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Re[2]: Probabilistic Definition of Seismic Hazards

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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  
______________________________ Reply Separator
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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>