Earthquake return periods for items to be replaced

[GraemeL]

In most loadings codes for earthquake areas, the design earthquakes are given as uniform hazard spectra with an assessed return period. For example, for an Ultimate Limit State = return period of 450 years, approximately 10% probability of exceedance in a design life of 50 years.

t = design life = 50 years
ts = return period = 450 years

probability of exceedance = 1 - [1 - 1/ts]^t

Can one make a case for an intermediate check of a physically deteriorating structure that has a design life of 50+ years but is deteriorating such that it will be refurbished within that 50 years?

That is, in its deteriorated state using a shorter design life (representing the time left before refurbishment) and using the same probability of exceedance, thus ending up with a shorter return period earthquake being the design check case for the deteriorated structure.

t1 = time left before structure refurbished (years)

tsr = Reduced Return Period with the same probability of exceedance
= 1 / [1 - (1-p)^(1/t1)]

One then could scale down the code uniform hazard spectra to check the weakened structure and see if the planned refurbishment has to be pulled forward or could be put back if the rate of deterioration is known.

I am struggling to see if there are holes in the logic of this or whether the approach is valid. I would appreciate the thoughts of others or whether anyone has applied this in their area of expertise.

As buildings or industrial plant ages and owners want to put off expenditure as long as possible, I would have thought others would have had to struggle with this (would also apply to wind loadings as well).

 

[VoyageofDiscovery]

Hi Graeme,

You have obviously grappled with this for some time as you are statistically justifying your point of view, as you should.

However, what I see from this is if your design life is less, I gather then that the event you are designing for or trying to justify is of less magnitude. This does not safeguard the public and to strike this balance is difficult if not impossible, since there are many unknowns. What one of my collegues mentioned to me was if all the structures in a region collapse during an event, you are not to blame due to current codes and understanding, however if your building is the only one to collapse you are to blame.

Clients tend to push us into doing some interesting things, however doing an extrapolation outside your code for the Client's benefit may come back to haunt you.

Regards

VOD

 

[HochwaltPE]

I agree with VOD's comments, though from a somewhat different perspective. While your proposal would target the same probability of failure for the building during it's "life", the risk to an occupant of the building during any given time period would be increased. Since our primary responsibility is to protect the occupants of our buildings, I have to agree with VOD discouraging you from this approach.

Having said that, the reality is that it is better to improve safety somewhat than not at all. For voluntary upgrades in the US, the usual minimum acceptable performance is "collapse prevention" in the code level event. There are several documents published by the Federal Emergency Management Agency that we use to define what is meant by collapse prevention.