pressure prism on the dam
and the (qualitative) location of the resulting force for the following two scenarios:
At the base of the dam there is a set of turbines connecting the reservoir of Lake Oroville to the
Feather River, similar to the scenario sketched in Figure 2. The turbines supply 819 megawatts to
the local electricity grid and have an efficiency 𝜂 = 0.9. Assume a max reservoir level of 770 ft,
an 𝑓 = 0.02 for the pipe, and a negligible minor head loss at the smoothly curved pipe entrance.
Figure 2: Schematic of the turbine located at the base of the dam, with water level 𝑧 = 770 𝑓𝑡 leading to
a pipe of 𝐷 = 35 𝑓𝑡 which begins at level 𝑧 = 70 𝑓𝑡 and ends at 𝑧 = 35 𝑓𝑡. The pipe is length 𝐿1 = 300
𝑓𝑡 before the turbine 𝑇 and length 𝐿2 = 60 𝑓𝑡 after the turbine before the jet outflow.
(a) Determine the head, H1, at the entrance of the turbines as a function of the discharge Q.
(b) Determine the head, H2, at the exit from the turbines as a function of the discharge Q.
(c) Are minor losses or friction losses more important in this pipe system?
(d) With the values of H1 and H2 from (a) and (b), determine the discharge, Q, through the
power plant required to achieve the specified power output (819 MW) from the turbines.
As the water levels rise, the turbines are shut off and the main spillway is opened to handle the
excess overflow from the lake. The main spillway is made of rough concrete and is 3,000 𝑓𝑡
long, 179 𝑓𝑡 wide, and extends 500 𝑓𝑡 to the river below.
Figure 3: Side view of the Oroville Dam with specific detail given to the spillway crest.
The spillway crown (see detail in Figure 3) acts as a broad-crested weir and has a smoothly
curving transition from horizontal to meet the downstream slope of the dam. The design head,
HD, is the elevation difference between reservoir level and spillway crest.
(a) Assuming the flow from the reservoir passes through critical depth at the spillway crest,
determine this depth, hc, and the discharge, Q, into the spillway as a function of HD.
Evaluate them for HD when the reservoir level reaches 900 𝑓𝑡 above the dam height of
(b) Estimate h1, the depth of flow as it enters the constant slope section after passing the
short smooth transition, at section 1-1. The elevation difference between the crest and
section 1-1 is ∆zc-1 = 10 ft.
(c) Assuming that the flow reaches normal depth at section 2-2, before the transition to
horizontal at the toe of the dam, determine the normal depth, hn = h2, the corresponding
velocity, Vn, and Froude number, Frn. Is the flow sub- or super-critical?
(d) Determine the pressure on the bottom of the spillway channel (i.e. at section 2-2), pbn,
corresponding to the solution in (c).
(e) Estimate the shear stress along the bed at point 2-2. Does any part of this solution cause
concern from an engineering perspective?
The dam crisis existed because the concrete bed of the spillway caved in at the location seen in
Figure 4, even though only a fraction of the spillway design flow rate was being used.
Discuss, in brief., one possible explanation for this erosion, and explain the engineering solution
you would use to prevent a similar failure in the future. Feel free to seek out reports of the actual
dam collapse, which are available in the public domain, for inspiration.
Figure 4: Sketch of the dam system, with design flowrates for the different portions of the system given