Logo for Vibrationdamage.com

 

Resonance/Fatigue

 Home Up Vibration Frequencies Vibration Standards Resonance/Fatigue Vibration Regulation

 

Home
Up

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:

"The safe level criteria established for blasting are often applied to these situations with little justification. Traffic is usually a steady-state source of low amplitude. Appropriate safe levels would have to be lower than for blasting, which is relatively infrequent and of shorter duration."11(emphasis added)
 

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:

"The safest approach is to consider the low-frequency part of the time history separately, and where it is below 40 Hz, use the 0.75 in/sec or 0.50 in/sec criteria. If Fourier spectral analysis is used, any spectral peak occurring below 40 Hz and within 6 dB (half amplitude) of the peak at the predominant frequency justifies the use of the lower criteria." (emphasis added)

Construction Vibration Frequencies

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.

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 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.

Construction vs. Blasting Vibration Exposure

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.

Activity
 
Approx.
Duration
Max Ground PPV
 (in/sec)
Approx.
Seis.
 Distance
Dt (t)
 (in.)
Dt (v)
(in.)
Dt (l)
 (in.)
Est.
Blasting
Dt
Asphalt Paving/Compaction, 1st mat, 1st lane 15 min. 0.34 7 ft. 19.45 16.55 33.825 1.5
Asphalt Paving/Compaction, 1st mat, 2nd lane 7 min 0.23 20 ft. 8.925 8.55 17.95 1.5
Asphalt Paving/Compaction, 1st mat, 4th lane 2 hr. 0.33 5 ft. 51.575 33.45 22.525 1.5
Excavator Drive-by 1 min. 0.085 20 ft. 1.75 1.75 1.6 1.5
Pavement Milling 2.25 hr. 0.165 5 ft. 56.125 46.025 33.575 1.5
Excavation 8 hr. 0.170 35 ft. 133.1 56.675 58.025 1.5
Pavement Removal 6.5 hr. 0.150 70 ft. 34.675 9.225 22.975 1.5

Activities are derived from videotape records. Seismograph distances are for the closest approach point to an in-calibration seismograph. Vibrations with nearly a factor of two greater PPV's were recorded at another location by an out-of-calibration seismograph, but are excluded entirely from this analysis. They were obtained from video records of location of work and placement of seismograph, using Google Earth to determine distances from the locations. Estimated distance error is ▒10%. Seismographic information comes from original raw data, exported to ASCII and analyzed in Excel«. Data for all three measurement vectors are included. Blasting displacements are derived from a "worst case" allowable 2.0 in/sec PPV, with durations estimated from data in USBM RI 8507.7 Max PPV's are for a single zero crossing frequency, not the entire frequency distribution, since very few cases had complete waveform data for the day or operation. These data are not weighted for frequency distribution and do not represent house vibration velocities for the same reason.

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.

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 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

Damping

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.


1. Structure Response and Damage Produced by Ground Vibration From Surface Mine Blasting, USBM RI 8507, pp. 30-31
2. Ibid., p. 33, et seq.
3. Ibid., p. 59
4. Ibid., p. 44
5. Ibid., pp. 30-31
6. COMPARATIVE STUDY OF STRUCTURE RESPONSE TO COAL MINE BLASTING, Prepared for Office of Surface Mining Reclamation and Enforcement Appalachian Regional Coordinating Center, C. T. Aimone-Martin, M. A. Martell, L. M. McKenna, D. E. Siskind, C. H. Dowding
7. Structure Response and Damage Produced by Ground Vibration From Surface Mine Blasting, USBM RI 8507, p. 30
8. The equation by which these total displacements can be calculated from ASCII exports of histogram data is:

D= ti*(Σ(PPVaxis)-bc*np)

where: Dt = total displacement
ti = seismograph data interval in seconds
PPVaxis = individual PPV's for each recording axis separately
bc = lowest PPV level recorded for background
np = number of data points in summed range
Σ = Greek capital letter sigma, denoting a summation of the PPV's for each axis

The CVDG Pro page, Vibration Exposure, has details on the calculation, including use of frequency weightings, equation applications and discussion of its limitations. It also includes a paste-in Excel formula for doing this analysis for other exported histogram data.
9. C. H. Dowding, Measure the Crack Instead of Construction Vibrations, http://www.iti.northwestern.edu/acm/articles/geostrata.html

10. Structure Response and Damage Produced by Ground Vibration From Surface Mine Blasting, USBM RI 8507, p. 45; Effects of Repeated Blasting on a Wood-Frame House, USBM RI 8896, p. 40
11. Structure Response and Damage Produced by Ground Vibration From Surface Mine Blasting, USBM RI 8507, p. 72
12. One of the open questions regarding resonance in homes is just how broad a range of frequencies are capable of exciting the resonances, either directly or by energy transfer. For blasting, this question has been addressed by calculations of "response spectra" from mathematical models of the house vibrations. The response spectra show the relative amount of vibration calculated to be caused in the home by ground vibrations across a given frequency range. In one such example, the calculations show that the home response occurs around the resonances over a fairly wide range of frequencies (see OSM Blasting Guidance Manual, p. 99), suggesting that those frequencies which can excite the resonances cover a relatively wide range. It is not clear how far these blasting simulations can be extended to construction vibration situations, although one would not expect large variations in the shape of the spectra for construction vibration, even if, as is likely, there are significant changes in the maximum house vibration velocities.
13. Even if the incoming ground vibration waves and the house vibrations are completely unsynchronized ("out of phase" or "out-of-sync"), such that incoming wave peaks coincide exactly with wave troughs in the house vibration movement, resonance still makes itself felt. To see how this works, consider the case where we have complete out of phase interaction, i.e. where the incoming ground vibration wave peaks exactly match the house vibration wave troughs and have the same intensities. This will result in a complete loss of the house vibration at that frequency, due to interference effects, in one cycle of the ground vibration wave. However, the very next incoming wave peak will start the house moving again, but this time, in synchronization ("in phase") with the incoming wave train. Subsequent wave peaks will now all be in sync with the house motion and will add their energy to it.

In effect, interference between the house movement and the ground movement quickly "pulls" the house movement into phase sync with the resonant ground vibration. If the house resonant frequency is at 10 Hz (i.e. 10 passing wave peaks per second), this means that, within 0.2 second, the house vibration and the 10 Hz component of the ground vibration will come into sync. A little thought will show that, even if the ground vibration wave peaks do not coincide exactly with the house vibration troughs, interference will eventually bring the house and ground movements into phase by canceling out-of-phase components and reinforcing in-phase components. It may take one or two seconds, but it will happen quickly relative to the time scale of typical construction vibrations.  So, resonant effects are always felt if the vibration frequencies are close enough to those of the house, irrespective of the initial phase relationship of the incoming ground vibration and the house vibration.
14. Although the pavement demolition by repeated pounding with an excavator, which did the initial damage to numerous homes, was not vibration monitored, there were a number of monitored incidents of 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.


This page is a chapter from the Construction Vibration Damage Guide for Homeowners (CVDG), a 100+ page free document with over 200 color photos, diagrams and other illustrations. It is available at http://vibrationdamage.com as a series of web pages or in full, web navigation and ad-free, as a downloadable PDF document, with additional content not available on the web. The free version of the CVDG is licensed to homeowners and others for personal, at-home use only. A Professional Edition (CVDG Pro), licensed for business use and with over three times as much content, can be ordered from our Order the CVDG Pro page, usually with same-day delivery. You can comment about this page or ask questions by using our Visitor Comment form. If you would like to discuss vibration damage issues, join us on Facebook.

 

 Home Up Contact Us Site Contents CVDG Overview CVDG Pro - Overview Order the CVDG Pro Information Download Site Policies About

Send e-mail to drzeigler@vibrationdamage.com with your questions or comments about this web site.
www.vibrationdamage.com,  ęCopyright 2013-2017 Vibrationdamage.com
Last modified: 05/15/17