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Experimental evidence of contact loss during stick-slip: possible implications for seismic behaviour
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Tectonophysics 295 (1998) 341–350
Experimental evidence of contact loss during stick-slip: possible implications for seismic behaviour S. Bouissou a,Ł , J.P. Petit a , M. Barquins b a
Laboratoire de geophysique et tectonique (URA 1760), c.c. 060, Universite´ Montpellier II, Place Euge`ne Bataillon, 34095 Montpellier, cedex 5, France b LPMMH (URA 857), ESPCI, 10 rue Vauquelin, 75321 Paris, cedex 5, France Received 19 November 1997; accepted 20 May 1998
Abstract We present results of an experimental study on the stick-slip phenomenon focused on detailed measurements of the relative normal displacement. This was done mainly to determine whether or not the sliding surfaces become separated during the slip phase as suggested in previous works. Experiments were performed on PMMA as it has mechanical properties comparable to those of brittle rocks and has proved to be a good analogue for rocks in rupture mechanics experiments. Results show clearly that normal displacement occurs during and after the slip phase. The characterisation of the sliding surface enables us to compare the maximum relative normal displacement during the slip phase with asperity height. In most cases, the maximum relative normal displacement was found to be higher than the average value of the peak-to-trough relief of the surface, showing that sliding surfaces were at least partially separated. The phenomenon generally consists of a monotonous slip opening phase followed by a monotonous slip closure phase. In some cases, the slip closure phase shows oscillations which have been interpreted as elastic bounces. This last phenomenon was observed irrespective of the experimental conditions with a probability ranging from 0.1 to 0.3 but no clear variations of this probability have been found as a function of normal stress and roughness. These observations may give insights for the explanations of earthquake-related problems such as the heat flow paradox, anomalous P-wave radiation or the inferred low average friction coefficients in subduction zones. 1998 Elsevier Science B.V. All rights reserved. Keywords: stick-slip; earthquakes; normal displacement; contact loss; roughness; normal stress
1. Introduction A key problem in fault friction, which is crucial for the question of energy dissipation during earthquakes, is to determine whether or not normal stress release can occur in association with the propagation of the seismic pulse. The most commonly invoked mechanism to achieve this release is normal vibraŁ Corresponding
author. E-mail: [email protected]
tions. This has been suggested by Haskell (1964) because the P-wave energy from large earthquakes was too high for pure shear stress. Blandford (1975) proposed a spectral model containing both shear sources and tensile sources and was able to increase the ratio of compressional wave to shear wave energy. Since then, many indications of anomalous P-waves have been found (Molnar et al., 1973; Castro et al., 1991) which might be produced by normal vibrations. Furthermore, as suggested by Brune et al. (1993), normal
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vibrations could also give an explanation for the heat flow paradox on the San Andreas fault (Brune et al., 1969; Henyey and Wasserburg, 1971; Lachenbruch and Sass, 1973, 1980). It might also give a complementary explanation for the low average friction coefficient estimated in subduction zones (Molnar and England, 1990; Kao and Chen, 1991; Tichlaar and Ruff, 1993) which is generally attributed to the presence of fluids (Lachenbruch and Sass, 1992). In experimental work, since the analogy between seismic recurrence and stick-slip made by Brace and Byerlee (1966), a large number of studies dealing with seismic sliding mechanisms have been performed. However, most of them were devoted to the analysis of the slip prior to instability by using discontinuous step change in the sliding velocity rather than the analysis of the instability itself (Tullis, 1988). Thus, physical evidence of normal displacement during the slip event is scarce. Some studies have shown that vibrations normal to the interface during the stick-slip process occur in different materials. In metals, normal vibrations, inferred from decreases in electrical conductivity across the stickslip interface (Bowden and Tabor, 1939), have been measured directly (Tolstoı¨, 1967; Bo and Pavelescu, 1982; Tudor and Bo, 1982). The same vibrations have also been observed in foam rubber using a photographic technique in which the displacement of a light emitting diode (LED) embedded at a few centimetres below and above the sliding surface was filmed by a camera (Brune et al., 1990, 1993). A particular behaviour was observed by Anooshehpoor and Brune (1994) in an experimental study on foam rubber where particle motions (LED) were analysed: at some time during the slip, the two blocks were not in contact. This last study suggests that during stick-slip, decrease in normal pressure during the slip phase could be related not only to normal vibrations but also to complete contact loss which means that the normal pressure could become negative. However, in these last experiments, stick-slip was observed only when normal stress was very low and it is not clear whether sliding surfaces could really be separated under high normal stress as was suggested from numerical studies by Comninou and Dundurs (1977, 1978a,b) and Tworzydlo and Hamzeh (1997) and whether roughness of the sliding surface could play a role in this behaviour.
In this paper we present a study demonstrating that sliding surfaces are separated during stick-slip under a wide range of normal stresses. This study is a part of an extensive experimental study using PMMA in which the influence of normal stress, loading velocity and roughness on the stable sliding to stick-slip transition has been analysed (Bouissou et al., 1998a) together with a detailed characterisation of the stick-slip phenomenon (Bouissou et al., 1998b). Although it is not proved that scaling law can be applied to this material, PMMA has mechanical properties comparable to those of brittle rocks in the upper crust and has been shown to be a good analogue of rocks in rupture mechanics experiments (Nemat-Nasser and Horii, 1982; Petit and Barquins, 1987; Barquins and Petit, 1992) and in friction experiments (Dieterich and Kilgore, 1994). With help of an original experimental device developed by Petit et al. (1997) which includes a high-speed data acquisition system, we were able to measure with a precision of 2 µm the relative normal displacement of the sliding surface during stick-slip. In the present study, experiments have been performed for five normal stresses and five roughnesses of the sliding surface ground with sandpapers of controlled granulometry. Only one loading velocity has been investigated because we observed that it did not influence stick-slip behaviour (Bouissou et al., 1998b).
2. Apparatus, recording system and experimental procedure Experiments have been done on PMMA (polymethylmethacrylate) samples with dimensions of 100 ð 65 ð 5 mm3 . All the samples were cut from the same plate of Altuglas to be sure that they have the same physical and mechanical properties. The dimensions of the sliding surface, fixed during experiments, was 15 ð 5 mm2 (Fig. 1). We used five different roughnesses ground with sandpaper of 16, 36, 60, 120 and 180 grit. To prepare sliding surfaces we used rotating sandpaper disks. Asperities on a surface were produced in such a way that their direction was perpendicular to the sliding surfaces. The topography of each surface was measured with a stylus profilometer and was characterised by the RMS (root mean square) value which gives a measure of
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Fig. 1. Sample diagram (the sliding surface is represented in grey).
the average value of the peak-to-trough relief of the surface. The RMS values were respectively 128, 49, 24, 8 and 3 µm. The maximum values of the peak-to-
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trough relief of the surfaces were respectively about 600, 300, 100, 50 and 30 µm. The experimental device comprised a testing machine developed by Davenport and a normal loading apparatus (Fig. 2). The normal load was imposed by means of springs which insure a nearly constant normal stress (š2%). The stiffness of the testing machine and of one spring were respectively 2:33 ð 106 N m 1 and 5 ð 104 N m 1 . Good guidance between samples was imposed by ball bearings. This guidance system enabled samples to deform or to slide in the shear direction, whilst preventing any lateral displacement. By using a recyclable roller slide, the normal load imposed between samples was always in front of the sliding surface of the fixed sample. This system prevents any moment which would tend to rotate samples. Shear load was transmitted by the testing machine which imposed a global movement at a constant loading velocity on the moving sample. The relative normal displacement was measured with two laser displacement transducers whose two targets were situated as close as possible against the sliding surface of each side. Thus the recorded dis-
Fig. 2. Testing apparatus diagram: 1 D fixed sample, 2 D moving sample, 3 D laser displacement transducer, 4 D target, 5 D laser beam, 6 D recyclable roller slide, 7 D ball bearings, 8 D head of the testing machine, 9 D normal loading apparatus.
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placement reflects that of asperities and not that of a wider zone situated under them. These two laser displacement transducers had micron sensitivity with a frequency response of 40 kHz. Data were recorded with a MSDAS-12 card developed by Analogic Corporation associated to the Snap-Master software developed by HEM Data Corporation. This system enabled us to record each signal (displacement sensors) at a rate up to 100,000 samples per second. Fig. 3 summarizes the two parameters measured during an experiment. It shows the record of the relative normal displacement between samples as a function of time. Fig. 3a and c show two jerks, each jerk being composed of a stick phase and a slip one. These two figures correspond to the different records obtained as a function of the normal stress. Fig. 3b and d correspond to a magnification
of the relative normal displacement during the slip phase. During this phase, we measured the maximum relative displacement (called dmax ). Just after the slip phase, during the targets oscillations, we measured a relative normal displacement called DN . This last parameter corresponds also to the relative normal displacement which occurs during the stick phase. Experiments have been done for five normal stresses (10, 15, 20, 25 and 50 MPa) at a 1 mm min 1 loading velocity. In order to measure a periodic stick-slip, the measurements of relative normal displacement were triggered after a small amount of slip displacement. This was necessary to generate a stabilised stick-slip sequence. The measurements were performed on seven consecutive events at a rate of 50 kHz immediately after stabilised stick-slip periodicity was achieved. Each type of experiment was
Fig. 3. Schematic diagram of the two parameters measured during experiments: (a) and (c) show the two kinds of records of relative normal displacement as a function of time observed depending on normal stress condition; (b) and (d) enlarge the details of the relative normal displacement occurring during and after the slip phase of the stick-slip motion.
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repeated three times at a temperature of 23ºC and a relative humidity of 30%. Each point plotted on the figures showing the variations of the parameters dmax and DN as a function of the normal stress is the mean value of 21 experimental measurements.
3. Experimental results For each experiment we recorded the relative normal displacement as a function of time. In these records, an increase in the normal displacement during sliding indicates a tendency to opening between the sliding surfaces and a decrease in the normal displacement a tendency to closure. Fig. 4a and b show a record for a rough surface (49 µm RMS value) at a
Fig. 4. Record of the relative normal displacement during the slip phase of the stick-slip motion as a function of time for rough surfaces (49 µm RMS value) at 50 MPa normal stress.
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50 MPa normal stress. Fig. 4a shows that the relative normal displacement recorded during the slip phase is followed by oscillations of the two targets which appear when the slip phase stopped. The relative normal displacement during the slip phase cannot be confused with the targets oscillations and can be clearly identified for three reasons. First, the slip duration even if it cannot be measured together with the relative normal displacement is nearly constant because it has been measured from 375 experiments made by Bouissou et al. (1998b) in the same conditions. Second, the relative normal displacement during the slip phase and the targets oscillations have not the same period. Third, the amplitude of the relative normal displacement is much lower than the first targets oscillations. Fig. 4a also shows that during the targets oscillations (after the slip phase) a residual normal displacement, DN , is present. At the end of the slip phase, the value of the relative normal displacement is much less than the value recorded when targets oscillations stopped. The actual relative normal displacement is not detectable but it may be inferred to be the half value of each oscillation (dashed line in Fig. 4a). During the slip phase, in most of the cases, the variation of the relative normal displacement as a function of time is as shown in Fig. 5. In this case, the increase in the relative normal displacement indicates that sliding surfaces are pulled-apart (slip opening phase), and the decrease indicates that
Fig. 5. Record of the relative normal displacement during the slip phase of the stick-slip motion as a function of time for rough surfaces (49 µm RMS value) at 50 MPa normal stress.
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Fig. 6. Record of the relative normal displacement during the slip phase of the stick-slip motion as a function on time for smooth surfaces (3 µm RMS value) at 10 MPa normal stress.
sliding surfaces tend to come back in closer contact (slip closure phase). Increase and decrease were monotonous. In some experiments, a more complex behaviour, with several oscillations, was observed as in Figs. 4 and 6. In Fig. 4a, these oscillations were of second order and present during the closing phase. This last behaviour was observed irrespective of the experimental conditions with a probability ranging from 0.1 to 0.3. For each set of experimental conditions, this probability has been calculated by dividing the number of slip events in which several oscillations have been observed by the total number of slip events measured (i.e. 21 measurements). No clear variations of this probability have been found as a function of normal stress and roughness so that this behaviour seems to be random.
Finally, for each experimental conditions, we measured the two parameters dmax and DN defined previously (Fig. 3b). It was found that these parameters increase with increasing normal stress (Figs. 7 and 8). Moreover, for dmax , roughness is influential only at high normal stress. Conversely, for DN , roughness is influential for all normal stress investigated except at 10 MPa. In fact, at 15 and 20 MPa, DN has been found to be negative (which corresponds to the case shown in Fig. 3c) for rough surfaces and positive for smooth ones (which corresponds to the case shown in Fig. 3a).
4. Interpretation These results show clearly that a relative normal displacement occurs during and after the slip phase. The occurrence of a complete or partial separation between surfaces can be demonstrated by the comparison of the maximum relative displacement during the slip phase with the average (RMS value) and the maximum values of the peak-to-trough relief of the surface measured before the experiments. Except for the experiments at 10 and 15 MPa for rough surfaces (128 and 49 RMS values), the maximum value of the normal displacement, dmax , is higher than the RMS value of the sliding surface, which implies a contact loss on most of the surface during the slip phase. This seems especially likely
Fig. 7. Graph of the maximum relative normal displacement, dmax , versus normal stress for the different roughnesses investigated.
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Fig. 8. Graph of the relative normal displacement, DN , versus normal stress for the different roughnesses investigated.
when rare very high asperities collide at dmax (i.e. when the aperture between the sliding surfaces is maximum). At 50 MPa, for smooth surfaces (3, 8, and 24 RMS values), dmax is higher than the maximum value of the peak-to-trough relief of the surface unambiguously showing evidence of the total contact loss. At 50 MPa for rough surfaces, and at lower normal stresses for all roughnesses, dmax is lower than the maximum value of the peak-to-through relief of the surface but it is higher than the RMS value (with the exception of the experiments at 10 and 15 MPa for the rougher surfaces). However, the contact loss is probable for two reasons: first, the probability of having two asperities with the maximum height facing one another at dmax is very low and second, after a few jerks, when the measurements are triggered, the higher asperities are deformed plastically or broken (Bouissou et al., 1998b) which results in the fact that RMS values are overestimated. For rougher surfaces, at low normal stress (10 and 15 MPa) the value of the parameter dmax is lower than the RMS value. Even so, we can argue that the sliding surfaces are probably separated during the slip phase. Indeed, at low normal stress and for rough surfaces, we observed that during the stick phase, sliding surfaces are only very slightly interlocked so that the relative normal displacement necessary to separate the sliding surfaces is much lower than the RMS value. In fact, the parameter DN gives the value of the relative normal displacement which occurs
just after the slip phase but reflects also the relative normal displacement which occurs during the stick phase (Fig. 3). When DN is negative (for rough surfaces at 15 and 20 MPa normal stress) this indicates that sliding surfaces are pulled off during the stick phase (Fig. 3c). In these conditions, sliding surfaces are very slightly interlocked just before the sliding phase. This last observation also explains why the parameter dmax decreases when normal stress decreases and why it becomes insensitive to roughness at low normal stress. Indeed, at high normal stress, the strong asperities interlocking impose a higher relative normal displacement required to separate the sliding surfaces. The rougher the surfaces the higher the relative normal displacement necessary to separate the surfaces. Conversely, at low normal stress, the rougher the surfaces the higher the pulloff during the stick-phase. This results in the fact that the maximum relative normal displacement increases with increasing normal stress and depends on roughness only at high normal stress. The increasing relative normal displacement which may occur just after the slip phase, during oscillations of the targets, can be attributed to the fact that after the asperities have come back into contact, they dilate viscoelastically. Another very important observation, made in some experiments, is that the relative normal displacement fluctuates during the slip phase (Fig. 4b and Fig. 6). In Fig. 4b, during the relative normal
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displacement decrease, the three steps are interpreted as the result of a transient contact between some asperities before the end of the slip phase. The first two steps (labelled A and B in Fig. 4b) are followed by a small increase in relative normal displacement indicating that the surfaces tend to separate once again. This indicates that sliding surfaces bounce off each others before a stable configuration can be found. Such a rebound behaviour is also clear in Fig. 6 where the normal displacement was recorded as a function of time for smooth surfaces (3 µm RMS value) at a 10 MPa normal stress. Here, two bounces are observed. The random occurrence of the bouncing behaviour could correspond to instantaneous contact configurations of particular asperities, in which a set of high asperities from each of the surfaces meet one another during the slip closure phase. Within this hypothesis, the fact that in Fig. 4b the two steps are recorded at decreasing values of the relative normal displacement, could be explained as follows. In the first step a set of the highest asperities of each surface come into contact, but as the relative velocity component in the shear direction is still high, due to the fact that a large amount of elastic energy stored in samples has not yet been released, the contact between the set of asperities occur with an ‘elastic rebound’ and the two surfaces are once again separated (small increase of the relative normal displacement). The smaller rebound in B can be attributed to new contacts on asperities which have lower heights. Once again the relative velocity in the shear direction is sufficiently high that the two surfaces are separated once again (small increase of the relative normal displacement) before a stable configuration is found (C in Fig. 4b). Conversely, in Fig. 6, the first contact may occur in strong asperity interlocking because the first slip closure phase is comparable in magnitude to the first slip opening phase. The fact that the slip phase does not stop at this time can be explained by the high relative velocity in the shear direction (which reflects the fact that a large amount of elastic energy stored in samples has not been yet released). This can be supported by the fact that high-amplitude rebounds follow, which are made easy by the high relative velocity and the low normal stress conditions. Thus, the parameter which seems to be responsible for the end of the slip
phase is the amount of elastic energy released rather than the random asperities which face each other. This is in complete agreement with our previous study in which the slip duration had been found to be independent of roughness (Bouissou et al., 1998b).
5. Insights into seismic behaviour. Even if PMMA is a good analogue for rock, it must be clearly stated that the two sliding samples in this experiment cannot obviously be seen as a model of a seismogenic fault. In particular from a geometrical point of view, in the experiment the dislocation occurs throughout the whole sample, whereas seismic dislocations are of limited extent and are not uniform. However, in so far as stick-slip (which is a behaviour observed in various materials and techniques) can be seen as a conceptual model of seismic behaviour, the accurate understanding of stick-slip dynamics may give insight for the theoretical analysis of fault behaviour. Thus, the contact loss evidenced in this study needs some discussions in terms of friction reduction. Several arguments support the idea of low friction during earthquakes.The first is the lack of frictional heat generation along the San Andreas fault (Brune et al., 1969; Henyey and Wasserburg, 1971; Lachenbruch and Sass, 1973, 1980). Second, the average friction coefficient in subduction zones, estimated from heat flow data, has been inferred to range from 0.03 to 0.15 (Molnar et al., 1973; Kao and Chen, 1991; Tichlaar and Ruff, 1993). Third, a numerical study of the average long-term steady state coefficient of friction in three subduction zones (northern Chile, northern Japan and Tonga) has shown that the observed topography of forearc regions is inconsistent with an average coefficient of friction larger than 0.2 (Cattin et al., 1997). These values of friction coefficients are very low in comparison with values measured at the laboratory scale in various rock types, which range from 0.6 to 0.8 (Byerlee, 1978). A contribution from fluids and=or low friction clay gouge to this reduction of friction has often been invoked. In subduction zones water probably plays an important role (Lachenbruch and Sass, 1992). In the case of the San Andreas fault system this contribution seems limited (Williams et al., 1988).
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Furthermore, the presence of low friction clays at all seismogenic depths is doubtful. In fact, their presence may be to stabilize fault slip rates (Logan and Rauenzahn, 1987) and thus may be incompatible with seismic slip. Thus, as suggested by Brune et al. (1993), the heat flow paradox could be explained by normal vibrations during earthquakes. Such behaviour could also give a complementary explanation of the low apparent coefficient of friction estimated in subduction zones as suggested by Brune (1996). Another type of argument dealing with the general behaviour of seismic faults gives an insight into normal stress reduction: during earthquakes, many works have shown that the duration of slip at a particular point on the fault was short compared to the overall rupture time (Anderson et al., 1986; Heaton, 1990; Beroza, 1991). To explain this observation, Heaton (1990) proposed the ‘self-healing model’, where the rupture occurs in a narrow self-healing pulse of slip that travels along the fault plane. The suggested mechanism which causes the fault to heal itself shortly after the passage of the rupture front is a dynamic fault friction that decreases with increasing slip velocity. In this model, the frictional strength on the fault is high everywhere except in the immediate vicinity of the rupture pulse “perhaps caused by intense compressional waves that would tend to decrease confining stresses locally in the region of the slip pulse” (Heaton, 1990). This last concept can be discussed in the light of our experiments. We observed that a complete separation could occur during the slip phase. In the case of compressional waves occurring during an earthquake in the narrow self-healing pulse of slip, we propose that the decrease in confining (normal) stresses could be such that the fault surfaces could be physically separated at least in a part of the slip pulse area. As the sliding surfaces are separated in this area, the normal stress could have a negative (tensile) value. For Heaton, the self-healing mechanism is attributed to an increase in a dynamic fault friction with decreasing slip velocity. From our experiments this mechanism can be seen as a result of interlocking of ‘asperities’ when sliding surfaces come back into contact. Finally, an interesting result of our experiments is the presence of rebounds during the closure phase. If such behaviour could occur in seismic sources, it
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could not only contribute to reduce the coefficient of friction but also give an explanation for multiple source events. Indeed, it has been established that most earthquake mainshocks have complex sources with multiple events (see Brune, 1991 for a review).
6. Conclusion The two main results of these experiments are the following. First, sliding surfaces are separated during the slip phase of the stick-slip phenomenon for all normal stresses and roughnesses investigated. Secondly, we have sometimes observed bounces between sliding surfaces. Bounces were observed for whatever the experimental conditions with a probability ranging from 0.1 to 0.3. No clear variations of this probability have been found as a function of normal stress and roughness. Rebounds seem to be a random process. These observations are in agreement with previous experimental studies performed on other materials and with other experimental conditions. This suggests that relative normal displacement plays an important role in stick-slip behaviour and could also be important in earthquake rupture.
Acknowledgements We are grateful to J. Brune, E.H. Rutter and an unknown reviewer for their helpful comments and suggestions.
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Tectonophysics 295 (1998) 341–350
Experimental evidence of contact loss during stick-slip: possible implications for seismic behaviour S. Bouissou a,Ł , J.P. Petit a , M. Barquins b a
Laboratoire de geophysique et tectonique (URA 1760), c.c. 060, Universite´ Montpellier II, Place Euge`ne Bataillon, 34095 Montpellier, cedex 5, France b LPMMH (URA 857), ESPCI, 10 rue Vauquelin, 75321 Paris, cedex 5, France Received 19 November 1997; accepted 20 May 1998
Abstract We present results of an experimental study on the stick-slip phenomenon focused on detailed measurements of the relative normal displacement. This was done mainly to determine whether or not the sliding surfaces become separated during the slip phase as suggested in previous works. Experiments were performed on PMMA as it has mechanical properties comparable to those of brittle rocks and has proved to be a good analogue for rocks in rupture mechanics experiments. Results show clearly that normal displacement occurs during and after the slip phase. The characterisation of the sliding surface enables us to compare the maximum relative normal displacement during the slip phase with asperity height. In most cases, the maximum relative normal displacement was found to be higher than the average value of the peak-to-trough relief of the surface, showing that sliding surfaces were at least partially separated. The phenomenon generally consists of a monotonous slip opening phase followed by a monotonous slip closure phase. In some cases, the slip closure phase shows oscillations which have been interpreted as elastic bounces. This last phenomenon was observed irrespective of the experimental conditions with a probability ranging from 0.1 to 0.3 but no clear variations of this probability have been found as a function of normal stress and roughness. These observations may give insights for the explanations of earthquake-related problems such as the heat flow paradox, anomalous P-wave radiation or the inferred low average friction coefficients in subduction zones. 1998 Elsevier Science B.V. All rights reserved. Keywords: stick-slip; earthquakes; normal displacement; contact loss; roughness; normal stress
1. Introduction A key problem in fault friction, which is crucial for the question of energy dissipation during earthquakes, is to determine whether or not normal stress release can occur in association with the propagation of the seismic pulse. The most commonly invoked mechanism to achieve this release is normal vibraŁ Corresponding
author. E-mail: [email protected]
tions. This has been suggested by Haskell (1964) because the P-wave energy from large earthquakes was too high for pure shear stress. Blandford (1975) proposed a spectral model containing both shear sources and tensile sources and was able to increase the ratio of compressional wave to shear wave energy. Since then, many indications of anomalous P-waves have been found (Molnar et al., 1973; Castro et al., 1991) which might be produced by normal vibrations. Furthermore, as suggested by Brune et al. (1993), normal
0040-1951/98/$19.00 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 1 9 5 1 ( 9 8 ) 0 0 1 2 5 - 5
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vibrations could also give an explanation for the heat flow paradox on the San Andreas fault (Brune et al., 1969; Henyey and Wasserburg, 1971; Lachenbruch and Sass, 1973, 1980). It might also give a complementary explanation for the low average friction coefficient estimated in subduction zones (Molnar and England, 1990; Kao and Chen, 1991; Tichlaar and Ruff, 1993) which is generally attributed to the presence of fluids (Lachenbruch and Sass, 1992). In experimental work, since the analogy between seismic recurrence and stick-slip made by Brace and Byerlee (1966), a large number of studies dealing with seismic sliding mechanisms have been performed. However, most of them were devoted to the analysis of the slip prior to instability by using discontinuous step change in the sliding velocity rather than the analysis of the instability itself (Tullis, 1988). Thus, physical evidence of normal displacement during the slip event is scarce. Some studies have shown that vibrations normal to the interface during the stick-slip process occur in different materials. In metals, normal vibrations, inferred from decreases in electrical conductivity across the stickslip interface (Bowden and Tabor, 1939), have been measured directly (Tolstoı¨, 1967; Bo and Pavelescu, 1982; Tudor and Bo, 1982). The same vibrations have also been observed in foam rubber using a photographic technique in which the displacement of a light emitting diode (LED) embedded at a few centimetres below and above the sliding surface was filmed by a camera (Brune et al., 1990, 1993). A particular behaviour was observed by Anooshehpoor and Brune (1994) in an experimental study on foam rubber where particle motions (LED) were analysed: at some time during the slip, the two blocks were not in contact. This last study suggests that during stick-slip, decrease in normal pressure during the slip phase could be related not only to normal vibrations but also to complete contact loss which means that the normal pressure could become negative. However, in these last experiments, stick-slip was observed only when normal stress was very low and it is not clear whether sliding surfaces could really be separated under high normal stress as was suggested from numerical studies by Comninou and Dundurs (1977, 1978a,b) and Tworzydlo and Hamzeh (1997) and whether roughness of the sliding surface could play a role in this behaviour.
In this paper we present a study demonstrating that sliding surfaces are separated during stick-slip under a wide range of normal stresses. This study is a part of an extensive experimental study using PMMA in which the influence of normal stress, loading velocity and roughness on the stable sliding to stick-slip transition has been analysed (Bouissou et al., 1998a) together with a detailed characterisation of the stick-slip phenomenon (Bouissou et al., 1998b). Although it is not proved that scaling law can be applied to this material, PMMA has mechanical properties comparable to those of brittle rocks in the upper crust and has been shown to be a good analogue of rocks in rupture mechanics experiments (Nemat-Nasser and Horii, 1982; Petit and Barquins, 1987; Barquins and Petit, 1992) and in friction experiments (Dieterich and Kilgore, 1994). With help of an original experimental device developed by Petit et al. (1997) which includes a high-speed data acquisition system, we were able to measure with a precision of 2 µm the relative normal displacement of the sliding surface during stick-slip. In the present study, experiments have been performed for five normal stresses and five roughnesses of the sliding surface ground with sandpapers of controlled granulometry. Only one loading velocity has been investigated because we observed that it did not influence stick-slip behaviour (Bouissou et al., 1998b).
2. Apparatus, recording system and experimental procedure Experiments have been done on PMMA (polymethylmethacrylate) samples with dimensions of 100 ð 65 ð 5 mm3 . All the samples were cut from the same plate of Altuglas to be sure that they have the same physical and mechanical properties. The dimensions of the sliding surface, fixed during experiments, was 15 ð 5 mm2 (Fig. 1). We used five different roughnesses ground with sandpaper of 16, 36, 60, 120 and 180 grit. To prepare sliding surfaces we used rotating sandpaper disks. Asperities on a surface were produced in such a way that their direction was perpendicular to the sliding surfaces. The topography of each surface was measured with a stylus profilometer and was characterised by the RMS (root mean square) value which gives a measure of
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Fig. 1. Sample diagram (the sliding surface is represented in grey).
the average value of the peak-to-trough relief of the surface. The RMS values were respectively 128, 49, 24, 8 and 3 µm. The maximum values of the peak-to-
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trough relief of the surfaces were respectively about 600, 300, 100, 50 and 30 µm. The experimental device comprised a testing machine developed by Davenport and a normal loading apparatus (Fig. 2). The normal load was imposed by means of springs which insure a nearly constant normal stress (š2%). The stiffness of the testing machine and of one spring were respectively 2:33 ð 106 N m 1 and 5 ð 104 N m 1 . Good guidance between samples was imposed by ball bearings. This guidance system enabled samples to deform or to slide in the shear direction, whilst preventing any lateral displacement. By using a recyclable roller slide, the normal load imposed between samples was always in front of the sliding surface of the fixed sample. This system prevents any moment which would tend to rotate samples. Shear load was transmitted by the testing machine which imposed a global movement at a constant loading velocity on the moving sample. The relative normal displacement was measured with two laser displacement transducers whose two targets were situated as close as possible against the sliding surface of each side. Thus the recorded dis-
Fig. 2. Testing apparatus diagram: 1 D fixed sample, 2 D moving sample, 3 D laser displacement transducer, 4 D target, 5 D laser beam, 6 D recyclable roller slide, 7 D ball bearings, 8 D head of the testing machine, 9 D normal loading apparatus.
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placement reflects that of asperities and not that of a wider zone situated under them. These two laser displacement transducers had micron sensitivity with a frequency response of 40 kHz. Data were recorded with a MSDAS-12 card developed by Analogic Corporation associated to the Snap-Master software developed by HEM Data Corporation. This system enabled us to record each signal (displacement sensors) at a rate up to 100,000 samples per second. Fig. 3 summarizes the two parameters measured during an experiment. It shows the record of the relative normal displacement between samples as a function of time. Fig. 3a and c show two jerks, each jerk being composed of a stick phase and a slip one. These two figures correspond to the different records obtained as a function of the normal stress. Fig. 3b and d correspond to a magnification
of the relative normal displacement during the slip phase. During this phase, we measured the maximum relative displacement (called dmax ). Just after the slip phase, during the targets oscillations, we measured a relative normal displacement called DN . This last parameter corresponds also to the relative normal displacement which occurs during the stick phase. Experiments have been done for five normal stresses (10, 15, 20, 25 and 50 MPa) at a 1 mm min 1 loading velocity. In order to measure a periodic stick-slip, the measurements of relative normal displacement were triggered after a small amount of slip displacement. This was necessary to generate a stabilised stick-slip sequence. The measurements were performed on seven consecutive events at a rate of 50 kHz immediately after stabilised stick-slip periodicity was achieved. Each type of experiment was
Fig. 3. Schematic diagram of the two parameters measured during experiments: (a) and (c) show the two kinds of records of relative normal displacement as a function of time observed depending on normal stress condition; (b) and (d) enlarge the details of the relative normal displacement occurring during and after the slip phase of the stick-slip motion.
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repeated three times at a temperature of 23ºC and a relative humidity of 30%. Each point plotted on the figures showing the variations of the parameters dmax and DN as a function of the normal stress is the mean value of 21 experimental measurements.
3. Experimental results For each experiment we recorded the relative normal displacement as a function of time. In these records, an increase in the normal displacement during sliding indicates a tendency to opening between the sliding surfaces and a decrease in the normal displacement a tendency to closure. Fig. 4a and b show a record for a rough surface (49 µm RMS value) at a
Fig. 4. Record of the relative normal displacement during the slip phase of the stick-slip motion as a function of time for rough surfaces (49 µm RMS value) at 50 MPa normal stress.
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50 MPa normal stress. Fig. 4a shows that the relative normal displacement recorded during the slip phase is followed by oscillations of the two targets which appear when the slip phase stopped. The relative normal displacement during the slip phase cannot be confused with the targets oscillations and can be clearly identified for three reasons. First, the slip duration even if it cannot be measured together with the relative normal displacement is nearly constant because it has been measured from 375 experiments made by Bouissou et al. (1998b) in the same conditions. Second, the relative normal displacement during the slip phase and the targets oscillations have not the same period. Third, the amplitude of the relative normal displacement is much lower than the first targets oscillations. Fig. 4a also shows that during the targets oscillations (after the slip phase) a residual normal displacement, DN , is present. At the end of the slip phase, the value of the relative normal displacement is much less than the value recorded when targets oscillations stopped. The actual relative normal displacement is not detectable but it may be inferred to be the half value of each oscillation (dashed line in Fig. 4a). During the slip phase, in most of the cases, the variation of the relative normal displacement as a function of time is as shown in Fig. 5. In this case, the increase in the relative normal displacement indicates that sliding surfaces are pulled-apart (slip opening phase), and the decrease indicates that
Fig. 5. Record of the relative normal displacement during the slip phase of the stick-slip motion as a function of time for rough surfaces (49 µm RMS value) at 50 MPa normal stress.
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Fig. 6. Record of the relative normal displacement during the slip phase of the stick-slip motion as a function on time for smooth surfaces (3 µm RMS value) at 10 MPa normal stress.
sliding surfaces tend to come back in closer contact (slip closure phase). Increase and decrease were monotonous. In some experiments, a more complex behaviour, with several oscillations, was observed as in Figs. 4 and 6. In Fig. 4a, these oscillations were of second order and present during the closing phase. This last behaviour was observed irrespective of the experimental conditions with a probability ranging from 0.1 to 0.3. For each set of experimental conditions, this probability has been calculated by dividing the number of slip events in which several oscillations have been observed by the total number of slip events measured (i.e. 21 measurements). No clear variations of this probability have been found as a function of normal stress and roughness so that this behaviour seems to be random.
Finally, for each experimental conditions, we measured the two parameters dmax and DN defined previously (Fig. 3b). It was found that these parameters increase with increasing normal stress (Figs. 7 and 8). Moreover, for dmax , roughness is influential only at high normal stress. Conversely, for DN , roughness is influential for all normal stress investigated except at 10 MPa. In fact, at 15 and 20 MPa, DN has been found to be negative (which corresponds to the case shown in Fig. 3c) for rough surfaces and positive for smooth ones (which corresponds to the case shown in Fig. 3a).
4. Interpretation These results show clearly that a relative normal displacement occurs during and after the slip phase. The occurrence of a complete or partial separation between surfaces can be demonstrated by the comparison of the maximum relative displacement during the slip phase with the average (RMS value) and the maximum values of the peak-to-trough relief of the surface measured before the experiments. Except for the experiments at 10 and 15 MPa for rough surfaces (128 and 49 RMS values), the maximum value of the normal displacement, dmax , is higher than the RMS value of the sliding surface, which implies a contact loss on most of the surface during the slip phase. This seems especially likely
Fig. 7. Graph of the maximum relative normal displacement, dmax , versus normal stress for the different roughnesses investigated.
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Fig. 8. Graph of the relative normal displacement, DN , versus normal stress for the different roughnesses investigated.
when rare very high asperities collide at dmax (i.e. when the aperture between the sliding surfaces is maximum). At 50 MPa, for smooth surfaces (3, 8, and 24 RMS values), dmax is higher than the maximum value of the peak-to-trough relief of the surface unambiguously showing evidence of the total contact loss. At 50 MPa for rough surfaces, and at lower normal stresses for all roughnesses, dmax is lower than the maximum value of the peak-to-through relief of the surface but it is higher than the RMS value (with the exception of the experiments at 10 and 15 MPa for the rougher surfaces). However, the contact loss is probable for two reasons: first, the probability of having two asperities with the maximum height facing one another at dmax is very low and second, after a few jerks, when the measurements are triggered, the higher asperities are deformed plastically or broken (Bouissou et al., 1998b) which results in the fact that RMS values are overestimated. For rougher surfaces, at low normal stress (10 and 15 MPa) the value of the parameter dmax is lower than the RMS value. Even so, we can argue that the sliding surfaces are probably separated during the slip phase. Indeed, at low normal stress and for rough surfaces, we observed that during the stick phase, sliding surfaces are only very slightly interlocked so that the relative normal displacement necessary to separate the sliding surfaces is much lower than the RMS value. In fact, the parameter DN gives the value of the relative normal displacement which occurs
just after the slip phase but reflects also the relative normal displacement which occurs during the stick phase (Fig. 3). When DN is negative (for rough surfaces at 15 and 20 MPa normal stress) this indicates that sliding surfaces are pulled off during the stick phase (Fig. 3c). In these conditions, sliding surfaces are very slightly interlocked just before the sliding phase. This last observation also explains why the parameter dmax decreases when normal stress decreases and why it becomes insensitive to roughness at low normal stress. Indeed, at high normal stress, the strong asperities interlocking impose a higher relative normal displacement required to separate the sliding surfaces. The rougher the surfaces the higher the relative normal displacement necessary to separate the surfaces. Conversely, at low normal stress, the rougher the surfaces the higher the pulloff during the stick-phase. This results in the fact that the maximum relative normal displacement increases with increasing normal stress and depends on roughness only at high normal stress. The increasing relative normal displacement which may occur just after the slip phase, during oscillations of the targets, can be attributed to the fact that after the asperities have come back into contact, they dilate viscoelastically. Another very important observation, made in some experiments, is that the relative normal displacement fluctuates during the slip phase (Fig. 4b and Fig. 6). In Fig. 4b, during the relative normal
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displacement decrease, the three steps are interpreted as the result of a transient contact between some asperities before the end of the slip phase. The first two steps (labelled A and B in Fig. 4b) are followed by a small increase in relative normal displacement indicating that the surfaces tend to separate once again. This indicates that sliding surfaces bounce off each others before a stable configuration can be found. Such a rebound behaviour is also clear in Fig. 6 where the normal displacement was recorded as a function of time for smooth surfaces (3 µm RMS value) at a 10 MPa normal stress. Here, two bounces are observed. The random occurrence of the bouncing behaviour could correspond to instantaneous contact configurations of particular asperities, in which a set of high asperities from each of the surfaces meet one another during the slip closure phase. Within this hypothesis, the fact that in Fig. 4b the two steps are recorded at decreasing values of the relative normal displacement, could be explained as follows. In the first step a set of the highest asperities of each surface come into contact, but as the relative velocity component in the shear direction is still high, due to the fact that a large amount of elastic energy stored in samples has not yet been released, the contact between the set of asperities occur with an ‘elastic rebound’ and the two surfaces are once again separated (small increase of the relative normal displacement). The smaller rebound in B can be attributed to new contacts on asperities which have lower heights. Once again the relative velocity in the shear direction is sufficiently high that the two surfaces are separated once again (small increase of the relative normal displacement) before a stable configuration is found (C in Fig. 4b). Conversely, in Fig. 6, the first contact may occur in strong asperity interlocking because the first slip closure phase is comparable in magnitude to the first slip opening phase. The fact that the slip phase does not stop at this time can be explained by the high relative velocity in the shear direction (which reflects the fact that a large amount of elastic energy stored in samples has not been yet released). This can be supported by the fact that high-amplitude rebounds follow, which are made easy by the high relative velocity and the low normal stress conditions. Thus, the parameter which seems to be responsible for the end of the slip
phase is the amount of elastic energy released rather than the random asperities which face each other. This is in complete agreement with our previous study in which the slip duration had been found to be independent of roughness (Bouissou et al., 1998b).
5. Insights into seismic behaviour. Even if PMMA is a good analogue for rock, it must be clearly stated that the two sliding samples in this experiment cannot obviously be seen as a model of a seismogenic fault. In particular from a geometrical point of view, in the experiment the dislocation occurs throughout the whole sample, whereas seismic dislocations are of limited extent and are not uniform. However, in so far as stick-slip (which is a behaviour observed in various materials and techniques) can be seen as a conceptual model of seismic behaviour, the accurate understanding of stick-slip dynamics may give insight for the theoretical analysis of fault behaviour. Thus, the contact loss evidenced in this study needs some discussions in terms of friction reduction. Several arguments support the idea of low friction during earthquakes.The first is the lack of frictional heat generation along the San Andreas fault (Brune et al., 1969; Henyey and Wasserburg, 1971; Lachenbruch and Sass, 1973, 1980). Second, the average friction coefficient in subduction zones, estimated from heat flow data, has been inferred to range from 0.03 to 0.15 (Molnar et al., 1973; Kao and Chen, 1991; Tichlaar and Ruff, 1993). Third, a numerical study of the average long-term steady state coefficient of friction in three subduction zones (northern Chile, northern Japan and Tonga) has shown that the observed topography of forearc regions is inconsistent with an average coefficient of friction larger than 0.2 (Cattin et al., 1997). These values of friction coefficients are very low in comparison with values measured at the laboratory scale in various rock types, which range from 0.6 to 0.8 (Byerlee, 1978). A contribution from fluids and=or low friction clay gouge to this reduction of friction has often been invoked. In subduction zones water probably plays an important role (Lachenbruch and Sass, 1992). In the case of the San Andreas fault system this contribution seems limited (Williams et al., 1988).
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Furthermore, the presence of low friction clays at all seismogenic depths is doubtful. In fact, their presence may be to stabilize fault slip rates (Logan and Rauenzahn, 1987) and thus may be incompatible with seismic slip. Thus, as suggested by Brune et al. (1993), the heat flow paradox could be explained by normal vibrations during earthquakes. Such behaviour could also give a complementary explanation of the low apparent coefficient of friction estimated in subduction zones as suggested by Brune (1996). Another type of argument dealing with the general behaviour of seismic faults gives an insight into normal stress reduction: during earthquakes, many works have shown that the duration of slip at a particular point on the fault was short compared to the overall rupture time (Anderson et al., 1986; Heaton, 1990; Beroza, 1991). To explain this observation, Heaton (1990) proposed the ‘self-healing model’, where the rupture occurs in a narrow self-healing pulse of slip that travels along the fault plane. The suggested mechanism which causes the fault to heal itself shortly after the passage of the rupture front is a dynamic fault friction that decreases with increasing slip velocity. In this model, the frictional strength on the fault is high everywhere except in the immediate vicinity of the rupture pulse “perhaps caused by intense compressional waves that would tend to decrease confining stresses locally in the region of the slip pulse” (Heaton, 1990). This last concept can be discussed in the light of our experiments. We observed that a complete separation could occur during the slip phase. In the case of compressional waves occurring during an earthquake in the narrow self-healing pulse of slip, we propose that the decrease in confining (normal) stresses could be such that the fault surfaces could be physically separated at least in a part of the slip pulse area. As the sliding surfaces are separated in this area, the normal stress could have a negative (tensile) value. For Heaton, the self-healing mechanism is attributed to an increase in a dynamic fault friction with decreasing slip velocity. From our experiments this mechanism can be seen as a result of interlocking of ‘asperities’ when sliding surfaces come back into contact. Finally, an interesting result of our experiments is the presence of rebounds during the closure phase. If such behaviour could occur in seismic sources, it
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could not only contribute to reduce the coefficient of friction but also give an explanation for multiple source events. Indeed, it has been established that most earthquake mainshocks have complex sources with multiple events (see Brune, 1991 for a review).
6. Conclusion The two main results of these experiments are the following. First, sliding surfaces are separated during the slip phase of the stick-slip phenomenon for all normal stresses and roughnesses investigated. Secondly, we have sometimes observed bounces between sliding surfaces. Bounces were observed for whatever the experimental conditions with a probability ranging from 0.1 to 0.3. No clear variations of this probability have been found as a function of normal stress and roughness. Rebounds seem to be a random process. These observations are in agreement with previous experimental studies performed on other materials and with other experimental conditions. This suggests that relative normal displacement plays an important role in stick-slip behaviour and could also be important in earthquake rupture.
Acknowledgements We are grateful to J. Brune, E.H. Rutter and an unknown reviewer for their helpful comments and suggestions.
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