Stress Reduction ( r sub d ) Calculation Questions

[theCorkster]

I'm updating a spread sheet used for calculating liqueaction potential. The sheet incorporates a formula for stress reduction presented in 1997 NCEER workshop. A paper presented in 2004 by Idriss and Boulanger at the combined conference for ICSDEE and ICEGE recommended an alternate calculation that incorporates the earhtquake magnitude. Both the oridignal Seed and Idriss and Idriss and Gokesorkhi calculation are shown on the attached spreadsheet.

I've attempted to use the Idriss and Golesorkhi calculation, but my results for a M7-1/2 earthquake do not match the presented data (both excel and manual).

Q1 - Is the Idross and Golesorkhi equation being used to calculate r sub d ? and

Q2 - Any thoughts on where my excel calculation is incorrect?

Thanks for the input!

 

[dgillette]

Q1: I didn't know where to look for the Idriss and Golesorkhi formula so can't comment, but I'm pretty sure SOMETHING is amiss, because Rd is 1.0 at the ground surface, by definition.

My opinion is that you shouldn't worry too much about which one you use, because the actual value that you would backfigure from a response analysis is very sensitive to freq content of the EQ and the SWV profile of the soil, so the variability is very large. I recommend that you track down one of the papers from 2001 or later in which Raymond Seed, Onder Cetin, and others present a different Rd correlation, based on more SHAKE runs than the original one was. (The original one was created by somebody sitting down with all the SHAKE outputs that they had on hand, and plotting backfigured Rd.) [Maybe if you google Cetin + Seed + liquefaction.] They show backfigured Rd profiles from a huge number of SHAKE runs, and the variability is pretty large, like 20% or so (0.8 to 1.0) at 10 feet, and very large at depths greater than that. They show that Rd drops off more quickly with depth than the older curve does, but also that there isn't much dependence on magnitude, or at least that the magnitude effect gets buried by the other sensitivities. I have never seen Idriss's SHAKE results from which he drew that family of curves, so I don't know how strongly they show the trend with depth.

Every time I turn around, the "simplified method" gets more complicated.

 

[theCorkster]

dgillette;

Thanks for the information. I've located a copy of the Seed & Cetin paper, and resolved the issue with the calculation of r sub d.

And you're correct; simplified no longer means simple.

Thanks

 

[msucog]

yes, i went through similar issues not too far back and finally tracked down some examples and other documentation on the subject. may i suggest:

http://nisee.berkeley.edu

pay the $25 and get full access to a great database of papers

 

[Adrianopipiolo]

Hello,

the r sub d Idriss equation works!!!... but you typed it bad (in excel)!!!

You have not to change it to radians because it is in rad, and then you don't have to put the parentesis ()
you have to write in excel:

Alfa=-1.012-1.126*SENO(depth/11.73+5.133)

Sorry for my english, I kwow that I have to improve it...

Good luck!

 

[theCorkster]

Adrianopipiolo:

Thanks for your reply - sorry for the tardy response. You're exactly right. Back to basic programming .....