**Gangjin Li**
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how to impose Lysmer BC and input ground motion in OpenSees

Hi,

I would like to know how to impose the Lysmer(fully reflective) BC in OpenSees. I am building a model to simulate the shake table test of liquefiable soil. Basically, I am following the example “Three-dimensional site response analysis of sloping ground” on OpenSees website. The bottom boundary of the example is bedrock, and the Lysmer dashpot coefficient is calculated as the product of the shear wave velocity and the mass density of the bedrock and the area of the base of the soil column. However, in my case, I need to set the lateral boundaries as the Lysmer BC and the bottom as fixed BC. I am confused to define my Lysmer dashpot coefficient. Besides, it seems there is only one Lysmer dashpot set up at the origin point in that example, I am wondering whether I should assign one dashpot for each lateral node in my model rather than adopting the same policy as the example. Last but not least, I feel confused about the input of the ground motion. Simply, the ground motion is applied as a force time history to the base of the soil column at the node which shares equal DOF with the Lysmer dashpot and This force history is obtained by multiplying the velocity time history of the recorded ground motion by the Lysmer dashpot coefficient, which is so-called the method of Joyner and Chen. I am susceptible if this method can work for my case. Or there exists other ways to input ground motion in OpenSees?

Thanks a lot for answering my questions in advance.

Regards,

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Rachelle Howell@ onGangjin,

I’ve only ever tried to implement the dashpot as shown in the example you are referencing, but here are some additional resources that may be useful.

This is a presentation given by Dr. Arduino. Slide 16 shows how to define a Lysmer dashpot for a side node. http://opensees.berkeley.edu/OpenSees/workshop/OpenSeesDays2008/A08_GeotechModels.pdf

This is a report by Preisig and Jeremic. Page 15 discusses the calculation of the dashpot coefficients. http://sokocalo.engr.ucdavis.edu/~jeremic/SFSIreport/report01.pdf

Between the two, if I had to guess, I would say that the a and b in Arduino’s equations correspond to element area, but that’s just a guess based on what I was reading in the Preisig and Jeremic paper. You should check into that further.

As for alternative loading, you may want to look into the uniformexcitation pattern. I use this command to apply an input acceleration-time history to all of the nodes in my model. My tcl code for it looks like this:

pattern UniformExcitation 2 1 -accel “Series -fileTime $timeFile -filePath $accFile -factor 1”

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