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Intermittent lab earthquakes in dynamically weakening fault gouge

Nature volume 606, pages 922–929 (2022)Cite this article

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Abstract

Large and destructive earthquakes on mature faults in Earth’s crust occur as slip in a layer of a fine granular material—fault gouge—produced by comminution during sliding1,2. A range of insights into the frictional resistance of faults—one of the main factors controlling earthquake nucleation, dynamic propagation and arrest, and hence the destructive ground shaking of earthquakes2,3—has been obtained in experiments with spatially uniform slip imposed in small samples2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21. However, how various features of gouge friction combine to determine spontaneous progression of earthquakes is difficult to study in the lab owing to substantial challenges with sample sizes and adequate imaging22. Here, using lab experiments, we show that spontaneously propagating dynamic ruptures navigate a fault region with fine rock gouge through complex, intermittent slip processes with dramatic friction evolution. These include repeated arrest of rupture propagation caused by friction strengthening at lower slip rates and dynamic earthquake re-nucleation enabled by pronounced rapid friction weakening at higher slip rates consistent with flash heating8,12,23. The spontaneous repeated weakening and strengthening of friction in fine rock gouge highlights the fundamental dependence of friction on slip rate and associated processes, such as shear heating, localization and delocalization of shear, and dilation and compaction of the shear layer6,7,9,10,11,12,13,14,15,16,17,18,19,20,21. Our findings expand experimental support9,11 of the concept that co-seismic weakening may enable earthquake rupture to break through stable fault regions24,25, with substantial implications for seismic hazard.

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Fig. 1: Intermittent lab earthquake rupture sequences in rock gouge.
Fig. 2: Slip history for the two rupture sequences.
Fig. 3: Evolution and characteristics of the two sub-events in the second rupture sequence.
Fig. 4: Evolution of dynamic friction within the rock gouge with repeated strengthening, pronounced weakening and healing.

Data availability

The data generated in this study are available through the CaltechDATA repository at https://data.caltech.edu/records/2155. Source data are provided with this paper.

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Acknowledgements

This study was supported by the US National Science Foundation (NSF) (EAR-2045285 and EAR-1651235), the US Geological Survey (USGS) (grants G20AP00037 and G16AP00106), the NSF-IUCRC at California Institute of Technology-Center for Geomechanics and Mitigation of Geohazards (GMG), and the Southern California Earthquake Center (SCEC), contribution number 11854. SCEC is funded by NSF Cooperative Agreement EAR-1600087 and USGS Cooperative Agreement G17AC00047.

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Authors and Affiliations

  1. Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA, USA

    V. Rubino & A. J. Rosakis

  2. Mechanical and Civil Engineering, California Institute of Technology, Pasadena, CA, USA

    N. Lapusta

  3. Seismological Laboratory, California Institute of Technology, Pasadena, CA, USA

    N. Lapusta

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  1. V. Rubino
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Contributions

V.R., AJ.R. and N.L. contributed to developing the main ideas, interpreting the results and producing the manuscript. V.R. performed the measurements and analysed the data.

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Correspondence to V. Rubino.

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Extended data figures and tables

Extended Data Fig. 1 Specimen loading time history.

The specimen is compressed in the axial direction by a load P, which results in a resolved normal and shear stresses on the interface inclined at an angle \(\alpha \), given by \({\sigma }_{0}=P{{\rm{\cos }}}^{2}\alpha \) and \({\tau }_{0}=P{\rm{\sin }}\alpha {\rm{\cos }}\alpha \), respectively. The load is quasi-statically increased up to P = 14.3 MPa, then the first sequence of ruptures is triggered by the discharge of wire W1. After the first sequence of recorded events, and additional slip occurring after the end of recording, the load drops to P = 13.3 MPa. The far-field loading is subsequently increased to P = 14.4 MPa and the second sequence of events is triggered by the discharge of W2. The inset to the right shows the bottom half of the sample with the gouge insert and the location of the lower half of the field of view with the speckle pattern used to analyse the sequence of images with the digital image correlation method.

Extended Data Fig. 2 Slip-velocity time history.

a, b, Slip-velocity maps as in Fig. 1 b,c plotted over the same time and space range but using a different slip-velocity scale of 4 m s−1 and 9 m s−1, respectively. c, Slip-velocity time history for a reference rupture propagating in a Homalite interface, displaying a supershear rupture followed by a trailing-Rayleigh signature (data from ref. 37). d, Slip-velocity time history for the second rupture sequence at the location \({x}_{1}=6.9\) mm, shown by a dashed white line in b.

Extended Data Fig. 3 Snapshots of the full-field distributions of fault-parallel particle velocity and shear stress change during the initial phase of the first rupture sequence.

The full-field maps show, top to bottom, the supershear rupture arrest (event A) at t = 38.6 μs, the arrival of the sub-Rayleigh rupture (event B) at t = 44.6 μs, its propagation (t = 50.6 μs), and subsequent arrest (t = 56.6 μs). Note that the stress concentration at the arrest time of event B is relatively minor and at a different location from where event E is dynamically re-nucleated later (Extended Data Fig. 4).

Extended Data Fig. 4 Snapshots of the full-field distributions of fault-parallel particle velocity and shear stress change during the later phase of the first rupture sequence.

The full-field maps of the propagation of a triggering attempt (event D) at t = 72.6 μs (top row) indicate that, even at this intermediate time between the arrest of event B at 56.6 μs (Extended Data Fig. 3) and dynamic initiation of event E at t = 87.6 μs (second row), the largest stress concentration is not where event E initiates, highlighting the dynamic and transient nature of shear stress changes that balance the evolving frictional resistance. The third and bottom rows illustrate the subsequent propagation of event E (t = 88.6 μs and 92.6 μs).

Extended Data Fig. 5 Snapshots of the full-field distributions of fault-parallel particle velocity and shear stress change during the early phase of the second rupture sequence.

The full-field maps show the arrest of the sub-Rayleigh rupture (event B) at t = 30.8 μs; slower slip occurring at the edge at t = 35.8 μs, with the corresponding increasing shear stress illustrating how strengthening occurs; nucleation of event C at t = 41.8 μs; and its progression (t = 54.8 μs and t = 65.8 μs).

Extended Data Fig. 6 Snapshots of the full-field distributions of fault-parallel particle velocity and shear stress change during the later phase of the second rupture sequence.

The full-field maps show the fields right after the arrest of event C (t = 72.6 μs), featuring a relatively mild stress concentration where event E is eventually triggered; a triggering attempt (event D) at t = 73.6 μs; dynamic nucleation of event E at t = 81.8 μs, with substantial dynamic increase in shear stress since event D; and subsequent propagation of event E at t = 85.8 μs and 89.8 μs. The rupture initially propagates bilaterally (t = 83.8 – 87.8 μs), with the left front eventually losing steam, and the right front exiting the field of view as a strong rupture. This rupture results in a pronounced shear stress drop of \(\triangle \tau \) = 7.5 MPa (t = 83.8 – 89.8 μs).

Extended Data Fig. 7 Model showing the actual and apparent rupture speeds.

a, Schematics showing a dynamic rupture originating within the gouge layer at O and reaching the surface of observation at the location A at time \({t}_{0}\), while propagating at a rupture speed Vact. As the rupture front swipes through the free surface, where measurements are performed, it results in an apparent rupture speed Vapp. b, c, Maps of slip-velocity histories for ruptures E, with black lines outlining the position of the rupture front. d, e, Contour lines of the rupture fronts (black lines), the same as in b, c, and the fit using the analytical model (blue lines) described in the text. f, g, The apparent rupture speed on the free surface, for events E in sequences 1 and 2, respectively, showing unphysical initially supersonic rupture speeds. Using the model in a, these unphysical apparent rupture speeds can be explained by the actual rupture speeds of 0.16 cs and 0.36 cs, respectively.

Extended Data Fig. 8 Friction and slip-velocity time histories within the rock gouge with pronounced and repeated strengthening, enhanced weakening, and healing.

Friction versus time (a, b, e, f) and slip rate versus time (c, d, g, h) or the two rupture sequences, for selected locations along the interface. As in Fig. 4, but with friction and slip rate plotted versus time rather than versus slip. Colours are the same as in Fig. 2. Similarly to the friction evolution with slip (Fig. 4), the friction time histories shown here are characterized by marked strengthening, for slip rates as high as 0.5–2 m s−1, followed by dramatic weakening at higher slip rates consistent with flash heating. In both sequences, the first supershear ruptures are arrested, with velocity-strengthening behaviour, whereas the trailing-Rayleigh ruptures and subsequent dynamic events result in substantial velocity weakening. The plots of friction versus time emphasize the strengthening, which is more compressed in the plots versus slip. The slip-rate time histories show how rapidly the slip rate changes.

Extended Data Fig. 9 Friction and shear stress time histories along the interface for the two sequences of laboratory earthquakes.

a, b, First (a) and second (b) sequence of ruptures (same as in Fig. 1e). This figure presents the two cases next to each other for comparison. The friction coefficient before ruptures arrival, \({f}_{0}={\tau }_{0}/{\sigma }_{0}=0.55\), is represented in black, while the red regions indicate the friction coefficient increase associated with strengthening and the blue regions corresponding to the pronounced weakening, consistent with flash heating. Planes intersecting the friction surface are shown at the two locations analysed in Fig. 4 and Extended Data Fig. 8. The planes are at x1 = 8 mm and x1 = 18 mm, and at x1 = 5 mm and x1 = 40 mm, for the first and second sequences, respectively. c, d, Maps of the shear stress for the first and second sequence, respectively, showing the highly variable and transient nature of the stress field. The shear stress increase (yellow-to-red) and then decrease (blue) traversing the entire field of view (from approximately 35 to approximately 80 and approximately 20 to approximately 60 microseconds for the first and second sequence, respectively) are associated with slip in events B and then correspond to the continued propagation of the pressure and shear waves that increase stress as well as Rayleigh waves that decrease stress associated with the prior slip of (now arrested) rupture B; note that the (dynamic) shear stress decrease is not associated with any slip occurring on the interface. Arrest of slip events leads to stress concentrations which, together with dynamic stress waves from ongoing slip on the Homalite interface as well as intermitted slip in the gouge, and dynamic weakening, promote dynamic nucleation of subsequent slip events.

Extended Data Fig. 10 Additional evidence for velocity strengthening in quartz gouge.

Friction versus slip (a, b) and slip rate versus slip (c, d) for rupture sequence 1 at the edge of the gouge layer, \({x}_{1}=1{\rm{mm}}\) and \({x}_{2}=2{\rm{mm}}\). These plots show that friction increases during event A over slips of roughly 5 μm, while the slip velocity increases from roughly 0.5 m s−1 to a peak value of over 1 m s−1. In event B (red), substantial weakening of ~0.15 in friction coefficient occurs over slip scales of just 2 μm or so as slip rate increases. At \({x}_{1}=8{\rm{mm}}\) (Fig. 4a), weakening of 0.22 occurs over slip scales of approximately 5 μm, again indicating that weakening of 0.1 in friction occurs over slips of 2–3 μm. Hence the strengthening and weakening occur over similar slip scales indicating that both are sustained friction response. Note that if the strengthening were due to the direct effect of otherwise rate-weakening rate-and-state friction, then the strengthening would occur over negligible slips compared to the weakening.

Supplementary information

Supplementary Video 1

Experimental measurements of the particle velocity during the first sequence of lab earthquakes along a rock-gouge fault. The video shows the full-field fault-parallel (top left) and fault-normal (top right) particle velocity over the imaging window, together with their traces along the interface (bottom panels). The first rupture sequence shows the arrival of a supershear rupture (labelled as A in the figure set) entering the field of view at \(t=34.6{\rm{\mu }}{\rm{s}}\) and being partially arrested shortly after. The supershear rupture is followed by a sub-Rayleigh rupture (labelled as B) at \(t=41.6{\rm{\mu }}{\rm{s}}\), which, in turn, also loses steam shortly after entering the portion of the gouge interface, leaving slower slip in its wake. It is noted that the full-field pattern of these ruptures is consistent with observations of supershear and sub-Rayleigh ruptures in Homalite37. Several attempts to penetrate the rock gouge layer are observed thereafter. Most notably, a rupture (C) at \(t=65.6{\rm{\mu }}{\rm{s}}\), and a weaker attempt (D) at \(t=78.6{\rm{\mu }}{\rm{s}}\). Next, in sharp contrast with the previous attempts of penetrating the gouge from the left, a prominent dynamic rupture emerges from within the gouge at \(t=86.6{\rm{\mu }}{\rm{s}}\) (labelled as E in the figure set). This dynamic rupture is initiated close to the location where the previous rupture event arrested (\({x}_{1}\approx 12{\rm{mm}}\)), concentrating shear stress. The rupture initially grows bilaterally, it then expands into the gouge and finally slows down and arrests within the field of view.

Supplementary Video 2

Experimental measurements of the particle velocity during the second sequence of lab earthquakes along a rock-gouge fault. The video shows the full-field fault-parallel (top left) and fault-normal (top right) particle velocity over the imaging window, together with their traces along the interface (bottom panels). The second rupture sequence shows the arrival of a supershear rupture (labelled as A in the figure set) entering the field of view at \(t=13.8{\rm{\mu }}{\rm{s}}\) and being partially arrested shortly after. The supershear rupture is preceded by some perturbation in slip at earlier times, consistent with a triggering attempt associated with the arrival of pressure waves from the rupture nucleation. The supershear rupture is followed by a sub-Rayleigh rupture (B) at \(t=21.8{\rm{\mu }}{\rm{s}}\), which in turn is also arrested after penetrating a portion of the gouge interface. It is noted that the rupture arrival times are shorter in this case as this rupture sequence is nucleated at a site closer to the field of view compared to the previous sequence (Extended Data Fig.1). The full-field pattern of these ruptures is similar to that observed for the previous sequence. However, unlike in the first sequence, slip continues across the field of view, with slip rates of 0.5–1 m s−1. After several microseconds, at \(t=41.8{\rm{\mu }}{\rm{s}}\), slip rate accelerates and event C propagates along most of the interface reaching peak slip rates of 9 m s−1, and partially arresting around \({x}_{1}=40{\rm{mm}}\). In a departure from previous events, accelerated, albeit small, slip (event D) propagates from the other side of the fault gouge starting at \(t=73.8{\rm{\mu }}{\rm{s}}\) and also runs out of steam. Then a clear dynamic re-nucleation (rupture E) occurs at \(t=81.8{\rm{\mu }}{\rm{s}}\) from within the area spanned by event D, with associated slip rates of 6 m s−1.

Supplementary Video 3

Experimental measurements of friction during the second sequence of lab earthquakes along a rock-gouge fault. The video shows the friction coefficient plotted versus time and versus distance along the interface. The friction coefficient before ruptures arrival \({f}_{0}={\tau }_{0}/{\sigma }_{0}=0.55\) is represented in black. The red regions indicate the friction coefficient increase associated with the direct effect and the blue region indicates the pronounced weakening owing to flash heating. A plane plotted at x1 = constant (in light grey) with increasing values of x1 intersects the friction surface, generating a friction time history (shown as a green curve). When the plane reaches the locations at x1 = 5 mm and x1 = 40 mm (corresponding to those shown in Fig. 3c and analysed in Fig. 4), the friction time history is plotted at increasing value of time (red curve). The friction surface is then spun around to show the topography.

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Rubino, V., Lapusta, N. & Rosakis, A.J. Intermittent lab earthquakes in dynamically weakening fault gouge. Nature 606, 922–929 (2022). https://doi.org/10.1038/s41586-022-04749-3

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