Earthquakes as dynamic fracture phenomena
Commentary by
Ze’ev Reches, University of Oklahoma, and Jay Fineberg, Hebrew
University
ABSTRACT
A large earthquake unlocks a fault-zone via dynamic rupture while
releasing part of the elastic energy stored during the interseismic
stage. As earthquakes occur at depth, the analyses of earthquake physics
rely primarily on experimental observations and conceptual models. A
common view is that the earthquake instability is necessarily related to
the frictional weakening that is commonly observed in shear experiments
under seismic slip velocities. However, recent experiments with
frictional interfaces in brittle acrylics (Svetlizky & Fineberg, 2014)
and rocks (e.g., Passelegue et al., 2020) have explicitly demonstrated
that no characteristic frictional strength exists; a wide range of
stresses (‘overstresses’) are sustained prior to rupture nucleation.
Moreover, the experimentally observed singular stress-fields and rupture
dynamics are precisely those predicted by fracture mechanics
(Freund, 1998). We therefore argue here that earthquake dynamics are
best understood in terms of dynamic fracture mechanics: rupture dynamics
are driven by overstresses, but not directly related to the fault
frictional properties.
PLAIN-LANGUAGE SUMMARY
A large earthquake occurs when a “locked” fault becomes unlocked and
starts slipping rapidly while releasing stored elastic energy. As
earthquakes occur at depth, earthquake analyses rely primarily on
experimental observations and conceptual models. One common view
attributes the earthquake instability to the transition from the strong
‘static friction’ to the weaker ‘dynamic friction’. Recent observations
of experimental earthquakes along brittle faults cause us to challenge
this common view. These experiments have explicitly demonstrated that
faults may stay locked under a wide range of stress levels making the
assumption of a characteristic ‘static friction’ irrelevant. Moreover,
the features of these earthquakes fit precisely the predictions
of fracture mechanics theory (Freund, 1998), by taking these stress
differences into account. We therefore argue here that earthquake
dynamics is best understood in terms of dynamic fracture mechanics, a
process not directly related to the fault frictional properties.
INTRODUCTION
A large earthquake is preceded by an interseismic period during which
the fault-zone stays “locked”, and elastic energy is “stored” in the
crustal rocks. The earthquake will unlock the fault-zone via dynamic
rupture of the fault while releasing part of the stored elastic energy.
Earthquake physics analyses rely primarily on experimental observations
and conceptual models, because we have “…..near zero direct
constraints on the dynamic processes … associated with …
earthquake ruptures” (Ben-Zion, 2019). In this commentary, we examine
the rupture character of earthquakes in light of recent experimental
observations; we start by inspecting the earthquake process in the
framework of dynamic fracturing.
Figure 1 displays three idealized cases of dynamic fracturing: tensile
fracturing (mode I), shear fracturing without friction (mode II), and
shear fracturing along a frictional fault, that is an idealized
earthquake rupture. The processes of tensile and shear fracturing (modes
I and II) have been under detailed investigation since (Griffith, 1920)
and are well understood by the theory of ‘fracture mechanics’ (Freund,
1998). This theory indicates that both tensile and shear fractures will
propagate when the rate of elastic energy flow towards the tip of a
rapidly moving fracture surpasses the rate of local energy dissipation
required for creating the new fracture surfaces (Freund, 1998; Svetlizky
et al., 2017). In modes I and II, resulting fractured surfaces (white
slits in Fig. 1a, b) are stress-free, and thus, the only site where
energy is dissipated is within the fracture tip zone (yellow zone in
Fig. 1a, b). Fracture mechanics theory provides analytical solutions of
the stress-field around the fracture as a function of the available
energy and propagation velocity. The predicted stress-field indicates a
distinct stress singularity at the tip, and a stress-free zone in the
wake of the tip (dark blue zone of σ = 0 in Fig. 1d).
As anticipated, the situation becomes more complicated for a shear
fracture in which both sides of the fracture surfaces remain in
frictional contact (Fig. 1c). This configuration is the relevant one for
an earthquake rupturing a frictional fault. Theoretical work (Barras et
al., 2020; Palmer & Rice, 1973) has suggested that even this case can,
in general, be described by the same fracture mechanical framework as
the pure mode II case (Fig. 1b).
RUPTURING ALONG EXPERIMENTAL FRICTIONAL FAULTS
Recent experimental analyses use advanced high-speed techniques to
monitor dynamic ruptures along experimental faults (Svetlizky &
Fineberg, 2014; Wu & McLaskey, 2019; Xu et al., 2019; Passelegue et
al., 2020; Chen et al., 2021). These analyses revealed three fundamental
characteristics of shear rupturing along frictional faults with
significant implications for earthquake physics.
- Stresses and control of dynamic rupturing . It was
demonstrated (Svetlizky & Fineberg, 2014) that propagating ruptures
along a fault can be precisely described by fracture mechanics
theory (Freund, 1998). Fig. 2 displays the results for an experimental
fault (Fig. 2a) that was subjected to shear and normal loads where
ruptures were monitored by high-speed photography and strain-gages. In
a series of nine experiments, the fault was overstressed prior to
rupture initiation over a range of shear stresses that exceeded the
minimal stress for frictional sliding (about 1MPa) by 0.1-0.4 MPa (the
normal load was identical in all experiments) (Fig. 2b). Once slip
nucleated, spontaneous ruptures propagated at velocities that were
governed by the pre-slip overstress (Fig. 2c). The lowest overstress
triggered relatively slow ruptures, while the highest values gave rise
to rapidly accelerating ruptures that approached the limiting Raleigh
wave speed, CR. (Svetlizky et al., 2017) used the
measured elastic energy to show that all the propagation velocities
and accelerations in these experiments perfectly fit the
fracture mechanics predictions (black curve in Fig. 2d). Most
importantly, this perfect fit does not include any consideration of
the fault’s frictional properties. These experimental observations are
in agreement with fracture mechanics formulations which indicated that
fault friction does not affect the rupture characteristics (Barras et
al., 2020; Palmer & Rice, 1973). This quantitative agreement with
fracture mechanics theory, which was documented in both brittle
acrylics (Svetlizky & Fineberg, 2014; Bayart et al., 2016; Svetlizky
et al., 2017) and rocks (Wu & McLaskey, 2019; Xu et al., 2019;
Passelegue et al., 2020), requires a modification of the predicted
stress-field: the stress in the frictional zone equals the residual
frictional strength of the fault, τR, (grey area of σ
= τR, Fig. 1e).
- Energy balance of dynamic rupturing . The section above
indicates that the elastic energy dissipation can be separated into
two, quasi-independent entities (Fig. 1): (A) Localized dissipation
(fracture energy) at the near-singular tip zone of a shear fracture
(yellow zone, Fig. 1c), and (B) distributed energy dissipation by
frictional resistance of the sliding surfaces in the wake of the
rupture-front (red fault-zone, Fig. 1c). The rupture front may
propagate at velocities of a few km/s (Fig. 2c) while generating
extreme stresses, strain-rates and slip velocities, in the immediate
vicinity of rupture tip (Svetlizky & Fineberg, 2014). The near-tip,
cohesive zone of a typical earthquake dissipates only
~5-6% of the earthquake energy (Kanamori & Brodsky,
2004), but the extreme stresses developed there are expected to
“breakdown” the fault-zone by fragmentation and pulverization
(Reches & Dewers, 2005; Wilson et al., 2005). The trailing frictional
zone, which does not constrain the rupture front, is thought to
dissipate 70-90% of the earthquake energy. The above observations and
associated discussion raise a central question: What are the effects
of friction on the earthquake process?
- Fault frictional properties and the earthquake process . A
common view is that earthquake instability is controlled by frictional
weakening manifested by the drop from static to dynamic friction (Di
Toro et al., 2011; Dieterich, 1979). This view is used in earthquake
simulations with velocity weakening (Lapusta & Rice, 2003; Madariaga
et al., 1998) assuming experimentally derived friction laws, e.g.,
rate-and-state friction (Dieterich, 1979). Frictional weakening is
indeed observed in multiple experiments: a rock’s frictional strength
may decrease with increasing slip-velocity and/or slip-displacement.
Strengths drop particularly rapidly under seismic slip velocities of a
few m/s (Di Toro et al., 2011; Hirose & Shimamoto, 2005). We argue
that the utilization of frictional weakening as the controlling
mechanism of earthquake dynamics may lead to a few central
contradictions.
Sections I and II above indicate that the dynamic nature (e.g., stored
energy, stress field, or propagation velocity) of a rupture along
experimental faults can be fully understood in terms of fracture
mechanics formulation without consideration of the fault’s frictional
properties. The only requirement for earthquake rupture propagation is
the ability of a frictional system to develop and sustain sufficient
stored elastic energy, or ‘overstress’, prior to rupture nucleation
(e.g. Fig. 2b). This has been amply demonstrated (Ben-David et al.,
2010; Ben-David & Fineberg, 2011; Passelegue et al., 2020) in
experiments: for a given normal stress, an experimental fault can
sustain a large range of applied shear stresses. Therefore, the
concept of a characteristic static-friction that governs the onset of
instability is misleading (Ben-David & Fineberg, 2011), and a fault
system can store varying amounts of elastic energy above limits
imposed by friction-based models; mechanisms of overstress are
discussed later.
It is certainly possible to incorporate frictional weakening in
rupture dynamics simulations that correspond to fracture mechanics
formulations (Lapusta & Rice, 2003; Madariaga et al., 1998). However,
the required dependence on a ‘friction law’ and associated weakening
is not necessary , and, in fact, could impose unnecessary
restrictions. For example, the friction-based idea that an earthquake
cannot propagate under velocity strengthening is inaccurate,
because an earthquake can propagate if the fault system is
sufficiently overstressed. For instance, the mineral talc dominates
the composition of active fault-zones, e.g., the central San Andreas
fault (Moore, D. & Rymer, M., 2007) and mining–induced faults. Yet,
even though talc is documented as frictional-strengthening mineral for
both dynamic velocity and displacement (Chen et al., 2017),
earthquakes do occur along these zones.
DISCUSSION
We propose here that earthquakes should be described as dynamic ruptures
controlled by fracture mechanics processes that are unrelated to the
friction even though fault frictional properties do dominate the energy
dissipation processes. We refer to this concept as Fracture Earthquake
Rupture Mechanics, FERM. Beyond the experimental observations, the
proposed view can resolve a few paradoxical features of earthquake
processes.
Overshoot is a rupture state that can inherently be explained
by the FERM concept. Dynamic overshoot refers to the case of
“…shear stress reduction below dynamic friction” (Ide et al.,
2011), and according to common friction laws, an earthquake should be
arrested in such a case. A field example of overshoot is the Mw2.2
earthquake at 3.6 km depth in Tautona mine, South Africa. The in-situ
mapping at the focal depth revealed a rupture-zone of 3 to 4
non-parallel slip-surfaces (Heesakkers et al., 2011), and the associated
in-situ stress measurements (Lucier et al., 2009) revealed that the
[shear stress/normal stress] ratio on these slip-surfaces ranges
0.05-0.13. These measured stress ratios are significantly lower than the
dynamic friction, and according to FERM, this earthquake was facilitated
solely by the of potential elastic energy generated by mine operations
regardless of the resolved shear stresses and fault-zone strength.
Overshoot has also been experimentally documented (Bayart et al., 2016)
where rupture propagation was shown to continue at stress levels well
below measured values of \(\tau_{R}\).
Overstress. In FERM, the development of a dynamic rupture only
requires a measure of overstress, namely, mean stress levels that exceed
those necessary to overcome \(\tau_{R}\ \). Overstress can be achieved
by a strong barrier (Gvirtzman & Fineberg, 2021), fault-zone healing
(Heesakkers et al., 2011; Muhuri et al., 2003) ahead of an arrested
rupture (Ben-David et al., 2010; Passelegue et al., 2020) or due to
fault heterogeneities, whose strength may approach the theoretical rock
strength (Savage et al., 1996).
The stored elastic energy due to the overstress drives dynamic rupture
and controls the rupture velocity, style and energy dissipation after
the rupture nucleation (Fig. 2) (Svetlizky et al., 2017; Svetlizky &
Fineberg, 2014). The timing and location of rupture nucleation are
governed by local failure in regions of high local stress and/or low
local strength.
Complex fault system. A single seismic event may be complex
e.g. 2016 Mw 7.8 Kaikōura earthquake (Ulrich et al., 2019)
In conclusion, we believe that rupture fronts efficiently
(~5% of the total energy) control earthquake dynamics
by unlocking a fault, generating the requisite breakdown stress-drop,
and damaging the rock-blocks. An earthquake’s size and speed is
controlled by the magnitude of the elastic energy available relative to
the interface strength (fracture energy), while the overall dissipation
is primarily due to frictional processes along slipping faults.
ACKNOWLEDGMENTS
We thank the many colleagues who through countless discussions
unknowingly contributed to our understanding of earthquake processes. ZR
thanks the funding support by NSF grant EAR-1620330 “Investigating
earthquake source processes in the laboratory”, and partial support by
NSF grant EAR-1345087 “Experimental simulation of earthquake rupture
processes.” JF acknowledges the support of the Israel Science
Foundation (ISF Grant No. 840/19). Open Research and Data Availability:
No unpublished data was used in this commentary.