I need a shear stress-strain hysteresis loop in shallow depths by a surface record.
First you should clarify the dynamic properties of ground profile, and then you can use SHAKE to get the record of base and shear stress history of surface according to your record in ground surface. Combining the derived shear stress history with the known soil dynamic property, you can get the shear stress-strain hysteresis. Or you can further conduct dynamic ground response subjected to the derived base record in time domain using FLAC.
Your question make me to believe you don't want to use numerical techniques and you have no data from the soil layers. That is, you want to estimate soil behavior directly from the recorded acceleration. If it is, you need at least two recorded motion at two different depths (a vertical array). In this way you can estimate hysteresis behavior of the sandwiched layer (the layer between the two recorded motion) through the following relations,
strain= (d1-d2)/z
stress=0.5.rho.z.a1
where d1 and a1 are, respectively, displacement and acceleration at top of the sandwiched layer (ground surface) and d2 is the displacement at its bottom. Besides, z is thickness of the sandwiched layer and rho represents its density.
Hi Chih-Chieh
Thanks for your guide, but unfortunately the subsurface property of soil is not known. Probably, a mathematical approach can solve this problem.
Hi Amin
You understand this problem very well. Your proposed approach is "Shear Beam Theory" that offering by Zeghal & Elgamal in 1993 and for use it, there should be at least two accelerometers in different depths.
Unfortunately, I have only one time history record!
Yep the technique was also used by Zeghal and Elgamal (I think for Wildlife liquefaction site). Obtaining soil behavior through only one recorded motion would be a real challenge. To my knowledge, there is no recognized technique to do that. A recorded motion is a signal conveying a couple of things such as accel., vel, disp, frequencies, phases, etc. neither of them are directly related to soil behavior.
Dear Hamid.
You could use also a single station estimate method for dynamic deformations, assuming the incidence of one of this two possibilities: S body waves or Rayleigh Surface waves. In any case you will need to make assumptions about the soil properties.
Not possible. You need information about soil profile. Still you will assume conditions for 1D wave-propagation analysis, which is somewhat questionable.
Dear Omar
Thanks for your guide. Can you introduce me source of these functions and relations? I need to more evaluation.
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