Reaction of Soils and Foundations to Vibration

[DerekMG]

I am trying to gauge the effect of vibration (from generators and a rolling mill) on underlying soils, and subsequently the foundations on which the vibrating sources are supported. I have various calcs for particle velocity, particle acceleration, displacement, propogation and transfer factor, I just can't quire figure how to relate them all. Does anyone have any tips on how to gauge this? Unfortunately I don't have a frequency for the vibratory sources.

 

[molerat2210]

Bowles has a section on Dynamic Analysis. I believe you need to determine the dynamic modulus. I was recently involved in a project where seismic refraction was used to determine the dynamic modulus. I am mot familiar with the analysis beyond that.

 

[Mccoy]

That's a very interesting field.
The Bowles book chapter on foundation vibrations is pretty good.
The reference though is still Gazeta's "Foundation vibrations" in Foundation Engineering Handbook, Fang, 1991. Lots of plots, graphs, illustrations.
More recently, Wolf And Deeks 2004 proposed a cone-model, whose result are identical to Gazeta's model with axialsymmetrical foundations. Their book has a link to a standalone calculation program (CONAN).
Other authors are Puri and Prakash (various years of publication.
According to Gazetas when dealing with machinery vibrations the strains are so small that the dynamic shear modulus Go should be used (might not be the same when strong earthquakes are involved).
Go may be calculated from Vs, shear wave velocity, or Eo, young's modulus at small strains.
In the case of shallow rigid bedrock, I would suggest today to use Nakamura's method (microtremors) to measure directly the frequency of resonance of the ground, since the solutions give very high settlements when the frequency of machinery is close to that.

 

[molerat2210]

That sounds like good advice Mccoy. It was really Remi (Refraction Microtremble) we used I used on a recent project instead of seismic refraction, like you suggested.

 

[Mccoy]

Molerat, I actually meant the Nakamura method to measure the field of tenuos superficial waves (microtremors) which is naturally occurring in the ground. ReMi, (refraction microtremors) uses this same field to calculate by inversion a profile of S-waves (similarly to the MASW method). The HVSR method is the best one because you actually measure directly the resonance frequence(s) of the ground, whereas you can only estimate it from Vs profiles. I'm attaching a typical HVSR output from a project I followed, here there is a rigid layer at the depth of 7-8 meters, with an impedence contrast such to generate a pronounced peak at the frequence of about 7 Hz.
Now, you can imagine better than I what would happen should the machinery work with that same frequency. In the Gazetas model that would result in a very small dynamic subgrade modulus hence a substantial settlement.

 

[Patgeotech]

For dynamic modulus, one could undertake resonant column tests in the lab for your specific frequency or we use continous surface wave surveys that produce a continous dynamic shear modulus through the profile (sort of dynamic probe test in the true sense). Quite a quick test to do and provides an insight if there is a problem similiar to CPT testing.

Bear in mind, dynamic parameters can only be derived from dynamic tests and not static parameters - but you probably know that, so apologies if I am "telling you how to use a scewdriver'.