- Email: [email protected]
Modelling of blast vibrations
Inr. J. Rock Mech. Min. Sci. & Geomech. Abstr. Printed in Great Britain. All rights reserved
Vol. 25, No. 6, pp. 439A45,
1988 Copyright 0
0148~9062/88 $3.00 + 0.00 1988 Pcrgamon Press plc
Modelling of Blast Vibrations K.-G. HJNZENt A hybrid method for modelling the time history of blast vibrations from production blasts is developed. The seismic signal produced by the detonation of a single hole charge is recorded in situ. This record contains information about the complex mechanism of radiating seismic energy from an explosive source as well as the filtering effect of the travel path of the signal. Assuming a linear superposition of the seismic effects of the individual holes in a row shot, the vibrations produced by a production blast are simulated. The single shot signal is convolved with an impulse series that represents the firing sequence. By a systematic variation of firing times in the simulation procedure, their eflects on the vibrations are studied. The peak amplitudes of vibrations can be reduced. The application of an electronic initiation system allows the realization of optimized firing times in production blasts and a successful validation of the synthetic seismograms.
INTRODUCTION
HYBRID MODELLING IN TIME DOMAIN
Blast vibrations are an inevitable phenomenon in the vicinity of quarries, if raw material is produced by blasting techniques. In the case of a dense population in the neighbourhood of the quarry, which is often the case in countries like the Federal Republic of Germany, the vibration may degrade the environment. In the past, efforts toward forecasting and reducing of ground vibrations were based on observations of ground velocity peak values [l]. Many different empirical relations between charge weight and distance from the source were introduced [l-3]. For this purpose, the Federal Institute for Geosciences and Natural Resources (BGR) observed the vibrations in the vicinity of about 150 quarries in more than 400 production blasts in 8000 actual seismograms. Amplitude distance relations derived from these data, as well as relations derived by other authors [4] show large scatter in the parameters. This scatter makes it necessary to search for other techniques to describe the vibration effects caused by blasting. The well known formulae and tables allow only an uncertain forecast of maximum amplitudes. The modelling of the complete seismic wavefield radiated by a production blast, including all parameters, would overcome this problem. But modelling a production blast is a very complex task. On the one hand a variety of input variables to a realistic field model are uncontrollable, i.e. geology, material properties, structural faults [5]. On the other hand, the procedure must be as simple as possible, if it should be applied in practice and not remain “only” a research tool.
Modern seismology offers various techniques of calculating theoretical seismograms [6-81. These techniques make requirements to the source of seismic energy and the medium of wave propagation which are not fulfilled in the case of blast vibrations. The formation of seismic waves in the row shot of a production blast in an open pit mine is a very complex process and up to now not completely understood [9]. To overcome these difficulties, we developed a hybrid method to calculate theoretical seismograms of blast vibrations. “Hybrid” denotes a combination of field measurement and computer simulation. Anderson [lo] describes a technique to reduce the spectral amplitudes of the blast vibrations in those frequency ranges, which might be dangerous for buildings. The frequency spectra of multiple shots are modelled by superposition of a single shot spectrum in frequency domain. In this paper, we use the advantages of the single shot signal superposition in the time domain. In addition to spectral amplitudes, all phase effects from the superposition are included in the synthetic seismogram. The phase effects are the crucial point in optimizing firing times. The ground movement at a location x in time domain can be represented as
t Bundesanstalt fiir Geowissenschaften und Rohstoffe, Stilleweg 2, D-3000 Hannovcr 51, F.R.G. 439
u(x, 1) = m(t, r)*G(x,
t, C, T),
(1)
where m(& T) is the source time function of the row shot and G(x, t, 4,~) is the elastodynamic Green’s function, x the location of the observation point and < the source location. The representation theorem equation (1) gives the displacement from a realistic source, with the source time function m, synthesized from the displacement produced by the simplest possible source, which is the unidirectional unit impulse, localized precisely in
440
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Fig. 1. A flow chart of the hybrid modelling of blast vibrations in time domain
space and time [6]. The displacement field from such a simple source is the elastodynamic Green’s function. The ground velocity can be achieved by a differentiation of equation (1). Under the preposition that the displacement field of the row shot is a linear superposition of the displacements produced by the individual holes of the blast pattern, the source time function is separated into two parts (in the following formulae we drop the mathematical dependency on x, 4, t and T): m = ms*mR, m,=a,S(t-ti),
(2) i=l,...,N
(3)
N = number of charges, ti = firing time of charge i. In this formulation, the shape of the displacement or velocity signals is assumed to be identical for all individual holes. The source time function of a single hole is m,, whereas mR is an impulse series. The amplitudes of the impulses ai in equation (3) are the scaling factors for the seismic effects of individual holes. The superposition of the individual signals is mathematically expressed as a convolution. The arriving times of the P-waves from the detonation of the individual holes at the observation point are expressed by the position of impulses in the series. The displacement history from a single shot at a specific location can be written as: u,=m,*G
(4)
This displacement history can be measured in a field experiment. The measured seismogram is not the true displacement, because it is influenced by the transfer function of the geophone and recording system. This influence can be removed by a deconvolution. Com-
bining equations (1) and (2) we obtain the displacement of a complete row shot: u = m,*m,*G.
(5)
Due to the commutative character of the convolution process, we can rearrange equation (4) to: u = m,*G *ma;
(6)
u = u,*mR.
(7)
The impulse series mR can be calculated and the convolution in equation (7) combines the single shot measurement and the model calculation. Figure 1 shows a flow chart of the measuring technique and calculating procedure. It starts in the upper left with a single shot in situ experiment. A single hole is drilled and loaded similar to the holes which have to be fired in the row shot. The displacement history u is measured with a digital recording system at those locations for which the ground vibrations are to be predicted or reduced. These locations may be close to sensitive buildings, for example. The second step of the procedure, shown in the right part of Fig. 1 is the numerical simulation. Input data are the geometric parameters of the blast hole pattern and the P-wave velocity which is well known from the single shot experiment. Delay times between the firing of the holes and the seismic efficiency of the individual holes are free parameters. As a first approximation, the efficiency may be set proportional to the charge weight of a blast hole. From this input the time of first break can be calculated for each geophone position and blast hole. The result of the calculation is the impulse series mR for each geophone position. This series is convolved with u, to model the seismogram of the row shot at the specific locations. Numerical experiments can be made by
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Fig. 2. The left part is a section of 51 synthetic seismograms. The seismograms are calculated by the hybrid method described in the text (s. Fig. 1) for a row shot with two blast holes. The lower trace is the seismogram in case of simultaneous firing of the two holes. The delay time interval is increased from trace to trace by an increment of 1 msec. In the upper trace, the delay time is 50 msec. The diagram on the right-hand side gives the peak amplitudes of the seismograms vs the delay times.
varying the free parameters of the model. A systematic variation of delay times, for example, can give the firing times which produce the smallest peak amplitudes. The numerical experiments are followed by a verification test in a large scale experiment. A blast hole pattern with the optimized firing times is realized. The comparison of real seismograms and theoretical seismograms must prove whether the prediction was successful or not.
SYSTEMATIC DELAY TIME VARIATION A variety of numerical experiments have been conducted for optimizing single row shots. The optimizing of firing times starts with the superposition of signals from the first and second hole in the row. The left part of Fig. 2 is a section of 51 synthetic seismograms. The length of the time window is 240 msec. The single source wavelet used in this simulation was measured in situ. A charge of 71 kg was fired in a 30 m hole in marly limestone. The bottom trace of the section is the seismogram for simultaneous firing of the two holes. Delay times are increased in steps of 1 msec, up to the maximum delay time of 50msec for the top trace. The diagram in the right part shows the peak ground velocity vs delay times. As expected the largest amplitude occurs in the case of simultaneous firing. The peak amplitude rapidly decreases with increasing delay time until a minimum is reached at 15 msec. The peak amplitude is about 37% of the amplitude in case of simultaneous firing. A further increase of delay time increases the peak value of ground velocity. In case of 26 msec delay, the peak amplitude approaches that of simultaneously fired
holes. For delay times from 27 to 50 msec the peak amplitude decreases again. These effects can be seen in the seismic section as well. The optimum delay time between the first and second hole concerning the peak amplitude of ground velocity is 15 msec. Based on the seismogram of 15 msec delay, the signal for a third hole can now be added and the optimum delay for the third hole can be searched for. This procedure is continued until the desired number of holes is considered. In this study we have only used single row shots, which are common in the West German quarry industry. Nevertheless, the method can be used for multiple row shots, as long as the variations in the signal shape produced by charges in different rows are small or well known. In the example on Fig. 2 for delay times longer than 50 msec, the signals from two holes are individual events in the seismograms without significant interference. The maximum ground velocity is that of the single shot wavelet. Delay blast experience teaches that bad fragmentation is the result of such long delay times and the danger of misfires arises [l 11. Therefore these delay times are not practicable. The shape of the graph in Fig. 2 indicates that a high precision firing system is necessary to meet the desired amplitudes. If the optimum delay time of 15 msec is exceeded by only 4 msec, which is not unusual for pyrotechnic delay blasting caps, the maximum amplitude would be 63% of the simultaneous shot amplitude, nearly twice the desired value which is 37%. Figure 3 compares the peak amplitudes of ground velocity for two source wavelets. The first one with the lower frequency content was obtained in marly
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Fig. 3. The peak amplitude vs delay time curves (s. Fig. 2) for two single shot signals from different geologic formations are compared. The inserted singleshot signalsare plottedin the sametimescaleas the axisrepresentingthe delay times. The signals are the vertical components of ground velocity measured in a distance of 75 m from the single hole charge. In both cases a row shot of two holes was assumed to calculate the peak amplitudes.
limestone, the second one in limestone. The seismograms are plotted in the same timescale as the delay times in the diagrams. Source-receiver distance is 75 m in both cases. The diagrams are similar to that of Fig. 2. The maximum velocity amplitudes are normalized to the amplitude produced by simultaneous firing. For marly limestone the optimum delay time between firing of the first and second hole is 13 msec. The amplitude is reduced to 47%. If the same delay time is used in the limestone quarry, the amplitude is still 87% of simultaneous shot amplitude. The source wavelet in the second case requires a delay of 22 msec which gives a maximum amplitude of 45%. The optimized firing times are strongly dependent on the shape of the source wavelet. Individual source
wavelets require individual delay time design and results obtained for a special blasting technique at a specific geologic site are in general not transferable [12]. From the numerical experiments with different single shot wavelets, we draw the following demands on the firing system: -the smallest possible delay time increment should be 1 msec; -different delay time intervals must be possible in one row; -accuracy of firing times must be better than l-3 msec depending on the shape of the single shot wavelet. These demands cannot be fulfilled by common pyrotechnic delay blast systems.
fWgthms/lns tied meoared
60.0 64.0
w*sW
60.2 64.4
Fig. 4. The upper trace is the vertical component of ground velocity recorded at a distance of 75 m from a S-hole row shot in marly limestone. The steps in the lower trace give the firing times of the individual holes of the row shot. The inserted table compares desired and actual firing times. The largest deviation is 0.4 msec.
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1
synthetic
Fig. 5. Comparison of measured (data) and synthetic seismograms for a 5-hole production shot. Both traces show the vertical component of ground velocity at a distance of 75 m from the charges. The seismic efficiencies for the 5 charges have been adjusted.
HIGH TECH FIRING
times of a 5-hole shot together with a velocity seismogram of the vertical component at a distance of 80 m. The total time window is 200 msec. Each step (l-5) in the delay time signal represents the firing time of a charge. Desired and actual delay time in the inserted list are referred to the firing time of the first hole. Maximum deviation time in this example is 400 psec. In all cases of application the bias of firing times was smaller than 1 msec in the range from 1 to 250 msec.
By application of a new microprocessor-controlled firing system all requirements of delay time accuracy which were mentioned above could be fulfilled [13]. In all large scale experiments and production blasts of this study the actual firing times of all charges were measured by a special registration circuit with an accuracy better than 50 psec. In this way, actual and desired firing times could be compared. Figure 4 shows a recording of firing
x - data
8) x - synthetic
y - dato 6) y - Synthetic
z - data
(41.3 mll/s)
F
0.m
,
I
0.05
’ O!lO ’
’ 0.11
’
I
0.20
I
o!ta
I
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0.0
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o!ss
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Q.lD
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0.40
,
z - synthetic
,
Q.rn
t/8
Fig. 6. Comparison of measured (data) and synthetic seismograms for a 5-hole production shot. The vertical, horizontal transversal and horizontal radial components of ground velocity are shown. The distance between the source and the point of observation is 75m.
444
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synthetic
dota
Fig. 7. Comparison of measured (data) and synthetic seismograms for a S-hole production shot. The vertical, horizontal transversal and horizontal radial components of ground velocity are shown. The distance between the source and the point of observation is 15OOm. VALIDATION
Validation tests have been made for the numerical simulated seismograms of blast vibrations. In these tests blast holes were drilled and charged similar to the holes of selected single shot experiments for which delay times had been optimized. Figures 5 to 7 show comparisons between measured seismograms (data) and the corresponding synthetic signals. In Fig. 5 the vertical
component of ground velocity at a distance of 75 m from a 5-hole row shot is exhibited. Due to different seismic efficiencies of the charges the amplitudes for the individual single shot wavelets had to be adjusted. The excellent fit between data and the synthetic seismogram confirms the presumption of a linear superposition of single hole wavelets. Figure 6 gives the horizontal radial component (x) and the horizontal transversal component (v) in addition. The seismograms are normalized
seismogram
dalq tiilies / Ills desired
0.0 16.0 26.0 74.0 92.0
measured
0.0 16.2 26.9 74.6 92.4
deconvolved
0.0
16.9
?
79.1 92.3
J Fig. 8. The upper trace is a single shot signal recorded at a distance of 75 m from a 71 kg charge in a 30 m blast hole in marly limestone. The vertical component of ground velocity is shown. The middle trace is the corresponding seismogram of a S-hole production shot. The lower trace is the result of a spike deconvolution of the middle trace. The inserted list compares desired and measured firing times with the times resulting from the deconvolution. The numbers at the small arrows give the normalized amplitudes of the spikes.
HINZEN:
MODELLING
to
their peak values given in brackets. Even at a distance of 1500 m (Fig. 7) synthetic seismograms and data for the same row shot fit fairly well. Note the different timescales and the different scales of the velocity amplitudes in Figs 6 and 7. SEISMIC
EFFICIENCY
Following our hypothesis, individual holes of a row shot produce identical displacement histories, if the blast parameters of the holes, i.e. their charge weight, are identical. Some of the seismograms from the production blasts show different seismic efficiencies for the holes of a row, in spite of similar blasting technique. The deconvolution of a measured seismogram from a production blast using the known displacement history from a single shot should give the impulse series mR. This is the reverse calculation process to that of formula (5). We used a standard spiking filter described by Robinson [ 141 to deconvolve row shot seismograms. Figure 8 shows the result of the deconvolution in the lower trace. The upper trace is the single shot signal and the middle trace a seismogram from a 5-hole production shot in marly limestone. The distance in both cases is 75 m. The inserted table reports the desired and measured firing times and the times derived by the deconvolution process. Only four impulses are found in the deconvolved seismogram, of which the third one is not very clear. The amplitudes of the impulses, given in Fig. 8 are normalized to the amplitude of the second impulse, which is the largest. No impulse is found which corresponds to the firing of the third hole, and the impulse corresponding to the fourth hole is very weak. The seismic efficiency in this case is only 20% of that from the second hole, while the first hole shows about 86% and the fifth hole 61%. The measured delay times and the position of the impulses agree quite well for holes number 2 and 5. The deviation is less than 1 msec. In case of hole 4 the deviation is 4.3 msec which may be due to the small efficiency. The efficiencies differ, though the charge weight was 75 kg in all holes. A series of experiments is necessary to solve this problem and the complete answer is outside of the scope of this paper.
CONCLUSIONS
The hybrid modelling of blast vibrations in the time domain provides a new approach to the prediction and reduction of blast vibrations. The combination of field recordings and numerical simulation of seismograms makes it possible to optimize firing times with a minimum amount of expensive field surveys. In situ validation experiments proved the applicability of the suggested method in practice. The modelling procedure
OF BLAST VIBRATIONS
445
and the application of a new generation of firing systems can help to overcome “avoidable blast vibrations”. Furthermore the reverse calculation process of modelling makes the seismic recordings become a tool for observing the internal blasting processes in production blasts. Acknonzledgemenrs-This study was made with financial support from the Umweltbundesamt (Berlin) and the Deutsche Kalksteinindustrie. The author would like to thank H.-J. Alheid and R. Luedeling for helpful discussions and R.-G. Ferber for carefully reading the manuscript. The important field work was only possible because of the engagement of G. Boettcher, D. Boeddener, W. Hoekendorff and W. Sydekum. The good co-operation with Dynamit Nobel AG (Troisdorf), who applied their new electronic firing system, was a pleasure during this study. Received 15 July 1987: revised 18 May 1988.
REFERENCES 1. Siskind D. E.. Staggs M. S., Kopp J. W. and Dowding C. H.
2.
3.
4
5
6 7
8.
Structural response&d damage produced by ground vibration from surface mine blastine. USBM RI 8507 (1980). Devine J. F., Beck R. H., Meyer A. V. C. and‘Du&ll W. J. EIfect of charge weight on vibration levels from quarry blasts. USBM RI 6774, p. 37 (1966). Koch H. W. Zur Moeglichkeit der Abgrenzung von Ladetnengen bei Steinbruchsprengungen nach festgestellten Erschuetterungsstaerken. Nobel Hft. 24, 92-96 (1958). Luedeling R. and Hinzen K.-G. Erschuetterungsprognosen und Erschuetterungskataster-Forschungsarbeit auf dem Gebiet der Sprengerschuetterungen. Nobel Hfl. 52, 105-123(1986). Chiappetta R. F. and Borg D. G. Increasing productivity through field control and high-speed photography. fsf Int. Symp. on Rock Fragmentation by Blasting, Lulea, Sweden (1983). Aki K. and Richards P. Quantitative Seismology-Theory and Methods. Freeman, San Francisco (1980). Fertig J. Synthetische Seismogramme und ihre Anwendung in der Explorationsseismik. Paper in Seismic Waves in Laterally Inhomogenious Media, Liblice (1983). Kennett 9. L. N. and Harding A. J. Is ray theory adequate for reflection seismic modelling? (A survey of modelling methods).
First Break 3, 9-14 (1985). 9. Davis W. C. Die Detonation von Sprengstoffen. Q&rum der Wissenschaft 7, 70-77 (1987). 10. Anderson D. A. Synthetic delay vs frequency plots for predicting ground vibration from blasting. 3rd Int. Symp. on Computer Aided Seismic Analysis and Discrimination, Washington, IEEE, pp. 15-l 7 (1983). 11. Chiappetta R. F., Burchell S. L., Reil J. W. and Anderson D. A.
Effects of accurate ms delays on productivity, energy consumption at the primary crusher, oversize, ground vibrations and airblast. 12th Con$ on Explosives and Blasting Technique, Atlanta (1986). 12. Hinxen K.-G. and Luedeling R. Minderung von Erschuetterungsemissionen durch Entwicklung problemangepasster Sprengtechniken. Umweltbundesamt Berlin, Rept no. 87-10502809, p. 111 (1987). 13. Hinxen K.-G., Luedeling R., Heinemeyer F., Roeh P. and Steiner U. A new approach to predict and reduce blast vibrations by modelling of seismograms and using a new electronic initiation system. 13th Conf. on Explosives and Blasting Technique, Miami (1987). 14. Robinson E. A. Multichannel Time Series Analysis with Digital Computer Programs, p. 298. Holden-Day, San Francisco (1967).
Vol. 25, No. 6, pp. 439A45,
1988 Copyright 0
0148~9062/88 $3.00 + 0.00 1988 Pcrgamon Press plc
Modelling of Blast Vibrations K.-G. HJNZENt A hybrid method for modelling the time history of blast vibrations from production blasts is developed. The seismic signal produced by the detonation of a single hole charge is recorded in situ. This record contains information about the complex mechanism of radiating seismic energy from an explosive source as well as the filtering effect of the travel path of the signal. Assuming a linear superposition of the seismic effects of the individual holes in a row shot, the vibrations produced by a production blast are simulated. The single shot signal is convolved with an impulse series that represents the firing sequence. By a systematic variation of firing times in the simulation procedure, their eflects on the vibrations are studied. The peak amplitudes of vibrations can be reduced. The application of an electronic initiation system allows the realization of optimized firing times in production blasts and a successful validation of the synthetic seismograms.
INTRODUCTION
HYBRID MODELLING IN TIME DOMAIN
Blast vibrations are an inevitable phenomenon in the vicinity of quarries, if raw material is produced by blasting techniques. In the case of a dense population in the neighbourhood of the quarry, which is often the case in countries like the Federal Republic of Germany, the vibration may degrade the environment. In the past, efforts toward forecasting and reducing of ground vibrations were based on observations of ground velocity peak values [l]. Many different empirical relations between charge weight and distance from the source were introduced [l-3]. For this purpose, the Federal Institute for Geosciences and Natural Resources (BGR) observed the vibrations in the vicinity of about 150 quarries in more than 400 production blasts in 8000 actual seismograms. Amplitude distance relations derived from these data, as well as relations derived by other authors [4] show large scatter in the parameters. This scatter makes it necessary to search for other techniques to describe the vibration effects caused by blasting. The well known formulae and tables allow only an uncertain forecast of maximum amplitudes. The modelling of the complete seismic wavefield radiated by a production blast, including all parameters, would overcome this problem. But modelling a production blast is a very complex task. On the one hand a variety of input variables to a realistic field model are uncontrollable, i.e. geology, material properties, structural faults [5]. On the other hand, the procedure must be as simple as possible, if it should be applied in practice and not remain “only” a research tool.
Modern seismology offers various techniques of calculating theoretical seismograms [6-81. These techniques make requirements to the source of seismic energy and the medium of wave propagation which are not fulfilled in the case of blast vibrations. The formation of seismic waves in the row shot of a production blast in an open pit mine is a very complex process and up to now not completely understood [9]. To overcome these difficulties, we developed a hybrid method to calculate theoretical seismograms of blast vibrations. “Hybrid” denotes a combination of field measurement and computer simulation. Anderson [lo] describes a technique to reduce the spectral amplitudes of the blast vibrations in those frequency ranges, which might be dangerous for buildings. The frequency spectra of multiple shots are modelled by superposition of a single shot spectrum in frequency domain. In this paper, we use the advantages of the single shot signal superposition in the time domain. In addition to spectral amplitudes, all phase effects from the superposition are included in the synthetic seismogram. The phase effects are the crucial point in optimizing firing times. The ground movement at a location x in time domain can be represented as
t Bundesanstalt fiir Geowissenschaften und Rohstoffe, Stilleweg 2, D-3000 Hannovcr 51, F.R.G. 439
u(x, 1) = m(t, r)*G(x,
t, C, T),
(1)
where m(& T) is the source time function of the row shot and G(x, t, 4,~) is the elastodynamic Green’s function, x the location of the observation point and < the source location. The representation theorem equation (1) gives the displacement from a realistic source, with the source time function m, synthesized from the displacement produced by the simplest possible source, which is the unidirectional unit impulse, localized precisely in
440
HINZEN:
MODELLING
OF BLAST VIBRATIONS
Fig. 1. A flow chart of the hybrid modelling of blast vibrations in time domain
space and time [6]. The displacement field from such a simple source is the elastodynamic Green’s function. The ground velocity can be achieved by a differentiation of equation (1). Under the preposition that the displacement field of the row shot is a linear superposition of the displacements produced by the individual holes of the blast pattern, the source time function is separated into two parts (in the following formulae we drop the mathematical dependency on x, 4, t and T): m = ms*mR, m,=a,S(t-ti),
(2) i=l,...,N
(3)
N = number of charges, ti = firing time of charge i. In this formulation, the shape of the displacement or velocity signals is assumed to be identical for all individual holes. The source time function of a single hole is m,, whereas mR is an impulse series. The amplitudes of the impulses ai in equation (3) are the scaling factors for the seismic effects of individual holes. The superposition of the individual signals is mathematically expressed as a convolution. The arriving times of the P-waves from the detonation of the individual holes at the observation point are expressed by the position of impulses in the series. The displacement history from a single shot at a specific location can be written as: u,=m,*G
(4)
This displacement history can be measured in a field experiment. The measured seismogram is not the true displacement, because it is influenced by the transfer function of the geophone and recording system. This influence can be removed by a deconvolution. Com-
bining equations (1) and (2) we obtain the displacement of a complete row shot: u = m,*m,*G.
(5)
Due to the commutative character of the convolution process, we can rearrange equation (4) to: u = m,*G *ma;
(6)
u = u,*mR.
(7)
The impulse series mR can be calculated and the convolution in equation (7) combines the single shot measurement and the model calculation. Figure 1 shows a flow chart of the measuring technique and calculating procedure. It starts in the upper left with a single shot in situ experiment. A single hole is drilled and loaded similar to the holes which have to be fired in the row shot. The displacement history u is measured with a digital recording system at those locations for which the ground vibrations are to be predicted or reduced. These locations may be close to sensitive buildings, for example. The second step of the procedure, shown in the right part of Fig. 1 is the numerical simulation. Input data are the geometric parameters of the blast hole pattern and the P-wave velocity which is well known from the single shot experiment. Delay times between the firing of the holes and the seismic efficiency of the individual holes are free parameters. As a first approximation, the efficiency may be set proportional to the charge weight of a blast hole. From this input the time of first break can be calculated for each geophone position and blast hole. The result of the calculation is the impulse series mR for each geophone position. This series is convolved with u, to model the seismogram of the row shot at the specific locations. Numerical experiments can be made by
HINZEN:
I 0
,
I
1
I
t/ms
1
I
I
MODELLING
OF BLAST VIBRATIONS
I
240 delay
time/ms
50
Fig. 2. The left part is a section of 51 synthetic seismograms. The seismograms are calculated by the hybrid method described in the text (s. Fig. 1) for a row shot with two blast holes. The lower trace is the seismogram in case of simultaneous firing of the two holes. The delay time interval is increased from trace to trace by an increment of 1 msec. In the upper trace, the delay time is 50 msec. The diagram on the right-hand side gives the peak amplitudes of the seismograms vs the delay times.
varying the free parameters of the model. A systematic variation of delay times, for example, can give the firing times which produce the smallest peak amplitudes. The numerical experiments are followed by a verification test in a large scale experiment. A blast hole pattern with the optimized firing times is realized. The comparison of real seismograms and theoretical seismograms must prove whether the prediction was successful or not.
SYSTEMATIC DELAY TIME VARIATION A variety of numerical experiments have been conducted for optimizing single row shots. The optimizing of firing times starts with the superposition of signals from the first and second hole in the row. The left part of Fig. 2 is a section of 51 synthetic seismograms. The length of the time window is 240 msec. The single source wavelet used in this simulation was measured in situ. A charge of 71 kg was fired in a 30 m hole in marly limestone. The bottom trace of the section is the seismogram for simultaneous firing of the two holes. Delay times are increased in steps of 1 msec, up to the maximum delay time of 50msec for the top trace. The diagram in the right part shows the peak ground velocity vs delay times. As expected the largest amplitude occurs in the case of simultaneous firing. The peak amplitude rapidly decreases with increasing delay time until a minimum is reached at 15 msec. The peak amplitude is about 37% of the amplitude in case of simultaneous firing. A further increase of delay time increases the peak value of ground velocity. In case of 26 msec delay, the peak amplitude approaches that of simultaneously fired
holes. For delay times from 27 to 50 msec the peak amplitude decreases again. These effects can be seen in the seismic section as well. The optimum delay time between the first and second hole concerning the peak amplitude of ground velocity is 15 msec. Based on the seismogram of 15 msec delay, the signal for a third hole can now be added and the optimum delay for the third hole can be searched for. This procedure is continued until the desired number of holes is considered. In this study we have only used single row shots, which are common in the West German quarry industry. Nevertheless, the method can be used for multiple row shots, as long as the variations in the signal shape produced by charges in different rows are small or well known. In the example on Fig. 2 for delay times longer than 50 msec, the signals from two holes are individual events in the seismograms without significant interference. The maximum ground velocity is that of the single shot wavelet. Delay blast experience teaches that bad fragmentation is the result of such long delay times and the danger of misfires arises [l 11. Therefore these delay times are not practicable. The shape of the graph in Fig. 2 indicates that a high precision firing system is necessary to meet the desired amplitudes. If the optimum delay time of 15 msec is exceeded by only 4 msec, which is not unusual for pyrotechnic delay blasting caps, the maximum amplitude would be 63% of the simultaneous shot amplitude, nearly twice the desired value which is 37%. Figure 3 compares the peak amplitudes of ground velocity for two source wavelets. The first one with the lower frequency content was obtained in marly
HINZEN:
442
MODELLING
OF BLAST VIBRATIONS
I
0.5
delay
time/ms
50
0
delay
.
50
time/m8
Fig. 3. The peak amplitude vs delay time curves (s. Fig. 2) for two single shot signals from different geologic formations are compared. The inserted singleshot signalsare plottedin the sametimescaleas the axisrepresentingthe delay times. The signals are the vertical components of ground velocity measured in a distance of 75 m from the single hole charge. In both cases a row shot of two holes was assumed to calculate the peak amplitudes.
limestone, the second one in limestone. The seismograms are plotted in the same timescale as the delay times in the diagrams. Source-receiver distance is 75 m in both cases. The diagrams are similar to that of Fig. 2. The maximum velocity amplitudes are normalized to the amplitude produced by simultaneous firing. For marly limestone the optimum delay time between firing of the first and second hole is 13 msec. The amplitude is reduced to 47%. If the same delay time is used in the limestone quarry, the amplitude is still 87% of simultaneous shot amplitude. The source wavelet in the second case requires a delay of 22 msec which gives a maximum amplitude of 45%. The optimized firing times are strongly dependent on the shape of the source wavelet. Individual source
wavelets require individual delay time design and results obtained for a special blasting technique at a specific geologic site are in general not transferable [12]. From the numerical experiments with different single shot wavelets, we draw the following demands on the firing system: -the smallest possible delay time increment should be 1 msec; -different delay time intervals must be possible in one row; -accuracy of firing times must be better than l-3 msec depending on the shape of the single shot wavelet. These demands cannot be fulfilled by common pyrotechnic delay blast systems.
fWgthms/lns tied meoared
60.0 64.0
w*sW
60.2 64.4
Fig. 4. The upper trace is the vertical component of ground velocity recorded at a distance of 75 m from a S-hole row shot in marly limestone. The steps in the lower trace give the firing times of the individual holes of the row shot. The inserted table compares desired and actual firing times. The largest deviation is 0.4 msec.
HINZEN:
MODELLING
OF BLAST VIBRATIONS
443
1
synthetic
Fig. 5. Comparison of measured (data) and synthetic seismograms for a 5-hole production shot. Both traces show the vertical component of ground velocity at a distance of 75 m from the charges. The seismic efficiencies for the 5 charges have been adjusted.
HIGH TECH FIRING
times of a 5-hole shot together with a velocity seismogram of the vertical component at a distance of 80 m. The total time window is 200 msec. Each step (l-5) in the delay time signal represents the firing time of a charge. Desired and actual delay time in the inserted list are referred to the firing time of the first hole. Maximum deviation time in this example is 400 psec. In all cases of application the bias of firing times was smaller than 1 msec in the range from 1 to 250 msec.
By application of a new microprocessor-controlled firing system all requirements of delay time accuracy which were mentioned above could be fulfilled [13]. In all large scale experiments and production blasts of this study the actual firing times of all charges were measured by a special registration circuit with an accuracy better than 50 psec. In this way, actual and desired firing times could be compared. Figure 4 shows a recording of firing
x - data
8) x - synthetic
y - dato 6) y - Synthetic
z - data
(41.3 mll/s)
F
0.m
,
I
0.05
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I
0.20
I
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I
,
0.0
I
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I
I
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,
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,
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Fig. 6. Comparison of measured (data) and synthetic seismograms for a 5-hole production shot. The vertical, horizontal transversal and horizontal radial components of ground velocity are shown. The distance between the source and the point of observation is 75m.
444
HINZEN:
MODELLING
OF BLAST VIBRATIONS
synthetic
dota
Fig. 7. Comparison of measured (data) and synthetic seismograms for a S-hole production shot. The vertical, horizontal transversal and horizontal radial components of ground velocity are shown. The distance between the source and the point of observation is 15OOm. VALIDATION
Validation tests have been made for the numerical simulated seismograms of blast vibrations. In these tests blast holes were drilled and charged similar to the holes of selected single shot experiments for which delay times had been optimized. Figures 5 to 7 show comparisons between measured seismograms (data) and the corresponding synthetic signals. In Fig. 5 the vertical
component of ground velocity at a distance of 75 m from a 5-hole row shot is exhibited. Due to different seismic efficiencies of the charges the amplitudes for the individual single shot wavelets had to be adjusted. The excellent fit between data and the synthetic seismogram confirms the presumption of a linear superposition of single hole wavelets. Figure 6 gives the horizontal radial component (x) and the horizontal transversal component (v) in addition. The seismograms are normalized
seismogram
dalq tiilies / Ills desired
0.0 16.0 26.0 74.0 92.0
measured
0.0 16.2 26.9 74.6 92.4
deconvolved
0.0
16.9
?
79.1 92.3
J Fig. 8. The upper trace is a single shot signal recorded at a distance of 75 m from a 71 kg charge in a 30 m blast hole in marly limestone. The vertical component of ground velocity is shown. The middle trace is the corresponding seismogram of a S-hole production shot. The lower trace is the result of a spike deconvolution of the middle trace. The inserted list compares desired and measured firing times with the times resulting from the deconvolution. The numbers at the small arrows give the normalized amplitudes of the spikes.
HINZEN:
MODELLING
to
their peak values given in brackets. Even at a distance of 1500 m (Fig. 7) synthetic seismograms and data for the same row shot fit fairly well. Note the different timescales and the different scales of the velocity amplitudes in Figs 6 and 7. SEISMIC
EFFICIENCY
Following our hypothesis, individual holes of a row shot produce identical displacement histories, if the blast parameters of the holes, i.e. their charge weight, are identical. Some of the seismograms from the production blasts show different seismic efficiencies for the holes of a row, in spite of similar blasting technique. The deconvolution of a measured seismogram from a production blast using the known displacement history from a single shot should give the impulse series mR. This is the reverse calculation process to that of formula (5). We used a standard spiking filter described by Robinson [ 141 to deconvolve row shot seismograms. Figure 8 shows the result of the deconvolution in the lower trace. The upper trace is the single shot signal and the middle trace a seismogram from a 5-hole production shot in marly limestone. The distance in both cases is 75 m. The inserted table reports the desired and measured firing times and the times derived by the deconvolution process. Only four impulses are found in the deconvolved seismogram, of which the third one is not very clear. The amplitudes of the impulses, given in Fig. 8 are normalized to the amplitude of the second impulse, which is the largest. No impulse is found which corresponds to the firing of the third hole, and the impulse corresponding to the fourth hole is very weak. The seismic efficiency in this case is only 20% of that from the second hole, while the first hole shows about 86% and the fifth hole 61%. The measured delay times and the position of the impulses agree quite well for holes number 2 and 5. The deviation is less than 1 msec. In case of hole 4 the deviation is 4.3 msec which may be due to the small efficiency. The efficiencies differ, though the charge weight was 75 kg in all holes. A series of experiments is necessary to solve this problem and the complete answer is outside of the scope of this paper.
CONCLUSIONS
The hybrid modelling of blast vibrations in the time domain provides a new approach to the prediction and reduction of blast vibrations. The combination of field recordings and numerical simulation of seismograms makes it possible to optimize firing times with a minimum amount of expensive field surveys. In situ validation experiments proved the applicability of the suggested method in practice. The modelling procedure
OF BLAST VIBRATIONS
445
and the application of a new generation of firing systems can help to overcome “avoidable blast vibrations”. Furthermore the reverse calculation process of modelling makes the seismic recordings become a tool for observing the internal blasting processes in production blasts. Acknonzledgemenrs-This study was made with financial support from the Umweltbundesamt (Berlin) and the Deutsche Kalksteinindustrie. The author would like to thank H.-J. Alheid and R. Luedeling for helpful discussions and R.-G. Ferber for carefully reading the manuscript. The important field work was only possible because of the engagement of G. Boettcher, D. Boeddener, W. Hoekendorff and W. Sydekum. The good co-operation with Dynamit Nobel AG (Troisdorf), who applied their new electronic firing system, was a pleasure during this study. Received 15 July 1987: revised 18 May 1988.
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Structural response&d damage produced by ground vibration from surface mine blastine. USBM RI 8507 (1980). Devine J. F., Beck R. H., Meyer A. V. C. and‘Du&ll W. J. EIfect of charge weight on vibration levels from quarry blasts. USBM RI 6774, p. 37 (1966). Koch H. W. Zur Moeglichkeit der Abgrenzung von Ladetnengen bei Steinbruchsprengungen nach festgestellten Erschuetterungsstaerken. Nobel Hft. 24, 92-96 (1958). Luedeling R. and Hinzen K.-G. Erschuetterungsprognosen und Erschuetterungskataster-Forschungsarbeit auf dem Gebiet der Sprengerschuetterungen. Nobel Hfl. 52, 105-123(1986). Chiappetta R. F. and Borg D. G. Increasing productivity through field control and high-speed photography. fsf Int. Symp. on Rock Fragmentation by Blasting, Lulea, Sweden (1983). Aki K. and Richards P. Quantitative Seismology-Theory and Methods. Freeman, San Francisco (1980). Fertig J. Synthetische Seismogramme und ihre Anwendung in der Explorationsseismik. Paper in Seismic Waves in Laterally Inhomogenious Media, Liblice (1983). Kennett 9. L. N. and Harding A. J. Is ray theory adequate for reflection seismic modelling? (A survey of modelling methods).
First Break 3, 9-14 (1985). 9. Davis W. C. Die Detonation von Sprengstoffen. Q&rum der Wissenschaft 7, 70-77 (1987). 10. Anderson D. A. Synthetic delay vs frequency plots for predicting ground vibration from blasting. 3rd Int. Symp. on Computer Aided Seismic Analysis and Discrimination, Washington, IEEE, pp. 15-l 7 (1983). 11. Chiappetta R. F., Burchell S. L., Reil J. W. and Anderson D. A.
Effects of accurate ms delays on productivity, energy consumption at the primary crusher, oversize, ground vibrations and airblast. 12th Con$ on Explosives and Blasting Technique, Atlanta (1986). 12. Hinxen K.-G. and Luedeling R. Minderung von Erschuetterungsemissionen durch Entwicklung problemangepasster Sprengtechniken. Umweltbundesamt Berlin, Rept no. 87-10502809, p. 111 (1987). 13. Hinxen K.-G., Luedeling R., Heinemeyer F., Roeh P. and Steiner U. A new approach to predict and reduce blast vibrations by modelling of seismograms and using a new electronic initiation system. 13th Conf. on Explosives and Blasting Technique, Miami (1987). 14. Robinson E. A. Multichannel Time Series Analysis with Digital Computer Programs, p. 298. Holden-Day, San Francisco (1967).