Fracture, friction and damage processes in earthquake rupture zones

doi:10.21203/rs.3.rs-1861418/v1

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Fracture, friction and damage processes in earthquake rupture zones

https://doi.org/10.21203/rs.3.rs-1861418/v1

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We discuss properties and processes of earthquake rupture zones based on field studies, laboratory observations, theoretical models and simulations, with the goal of assessing the possible dominance of different processes in different parts of the rupture and validity of commonly used models. Rupture zones may be divided into front, intermediate, and tail regions that interact to different extents. The rupture front is dominated by fracturing and granulation processes and strong dilatation, producing faulting products that are reworked by subsequent sliding behind. The intermediate region sustains primarily frictional sliding with relatively high slip rates that produce appreciable stress transfer to the propagating front. The tail region further behind is characterized by low slip rates that effectively do not influence the propagating front, although it (and the intermediate region) can spawn small offspring rupture fronts. Earthquake ruptures are often spatially discontinuous and intermittent with a hierarchy of asperity and segment sizes that radiate waves with different tensorial composition and frequency bands. While different deformation processes dominating parts of the rupture zones can be treated effectively with existing constitutive relations, a more appropriate analysis of earthquake processes would require a model that combines aspects of fracture, damage-breakage, and frictional frameworks.

Earthquakes are manifestations of dynamic ruptures that release rapidly elastic strain energy stored in the surrounding rocks (Reid, 1910). Faults are commonly modeled as infinitely thin surfaces (idealized typically as planar) sustaining only shear deformation. This classical view has been driven by far-field observations of attenuated low-pass filtered information. However, near-fault studies unambiguously show that ruptures consist of zones that can be tens to hundreds of meters wide with broken and granular (damaged) materials, and that shear deformation is accompanied locally by dynamic dilation (Fig. 1). These phenomena, although localized, strongly affect the partitioning of the stored elastic energy between dissipation and seismic radiation, changes of permeability and fluid flow, and other key aspects of earthquake physics (e.g., Kurzon et al., 2019; Okubo et al., 2019; Aben et al., 2020). Theoretical and laboratory studies of earthquake ruptures consider fracture, friction and damage processes, with most studies in the last few decades focusing on friction. In the present paper we attempt to clarify how these different processes operate in different regions of earthquake rupture zones.

The rupture front has a process zone dominated by fracturing processes, where stresses beyond the elastic limit produce distributed cracking and granulation/pulverization of rocks. The amount of inelastic strain (or slip in a planar approximation) in the process zone is negligible, so friction has little relevance in the process zone. As the rupture propagates, the process zones at locations passed by the rupture front produce together a slip zone with highly cracked and granulated materials sustaining growing amounts of inelastic strain and frictional sliding. The rupture speed of a typical crustal earthquake is ~ 3 km/s, although some earthquakes can propagate at supershear speed (Archuleta, 1984; Rosakis, 2002), and there is also a class of slow slip events that propagate much slower (Okal and Stewart, 1982; Hirose and Obara, 2005). Since particle velocity in a continuum is proportional to stress, and the stress drops rapidly behind the rupture front, the rate of inelastic strain (or slip rate) also drops rapidly behind the propagating front (Fig. 1). Sections of the rupture zone close to the front with slip rates of ~ 1 m/s or more produce dynamic stress transfer that can interact significantly with the propagating front, but the interactions of sliding sections further behind diminish rapidly with increasing distance from the front. As an example, a fault section with a slip rate of 1 cm/s can hardly affect the rupture front that propagates in 1 s several km forward.

The rupture zone can be separated into several regions (Fig. 1). The rupture tip or front is dominated by fracturing processes and controls the path of the propagating rupture. Sliding sections of the rupture behind the process zone with slow slip velocities, and hence small dynamic stress transfer to the front, belong to a tail region that does not interact with the rupture front. Sliding sections closer to the front with higher slip velocities, which produce sufficient dynamic stress transfer to affect appreciably the energy balance at the front, belong to an intermediate region relevant for the continuing motion of the rupture front. The extent of the intermediate region depends strongly on the geometrical properties of the rupture zone (and perhaps other features such as rock type, existence of gouge, etc.).

Earthquake ruptures often propagate over multiple disconnected fault zones (e.g., 1992 Landers CA earthquake in California, 2010 El Mayor-Cucapah Earthquake in Baja California; 2016 Kaikoura in New Zealand), during which the rupture fronts jump to non-contiguous locations and abandon their tails. Evidently, the frictional processes at the tails are not essential for the rupture trajectories and ultimate size of earthquakes, although they contribute significantly to energy dissipation and changes to fault zone structures. We also note that seismic radiation is a superposition of contributions from different parts of the earthquake rupture. The radiation from the process zone can be dominated by dilatational components generated by fracturing and reduction of elastic moduli (e.g., Ben-Zion and Ampuero, 2009; Lyakhovsky et al., 2016; Kurzon et al., 2021), the radiation from the tail region involves primarily shear motion with variable local dilatation (e.g., Aki and Richards, 2002; Lyakhovsky and Ben-Zion, 2020), and the general breaking of multi-scale asperities in the rupture zone is expected to produce enhanced radiation at different frequency bands.

In the next section we describe observational results highlighting aspects of earthquake rupture zones and failure processes represented in Fig. 1, starting with field studies and continuing with laboratory stick-slip experiments that include fracture and friction. In section 3 we briefly discuss constitutive laws for planar fracture and friction, along with nucleation of dynamic failures on a plane and in a deforming volume. In section 4 we discuss the results and suggest future studies that can significantly improve the understanding of earthquake and fault processes.

2.1. Field Studies

Geological and seismological studies document abundantly the ubiquitous existence in natural fault zones of hierarchical geometrical heterogeneities (Wesnousky 1988; Wechsler et al., 2010; Sagy et al., 2007; Candela et al., 2012) and hierarchical damage zones generated by the failure events (Dor et al., 2006; Allam and Ben-Zion, 2012; Ostermeijer et al., 2020; Qiu et al., 2021; Rodriguez Padilla et al., 2022). Even major faults with very large cumulative slip have finite width, roughness, segmentation, and varying strengths that are expected to evolve with further deformation (e.g., Scholz et al., 1993; Ben-Zion and Sammis, 2003; Manighetti et al., 2007). Heterogeneous fault properties lead to strong stress heterogeneities that affect rupture dynamics (e.g., Rippberger et al., 2007; Ampuero et al., 2006; Romanet et al., 2018) and produce variable slip distributions in one or multiple simultaneously occurring rupture zones (Fig. 1c, d). The general existence of heterogeneous fault structure and pre-existing stress may lead to multiple rupture fronts nucleating simultaneously from several asperities (Lebihain et al., 2021; Dublanchet et al., 2013; Mai and Beroza, 2002; Campillo et al., 2001), complex collective slip fronts in 3D, jumps of the rupture front, and repeated acceleration and deceleration of the failure process. Source time functions of earthquakes are frequently complex, showing multiple peaks that reflect these processes. The literature on field studies of earthquake ruptures is vast. To illustrate key aspects of fracture and friction processes in earthquake rupture zones, we present three examples at different scales, starting with small-scale field results and continuing with ruptures and fault zones occupying larger crustal volumes. Some of the discussed features are also observed in laboratory experiments (section 2.2).

Figure 2 shows observed damage (fracturing) and melt (friction) products in a fossilized rupture zone of a single earthquake in lower crust rocks in the Bergen arc, Norway (Petley-Ragan et al., 2019). These observations allow inferences on the space-space evolution of rupture processes, which correspond to Fig. 1d, generally not possible in large fault zones reflecting properties of many earthquake ruptures. The results show fragmented/pulverized particles surrounded by melt products within an asymmetric damage zone, and tensile cracks normal to the main fault, some of which have injection products. The field and microstructural observations were interpreted to reflect the following evolution of processes. Initial fragmentation with minimal shear occurred in the process zone around the propagating rupture tip and extended into one wall rock, followed by comminution of the fragments with increasing shear motion behind the tip. As shear heating progressed with slip accumulation further behind the tip, the cataclasites began to melt with higher melt fractions in locations with greater volume of damaged wall rock, and injection of melt products to some of the fault-normal tensile cracks (Petley-Ragan et al., 2019).

Figure 3 presents an example documenting the activation of multiple localized slip bands, within a fairly large normal fault zone in a deep south African mine, during a single earthquake rupture, corresponding to the representation in Fig. 1d. The normal fault was likely activated in response to mining activity, producing a comparatively large seismic event with Mw 5.1. This example shows that the rupture activated three slip bands in the fault damage zone exposed in the tunnel site shown in Fig. 3, with slip not limited to a single planar ‘principal slip zone’. The full extent of the rupture zone of that earthquake is not clear but likely includes additional volumetric components. Larger-scale activation of multiple slip and rupture zones during single earthquakes (e.g. Figure 1b) has been observed in geological and seismological studies of many recent large events, and appears increasingly to be the norm rather than the exception. One prominent example is the 2016 M7.8 Kaikoura earthquake in New Zealand, which “ruptured at least 17 faults, only about half of which were recognized before.” (Clark et al., 2017; Nicol et al., 2018). Other examples among many others include the 2010 M_W 7.2 El Mayor-Cucapah earthquake in Baja California (e.g., Wei et al. 2011; Fletcher et al., 2014), the 2012 M_W 8.6 Indian Ocean event (e.g., Yue et al., 2012), the 2016 Mw 7.0 Kumamoto earthquake in Japan (e.g., Asano and Iwata, 2016; Shirahama et al., 2016), and the various large earthquakes in the Eastern California Shear Zone in the last 30 years. In addition to rupturing multiple disconnected fault segments, earthquake ruptures often produce significant distributed off-fault inelastic strain in the surrounding volume as illustrated by Fig. 4 in the context of the 1992 Mw7.3 Landers earthquake in California.

2.2. Laboratory Experiments

Laboratory fracture and friction experiments culminating in a sample-size stick-slip motion and rapid stress drop represent lab analogues for crustal earthquakes (Brace and Byerlee, 1966). Here we briefly summarize some results from a series of lab tests with different geological materials (claystone, sandstone, quartzite, granite) performed at varying loading conditions and confining pressures up to 150 MPa (Goebel et al., 2012; 2017; Guerin-Marthe et al., 2022). Depending on material and loading conditions, the samples mostly failed in episodic stick slip events accompanied by rapidly evolving bursts of AE activity (Fig. 5). Typically, AE cumulative numbers follow t_f⁻¹ where t_f is time to failure. On rough fractured faults, the AE activity spreads across the surface forming a single or a few expanding clusters (Fig. 5), while on smooth faults the AE activity is generally low or in some cases non-existent (Simon Guerin-Marthe et al., 2022; Dresen et al., 2020). The AE clusters highlight larger asperities that persist over several stick-slip cycles. This suggests a collective failure of growing AE clusters, with jumps of the rupture front, finally leading to a system-size slip event (Goebel et al., 2012; 2017). Slip rates along the faults measured at different tests ranged from about 2 µm/s to over 160 mm/s. Often contained or system-wide slip events start with a single large acoustic emission. Here macroscopic stress drop and failure were initiated by large acoustic emissions with amplitudes significantly larger than background events (and partly clipped). The events occurred at peak stress or slightly below (Fig. 5a, A-C). The space-time sequence of large AEs A-C (Fig. 5) indicates propagation of the rupture front. AE clusters remain active for the entire duration of the slip event after the rupture front has passed, i.e., the rupture front and frictional tail were ‘detached’.

The elastic waves radiated from the rupture produce strain signals in gauges attached locally at a small distance from the fault (Guerin-Marthe et al., 2022.) indicating a passing rupture front. The offset time between signals from strain gauges often allows a rough estimate of the rupture velocity. Bulk stress drop measurements using an internal load cell represent an average that includes both rupture and slip components. In contrast, the strain gauges allow estimating local stress drops, which occur often more abruptly and over smaller slip distances (Fig. 6). The observations of separation of rupture front and slip are consistent with the representation in Fig. 1a, and in agreement with results from additional triaxial tests by Passelegue et al. (2017), rotary shear tests (Chen et al., 2021), experiments on large laboratory faults (e.g. Ohnaka and Shen 1999; Xu et al., 2018; Kammer and McLaskey, 2019; Ke et al., 2021) and experiments on analogue materials at low normals stresses (Rubino et al., 2022, Gvirtzman and Fineberg, 2021; Paglailunga et al., 2022).

Double direct shear tests were used to extensively investigate frictional rock properties of planar fault surfaces and gouge layers with evolving fabric, spatio-temporal evolution of granular slip and the transition from stable to slow and fast slip, covering a wide spectrum of slip velocities (Marone et al., 1998; Im et al., 2020). Frictional tests on gauges with varying mineralogical composition show relations between microstructural fabric evolution (i.e localization) and stability of slip (Scuderi et al., 2017, 2020). A key observation is that a single fault with identical constitutive properties may host both stable slow slip and dynamic rupture events (Scuderi et al., 2017; Ye and Ghassemi, 2021). More recently, the interplay of slip modes from slow to fast was studied with high-frequency (AE) signals (Bolton et al., 2022). Complex rupture fronts were observed to arise from local slip events across a range of slip rates from aseismic failure to dynamic events (e.g. McLaskey, 2019; Bolton et al., 2022), and the combined failure of asperities of varying sizes in the sliding region were also observed to produce new rupture fronts (de Geus et al., 2019; Lebihein et al., 2021). These results converge with those of triaxial tests at high pressure with AE monitoring (Figs. 5, 6), showing superposition of local events that range from high-frequency AEs with source radii on the µm-mm scale to slip events affecting the entire sample.

The onset and continuing motion of the rupture front is controlled by an energy balance between the flow of strain energy to the front and dissipation in the process zone to fracturing the material ahead and around the front (Freund, 1990; Kammer et al., 2015; Svetlitzki et al., 2017). As mentioned, the rupture front can jump to one or several discontiguous locations abandoning the tail. On the other hand, the sliding process in the tail and intermediate regions can spawn new local rupture fronts, thus affecting the collective rupture front. The coupled fracture-friction nature of fault failure is reflected in classical constitutive models that typically assume a planar fault relating shear stress drop to slip and accounting for slip- and rate-dependent aspects of the process for defined conditions of pressure, temperature, etc. (e.g., Dietrich, 1972; Rice, 1983; Marone, 1998). These constitutive laws rest on Linear Elastic Fracture Mechanics (LEFM), cohesive zone slip-weakening and rate-and-state friction, as briefly described below.

Frictional slip is controlled by shear crack-like rupture fronts propagating along a fault (Aki et al., 1979; Rubinstein et al., 2004). Griffith’s energy balance defines a condition for the stability and onset of rupture propagation. When the stress intensity factor reaches a critical value K_c, the material fails producing rupture. For continuing rupture propagation, the energy release rate from the bulk to the rupture front, G, should reach a critical value G_c (e.g., Freund, 1990; Ben-Zion, 2003). Since the stress drops rapidly behind the rupture front (Fig. 1), slip rate is reduced with distance from the front but the slip trailing the rupture continues to accumulate for the duration of sliding at different positions.

The classical slip-weakening model (Ida, 1972; Palmer and Rice, 1973) is a shear fracture variant of the well-known Dugdale-Barenblatt cohesive zone fracture mechanics model. This describes the propagation of a planar shear band through a finite process zone of length $L$, where the peak strength of the fault ${\tau }_{p}$ degrades over a critical slip distance ${d}_{c}$ to some residual dynamic friction ${\tau }_{r}$. The slip gradient u/L and gradual strength reduction avoid the unrealistic stress singularity at the fracture tip of LEFM. This constitutive formulation on a planar surface has been used extensively to estimate fracture energy and rupture process zone from laboratory results (Rice, 1980; Wong, 1982; Viesca and Garagash, 2015), as well as from seismological data (e.g., Cocco et al., 2016, Abercrombie and Rice, 2005). We note that using this framework for field data involves multiple assumptions, including that a planar projection of the natural process to the slip-weakening diagram (ignoring, e.g., volumetric deformation) is valid.

The slip-weakening model does not consider potential rate-dependence of shear strength and post-failure strength recovery. Field evidence and experiments show that faults and frictional contacts exhibit healing and rate-dependent effects. Dieterich (1978, 1979a,b) proposed a rate-and-state frictional model including strength recovery of frictional contacts with time and dependency of the frictional strength on slip velocity. In particular, strength may decrease (velocity weakening) or increase (velocity strengthening) as slip rate increases, depending on pressure, temperature and other conditions. This model and subsequent formulations of rate-and-state friction (e.g. Marone, 1998) can be used to study the transition of creep to unstable slip in terms of material-dependent parameters and boundary conditions. Rotary shear experiments with slip rates of over 1 m/s examined effects of high slip velocities and accelerating and decelerating slip rates on the friction, slip process, and evolving properties of the gouge (e.g., Sone and Shimamoto, 2009; Di Toro et al., 2011; Chen et al. 2021). Laboratory measurements also show that the nominal friction coefficient depends on changes of normal stress (Linker and Dieterich 1992; Prakash and Clifton, 1993). As discussed in the next section, multiple processes are expected to produce strong dynamic changes of normal stress during fault failure that can significantly affect the frictional energy.

Slip weakening and rate-and-state friction constitutive models predict a critical nucleation patch ${L}_{C}$ that is related to critical displacement ${d}_{c}$, stress drop $\varDelta \tau$ and elastic shear modulus $\mu$of the fault surroundings (Eshelby, 1957)

$${L}_{C}=C\frac{\mu }{\varDelta \tau }{d}_{c}$$

where $C$is a constant of order 1. For a circular shear crack in elastic solid, a linear relation is predicted between displacement and crack radius (Eshelby, 1957). This implies a material-specific constant strain change and stress drop with a constant displacement-length scaling consistent generally with observations (Manighetti et al., 2007). Eshelby’s model also implies that the velocity of the rupture (crack) front ${v}_{R}$ scales with slip (particle) velocity ${v}_{S}$ (Freund and Lee, 1990; Udias et al., 2014),

$${v}_{R}=C\frac{\mu }{\varDelta \tau }{v}_{S} .$$

For dynamic ruptures radiating seismic waves, a related threshold slip rate value is often assumed as ${v\text{'}}_{s}\approx \frac{\varDelta \tau }{\mu }{c}_{s}$ (Rice 1993, Wynants-Morel, 2021) with a threshold slip velocity ${v\text{'}}_{s}$ of a few mm/s.

Rupture nucleation may involve collective failure of asperities across a segmented and rough frictional fault (e.g. Dahmen et al., 1998, Campillo et al., 2001), and its propagation involves shear and volumetric deformation as the rupture accelerates and its trace follows a tortuous path generating off-fault damage (Poliakov et al., 2002; Gabriel et al., 2013; Goebel et al., 2014; Renard et al., 2019). The trailing slip motion in wake of the rupture front is governed by frictional contact forces, re-rupturing of asperities, comminution, granular flow and heat dissipation that may cause local melting and thermal pressurization.

In a rock volume not dominated by a pre-existing unhealed frictional surface, the nucleation process leading to dynamic instability is different and involves localization of distributed cracking and solid-granular transition (Ben-Zion, 2008). When the density of microcracks reaches at some location a critical level, there is dynamic instability and a phase transition of material at the rupture front from a damaged (cracked) rock to a granular phase. The subsequent shear failure is associated under sufficient compressive stress with a granular flow in the generated finite-width “slip zone”, while under low confining stress the material is fragmented (Lyakhovsky and Ben-Zion, 2014a). Following failure and stress reduction, there is a reversed transition from a granular phase to a damaged solid (Lyakhovsky and Ben-Zion, 2014b). A process of this type involving localization of brittle deformation has been documented recently before several large earthquakes (Ben-Zion and Zaliapin, 2020), and was also observed before system-size events in laboratory fracturing experiments (e.g., Lockner et al., 1992; Stanchits et al., 2006; Goebel et al., 2012; McBeck et al., 2022).

Faults are inherently heterogeneous over all observed scales. This is seen in laboratory fracture experiments (e.g., Sharon et al., 1995; Goebel et al., 2012; 2017) and amplified in the crust by the heterogeneous geological inheritance of any natural fault zone (e.g. Ben-Zion and Sammis, 2003). Laboratory experiments show heterogeneous slip and rupture events even on pre-existing surfaces. Earthquake rupture zones have a finite-width that can be hundreds of meters, and they sustain during shear-dominated failure also local volumetric deformation that can impact significantly the governing physics. In the present paper we attempt to clarify whether fracture, friction and volumetric damage/granulation processes are dominant in different parts of a rupture zone, or are inseparable and should be considered in all fault sections. Another issue we attempt to address is for what conditions the commonly used planar representation of faults and associated constitutive laws provide adequate (approximate) descriptions for natural earthquake ruptures.

Laboratory tests with multiple rock types indicate that Eshelby’s Eq. (2) relating slip and rupture velocities holds for slip rates ranging over about six orders (µm/s – m/s). For all tested fault rheologies/materials (clay-rich rocks, sandstone, granite), the estimated rupture velocities are about 3–4 orders larger than the directly measured slip rates ranging between tens of µm/s up to tens of cm/s. In experiments, rupture propagation associated with slip events are inferred either indirectly from sequences of large AEs (Fig. 5), spreading of AE clusters (Wang et al., 2020), or time offset of strain signals at different positions. Strain gauges in lab experiments show a rapid strain/stress drop followed by a slow decrease (Fig. 6), consistent with an initial reduction of the stored strain energy at the rupture front and continuing reduction by the frictional sliding in the intermediate and tail regions.

The processes involved in frictional sliding are assumed to dominate the overall energy balance, as current estimates of fracture energy G based on measurements of fracture and gouge surface area indicate its contribution is < 10% and possibly < 1% of the total strain energy released in an earthquake (Olgaard and Brace, 1983; Chester et al., 2005; Rockwell et al., 2009). Seismological estimates of the fracture energy and stress drop may not provide reliable results since they rely on model assumptions and limited resolution of the source time function at the rupture front (Cocco et al., 2016; Ben-Zion, 2019). Also, seismological estimates of breakdown work (Viesca and Garagash, 2015) may include dissipation by frictional sliding, melting and possibly arrest (Ke et al., 2021). Numerical simulations of dynamic rupture on a frictional interface with off-fault plasticity show that early on the dominant energy components are the stored elastic strain and kinetic energy (radiation), but that with progressive propagation the frictional heat and off-fault dissipation become dominant (Shi et al., 2010).

While dissipation over the entire rupture zone may dominate the total energy budget, the stress concentration in the process zone and energy flux at the rupture front still control rupture propagation (Freund 1972; Reches and Fineberg, 2022). The size of the process zone surrounding the front (Fig. 1) is expected to depend on rupture propagation distance, crack vs. pulse mode, and velocity (Andrews, 2005; Ben-Zion and Shi, 2005; Svetlitzki and Fineberg, 2014). We note that dynamic changes of normal stress in the rupture zone can significantly reduce the frictional heat, as demonstrated in simulations of rupture on a bimaterial interface (Andrews and Ben-Zion, 1997). In addition to bimaterial ruptures, numerous other mechanisms are expected to produce strong changes of normal stresses in earthquake rupture zones. These include collisions of gouge particles and rough surfaces (Melosh, 1979; Lomnitz-Adler, 1991), fluid-assisted effects (e.g., Sibson, 1973, Rice, 2006), and isotropic radiation from source volumes (and especially the process zone) sustaining reduction of elastic moduli (Ben-Zion and Ampuero, 2009; Lyakhovsky et al., 2016). It is important to study further with laboratory experiments, field data, and model simulations the effects of volumetric deformation on constitutive laws, energy partitioning, and other other aspects of earthquake physics.

Rupture of a planar interface in experiments with PMMA-type materials was shown to be quantitatively described by fracture mechanics over a range of rupture velocities (e.g. Svetlitzki and Fineberg, 2014). If shear crack or pulse-like ruptures control the initiation, propagation and arrest of earthquakes, this has important consequences for the stability transition of faults, and the potential role of friction for slip stability analysis that is often used (Rice, 1980; Ben-Zion, 2001; Barras et al., 2019; Svedlitzki et al., 2019; Brener and Bouchbinder, 2021). However, the failure of rough surfaces and gouge layers amplifying stress and strength heterogeneities involves intermittent rupture propagation and an interplay of rupture and sliding friction processes navigated by long-range elastic stress transfer, which may also cause re-rupturing of frictional slip patches behind the initial rupture front (Xu et al., 2018; Rubino et al., 2022). As the elastic strain energy is stored in the entire crustal volume, frictional sliding in the rupture zone can interact with the rupture front. While this suggests “no separation of scales” in the rupture zone (Brener and Bouchbinder, 2021; Rubino et al., 2022), if the rate of stress transfer during rupture propagation to the front is sufficiently small, the interaction is negligible. This allows a separation of scales (Fig. 1) to the rupture front, an intermediate region where the stress interaction with the front is appreciable, and a tail region effectively non-interacting with the front (although it can still spawn minor offspring local rupture fronts).

Lab experiments clearly show a hierarchical complexity of the rupture process in space and time, particularly on rough surfaces. Rupture of heterogeneous faults likely involves a hierarchy of asperity and segment sizes, and numerous laboratory tests show that slow and fast rupture and slip events may coexist (Dresen et al., 2020; Yamashita et al., 2021; Bolton et al., 2022). This implies, for example, that the stability transition in a heterogeneous fault can depend on the size of the event in an opposite fashion to the nucleation of dynamic instability beyond a critical slip patch size (e.g., Dieterich 1992; Rice, 1993). Specifically, stable large-scale (system-wide) slip and unstable small-scale (grain-scale) acoustic emissions coexist and interact mutually (de Geus et al., 2019; Fisher 1998, Ben-Zion, 2008). Classic estimates of the stability transition and nucleation patch size based on a smooth fault model may yield erroneous results. The fact that slow or even stable large slip events may include dynamic ruptures on the grain-asperity scale (AEs) is reminiscent of slow slip events hosting tremor. Faults may also have slow or fast slip events depending on local ratios of shear to normal stress, which may far exceed the average frictional strength (Ben-David et al., 2010, Bolton et al., 2022). Slow and fast slip events with duration times 0.1–10s may be contained or system-wide affecting the entire fault. Associated AE bursts shorter than 10^− 5s (Figs. 5, 6) attest to loading and dynamic failure of grain-scale and larger asperities across different length scales (Ohnaka and Shen, 1999; Goebel et al., 2017; Dresen et al., 2020). As AE activity relates to roughness, preparatory fault slip on smooth faults is often dominantly aseismic and small, involving a few and generally large AEs close to failure at peak stress that initiate a macroscopic slip event (Guerin-Marthe et al. 2022).

Stick slip failure of lab faults with varying degree of heterogeneity captures important aspects of unstable failure in nature. However, several key processes are not accounted for in the constitutive models used to interpret earthquake data. These include intermittent rupture propagation, generation of rock damage and granulation, separation of rupture front and frictional tail, strong dynamic changes of normal stresses during failure, and superposition of processes in the rupture zone radiating waves with different tensorial components and different frequency bands. Fracture mechanics, frictional constitutive laws, damage rheology, and granular mechanics describe (each) certain aspects of rupture and slip processes, but not the entire physics of earthquake rupture zones. Elements from all these frameworks are combined in a damage-breakage rheology model (Lyakhovsky and Ben-Zion, 2014a,b; Lyakhovsky et al., 2016), but the development of a more complete model that accounts for the various processes in earthquake rupture zones remains a fundamental challenge. Using up-scaling methods (Matouš et al., 2017; Kovachki et al., 2022) to extrapolate results of laboratory experiments for conditions of natural faults will aid significantly the development of a more complete model for earthquake and fault phenomena.

Acknowledgments

The study was supported by the National Science Foundation (grant EAR-2122168) and the GeoForschungsZentrum Potsdam. Manuela Dziggel helped preparing Fig. 1.

Funding

The study was supported by the National Science Foundation (grant EAR-2122168). Support from GFZ is also acknowledged.

Competing interests

The authors have no relevant financial or non-financial interests to disclose.

Author contributions

YBZ and GD contributed to the conception and design of the study. Material preparation, data collection and analysis were performed by both authors. The first draft of the manuscript was written jointly by YBZ and GD and both authors improved the versions of the manuscript. Both authors read and approved the final manuscript.

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No competing interests reported.

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Fracture, friction and damage processes in earthquake rupture zones

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1. Introduction

2. Observations

2.1. Field Studies

2.2. Laboratory Experiments

3. Constitutive Models

4. Discussion And Conclusions

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