Lives lost due to dam failure

Obviously, we want to avoid having dams fail and lives lost. We can do this by modelling dams that are cracked to simulate how the crack might grow -- and if the dam might fail. As you learn about dam failure, try a simulation yourself!

But first, can we predict how many lives will be lost in the event of a dam failure?

First, look up a dam in the National Inventory of Dams and find out what the nearest city and the downstream hazard potential are (or look up a city and find a dam in that city).

Second, look up the population of the city nearest to your dam in the US Census Bureau database. Be sure to get the most recent information.

Now you're ready to assess the hazard of that dam yourself. Here we have a formula that Curtiss A. Brown and Wayne J. Graham published in 1988 to estimate the loss of life due to a dam failure.

In their analysis of the threat to human life by dam failures, Brown and Graham developed a formula that would calculate the potential risk at hand for each dam. Creating the formula first required an analysis of previous dam failures.

Brown and Graham looked at three characteristics for each dam which failed in the past:

the size of the population at risk of losing their lives due the dam failure
the total loss of life
and the amount of warning time

How many people are at risk if your dam fails?
(don't use commas)

The warning time is the amount of time before the dam fails that the people at risk realize the dam is going to fail; in other words, it is the time between when the people find out the dam is going to fail and when the dam actually fails, usually in hours.

If your dam was going to fail, how much time would the people in the nearest city have to try to escape?

What is the amount of warning time (in hours) before the dam fails?
(time less than 0.75 hrs won't work due to the nature of the equation)

Using their analyses of the past, they found that for dam failures with insufficient warning times, the unadjusted estimate is equal to the population taken to the 0.6 power. For example, with a population of 1000 people, the unadjusted estimated death rate would be about 63. However if there is enough warning time, then the unadjusted estimate is equal to .0002 times the population size. That means that if the same group of people is given ample warning time, then there should not be a single death.

But their analyses were not always consistent. Brown and Graham found that areas with a warning time below an hour and a half had an average fatality rate of 13%. Those with a warning time above an hour and a half had an average fatality rate of .04%. They found that there was a large difference between the low and high in each average. Upon further investigation, Brown and Graham linked this to the surrounding landscape of the dam. Areas that can be flooded easily, such as canyons, had a higher fatality rate than did the flatlands, or plains.

What is the landscape around your dam like? Canyon Plain
(try both)

They then devised a formula to estimate the loss of life with the four crucial variables:

population size
warning time
landscape conditions

The equation is as follows:

Estimated loss of life = population at risk/{(1+5.207)[(5.838*warning time)-X]}

X is equal to 4.012 for canyon terrain and 0 for flatlands.

An engineer might think of it like this: L = estimated loss of life
P = population at risk
R= warning time

L = P / {(1+5.207)[(5.838T - X]}

If you filled out the boxes with your own data, click here to get your own estimate:

reference: Brown and Graham, 1988

Does your estimate agree with the National Inventory of Dams' downstream hazard potential estimate? Here is the classification they use:

Hazard Potential Classification Loss of Human Life Economic, Environmental, Lifeline Losses

Low None expected Low and generally limited to owner of dam

Significant None expected Yes

High Probable. One or more expected. Yes (but not necessary for this classification)

taken from the National Inventory of Dams