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# Re[2]: Probabilistic Definition of Seismic Hazards

• To: seaoc(--nospam--at)seaoc.org
• Subject: Re[2]: Probabilistic Definition of Seismic Hazards
• From: "Haninger, Ed" <ed.haninger(--nospam--at)fluordaniel.com>
• Date: Tue, 31 Dec 1996 08:43:00 -0800

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A little bit on exceedance probability verses return
period.  These two are related but it is not a simple
linear equation.  The relationship between the two is
given by the equation:
EP = 1 - e ^(-n/T).
(one minus e to the power (-n/T))

where: EP is the exceedance probability
e is the constant 2.718...
n is the design life
T is the return period

For example, with a return period (T) of 72 years (a
common earthquake) and a design life (n) of 50 years the
exceedance probability (EP) is 0.50.  In other words, if
you have a structure designed for a 72 year event there
is a 50% probability that this level will be exceeded in
the normal structure design life of 50 years.  Another
good example is the UBC design earthquake.  It has a
return period of 475 years which equates to a 10%
probability of being exceeded in a 50 year period.

Ed Haninger
Fluor Daniel
_________________________________
Subject: Re: Probabilistic Definition of Seismic Hazards
Author:  seaoc::(SEAOCAA) at ~FABRIK
Date:    12/30/96 8:54 PM

...Please clarify what the difference is between annual frequency of
occurrence and annual frequency of exceedance - aren't these different ways of
expressing the same thing?  I do prefer the method of expressing events in
terms of probability of exceedance during a given period, since it gives a
better sense of the risk involved, but I am not clear on what the mathematical
difference is.

If an event has an annual frequency of occurrence of 0.002, then it has a 500
year expected return period.  Then in 50 years, doesn't it have a 10%
probability of being exceeded (0.002x50 = 0.10)?  and statistically, wouldn't
it have a 100% probability of occurring in 500 years?

The problem with using return periods to describe probabilistic events is that
it seems to give a false sense of security.  For example, consider design for
flotation resistance against a 100-year flood.  Such a flood would have a 0.01
annual probability of occurrence. For a 50 year design period, is seems to me
it would have a "50% probability of being exceeded" (0.01/year x 50 years).
If you are concerned with flotation of a structure, designing for a 100-year
flood for a 50-year design life sounds conservative.  But having a 50% risk of
exceedance during the design life sounds very risky.

From: "Bill Sherman" <SHERMANWC(--nospam--at)cdm.com>

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