Características de propagação blast

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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 atten-

tion 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 predomi-

nant strike of joints. In this paper, the results of field

measurement are presented and analysed, and the mechan-ism 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 RS1RS5,

were set up along a measuring line which is parallel to the

predominant joint strike, to examine shock wave propaga-tion 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 45 and 90

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 onthe 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 trig-

gering model of the data logger was selected to simulta-

neously record the acceleration wave histories from all the

accelerometers. The automatic trigging level was set as 0.1g

(g 9.8 m/s2) which was slightly higher than the environ-

mental noise level.

The rock at the site is of very good quality. Its average P-

wave velocity (Vp) is approximately 5790 m. The predomi-

nant joint sets are sub-vertical, with the spacing ranging

from 30 to 50 cm.

Three cylindrical charges were detonated with theequivalent TNT charge weights of 10, 20 and 40 kg, corre-

sponding to the loading densities of 5, 10 and 20 kg/m3,

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

Dowdings empirical equation11 which is widely applied

in mining and civil engineering:

A 0:81 g30:5 m

R

1:84c

3050 m=s

1:45

Q

4:54 kg

0:28 2:4

r

0:28

1

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 5790 m/s), and r is the

rock density (r 2.6 g/cm3).

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 describ-ing ground motions in this study.

Fig. 1. Configuration of measurement.

408 Y. K. Wu et al.


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3 RESULTS AND DISCUSSION

3.1 Propagation velocity of shock waves

Points RS1RS5 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 10 m/s). It is

slightly (approximately 5%) smaller than the average P-

wave 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 propaga-

tion 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.

3.2 Rock surface motions

Fig. 3 shows the peak horizontal and vertical accelerations

measured at the points RS1RS5 against the horizontal dis-

tance from the explosion centre, respectively. As can be

seen, the horizontal and vertical surface motions show dif-ferent 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 hori-

zontal 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 wasnoted 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 esti-

mating ground motion effects on the surface structures at

different distances from the charge centre, because struc-

tures respond to horizontal and vertical vibrations differ-

ently. 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 accelera-

tions Ah and Av at a point occur at the same time, theresultant peak acceleration can then be calculated by

A (A2h A

2v). This assumption may result in a larger esti-

mation of the absolute peak acceleration than the actual one.

From the engineering point of view, however, the assump-

tion 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 par-

ticle 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. There-fore, the measured peak accelerations and peak velocities

are plotted against the scaled range in Figs 4 and 5, respec-

tively, where the particle velocities are obtained by numeri-

cally integrating the recorded accelerations after baseline

corrections. The recorded data can be used to derive empiri-

cal attenuation for peak accelerations and peak particle

velocities. The least-squares-fitted empirical attenuation

relations are given in the following:

A 2540:4 R=Q1=3

1:59(2)

PPV 487:71 R=Q1=3

1:25

(3)

where A is the peak acceleration in g, PPV(mm/s) is the peakparticle velocity, and R/Q1/3 (m/kg1/3) is the scaled range.

Fig. 2. Propagation velocity of shock waves.

Fig. 3. Horizontal and vertical acceleration attenuation withdistance.

Blast-induced shock waves 409


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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 attenua-

tion equations of acceleration and particle velocity obtainedby Dowding11 are also drawn in Figs 4 and 5, where the

particle velocity attenuation equation is:

PPV 18:3 mm=s30:5 m

R

1:46Q

4:54 kg

0:48 2:4r

0:48

(4)

As can be seen, the accelerations obtained from the present

tests are in good agreement with Dowdings 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 fully-

coupled charge of loading density 14001600 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 blast-

induced 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 alsoimportant 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

SX1X1(q) 1

T

M

m M

WMX1 q 2pm

T

X1 q

2pm

T

(5)

where X1(q) is the Fourier transformation of the accelera-

tion wave x1(t), X1(q) is its complex conjugate, q is the

circular frequency, Tis the duration of the time history, WM

is a smooth window, and 2M 1 is the number of smooth-ing points (here, M 1).

Fig. 6 shows the typical shock waves from Test 3

recorded at RS5, RS6 and RS7 at the incident angles of 0,

45 and 90, 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, andthen 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

The theory of wave propagation across a joint indicates that

the existence of a joint will change the amplitude and fre-

quency 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 0 to 90. The decrease is faster when the angle

increases from 0 to 45 than when it increases from 45 to90. This trend is related to the increase of the joint number

Fig. 4. Acceleration versus scaled range.

Fig. 5. Particle velocity versus scaled range.

410 Y. K. Wu et al.


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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 0

to 45,

and then slowly when the angle varies from 45 to 90.

Fig. 10 shows the principal frequencies of the accelera-

tion waves recorded at RS5, RS6 and RS7. The principal

frequencies at these points decrease approximately 70%

when the incident angle varies from 0 to 90. Similar to

the peak acceleration, the frequency attenuation is slightly

faster when the angle increases from 0 to 45, than when the

angle varies from 45 to 90.

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 attenuatesthe slowest when its propagation path is parallel with the

joint strike.

3.5 Discussion of mechanism

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. 6. Typical shock waves (Test 3). Top: RS5 (0); middle: RS6(45); bottom: RS7 (90).

Fig. 7. Power spectrum of shock waves.

Fig. 8. Principal frequency versus distance.

Fig. 9. Accelerations versus incident angles (R 50 m).

Blast-induced shock waves 411


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