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Vibration and Distance

 Home Up Vibration 101 Is Damage Possible? Pre-Construction Vibration and Damage Vibration and Distance Vibration Potential Pursuing A Claim Vibration Monitoring Non-construction Vibrations More Information Closing Thoughts Appendix D - Homeowner Checklist Appendix E - Damage Inspections



Most people understand that the farther you are away from an event, the less likely you are to be significantly and directly affected by it. Indeed, distance from the source of a vibration is probably the single most important factor, after the source energy, in determining whether a vibration will have damaging effects on a home or structure (and on the human perception of the vibration). Here, I'll provide an introduction to the complex matter of distance effects on vibration intensities, with an eye toward understanding the basic factors which affect vibration movement through the ground, how vibration velocities can be mathematically estimated (as plotted at left) and the cautions that one must observe in using those estimates.

Spreading of Vibration Energy

As discussed generally in the CVDG's Vibration 101 chapter, ground vibration intensities (usually measured as vibration Peak Particle Velocities, PPV's) decrease as distance from the source increases (i.e. the vibration velocities depend "inversely" on distance). This is, at root, a geometric effect. The vibration decreases as a given amount of source vibration energy spreads over a sphere (or surface layer) of increasing size.

But, the specific way that the vibration velocity decreases with distance is affected by many variables, some of which are listed below:

  • vibration energy, type, and source,
  • frequency distribution of the vibration components,
  • predominant direction of source vibration (e.g. up/down vs. side/side),
  • the specific vibration path through the soil (e.g. whether on the surface or at depth),
  • specific pattern of soil particle movement with respect to the vibration propagation direction,
  • vibration vector (e.g. longitudinal vs. vertical),
  • soil type and composition,
  • soil moisture,
  • soil stratification (i.e. layering),
  • embedded soil obstacles (e.g. sub-surface boulders in glacial till and mountain soils)
  • underlying geology,
  • wave interference and reflection,
  • presence of structures,
  • landscaping features

Many of these factors can be included in calculations, at least in principle, if enough information is known about the vibration source and locale. Others are so site-specific and require so much information (e.g. embedded objects, reflection and interference effects, presence of buildings, landscaping) that they are virtually impossible to account for in the general-use equations often employed for predicting vibration velocities.

The many variables which affect vibration transmission can make accurate calculations of vibration velocities challenging, in the absence of substantial validation of the results by comparison with measurements made on the site of interest. However, calculating (and measuring) how vibration velocity changes with distance is central to an ability to estimate "safe distances" (check the CVDG Pro's "Vibration Safety chapter for more on such estimates) from construction work or to use vibration propagation equations meaningfully in any other way. Thus, such calculations are widely used, even if, sometimes, questionably so.

Simple Estimates of Vibration Velocities

One of the most commonly used relationships for estimating construction-related vibration velocities is that offered in the U.S. Federal Transit Administration's Noise and Vibration Manual:1

PPVequip = PPVref  x  (25/D)1.5

where: PPV(equip) is the calculated peak particle velocity in in/sec of the construction equipment type at the distance of interest, PPV(ref) is the reference vibration level for that type of construction heavy equipment in in/sec at the reference distance of 25 feet, from Table 12-2 of the FTA Noise and Vibration Manual,1 and D is the distance from the equipment to the structure or seismograph, in feet. This equation combines all the physical details of vibration movement ("propagation") through the ground in the 1.5 exponent and all the details of the source vibration properties in the reference velocity, PPV(ref), which is related to the source energy. In this equation, the distance from the vibration source, D, is in the denominator of the fractional rightmost factor. So, the calculated vibration PPV decreases as the distance increases, just as you would expect.

The FTA equation is phenomenological (i.e. it is fitted to vibration data, rather than taking into account directly in its factors most or all of the known physical variables which affect vibration propagation). Thus, there is little direct relationship between its parameters and measurable quantities affecting vibration transmission which one can relate back to physical laws and material properties. It is a considerably simplified, but often useful, approach to portraying some aspects of vibration transmission through the ground.

Using the FTA Equation

Immediately below is plot of calculated ground vibration velocities for vibratory compactors, according to the FTA equation, for various values of the exponent, n, and for two different values of PPV(ref). In this semilog plot, the velocities are plotted on the vertical scale with equal distances between equal values (i.e. linear), while the distance scale is logarithmic,7 with powers of ten (10, 100, 1000, etc.) of the distance having equal separations. Such logarithmic plots enable one to see better the relationships when large spans of numbers are to be shown. That fact can be easily seen by comparing this plot with the small all-linear version at the start of this chapter.

You can view, in a new tab or window, (and print a copy from your web browser for personal use, if you wish) a full-size version of this diagram, as well as all the other distance-ground vibration velocity relationships in this CVDG chapter just by clicking on each diagram.8 Calculated ground vibration velocities can be read off any of the diagrams in this chapter for any distance from 5 to 250 feet from the vibration source just by noting where the distance to the construction work15 intersects the appropriate curve, then reading the velocity at that intersection from the vertical scale.

The velocities calculated in the diagram above are for various values of the FTA equation exponent, as might be needed for soils of differing type, using a vibratory compactor with an FTA reference velocity of 0.210 in/sec. Also shown are values calculated from more recent, revised values of the exponent and PPV(ref) from a U.S. state of New Hampshire Department of Transportation (NHDOT) study.2,3

This diagram illustrates that the value one calculates for a vibration velocity at a specific distance is determined by the choices of PPV(ref) and the exponent that one makes. If values for these parameters are chosen which do not reflect or properly account for the actual source vibration characteristics, the local soil and geology conditions, or other factors not included in the equation (e.g. wave reflection and interference), the calculated values will differ, sometimes substantially, both from each other and from measured vibration velocities.

The OSM blasting standard limit for vibration mid-frequencies in undamaged homes of modern construction, without plastered walls and the FTA Class III limit for timber-framed homes are also shown as horizontal lines in the diagram. "Acceptable" vibration peak particle velocities for each of those two standards lie below the lines shown. Velocities exceeding those standards lie above the dotted horizontal lines.  Any vibration velocity above these standards has a higher probability of causing damage than one below the standard, at least in the circumstances for which the standards are intended (see Vibration Standards for more about ground vibration standards and their use).

The OSM standard is only applicable to examples where the vibration source is blasting, either in mining or, with less assurance, in construction. Construction heavy equipment-caused vibration should be governed by the one of the FTA limits in the U.S., of which the Class III limit is shown in the diagrams in this chapter.  The related Swiss machines and traffic standard is relevant and less lenient than the FTA standard (see Vibration Standards for more detailed information). None of the curves in this chapter show home or building vibration velocities, which may be substantially higher (see Resonance/Fatigue for more on this), due to varying degrees of resonant amplification of the ground vibration in the structure.27

Another Depiction

In the next diagram below, the same calculations are represented on a "log-log" plot, in which both the calculated velocity on the vertical scale and the distance on the horizontal scale are logarithmic. This depiction is the way that such vibration velocity/distance relationships are usually shown in the scientific literature. It allows a wide range of values to be shown on both the vertical and horizontal axes. Plotting the calculations in this way has the effect of turning the curves into lines with a slope, -n, of the equation exponent.

As the diagram shows, there are significant differences in the calculated velocities as one changes the value of the exponent. The lower the value of the exponent, the farther the vibrations move before their ground peak particle velocities fall below standard limits. Indeed, the NHDOT studies, based on newer data and more modern road construction equipment,2 found significant deviations from the FTA suggested values of 1.5 for the exponent, n, and the FTA suggested PPV(ref) value of 0.210 in/sec for vibratory compactor use at 25 feet.  For example, NHDOT found that its own data were fit better by an exponent of 1.1 and a PPV(ref) for vibratory compactors of 0.45 in/sec (c.f. FTA PPV(ref)=0.21 in/sec), as shown in the diagram above.3,16

Both these changes have the effect of making the "safe distance" for such compactors considerably larger than the FTA equation calculation indicates, as seen in the plots in this chapter. The more up-to-date NHDOT data have the effect of doubling one estimation of "safe distance" (i.e. that distance at which the calculated vibration velocity drops below the FTA Class III standard for timber-framed homes) for vibratory compactors (as seen at left) from about 30 feet to over 60 feet. Note that the compactor in the photo is being used considerably closer to homes than 60 feet.4,24

The New Hampshire experience and parameters may not be representative of all locales. Indeed, there are some areas where vibration propagation is more favored than in New Hampshire. For example, a study for the U.S. state of Florida DOT, with 170 data points involving vibratory and static compactor use over various compaction bases, shows an exponent, n, of 0.6, with an apparent range of PPV's at or near 25 feet (the FTA reference distance) for the compaction work of from 0.05 in/sec to 0.5 in/sec, depending on compacted material.20 Just below is a comparison of calculated vibration velocities for vibratory compactors, using the FTA, FLDOT and NHDOT parameters in the FTA equation. The diagram shows that a calculated "safe distance" (i.e. that distance at which the vibration velocity falls below the FTA Class III limit) ranges from around 25 feet for the FTA parameters, to nearly 60 feet for the NHDOT parameters, to 100 feet for those calculated from the extensive FLDOT study results.21,24

We consider the New Hampshire data to be instructive, representative and reasonably conservative with respect to vibrations in most, but not all, other locations. When there is predictable potential for damage to the property of uninvolved third parties, as is almost always the case in construction damage incidence, the conservative approach is the one which should be followed. Therefore, the New Hampshire values for PPV(ref) and the exponent of 1.1 in the FTA equation are currently the recommended ones to use,6 in the absence of specific and detailed vibration propagation data (e.g. like those from Florida), pertaining directly to the location of interest, which indicate use of different parameters.

Other, modified versions of the FTA equation have been proposed and utilized for specific equipment types (e.g. pile drivers) and situations. In most of these examples, the value of the exponent n suggested is 1.1,6 in accord with the NHDOT study. The lower value of n results in a slower reduction of the vibration intensity with increasing distance than the FTA equation value of 1.5 would indicate. The NHDOT  and FLDOT studies, among others,6 demonstrate that neither the 1.5 exponent nor the reference equipment velocities given in the FTA vibration manual are current or appropriate in all circumstances.2,6

Other Equipment Types

While vibratory compaction is the most common damage cause reported to Vibrationdamage.com, it is not the only type of construction operation with damage potential. Following is a comparison between FTA equation velocities calculated with parameters for both compactors and pile drivers, another class of equipment with significant damage potential.

As the diagram shows, both pile drivers and vibratory compactors can produce ground vibrations whose velocities exceed the FTA Class III limit for timber-framed homes and, close in, even the OSM mid-frequency blasting limit.

The NHDOT study also provides updated PPV(ref) values for a broader variety  of different equipment types and operations, along with the suggested value for the exponent of 1.1, for use in the FTA equation. Just below is a log-log plot of calculations with the NHDOT PPV(ref) values for a wider range of construction equipment.22


The plot shows that some operations, particularly vibratory compaction, pile driving, use of hoe rams (hydraulic rack breakers mounted on excavators) and driving tracked vehicles over distance, can be expected to exceed one or both standard limits over at least some distance ranges. Particular attention must be paid to those operations to make certain that they are not carried out within those distance ranges and/or are appropriately mitigated to reduce damage probabilities (see Vibration 101 in the CVDG and Vibration Mitigation in the CVDG Pro for details). These calculations are only extended to 250 feet from the source, as the diagrams demonstrate that most forms of equipment vibration will be below the FTA Class III limit for homes at that distance in most locales with "normal" vibration attenuation, even when a factor of two "safety factor" is included. Conditions of low vibration attenuation (e.g. localities in Florida), interference effects in the ground vibration, or vibration frequency-related resonance effects in the home may act to make specific examples of equipment use dangerous for homes at distances well beyond 250 feet in some circumstances.27

Using Vibration Calculations

It is relatively rare for vibration monitoring to be done on construction jobs (as at right), even though most public construction contracts require it as part of their "boilerplate" conditions. Thus, the typical homeowner facing construction vibration, and possible damage from it, will have no or limited access to measurements of vibration velocities to compare with the diagrams on this page. This is one of the reasons that we have recommended that homeowners do some monitoring of their own (see our Vibration Monitoring chapter for more on this point) to get an idea if felt vibrations actually have damage potential. However, in the absence of actual data, it is important for homeowners to know which operations have significant damage potential and which ones are of lower risk. Such information will help them in making knowledgeable judgments about felt vibrations and in understanding the real meaning of vibration data, when the data are available or when conclusions from monitoring or calculations are offered to homeowners.

Indeed, even the more recent NHDOT data underestimate vibration velocities at distance in some areas (e.g. many parts of the U.S. state of Florida9,12) which have especially low vibration attenuation (i.e. loss of vibration velocity with distance), as indicated above. Correlations also exist between soil type and the value of the equation exponent, with softer soils attenuating vibration more efficiently (producing exponents up to 1.4); a 1.0 exponent is suggested for hard rock.6 There are even variations within types of operations done with different pieces of the same general equipment type.11

Calculating Ground Vibration Velocities for Vibratory Compactors

Vibratory compactors (like the examples shown at left and above)19 and rollers present special problems in prediction of their produced ground vibrations and, thereby, their damage potential. Different models have different drum weights, different and often variable centrifugal force limits, operator-variable compaction amplitudes, different rates of travel, different types of vibration motions (cf. up-down vibratory vs. back-forth oscillatory compactors11,26) and different, sometimes operator-modifiable, vibration frequencies.16,19 All of these parameters are known to affect the velocity and frequency of the ground vibrations produced when compactors are used.23 Yet, full knowledge of all of them is rarely available in real-life compaction situations.

Compactors using lower frequency vibrations create vibrations in the ground which have greater range (and larger safe distances) than those compactors whose nominal vibration frequencies are higher, due to greater attenuation (loss) of the higher frequency vibrations in the ground.17 Low frequency vibrations also transfer vibration more efficiently to home resonant motions than higher frequency ones. The same compactor may display different dominant frequencies, depending on distance from it, as a result of interference effects between the vibrations from the two drums (see Vibration and Damage for an example and Vibration Signatures in the CVDG Pro for more on this issue). Similarly, if vibration is not turned off when the compactor changes direction, as is often the case in construction work,18 relatively short duration ("transient") vibrations, of considerably higher velocity than the normal, "steady-state" ones, can be generated as a result of "pile-up" of vibrations.11,18 The effect of the many variables which affect compactor vibrations, whose values are often unknown in a given situation, can mean that calculated ground velocity values for compactors, even when reasonably close to some measured values, may not correctly reflect true damage potential.19

About Construction Blasting Vibration and Distance

Although Vibrationdamage.com and its Facebook page emphasize construction effects of vibration from heavy equipment, blasting is sometimes done in construction contexts to remove rock or level sites on rock. Construction blasting differs substantially from mine and quarry blasting in the typical amounts of explosive used per delay and the frequency distribution of the produced vibration.29 Of course, it differs from heavy equipment vibration production, too, even though it is another energy source driving vibration, broadly similar to the driving energy provided by heavy equipment.

Blasting vibration distance relationships are usually depicted differently in scientific contexts than other kinds of construction vibration. The diagram below shows how blasting vibration velocities are typically plotted vs. a quantity called "scaled distance",9 rather than measured absolute distance. The scaled distance, usually denoted as SD or Ds, is just the measured distance between the blast and the seismograph recording the vibrations, divided by the square root of the charge weight of explosive used per explosion delay. Charge weights per delay (usually around 8-9 milliseconds between the multiple closely-timed detonations which comprise one "shot") are nearly always reported in documents to local regulatory authorities, as required by local and state blasting regulations, along with the measured vibrations at the seismograph locations and their absolute distances from the blast site.


Because the vibration velocity often is directly dependent upon the square root of the explosive charge weight per delay, dividing by the square root of the charge weight can remove most or all of the charge weight dependence of the vibration, leaving only the distance effects from vibration propagation and attenuation. This division of the distance by the square root of the charge weight is usually referred to as "square root scaling" in the scientific literature, since its goal is to place a series of blasts with different amounts of explosive on the same source energy basis.  Square root scaling is normally used for any vibration data resulting from blasting in drill holes with multiple charges along a more or less line-like front - perhaps the most common situation in construction and mine blasting. For point source blasting in particular, cube root scaling, i.e. dividing the distance by the cube root of the charge weight per delay, sometimes provides better correlation of the observed velocities with distance.30,31

When plotted with logarithmic scales7 on both axes, as shown above in the diagram, the equation describing the vibration intensity as a function of scaled distance produces a line, whose slope is related to the type of soil through which the vibration moves. Very soft soils or soft rock produce values of b up to about 1.8; harder soils or rock produce values of b as low as 1.0. This kind of exponential equation transformation on a log-log plot is analogous to that generated in log-log plots of heavy equipment vibration propagation shown earlier in this chapter. The diagram shown here depicts actual blasting vibration data from a construction project involving leveling and terracing of a planned housing development area on a volcanic rock site.32

This may be more information than most people want to know about construction blasting. But, if your home is ever damaged by it, you may well be presented with a plot like the one here. Other information about blasting vibration science is found throughout the CVDG. The CVDG Pro chapter, Calculating Vibration Amplitudes, has considerably more information about blasting vibration and its decrease with distance.

How Far Away Is "Far Enough"

There is no single answer to the question, "How far away must my building be from a vibration source to be considered safe from vibration damage". Buildings have different degrees of resistance to vibration damage depending on design, construction materials and age, among other factors.28 As discussed above, both vibration source properties (e.g. pile driving vs. compaction) and vibration movement through the ground can be very different, depending on locale and presence or absence of structures and other obstructions which can damp, reflect or modify vibration waves. Resonance effects in homes can turn an "allowable" ground vibration into a home vibration which is damaging at considerably greater distance than the direct ground vibration itself might be. Statements like, "You are too far away from the source to have damage", have meaning, at most, only in the very limited sense of relative probability of damage (see Vibration and Damage), even when correctly founded upon real scientific insight.

The FTA equation, and modifications of it, are widely used to approximate "safe distances" for construction operations, as illustrated in the diagrams above. However, sometimes, that is done improperly and without benefit of current scientific understanding of the appropriate exponent and PPV(ref) for use in a given construction location and operation.24 Anyone presented with the results of such calculations should take care to determine which vibration propagation equation was employed for the calculation and the appropriateness of the parameters used in it. These factors entirely determine the result, its meaning and its applicability in a given situation and locale.

In the end, correct and judicious use of proper ground vibration standards, combined with careful and scientifically valid vibration monitoring, can provide a sense of reassurance regarding vibration damage potential. Such an approach is not the same as a "guarantee" of vibration safety, but it is far better than guessing or hoping that damage will not be done. It is overwhelmingly more desirable than dealing with actual damage after it has occurred.

A Note on Historic, Culturally-Important or Damaged Structures

The OSM velocity limit for blasting and the much lower construction-based FTA Class III limit for timber-framed homes, shown in the diagrams above, are not applicable for historic structures or those which have already suffered vibration damage. Typically, among the higher limits recommended in the scientific literature for such structures is the FTA Class IV limit of 0.12 in/sec (cf. FTA Class III limit of 0.2 in/sec shown in the diagrams above). A limit of 0.08 in/sec has been advised for the thousand-year-old Pueblo Bonito (seen at right) in Chaco Culture National Historic Park in New Mexico, USA.13 Vibration velocity limits as low as 0.05 in/sec appear in the literature for other historic structures.14 These lower limits have the effect of increasing safe distances, calculated using diagrams like the ones in this chapter, for historic structures (see Vibration Safety in the CVDG Pro for examples illustrating this point).

Other Ways of Calculating Vibration Velocities

There are other, more complicated, less phenomenological, equations which can be used to calculate predicted vibration velocities in construction and blasting environments. Some are simple adaptations of the FTA equation, whose modifications better account for those types of equipment which have variable source energies (e.g. pile drivers, vibratory compactors and pavement breakers).6 A few variations in vibration calculation approaches are discussed in more detail in the CVDG Pro chapter, Calculating Vibration Amplitudes.9 However, none of them, no matter how many physical parameters are included, take into account location-specific variables like vibration wave interference, wave reflection from nearby building foundations, underlying rock layers, buried obstructions, and landscaping effects. Nor do they directly account for resonant amplification-related damage potential in homes, especially where vibration duration becomes a factor, as in construction.10

Applicability of Vibration Calculations

I have not tried to present here a complete analysis of all the ways of calculating vibration velocities, as such an analysis is probably beyond the needs of most people. Some of these other, more complicated, approaches25 are discussed in the CVDG Pro's Calculating Vibration Amplitudes chapter.  However, it is fair to say that all the calculation approaches that have been developed to date have limitations in scope, accuracy and applicability.

Both comparison of calculated velocities with measured data and the physical limitations of the equations themselves suggest that even the more physically-realistic equations can be considered only as ways of approximating actual ground vibration velocities. Even when local soil conditions are explicitly measured and taken into account, these more advanced approaches to vibration velocity/distance relationships can be in error with respect to measured vibrations by a factor of two or more.5

This is the reason that we have recommended throughout the CVDG (e.g. Vibration Regulation) that, when calculations are used to estimate vibration velocities, they be subjected to careful validation in the locale of interest and at least a two-fold safety factor be built into any velocity standard or "safe distance" derived from them.31 Any vibration with a calculated PPV near the upper limit of that two-fold safety factor calls for implementation of mitigation measures. Vibration velocity calculations can be very valuable in understanding how far from the vibration source damage might occur and under what conditions. But, that value is greatly increased when the equations are employed with real understanding of how they can be scientifically applied in the local vibration environment and what their limitations might be.

1. Transit Noise and Vibration Impact Assessment, Carl E. Hanson, David A. Towers, and Lance D. Meister, FTA-VA-90-1003-06, May 2006, p. 12-11;  A later version, with the same standards and equations is: High-Speed Ground Transportation Noise and Vibration Impact Assessment, Carl E. Hanson, P.E., Jason C. Ross, P.E., and David A. Towers, P.E., DOT/FRA/ORD-12/15, September 2012
Ground Vibrations Emanating from Construction Equipment, R. M. Lane and K. Pelham, New Hampshire Department of Transportation, Report # FHWA-NH-RD-12323W, 2012, p. 47.
3. In this diagram and the subsequent ones, the FTA PPV(ref) used is the one characterized by the FTA report writers as "typical", not those listed as "upper range". Similarly, the PPV(ref) referenced in the NHDOT study mentioned later is the one characterized as "average", not the highest measured. For equipment with "upper range" PPV(ref), the effect is to "raise" the lines on the log-log plots shown in this chapter by the difference between the "typical" and "upper range" values, without changing their slopes. This increases "safe distances" accordingly. The original source data from which the FTA PPV(ref) values are derived range from over 20 to over 50 years old, while those from the New Hampshire study are for considerably more modern (2012) equipment.
4. This increased safe distance for vibratory compactors may help explain why one contractor, in two different projects, did extensive damage using vibratory compactors less than 40 feet from homes. Also contributing to the damage was the contractor's improper choice of the OSM blasting vibration standards, rather than construction standards. The contractor's own partial (in several senses) vibration monitoring data showed that it exceeded even the blasting standards in at least ten examples during one of those two road reconstruction projects. The contractor did not perform vibration monitoring on the second project, though mandated to do so by the bidding instructions.
5. See, for example, Soil and Structure Vibrations from Construction and Industrial Sources, Svinkin, Mark R., International Conference on Case Histories in Geotechnical Engineering. 8. (2008). (available online)
6. For a good summary of these, see Transportation and Construction Vibration Guidance Manual, Jim Andrews, David Buehler, Harjodh Gill, Wesley L. Bender, California Department of Transportation, Division of Environmental Analysis, Environmental Engineering, Hazardous Waste, Air, Noise, & Paleontology Office, Sacramento, CA, 2013, Chapter 7.
7. Logarithms are simply the power to which a number has to be raised to produce a given number. 10 raised to the power of 1 is 10; hence the logarithm (log) of ten is one. 10 raised to the power of 2 (10x10 or 102) is 100. Thus, for logarithms of base ten ("log10 x", "log x", "base ten log of x"), the log of 100 is 2. The log of 1000 (10x10x10 or 103) is 3, i.e. 103 is 1000. Fractions of ten are denoted by negative exponents. 0.1 is 10-1 and the log of 0.1 is -1. Many scientific equations use "natural logarithms", which are usually denoted as "ln". The base of the natural logarithm system is the number, e, (approximate value, 2.7182818...), a non-repeating, non-terminating transcendental number, like π (the ratio of a circle's circumference to its diameter, 3.1415926...). When you read scientific papers, you'll often see equations using e and ln. All the log plots in this chapter use base ten logs.
8. Diagrams like those on this page, which were generated in Excel, can be easily created on a computer or graphing calculator, by providing the desired values for the exponent and the PPV(ref) in the FTA equation or any of the related ones. A hand calculator or smart phone can be used in the same way to produce values of calculated velocities at single distances. Even if the PPV(ref) isn't known for a given piece of equipment or locale, you can easily fit the data from vibration measurements at various distances, if those are available to you. If you have sufficient velocity/distance data, you can derive your own effective PPV(ref) and exponent from it.
9. Mining operations which carry out blasting use the scaled-distance equation, v=K(D/√W)-b to calculate vibration velocities at distance from the blast. The quantity, D/√W, is the scaled distance. The equation W = (D/Ds)2, can be employed to determine the allowable charge-weight of explosives to be detonated in any specified delay period without required seismic monitoring, where W = the maximum weight of explosives, in pounds; D = the distance, in feet, from the blasting site to the nearest protected structure; and Ds = the scaled-distance factor. Ds has units of ft/(lb)0.5. Blasts are usually set off with very short (typically a few thousandths of a second) delays between blasts, both to minimize ground vibration and do a better job of pushing the broken rock away from the mine face. Allowable scaled distance factors for mining are set by government regulations of the Office of Surface Mining (OSM) in the U.S. Such equations involve distances, but the main focus of them is the charge weight of explosive which can legally be used in blasting. Scaled distances are widely used in the scientific literature for analysis of vibrations caused by blasting in construction, as well as mining. For more on scaled distance approaches in blasting and regulatory requirements in the U.S., see OSM Blasting Performance Standards, 30 Code of Federal Regulations, Sec. 816.67 and OSMRE Blasting Guidance Manual, Michael F. Rosenthal and Gregory L. Morlock, 1987

A variation of a scaled distance equation, v=k(D/Wr)-n, where v is the velocity, D is the distance, Wr= energy of source, and k = value of velocity at one unit of scaled distance, (D/Wr), has been used successfully for construction vibration settings, particularly for pile driving. The value of n is related to the vibration attenuation in the soil. The higher the value of n, the faster the vibration velocity drops with distance. The value of k is inversely proportional to the attenuation in the soil. It provides a measure of the vibration velocity at one unit of scaled distance. The point of scaled distance approaches to estimating vibration intensities is to place the source energy differences from the vibration propagation on the same scale, by the square root scaling, thereby isolating soil attenuation effects.  See Evaluation of Vibration Limits and Mitigation Techniques for Urban Construction, E. Bayraktar, Y. Kang, M. Svinkin, F. Arif, Florida Department of Transportation Report, October 31, 2013, p. 42, et seq., for some field measurements of k.
10. The calculated FTA PPVequip, using the FTA 1.5 exponent and the FTA PPVref,  was 0.374 in/sec for a compaction operation, over soil classified as silty sand, in one road reconstruction project in New Mexico, USA. The observed maximum PPV was 0.660 in/sec, a value in violation of all building class limits in the FTA standard, as well as the 0.5 in/sec Safe Blasting Level for homes with plastered walls in USBM RI 8507. There were over twenty measurements above 0.5 in/sec in front of this home. Another home, one intervening property from the one above, the same distance away from the paving operation, using the same vibratory compactor at the same compaction vibration amplitude a few minutes after 0.660 measurement at the other property, experienced a maximum vibration velocity of 0.315 in/sec (cf. calculated value of 0.374 above), measured with the same seismograph. It is very unlikely that such large difference can be attributed to soil, geology or equipment use variations under these conditions. Probably, these differences were due to vibration wave interference effects, perhaps resulting from the much different landscaping of the two properties. Whatever the cause of these differences from calculated values might be, this real-life road construction example shows why vibration calculations should be considered as approximate, with factor of two errors easily possible in the calculation. It isn't known if the two homes mentioned here were damaged in the work, but extensive damage appeared in many other homes along the path of the work, which experienced lower measured vibration velocities, as indicated in footnote 4.
11. Ambient vibration of oscillating and vibrating rollers, J Pistrol, F. Kopf, D. Adam, S. Villwock, W. Völkel, Vienna Congress on Recent Advances in Earthquake Engineering and Structural Dynamics 2013 (book), p. 6 (available online)
12.  Assessment of Blast Vibration Impacts from Quarry Blasting in Dade County, David E. Siskind & Mark S. Stagg, May 10, 2000
13. Seismic and Vibration Hazard Investigations of Chaco Culture National Historical Park, Kenneth W. King, S. T. Algermissen, and P. J. McDermott, USGS Open-File Report 85-529, 1985; Bonito Vibration Tests, Chaco Culture Historical Park, K. King, D. Carver, and B. Winslow, Open-File Report 91-444, 1991
14. A good summary of some of that literature can be found in Construction Practices to Address Construction Vibration and Potential Effects on Historic Buildings Adjacent to Transportation Projects, National Cooperative Highway Research Program (NCHRP), Project 25-25 (Task 72), Richard A. Carman, September 2012
15. You can get distances from your home or building to construction work sites from a free, downloadable computer program, Google Earth, using it's Ruler feature. Google Earth uses satellite photos to allow you to measure distances without ever leaving your home or office. Virtually the entire land surface of the planet has coverage. The program also allows you to look at street-level photos for most towns and cities in developed countries.
16. The only identification in the NHDOT report (footnote 2) of which vibratory compactor model(s) were represented in vibration data collected for the report is a photo of an Ingersoll-Rand SD-122DX vibratory roller in Figure 3 of the report. Published specifications for this model indicate that it has vibration frequencies of 30.9 and 33.8 Hz, with high and low centrifugal force limits of 281 and 206 kiloNewtons, kN, respectively.
17. Construction Vibrations and Their Impact on Vibration-Sensitive Facilities, Hal Amick and Michael Gendreau, Presented at ASCE Construction Congress 6, Orlando, Florida, February 22, 2000 (available online)
Ground Vibrations Emanating from Construction Equipment, R. M. Lane and K. Pelham, New Hampshire Department of Transportation, Report # FHWA-NH-RD-12323W, 2012, p. 9.
19. Illustrating this point are the very different vibratory compactors used in two jobs done by the same contractor in the same municipality. The Caterpillar CB-334 compactor shown above has a maximum centrifugal force of 33.1 kN, per drum, with a nominal vibration frequency of 69 Hz. Another compactor, used on the same job, an Ingersoll-Rand DD70HF, seen in the second compactor photo, has a specification centrifugal force range of 34-94 kN, with a vibration frequency of 66.7 Hz. Yet another compactor, used by the same contractor on a nearby job in the same municipality, a Volvo SD-115B, had a specified vibration frequency range of 30.8-33.8 Hz, with a centrifugal force range of 208 to 258 kN.
20. Evaluation of Vibration Limits and Mitigation Techniques for Urban Construction, E. Bayraktar, Y. Kang, M. Svinkin, F. Arif, Florida Department of Transportation Report, October 31, 2013, p. 76. This study also provides some comparison numbers for static compaction. There is little information in the study about the compactors used, their frequencies or their centrifugal force limits.
21. The unusually low attenuation of vibrations in Florida may help explain why Florida is over-represented, relative to construction value in the state, among reports of damage to Vibrationdamage.com. See Damage Statistics in the CVDG Pro for more on this matter.
22. For those who may be unfamiliar with the names and appearance of different types of construction equipment, the NHDOT report (footnote 2) has example photos of most of these equipment types in use. Although equipment appearance can vary substantially from model to model, there are usually enough common features to allow identification of the equipment from such photos.
23. Basic Principles of Asphalt Compaction, BOMAG GmbH, 2009
24. None of the "safe distances" discussed in this chapter, arrived at by noting where the velocity/distance curve crosses the FTA Class III limit shown, have safety factors included. The FTA construction standards, which are based on the "Swiss standards", have safety factors built into them. Safety factors built into construction standards are probably adequate in most environments. However, one still must add safety factors to any velocities derived from calculations for the reasons indicated in the main text. Pre-construction survey distances, used by contractors in planning pre-construction surveys, are related to safe distances, but are usually larger, since they must account, at a minimum, for normal statistical variation that can lead to damage farther from the work than the "safe distance".
25. Soil and Structure Vibrations from Construction and Industrial Sources, Svinkin, Mark R., International Conference on Case Histories in Geotechnical Engineering. 8. (2008). (available online)
26. Oscillatory compactors impart only about 15-25% as much energy to the soil as vibratory compactors operating under the same conditions. This nearly halves the "safe distance" for them, relative to vibratory compactors, calculated according to several standards. An additional benefit is that they achieve higher degrees of compaction faster than vibratory compactors, thereby saving the contractor time and money and nearby homes greater vibration exposure. See Ambient vibration of oscillating and vibrating rollers, J. Pistrol, F. Kopf, D. Adam, S. Villwock, W. Völkel, Vienna Congress on Recent Advances in Earthquake Engineering and Structural Dynamics 2013 (VEESD 2013), C. Adam, R. Heuer, W. Lenhardt & C. Schranz (eds) (available online)
27.  "The condition of resonance can be triggered at large distances of a few hundred meters from a pile driving site and even more than one kilometer from a blasting site.", Soil and Structure Vibrations from Construction and Industrial Sources, Svinkin, Mark R., International Conference on Case Histories in Geotechnical Engineering. 8. (2008), p. 3. (available online)
28. Effects of Repeated Blasting on a Wood-Frame House, Mark S. Stagg, David E. Siskind, Michael G. Stevens, and Charles H. Dowding, United States Bureau of Mines Report of Investigations 8896 (USBM RI 8896), 1984
29. See, for example, Structure Response and Damage Produced by Ground Vibration From Surface Mine Blasting, D. E. Siskind, M. S. Stagg, J. W. Kopp, and C. H. Dowding, United States Bureau of Mines Report of Investigations 8507 (USBM RI 8507), 1980, p. 6, et seq.
30. The "best-fit line" in the construction blasting scaled distance diagram example is generated from statistical "least squares" calculations, whose goal is to determine the line which has the smallest sum of the squares of differences between the calculated line and the actual data points. The slope, b, of the calculated line is usually related to the type of soil or rock in which the vibration measurements are recorded, with larger values of b generated in softer soils, just as in heavy equipment-caused vibration. The constant K is the calculated value of the vibration velocity at a scaled distance of 1 (i.e. very close to the blast). K reflects both the source energy and the vibration propagation efficiency through the soil. The "correlation coefficient", r2, is a measure of how well the data points match the calculated least squares line. If all the points were exactly on the line, r2 would be 1.0. If all the points were completely uncorrelated with the calculated line (e.g. at the four corners of a square), it would be 0.
31. The 0.63 correlation coefficient seen in this case is fairly typical of actual blasting vibration data; some sets of data show much lower r2 values. Such data scatter in these plots is a good illustration of yet another reason why calculations of vibration velocities should be treated as approximate. For example, if we look at the blasting plot at a scaled distance of 90, the best-fit line predicts a velocity of 0.19 in/sec. Some data points are close to this value, but others go up to 0.49 in/sec, more than a factor of two difference.
32. The data for blasting in volcanic rock (probably dacite or rhyodacite, by appearance) shown here come from 4 different seismographs mounted in different locations at various absolute distances from the 13 blasts which occurred over a period of 6 weeks, approximately. In the case of the seismograph furthest from the blasts, some explosions did not produce vibrations of velocity sufficient to trigger the seismograph to record. These imprecise, non-triggered data were removed from the data set and do not appear on the plot.

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