## scale factor

02-Analytical capabilities
danielteruna
Posts: 10
Joined: 28 Jan 2013, 21:29

### scale factor

Dear All
I would like to know the physically meaning of scale factor in scaling of ground motion to response spectra design using seismomatch.
If this scale factor not amplitude scaling, what does it mean?.

Regards
Daniel
huffte
Posts: 978
Joined: 22 Jul 2011, 10:19
Location: Cookeville, Tennessee, USA
Contact:

### Re: scale factor

In SeismoMatch, the scale factor is applied to the input response spectrum. This allows the user to develop ground motion pairs without having to input a new response spectrum.

For example, suppose I wish to synthesize a record pair with one component being matched to 1.25 times the target response spectrum and the other component matched to 0.80 times the target spectrum. Then I could match the first component with the scale factor on the response spectrum set to 1.25 and match the second component with the scale factor on the response spectrum set to 0.80.

The geometric mean of the two components is thus preserved - SQRT[1.25(SA) X 0.80(SA)] = 1.00(SA).

This is useful because the maximum component of real ground motion pairs is typically in the range of 1.10-1.30 times the geometric mean of the two components.

So it is important to know if your input response spectrum is a geometric mean based spectrum or a maximum direction based spectrum. In the US, bridge design spectra are currently geometric mean based, while building design spectra are maximum direction based.

In the literature when you see scale factor with regard to ground motion selection and modification, it typically is amplitude scaling of a ground motion record, as you say.

In SeismoMatch, the scale factor is applied to the response spectrum, not the ground motion record.
Tim Huff
danielteruna
Posts: 10
Joined: 28 Jan 2013, 21:29

### Re: scale factor

Dear Huffte
You said the scale factor in seismomatch is scaling of the input response spectrum not the original ground motion record. I need your more explanation. In fact, we have response spectrum design, for example, T=0 is PGA =0.4g dan at T=0.2-0.5 is constant 2.5x0.4=1g and etc., and we have original acceleration record, let say imperial valley. in seismomatch I do not scale this input response spectrum but just input in seismomatch as target spectrum. To obtain the ground motion compatible to the target response spectrum, I adjust the scale factor (trial and error) until the response spectrum of the input acceleration record matching with the targeted and then We obtain the new acceleration time history from output. So, I still confuse about the meaning of scale factor in seismomatch.

Regards
Daniel
huffte
Posts: 978
Joined: 22 Jul 2011, 10:19
Location: Cookeville, Tennessee, USA
Contact:

### Re: scale factor

There are 2 different scale factors in SeismoMatch. When you define a ground motion, there is a scale factor you can specify by which all points of the input accelerogram will be multiplied.

I assume you are referring to the second scale factor - the one in the Define Target Spectrum box.

This second scale factor is applied to the response spectrum.

Let's take a simple example.

I load the chichi accelerogram which comes with SeismoMatch.

For a target spectrum, I define the spectrum from an accelerogram and select the same chichi record. You would never do this in practice, it would serve no purpose. I am just trying to demonstrate what the scale factor does.

If I leave the scale factor at 1.0, and perform the matching, the original and modified records are identical as expected.

If I change the scale factor to 2 and redo the matching, I will find that the modified record is double the intensity of the original record. So the matching process in this case was performed using the input spectrum multiplied by 2.

Hopefully that makes it clear.

Note that SeismoMatch is not simply scaling the ground motion when you perform matching. The program is adding wavelets to the input accelerogram to try to get a close match to the target spectrum.

I am not sure what you mean by changing the scale factor by trial and error. This is unnecessary.

Best of luck, danielteruna. If you are still confused, I will try again.
Tim Huff
danielteruna
Posts: 10
Joined: 28 Jan 2013, 21:29

### Re: scale factor

Dear Huffte

Thank you for your response. as you explained in example for the same accelerogram with scale factor 2.0, we get modified accelerogram double intensity. What do you mean intensity in this context? is it aries intensity or ordinate spectrum double?. when the modified accelerogram still matching for scale factor 2.0, so what are differences in the modified accelerogram exactly for both scale factor?

Regards
Daniel
huffte
Posts: 978
Joined: 22 Jul 2011, 10:19
Location: Cookeville, Tennessee, USA
Contact:

### Re: scale factor

Run the example I gave above with a scale factor of 1 and look at the tab where you can compare original and matched accelerograms. You will find that they are exactly on top of one another - indistinguishable.

Then run the example with a scale factor of 2 and compare displacement histories. They are no longer on top of each other but the modified history is double amplitude of the original.

Or, you could also compare the response spectra for the matched accelerogram in the second case to the one in the first case. There is a tab in SeismoMatch where you can easily do that as well. You will see the same thing. In the first case, the matched response spectrum is coincident with the original. In the second case, the matched response spectrum is 2 times the original input spectrum.

I hope this clears it up danielteruna. Best of luck.
Tim Huff
danielteruna
Posts: 10
Joined: 28 Jan 2013, 21:29

### Re: scale factor

Dear Huffte
I have tried to match chi-chi with scale factor 1.0 and 2.0. When I got the acceleration and velocity for scale factor 2.0 is double of accel. and velocity for scale factor 1.0. However, I got different results when the target spectrum is not from original records, let say EC8. the acceleration and velocity more than a little bit 2times (around 2.1). That's mean there are dependency on the target spectrum type.

Regards
daniel
huffte
Posts: 978
Joined: 22 Jul 2011, 10:19
Location: Cookeville, Tennessee, USA
Contact:

### Re: scale factor

When matching a record to a multiple of its own response spectrum (something you would likely only do in a case like this where you are trying to see exactly what the software is doing), the match is exact. Only scaling and no added wavelets is required.

In practical applications, you will be performing spectral matching to match the response spectrum of a ground motion to a design, target response spectrum (EC8, for example).

IT is not possible to get a perfect match using spectral matching techniques. The response spectrum will fall below the target in some places, above the target in others, and will coincide with the target in isolated locations. This is to be expected.

Even if a record does not converge to your matching criteria, it may still be useable. Most current selection and modification criteria require the average of several records to be within a certain range of the target over the period range of interest.

So your results do not appear to be outside the realm of what might be expected. By the time you match several records and take their average spectrum, you should be able to get quite close to the target.
Tim Huff