Typical construction ground vibrations are usually composed of many frequency components, as shown in the vibration frequency spectrum at left, attributable to an operating tracked excavator. When added together, the sum of the components creates the complex vibration seen. The specific makeup of the vibration components is a critical determinant of the vibration damage potential.
It is well-known and understood that structures themselves have natural vibration frequencies, called "resonances", a little like those of a tuning fork or a bell. At the home's resonant frequency, any repeated or continuous ground vibrations, like some of those caused by construction, can add to ("amplify") one another in the house vibration. This causes the vibration in the house to grow progressively larger than the ground vibration, rather than dying away due to the natural damping in the house structure. Thus, even low velocity components of a vibration which occur repeatedly or continuously at the resonant frequency, as is often the case in construction using heavy equipment, are potentially dangerous to the home.
A Simple Analogy
As an example illustrative of how resonance works, imagine that you are pushing someone on a swing. If you time your pushes to coincide exactly with beginning of the forward movement of the swing, the person in the swing will go higher and higher. That's because you have timed your pushes to be in resonance (in physics terms, "in phase") with the period of the pendulum motion of the swing. The growth in the swing's motion with repeated resonant pushes is an example of amplification, discussed below in the context of home vibrations. If your timing is a little less than perfect, you may still contribute to the swing's motion, but far less efficiently than if you had timed it perfectly. These less-than-perfectly-timed pushes are said to be "non-resonant". If you stop pushing, the swing's momentum will slowly die out, due to friction and air resistance. Those factors which act to reduce movement and vibration over time are forms of damping (discussed below in the context of home structures).
Suppose now that, instead of pushing just at the right moment, you push both then and at a time when the swing is at the top of its arc. On every second push, you will provide forward momentum to the swing, but the push at the top of the arc will be wasted (in physics terms, "out of phase"). That example shows why pushes at even multiples of the "resonance frequency" of the swing will still contribute to its motion, though progressively less effectively as the frequency of the pushes increases. These even multiple, higher frequency pushes are called "overtones" in physics; they contribute to the swing motion, even though they are not directly at the resonance frequency.
Additive Vibrations in Homes
Going back now to vibrations in homes, it's easy to see that vibration frequencies whose wave peak intensities or "amplitudes" ("pushes") are equal to or are at even multiples of the home resonance frequency will cause vibrations in the home much more efficiently than those frequencies which do not meet these conditions. Each passing ground vibration wave peak in resonance with the home's natural vibration frequency and matching a peak in the house vibration causes an increase in the vibration in the home. Since a given vibration can have many additive peaks in the minute or more that a typical construction vibration lasts, such vibrations are of considerably more concern than those which last only a few seconds. For a 20 Hz vibration frequency, there are 20 peaks per second times 60 seconds = 1200 such peaks in one minute, each of which can reinforce the vibration in the house structure. The reinforcement and growth of resonant vibrations makes these particular vibrations unusually dangerous for the structure.13
The longer the vibration lasts, the worse the situation can get. For long lasting vibrations, even small resonant components whose velocities are below any vibration standard can become dangerous for the home. The greater danger of long duration vibrations has been recognized even in blasting studies:
Duration also affects human perception of vibrations, with longer duration vibrations being less acceptable than short duration ones of the same velocity. See Vibration and Damage for more about human reactions to vibration.
Resonance Effects and Damage Potential
Actual home resonance frequencies can be easily determined by attaching a seismograph to the house wall, vibrating the house, then turning off the vibration. The house will continue to vibrate for a few seconds at its resonant frequencies. For whole home vibrations, the resonance frequency is in the range of 8-12 Hz, typically. For vibrations of individual walls, that frequency is around 20-25 Hz (see USBM RI 85071). Such vibration frequencies are more felt than heard. Structure resonant frequencies can also be calculated from engineering principles, but the results are often inaccurate in the simplest such calculations.
The growth of vibrations in a house due to resonance is referred to as "amplification". Amplification in houses has been measured and reported in USBM RI 85072 (as well as for a greater range of structural types6) for blasting-produced vibrations. For mid-wall vibrations (i.e. those responsible for pictures rattling, for example), the amplification can be as high as a factor of eight in blasting vibrations. For corner vibrations (those responsible for cracking at wall penetration corners), it can be as high as a factor of four in short-lived blasting vibrations. It is highly likely that long-lasting construction vibrations could produce even higher amplification factors. Note that, even though we have discussed mid-wall and whole house vibrations as separate entities, the mid-wall vibrations can transfer their energy to whole house vibrations. Thus, ground vibration frequency components in resonance with the mid-wall vibrations can still cause ("excite") the lower frequency (and, hence, lower energy) whole house vibrations.
Due to these resonance phenomena, most ground vibration standards take into account the frequency dependence of the vibration damage potential, setting more rigorous standards at lower frequencies than at higher ones. Because of the self-reinforcing nature of vibrations with components at the resonant frequency, continuous vibrations associated with construction are considerably more worrisome than the occasional short duration ones caused by surface mine blasting. For example, USBM RI 85073 has this quote:
Below is a chart display of the dominant frequencies of vibrations in a road construction job, extracted by FFT analysis (CVDG Pro) of the waveform vibration data. Those above 40 Hz which have secondary peaks below 40 Hz, meeting the USBM RI 8507 criterion for using lower vibration standards, are shown as well. These data reflect most kinds of road construction activities, though they do not include the majority of the most intense vibrations (due to early seismograph Memory Full Exits), nor the tracked excavator pavement demolition pounding that was most damaging.14
Directly contradictory to sworn statements made by the construction company and their "experts" - that the predominant vibration frequencies from the construction were over 60 Hz in frequency - you can see from the diagram that a large majority of the vibrations for which waveform data were obtained to allow FFT analysis had dominant frequencies below the 40 Hz cutoff mentioned in the RI 8507 quotation above. Not only was the predominant frequency of most vibrations in that road reconstruction construction project below this 40 Hz frequency criterion; those peaks meeting the half-amplitude criterion of USBM RI 85073 added a large number of additional cases to the concerning vibrations below 40 Hz. This is a good example of why one must look carefully at vibration monitoring data to make sure they are being properly presented and interpreted.
Resonant vibrations and frequencies are of most concern in causing damage, simply because they are most efficient at exciting vibrations in the house. However, vibrations at other frequencies are not entirely benign. The reason for this caution is that, no matter what the frequency of the exciting vibration, some portion of the energy of the non-resonant vibration ultimately is "partitioned" (i.e. distributed) into the home resonant frequencies, which persist for several seconds after the vibration stops.12 This is the reason that one can determine the home resonance frequencies by vibrating the house, then monitoring the vibrations in the home after the exciting vibration ceases.
Non-resonant vibrations don't have the self-reinforcing character of resonant ones, but, if they continue for a long time or they are large enough, they can cause damage by their partitioning into the resonant frequencies of the house. Thus, it is inaccurate and potentially misleading to say that a vibration of any duration, whose frequency is not in resonance with the house and whose peak velocity is below any standard cited, is "safe". This topic is developed more fully in the CVDG Pro page, Vibrations and Homes.
Below are some tabulated total displacements, Dt, (accumulated movement in inches), one measure of total vibration exposure, determined by me from actual vibration data in a road reconstruction job. The displacements are obtained by calculating in a spreadsheet program the areas under the PPV vs. time curves (see example at right) for ASCII-exported histogram vibration data.8 Details of the calculations and interpretation of these data are found in the CVDG Pro page, Vibration Exposures.
The main reason for the small total displacement in blasting is the short duration of the vibrations. Construction vibrations cause so much more integrated displacement because they last far longer and are repeated far more times. The first two entries in the table above are for two different passes of paving over soil on the same day, with the third occurring the following day. When we add those results together, we can see that houses on that street experienced in a little over 20 minutes of one day vibration displacements that would take over a month of once daily, worst-case blasting to bring about. Of course, many mines may not blast daily, nor do they normally allow blasting at the 2.0 in/sec worst-case vibration limit, so construction vibration would cause correspondingly greater exposure over those mines which have less frequent, lower velocity vibrations from blasts.
The data above are only a sample of data from a job that lasted 5 months at the location where the data were recorded. As has been discussed several times in the CVDG, most of the likely highest (and longest) readings were "lost" by the vibration technician, his company, the contractor and another "expert". The total amount of time reported above is equivalent to less than two days of work in that 5 month-long job. While not all days produced vibrations with large PPV's, nor is a large maximum PPV necessary to produce large integrated displacements, it is easy to see that the total vibration exposure in construction jobs for single days is tens to over a hundred times higher than "worst case" blasting near an active surface mine over the same period.8
There are few cases, if any, in the vibration literature of comparisons of amounts of vibration exposure from construction operations vs. those from blasting. Although peak particle velocity (PPV) is the basic criterion used in vibration standards to estimate damage potential, displacement has been advocated as a more appropriate measure of damage.9 While it is known that fatigue effects in blasting are dependent on vibration exposure (see just below)4,10, establishing a quantitative relationship between damage and vibration exposure in construction must await further research. In particular, the displacement might be expected to be most relevant to possible damage in cases where the vibrations have significant components at the self-reinforcing resonant frequencies of homes, as in construction vibration generally (see above). Total displacement calculations demonstrate the limitations of blasting standards in construction environments, the need for more research directly relevant to construction vibrations, and a necessity for far greater concern about construction damage.
Most of us are familiar with the experience of breaking a paper clip or a piece of hard plastic. If we bend it once, nothing much happens beyond the bending. If we continue to bend back and forth in the same spot, eventually the paper clip will break. This is an example of material "fatigue" in the technical sense. Different materials experience fatigue for different reasons, depending on their innate molecular structures and properties. For example, in bendable metals, the primary fatigue process is the movement to and accumulation at the bend site of "dislocations" (faults in location or filling of atomic positions) in the regular metal crystal structure.
Houses can also experience fatigue if they are vibrated many times or, worse yet, continuously. In blasting settings, it can take many blasts for the house to develop fatigue cracking.10 However, because construction vibrations are often continuous for minutes, hours, days or even months at a time, they can give the house an accumulation of vibrations over the length of the project that would take many thousands of blasts and several to many years to achieve in blasting at a mine or quarry site (see failure strain and fatigue effect diagram in USBM RI 85074), as calculated quantitatively above.
Fatigue effects in construction vibration are an area of current research, since they are not well understood for construction settings. However, most scientists acknowledge that fatigue is more likely to manifest itself with construction vibrations than with blasting vibrations. The total displacement calculations discussed above provide strong support for that expectation. There is more extensive discussion of fatigue effects and their role in construction vibration on the CVDG Pro page, Vibration and Homes. In short, while excellent blasting vibration studies like USBM RI 8507 have real value, blasting standards, by themselves, are likely to be poor predictors of damage potential in continuous or extended vibration settings, like those in construction.11
While resonance tends to reinforce and prolong structure vibrations, its opposite is damping, whose effect is to cause vibrations ultimately to die away. Damping values for homes have been measured and reported in USBM RI 8507.5 They are typically in the range of 2 to 4% of "critical damping" (i.e. that level of damping which causes instantaneous loss of the vibration). The low damping value for homes means that vibrations can persist for long enough that resonance reinforcement by continuous vibrations can easily occur.
This discussion of resonance, amplification, fatigue and damping is, by no means, exhaustive of all the matters that should be considered in evaluating resonance effects and their role in causing damage. I hope that it will help homeowners better understand the terms and their importance, so they can read the literature more productively and place claims about damage potential based on blasting studies in proper scientific context.
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