×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Forcing function of ground shaking

Forcing function of ground shaking

Forcing function of ground shaking

(OP)
I have a situation where a large equipment foundation (with a lot of unbalanced force) is causing some framing on a adjacent foundation (they are not physically connected) to shake. From what I have been told, they know it's from that because it didn't shake until the vibrating machinery (nearby) was added. I've thought about just adding some framing to make it stout.......but i am wary of doing anything about a vibration issue without a model to understand what is going on.

I have the calculations for the new foundation (for some reason they did not want this guy to fix the problem; apparently they are mad at him for not anticipating the problem to start with; they'll probably be mad at me before it is over smile). But what I don't have is: dynamic properties of the soil (what else is new) or displacement/velocity measurements from this stuff shaking (client won't spring for that either). I think the other engineer made some pretty valid assumptions for the soil and came out with some decent spring constants: I've been out there, and (just based on "feel") it doesn't seem to me to be an annoying level of vibration.

So as far as my model goes, I've got it set up in STAAD but I am facing a dilemma: the forcing function. My solution is (in the absence of measurements) to assume a believable level of displacement at the source point (that compares well to the calculations) and then to calculate it's attenuation based on distance to the foundation in question. I did this using a formula I found in a soil dynamics book for Rayleigh/S&P waves in soil. From that (and figuring the dynamic stiffness of the existing base) I was able to figure a amplitude [Fo in lbs] for my forcing function. As far as the frequency of the forcing function, I was able to figure that based on a formula I found for a site's period (with shear wave velocity being one of the variables; another assumption on my part) and got the frequency that way.

Applying this at the base level of the foundation in question, i get believable results (compared to what I see in the field). But I still would like a second opinion here on some of my assumptions (aside from the soil data):

1. Is correlating wave attenuation (in the soil) with displacement attenuation really a valid assumption? (I.e. do they attenuate at the same rate in soil?)

2. Is the ground forcing frequency calculation valid? I am saying here that the ground is causing the vibration.....but does the forcing function of the adjacent machine have any impact? I'm assuming "no" because Rayleigh waves tend to be the vast majority of the waves produced by a ground disturbance and I don't think their period is altered by the source.

Any feedback is welcome.

RE: Forcing function of ground shaking

Oh? I'd think that the soil waves are directly dependent on the adjacent machine's load and frequency, attenuated by radiation distance.

What kind of machine and operating frequency?

You might make some progress by excavating a trench between the two, if you have room to do so, then covering the trench if you need to. It would seem that isolation is necessary in one form or another.

RE: Forcing function of ground shaking

(OP)
I think the soil waves are affected in terms of amplitude (not frequency) by the machinery. But I'm not 100% sure.

I cannot cut any trench because there is an underground obstruction. The machine is running at about 1800 rpm.

RE: Forcing function of ground shaking

WARose -

Ugh, this is a tough series of questions. Probably best addressed by a geotech. Even then, my guess you'd want one who specializes in soil dynamics. And, this stuff is probably not simple even to them.

But, as far as a simplistic answer from a humble structural guy....

I think it depends on how far away you are from this "adjacent" machinery. If it's very close, then the frequency of the equipment will be the frequency of the forcing function on your structure, or very nearly the same. I've been nearby (maybe 100ft) when folks are driving piles or when other heavy equipment is being used. I don't think the frequency changed at all.

If the equipment is far away, then it is possible that the forcing function will change based on the properties of the soil and such. But, then I would think the soil and distance would completely attenuate the response. To the point where it's not virtually unnoticeable. You just get so much radiation damping from the surrounding soil that the magnitudes should drop pretty quickly.

The propagation of earthquake waves is on a different order of magnitude from dynamic equipment. So, I don't know that using wave propagation theory for earthquakes would be 100% valid. Just my 2 cents.

RE: Forcing function of ground shaking

(OP)
Thanks for the feedback JP. I did run it (to be on the safe side) with a forcing frequency identical to the forcing function from the source (just to be safe). That's good info on the pile driving....thanks.

The reason I felt the attenuation formula I used was applicable is because in the book I got it from (i.e. 'Vibration of Soils and Foundations', by: Richart, et al. 1970, p. 246.), it seemed to be brought up in connection to vibrating machinery and for the purposes of isolation. So I thought there could be some sort of correlation.

RE: Forcing function of ground shaking

At 1800 rpm you should be above the typical problem frequencies 400-800 Hz. Are you sure that something isn't wrong with the machine? Is it properly balanced? Is it reciprocating, or centrifugal. What weight, power rating? Normally if the machine isn't shutting down on excess vibration, they don't cause all that much trouble. Is there a vibration sensitive process going on next door?

Otherwise the machine's foundation itself is extremely under designed. For machines over 500 HP the mass of foundation alone should be enough to dampen much of the vibrations at 1800Hz. The foundation should generally have about 4-5 times the mass of the machine.

What soil do you have there? I have seen instances where the depth of bottom of foundation to "solid" layers is just right such that reflection and a net amplification has occurred within the soil layer above. What obstruction?

RE: Forcing function of ground shaking

(OP)
No, there is nothing wrong with the source machine. It's fairly new but it produces a great deal of unbalanced force (at least according to the manufacturer’s data). The framing on the new foundation is pretty flimsy and I could probably fix it without doing this.....but like I said in the OP I'm not comfortable with fixing the problem without such a model. The underground obstruction (to cutting a trench) is electrical and other utilities (from what I've been told).

RE: Forcing function of ground shaking

So the machine is on a steel skid? Is that the frame you talk about? Are the frame beams in contact with the foundation continuously grouted in place with epoxy grout? All the anchor bolts in place? Most skids these days tend to be pretty flimsy and are not designed to transmit loads to anchor bolt locations. They need firm contact with the grout. Beef up the frame? If it's not that easy, it's going to get expensive fast.

RE: Forcing function of ground shaking

(OP)
The machine is on a steel skid yes. Those frame beams are held down by anchors that are torqued down pretty good. Looking at the skid drawings, I don't think there is a problem there. The issue at hand is the forcing function and attenuation of amplitude....but I've got some good feedback there.

RE: Forcing function of ground shaking

It doesn't sound like you're going to have enough information to make a useful model. You'll just end up spending a bunch of time crunching numbers that don't necessarily mean anything. Since you'll end up calibrating your model to match whatever you're seeing, it'll just match you assumptions anyway.

I'd probably write a report saying that I recommend further information gathering, but in lieu of that information I recommend attempting to mitigate via a, b and c. I'd make it clear that they are just best practice measures and without further data I can't make informed recommendations specific to the scenario in the field. If the original engineer did a reasonable job of design and seems to have gotten kicked by the unlucky vibration fairy, I'd also point out the ways in which he followed standard engineering practice.

If the issue is amplitude, and they aren't willing to pay for measurement that would allow for a detailed analysis, my first instinct is to add mass and isolate in any way possible. Then maybe add some stiffness to the frame. I'd also see if they can fiddle with the rpm while I'm around. Ramp the system up and down and see if things spike or get better. That'd be a quick check to see if it's a resonance problem. It's good to check even if your math shows it shouldn't be a problem. You can have resonance in modes that don't necessarily show up in a simplified model that hum or otherwise cause irritating side effects.

While writing that paragraph, I also realized that you might be able to vary the equpment RPM to come up with the frequency of the forcing function on the affected nearby structure. If you see resonance events while ramping up the equipment and can get a good calculation of the natural frequency of the forced structure you could estimate the frequency of the forcing function at the forced structure. Then using the RPM of the forcing equipment at that same point in time you can come with a transformation between the two. That could get you a rough frequency. Doesn't get you an amplitude.

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources