A_95 Parameter Calculation issue

03-Unexpected behaviour/errors
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Joined: 25 Sep 2020, 16:28

A_95 Parameter Calculation issue

Post by Wael.Aloqaily »

I will appreciate your help on the following issue regarding A_95 parameter calculation.

I am wondering how SesimoSignal calculates A_95 parameter. As I tried to verify it with the following simple step-signal example:
a = 0 for t = [0,1)
a = 1g for t =[1,2)
a = 0 for t = 2
where "[" means including, "(" means excluding, a is acceleration and t is the time.

According to my simple hand calculation, and considering the area under a^2 since pi and 2g are constants in Arias intensity formula:
The area under a^2 is = 1.0.
To achieve 95% of that area, the acceleration threshold required = sqrt(95)*1 = 0.974679434g.

However using Seismsignal for this example, the value reported for A_95 is 0.99750g.
If we calculate the corresponding area = (A_95)^2*t = (0.9975)^2*(1) = 0.99501, which correspond to 99.5% of Arias intensity.

Thank you in advance!
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Posts: 956
Joined: 06 Jul 2007, 04:55

Re: A_95 Parameter Calculation issue

Post by seismosoft »

The small error (0.974679434 vs 0.975) is probably due to the fact that the arias intensity is checked in steps of 1%. If you check the table in the Ground Motion Parameters with the Arias Intensity build-up at t=1.95 the Arias Intensity is 95.04950%, which gives this small difference with your hand calculations.
In any case note that your simple example is not ideal for checking the A95 parameter, due to the abrupt change in the acceleration. A triangular shape for the acceleration (with a gradation of the acceleration values) is probably better suited for these kind of checks.
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