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Vibration Calculator
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I have provided many diagrams like those at left, which allow visitors to read from them predicted vibration velocities (PPV's) and safe distances for construction operations. These can be downloaded free from the direct links in the Vibration Analysis Tools chapter of the CVDG and CVDG Pro. However, some may prefer to carry out calculations, with greater flexibility and specificity, in their own vibration situations. With that in mind, I have prepared the easy-to-use, free, downloadable Vibrationdamage.com Ground Vibration and Safe Distance Calculator (©Copyright 2018-2022 John M. Zeigler) for use in construction settings where vibration results from heavy equipment use or blasting. I use it regularly in my vibration damage consulting, for which it was created. Its three calculators can be valuable to attorneys, homeowners, consultants and contractors who might need to understand the potential for damage from construction operations, determine in advance which operations might require vibration mitigation, estimate blasting PPV's, or get an idea of the damage probabilities associated with blasting PPV's. Read on to learn about what the Calculator does, how to use it, and how to get it. About the Vibration Calculator The Vibrationdamage.com Ground Vibration and Safe Distance Calculator is in the form of a locked Excel® spreadsheet workbook (.XLS format). In its current version, it is comprised of three worksheets, the Construction Vibration Calculator, the Blast Vibration Calculator, and the Blasting Damage Probability Calculator. Although there are many calculators on the Internet which will do simple vibration calculations, the Vibrationdamage.com Ground Vibration and Safe Distance Calculator has lots of extra capabilities and uses which are not found in those calculators available elsewhere. Each calculator worksheet works independently and uses a different, accepted approach to calculating vibration velocities, safe distances, scaled distances and blasting damage probabilities. To choose the calculator you want to use, click the appropriate worksheet tab near the bottom of your Excel or other spreadsheet program screen. All you need to use the Vibrationdamage.com Ground Vibration and Safe Distance Calculator is any device with software which can read .xls files. More information on the system or device requirements are found at the end of this chapter. Read below to find out how to get the Calculator free. The Construction Vibration Calculator
As seen above, the Construction Calculator ("Const. Vib. Calc." worksheet tab) allows you to enter your own values for the reference or measured ground velocity (PPV), the distance measured to the work or referenced for the reference velocity, and the distance from the work to the structure of interest. With these three pieces of information, the Calculator will display calculated PPV's at the structure for different values of the attenuation (propagation) exponent, n. The appropriate value for n changes with soil type and other variables (see Vibration and Distance for more on this point). Ideally, it is determined for the site in question by a careful series of vibration monitoring measurements at varying distances from the source of the vibration, but the Calculator provides references and tips for choosing the best value of the exponent, when it has not been measured. The Calculator also shows calculated safe distances, based on the FTA construction peak particle velocity limits, for the ground vibration velocity entered.[1] You can enter velocities and distances in either metric or U.S. units, as shown in the screen shot. The metric and U.S. units panes work independently of each other, allowing one to enter different values, having the appropriate units, in each. Each calculation pane provides calculated PPV's in both metric and U.S. units and minimum safe distances in the units chosen. The Vibrationdamage.com Ground Vibration and Safe Distance Calculator works with any spreadsheet program (Excel, Lotus SmartSuite, Quattro Pro and the free OpenOffice office suite program, Calc, have been tested successfully) and on any device which can read .XLS files. So long as you have a compatible spreadsheet program installed, the Calculator will work in any operating system (Windows, MacOS, iOS, Android). If you use an online spreadsheet, the Calculator should work in it, as long as the spreadsheet will read .XLS files. Using Other Standard Limits and Exponents The calculated safe distances are based on the U.S. FTA limits for the four different structural types (described in the Calculator Reference section), defined in that standard. Optionally, should you want to determine a safe distance for some other vibration standard velocity limit (e.g. in another country or jurisdiction), you can enter that limit in the Optional Limit cell at the right of either of the U.S. units or metric units panes, as appropriate. Safe distances will then be calculated for that limit as well. You can also modify the label above the optional calculation results to reflect that standard. Similarly, if the preset values for the attenuation exponent don't work for your situation, you can enter your own, optional, attenuation exponent below the ones already present, to see how specific changes in the exponent affect results. Using the Vibration Calculator
Because the Calculator allows you to make changes in some cells in the locked spreadsheet, it also permits you to save the Calculator with the changed values. This is a good way to preserve results, although you can print them or get a screen image by copying it to the Clipboard (Alt-PrtScr) in Windows or using the Windows screen snip tool. You can then paste the image into another program (e.g. Windows Paint) for further editing if you wish or directly into its final destination (e.g. a word processing program). Use with Vibration Monitoring Data To illustrate use of the Vibration Calculator, let's look at a real-life example shown at right, obtained from vibration monitoring of vibratory compaction during a road reconstruction job. The monitoring measured a vibration of 0.45 in/sec (in right "Measured PPV" input cell) at about 25 feet (left "Distance of Measured Velocity" input cell) from the compaction work; the house was 40 feet from the compaction (middle "Structure Distance from Vibration Source" input cell). We see that the calculated velocity at the home was 0.22 in/sec for the FTA exponent of 1.5 (Exponent n of 1.5 line), above the Class III limit. The calculated safe distance, without any safety factor, is 52 feet - greater than the 40 feet distance at which the work was performed. With a 2x safety factor, that distance is 104.6 feet, well more than the distance from the home at which the compaction was done. The home had been already damaged from the pavement pounding which characterized this job; the calculated safe distance for such a Class IV structure is 83 feet. Use without Vibration Monitoring Data This job was unusual in that a report of damage had forced the contractor to begin, well after the job start, the vibration monitoring required in the contract. If no monitoring had been done, as is usually the case, the Calculator could still have helped us. In that case, we simply use the FTA or (preferably) the more current NHDOT compactor reference PPV's for the measured velocity (either one coming from the reference tables below the calculator panels), the FTA reference distance of 25 feet for the distance of the measured velocity, and the actual distance to the home to calculate a likely velocity at the home and the safe distance for the reference velocity for various values of the propagation exponent n. If our data or standard had been in metric units, the metric units pane of the Calculator on the right easily handles that, without any need for us to do unit conversions. The Reference Section
Below the calculation panels are tabulations of reference PPV's and suggested values for the propagation exponent from the vibration damage scientific literature to help users of the Calculator choose the results most relevant to
their situation.
Blasting Calculations in the Construction Calculator The Construction Calculator can be used for blasting vibration, provided that the distances and a measured PPV at one of the distances are known. It does not use the scaled distance approach most often used by blasters to determine acceptable charge weights per delay. However, since the physical laws governing vibration propagation are the same, subject to correct choice for the attenuation exponent, n, for the locale, the Calculator can still be used for calculating PPV's at structures when a PPV is known for a given distance from the blast. Such information is nearly always available from blast logs required of blasters by U.S. Federal regulations, unless they qualify for no vibration monitoring, because the calculated scaled distance is below thresholds set in U.S. Federal regulations. Blasting vibrations are often reported individually in the same format as construction vibrations, since blasting seismographs are usually used to measure construction vibration. Just substitute the measured values for PPV's and distance into the proper locations in the Calculator and distance to the structure to calculate expected vibrations at a different distance than that measured. The Blasting Calculator
The Blasting Vibration Calculator worksheet, shown in part just above, works much like the Construction Calculator, but uses the scaled distance (SD or Ds) approach, according to the equation,
commonly used to calculate blasting vibration velocities. The Blasting Calculator will estimate velocities, scaled distances, maximum charge weights and safe distances for the charge weight entered. A Reference section of the Blast Vibration Calculator includes acceptable velocities and scaled distances under U.S. OSM regulations and USBM RI 8507 suggested limits, in both U.S. and metric units. Above the Calculator itself are some brief use instructions; additional tips for its use are provided below the Parameter Variations table. To use it, load vibcalc.xls into your compatible spreadsheet program, then choose the "Blast PPV Calc." worksheet tab near the bottom of your spreadsheet screen. This will bring up the Blasting Calculator. Then, you just provide the information required in at least the first data row (see below). You must enter:
Typical values are indicated for most of the variables in the scaled distance equation, so that non-experts can use the calculator right away. Experts can use other, known values for the input parameters or values thought to be more appropriate to a given situation or locale. You can calculate up to fourteen different sets of input data in either U.S. (ft and lb) or metric (kg and m - MKS, SI) units. Once you choose the input units you want to use, metric values are portrayed in green, U.S. units are shown in blue. You can mix different unit types on separate data rows, as seen in the screenshot above. Also seen in the screenshot, some U.S. OSM-related calculations will not be displayed, if you choose a charge weight scaling other than 0.5. OSM-compatible calculations require that the scaling be 0.5. Data validation in the Blasting Calculator will prevent you from accidentally entering physically unrealistic values for the various parameters, although it cannot prevent you from using erroneous values or ones inappropriate for your situation. A Messages area gives prompts for filling the data cells and will help with some errors you might make in data input. If necessary data are missing, the message area will warn you and the affected cells in the Results area will remain blank until all the necessary inputs are entered. You cannot enter data in any other than the Parameters area, as the other cells are locked. Once you've supplied all the necessary information, the Blasting Calculator will provide in the Results area:
If any of the calculated values exceed OSM limits, they will be shown in red bold italic to alert you.
As with all such parameter-based calculations of vibration velocities, one should assume the possibility of factor of two or more variation from measured values - either higher or lower. I have seen cases where the variation of the calculated PPV from the measured value was over a factor of three. Thus, the calculations of the blasting calculator, while done by accepted methods in the blasting field, should be seen as approximate, with at least a factor of two safety factor built into any use of them in the field. Using Your Own Data The Blasting Calculator provides ranges and typical values for most of the relevant parameters in its calculations, but you can use your own experimentally determined data, if you have them. This will likely yield more accurate calculation results for the area for which your data apply. In particular, having K values and attenuation exponents for the specific area of the blasts is very helpful.
Using the Blasting Calculator for Construction Vibration Just as the Construction Vibration Calculator can be used to estimate blasting vibrations, the Blasting Calculator can be used for construction vibration. To do so, you will need the source energy parameters equivalent to charge weight (usually referred to as Wr values) and the equivalent of the K proportionality constant for the construction operation of interest. Scaled distance calculations are recognized as valuable for estimating construction vibrations, so such a use of the Blasting Calculator approach in construction is well-precedented. The Blasting Damage Probability Calculator
This calculator, on the Damage Probability Calc. worksheet tab of the vibration calculator workbook, is intended to allow one to estimate blasting damage probabilities when the vibration PPV is known or can be reliably estimated (e.g. with the Blasting Calculator). Basic use instructions are just above the calculator; explanatory notes follow the calculator. It is simple to use (see screenshot at right), requiring the user only to choose his desired input units (U.S. or metric) and a PPV in the chosen units on the left side of the calculator. Metric PPV values are displayed in green, those in U.S. units are shown in blue. With units and PPV choices entered, the calculator will estimate the damage probabilities for three levels of damage, "threshold", "minor" and "major", as defined in USBM RI 8507.[2] It uses the damage probability curve for blasting damage found in the same document as the basis for its calculations.[3] As the screenshot shows, you can enter as many as 24 different PPV's, in any combination of U.S. or metric units. the damage probabilities for each PPV are calculated automatically as you enter the PPV's. The calculator will sum the damage probabilities for all the entered PPV's in its last line. The sum is useful in the common case where a home experiences multiple blasts of different individual PPV's and damage probabilities.[4] Because the actual damage probabilities are known to deviate from typical log normal behavior at damage probabilities below 5% and above 95%, the calculator shows those low and high probabilities in a different font and background color to alert the user.[5],[6] The decimal part of the calculated damage probability % is not significant statistically, but is included to allow low probabilities below 1% to be seen. The Blasting Damage Probability Calculator is not for use in construction vibration situations, other than those involving blasting, as damage probabilities are not generally well-known for construction operations, where vibration caused by heavy equipment use has such variable characteristics. However, since construction vibration standards set much lower limits for construction (e.g. 0.2 in/sec for timber-framed homes vs. 0.75 in/sec for blasting limits) than for blasting, the damage probabilities for a given construction vibration PPV are undoubtedly considerably higher than those for the same blasting PPV. Using the Vibration Calculator Results Vibration standard velocity limits and safe distances represent minimum guidelines; an operation carried out at less than the safe distance or producing a ground vibration PPV over a standard limit has a higher probability of causing damage than one done at more than the safe distance or producing a PPV under the standard limit. Given the sigmoidal shape of the damage probability-velocity curves (see Vibration and Damage), the damage probability increases rapidly, the further inside the safe distance one encroaches. Calculated values for these quantities can help determine which operations run the greatest risk of damage to structures, whether a given operation of known PPV was close enough to a structure to have an unacceptably high probability of damage, whether a type of operation has a reference PPV high enough to damage a home a specific distance away from it, and what operations are in sufficient proximity to homes and other structures to require vibration mitigation. Note that, because of the limitations of both the standards on which the calculations are based and the calculation algorithms themselves, all the calculated PPV's and safe distances should be multiplied by a minimum a factor of 2 to provide a reasonable safety factor. See the Vibration and Distance chapter of the Construction Vibration Damage Guide at https://vibrationdamage.com/vibration_and_distance.htm for much more information on the correct use, and meaning of, such calculations.[1] Please note that we are not responsible for any use that you may make of the Calculator. You assume full responsibility for its proper use and interpretation (see disclaimer below). Please read all the documentation included with the calculators to help understand the appropriate meaning and use of the results. Security The Calculator is not an executable program and does not employ Excel macros. The file has been checked for viruses with two antivirus programs and found clean. If you have concerns about virus contamination on your machine, run your own antivirus program on the file after you download it. No parameters or results of your own calculations with it are communicated back to us at Vibrationdamage.com or anybody else. The Calculator, and other vibration analysis tools, are available for free download to registered users of the free Homeowner's or Professional PDF e-book versions of the CVDG from the direct links provided in their Vibration Analysis Tools chapters. At this time, the only registration required to obtain the Calculator and other tools free from Vibrationdamage.com is that of the CVDG itself (either the Pro or free Homeowners versions). If you have previously downloaded an earlier version of the Calculator, the link in your CVDG PDF Vibration Analysis Tools chapter will work to get the latest version with the two new blasting calculators in it. Get your free copy of both the CVDG for Homeowners and the Vibration Calculator today! Vibrationdamage.com Ground Vibration and Safe Distance Calculator requirements: any spreadsheet program which can read Excel (.XLS) files (including Excel in most versions, Lotus 1-2-3, Quattro Pro, OpenOffice's Calc program, and most other spreadsheets) with any computer or device which can run such programs. Basic familiarity with using spreadsheet programs is necessary. The Calculator is licensed for personal, non-business use only. If you don't have a spreadsheet program, the OpenOffice suite, which includes a spreadsheet application (Calc), can be downloaded and used free.
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E-mail to drzeigler@vibrationdamage.com or send online questions or comments about Vibrationdamage.com.
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As you replace the test values in the entry cells with your numbers, the calculated values change automatically, if you have automatic recalculation
enabled. You cannot enter anything into any other than the appropriate cells
in the input row and in the cells for optional information. So, as long as you enter the three values in the
right three cells, you will get your PPV and safe distance results without any other intervention on your part. The results table displays calculated ground vibration velocities and safe distances for various values of the
attenuation exponent n. You can then choose which value of n is most appropriate for your ground vibration situation. Some short tips on choosing the appropriate exponent appear in the results table, with more extensive information in the Reference section below the
results. You can print the results, if you wish, using the Print dialog of your spreadsheet program. 
The reference section has tabulations of the propagation exponent n suggested by various agencies in the U.S. for different soil types and equipment reference PPV's for various operations (shown in part at left) to allow the user to make
informed choices about which calculated numbers are most applicable for them. This information can be used to choose calculated PPV's (and safe distances) appropriate to a given local geology or standard. If no vibration monitoring is done, you can use the reference
section PPV values for heavy equipment to get an estimate of the PPV at a given distance from the equipment
and the safe distance for the reference PPV of that piece of construction equipment.
One of the unique features of the Blasting Calculator is its
"what-if" capability. It shows how the calculated velocities change as each
parameter is varied individually, while keeping the others constant. This facility is only available for
the data in the first data row of the Blasting Calculator, whose contents are repeated for easy reference on the first row of the Parameter Variations table, seen at right. The calculated PPV's for variations in the parameters follow in the subsequent rows. If you're not
sure what parameters you should use or would like to see how differences from those values you entered would affect the result, the Parameter Variations section of the Blasting Calculator will give you the answers.
