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Propagation characteristics of blast-induced shock waves in a jointed rock mass
Soil Dynamics and Earthquake Engineering 17 (1998) 407–412 q 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain PII: S 0 2 6 7 - 7 2 6 1 ( 9 8 ) 0 0 0 3 0 - X 0267-7261/98/$ - see front matter
Propagation characteristics of blast-induced shock waves in a jointed rock mass Y.K. Wu a,*, H. Hao a, Y.X. Zhou b & K. Chong b a Nanyang Technological University, Singapore Lands and Estates Organisation, Ministry of Defence, Singapore
b
(Received 5 May 1998) The propagation characteristics of blast-induced shock waves in a jointed rock mass have been monitored and studied. Accelerometers were set up on a rock surface along three lines, at 08, 458 and 908 with respect to the orientation of the predominant joint strikes. Cylindrical charges were detonated in a charge hole, and ground accelerations in both vertical and radial directions at various points on the rock surface were recorded. Results show that rock joints have significant effects on the propagation characteristics of blast-induced shock waves. The amplitude and principal frequency of shock waves attenuate with the increase of distance from the charge centre, and the increase of incident angle between the joint strike and the wave propagation path. The measured data were compared with the empirical equations of shock wave attenuation proposed by other authors. The mechanism of rock joint effect, the attenuation of shock waves in relation to the propagation distance, the charge weight and the incident angle, are discussed in this paper. q 1998 Elsevier Science Ltd. All rights reserved Key words: incident angle, shock waves, principal frequency.
earthquake engineering, mining engineering, petroleum engineering, hydrogeology and waste disposal.2 Many efforts have been made to study the effects of rock joints on wave propagation theoretically and experimentally. For instance, Blair and Spathis3 measured the attenuation of explosion-generated pulse in rock mass. King4 measured the amplitudes and travel times of high-frequency seismic waves propagated parallel and perpendicular to columnar joints in basalt, and noted lower particle velocities and greater high-frequency attenuation in the direction perpendicular to the joints than in the direction parallel to them. Robert and Stump5 studied the effect of geological inhomogeneity on near-field ground motion. Their observation suggested that scattering by geological inhomogeneity is responsible for the frequency-dependent spatial variability in ground motion. Yu and Telford6 investigated the effect of joint width and wave frequency, and concluded that wave propagation across joints is frequency dependent. Efforts have also been spent on theoretical study of joint effects on wave propagation in rock mass. There are two approaches in the theoretical study. One is to examine the effects of a single joint,7,8 and the other is to investigate the comprehensive effects of joints by using equivalent material properties.9 The application of these two approaches is
1 INTRODUCTION Drilling and blasting are the most widely adopted excavation techniques for underground mining and civil engineering. Rock blasting results in ground shock and vibration which may cause damage to the surrounding structures such as buildings, bridges, dams and tunnels, etc., therefore, blast-induced ground shocks and their propagation in rock mass have been drawing more and more attention.1 The research is particularly significant for underground blasts in urban areas, in order to reduce the induced vibration to an acceptable level. Rock mass is usually broken up by joints into rock elements, which are continuous and may be regarded as elastic bodies. The properties of rock mass are determined by the properties of the rock elements and the joints, as well as by the geometry of the system. The term joint covers all discontinuities such as joints, faults, bedding planes or other surfaces of weakness. The existence of rock joints not only significantly affects the properties of rock mass, but also their seismic response, which is closely connected to problems in geophysics, *Corresponding author 407
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Fig. 1. Configuration of measurement.
dependent on the size of joints in comparison with the wave length.10 The first method is usually adopted to a single joint characterised by a large size, whereas the second is used when fractures are dense and small in size compared with the shock wave length. In comparison with the effects of rock joints on the mechanical properties of rock mass, however, less attention has been paid to their effects on wave propagation.2 There are fewer reports on field test study of rock joint effect on shock wave propagation. In the present study, blast-induced ground motions were recorded on a rock surface at different distances from the explosion centre, and in different orientations with respect to the predominant strike of joints. In this paper, the results of field measurement are presented and analysed, and the mechanism of rock joint effects on wave propagation are discussed.
2 MEASUREMENT CONFIGURATION AND INSTRUMENTATION The field layout, as shown in Fig. 1, consists of a charge borehole of 11 m in depth and seven measuring points on the rock surface. The measuring points, labelled RS1–RS5, were set up along a measuring line which is parallel to the predominant joint strike, to examine shock wave propagation and attenuation in rock mass. The measuring points are 2.5, 5, 10, 25 and 50 m from the charge borehole, with the corresponding absolute distances of 8.8, 9.8, 13.1, 26.4 and 50.7 m from the explosion centre, respectively. To examine the orientation effects of rock joints, two extra measuring points, labelled RS6 and RS7, were arranged surrounding the explosion centre at a distance of 50 m. They are 458 and 908 with respect to the strike of predominant joint sets, respectively. At each point, two pieces of ENDEVCO piezoelectric accelerometers were set up to record the radial (horizontal) and vertical accelerations. The accelerometers were mounted on magnetic bases which were tightly secured on the steel plates cemented onto the rock surface. The detected
signals were amplified by ENDEVCO signal conditioners and then transmitted to a data recorder. A TEKTRONIX data logging system was used to record the ground motions. The sampling rate was taken as 100 ms, and the recording duration as 2 s for each channel. An automatic signal triggering model of the data logger was selected to simultaneously record the acceleration wave histories from all the accelerometers. The automatic trigging level was set as 0.1g (g ¼ 9.8 m/s 2) which was slightly higher than the environmental noise level. The rock at the site is of very good quality. Its average Pwave velocity (V p) is approximately 5790 m. The predominant joint sets are sub-vertical, with the spacing ranging from 30 to 50 cm. Three cylindrical charges were detonated with the equivalent TNT charge weights of 10, 20 and 40 kg, corresponding to the loading densities of 5, 10 and 20 kg/m 3, respectively. The surface motions, i.e. the radial and vertical accelerations induced by blasting, were monitored during the tests. The blast-induced accelerations were estimated using Dowding’s empirical equation11 which is widely applied in mining and civil engineering:
1:45 30:5 m 1:84 c R 3050 m=s 0:28 0:28 Q 2:4 3 4:54 kg r
A ¼ 0:81 g
ð1Þ
where A is the peak acceleration in g, Q (kg) is the charge weight, R (m) is the distance from the explosion centre, c is the P-wave velocity of rocks (c ¼ 5790 m/s), and r is the rock density (r ¼ 2.6 g/cm 3). To avoid signal peak cut-off, the recording range of the instruments was taken as six times the estimated value. Particle velocities and displacements were derived by numerical integration from the acceleration data. Since the displacement might contain a large error resulting from double integration, it was not treated as a parameter describing ground motions in this study.
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3.2 Rock surface motions
Fig. 2. Propagation velocity of shock waves.
3 RESULTS AND DISCUSSION 3.1 Propagation velocity of shock waves Points RS1–RS5 were set on the same measurement line with different distances from the charge centre, therefore, the arrival times of shock waves at these points and their corresponding distances, can be used to calculate the wave propagation velocity in the rock mass. In Fig. 2, the arrival times of shock waves versus the corresponding distances, and the best fitted trend-lines, are presented. As can be seen, the trend-lines of arrival times and distances from all tests, are consistently parallel to each other. Regardless of the different triggering times of the data logging system during each test, the mean propagation velocity, i.e. the average slope of the trend-lines, is 5520 6 10 m/s). It is slightly (approximately 5%) smaller than the average Pwave velocity of 5790 m/s obtained from seismic surveys. The error is acceptable in the realm of engineering geology. In the seismic surveys, mechanical impacts were used as the energy sources. The results indicate that the wave propagation velocity in a rock mass is independent of the type of energy source generating elastic waves. The consistent velocities at different distances from the charge centre, imply the homogeneity of rock mass in its property along the measuring line.
Fig. 3. Horizontal and vertical acceleration attenuation with distance.
Fig. 3 shows the peak horizontal and vertical accelerations measured at the points RS1–RS5 against the horizontal distance from the explosion centre, respectively. As can be seen, the horizontal and vertical surface motions show different attenuation trends. In the close vicinity of the charge hole, the vertical component of ground motion is larger than the horizontal. With the increase of the horizontal distance from the charge hole, the horizontal component increases initially then decreases, whereas the vertical component decreases continuously with the distance. The initial increase of horizontal motions is caused by the very large incident angle of the shock wave. Theoretically, the horizontal component is zero, if the shock wave is vertically incident to the ground surface. From the present test results, it can be seen that the maximum horizontal acceleration occurs at approximately 10 m from the charge hole. it was noted that either the horizontal or vertical components of ground motions could be larger. In general, at near-field to the charge centre, vertical motion is more pronounced, and horizontal motion becomes dominant at large distances from the charge centre. The results are significant for estimating ground motion effects on the surface structures at different distances from the charge centre, because structures respond to horizontal and vertical vibrations differently. Usually, structures are more prone to horizontal excitations as a result of their great weight, which, however, requires a very large vertical motion to excite. Assuming that the peak horizontal and vertical accelerations A h and A v at a point occur at the same time, the resultant peak acceleration can then be calculated by A ¼ Î(A2h þ A2v ). This assumption may result in a larger estimation of the absolute peak acceleration than the actual one. From the engineering point of view, however, the assumption will result in a conservative assessment of structural safety. The resultant peak particle velocity can be similarly calculated from the horizontal and vertical velocity components. It is well known that blast-induced accelerations and particle velocities are closely related to cube-root scaled range,11 i.e. the absolute distance from the explosion centre scaled by the cube-root of the charge weight. Therefore, the measured peak accelerations and peak velocities are plotted against the scaled range in Figs 4 and 5, respectively, where the particle velocities are obtained by numerically integrating the recorded accelerations after baseline corrections. The recorded data can be used to derive empirical attenuation for peak accelerations and peak particle velocities. The least-squares-fitted empirical attenuation relations are given in the following: ÿ ¹ 1:59 (2) A ¼ 2540:4 R=Q1=3 ÿ ¹ 1:25 (3) PPV ¼ 487:71 R=Q1=3 where A is the peak acceleration in g, PPV (mm/s) is the peak particle velocity, and R/Q 1/3 (m/kg 1/3) is the scaled range.
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Fig. 4. Acceleration versus scaled range.
The correlation factors (r) are 0.98 and 0.97, respectively. The best fitted attenuation relations are also shown in Figs 4 and 5, respectively. For comparison, the empirical attenuation equations of acceleration and particle velocity obtained by Dowding11 are also drawn in Figs 4 and 5, where the particle velocity attenuation equation is: 0:48 0:48 30:5 m 1:46 Q 2:4 PPV ¼ 18:3 mm=s R 4:54 kg r (4) As can be seen, the accelerations obtained from the present tests are in good agreement with Dowding’s equation, whereas the particle velocities are approximately 30%– 50% smaller than those from eqn (4). However, the data are still within the lower bound of the data that are used to deduce this equation. The discrepancy in velocity data could be attributed to the different charge conditions, because the equation is based on blasting with a fullycoupled charge of loading density 1400–1600 kg/m 3, and the present blasting are decoupled with a very low-loading density. 3.3 Frequency attenuation Frequency content is an important characteristics of blastinduced shock waves besides the amplitude. It affects the performance and safety of structures under shock wave excitation, because the structural response is highly
frequency-dependent. Some commonly applied criteria for assessing the structure safety under the influence of shock waves are also frequency dependent.12 When the principal frequency of a shock wave is higher or lower than the modal frequency of structures, the allowable critical vibration level of structures is accordingly raised. Therefore, it is also important to analyse the change of frequency contents of shock waves with the increase of distance to the charge centre. The frequency contents were estimated by using the power spectral density function:13 M 1 X 2pm p 2pm SX1 X1 (q) ¼ W X qþ X1 q þ T m¼ ¹M M 1 T T (5) where X 1(q) is the Fourier transformation of the acceleration wave x 1(t), X1p (q) is its complex conjugate, q is the circular frequency, T is the duration of the time history, W M is a smooth window, and 2M þ 1 is the number of smoothing points (here, M ¼ 1). Fig. 6 shows the typical shock waves from Test 3 recorded at RS5, RS6 and RS7 at the incident angles of 08, 458 and 908, respectively. Fig. 7 shows the corresponding power spectral density functions of these waves. As can be seen, the principal frequency of the shock wave at RS5, RS6 and RS7 is approximately 510, 280 and 100 Hz, respectively. Fig. 8 shows the attenuation of the principal frequencies of acceleration waves with the increase of distance. As can be seen, the principal frequencies of acceleration waves decrease dramatically in the near-field of detonation, and then slowly when the distance from the charge centre is more than 10 m. The result implies that high-frequency components are damped out in the rock mass within 10 m surrounding the explosion centre. It is noteworthy that a smaller charge weight corresponds to a higher principal frequency. Similar results were also reported by other authors.12 This result is probably due to the size of the damage zone and plastic region. A larger charge results in a larger damage zone and plastic region surrounding the charge centre, which can dramatically attenuate the high-frequency components of the shock wave. 3.4 Effects of rock joints orientation
Fig. 5. Particle velocity versus scaled range.
The theory of wave propagation across a joint indicates that the existence of a joint will change the amplitude and frequency contents of the wave.10 This is confirmed from the results measured at the field. Fig. 9 shows the accelerations recorded at 50 m from the charge centre versus the incident angles of the wave path, relative to the joint strike. As can be seen, the accelerations decrease by approximately 60%, while the incident angle varies from 08 to 908. The decrease is faster when the angle increases from 08 to 458 than when it increases from 458 to 908. This trend is related to the increase of the joint number
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Fig. 8. Principal frequency versus distance.
that the shock wave propagates across. As shown in Fig. 1, the joint number that shock waves propagate across increases rapidly when the angle varies from 08 to 458, and then slowly when the angle varies from 458 to 908. Fig. 10 shows the principal frequencies of the acceleration waves recorded at RS5, RS6 and RS7. The principal frequencies at these points decrease approximately 70% when the incident angle varies from 08 to 908. Similar to the peak acceleration, the frequency attenuation is slightly faster when the angle increases from 08 to 458, than when the angle varies from 458 to 908. The decreases of the peak acceleration and the principal frequency with the increase of the incident angle, reflect the comprehensive effects of joints. As can be seen, when the wave propagation path is perpendicular to the joint strike, the shock wave attenuates the fastest, whereas it attenuates the slowest when its propagation path is parallel with the joint strike. 3.5 Discussion of mechanism Fig. 6. Typical shock waves (Test 3). Top: RS5 (08); middle: RS6 (458); bottom: RS7 (908).
Fig. 7. Power spectrum of shock waves.
A laboratory study carried out by Fourney et al.14 can be used to explain the joint effects on shock-wave propagation observed in these tests. It has been found that, for a seismic wave characterised by a principal wave length, there exists a critical aperture width of joints, below which the amplitude of the wave changes very little. For joints wider than the critical value, the wave amplitude significantly decreases
Fig. 9. Accelerations versus incident angles (R ¼ 50 m).
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Fig. 10. Principal frequencies versus incident angles (R ¼ 50 m).
with the increase of the aperture width of joints. A rock mass usually contains various joints with different aperture widths, and a blast-induced shock wave contains various frequency contents. When the wave propagates through a jointed rock mass, rock joints act as a series of connected low-pass filters.15 The high-frequency signal contents whose wave lengths are shorter than the joint widths are filtered out, and low-frequency signals are allowed to pass with little change, and accordingly, the amplitude and frequency contents of the wave decrease. The extent to which the individual frequency component is attenuated is dependent on the characteristics of the rock joints. The orientation of joints relative to the wave-propagation path is another important factor. theoretically, the transmission and reflection of a wave on a joint surface are closely related to the incident angle,10 i.e. the transmission decreases with the increasing incident angle, whereas the reflection increases. In situ, the number of joints that a shock wave propagates across, normally varies with the incident angle. Therefore, the attenuation of shock waves in a jointed rock mass reflects the comprehensive effects of the aperture, number and orientation of rock joints. In other words, the attenuation characteristics of shock waves in a rock mass are an indication of the rock joint characterisation and, furthermore, the rock quality. The rock joint effect on shock-wave propagation can be used to protect structures surrounding explosions from blast-induced damage, e.g. an artificial slit can effectively attenuate blast-induced shock waves, if it is perpendicular to the wave propagation path, and its aperture is wider than the principal wave length of the shock waves.
4 CONCLUSION Rock joints have significant effects on blast-induced shockwave propagation. The aperture, number of rock joints, and
the incident angle of shock waves relative to the rock joints, are the most important factors. The amplitude and frequency of shock waves dramatically decrease in the near-area of the charge centre, and then attenuate slowly with the increase of distance. Shock waves attenuate most rapidly if propagating in the direction perpendicular to the strike of rock joints. When shock waves pass through a jointed rock mass, rock joints act as a series of connected low-pass filters. Highfrequency contents are filtered out and the shock wave significantly attenuates in both the amplitude and the frequency contents. The effects of rock joints on shock-wave propagation, can be used to assess the quality of rocks and to protect structures from blast-induced damage.
REFERENCES 1. Berta, G. Blasting-induced vibration in tunnelling. Tunnelling Underground Space Technol., 1994, 9, 175–187. 2. Cook, N. G. W. Natural joints in rock: mechanical, hydraulic and seismic behaviour and properties under normal stress. Int. J. Rock. Min. Sci. Geomech., 1992, 29, 198–223. 3. Blair, D. P. and Spathis, A. T. Attenuation of explosiongenerated pulse in rock masses. J. Geophys. Res., 1982, 87, 3885–3892. 4. King, M. S., Myer, L. R. and Rezowalli, J. J. Experimental studies of elastic-wave propagation in a columnar-jointed rock mass. Geophys. Prospecting, 1986, 34, 1185–1199. 5. Robert, E. R. and Stump, B. W. Stochastic geological effects on near-field ground motions in alluvium. Bull. Seismological Soc. Am., 1988, 78, 1037–1058. 6. Yu, T. R. and Telford, W. M. An ultrasonic system for fracture detection in rock faces. Can. Mining Metall. Bull., 1973, 66, 96–101. 7. Schoenberg, M. Elastic wave behaviour across linear slip interfaces. J. Acoustic Soc. Am., 1980, 68, 1516–1521. 8. Pyrak-Nolte, L. J., Seismic visibility of fractures, Ph.D. Thesis. University of California, Berkeley, 1988. 9. Brady, H. G., Dynamic behaviour of rock. In Comprehensive Rock Engineering, Vol. 1, Pergamon Press, Oxford, pp. 611– 623, 1992. 10. Myer, L. R., Pyrak-Nolte, L. J. and Cook, N. G. W., Effects of single fracture on seismic wave propagation. Proc. ISRM Symp. Rock Joints, Balkema, Rotterdam, pp. 467–473, 1990. 11. Dowding, C. H., Construction Vibrations, Prentice-Hall, Englewood Cliffs, 1996. 12. By, T. L. Vibration in rock and soil. Norwegian practice regarding damage criteria and ground vibration limits in urban areas. Norwegian Geotech. Inst. Pub., 1986, 164, 1–5. 13. Bolt, B., Seismic Strong Motion Synthetics, Academic Press, New York, 1987. 14. Fourney, W. L., Dick, R. D., Fordyce, D. F. and Weaver, T. A. Effects of open gaps on particle velocity measurements. Rock Mech. Rock Engng, 1997, 30, 95–111. 15. Young, R. P. and Hill, J. J. Seismic attenuation spectra in rock mass characterisation; a case study in open-pit mining. Geophysics, 1986, 51, 302–323.
Propagation characteristics of blast-induced shock waves in a jointed rock mass Y.K. Wu a,*, H. Hao a, Y.X. Zhou b & K. Chong b a Nanyang Technological University, Singapore Lands and Estates Organisation, Ministry of Defence, Singapore
b
(Received 5 May 1998) The propagation characteristics of blast-induced shock waves in a jointed rock mass have been monitored and studied. Accelerometers were set up on a rock surface along three lines, at 08, 458 and 908 with respect to the orientation of the predominant joint strikes. Cylindrical charges were detonated in a charge hole, and ground accelerations in both vertical and radial directions at various points on the rock surface were recorded. Results show that rock joints have significant effects on the propagation characteristics of blast-induced shock waves. The amplitude and principal frequency of shock waves attenuate with the increase of distance from the charge centre, and the increase of incident angle between the joint strike and the wave propagation path. The measured data were compared with the empirical equations of shock wave attenuation proposed by other authors. The mechanism of rock joint effect, the attenuation of shock waves in relation to the propagation distance, the charge weight and the incident angle, are discussed in this paper. q 1998 Elsevier Science Ltd. All rights reserved Key words: incident angle, shock waves, principal frequency.
earthquake engineering, mining engineering, petroleum engineering, hydrogeology and waste disposal.2 Many efforts have been made to study the effects of rock joints on wave propagation theoretically and experimentally. For instance, Blair and Spathis3 measured the attenuation of explosion-generated pulse in rock mass. King4 measured the amplitudes and travel times of high-frequency seismic waves propagated parallel and perpendicular to columnar joints in basalt, and noted lower particle velocities and greater high-frequency attenuation in the direction perpendicular to the joints than in the direction parallel to them. Robert and Stump5 studied the effect of geological inhomogeneity on near-field ground motion. Their observation suggested that scattering by geological inhomogeneity is responsible for the frequency-dependent spatial variability in ground motion. Yu and Telford6 investigated the effect of joint width and wave frequency, and concluded that wave propagation across joints is frequency dependent. Efforts have also been spent on theoretical study of joint effects on wave propagation in rock mass. There are two approaches in the theoretical study. One is to examine the effects of a single joint,7,8 and the other is to investigate the comprehensive effects of joints by using equivalent material properties.9 The application of these two approaches is
1 INTRODUCTION Drilling and blasting are the most widely adopted excavation techniques for underground mining and civil engineering. Rock blasting results in ground shock and vibration which may cause damage to the surrounding structures such as buildings, bridges, dams and tunnels, etc., therefore, blast-induced ground shocks and their propagation in rock mass have been drawing more and more attention.1 The research is particularly significant for underground blasts in urban areas, in order to reduce the induced vibration to an acceptable level. Rock mass is usually broken up by joints into rock elements, which are continuous and may be regarded as elastic bodies. The properties of rock mass are determined by the properties of the rock elements and the joints, as well as by the geometry of the system. The term joint covers all discontinuities such as joints, faults, bedding planes or other surfaces of weakness. The existence of rock joints not only significantly affects the properties of rock mass, but also their seismic response, which is closely connected to problems in geophysics, *Corresponding author 407
408
Y. K. Wu et al.
Fig. 1. Configuration of measurement.
dependent on the size of joints in comparison with the wave length.10 The first method is usually adopted to a single joint characterised by a large size, whereas the second is used when fractures are dense and small in size compared with the shock wave length. In comparison with the effects of rock joints on the mechanical properties of rock mass, however, less attention has been paid to their effects on wave propagation.2 There are fewer reports on field test study of rock joint effect on shock wave propagation. In the present study, blast-induced ground motions were recorded on a rock surface at different distances from the explosion centre, and in different orientations with respect to the predominant strike of joints. In this paper, the results of field measurement are presented and analysed, and the mechanism of rock joint effects on wave propagation are discussed.
2 MEASUREMENT CONFIGURATION AND INSTRUMENTATION The field layout, as shown in Fig. 1, consists of a charge borehole of 11 m in depth and seven measuring points on the rock surface. The measuring points, labelled RS1–RS5, were set up along a measuring line which is parallel to the predominant joint strike, to examine shock wave propagation and attenuation in rock mass. The measuring points are 2.5, 5, 10, 25 and 50 m from the charge borehole, with the corresponding absolute distances of 8.8, 9.8, 13.1, 26.4 and 50.7 m from the explosion centre, respectively. To examine the orientation effects of rock joints, two extra measuring points, labelled RS6 and RS7, were arranged surrounding the explosion centre at a distance of 50 m. They are 458 and 908 with respect to the strike of predominant joint sets, respectively. At each point, two pieces of ENDEVCO piezoelectric accelerometers were set up to record the radial (horizontal) and vertical accelerations. The accelerometers were mounted on magnetic bases which were tightly secured on the steel plates cemented onto the rock surface. The detected
signals were amplified by ENDEVCO signal conditioners and then transmitted to a data recorder. A TEKTRONIX data logging system was used to record the ground motions. The sampling rate was taken as 100 ms, and the recording duration as 2 s for each channel. An automatic signal triggering model of the data logger was selected to simultaneously record the acceleration wave histories from all the accelerometers. The automatic trigging level was set as 0.1g (g ¼ 9.8 m/s 2) which was slightly higher than the environmental noise level. The rock at the site is of very good quality. Its average Pwave velocity (V p) is approximately 5790 m. The predominant joint sets are sub-vertical, with the spacing ranging from 30 to 50 cm. Three cylindrical charges were detonated with the equivalent TNT charge weights of 10, 20 and 40 kg, corresponding to the loading densities of 5, 10 and 20 kg/m 3, respectively. The surface motions, i.e. the radial and vertical accelerations induced by blasting, were monitored during the tests. The blast-induced accelerations were estimated using Dowding’s empirical equation11 which is widely applied in mining and civil engineering:
1:45 30:5 m 1:84 c R 3050 m=s 0:28 0:28 Q 2:4 3 4:54 kg r
A ¼ 0:81 g
ð1Þ
where A is the peak acceleration in g, Q (kg) is the charge weight, R (m) is the distance from the explosion centre, c is the P-wave velocity of rocks (c ¼ 5790 m/s), and r is the rock density (r ¼ 2.6 g/cm 3). To avoid signal peak cut-off, the recording range of the instruments was taken as six times the estimated value. Particle velocities and displacements were derived by numerical integration from the acceleration data. Since the displacement might contain a large error resulting from double integration, it was not treated as a parameter describing ground motions in this study.
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3.2 Rock surface motions
Fig. 2. Propagation velocity of shock waves.
3 RESULTS AND DISCUSSION 3.1 Propagation velocity of shock waves Points RS1–RS5 were set on the same measurement line with different distances from the charge centre, therefore, the arrival times of shock waves at these points and their corresponding distances, can be used to calculate the wave propagation velocity in the rock mass. In Fig. 2, the arrival times of shock waves versus the corresponding distances, and the best fitted trend-lines, are presented. As can be seen, the trend-lines of arrival times and distances from all tests, are consistently parallel to each other. Regardless of the different triggering times of the data logging system during each test, the mean propagation velocity, i.e. the average slope of the trend-lines, is 5520 6 10 m/s). It is slightly (approximately 5%) smaller than the average Pwave velocity of 5790 m/s obtained from seismic surveys. The error is acceptable in the realm of engineering geology. In the seismic surveys, mechanical impacts were used as the energy sources. The results indicate that the wave propagation velocity in a rock mass is independent of the type of energy source generating elastic waves. The consistent velocities at different distances from the charge centre, imply the homogeneity of rock mass in its property along the measuring line.
Fig. 3. Horizontal and vertical acceleration attenuation with distance.
Fig. 3 shows the peak horizontal and vertical accelerations measured at the points RS1–RS5 against the horizontal distance from the explosion centre, respectively. As can be seen, the horizontal and vertical surface motions show different attenuation trends. In the close vicinity of the charge hole, the vertical component of ground motion is larger than the horizontal. With the increase of the horizontal distance from the charge hole, the horizontal component increases initially then decreases, whereas the vertical component decreases continuously with the distance. The initial increase of horizontal motions is caused by the very large incident angle of the shock wave. Theoretically, the horizontal component is zero, if the shock wave is vertically incident to the ground surface. From the present test results, it can be seen that the maximum horizontal acceleration occurs at approximately 10 m from the charge hole. it was noted that either the horizontal or vertical components of ground motions could be larger. In general, at near-field to the charge centre, vertical motion is more pronounced, and horizontal motion becomes dominant at large distances from the charge centre. The results are significant for estimating ground motion effects on the surface structures at different distances from the charge centre, because structures respond to horizontal and vertical vibrations differently. Usually, structures are more prone to horizontal excitations as a result of their great weight, which, however, requires a very large vertical motion to excite. Assuming that the peak horizontal and vertical accelerations A h and A v at a point occur at the same time, the resultant peak acceleration can then be calculated by A ¼ Î(A2h þ A2v ). This assumption may result in a larger estimation of the absolute peak acceleration than the actual one. From the engineering point of view, however, the assumption will result in a conservative assessment of structural safety. The resultant peak particle velocity can be similarly calculated from the horizontal and vertical velocity components. It is well known that blast-induced accelerations and particle velocities are closely related to cube-root scaled range,11 i.e. the absolute distance from the explosion centre scaled by the cube-root of the charge weight. Therefore, the measured peak accelerations and peak velocities are plotted against the scaled range in Figs 4 and 5, respectively, where the particle velocities are obtained by numerically integrating the recorded accelerations after baseline corrections. The recorded data can be used to derive empirical attenuation for peak accelerations and peak particle velocities. The least-squares-fitted empirical attenuation relations are given in the following: ÿ ¹ 1:59 (2) A ¼ 2540:4 R=Q1=3 ÿ ¹ 1:25 (3) PPV ¼ 487:71 R=Q1=3 where A is the peak acceleration in g, PPV (mm/s) is the peak particle velocity, and R/Q 1/3 (m/kg 1/3) is the scaled range.
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Fig. 4. Acceleration versus scaled range.
The correlation factors (r) are 0.98 and 0.97, respectively. The best fitted attenuation relations are also shown in Figs 4 and 5, respectively. For comparison, the empirical attenuation equations of acceleration and particle velocity obtained by Dowding11 are also drawn in Figs 4 and 5, where the particle velocity attenuation equation is: 0:48 0:48 30:5 m 1:46 Q 2:4 PPV ¼ 18:3 mm=s R 4:54 kg r (4) As can be seen, the accelerations obtained from the present tests are in good agreement with Dowding’s equation, whereas the particle velocities are approximately 30%– 50% smaller than those from eqn (4). However, the data are still within the lower bound of the data that are used to deduce this equation. The discrepancy in velocity data could be attributed to the different charge conditions, because the equation is based on blasting with a fullycoupled charge of loading density 1400–1600 kg/m 3, and the present blasting are decoupled with a very low-loading density. 3.3 Frequency attenuation Frequency content is an important characteristics of blastinduced shock waves besides the amplitude. It affects the performance and safety of structures under shock wave excitation, because the structural response is highly
frequency-dependent. Some commonly applied criteria for assessing the structure safety under the influence of shock waves are also frequency dependent.12 When the principal frequency of a shock wave is higher or lower than the modal frequency of structures, the allowable critical vibration level of structures is accordingly raised. Therefore, it is also important to analyse the change of frequency contents of shock waves with the increase of distance to the charge centre. The frequency contents were estimated by using the power spectral density function:13 M 1 X 2pm p 2pm SX1 X1 (q) ¼ W X qþ X1 q þ T m¼ ¹M M 1 T T (5) where X 1(q) is the Fourier transformation of the acceleration wave x 1(t), X1p (q) is its complex conjugate, q is the circular frequency, T is the duration of the time history, W M is a smooth window, and 2M þ 1 is the number of smoothing points (here, M ¼ 1). Fig. 6 shows the typical shock waves from Test 3 recorded at RS5, RS6 and RS7 at the incident angles of 08, 458 and 908, respectively. Fig. 7 shows the corresponding power spectral density functions of these waves. As can be seen, the principal frequency of the shock wave at RS5, RS6 and RS7 is approximately 510, 280 and 100 Hz, respectively. Fig. 8 shows the attenuation of the principal frequencies of acceleration waves with the increase of distance. As can be seen, the principal frequencies of acceleration waves decrease dramatically in the near-field of detonation, and then slowly when the distance from the charge centre is more than 10 m. The result implies that high-frequency components are damped out in the rock mass within 10 m surrounding the explosion centre. It is noteworthy that a smaller charge weight corresponds to a higher principal frequency. Similar results were also reported by other authors.12 This result is probably due to the size of the damage zone and plastic region. A larger charge results in a larger damage zone and plastic region surrounding the charge centre, which can dramatically attenuate the high-frequency components of the shock wave. 3.4 Effects of rock joints orientation
Fig. 5. Particle velocity versus scaled range.
The theory of wave propagation across a joint indicates that the existence of a joint will change the amplitude and frequency contents of the wave.10 This is confirmed from the results measured at the field. Fig. 9 shows the accelerations recorded at 50 m from the charge centre versus the incident angles of the wave path, relative to the joint strike. As can be seen, the accelerations decrease by approximately 60%, while the incident angle varies from 08 to 908. The decrease is faster when the angle increases from 08 to 458 than when it increases from 458 to 908. This trend is related to the increase of the joint number
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Fig. 8. Principal frequency versus distance.
that the shock wave propagates across. As shown in Fig. 1, the joint number that shock waves propagate across increases rapidly when the angle varies from 08 to 458, and then slowly when the angle varies from 458 to 908. Fig. 10 shows the principal frequencies of the acceleration waves recorded at RS5, RS6 and RS7. The principal frequencies at these points decrease approximately 70% when the incident angle varies from 08 to 908. Similar to the peak acceleration, the frequency attenuation is slightly faster when the angle increases from 08 to 458, than when the angle varies from 458 to 908. The decreases of the peak acceleration and the principal frequency with the increase of the incident angle, reflect the comprehensive effects of joints. As can be seen, when the wave propagation path is perpendicular to the joint strike, the shock wave attenuates the fastest, whereas it attenuates the slowest when its propagation path is parallel with the joint strike. 3.5 Discussion of mechanism Fig. 6. Typical shock waves (Test 3). Top: RS5 (08); middle: RS6 (458); bottom: RS7 (908).
Fig. 7. Power spectrum of shock waves.
A laboratory study carried out by Fourney et al.14 can be used to explain the joint effects on shock-wave propagation observed in these tests. It has been found that, for a seismic wave characterised by a principal wave length, there exists a critical aperture width of joints, below which the amplitude of the wave changes very little. For joints wider than the critical value, the wave amplitude significantly decreases
Fig. 9. Accelerations versus incident angles (R ¼ 50 m).
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Fig. 10. Principal frequencies versus incident angles (R ¼ 50 m).
with the increase of the aperture width of joints. A rock mass usually contains various joints with different aperture widths, and a blast-induced shock wave contains various frequency contents. When the wave propagates through a jointed rock mass, rock joints act as a series of connected low-pass filters.15 The high-frequency signal contents whose wave lengths are shorter than the joint widths are filtered out, and low-frequency signals are allowed to pass with little change, and accordingly, the amplitude and frequency contents of the wave decrease. The extent to which the individual frequency component is attenuated is dependent on the characteristics of the rock joints. The orientation of joints relative to the wave-propagation path is another important factor. theoretically, the transmission and reflection of a wave on a joint surface are closely related to the incident angle,10 i.e. the transmission decreases with the increasing incident angle, whereas the reflection increases. In situ, the number of joints that a shock wave propagates across, normally varies with the incident angle. Therefore, the attenuation of shock waves in a jointed rock mass reflects the comprehensive effects of the aperture, number and orientation of rock joints. In other words, the attenuation characteristics of shock waves in a rock mass are an indication of the rock joint characterisation and, furthermore, the rock quality. The rock joint effect on shock-wave propagation can be used to protect structures surrounding explosions from blast-induced damage, e.g. an artificial slit can effectively attenuate blast-induced shock waves, if it is perpendicular to the wave propagation path, and its aperture is wider than the principal wave length of the shock waves.
4 CONCLUSION Rock joints have significant effects on blast-induced shockwave propagation. The aperture, number of rock joints, and
the incident angle of shock waves relative to the rock joints, are the most important factors. The amplitude and frequency of shock waves dramatically decrease in the near-area of the charge centre, and then attenuate slowly with the increase of distance. Shock waves attenuate most rapidly if propagating in the direction perpendicular to the strike of rock joints. When shock waves pass through a jointed rock mass, rock joints act as a series of connected low-pass filters. Highfrequency contents are filtered out and the shock wave significantly attenuates in both the amplitude and the frequency contents. The effects of rock joints on shock-wave propagation, can be used to assess the quality of rocks and to protect structures from blast-induced damage.
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