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Resonance/Fatigue
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Typical construction ground vibrations are usually composed of many frequency components, as shown in the vibration frequency spectra at left, attributable to an operating excavator. When added together, the sum of the component intensities and frequencies creates the complex vibration typically seen on a seismograph trace. 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 or near 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 or near the resonant frequency, as are often found in vibrations from construction using heavy equipment, are potentially dangerous to the home. In this chapter of the CVDG, we'll take a closer look at what resonance is and how it can dramatically increase damage probabilities. 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 (the time required to complete a cycle of pendulum movement) 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. Amplification occurs because repeated "pushes" add energy to produce a larger and larger motion. 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 add to the forward movement of the swing, but the push at the top of the arc will be wasted on the surrounding air (in physics terms, "out of phase"). This 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 number ("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, but at whole number multiples of it. 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") occur at, or at even multiples of, the home natural 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 additive 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],[15],[16] The longer the vibration lasts, the worse the situation can get. For long lasting vibrations, even small resonant vibration 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 (sometimes seen referred to by scientists as the "eigenfrequency") is in the range of 8-12 Hz, typically. For vibrations of individual walls, that frequency is around 20-25 Hz (see USBM RI 8507)[1]. 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. Resonant amplification of ground vibration in house structures has been measured and reported in USBM RI 8507[2] (as well as for a greater range of structural types)[6] for short-lived 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 due to shearing forces), it can be as high as a factor of four in blasting vibrations. It is highly likely that long-lasting construction vibrations could produce even higher amplification factors.[17] 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 which are mostly responsible for damage. 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, the balsting vibration study, USBM RI 8507 has this quote:[3]
Construction Vibration Frequencies
Directly contradictory to sworn statements made by the construction company and its "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 "unsafe" 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 project below this 40 Hz frequency criterion; those peaks meeting the half-amplitude criterion of USBM RI 8507[3] added a large number of additional "unsafe" cases to the concerning vibrations below 40 Hz. This is a good illustration of why one must look carefully at vibration monitoring data to make sure they are being properly presented and interpreted. Non-resonant Vibrations 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 non-resonant frequencies are not entirely benign, as indicated earlier. 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], [18] This is the reason that we can find out the home resonance frequencies by vibrating the house at non-resonant frequencies, 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 entirely "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 the same road reconstruction job. The displacements are obtained by calculating in a spreadsheet program the areas ("integrated displacement") 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 most normally allow blasting at the 2.0 in/sec worst-case, high frequency vibration limit, so construction vibration would cause correspondingly greater exposure over the majority of mines which have less frequent, lower velocity vibrations from blasts.[19],[20] 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 indicated above, most of the likely highest (and longest) readings were "lost" by: the vibration technician, his company, the contractor and an engineer "expert" working on behalf of the contractor. 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 ground 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],[23] 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. Soil Resonance There is a known, but relatively little discussed or considered, resonance effect in the ground itself. Layering in the ground (e.g. the layering between the topsoil and the subsoil) can produce a resonant effect much like that produced in a home structure, when the frequency of the vibration wave is at or near the natural vibration frequency of the soil layer. The natural frequency is determined largely by the thickness and width of the resonant layer.[21] Since the effect of such resonance is to amplify ground vibrations in the soil layer on which a structure sits, the structure itself experiences a correspondingly higher vibration velocity. That velocity can, itself, be further amplified in the home structure resonance. These effects can contribute to the difficulties in predicting vibration velocities from simple propagation equations of the sort discussed in the CVDG chapter, Vibration and Distance.
The wavelength of the vibration can be calculated from the ratio of the wave propagation velocity (about 450-2000 m/sec in sand for pressure waves, about 300 -1700 m/sec in clay for pressure waves, about 200-400 for shear waves)
over the frequency of the vibration. When the wavelength is at, or at a multiple of, the distance between the home foundation and the retaining structure, such resonant amplification in the ground is possible. Since ground
vibrations tend to be broad in frequency distribution, this means that many components of the vibration may be amplified by resonance in the ground of such raised landscaping. Every such example of
landscaping will not necessarily resonate strongly, but those who have such landscaping features should pay attention to nearby construction.
Fatigue Effects 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 positions of atoms in the metal crystal structure. The materials used to construct 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 8507)[4], 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 of 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 scientific literature more productively and place claims about damage potential, often based on largely irrelevant blasting studies, in proper scientific context.
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At right is a chart display of
the dominant frequencies of vibrations in a road construction job, extracted
by me using Fast Fourier Transform (FFT) spectral analysis (
The pavement demolition by repeated pounding with an excavator, which did the initial damage to numerous homes, was not vibration monitored.
However,
there were a number of monitored incidents of much less intense excavator pounding which occurred after the contractor was notified of the initial damage and its cause. These all showed broad FFT vibration frequency spectra, similar to
the example at right, with most of the integrated intensity below 40 Hz and dominant FFT frequencies close to 20 Hz, near the mid-wall resonance frequencies for most types of home structures. The PPV of 0.150 in/sec
for this vibration was above the Class IV FTA vibration standard. Most types of ground impact
vibrations, like these, show similar frequency spectra. It is, thus, likely that the unmonitored pounding of far greater intensity would have shown similar FFT vibration spectra, albeit with far larger PPV's.
