How to think about footfall vibration from walkers in buildings

A lot of our work happens deep in underground basements, where high-end nanotech imaging tools are best-protected from both environmental as well as locally-generated vibrations. But even in buildings with cutting edge imaging suites, there’s often tens or hundreds of square feet of laboratory and office space for every square foot of basement-level SEM/TEM Room space. Those labs and office workers aren’t nearly as sensitive to vibrations as the molecular and atomic-scale imaging going on downstairs, but they are still sensitive. And that means that our job isn’t finished when we’ve made the electron microscopes and scanning probes happy; we still need to make everyone upstairs comfortable and productive, too.

On the upper floors of most facilities, people moving around the building are (or at least, should be) the dominant source of floor vibrations. Walker-induced vibration criteria are usually specified in terms of an overall velocity limit, say “8,000 uin/sec”. In real structures, though, the impact of footfall vibration scales non-linearly with walking pace. That is to say, someone walking at 110 paces per minute creates more than 10% more vibration than another walking at 100 paces per minute. Walker weight matters a little bit (and shoes and floor finish matter far less than you’d expect), but the walker speed is by far the most important variable for a given structure.

This means that we need to do some thinking about what walker speed we should use in any evaluation, whether it’s a vibration test of an existing structure or a model analyzing a proposed structural vibration design. 

Of course, some people walk faster than others; furthermore, the sensitivities of people, animals, and laboratory instruments vary, too. So, how exactly should we think about floor vibration due to footfall impacts from people walking around in buildings?

These kinds of criteria are quasi-qualitative: we choose a sensitivity level (micro-vibration velocity; we’ll use micro-inches/sec, or uin/sec) and a walker speed (paces per minute, ppm), with the understanding that neither of these parameters is precisely applicable to all walkers and all sensitive receivers. What this means is that any pair (velocity + pace) is attempting to guide the general result to a particular kind of outcome. 

Do we want the average person in a given setting -- office, bedroom, hospital room -- to frequently or infrequently notice nearby walkers? Do we want the work of laboratory users to be interrupted by only the highest-speed walkers? Just how often do “high-speed walkers” appear? And what are the consequences of that interruption? 

All of these parameters and questions fall into some sort of continuum, so it would make sense to think statistically about these building vibration problems

We can start by accepting that both walker speeds and sensitivities aren’t single numbers; instead, they’re actually distributions:

Not everyone walks the same speed, and people can be more or less sensitive to vibrations. I don’t know what the actual distributions look like, but I think we can safely say that, on some level, a "normal" distribution is a decent first guess.

Not everyone walks the same speed, and people can be more or less sensitive to vibrations. I don’t know what the actual distributions look like, but I think we can safely say that, on some level, a "normal" distribution is a decent first guess.

When it comes to vibration sensitivities, the threshold of perception varies for all kinds of reasons, from biomechanics to body awareness to setting. But overall, most people’s thresholds probably fall somewhere between 4,000 and 8,000 uin/sec:

 
Again, I’m just guessing at the shape of the distribution here, but suffice to say that for most people, the threshold of perception falls somewhere between 4,000 and 8,000. 

Again, I’m just guessing at the shape of the distribution here, but suffice to say that for most people, the threshold of perception falls somewhere between 4,000 and 8,000. 

 

That means that only a few people even notice vibrations below 4,000 uin/sec. Conversely, relatively few people will fail to notice vibrations above 8,000 uin/sec.

In laboratories, a similar thing is going on with vibration-sensitive instruments. Of course, there’s a huge variety of tools and experiments out there, so the distribution is comparatively really, really wide. There are a few monuments along the way, as instrument vendors struggle to make their tools work in environments that meet a few standardized criteria. Even amongst tools, however, there is still some variation in vibration. Equipment manufacturers state their criteria more or less conservatively, or sell instrument options and accessories that result in minor changes, whether or not the vendor tells customers. Even the different uses of a single instruments matters, as some scans or experiments push the tool “harder” than others:

 
I have no idea if this distribution is remotely accurate; the point is that there is indeed a distribution, even amongst classes of tools. Note that there are plenty of instruments far more sensitive to floor vibrations than VC-D/E, but you probably shouldn’t be thinking of putting these on upper floors of buildings, to begin with.

I have no idea if this distribution is remotely accurate; the point is that there is indeed a distribution, even amongst classes of tools. Note that there are plenty of instruments far more sensitive to floor vibrations than VC-D/E, but you probably shouldn’t be thinking of putting these on upper floors of buildings, to begin with.

 

It should now be clear that sensitivities are not singular numbers, but ranges. So, selecting a threshold means finding a place on the sensitivity curve that you can live with. A statistical perspective will help us think about these ideas from the sensitivity side. However, there’s still the matter of distributions in walker speeds, which is what determines how much vibration gets generated to begin with:

 
It’s no surprise that some people walk faster than others. In a given setting, the walker pace depends mostly on personal gait and just how anxious someone is to get somewhere else.

It’s no surprise that some people walk faster than others. In a given setting, the walker pace depends mostly on personal gait and just how anxious someone is to get somewhere else.

 

The distribution in walker speed depends a lot on setting. Since the vibration impacts of walkers scales strongly with walker speed, we should probably pay attention to this:

 
The absolute numbers might vary, but on average, people move more briskly in long, straight, open corridors as compared with small rooms. We can think of this as two different distributions, each centered around its own average.

The absolute numbers might vary, but on average, people move more briskly in long, straight, open corridors as compared with small rooms. We can think of this as two different distributions, each centered around its own average.

 

Inside enclosed rooms, the majority of people will walk more slowly than 100 paces-per-minute. In corridors, speeds above 110 ppm aren’t unexpected. For some rooms, like laboratories with multiple parallel lab modules, most of the walking that happens is from one part of the bench to another. It’s not unreasonable to expect low average speeds for these walkers, since they’re not going far.

Of course, if all of the modules are tied together by a long pathway along one or both sides, then you should not be surprised to find that people moving between modules will walk considerably faster. And in the corridor outside you’ll find the fastest walkers of all – although beware that “outside” in terms of partitions isn’t necessarily “outside” in terms of the structural grid. So, when we consider the distribution of walker speeds, we have to think about all of the walkers that we might encounter. This is true even if in the end we chose to ignore (or accept) the impacts of some of those walkers.

Understanding how sensitivities and walker speeds can vary, we now have the tools to be able to speak intelligently about walker-induced floor vibrations, whether in labs or office buildings or hotels.

If we look inside an office, far from the corridors, we might guess that the “average” walker moves at 75 ppm. Since that means that only occasionally will a walker will move at more than 90 ppm, and since most people can’t feel vibrations of 4,000 uin/sec or less, meeting a criterion like 4,000 uin/sec for walkers at 90 ppm effectively means that “most people won’t feel most walkers”

Conversely, since the average walker moves at 75 ppm, and since most people can at least barely feel vibrations of 8,000 uin/sec or more, a criterion like 8,000uin/sec for walkers at 75ppm means that “most people will indeed feel the average walker”.

With this kind of thinking, you can speak to everything from the comfort of hospital patients to the anxieties of laboratory researchers. Do you demand 99.999% reliability in your experimental apparatus? Is it OK if your patients feel the floor tremble when residents walk past? What if they are jolted awake when the nursing staff scrambles for an unexpected emergency? Can our office workers tolerate occasionally feeling people walk past their desks? How “occasional” is acceptable, anyway? 

Byron has been measuring people walking around in buildings for nearly 20 years. Contact him if you’re worried about floor vibrations in your building, whether it’s a laboratory, office, or medical center.