Equipment is available for monitoring both ground vibration and overpressure. If noise measurements are also required, they are usually made with a separate Sound Level Meter. Synchronisation of the instrument with the blast is not necessary as blast monitors have trigger levels set for ground vibration and overpressure, and they also have facility for pre-trigger memory, so that no signal is lost.

Monitoring can be carried out for a number of reasons such as problem recognition and diagnosis, documentation, control or compliance monitoring and prediction of future levels¹². It is the last two that are the most significant and shall now be considered further.

Monitoring should be carried out to ensure that limits have been complied with. This means there should be a comprehensive monitoring strategy in place, which monitors at specified locations and occasions. Ideally, all blasts should be monitored at the nearest property as a minimum, although this is still rarely achieved.

A statistical method (e.g. 95% should not exceed 4mm/s) must specify to which blasts it refers, otherwise there is the possibility of manipulation of the results. Ideally, it should refer to all blasts, thus requiring all blasts to be monitored, but then the problem arises that compliance or otherwise cannot be established until operations have ceased. One possibility is to include all blasts "up to the present" to ensure ongoing compliance. Other options would be to take periods of 3 or 4 months, or to consider blasts in certain areas or benches of the site.

There is also the question of whether to include blasts which have been monitored but not produced vibration levels high enough to give a recording (i.e. close to zero). Again the intuitive answer is that they should be included in the statistics, but this again can give opportunity to "allow" high vibration levels. The more blasts there are which are included, the higher the number of blasts which form the 5% that can exceed the limit. Whichever method is chosen, it is clear that agreement must be reached before the commencement of blasting on a particular site.

One solution to this problem would be to agree that a blast should never be designed to exceed the 95% PPV level. This would avoid the situation where, if compliance has so far been high (i.e. more than 95%), a blast could be designed to exceed the 95% PPV level, and yet still be in compliance because 95% of the blasts still remain below that level. This could be checked in the blast design records and would ensure that there was no manipulation of the results to allow "big" blasts.

When vibration limits are set, they usually refer to recordings taken at ground level at specified properties (usually the closest). BS7385:Part 1¹² states "Where the purpose is to monitor with regard to imposed vibration, the preferred position is at the foundation, a typical location being at a point low on the main load-bearing external wall at ground floor level when measurements on the foundations proper are not possible". The reason for this is that structural damage criteria from around the world specify vibration limits that apply at foundation level. Indeed the vast majority of damage noted in studies does not occur on upper floors in structures but mainly on lower floors where the strains are greatest due to the confinement of the foundation.

Some operators and MPAs take measurements inside buildings, particularly following a complaint, because ground vibrations can be amplified by the buildings by a factor of three. Measurement inside a building can also help to engender good relations with the occupants. However, this can be fraught with difficulty as the question then arises, "where in the property should the monitoring take place?", with a large number of rooms and locations possible. It would also be highly impractical to monitor inside a house on a permanent basis. It may be possible to monitor a few "test blasts" with a number of recorders in different locations, and produce transfer functions from outside to different locations inside, after which the function could be applied to external readings to determine the probable value at an internal location. However, this is a complex and time consuming exercise and will probably only be carried out in extreme circumstances.

Transducer Coupling

If transducers are placed on the ground alongside the building being monitored, the recorded vibrations can be significantly affected by surface or near-surface features which may have a very localised affect. At high levels of vibration which occur at certain frequencies, it is also possible for transducers to leave the ground. BS7385:Part 1¹² suggests that when monitoring on the ground, a stiff steel rod should be driven into the ground, through the loose surface layer, and the transducer attached to ensure close contact with the ground. In reality this is difficult to achieve. Alternatively it can be fixed to a rigid surface plate such as a well-bedded paving slab. Some equipment manufacturers suggest placing a small sandbag on top of the transducer if it is simply placed on a hard surface. However, even if good coupling is achieved, the nature of the ground under the hard surface is unknown and could be very broken and affect the vibrations.

Better coupling can be achieved if the transducers are buried in a density matching box, but this is only practicable for permanent monitoring stations.

Because there are so many variables involved in blasting and the transmission of vibrations away from the blast, it is impossible to theoretically predict what levels of vibration are going to be produced by a blast. The easiest way is to record the vibrations from blasts on a particular site and use that data to predict for future events. In general, the more data that can be collected, the more accurate your predications will be. The method of determining a relationship which can be used for prediction is best fit or least-squares regression analysis.

It is well known that the vibrations recorded at a certain location will depend principally on the amount of explosive detonated at a moment in time (MIC), the distance between explosive and monitor (d), and the ground conditions (site factors a & b). Dividing the distance by a scaling factor of the charge weight allows comparisons between blasts of different sizes. Most analyses use the square root Scaled Distance, although some use cube root (mostly used for overpressure) and it is possible to employ a site specific best-fit scaling.⁴⁵ This latter case uses multivariate regression analysis techniques which does not assume a relationship between distance and charge weight, but finds the best factor for each to fit the data. With increased computing power of programs like Microsoft Excel, this is now fairly simple to do and it certainly will give better statistical fit. However, it has not been widely accepted and one possible reason is that it is much harder to visually inspect a relationship between three variables (PPV, distance and MIC) than it is to plot the data for 2 variables (PPV and Scaled Distance) on a simple graph.

If square root scaling is used then PPV is related to MIC and distance in the following way.

PPV = a.(d/MIC^0.5)^b

The value of d/MIC^0.5 (or d/√MIC as it is sometimes displayed) is known as the Scaled Distance (SD), so this equation is often given as

PPV = a.(SD)^b

The normal way for site factors a & b to be determined is empirically, collecting real data from blasts. This is straightforward because if the log₁₀ of both sides of the equation are taken it gives the following,

log(PPV) = b.log(SD) + log a

which is the equation of a straight line (y=m.x+c), where site factor b is the gradient of the line (m) and the log of the site factor a (log(a)) is the intercept (c). Therefore, if a number of vibration recordings are made and log(PPV) plotted against log(SD), the points should lie approximately on a straight line (e.g. Figure 7) which will have a gradient of b and an intercept of log(a) which can be determined from least-squares regression analysis, such as that available on Microsoft Excel and shown in Table 2.

The site factors a and b are obtained from the coefficients of the intercept and X variable 1 (i.e. the gradient). It is important to remember the coefficient of intercept is actually log(a) so the antilog (10^a) of the coefficient is needed to obtain a. For the example in Table 2, b = -2.0643 and a = 10^2.3798 = 239.7

The log(SD) should be taken as the independent variable (x axis) as this can be determined exactly because the distance and charge weight can be measured, while the log(PPV) is considered the dependent variable (i.e. its value is thought to depend on the value of the log(SD)) and so should be plotted on the y axis.

Once the site factors are obtained, future vibration levels can be predicted if the distance and MIC are known.

The reliability of the prediction will depend on the scatter of the points used to produce the best fit line, which can be considered in terms of the correlation coefficient (r²) and the Standard Error (SE). Figures 8-10 show how the r² and SE vary with the scatter of the data points. The ideal is for r² to approach 1 and the SE to approach 0, which would represent a perfect fit.

Figure 8 shows an excellent data set taken from a series of test blasts. There is a good range of



Scaled Distances which have been obtained because the blasts have been monitored at a very wide range of distances, from close in to far away.

Figure 9 is a subset of the data in Figure 8. It has a cluster of points with a small range of Scaled Distances such as might be obtained if the blasts were monitored at a distances which were very similar. It is clear that the best fit line could be drawn at almost any angle through this data set and this is reflected by the extremely poor correlation coefficient.



The scattering of the data results in the high Standard Error. It is still possible to get a rough idea of the likely levels if the Scaled Distance used for the prediction lies within this cluster (e.g. SD=100). However to use the best fit line to predict outside this range (e.g. for a SD of 10) would be extremely risky and would be unlikely to produce accurate results.

Figure 10 is the same data set as Figure 9 but with a single additional data point added at a distance, probably the result of one monitoring location close to the blast. This has had a significant impact on the best fit line, which now runs very close to this point and is similar to the line for the complete data set in Figure 8. It has also produced an excellent r² and a reasonable SE. However, it is important to note that any predictions based on this will in reality be based on that single point of low Scaled Distance, so if this were erroneous, it would have a major effect on the gradient of the best fit line.



A good understanding of least squares regression analysis is therefore very important, otherwise results may be treated with confidence which is not warranted.

The explanation so far has focussed on obtaining the best fit line, which will enable predictions of a average PPV level. This means 50% of blasts will be above that level and 50% will be below. What is usually required is a prediction of the PPV value from a given Scaled Distance, which will only be exceeded on a certain number of occasions (e.g. 5%, giving 95% below that level). This can be determined using the Standard Error of the PPV data together with the appropriate multiplier (i.e. number of Standard Errors) which can be obtained from statistics tables.

In the past there has been some confusion as to which Standard Error and which multiplier should be used. The Standard Error is confusing because of the different terms which are often used for the same thing. These include the standard error of estimate, standard error of regression, estimated standard deviation of errors, etc. The Excel regression routine gives a table of results as shown in Table 2, where there are a number of Standard Errors shown. The one that is required here is the upper one, shown in the regression statistics, and not the two relating to the coefficients of the intercept and gradient.

The confusion over which multiplier to use arises because with a normal distribution, a confidence limit normally applies above and below the mean (twin tailed). However, with blasting a single tailed test is used because the concern is to include everything below an upper limit as it doesn't matter how low the vibrations get.

Figures 11 & 12 show why a multiplier of 1.645 gives the required 95% level and why it should be used. In programmes such as Microsoft Excel, the confidence limits which can be calculated during the regression analysis are for a twin tail and would therefore give the wrong results. It can be seen that the correct result for a 95% level would be obtained if a value for 90% was put into the programme (i.e. the number of Standard Errors is the same for a single tail 95% level and a twin tail 90% level).




The equation for the 95% PPV level (i.e. that level of vibration which for a given Scaled Distance will only be exceeded once in twenty blasts) is given as follows.

log(PPV) = b.log(d/√MIC) + log(a) + (1.645 x Standard Error),

where (d/√MIC) = Scaled Distance.

This equation shows that a value is being added to the intercept which means the 95% will always be higher than the best fit line, the difference being proportional to the Standard Error (degree of scatter).

Very often a 95% PPV level is set as a limit, in which case, the above equation can be rearranged to make the MIC the subject which will give the blasting engineer the maximum amount of explosive which should be detonated at any one time.

log(MIC) = 2.(log(d) - ((log(PPV) - log(a) - (1.645 S.E.)) / b))

When the site factors, distance and 95% PPV limit are substituted into the equation, it will give the MAXIMUM instantaneous charge weight which can be used to ensure a 95% probability of being within the limit (i.e. one blast on twenty will be over the limit). If a lower MIC is used then the likely PPV will be lower and there will be a greater probability of being below the 95% limit.

Figure 13 shows the best fit and 95% lines for a good data set, together with the Scaled Distances which are related to a PPV of 10mm/s. If the blast engineer wanted to design a blast which produced an average (50% limit) PPV of 10mm/s, then the Scaled Distance of 14.8 would be used. Table 3 shows how this Scaled Distance gives different MICs which could be used, depending on the distance between blast and monitoring location (SD = distance/√MIC, or rather MIC = (distance/SD)²). More usually, the blast will be designed to a 95% limit, which for 10mm/s gives a Scaled Distance of 21.4 with its own set of MICs for particular distances. These charge weights will of course be lower than the 50% limit as more blasts must fall below the 10mm/s level.

Figure 13a is an interactive version of Figure 13, but this time the limiting PPV is 6mm/s rather than 10mm/s. This figure also shows the effect that "false" data points can have on the results.

Click to enlarge

Figure 14 shows the distance/MIC curve, from which the maximum charge weight to ensure compliance can be obtained for a range of distances. This curve is based on the Scaled Distance of 21.4, which is obtained from the 95% level for 10mm/s in Figure 13.

The fact that the 95% line is being used for the predictions means that the scatter of the data (which can be quantified by the correlation coefficient and Standard Error) is already being considered. This is because the greater the scatter, the higher the Standard Error and the further away the 95% line will be from the best fit line, thus resulting in higher Scaled Distance for a given PPV and therefore lower permitted MICs.



What is now clear is that IF it is possible to predict PPV's very accurately, then the permitted charge weights will be higher. It is true that this will result in higher average PPVs, but 95% of the blasts will still be below the limit.

The example given is an extremely good data set with excellent predictability, and reduced the data to make it more variable and the resulting MICs more restrictive. The question arises, if we start with a mass of data which does not show a good regression line, can we legitimately reduce the data with the intention of improving the correlation coefficient and Standard Error, resulting in higher permitted MICs? The answer is that this can be achieved in a number of ways and these will be explored under good practice.

Very often the site factors are determined by means of a test blast before production begins. This will involve monitoring a number of shots, often single hole, and recording at a number of different locations with a broad range of distances. There are severe limitations on this which will again be considered in the next section.