Earthquake energy dissipation in a fracture mechanics framework

Earthquakes are rupture-like processes that propagate along tectonic faults and cause seismic waves. The propagation speed and final area of the rupture, which determine an earthquake's potential impact, are directly related to the nature and quantity of the energy dissipation involved in the rupture process. Here, we present the challenges associated with defining and measuring the energy dissipation in laboratory and natural earthquakes across many scales. We discuss the importance and implications of distinguishing between energy dissipation that occurs close to and far behind the rupture tip, and we identify open scientific questions related to a consistent modeling framework for earthquake physics that extends beyond classical Linear Elastic Fracture Mechanics.

Frictional melting mechanisms of rocks during earthquake fault slip

Rapid slip, at rates in the order of 1 m/s or more, may induce frictional melting in rocks during earthquakes. The short-lived melting has been thought to be a disequilibrium process, for decades. We conducted frictional melting experiments on acidic, basic, and ultrabasic silicate rocks at a slip rate of 1.3 m/s. The experiments and microstructural observations reveal that all minerals in the rocks are melted at temperatures below their known melting temperatures (Tm); e.g., quartz is melted at ~ 1000-1200 °C, not ~ 1720 °C, while olivine at ~ 1300 °C, rather than ~ 1700 °C. The low-temperature melting is incompatible with the conventional disequilibrium melting, and may be caused predominantly by grain size reduction and phase boundary reactions during the early and later stages of slip, respectively. The newly estimated Tm and the melting mechanisms should be considered for understanding the mechanics of earthquakes, landslides, and caldera collapses.

Frictional Melting in Hydrothermal Fluid-Rich Faults: Field and Experimental Evidence From the Bolfín Fault Zone (Chile)

Tectonic pseudotachylytes are thought to be unique to certain water-deficient seismogenic environments and their presence is considered to be rare in the geological record. Here, we present field and experimental evidence that frictional melting can occur in hydrothermal fluid-rich faults hosted in the continental crust. Pseudotachylytes were found in the >40 km-long Bolfín Fault Zone of the Atacama Fault System, within two ca. 1 m-thick (ultra)cataclastic strands hosted in a damage-zone made of chlorite-epidote-rich hydrothermally altered tonalite. This alteration state indicates that hydrothermal fluids were active during the fault development. Pseudotachylytes, characterized by presenting amygdales, cut and are cut by chlorite-, epidote- and calcite-bearing veins. In turn, crosscutting relationship with the hydrothermal veins indicates pseudotachylytes were formed during this period of fluid activity. Rotary shear experiments conducted on bare surfaces of hydrothermally altered rocks at seismic slip velocities (3 m s-1) resulted in the production of vesiculated pseudotachylytes both at dry and water-pressurized conditions, with melt lubrication as the primary mechanism for fault dynamic weakening. The presented evidence challenges the common hypothesis that pseudotachylytes are limited to fluid-deficient environments, and gives insights into the ancient seismic activity of the system. Both field observations and experimental evidence, indicate that pseudotachylytes may easily be produced in hydrothermal environments, and could be a common co-seismic fault product. Consequently, melt lubrication could be considered one of the most efficient seismic dynamic weakening mechanisms in crystalline basement rocks of the continental crust.

Intrinsic Effect of Alkali Concentration on Oxidation Reactivity and High-Temperature Lubricity of Silicate Melts between Rubbed Steel/Steel Contacts

The present study investigated oxidation reactivity and hot lubricity of a sodium silicate melt at different Na₂O/SiO₂ ratios under elevated temperature stimulation. Static oxidation prevention was achieved at 920 °C when the Na₂O/SiO₂ ratio reached 1:3 (trisilicate) and 1:2 (disilicate), but it started to deteriorate in the case of 1:1 (metasilicate). At a high concentration of sodium (metasilicate), a severe corrosion reaction between the melt and oxide took place that resulted in a composite coating on the steel substrate. This high-temperature reaction accelerated the formation of ionic charges from the steel base and promoted oxidation. However, friction and wear reduction is proportional to an increase in the sodium oxide fraction. Metasilicate (1:1) exhibited excellent lubricity under the hot frictional test at 920 °C compared to other lubricants. It was due to the formation of the sodium-saturated surfaces and an amorphous silica layer, which was associated with the high-temperature reactivity of sodium toward the oxide surface. In addition, the NaFeO₂-Fe₂O₃ composite film, as the reaction product of individual sodium charge and oxide, plays a significant role in maintaining the tribofilm stability for metasilicate, which was not present for disilicate. This study advances the understanding of how sodium-containing compounds perform oxidation prevention and generate lubricity at hot rubbed surfaces.

Mechanical behaviour of fluid-lubricated faults

Fluids are pervasive in fault zones cutting the Earth's crust; however, the effect of fluid viscosity on fault mechanics is mainly conjectured by theoretical models. We present friction experiments performed on both dry and fluid-permeated silicate and carbonate bearing-rocks, at normal effective stresses up to 20 MPa, with a slip-rate ranging between 10 μm/s and 1 m/s. Four different fluid viscosities were tested. We show that both static and dynamic friction coefficients decrease with viscosity and that dynamic friction depends on the dimensionless Sommerfeld number (S) as predicted by the elastohydrodynamic-lubrication theory (EHD).Under favourable conditions (depending on the fluid viscosity (η), co-seismic slip-rate (V), fault geometry (L/H₀²) and earthquake nucleation depth (∝σ_eff)), EHD might be an effective weakening mechanism during natural and induced earthquakes. However, at seismic slip-rate, the slip weakening distance (D_c) increases markedly for a range of fluid viscosities expected in the Earth, potentially favouring slow-slip rather than rupture propagation for small to moderate earthquakes.

The effect of fluid viscosity on fault mechanics is mainly conjectured by theoretical models. Here, the authors present experimental data from rock friction experiments, showing both static and dynamic friction coefficients to decrease with viscosity and dynamic friction to depend on the Sommerfeld number.

Frictional Instabilities and Carbonation of Basalts Triggered by Injection of Pressurized H2O- and CO2- Rich Fluids

The safe application of geological carbon storage depends also on the seismic hazard associated with fluid injection. In this regard, we performed friction experiments using a rotary shear apparatus on precut basalts with variable degree of hydrothermal alteration by injecting distilled H2O, pure CO2, and H2O + CO2 fluid mixtures under temperature, fluid pressure, and stress conditions relevant for large-scale subsurface CO2 storage reservoirs. In all experiments, seismic slip was preceded by short-lived slip bursts. Seismic slip occurred at equivalent fluid pressures and normal stresses regardless of the fluid injected and degree of alteration of basalts. Injection of fluids caused also carbonation reactions and crystallization of new dolomite grains in the basalt-hosted faults sheared in H2O + CO2 fluid mixtures. Fast mineral carbonation in the experiments might be explained by shear heating during seismic slip, evidencing the high chemical reactivity of basalts to H2O + CO2 mixtures.

From slow to fast faulting: recent challenges in earthquake fault mechanics

Faults-thin zones of highly localized shear deformation in the Earth-accommodate strain on a momentous range of dimensions (millimetres to hundreds of kilometres for major plate boundaries) and of time intervals (from fractions of seconds during earthquake slip, to years of slow, aseismic slip and millions of years of intermittent activity). Traditionally, brittle faults have been distinguished from shear zones which deform by crystal plasticity (e.g. mylonites). However such brittle/plastic distinction becomes blurred when considering (i) deep earthquakes that happen under conditions of pressure and temperature where minerals are clearly in the plastic deformation regime (a clue for seismologists over several decades) and (ii) the extreme dynamic stress drop occurring during seismic slip acceleration on faults, requiring efficient weakening mechanisms. High strain rates (more than 10⁴ s^-1) are accommodated within paper-thin layers (principal slip zone), where co-seismic frictional heating triggers non-brittle weakening mechanisms. In addition, (iii) pervasive off-fault damage is observed, introducing energy sinks which are not accounted for by traditional frictional models. These observations challenge our traditional understanding of friction (rate-and-state laws), anelastic deformation (creep and flow of crystalline materials) and the scientific consensus on fault operation.This article is part of the themed issue 'Faulting, friction and weakening: from slow to fast motion'.

Micromechanics of sea ice frictional slip from test basin scale experiments

We have conducted a series of high-resolution friction experiments on large floating saline ice floes in an environmental test basin. In these experiments, a central ice floe was pushed between two other floes, sliding along two interfacial faults. The frictional motion was predominantly stick-slip. Shear stresses, normal stresses, local strains and slip displacement were measured along the sliding faults, and acoustic emissions were monitored. High-resolution measurements during a single stick-slip cycle at several positions along the fault allowed us to identify two phases of frictional slip: a nucleation phase, where a nucleation zone begins to slip before the rest of the fault, and a propagation phase when the entire fault is slipping. This is slip-weakening behaviour. We have therefore characterized what we consider to be a key deformation mechanism in Arctic Ocean dynamics. In order to understand the micromechanics of sea ice friction, we have employed a theoretical constitutive relation (i.e. an equation for shear stress in terms of temperature, normal load, acceleration, velocity and slip displacement) derived from the physics of asperity-asperity contact and sliding (Hatton et al. 2009 Phil. Mag. 89, 2771-2799 (doi:10.1080/14786430903113769)). We find that our experimental data conform reasonably with this frictional law once slip weakening is introduced. We find that the constitutive relation follows Archard's law rather than Amontons' law, with [Formula: see text] (where τ is the shear stress and σ_n is the normal stress) and n = 26/27, with a fractal asperity distribution, where the frictional shear stress, τ = f_fractal T_mlw_s, where f_fractal is the fractal asperity height distribution, T_ml is the shear strength for frictional melting and lubrication and w_s is the slip weakening. We can therefore deduce that the interfacial faults failed in shear for these experimental conditions through processes of brittle failure of asperities in shear, and, at higher velocities, through frictional heating, localized surface melting and hydrodynamic lubrication.This article is part of the themed issue 'Microdynamics of ice'.

An empirically based steady state friction law and implications for fault stability

Empirically based rate-and-state friction laws (RSFLs) have been proposed to model the dependence of friction forces with slip and time. The relevance of the RSFL for earthquake mechanics is that few constitutive parameters define critical conditions for fault stability (i.e., critical stiffness and frictional fault behavior). However, the RSFLs were determined from experiments conducted at subseismic slip rates (V < 1 cm/s), and their extrapolation to earthquake deformation conditions (V > 0.1 m/s) remains questionable on the basis of the experimental evidence of (1) large dynamic weakening and (2) activation of particular fault lubrication processes at seismic slip rates. Here we propose a modified RSFL (MFL) based on the review of a large published and unpublished data set of rock friction experiments performed with different testing machines. The MFL, valid at steady state conditions from subseismic to seismic slip rates (0.1 µm/s < V < 3 m/s), describes the initiation of a substantial velocity weakening in the 1-20 cm/s range resulting in a critical stiffness increase that creates a peak of potential instability in that velocity regime. The MFL leads to a new definition of fault frictional stability with implications for slip event styles and relevance for models of seismic rupture nucleation, propagation, and arrest.

G: Fracture energy, friction and dissipation in earthquakes

Recent estimates of fracture energy G^' in earthquakes show a power-law dependence with slip u which can be summarized as G^' ∝ u^a where a is a positive real slightly larger than one. For cracks with sliding friction, fracture energy can be equated to G_f : the post-failure integral of the dynamic weakening curve. If the dominant dissipative process in earthquakes is friction, G^' and G_f should be comparable and show a similar scaling with slip. We test this hypothesis by analyzing experiments performed on various cohesive and non-cohesive rock types, under wet and dry conditions, with imposed deformation typical of seismic slip (normal stress of tens of MPa, target slip velocity > 1 m/s and fast accelerations ≈ 6.5 m/s²). The resulting fracture energy G_f is similar to the seismological estimates, with G_f and G^' being comparable over most of the slip range. However, G_f appears to saturate after several meters of slip, while in most of the reported earthquake sequences, G^' appears to increase further and surpasses G_f at large magnitudes. We analyze several possible causes of such discrepancy, in particular, additional off-fault damage in large natural earthquakes.

Scale dependence of rock friction at high work rate

Determination of the frictional properties of rocks is crucial for an understanding of earthquake mechanics, because most earthquakes are caused by frictional sliding along faults. Prior studies using rotary shear apparatus revealed a marked decrease in frictional strength, which can cause a large stress drop and strong shaking, with increasing slip rate and increasing work rate. (The mechanical work rate per unit area equals the product of the shear stress and the slip rate.) However, those important findings were obtained in experiments using rock specimens with dimensions of only several centimetres, which are much smaller than the dimensions of a natural fault (of the order of 1,000 metres). Here we use a large-scale biaxial friction apparatus with metre-sized rock specimens to investigate scale-dependent rock friction. The experiments show that rock friction in metre-sized rock specimens starts to decrease at a work rate that is one order of magnitude smaller than that in centimetre-sized rock specimens. Mechanical, visual and material observations suggest that slip-evolved stress heterogeneity on the fault accounts for the difference. On the basis of these observations, we propose that stress-concentrated areas exist in which frictional slip produces more wear materials (gouge) than in areas outside, resulting in further stress concentrations at these areas. Shear stress on the fault is primarily sustained by stress-concentrated areas that undergo a high work rate, so those areas should weaken rapidly and cause the macroscopic frictional strength to decrease abruptly. To verify this idea, we conducted numerical simulations assuming that local friction follows the frictional properties observed on centimetre-sized rock specimens. The simulations reproduced the macroscopic frictional properties observed on the metre-sized rock specimens. Given that localized stress concentrations commonly occur naturally, our results suggest that a natural fault may lose its strength faster than would be expected from the properties estimated from centimetre-sized rock samples.

Fast-moving dislocations trigger flash weakening in carbonate-bearing faults during earthquakes

Rupture fronts can cause fault displacement, reaching speeds up to several ms⁻¹ within a few milliseconds, at any distance away from the earthquake nucleation area. In the case of silicate-bearing rocks the abrupt slip acceleration results in melting at asperity contacts causing a large reduction in fault frictional strength (i.e., flash weakening). Flash weakening is also observed in experiments performed in carbonate-bearing rocks but evidence for melting is lacking. To unravel the micro-physical mechanisms associated with flash weakening in carbonates, experiments were conducted on pre-cut Carrara marble cylinders using a rotary shear apparatus at conditions relevant to earthquakes propagation. In the first 5 mm of slip the shear stress was reduced up to 30% and CO₂ was released. Focused ion beam, scanning and transmission electron microscopy investigations of the slipping zones reveal the presence of calcite nanograins and amorphous carbon. We interpret the CO₂ release, the formation of nanograins and amorphous carbon to be the result of a shock-like stress release associated with the migration of fast-moving dislocations. Amorphous carbon, given its low friction coefficient, is responsible for flash weakening and promotes the propagation of the seismic rupture in carbonate-bearing fault patches.

Recent advances in the understanding of fault zone internal structure: a review

It is increasingly apparent that faults are typically not discrete planes but zones of deformed rock with a complex internal structure and three-dimensional geometry. In the last decade this has led to renewed interest in the consequences of this complexity for modelling the impact of fault zones on fluid flow and mechanical behaviour of the Earth's crust. A number of processes operate during the development of fault zones, both internally and in the surrounding host rock, which may encourage or inhibit continuing fault zone growth. The complexity of the evolution of a faulted system requires changes in the rheological properties of both the fault zone and the surrounding host rock volume, both of which impact on how the fault zone evolves with increasing displacement. Models of the permeability structure of fault zones emphasize the presence of two types of fault rock components: fractured conduits parallel to the fault and granular core zone barriers to flow. New data presented in this paper on porosity–permeability relationships of fault rocks during laboratory deformation tests support recently advancing concepts which have extended these models to show that poro-mechanical approaches (e.g., critical state soil mechanics, fracture dilatancy) may be applied to predict the fluid flow behaviour of complex fault zones during the active life of the fault. Predicting the three-dimensional heterogeneity of fault zone internal structure is important in the hydrocarbon industry for evaluating the retention capacity of faults in exploration contexts and the hydraulic behaviour in production contexts. Across-fault reservoir juxtaposition or non-juxtaposition, a key property in predicting retention or across-fault leakage, is strongly controlled by the three-dimensional complexity of the fault zone. Although algorithms such as shale gouge ratio greatly help predict capillary threshold pressures, quantification of the statistical variation in fault zone composition will allow estimations of uncertainty in fault retention capacity and hence prospect reserve estimations. Permeability structure in the fault zone is an important issue because bulk fluid flow rates through or along a fault zone are dependent on permeability variations, anisotropy and tortuosity of flow paths. A possible way forward is to compare numerical flow models using statistical variations of permeability in a complex fault zone in a given sandstone/shale context with field-scale estimates of fault zone permeability. Fault zone internal structure is equally important in understanding the seismogenic behaviour of faults. Both geometric and compositional complexities can control the nucleation, propagation and arrest of earthquakes. The presence and complex distribution of different fault zone materials of contrasting velocity-weakening and velocity-strengthening properties is an important factor in controlling earthquake nucleation and whether a fault slips seismogenically or creeps steadily, as illustrated by recent studies of the San Andreas Fault. A synthesis of laboratory experiments presented in this paper shows that fault zone materials which become stronger with increasing slip rate, typically then get weaker as slip rate continues to increase to seismogenic slip rates. Thus the probability that a nucleating rupture can propagate sufficiently to generate a large earthquake depends upon its success in propagating fast enough through these materials in order to give them the required velocity kick. This propagation success is hence controlled by the relative and absolute size distributions of velocity-weakening and velocity-strengthening rocks within the fault zone. Statistical characterisation of the distribution of such contrasting properties within complex fault zones may allow for better predictive models of rupture propagation in the future and provide an additional approach to earthquake size forecasting and early warnings.