Orthogonal Ground Motion Component

02-Analytical capabilities
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tswilson
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Joined: 10 Mar 2014, 18:08

Orthogonal Ground Motion Component

Post by tswilson »

Hi,

I trying to create synthetic ground motion record pairs for a target design response spectrum. However, I am having trouble developing orthogonal (X and Y) ground motion pairs. Do you have any suggestions on how to develop the second (perpendicular) signal?
huffte
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Re: Orthogonal Ground Motion Component

Post by huffte »

There are a few options of which I am aware. There are probably many others.

One method I have used is this:

1. Select an appropriate real record pair. If you wish to use completely artificial records, then as long as the correlation coefficient between components is less than 0.30, you could use independently generated records as long as the seismological criteria are the same - magnitude, distance, tectonic setting, site conditions.

2. Compute the spectral acceleration of each orthogonal component at some key period, which for me was 1 second.

3. Here it can get a bit tricky. Most design spectra form codes and specifications are geometric mean in nature as opposed to maximum component or arbitrary component. So it is important to know the nature of your design target spectrum. I'll assume it is geometric mean, the typical case. Compute the geometric mean spectral acceleration of the two components at the key period. Recall that the geometric mean of two numbers is just the square root of their product.

4. Let's call the spectral accelerations of the 2 components SA1 and SA2, the geometric mean SA-GM, and the target value at the key period SA-TAR. To keep the relative intensities between the two components the same as the unmodified records, match the first component to SA1/SA-GM times the target spectrum and match the second component to SA2/SA-GM times the target spectrum. This will mean the geometric mean of the components has been matched to the target, at least at the specified key period and hopefully over a range of periods.

It sounds a bit involved, I know, but I think if you'll go through a simple example it will make more sense.

You might also be interested in a separate program - SGMS - which, I believe, generates three components simultaneously, and may be found at: http://civil.eng.buffalo.edu/engseislab/products.htm. This is perhaps the original program for the specific barrier model. However, I would say that I have had success using SeismoArtif and checking to ensure that the correlation is les than 0.30 on two components generated with the same seismological criteria.

Best of luck tswilson.
Tim Huff
tswilson
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Joined: 10 Mar 2014, 18:08

Re: Orthogonal Ground Motion Component

Post by tswilson »

Thank you for the explanation on the method huffte, it was extremely clear and helpful. I had previously looked into the product you cited below but found the seismoartif interface easier to work with. Also, when scaling as follows"(SA1/SA-GM)*Target Spectrum", you are matching each component to the target spectrum multiplied by (SA1/SA-GM) correct? Does SA-TAR factor in then?

One thing, I was wondering if you would be able to cite the source (or a reference) for the method you described?

Also, this may be outside of the scope of this forum, but there are correlation coefficients for the x and y components of ground motion developed in the following study. I was thinking your method could be further improved upon by applying these correlation coefficients to the target response spectrum between steps 3 and 4. Do you think this may be appropriate?

http://bssa.geoscienceworld.org/content ... l.pdf+html

My thought is that Equation (9) in the paper should relate to the longitudinal (or x), and 11 to the perpendicular (call it y). The correlation coefficients could be used to create two different target response spectra for an x and y component. Then move into step 4 and complete as described in your method. This is taken from the methodology presented in Baker and Cornell (2005):

(See page 65/400)

https://smartech.gatech.edu/bitstream/h ... sequence=1

Thanks again for your help,
tswilson
huffte
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Re: Orthogonal Ground Motion Component

Post by huffte »

Yes. When you match the first component to the target spectrum multiplied by (SA1/SA-GM), then the spectral acceleration at the key period for modified component 1 is SA-TAR*(SA1/SA-GM). When you match the second component to the target spectrum multiplied by (SA2/SA-GM), then the then the spectral acceleration at the key period for modified component 2 is SA-TAR*(SA2/SA-GM).

Hence, the ratio of spectral accelerations between the two components remains SA1/SA2, and the geometric mean of the two components becomes SA-TAR as desired.

Note that this is the real advantage of having the "Spectrum Factor" feature in SeismoArtif. You only have to define a single target spectrum, and can then adjust the Spectrum Factor depending on which component you wish to currently generate.

And a note on correlation. The BSSA paper primarily deals with correlation of spectral acceleration values and epsilons. The limitation on component correlation of 0.30 is actually a correlation between the two time histories themselves, not spectral values of the time histories. For rationale behind limiting the correlation coefficient of orthogonal time histories to no more than 0.30, it has been observed in at least two separate studies that such coefficients for real ground motions are generally no larger than 0.3. Two such studies are:

Hadjian, "ON THE CORRELATION OF THE COMPONENTS OF STRONG GROUND MOTION--PART 2", Bulletin of the Seismological Society of America, Vol 71, No 4, pp 1323-1331. August 1981.

NEHRP Consultants Joint Venture, "Selecting and Scaling Earthquake Ground Motions for Performing Response-History Analyses", NIST GCR 11-917-15, November 2011.

Best of luck tswilson. It's an interesting topic.
Tim Huff
tswilson
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Joined: 10 Mar 2014, 18:08

Re: Orthogonal Ground Motion Component

Post by tswilson »

Thanks huffte, your insight has been very helpful.

Best Regards,
tswilson
huffte
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Re: Orthogonal Ground Motion Component

Post by huffte »

I think the method in the Georgia Tech thesis which you reference is different form the one I proposed in that the spectral correlations from Baker are used to resolve the design spectrum into components, whereas my method merely multiplies the target by two different factors.
Tim Huff
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