VIBRATIONS FROM BLASTING FOR A ROAD TUNNEL -

A STATISTICAL REVIEW OF SCALING LAWS

J.K. Murfitt 1 & Billy Siu

2

Abstract : Current Hong Kong practice for monitoring of blast effects

on structures and utilities, from both surface and subsurface

construction blasting, is often limited to ensuring a defined peak

particle velocity (PPV) value for each sensitive receiver affected by

the blasting is not exceeded. Until frequency-related PPV monitoring

and monitoring of strains resulting from temperature and humidity

changes becomes more widely adopted within a regulatory framework,

PPV limits will continue to be the default controlling factor over

charge weight and thus rates of tunnel advancement. As charge weight

control is currently governed by empirical formulae related to these

limiting PPV’s, this paper reviews the reliability of the statistical

methods used in prediction of PPV’s using blast data along a 1km twin

3-lane road tunnel. Attenuation constants derived from blasts in a

section of tunnel are reviewed, using square root scaling, cube root

scaling and multiple linear regression techniques, along with statistical

goodness of fit tests, to determine the reliability of empirical predictor

equations. The paper also attempts to determine which tunnelling

factors, including expected surface wave transmission at the Portals,

close-in blasts, transmission medium, explosive type (emulsion vs.

cartridge explosive), confinement as defined by full face or

enlargement blasts and powder factor most affect resultant peak

particle velocities.

INTRODUCTION

Excavation progress in any drill & blast tunnel is dependent on a number of interrelated

parameters, some of which have a greater impact on progress than others, some of which are

variable (e.g. charge weight) and some which are not (e.g. surrounding geology), but all of

which combine to define the eventual rates of advance. Measures were put into place at the

Shatin Heights Tunnels to review some of these factors, with those identified as having the

greatest impact, and those with the greatest scope for improvement of progress being afforded

the closest attention during construction. One of the issues reviewed was propagation

equations for and the estimation of the magnitude of blast wave velocities (and amplitudes) at

any one sensitive receiver.

The main focus of this paper is the accuracy of prediction of the magnitude of blast wave

velocities that will arrive at a sensitive receiver, due to a blast using a known charge weight

per delay, at a known radial distance from that receiver. What is universally accepted is that

the attenuation constants should be derived as a site specific exercise as discussed by New

(1986), Dowding (1996), Hustrulid (1999) and Siskind (2002).

__________________________________________________________________________________________ 1

Resident Engineer (Geotechnical), Maunsell Consultants Asia Ltd 2

Assistant Resident Engineer (Geotechnical), Maunsell Consultants Asia Ltd

Using statistical analyses, this paper reviews :

(a) whether the blast data from this site follows a lognormal distribution and how well the

residuals follow the assumption of normality i.e. the goodness of fit. Normality is the

fundamental basis for prediction of the blast constants in the blast equation (Dowding

1996; Pegden et al. 2005).

(b) whether a relevant site specific blasting vibration attenuation relationship exists that

more closely models the attenuation of seismic blast waves at various sections along

this site, than that derived using the most-often used “square-root” scaling law and

whether there are identifiable locations or ground conditions where it is more

appropriate to use.

(c) the sensitivities of recorded blast vibrations to:

(i) surface wave transmission at the portals.

(ii) close-in blasts.

(iii) transmission medium.

(iv) explosive type: emulsion (vs. cartridge) explosive.

(v) confinement as defined by full face or enlargement blasts.

(vi) powder factor (PF).

SOURCE OF BLASTING DATA

A detailed discussion of current blasting practice in Hong Kong, including an explanation

of the derivation of the current baseline blasting constants adopted by the Mines Division of

the Geotechnical Engineering Office (GEO) of the Civil Engineering and Development

Department, is presented in Li & Ng (1992). It recommends the square-root scaling method

as being reliable enough for “local use”, and adds that the “Mines Regression Graph” is a

useful guide for calculating the maximum explosives charge weight per delay before a site

specific blasting vibration attenuation relationship is obtained.

A review of the USBM RI8507 Report (Siskind et al. 1980) indicates the USBM Report

conclusions were based largely on ground vibrations from surface coal mine and quarry

blasts. The GEO Mines Division blast attenuation formula is itself developed from a data set

of 520 combined blasts including quarrying, tunnelling, trench excavation, footing excavation

and submarine blasting, the latter blast type for which industry practice is to use a cube root

scaling law almost exclusively. This paper concentrates on blast attenuation solely from the

current tunnel project based on a total data set of 1132 blasts, resulting in excess of 3580

recorded data points, and attempts to identify which, if any, specific scaling law is the most

applicable along the tunnel alignment.

DETERMINATION OF THE ALLOWABLE CHARGE WEIGHT PER DELAY

The current general practice in Hong Kong for determining maximum charge weights per

delay for use in blasting works is to employ a form of the energy equation based on “square-

root scaling”. This ground velocity-distance-energy relationship calculates the predicted peak

ground velocity at a distance, R, from a source normalized by the input energy, as follows:

PPV = K * (R / W a )

b, (Eq 1)

where

PPV = peak particle velocity,

K = constant (intercept),

b = slope of regression line

a = charge weight exponent (0.5 for square-root scaling),

R = radial distance from the Blast Source and

W = charge weight per delay.

The term (R/W a) is also referred to as the scaled distance (SD). The term “per delay”

assumes an 8ms delay (industry standard practice for tunnel blasts) in this tunnel. In practice,

there may still be cancellation, or reinforcement (overlap) of wave forms. Constants K and b

in Eq. 1 above are normally derived on a site-specific basis.

THEORETICAL BASIS FOR SCALING LAWS

There are two main scaling laws based on Eq 1 in common use, square root scaling

(exponent a = 0.5) and cube root scaling (exponent a = 0.33).

(a) Square root scaling : Dowding (1996) noted that square-root scaling is based on

observations of the distribution of charge in a cylindrical hole. With density constant,

the diameter of the charge hole (Dh) is proportional to the square root of the charge

weight.

(b) Cube root scaling : Jimeno et al. (1995) observed that cube root scaling has as its

theoretical basis, the supposition that the explosive column is a sphere and that any

linear dimensions should thus be corrected by the cubic root of the explosive charge.

New (1986) proposed the use of multiple linear regression techniques to determine the

best fit.

A further detailed discussion on various scaling laws, including numerous variations of

the exponent a, can be found in Bollinger (1980), Blair (1990), Singh et al. (1993), Jimeno et

al. (1995), Dowding (1996) and Oriard (2002). Some attenuation laws do not take into

account any particular charge symmetry, while others are based on assumed wave form type,

e.g. Ghosh & Daemen (1983) related PPV to charge weight with different attenuation

relations for body waves and Rayleigh waves and the shape of the charge. Singh et al. (1993)

even observed that square-root scaling laws are more appropriately used when blasting in

softer rock types e.g. sandstones whereas the blast results for medium to hard rock masses,

represented by basalt, dolomite and granite, are near optimum when explosive charge per

delay is estimated using equations for both square root scaling and cube root scaling. Zhou et

al. (2000) noted that at a “sufficiently large distance”, the geometry effect should disappear

and the exponent “a” should approach 1/3.

Some authors also noted cube root scaling is used for vibration prediction only in the

extreme near field (Lucca 2003; Yang et al. 2000). Further details specific to cube root

scaling and case-histories where best-fit analyses resulted in cube-root scaling are discussed

in NAVFAC (1986), Siskind et al. (1977), Siskind et al. (1980), New (1989), Olsen et al.

(1974), Olson et al. (1972), Lucca (2003), Bacci et al. (2002), Wu et al. (2003) and Zhou et al.

(2000). Some of the above case histories determined cube root scaling as appropriate for their

site and some did not. However, while these references indicate that square root scaling is

still by far the most often used scaling law, other laws such as cube-root scaling continue to

be checked for and used by practitioners to determine the applicability of attenuation results

in various ground conditions.

MULTIPLE LINEAR REGRESSION ANALYSIS (MLR) New (1989) noted that an attenuation equation derived from a MLR is a more appropriate

predictor equation largely because it is site specific. This Paper discusses whether, using the

statistical methods below and using the site specific data recorded, the energy exponent “a”

derived from MLR, is close enough to 1/3 or 0.33, to justify use of cube root scaling in some

areas of the tunnel, such as close-in blasting and/or when using very small (essentially

spherical) charge weights. The multiple regression analyses in this paper were determined

using a procedure outlined in Singh et al. (1993).

ANALYSIS OF THE SHATIN HEIGHTS TUNNEL DATA

The Shatin Heights Data Set

The Shatin Heights Tunnel PPV data comprises records from 1132 blasts, with a total of

3580 data sets recorded. Charge weights varied between 0.066 and 3.841 kg/delay.

Numerous “no-results” were also recorded, where the trigger level of the instruments was not

met. This may be a function of both starting with very low charge weights (0.066kg/delay)

and instrumentation placement at a large radial distance from the blast.

The fundamental assumption behind the applicability of the blast vibration attenuation

equation is that the data follows a lognormal distribution (Dowding 1996). In order to test

how well the Shatin Heights data fits this assumption, analysis of the “Goodness of Fit” of the

regressed distribution, in a similar fashion to Pegden et al. (2005), was performed by

conducting univariate normality tests on the residuals of the data and the results plotted

against number of blasts (or results) used in the analysis. By plotting the data points in

conjunction with tunnel chainage, it is possible to visually determine the number of data

points required for normality and to also determine when the attenuation characteristics of the

data set from some distance down the tunnel no longer matches the initial data. A series of

normality tests has been carried out on several selected data sets, as described below.

Summary of Sensitivity Analyses Performed In order to identify the sensitivity of contributing factors such as distance and charge

weight in the predictor equations, residual plots, plots of PPV vs. range and plots of PPV vs.

charge weight were shown for the entire data set.

Summary of Statistical Analysis Tests Performed

To ensure the data follows the assumptions of the statistical model, i.e. the lognormal

distribution (for any form of scaling), selected data sets were checked using Frequency

Histograms, Normal Probability Test Plots and Normality (Goodness of Fit) Tests on the

residuals of the data.

SENSITIVITY ANALYSES

Residual Plots

Hunt et al. (2003) concluded that the log/log approach to regression equation

determination does not actually produce the best fitting power law equations connecting PPV,

distance and charge weight. Hunt et al. (2003) also noted that the construction of the 84%

and 95% confidence limits assumes not only normality of the log(PPV) on log(SD) data, but

also normality of the distribution of the residuals i.e. the variance of the distribution from

normality.

Variation of Residuals of logPPV vs. PPV

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 5.0 10.0 15.0 20.0

PPV mm/s

LogPPV Residuals

(mm/s)

Figure 1. Scatter Plot of the Residuals

The residual plot in Figure 1 indicates both nonlinearity and heteroskedasticity over the

range of PPV’s recorded, for PPV results above and below approx. 1mm/s.

Heteroskedasticity (also commonly spelled heteroscedasticity) is the violation of the

assumption that “the variance of the distribution from which the observations of the error term

are drawn is constant” (Studenmund 1992). While Studenmund (1992) noted a number of

tests (e.g. White’s test, the Breusch-Pagan test) can be performed to rigorously test for

heteroskedasticity, only the scatter plot is shown above, to graphically demonstrate

heteroskedastic variability. The variation in the residuals of the PPV’s recorded from the

SHT tunnel blasts, indicates that in general, the larger the PPV values (above 1mm/s), the

larger the error in the prediction of the PPV using the predictor equation of the form of Eq 1

above.

Sensitivity to Range and Charge Weight

Figure 2 show the expected variation of PPV with range and with charge weight, with

range being the dominant factor as evidenced by the steeper curve. The charge weight plot

rises up at a relatively flat gradient, indicating much lower sensitivity than the range.

Variation of PPV with Charge Weight

y = 2.084x0.195

0.1

1

10

100

0.01 0.1 1 10

Charge Weight/delay (kg)

PPV (mm/s)

Variation of PPV with Range

y = 51.241x-0.774

0.1

1

10

100

10 100 1000

Range (m)

PPV m

m/s

Figure 2. Sensitivity to Range and Charge Weight

STATISTICAL ANALYSES AND NORMALITY TESTING

Visual Inspection of Frequency Histograms & Normal Probability Plots

Inspection of a histogram of the residuals of the peak particle velocities, as shown below,

indicates that the data generally follows a lognormal distribution; however the log-transposed

distribution is in many cases some way from a symmetric Gaussian distribution, an

observation borne out by normality testing discussed below. This will influence any predictor

equation, and the data set should be closely examined before using to determine allowable

charge weights.

Log PPV Residuals Frequency

Histogram

0

5

10

15

20

25

-0.2 -0.1 0.0 0.1 0.2 0.3

Log PPV Residuals

Frequency

Q-Q Normality Plot : Log PPV Residuals

-3

-2

-1

0

1

2

3

4

-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

log PPV Residuals

Std. Dev

Figure 3. Blast data (100 data points) between Ch. 1477 and 1651

The histogram in Figure 3 clearly shows data both below and above the Gaussian curve

and deviation in the tails of a Quantile-Quantile (Q-Q) normality plot is readily observable.

While visual inspection of both the distribution of the residuals and the normal probability

“Q-Q plot” in Figure 3 would likely reject the assumption of normality, surprisingly the data

“passes” all the normality tests and three out of the four skewness and kurtosis tests.

Log PPV Residuals Frequency

Histogram

0

10

20

30

40

50

60

70

-0.5-0.4-0.3-0.2-0.1 0.

00.10.20.30.40.50.6

Log PPV Residuals

Frequency

Q-Q Normality Plot : Log PPV Residuals

-4

-3

-2

-1

0

1

2

3

4

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

log PPV Residuals

Std. Dev

Figure 4. Blast data (367 data points) between Ch. 1477 and 1831

In comparison to Figure 3, the histogram in Figure 4 for a larger data set appears to be

more normally distributed. Visual inspection of the distribution of the residuals would likely

accept the assumption of normality, however all five normality test and all four skewness and

kurtosis tests performed on the data set actually shows the data “fail”. The results of Figures

3 and 4 agree with the conclusions reached by Pegden et al. (2005) i.e. visual inspection alone

cannot satisfy the assumption of normality.

Continuously Increasing Data Sets and “Windowed” Data Sets

Pegden et al (2005) reviewed a series of quarry blast data, continuously adding new data

to the existing data set and checking for normality at each addition of new data. Physically,

this makes sense in a quarry situation where it is likely the ratio (A/R) of the advance of the

quarry face (A) with respect to the distance (R) to surrounding sensitive receivers remains

relatively small throughout the life of the quarry. Adding data to all preceding information is

thus statistically viable as it is likely subsequently added data will not skew the original

results, provided that scaled distances to the sensitive receivers remain in approximately the

same range, and that geology does not change. The first analyses below conduct normality

tests on a continuously increasing data set, similar to Pegden et al’s (2005) approach, with

data added in a batch size as shown on the plot.

However, in the case of a tunnel, the location of sensitive receivers most affected changes

with the location of the advancing face. The advancing face and different wave propagation

paths and travel lengths through different media, mean that adding a set of vibration results

from blasts e.g. 100 m apart, picked up by different sensitive receivers, is unlikely to yield

results which are consistent. As such, a discrete “window” of a fixed data size, “moving”

along the tunnel alignment and representative of the moving face, is considered a more

appropriate method of analysing tunnel vibration data. For the analyses below, a window of a

fixed size is defined and the window “moved” along the data set in a step size (generally

smaller than the window size), with normality tests conducted at each increment.

Normality Tests

There are quite a number of Normality Tests available for checking “Goodness of Fit”,

some of which have greater power than others and some are more proficient at picking up

deviations in the tails, or in the middle of the distribution. Thode (2002), Strom and

Stansbury (2000) and Poitras (2006) give specific details of normality testing, particularly on

the appropriateness of, and power of each type of normality tests for various sample sizes.

The “Goodness of Fit” tests used on the Shatin Heights data set are the Shapiro Wilk,

Kolmogorov Smirnov (with Lilliefors correction), Anderson Darling, Jarque Bera and

D’Agostino Omnibus Tests. Note that these tests only provide statistical evidence for certain

types of "non-normality", they do not guarantee "normality".

For this reason, although one test would be adequate, the above five tests have been

selected and rather than tabulate results which show that a data set has “passed” or “failed”

the normality test(s), a value of 1 is assigned to those passing the normality test and a value of

0 to those data sets for which the null hypothesis cannot be rejected. To pass a normality test

the observed significance level, termed P value (Pval), should exceed a chosen significance

level, which for the Shatin Heights Data, was set at 0.05, i.e. Pval>0.05. For the purposes of

graphical presentation only and for ease of identification of patterns of normal distribution,

we have defined a “Normality Index” as the sum of these assigned (0 or 1) values, with 5

being the largest index value (normality likely) and 0 the smallest (normality highly unlikely).

Skewness/Kurtosis Tests

Skewness characterizes the degree of asymmetry of a distribution around its mean and

Kurtosis characterizes the relative peakedness or flatness of a distribution compared with the

normal distribution. Similar to the normality index defined above, a value of 1 is assigned to

tests “passing” the Skewness or Kurtosis tests, and for the purposes of graphical presentation

only, we define a “SkewKurt Index” as the sum of the assigned values, with 4 being the

largest index value (normality likely) and 0 the smallest (normality highly unlikely, i.e.

significant Skewness and Kurtosis). The four tests are D’Agostino Skewness, D’Agostino

Kurtosis and the Z Scores of Skewness and Kurtosis (2 tests).

Normality tests and skewness tests were performed on several data sets as shown in Table

1, however only the results of Test I, shown in Figures 5 and 6, are presented in this Paper.

Normality tests were performed on both square root scaled data and on MLR-regressed data,

using the same data set. The results include a comparison against the R-squared correlation,

commonly used to determine whether a data set should be accepted as being appropriately

valid for use in determination of charge weights for blast designs.

TABLE 1. Summary of Normality Tests

TUNNEL BLAST RESULTS: AREAS TESTED FOR NORMALITY

Test A Confined (Pilot) *

Test B Unconfined (Benching, Pilot Enlargement) **

Test C All Data with PPV > 1mm/s

Test D All Data using Packaged Emulsion (Cartridge) Explosives

Test E All Data using Gassed Emulsion Explosives

Test F All Data within Range <20m

Test G All Southbound Tunnel Data (lower overburden thickness)

Test H All Northbound Tunnel Data (higher overburden thickness)

Test I All In-Borehole Vibrographs (Rock-Rock Transmission) only ***

* assumed confined, ** assumed lesser confinement, *** results presented in this Paper.

Continuous Run Results

Figures 5a~5f shows the results of the continuous run on a data set of raw results. No

outliers were removed. Even though R-squared values remained relatively high throughout

the data set, the normality tests (Normality Index and Skewkurt results), while initially good,

for the first 150 data points, thereafter indicated a poor fit to the normal distribution, for the

remainder of the entire run. This may be due to the addition of data from blasts where the

geology or topography was different than for the first 150 points or charge weights changed

markedly, or where sensitive receivers changed. Between 50 and 150 points the b-value for

the added data was fairly constant, but thereafter changed markedly. The K value remained

fairly constant throughout the tests sequence. The “a” index indicated the selected data best

fits a square root scaled distribution.

The following nomenclature is used in the following plots:

LR = Linear Regression using fixed exponent a (labelled LR on plots)

MLR = Multi-linear Regression using fixed exponent a (labelled MLR on plots)

Continuously Increasing Data Set (Square Root SD)

0

1

2

3

4

5

6

0 50 100 150 200 250 300 350 400

Cum. Data Points

Norm

ality Index

0.0

0.2

0.4

0.6

0.8

1.0

R Squared

Normality Index LR

R-Squared Value

Figure 5a. Square Root Scaled Distance Regression Analysis

(Southbound Tunnel in-borehole blasting data)

Continuously Increasing Data Set (MLR SD)

0

1

2

3

4

5

6

0 50 100 150 200 250 300 350 400

Cum. Data Points

Norm

ality Index

0.0

0.2

0.4

0.6

0.8

1.0

R Squared

Normality Index MLR

R-Squared Value MLR

Figure 5b. Multiple Linear Scaled Distance Regression Analysis

(Southbound Tunnel in-borehole blasting data)

Continuously Increasing Data Set

0

1

2

3

4

5

0 50 100 150 200 250 300 350 400

Cum. Data Points

SkewKurt Index SkewKurt Index LR

SkewKurt Index MLR

Figure 5c. Skewness/Kurtosis Scores from both Models: Continuous Run

Continuously Increasing Data Set (Square Root SD)

1032 1032

-1.22 -1.22

0

200

400

600

800

1000

1200

1400

0 50 100 150 200 250 300 350 400Cum. Data Points

Intercept K

-1.36

-1.34

-1.32

-1.30

-1.28

-1.26

-1.24

-1.22

-1.20

Slope b

50% Intercept K

84% Intercept K

95% Intercept K

HKMinesDept95K%

Slope b

HKMinesDeptb

Figure 5d. Blast Constants from Square Root Regression Analysis

Continuously Increasing Data Set (MLR SD)

1032 1032

-1.22 -1.22

0

200

400

600

800

1000

1200

1400

0 50 100 150 200 250 300 350 400Cum. Data Points

Intercept K

-1.38

-1.36

-1.34

-1.32

-1.30

-1.28

-1.26

-1.24

-1.22

-1.20

Slope b

50% Intercept KMLR

84% Intercept KMLR

95% Intercept KMLR

HKMinesDept95K%

Slope bMLR

HKMinesDeptb

Figure 5e. Blast Constants from MLR Analysis

Continuously Increasing Data Set

0.5 0.5

0.33 0.33

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0 50 100 150 200 250 300 350 400

Cum. Data Points

MLR Indice

Square Root Indice=0.5

Cube Root Indice=1/3

MLR Indice

Figure 5f. Index “a” from MLR Analysis (0.5 implies square root scaling,

0.3 implies cube root scaling)

Windowed Run Results

Figures 6a~6f show the results of the windowed run on a data set of raw results. Again, no

outliers were removed. The R-squared values remained relatively high (>0.7) until point 250

of the data set, at which point the normality tests (Normality Index and Skewkurt results),

while initially acceptable for the first 200 data points, drop to show poor normality. As the

window moved along the data however and the old data is “removed” and new data points

added to the data set, the fit to the normal distribution again improved, as did the R-squared

results. While not passing the normality test for every single window in the entire data set,

the results still indicate that analysing discrete sets of data specific to an area is likely to be

more appropriate than simply continuously adding data points to an existing set. The “a”

index variation shows the data best fit a square root distribution up to the point where

normality was rejected, then a cube root distribution after the non-normal section of data had

been passed.

Window Data Set: Size = 100 & Step = 20 (Square Root SD)

0

1

2

3

4

5

6

0 50 100 150 200 250 300 350 400

Data Point Range

Norm

ality Index

0.0

0.2

0.4

0.6

0.8

1.0

R Squared

Normality Index LR

R-Squared Value

Figure 6a. Square Root Scaled Distance Regression Analysis

(Southbound Tunnel in-borehole blast data)

Window Data Set: Size = 100 & Step = 20 (MLR SD)

0

1

2

3

4

5

6

0 50 100 150 200 250 300 350 400

Data Point Range

Norm

ality Index

0.0

0.2

0.4

0.6

0.8

1.0

R Squared

Normality Index MLR

R-Squared Value MLR

Figure 6b. ML Scaled Distance Regression Analysis

(Southbound Tunnel in-borehole blast data)

Window Data Set: Size = 100 & Step = 20

0

1

2

3

4

5

0 50 100 150 200 250 300 350 400

Data Point Range

SkewKurt Index

SkewKurt Index LR

SkewKurt Index MLR

Figure 6c. Skewness/Kurtosis Scores from both Models: Windowed Run

Window Data Set: Size = 100 & Step = 20 (Square Root SD)

1032 1032

-1.22 -1.22

0

200

400

600

800

1000

1200

1400

0 50 100 150 200 250 300 350 400

Data Point Range

Intercept K

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Slope b

50 % Intercept K

84% Intercept K

95% Intercept K

HKMinesDept95K%

Slope b

HKMinesDeptb

Figure 6d. Blast Constants from Square Root Regression Analysis

Window Data Set: Size = 100 & Step = 20 (MLR SD)

1032 1032

-1.22 -1.22

0

200

400

600

800

1000

1200

1400

0 50 100 150 200 250 300 350 400

Data Point Range

Intercept K

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Slope b

50% Intercept KMLR

84% Intercept KMLR

95% Intercept KMLR

HKMinesDept95K%

Slope bMLR

HKMinesDeptb

Figure 6e. Blast Constants from MLR Analysis

Window Data Set: Size = 100 & Step = 20

0.5 0.5

0.33 0.330.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350 400

Data Point Range

MLR Indice Square Root Indice=0.5

Cube Root Indice=1/3

MLR Indice

Figure 6f. Scaled Distance Index from the MLR Analysis

CORRELATIONS TO TUNNELLING AND BLASTING PARAMETERS

Chakraborty et al. (2004) identified and proposed to link together several tunnel blasting

parameters into an index, termed the Tunnel Blasting Index (TBI). While this Paper does not

propose any correlations with this Index, an attempt to identify the most sensitive parameters

which affect blast vibrations has been conducted. Chakraborty et al. (2004) found that the 7

most influencing parameters (from 15 originally identified) on resultant blast vibrations can

be divided into 3 groups comprising Rock Mass Parameters, Tunnel Configuration Parameters

and Blast Design. The sensitivities of recorded blast vibrations to the following parameters

were thus reviewed:

(a) Surface wave transmission at the portals.

(b) Close-in blasts.

(c) Transmission medium.

(d) Explosive type: Emulsion (vs. Cartridge) explosive.

(e) Confinement as defined by full face or enlargement blasts.

(f) Powder factor.

With reference to Figures 7 to 9, the results of PPV vs. scaled distance plots for cases (a)

to (f) are discussed below:

Portal Zone (within 10m of Tunnel Portal)

PPV Vs. Charge Weight (MLR)

25 25

y = 565.72x-1.132y = 416.83x

-1.132

y = 259.61x-1.132

R2 = 0.76650.1

1

10

100

1 10 100 1000R/(W^0.513)

Recorded PPV (mm/s)

Figure 7. Multi-linear Regression Analysis of data within 10m of

North Portal – Outliers Removed from Data Set.

From Figure 7, square root scaling appears the most appropriate based on the limited data

set, with a=0.513 close to 0.5.

Close-in Blasts

Figure 8 shows data extracted from the data set that falls within 20 m of a blast face

within the tunnel. Outliers were identified in the full data set and have been removed for these

regression analyses, as an R-squared value of 0.7 is considered the minimum acceptable value

(Eltschlager 2001). The multi-linear regression index “a” tends toward cube root scaling

(0.382), which agrees both with Lucca (2003) and the close-in blasting equations published in

USACE (1989).

PPV vs. Charge Weight - Data less than

20m from Blast

25

y = 242.14x-1.2921

R2 = 0.6899

y = 319.73x-1.2921 y = 382.51x-1.2921

1

10

100

1 10 100

Scaled Distance = R/W ̂0.5

Recorded PPV (mm/s)

PPV vs Charge Weight - Data less than

20m from Blast (MLR)

25

y = 615.05x-1.464y = 515.51x-1.464

y = 392.08x-1.464

R2 = 0.7025

1

10

100

1 10 100

R/(W^0.382)

Recorded PPV (mm/s)

Figure 8. Multi-Linear Regression Analysis of Close-in Blast (R<20m)

Transmission Medium

The Shatin Heights Project offered the unique opportunity to review the amplification

effects due to surface reflection and rock-soil transmission vs. rock-rock transmission, as the

same blasts were monitored with both in-borehole transducers in rock and by surface

instrumentation.

PPV vs Square Root Scaled Distance for In-Borehole and Surface Vibrograph

0.1

1

10

100

1 10 100 1000R / W1/2

PPV (mm/s)

In-Borehole Vibrograph

Surf ace Vibrograph

Surf ace Trendline

In-Borehole Trendline

Figure 9. Vibration Monitoring Records by Surface/In-Borehole Vibrographs

Figure 9 shows plotted surface vibration levels in the order of twice that of the in-borehole

results at equivalent scaled distances.

.

Explosive Type: Bulk Emulsion vs. Packaged Cartridge Emulsion explosive.

Bulk emulsion is theoretically more efficient at energy transfer than (tamped) cartridge

emulsion products (McKern et al. 2000), due to bulk emulsion providing improved coupling

between the side walls of the blasthole. In comparison, (tamped) cartridge emulsion products

often behave as decoupled charges, as energy is lost through gas expansion into the borehole

cavity following detonation. Improper tamping reduces the efficiency of the explosive and

the charge can act as a decoupled charge, actually reducing the vibration. McKern et al (2000)

noted that insufficient tamping can lead also to low fragmentation and reduced performance.

As noted by Jimeno et al. (1995) if the energy imparted to the rock is not enough to break the

rock due to too high confinement (stemming too long), or too high burden, higher vibrations

may occur. To determine if there was any difference in vibration levels due to explosive type

used, plots of vibrations due to both explosive types is shown in Figure 10, over a range of

scaled distances.

PPV vs Square Root Scaled Distance for Blasting with Emulsion and Cartridge

0.1

1

10

100

1 10 100 1000R / W1/2

PPV (mm/s)

Emulsion Explosiv e

Cartridge Explosiv e

Cartridge Trendline

Emulsion Trendline

Figure 10. Vibration Monitoring Records (Blasting with

Emulsion and Cartridge Explosives)

The vibration review shows a slight trend of lower PPV for bulk emulsion at (square root)

SD above 20. Between SD = 10~20, the vibration levels are slightly higher, although there is

little discernible difference between the two results. Note that a direct comparison is difficult

to make as bulk emulsion was used almost exclusively at charge weights above 2.5kg/delay,

whereas cartridge (packaged) emulsions was used below 2.5kg/delay.

Blast Confinement

Confinement was assumed, for purposes of reviewing this data set, as either the pilot, top-

heading or full face blasts, whereas unconfined was defined as bench blasting and blasting for

the enlargement where two free faces were available prior to blasting. High confinement

should theoretically increase PPV levels as noted by Li & Ng (1992), Blair & Armstrong

(2001) and the ISEE’s Blasters Handbook (1998), which noted that “if a charge is deeply

buried with no free face nearby, the rock is not displaced (although damaged around the

explosive) and more of the energy goes into seismic waves…lack of confinement has the

opposite effect”.

It was initially expected that the pilot tunnel/full face blasts would behave as confined

blasts in relation to the subsequent less confined stoping (enlargement) blasts. Surprisingly,

the results of the confined vs. unconfined blasts shown in Figure 11 indicate a trend of lower

PPV at (square root) SD above 15, but below SD = 20, the predicted PPV vibration levels

being slightly higher. While bench blasting may be considered largely unconfined, the

enlargement blasts are considered to be partially confined.

PPV vs Square Root Scaled Distance for Confined and Unconfined Blasts

R2 = 0.321

R2 = 0.5236

0.1

1

10

100

1 10 100 1000R / W1/2

PPV (mm/s)

Conf ined Blast

Unconf ined Blast

Unconf ined Blast Trendline

Conf ined Blast Trendline

Figure 11. Vibration Monitoring Records for Confined and Unconfined Blasts

Powder Factor

Figure 12 shows the variation of powder factor (PF) normalised by RQD, and PPV

normalised by radial distance. Normalisation of PF by RQD was chosen as it represents

energy (PF) imparted into the rock, with poorer rock quality not requiring as high a PF for

fragmentation as stronger rock. The PPV is normalised by the absolute distance R, as the

charge weight time is indirectly included in PF. There is no discernible correlation between

the two, indicating PPV is more strongly controlled by other factors, such as absolute

distance. Note the scatter of PF used around Ch. 1700 to 1900 results from powder factors

used first for pilot headings, then back over the same chainage for enlargement blasts

Powder Factor/RQD vs. Tunnel Chainage - T1 - Northbound

0.001

0.01

0.1

1147 1247 1347 1447 1547 1647 1747 1847 1947

Tunnel Chainage

Powder

Factor/RQD

0.00.20.40.60.81.01.21.41.61.82.0

PPV/Radial

Distance

PF/RQD

PPV/Radial Distance

Powder Factor/RQD vs. Tunnel Chainage - T2 -Southbound

0.001

0.01

0.1

1196 1296 1396 1496 1596 1696 1796 1896

Tunnel Chainage

Powder

Factor/RQD

0.0

0.5

1.0

1.5

2.0

PPV/Radial

Distance

PF/RQD

PPV/Radial Distance

Figure 12. Variation of Powder Factor (normalised by RQD) and PPV

(normalised by Radial Distance) along Tunnel Chainage

CONCLUSIONS

The blast data on this site follow a lognormal distribution only in specific sections of the

tunnel. As a tunnel, unlike a quarry, cavern or deep excavation, always moves away from the

plan location where blasting has previously taken place, the transmission media, its geometry

and its properties change with each advancing face. It is thus considered appropriate for the

attenuation constants and the scaling law itself to be checked as construction progresses. For

a tunnel, this does not simply mean adding more data to the existing data set and producing K

and b indices for the full set. A new set of independent data points should be checked at

defined chainages or with changes in topography and geology, against the previous data set.

Charge weights should thus be calculated from blast constants derived from data recorded

reasonably close to the current blast face or, in the absence of previously recorded data,

constants which are derived from blasts at locations which closely match the geology and

topography of the current tunnel section.

The cube root scaling law, which has a strong theoretical basis, is still in common use in

checking against actual blast results and is considered an appropriate expression for

determining charge weights that maintain PPV within acceptable limits. However the above

results show that it was not always appropriate for the Shatin Heights Tunnel blasts, with the

exception of possibly close-in blasts.

The outliers in the results once again emphasise the need for proper geophone mounting.

The International Society of Explosives Engineers (ISEE) publishes “good practice”

guidelines (Eltschalger 2002).

Numerous parameters influence blast vibrations recorded at any sensitive receiver;

however the parameters which had the largest controlling influence on the Shatin Heights

Tunnels were absolute distance, charge weight per delay and transmission medium.

While statistics is regularly used as a basis for any review of blasting vibration results, it

should not be used in isolation. Dowding (2004) observed that “any statistical review should

not exclude the practical issues affecting amplitudes such as geology, geometry, timing,

mounting of sensors, variable detection with distance and amplitude and the relatively

unimportant information obtained at very close distances (i.e. if the criterion is going to be

10mm/s, and never closer than 100m, the relevance of amplitudes of 100mm/s at 20m is not

great, nor is 0.3mm/s at 3000m). Statistics can never replace a careful design with accurate

consideration of timing, burden, etc. Systematic changes such as a 10% miscalculation in the

burden, differences in the propagation path and the use of pyrotechnic delays with their

inherent timing errors, all affect the results.”

REFERENCES

Bacci, D., and Landim, P. M. B. (2002). “Statistical methods applied to the analysis of

blasting vibrations in a Diabase Quarry in the City of Campinas, (SP) - Brazil.

International Society of Explosives Engineers, 2002 General Proceedings Collection,

Vol. 1.

Blair, D. P. (1990). “Some problems associated with standard charge weight vibration scaling

laws.” Proc., 3rd

International. Symposium on Rock Fragmentation by Blasting,

Brisbane, Australia. Balkema, 149-158.

Blair, D. P., and Armstrong, L. W. (2001). “The influence of burden on blast vibration.”

Fragblast, 5(1-2), 108-129.

Blasters Handbook. 17th

Edition (1998), International Society of Explosives Engineers,

Cleveland, Ohio.

Bollinger, G. A. (1980). Blast Vibration Analysis, Southern Illinois University Press.

Chakraborty, A. K., Raina, A. K., Ramulu, M., Choudhury, P. B., Haldar, A., Sahoo, P., &

Bandopadhyay, C. (2004). “Development of rational models for tunnel blast

prediction based on a parametric study.” Geotechnical and Geological Engineering,

22(4), 447-496.

Dowding, C. H. (1996). Construction Vibrations. Prentice Hall, Upper Saddle River.

Dowding, C. H. (2004). Personal communication.

Eltschlager, K. (2001). “Regulatory review of blasting related citizen complaints.” Proc.,

Annual Conference on Explosives and Blasting Technique, Conf. 27 Vol. 1, 235-246.

Eltschlager, K. (2002). “Blast vibration and seismograph section 2002.” International Society

of Explosives Engineers , 2003 General Proceedings Collection, Vol. 1.

Ghosh, A., and Daemen, J. K. (1983). “A simple new blast vibration predictor based on wave

propagation laws.” Proc., 24th

US Symposium on Rock Mechanics, 151-161.

Hunt, P., Wetherelt, A. & Powell, N. (2003). “The reliability of peak particle velocity analysis

methods.” International Society of Explosives Engineers, 2003 General Proceedings

Collection Vol. 2.

Hustrulid, W. A. (1999). Blasting Principles for Open Pit Mining. A.A. Balkema, Rotterdam.

Jimeno, C. L., Jimeno, E. L., & Carcedo, F. J. A. (1995). Drilling and Blasting of Rocks.

Geomining Tech. Inst. of Spain.

Li, U. K., and Ng, S. Y. (1992). “Prediction of blast vibration and current practice of

measurement in Hong Kong.” Proc., Conference Asia Pacific-Quarrying the Rim,

Institute of Quarrying (Hong Kong Branch).

Lucca, F. J. (2003). Effective Blast Design & Optimization. Terra Dinamica L.L.C.

McKern, E. J., Pearce, D. O., Duke, D. D., & Adamson, W. (2000). “The influence of

cartridge length and tamping practices on the efficiency of packaged emulsion

explosives in development blasting.” Proc., 1st World Conference on Explosives and

Blasting Technique, Munich.

NAVFAC (1986). Design Manual DM 7.02. Naval Facilities Engineering Command

(NAVFAC) Norfolk, Virginia.

New, B. M. (1986). Ground Vibration caused by Civil Engineering Works. Research Report

53, Transport and Road Research Laboratory (TRRL), Crowthorne, Berkshire.

New, B. M. (1989). Trial and Construction Induced Blasting Vibration at the Penmaenbach

Road Tunnel. Research Report 181, Transport and Road Research Laboratory

(TRRL), Crowthorne, Berkshire.

Olson, J. J., Fogelson, D. E., Dick, R. A., & Hendrickson, A. D. (1972). “Ground vibrations

from tunnel blasting in granite: Cheyenne Mountain (NORAD), Colorado.” Report of

Investigations 7653, U. S. Bureau of Mines.

Olson, J. J., Dick, R. A., Fogelson, D. E., & Fletcher, L. R (1974). “Mine roof vibrations

production blasts, Shullsburg Mine, Shullsburg, Wisconsin.” Report of Investigation

7462, U. S. Bureau of Mines

Oriard, L. L. (2002). Explosives Engineering, Construction Vibrations and Geotechnology.

International Society of Explosives Engineers, Cleveland, Ohio.

Poitras, G. (2006). “More on the correct use of Omnibus tests for normality.” Accepted for

publication in Economics Letters.

Pegden, M., Birch, W. J., & Wetherelt, A. (2005). “Is that normal? - Fundamental

observations for best practice blast vibration analysis.” Proc., 31st Annual Conference

on Explosives and Blasting Technique, International Society of Explosives Engineers,

Orlando, Florida.

Singh, B. & Pal Roy, P., & Singh, R. B. (1993). Blasting in Ground Excavations and Mines.

A.A. Balkema, Rotterdam.

Siskind, D. E., Snodgrass, J. J., Richard, A., & Quiring, J. N. (1977). “Mine roof vibrations

from underground blasts, Pilot Knob, Mo.” Report of Investigation 7764, U. S. Bureau

of Mines.

Siskind, D. E., Stagg, M. S., Kopp, J. W., & Dowding, C. H. (1980). “Structure response and

damage produced by ground vibration from surface mine blasting.” Report of

Investigation 8507, U. S. Bureau of Mines.

Siskind, D. (2000). Vibrations from Blasting. International Society of Explosives Engineers,

Cleveland, Ohio.

Strom, D. J., and Stansbury, P. S. (2000). “Determining parameters of lognormal distributions

from minimal information.” AIHAJ, (61).

Studenmund, A. H. (1992) with the assistance of Henry J. Cassidy. Using econometrics : a

practical guide. 2nd

edition. HarperCollins, New York.

Thode, H (2002). Testing for normality. Marcel Dekker, New York.

USACE (1989). Blasting Vibration Damage and Noise Prediction and Control. U.S. Army

Corps of Engineers, ETL1110-1-142.

Wu, C., Hao, H., Lu, Y., & Zhou, Y. (2003). “Characteristics of stress waves recorded in

small scale field blast tests on a layered rock-soil site.” Géotechnique, ICE, 53(6),

587-599.

Yang, N., Zhang, Z., & Liu, H. (2000). “The vibration characteristics of a tunnel induced by

adjacent blasting.” Proc., of the 1st World Conference on Explosives & Blasting

Technique, Munich, Germany.

Zhou, Y. X., Seah, C. C., Guah, E. H., Foo, S. T., Wu, Y. K., & Ong, P. F. (2000).

“Considerations for Ground Vibrations in Underground Blasting” Proc., of the

International Conference on Tunnels & Underground Structures, Singapore,

November 26-29, 2000.