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# Probabilistic....

• To: seaoc(--nospam--at)seaoc.org
• Subject: Probabilistic....
• From: "Ahmed Nisar (415)896-5858" <SFOAN(--nospam--at)AM.DAMES.COM>
• Date: Tue, 31 Dec 1996 08:54:54 -0700 (PDT)
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```Probabilistic methods used to specify ground motion express annual probability
of exceeding a certain ground motion level. i.e. a peak ground acceleration
or spectral acceleration of say 0.5g means that there is a 0.002 annual
probability that this value may be exceeded.

This annual probability can be expressed in terms of exceedence probabilities
for a given life using the following relationship.  This relationship assumes
a poisson probability distribution.

p = 1 - e^(-LT)

where:    p = probability of exceedence
L = annual probability of exceedence
T = time period

Therefore for a 0.002 annual probability of exceedence, p for a 50 year period
is 0.095 or 9.5%.  For p = 0.1 or 10% and T=50 years, L = 0.00210721 or an
equivalent average return period of 474.6 commonly rounded off to 475 years.

In some codes like the Standard Building Code (primarily used in the southeast)
a 10% rpobability of exceedence is referred to as a 90% probability of
nonexceedence in 50 year.

hope this helps

ahmed nisar
dames & moore
san francisco

```