Vibration and Distance

Most people understand that, the farther you are away from an event, the less likely you are to be affected by it. Indeed, distance from the source of a vibration is probably the single most important factor, after the amount of energy that goes into creating it (i.e. the "source energy"), in determining both whether the vibration will have damaging effects on a home or structure and how disturbing people will perceive the vibration. Here, I'll provide an introduction to the complex matter of distance effects on vibration velocities (intensities), with an eye toward understanding some of the basic factors which affect vibration movement through the ground, how vibration velocities (peak particle velocities, PPV's) can be mathematically calculated (as plotted at left) and the significant cautions that one must observe in using those estimates. About the PPV/Distance Diagrams There are several diagrams of calculated vibration velocities and safe distances in this chapter
of the CVDG, like
those at right and above. Calculated ground vibration velocities can be read off any of the diagrams
for any distance from 5 to 250 feet from the vibration source just by noting where the distance to the construction work (source)^{[15]} intersects the appropriate curve, then reading the velocity at that intersection from the vertical scale. You can view, in a new tab or window (and print a copy from your web browser for personal use, if you wish), a fullsize version of the distanceground vibration velocity and safe distance relationships which
follow just by clicking on each diagram.^{[8] }Registered CVDG for Homeowners and CVDG Pro purchasers can also see a gallery of all such diagrams available in the CVDG Pro, or get both a
free PDF
collection of fullsized versions of all the vibration velocity diagrams in this chapter of the CVDG. Registered CVDG and CVDG Pro users also gain free access to our Ground Vibration PPV and Safe Distance Calculator, which allows them to do calculations, specific to their own
situations, rapidly and simply.
Although it is often asked, 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
below, both vibration source properties (e.g. pile driving vs. compaction) and the way vibration velocity decays through movement in the
ground can be very different, depending on locale and presence or absence of structures and other obstructions which can damp, reflect, refract or modify vibration waves. Resonance effects in homes
and other buildings can turn an "allowable" ground vibration
into a structure vibration which is damaging at considerably greater distance than the direct ground vibration itself might be. Spreading and Decrease of Vibration Energy As discussed generally in the CVDG's Vibration 101 chapter, ground vibration intensities (usually measured by seismographs, like that shown at left, as vibration peak particle velocities, PPV's) decrease as distance from the source increases. Stated more scientifically, the vibration velocities depend "inversely" on distance. The inverse dependence is, at root, a geometric effect. The vibration velocity decreases as a given amount of source vibration energy spreads out over a sphere, whose area increases as the radius squared. Although the geometry can explain a good deal of the decrease of vibrations with distance, soils also affect the vibration intensity through damping. Variations in Created Vibrations and Their Transmission The specific way that the vibration velocity varies with distance is affected by many variables. Some of these pertain to the factors which govern the vibration velocity at the source, while others relate to the way in which vibrations propagate from the source and attenuate in the ground. A partial list of these effects follows: Source Vibration Energy Effects
Soil Vibration Transmission and Attenuation Effects
Not all these factors will play a significant role in affecting the vibration velocity in every setting, though, typically, a majority of them are likely to be relevant in most construction vibration situations. Many of these features can be included in calculations, at least in principle, if enough information is known about the vibration source, locale soil type and underlying geology. Such detailed information about both the vibration source and the vibration attenuation environment is only rarely available in real life construction vibration examples. Other factors are so sitespecific and require so much information (e.g. embedded objects, reflection and interference effects, presence of buildings, landscaping) that they are virtually impossible to take into account fully in the generaluse equations commonly employed for predicting vibration velocities. Note that none of the cited factors take into account directly variations in building resistance to vibration damage, which is a separate issue discussed in the CVDG chapter, Vibration and Damage. The many variables which affect vibration transmission can make accurate calculations of vibration velocities challenging, in the absence of substantial validation of the calculation results by comparison with measurements made literally 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, all too often, questionably so. I'll start with vibration attenuation effects on ground vibration velocities just below; source energy effects are examined in greater detail further on in this chapter of the CVDG. Simple Estimates of Vibration Velocities One of the most commonly used relationships for estimating constructionrelated vibration velocities is that offered in the U.S. Federal Transit Administration's Noise and Vibration Manual:^{[1]} PPV_{equip} = PPV_{ref} x (25/D)^{1.5} where: PPV_{equip} is the calculated peak particle velocity in units of 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 122 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" or "attenuation") through the ground in the 1.5 exponent and all the characteristics of the source vibration in the reference velocity, PPV_{ref}, which is related to the source energy.^{[36]} 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  it is fitted to vibration data, using measured reference values, 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 fundamental quantities affecting vibration transmission which one can relate back to physical laws and soil properties. It is a considerably simplified, but often useful, approach to portraying some aspects of vibration transmission through the ground in construction settings. Using the FTA Equation Immediately below is plot of calculated ground vibration velocities for vibratory compactors, according to the FTA equation. 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 (1, 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 alllinear version at the start of this chapter. 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, PPV_{ref}, 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 values calculated using other values for PPV_{ref} and the exponent  and from measured vibration velocities. The OSM blasting standard limit for vibration midfrequencies in undamaged homes of modern construction, without plastered walls, and the FTA Class III limit for timberframed 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, and rapidly increasing, probability of causing damage than one falling below the standard, at least in the circumstances for which the standards are intended (see the CVDG chapter 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 equipmentcaused vibration should be governed by the one of the FTA limits in the U.S., of which the Class III limit for timberframed homes (most homes in the U.S.) is shown in the diagrams in this chapter. The related Swiss machines and traffic standard is also relevant for construction ground vibration and more confining than the FTA standard (see Vibration Standards for more detailed information) in several ways. None of the curves in this chapter show predicted home or building vibration velocities. The structure velocities are both structure type and positiondependent. They may be substantially higher (see Resonance/Fatigue for more on this) than the ground velocity, 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 "loglog" 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 exponential curves into lines with a slope, n, of the equation exponent.^{[7]} 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 slower the vibration velocities decay with distance and the farther the vibrations move before their ground peak particle velocities fall below standard limits. Indeed, the NHDOT studies, based on newer data for 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],[36]} 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 uptodate 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 timberframed 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] } Extensive damage to many homes was done during this road reconstruction project. The New Hampshire experience and parameters may not be representative of all locales. Indeed, there are some areas where vibration propagation is much 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 throughout Florida,^{ }shows an exponent, n, of 0.6, indicating a much slower decrease in the PPV as distance increases than in either the New Hampshire or original FTA reports. The range of PPV's at or near 25 feet (the FTA reference distance) for the compaction work in Florida covers a range from 0.05 in/sec to 0.5 in/sec, depending on compacted material, with most measurements near the upper end of the range.^{[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],[36]} 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 even more conservative 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 apparent 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 timberframed homes and, close in, even the OSM midfrequency 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 loglog 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 rock 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 heavy 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 frequencyrelated resonance effects in the home may act to make specific examples of equipment use, and especially blasting, dangerous for homes at distances well beyond 250 feet in some circumstances.^{[25],[27]} Many types of construction heavy equipment, in different models, can be used in different ways by operators which substantially affect the ground vibration velocities they produce. For example, pile drivers can be divided into different "energy classes" which have a major influence on the amount of vibration energy transferred to the ground and the ground vibration they produce. Hammer pile drivers generate more vibration at the source than resonance pile drivers. Heavy truck traffic vibration depends on the speed of the truck and the road condition. The CVDG Pro chapter, Calculating Vibration Amplitudes, has much more information on source energy effects on vibration velocities. By way of illustration, we'll take one of the most common causes of vibration damage, vibratory compaction, and briefly explore here some of the factors which can influence how much compaction energy is transferred into ground vibrations. Vibratory compactors (like the examples shown at left and above)^{[19]} and rollers are the single most reported suspected cause of damage to homes at Vibrationdamage.com. They present special problems in prediction of their produced ground vibrations and, thereby, their damage potential.^{[38]} Different models have different drum weights and widths, different and often variable centrifugal force limits, operatorvariable compaction amplitudes, different rates of travel, different types of vibration motions (cf. updown vibratory vs. backforth oscillatory compactors^{[11],[26]} vs. vibratoryoscillatory compactors employing both types of motion) and different, sometimes operatormodifiable, vibration frequencies.^{[16],[19]} All of these factors are known to affect the velocity and frequency distribution of the ground vibrations produced when compactors are used in nonstatic modes.^{[23]} Yet, full knowledge of all of them is rarely available in reallife compaction damage situations. Compactors using lower frequency
(generally under 40 Hz) 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 more rapid attenuation (loss) of the higher frequency vibrations in the ground with distance.^{[17]} Low frequency vibrations also transfer vibration more efficiently to
home resonant motions than higher frequency ones. The same compactor, operating with the same setup and operator, may display different dominant frequencies, depending on distance from it, as a result of
wave 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). Using Vibration Calculations It is relatively rare for vibration monitoring to be done on construction jobs (as at right), even though many public construction contracts require vibration monitoring as part of their "boilerplate" contractual 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 much more on vibration monitoring, both "professional" and "doityourself") 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 Florida^{[9],[12]}) which have especially low vibration attenuation (i.e. loss of vibration velocity with distance), as indicated above. Correlations exist between soil type and the value of the equation exponent, n, with softer soils attenuating vibration more efficiently (producing typical exponents up to 1.4); a 1.0 exponent is suggested for hard rock.^{[6]} Some locales will show values of n outside the 1.01.4 range (e.g. 0.6 for vibratory compaction in the Florida data). About Construction Blasting Vibration and DistanceAlthough 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 vibrationdistance relationships are usually depicted differently in scientific contexts than other kinds of construction vibration. The diagram below, depicting actual blasting vibration data from a construction project
involving leveling and terracing of a planned housing development area on a volcanic rock site,^{[32]} 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 in the relevant literature as SD or D_{s}, 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.^{[30],[31]} Charge weights per delay (usually around 89 milliseconds between the multiple closelytimed detonations which comprise one blasting "shot") are nearly always reported in documents to local regulatory authorities, as required by local and state blasting regulations.
When seismograph monitoring is required by regulation, the measured vibrations at the seismograph locations and
their absolute distances from the blast site may also be disclosed to authorities. When plotted with logarithmic scales on both axes, as shown in the diagram at left, the equation describing the vibration intensity as a function of scaled distance, PPV = K(SD)^{b}, (often generally referred to in the scientific literature as "power law scaling") produces a line, whose slope is generally related to the type of soil or rock 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 loglog plot is directly analogous to that seen in loglog plots of heavy equipment vibration propagation shown earlier in this chapter. Other information about blasting vibration science is found throughout the CVDG, including an introduction to blasting and its effects in the CVDG chapter, Blasting Vibrations. The CVDG Pro chapter, Calculating Vibration Amplitudes, has considerably more information about blasting vibration and means of modeling its decrease with distance. The calculated distance at which a vibration velocity falls below a properly chosen standard limit can be suggestive of a "safe distance", at least for those types of activities for which the standard is intended and defined. Properly determined and applied safe distances have value because they are easily implemented and provide quick insight into which operations might be considered inherently unsafe with respect to damage potential, if they are expected to be done inside the calculated safe distance. Safe distances represent guidelines; an operation carried out at less than the safe distance has a higher probability of causing damage than one done at a distance greater than the safe distance for that operation. Given the sigmoidal shape of the damage probabilityvelocity curves (see Vibration and Damage), the damage probability increases rapidly, the further inside the safe distance one encroaches, or, put another way, the more one exceeds the ground vibration standard PPV limit.
The FTA propagation equation, and
modifications of it,
can be used to approximate "safe distances" for construction operations, as illustrated in the diagrams above and at left. Minimum safe distances can be derived by
calculating directly^{ } using a version of the FTA equation^{[33]} (or reading off the diagrams above) the distance at which the PPV drops below
the standard. Because safe distances determined in this way are
subject to the inherent errors and limitations of the velocity calculations, as well as the statistical uncertainties underlying the standards on which they are based, they are best considered as minimum values. For this reason and others,
prudence requires that
calculationbased safe distances always have at least a factor of two safety margin applied to them, as discussed further below. The safe distance values indicated may be conservative (i.e. "too far") in some locations having soils and geology exhibiting larger propagation exponents than the NHDOT suggested value of 1.1 and overly optimistic (i.e. "too close") in other locations, like much of Florida in the U.S., with lesser propagation exponents. The effect of the propagation exponent, n in the FTA equation, on the calculated safe distance (using the FTA Class III standard velocity limit of 0.2 in/sec) is shown in the graphic at right for several different heavy equipment types.^{[33]} As can be seen in the diagram, the higher the value of n, the faster the vibration dissipates and the lesser the calculated "safe distance". This variable is discussed more fully in the CVDG Pro's Calculating Vibration Amplitudes chapter. There are even variations within types of operations done with different pieces of the same general equipment type.^{[11]} Calculated safe distances, like those diagrammed above, should be construed as minimums with at least factor of two multipliers applied to the calculated safe distances to take into account the many variables which cannot be included in such calculations. There will be some circumstances in which construction operations must be performed inside safe distances. In those examples, simple mitigation steps must be taken to limit vibration and vibration monitoring carried out to assure the success of mitigation. More technical information on the meaning, applicability of, and cautions involved in using vibration safe distance calculations, with additional safe distance diagrams, can be found in the CVDG Pro's Vibration Safety chapter. You can calculate safe distances for your own construction situation using Vibrationdamage.com's free Ground Vibration PPV and Safe Distance Calculator. Proper Use of Vibration Calculations Sometimes, vibration propagation equations are used inappropriately and without benefit of current scientific understanding of the appropriate exponent and PPV_{ref} for a given construction location and operation. Such uncritical application of the equations can lead to even larger errors in calculated safe distances with respect to measured velocities than those inherent in the calculations and the standards. Anyone presented with the results of such calculations should take care to determine which vibration propagation equation was employed for the calculation and the suitability of the parameters used in it. These factors entirely determine the result, its meaning, and its applicability in a given situation and locale. Correct and judicious use of appropriate 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 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. Of course, there is simply no substitute for actual vibration monitoring done on the job itself. A Note on Historic, CulturallyImportant or Damaged Structures The OSM velocity limit for blasting and the much lower constructionbased FTA Class III limit for timberframed homes, shown in the diagrams above, are not applicable for historic structures or those which have already suffered vibration damage. Typically, among the highest 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 thousandyearold Pueblo Bonito (seen at right) in Chaco Culture National Historical 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 or damaged structures (see Vibration and Damage and 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],[38]} 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, can take into account all locationspecific variables like vibration wave interference, wave refraction and wave reflection from nearby building foundations, underlying rock layers, buried obstructions, and landscaping effects. Nor do they account for resonant amplificationrelated damage potential in homes, especially where vibration duration becomes a factor, as in construction.^{[10]} The more advanced forms of vibration velocity calculation are valuable scientifically and theoretically. Their importance should not be underestimated. However, they do not guarantee greater accuracy in calculation of velocities in a specific situation and at a specific structure than do simpler versions. Applicability of Vibration Calculations I have not tried to present here a complete analysis of all the ways of calculating how vibration velocities vary with distance, as such an analysis is probably well beyond the needs of most people. 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 limitations of the equations themselves suggest that even the more physicallyrealistic equations can be considered only as ways of approximating actual ground vibration velocities and the related "safe distances". 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 twofold 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 twofold 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.^{[34]}


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