P R O P A G A T I O N V E L O C I T Y A N D R A D I A T I O N P R O P E R T I E S

O F I N D U C E D T E N S I L E C R A C K S

JAN KOZ~K, TOMA~ LOKAJi~K, JAN SiLEN~

Geophysical Insti tute, CzeehosL Acad. Sci. , Pra#ue*)

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1. INTRODUCTION

At present, besides shear dislocation along a pre-existing fault also fast tensile fracturing of a solid body under compression is widely accepted as a mechanism which can contribute to energy release in shallow earthquakes. The shear mechanism of seismic energy release has been intensively studied especially since Brace and Byerlee [1] introduced the stick-slip idea for ex- plaining the shallow earthquake process. An overview of recent experimental work in this field performed on rock samples can be found, e.g., in [2]. In [3] also results of laboratory tests obtained with model materials are summarized.

As for tensile fracturing, the most attention was paid to laboratory tests such as drop weight and impact loading, mainly with the aim of determining the mechanical properties of the tested structures [4]. Although tensile fracruring of model and rock samples in seismological labora- tories has been studied since the early sixties (e.g. [5, 6]), the idea that tensile fracturing may be seismoactive was accepted only recently. Laboratory testing of physical models represents a con- Venient approach to determining the physical relations characterizing the tensile fracturing of a solid body under load. In this way, initiation, growth and interaction of tensile fractures, induced by an array of slits made in glass, perspex and rock samples, were investigated. The conditions for individual tensile fracturing combining into a marginal fault were formulated [6, 3]. Tensile cracks induced by stress concentration around a fault plane in perspex models under uniaxial load were analyzed in [7] where the results characterizing the decisive role of the fault plane inclination to the stress direction were presented. Two stages of tensile crack life were determined, i.e. the first, fast stage, accompanied by seismic energy release, and the second, characterized by the low velocity of crack propagation. The relation Of the fault-plane-induced tensile-crack trajectory to the primary tensile stress field was investigated in [8]. It was found that the trajectory of the crack is predetermined by the maximum gradient of the primary tensile stress component in both stages of crack propagation. Besides the study of crack morphology, load conditions and physical conditions of tensile crack initiation, as mentioned above, also

*) Address: BoSni II, 141 31 Praha 4-Spof'ilov.

Studia geoph, et geod. 27 [1983] 133

J. Kozdk, T. Lokajidek, J, Silen~

seismic energy release4 6y the tensile crack process was analyzed [9]. Records obtained proved that the parameters of seismic energy release (amplitudes and frequencies) do not depend on the angle of fault plane inclination. From the viewpoint of strong dependence of physical parameters characterizing tensile crack initiation and growth (such as the triggering pressure p*, fast stage crack length I~C and~crack: path geomet/y) on the fault plane inclination angle, the stability of radiated pulse parameters vs. this angle were surprising.

Therefore, an attempt was made tO determine the characteristics of the tensile crack, namely the crack propagation velocity.

2. 'EXPERIMENTAL

The tensile crack propagation velocity was measured on square perspex plate models 150 x. 150 mm in size (thickness 10 ram), in which a diagonally located linear slit with stress-freeboundaries was made. Thestit I was 30 mm long ana u-8 +_ L_+ 0.1 mm wide. To load the model, a controlled hydraulic loading device operating Up to 100 kN was used. A compressive loading rate of 0.4 MPa . s- 1 was applied in all the experiments. The models were compressed up to the moment ot tensile crack initiation. In the experiments, the angle of inclination c~ between the slit (its longitudinal axis) and the direction of uniaxial load varied from 20 ° to 70 °, in steps of 10 °. For each inclination angle, 3 - 4 models were treated. In general, the experi- mental arrangement as to model geometry and load conditions corresponded to that described in [7].

As to t tensile crack velocity measurements, we utilized the results of the previous crack geometry measurements reported in [9]; perpendicularly to the future crack trajectory we fixed (Loctite 495) 14 mangamne wires 50 gm thick. Expecting the largest changes of tensile crack propagation velocity to occur at the beginning of the crack propagation, we varied the density of measuring elements along the crack ~rajectory (Fig. 1). The times at which the individual wires fractured during tensile Crack propagation, determined on the basis of resistivity changes in an electric circuit, were recorded in the fofin of a step function on a transient recorder Dafal~/b 922 (Fig. 2)" The appropriate distances of the individual wires along the crack'i?ath were determined by means of a projection microscope. Besides the crack propagation velocity, also the triggering pressure p* and fast-stage crack length l* c were recorded.

3. RESULTS

The set ot diagrams characterizing tensile crack propagation velocities Vrc along the ,crack path for 6 inclination angles :~ is shown in Fig. 3; the positions of the velocity function maxima are plotted in the diagram in Fig. 4. The curves were constructed on the basis of three or four series Of measurements, average values being take~n. I tshouid be mentionedthat Vrc-measurements on models with the same slit inclination displayed some scatter of the values o f the maximum tensile crack

] 3 4 Studia geoph, et geod. 27 [1983]

Propagation Velocity and Radiation Properties...

A a

////~////////: Y /~ / / / / / / / / / / / / / / / / / / /~ t t t t

Fig. 1. Arrangement of the experiment. 1 -- length of the diagonal slit with stress-free boundaries, lTc-- crack length, TC-- t,ensile crack, c~-- slit inclination angle. Arrows denote the direction of uniaxial compression, A -- photograph of wire-set arrangement, B -- location of ultrasonic

pick-up (R).

[ 0.5 0.~ ~90 O~ 1.85 2.10 2.50 2.00 8,10 It, trc[r~]l 0.37 027 0.25 0.2_7 0,22 0.42 0,25 0.28 0.23 0,81

Iv]

1 2 3 4 5 ; 7 8 9

fl 10 1

' t

Fig. 2. An example of the step record of voltage changes as a function of time. The vertical step changes correspond to the interruption of appropriate wires during tensile crack propagation (see Fig. 1). t - time, U - - voltage, Nr. denotes the sequence of wires, A t - time intervals,

Alrc -- tensile crack path intervals.

veloci ty (V'c). This can be seen clearly in Fig. 5 where the Vrc-patterns are p lo t ted

for three different mode l s having t h e same slit inc l ina t ion angle ~ = 60 °. Never-

theless, the da t a ob ta ined were h o m o g e n e o u s enough to d isp lay dist inct relat ions.

The most ev ident fea ture o f the Vrc-Curves is the r ap id increase o f the Vrc-values

at the very beginning o f the crack pa th , fo l lowed by an immedia t e steep decrease.

Studia geoph, et geod. 27 [t983] ] 3 5

J. Kozdk, 7". Lokafigek, J. ~ilen~

For curves of higher inclination angles, e = 60 °, 70 °, this rapid Vrc-dro p runs into a slower decrease for Vrc < 300 ms-~.

, 0 o 0

400 n--- ~ .

0 0 4 . 5 0 7.00 8.5/0 15.{0 ~O

' [TC [rnrn]

Fig. 3. Propagation velocities of the tensile crack along its path lrc as a function of slit inclination ' ~ rc -- the average value of VTc.

lOOO

Vre [mq 750

500

250

5 10 15 20 25

, tT c [mm]

Fig. 4. As Fig. 3 (The ~Tc-patterns are presented with an identical crack origin-point in order to demonstrate the location of V'c-values and the values of the acceleration arc).

As expected, the slit inclination angle e rules both the fast stage crack length l*c and values of V'c: with increasing angle e both the said quantities grow mono- tonically (Fig. 6b, c). The fast stage crack length increases from 2 mm to 23 ram, which corresponds to 6 .6 -77 .0 per cent of the slit length l; maximum velocity * lYTC

136 Studia geoph, et geod. 27 [t9831

Propagation Velocity and Radiation Properties.,.

ranges f rom 400 to 1 000 ms -1, i.e. ~-, 3 0 - 7 0 per cent o f the shear wave velocity

Vs (Fig. 3). On the other hand, the locations o f the Vrc-Curve maxima display re-

markable stability no t being affected appreciably by the slit inclination. The values

IOO0

v ~

50(]

250

i i

5 10 15 20

, t,, [mm] Fig. 5. An example of propagation velocities VTC along the crack path lTc for ~ = 60 °. Three

different experiments.

a b

P~ [kN]

30

ZO

I0

1 i 1 i t

20 3O 40 5O ~ 70 ,#~[*]

.T( i m

25

/ .x/

5F

I I I ~ I I

20 30 40 50 ~0 70

i

X "

0 /

/ IC

I t I ! 1 t 0 ~ 30 40 ~ Go 70

,, ,~ , [ * ]

Fig. 6. Basic parameters of tensile crack propagation vs. slit inclination ~. p*-triggering load, l~c-length of fast stage crack propagation, V~-c-maximum values of vTc.

Studia geoph, et geod. 27 [1983] 137

J. Koz6k, 7". Lokaji~ek, J. Silen~

of the vrc-curve maxima locations are within the interval 0"65-1.00 mm (measured from the slit tip), which corresponds to 2 :2-3 .3 per cent of the slit length I. These results directed our attention also to the path length of the tensile crack in which the crack propagates faster than 400 ms -1, (Fig. 7). It follows from Fig. 7 that, while the positions of the V*c-Iocations are nearly constant the interval of the fast run of the tensile crack incre!ases with e.

The triggering load pattern p* = f(a), plotted in Fig. 6a, displays a larger scatter especially for c~ = 40 °, however, in general, it conforms to the more detailed results of the triggering load measurements presented in [7].

're

T

24

16

2

0

!

/,

t

30 ~0 90

oo [°]

Fig. 7. Seismoactive stage (hatched area) o f the tensile crack, l r c - c rack path , :~-slit inclination, I - - l~c curve, 4 - - enter ing and 2 - - leaving the crack tip velocity interval Vrc >= 400 m s - 1

a long the crack pa th , 3 - - locat ion o f m a x i m u m V}c values on 1TO.

4. D I S C U S S I O N

The results of measuring the propagation velocity of a fast tensile displacement on physical models under load are aimed at clarifying the initiation and propagation of tensile cracks and a better understanding of the manner in which seismic energy is released in dependence on the angle of fault inclination.

The most expressive feature of tensile crack life is - in the given arrangement -

138 Studia geoph, et geod. 27 [4983]

Propagation Velocity and Radiation Properties...

the typical pattern of the propagation velocity VTC of this crack; the rapid growth

of the vTc-vatues from zero to maximum is followed by a rapid velocity drop which is, for inclination angles e > 50 °, characterized by a certain lingering effect in the second half of the fast stage of the tensile crack path. The values of tensile crack acceleration aTc = OVTC/&, measured for the interval of Vrc-growth, were found to be nearly constant for the family of VTC = f ( tTc) curves corresponding to e > 40°; the values of aTC covered the interval 0-4 mm gs -2 < arc < 0-5 mm gs 2 . For c~ < 40 °, substantially lower aTc-Values were observed (0.1 mm las-2), see Fig. 8 A,

t

t

T

A

03 1.0 1.5 2.0

,t,c[mq

B

=40° /'(-;"

0.5 1.0 1.5 2D

, tTC [mm]

oC 30"

4O" 5 ¢

60 ° 70"

Fig. 8. T rave l - t ime cu rves o f t he tensi le c r ack tip. t - - t ime, lTc-c rack pa th , c~ - - slit i nc l i na t i on ,

A , B - - see text .

where tensile crack travel-time curves are plotted; the curves were constructed by means of averaging 3 - 4 travel-time curves for a given angle ~. One of these sets for e = 40 ° is shown in Fig. 8 B. The abrupt growth of Vrc-values immediately

of values of VTC in the whole range of fault after crack initiation results in the positions *

Studia geoph, et geod. 27 [1983] 139

J. Kozfk, T. LokajiEek, J. ,.~ilenf~

plane inclination covering a very narrow interval of 0-65-1.00 mm along the Irc axis normalized by the length of the slit 1 these values amount to 2-2-3-3 per cent of I.

* they increase monotonically from 400 ms -1 for Concerning the values of Vrc, = 30 ° up to ,-~ 1000 ms- 1 for e = 70 ° which can be expressed as ,-~ 3 0 - 70 per cent

of the shear wave velocity Vs (Vs is perspex = 1355 ms-l) . It should be pointed out that while the miximum values of the V~c-location (on the lrc'-axis) and also the common shape of the Vrc-curves display only slight changes with varying fault

* themselves and the values of l*c can be plotted as inclination, the values of Vrc an expressive monotonic function of the fault inclination.

In the previous studies dealing with the initiation and propagation of tensile cracks in physical models under toad, it was clearly shown that tensile displacement in its fast stage of propagation is seismoactive. It was assumed in these papers that the seismic energy is released during the whole Stage of fast crack propagation given by the length l~c. The results obtained in recent studies, however, indicated that most probably the radiation of seismic energy during tensile crack propagation should be related to the minor part of l~c only. Here, e.g., the failure in searching for the expected Doppler effect in recording simultaneously the pulses radiated by the tensile crack in the direction of crack propagation and in the opposite direction should be mentioned - see [10]: The latter information shows that the function V'rc = f( / rc) confronted with the source function of displacement (namely the frequency composi- tion of the radiated pulses) represents the prospective tool for more exact determina- tion of the space (time) interval where (when) the seismic energy is released.

It was found in previous ultrasonic studies of the pulses released during fast tensile displacement [7, 9, 10] that, in the given set-up, the source frequencies of radiat- ed pulses ranged from 90 to 120 kHz for 40 ° -< e _< 70 °, while for angles e < 30 ° the source frequencies were lower; they did not exceed 70 kHz. It should be mentioned the first onsets of the signals were analysed to determine the source frequencies. The other frequencies, found in the following part of the signals, should be related to the resonance properties of the model itself and to the ultrasonic receiver used. During the measurements, it was found that the resonance frequencies displayed only a slight attenuation with increasing epicentrat distance. The source frequencies, on the other hand, were recorded only in the vicinity of the tensile crack initiation point; at a distance of 10-15 mm the source frequency was already filtered out from the wave pattern recorded.

'Faking into account that the threshold radiation Vrc-value is commonly estimated at 300-400 ms - I and utilizing the determined source frequencies and Vrc = f( l rc) patterns, we are able to derive the hypothesis that the propagating tensile displacement releases the seismic energy only in a short time interval of 2 - 3 las, in which the velocity of tensile crack propagation reaches its maximum values. From this view point, it is possible to characterize the seismoactive tensile displacement as a quasi- point source of the "explosive" type. It agrees well with the fact that the Doppler

140 Studia geoph, et geod. 27 [t983]

Propagation Velocity and Radiation Properties...

effect has not been observed. Also the results of ultrasonic measurements of the pulses recorded in various directions (according to the tensile crack initiation point) supported the above hypothesis; independently of the direction of observation, all the records of radiated pulses had positive onsets which resulted in radiation charac- teristics without nodal lines [9].

The above results also make it possible to plot the time pattern of the tensile crack radiation. Firstly, the genuine crack radiation (quasi-point source) occurs, which is

- except for the lowest values of c~ - independent of the slit inclination. Afterwards, the high frequencies appear having their origin in the resonance of the free bounda- ries of the created crack; these frequencies depend on the inclination angle ~ as the l~c-values are a function of c~ as well. Finally, the low frequencies occur, being related to the resonance frequencies given by model dimensions.

The presented patterns of the velocity of the tensile crack propagating along its path were obtained using physical models built of homogeneous material in a time- loading regime, implying the properties of a homogeneous brittle elastic medium, whereas real geological structures in focal earthquake regions, subjected to long-term load, evidently display a higher degree of plasticity. Also the inclusions and inhomo- geneities of variable size magnify the complexity of real media. This will probably result in a commonly smaller share of brittle tensile faulting in global seismoactivity as compared with the model structures characterized by pure and well-defined physical conditions.

The existence of tensile cracks in geological reality now seems to be quite clearly proved; they can be detected in the whole scale of their size, from small surface crack series of the "en echelon" type to large orthogonal systems of faults of continen- tal dimensions [11]. It is namely the orthogonality which seems to be one of the major features indicating the existence of tensile cracks in a given system of fractures. On the other hand, it is the possible seismoactivity and its unambiguous verification in such a system which still remain an open question. Because of the above-mentioned inhomogeneity and more common rheology of the media, it seems that relatively shorter lengths of tensile cracks could be expected under real conditions than those presented as /*c-lengths for the model experiment. In spite of this possibly shorter length of tensile crack under real geologic conditions, the seismoactivity of this phenomenon could be expected, because, as shown above, the radiation of seismic energy is related to the very beginning of the crack path only.

It should be remembered that the generation of a tensile crack cannot be regarded as an isolated phenomenon; the causal relation of such a crack with the stress con- concentrator indicates that the tensile displacement must be accompanied by simulta- neous movements along the stress concentrating structure. If the tensile crack, e.g., is generated by stress concentration at a linear fault, it is accompanied by shear displacement along the fault (movement with the stick-slip mechanism). The seismo- activity of the tensile crack can be detected and expressed in the radiation pattern only if both the components of the source, i.e. the tensile crack and the stick-slip

Studia geoph, et geod. 27 [1983] 141

J. Kozdk, T. Lokafidek, J. ~ilenfi: Propagation Velocity and Radiation Properties...

along t he pre-existing fault, start to radiate simultaneously. I f the tensile displace-

ment lags behind the previous shear movement , the tensile crack radiat ion is super-

imposed on the wave pat tern o f the stick-slip with some time delay so that it cannot

practically be found in the radiation pattern using existing recording and interpreta-

t ion techniques. The majori ty o f existing theoretical models o f the ear thquake zone, because o f the

mathematical complexity o f the problem, is based on the simplyfied assumption that

the propagat ion velocity of a seismoactive event along a fault is constant. A seismo-

active shear displacement has not been discussed in this paper. As for fast tensile

displacement, however, it was demonst ra ted above, that the velocity of propagat ion

of the tensile crack tip along its path is characterized by a complex pattern. The

substitution o f such a pat tern by a constant is not justified even in the first approxim-

ation. Further, having in mind that during the fast tensile displacement the seismic

energy is radiated in a very short time and space interval, it is disputable to consider

any velocity o f this evenL The approximat ion of the seismoactive mechanism of ten-

sile fracturing by a quasi-point source seems to be more promissing. The authors are indebted to their colleagues from the Geophysical Institute of the Czech.

Acad. Sci., Prague: to Dr. L W a n i e k , DrSc, Dr. J. Van~k, DrSc and to Ing. Z. Pros, CSc for stimulating ideas and suggestions, to g.g.A. Spi6~ik, Ing. R. Zimov~i, Mrs. N. Pickov~i and Mr. J. Hradec for valuable assistance in evaluating the results of the experiment.

Received 14. 4. 1982 Reviewer: K. P~g

References

[I] W. F. Brace, J. D. Byerlee: Stick Slip as a Mechanism for Earthquakes. Science, 153 (1966), 990.

[2] Proc. of the Symposium on Experimental Studies of Rock Friction with Application to Earthquake Prediction. USGS, Menlo Park, May 1977.

[3] O. F. IIIaMg~a: Mo~eJIbable ~iccnez~oBaHa~ ~rt3m~ o~ara 3eMJIeTp~IceHHR. H~yKa, M. 1981. [4] Proc. of the IUTAM Symp. on Optical Methods in Mechanics of Solids, Poitiers, Sept.

1979. Sijthoff Noordhoff 1981. [5] W. F. Brace, E. G. Bombolak i s : A Note on Brittle Crack Growth in Compression.

J. Geoph. Res., 68 (1963), 3709. [6] E. G. Bombolak i s : Photoelastic Study of Initial Stages of Brittle Fracture in Compression.

Tectonophysics, 6 (1968), 461. [7] J. Koz~ik, J. ~ilen3~, L. Waniek: Laboratory Investigations on Fault Plane Induced

Tensile Cracks. Studia geoph, et geod., 25 (1981), 332. [8] J. Silen3): Trajectory of Fault Plane Induced Tensile Crack in Relation to the Primary

Stress Field. Studia geoph, et geod., 26 (1982), 352. [9] J. Koz~k et al.: Seismic Signals Generated in Fault Plane Induced Tensile Cracks. Proc.

of the Symp. on Phys. and Geod. Proc. in Earthq. Focal Regions; Potsdam, Nov. 1981, (in press).

[10] J. Koz~ik, J. ~iten3~, A. ~pi6~ik: Remarks on Seismic Energy Release Related to Strike Slip and Tensile Crack Mechanisms. Proc. of the Symp. on Phys. and Geod. Proc. in Earthq. Focal Regions, Potsdam, Nov. 1981, (in press).

[11] V. Babugka et al.: Physics of Seismic Wave Fields and Earthquake Foci. Geophysical Synthesis in Czechoslovakia, Veda, Bratislava 1981.

t 4 2 Studia geoph, et geod. 27 [1983]