We present a minimal one-dimensional model for the transition from crack-like to pulse-like propagation of frictional rupture. In its non-dimensional form, the model depends on only two free parameters: the non-dimensional pre-stress and an elasticity ratio that accounts for the finite height of the system. The model contains stable slip pulse solutions for slip boundary conditions, and unstable slip pulse solutions for stress boundary conditions. Results demonstrate that the existence of pulse-like ruptures requires only elastic relaxation and redistribution of initial pre-stress. The novelty of our findings is that pulse-like propagation along frictional interfaces is a generic elastic feature, whose existence is not sensitive to particular rate- or slip-dependencies of dynamic friction.
Dilatancy associated with fault slip produces a transient pore pressure drop which increases frictional strength. This effect is analysed in a steadily propagating rupture model that includes frictional weakening, slip-dependent fault dilation and fluid flow. Dilatancy is shown to increase the stress intensity factor required to propagate the rupture tip. With increasing rupture speed, an undrained (strengthened) region develops near the tip and extends beyond the frictionally weakened zone. Away from the undrained region, pore fluid diffusion gradually recharges the fault and strength returns…
Pulse-like ruptures arise spontaneously in many elastodynamic rupture simulations and seem to be the dominant rupture mode along crustal faults. Pulse-like ruptures propagating under steady-state conditions can be efficiently analysed theoretically, but it remains unclear how they can arise and how they evolve if perturbed. Using thermal pressurisation as a representative constitutive law, we conduct elastodynamic simulations of pulse-like ruptures and determine the spatio-temporal evolution of slip, slip rate and pulse width perturbations induced by infinitesimal perturbations in background s…
The onset of frictional motion at the interface between two distinct bodies in contact is characterized by the propagation of dynamic rupture fronts. We combine friction experiments and numerical simulations to study the properties of these frictional rupture fronts. We extend previous analysis of slow and sub-Rayleigh rupture fronts and show that strain fields and the evolution of real contact area in the tip vicinity of supershear ruptures are well described by analytical fracture-mechanics solutions. Fracture-mechanics theory further allows us to determine long sought-after interface proper…
Frictional heat during earthquake rupture raises the pressure of fault zone fluids and affects the rupture process and its seismic radiation. Here, we investigate the role of two key parameters governing thermal-pressurization of pore fluids -- hydraulic diffusivity and shear-zone half-width -- on earthquake rupture dynamics, kinematic source properties and ground-motions. We conduct 3D strike-slip dynamic rupture simulations assuming a rate-and-state dependent friction law with strong velocity-weakening coupled to thermal-pressurization of pore fluids. Dynamic rupture evolution and ground-sha…
Potential energy stored during the inter-seismic period by tectonic loading around faults is released during earthquakes as radiated energy, heat and fracture energy. The latter is of first importance since it controls the nucleation, propagation and arrest of the seismic rupture. On one side, fracture energy estimated for natural earthquakes (breakdown work) shows a clear slip-dependence. On the other side, recent experimental studies highlighted that, fracture energy is a material property limited by an upper bound value corresponding to the fracture energy of the intact material independent…
The failure of frictional interfaces -- the process of frictional rupture -- is widely assumed to feature crack-like properties, with far-reaching implications for various disciplines, ranging from engineering tribology to earthquake physics. An important condition for the emergence of a crack-like behavior is the existence of stress drops in frictional rupture, whose basic physical origin has been recently elucidated. Here we show that for generic and realistic frictional constitutive relations, and once the necessary conditions for the emergence of an effective crack-like behavior are met, f…
The process of frictional rupture, i.e. the failure of frictional systems, abounds in the technological and natural world around us, ranging from squealing car brake pads to earthquakes along geological faults. A general framework for understanding and interpreting frictional rupture commonly involves an analogy to ordinary crack propagation, with far-reaching implications for various disciplines, from engineering tribology to geophysics. An important feature of the analogy to cracks is the existence of a reduction in the stress-bearing capacity of the ruptured interface, i.e. of a drop from t…
An elastic layer slides on a rigid flat governed by Coulomb's friction law. We demonstrate that if the coefficient of friction is high enough, the sliding localizes within stick-slip pulses, which transform into opening waves propagating at intersonic speed in the direction of sliding or, for high Poisson's ratios, at supersonic speed in the opposite direction. This sliding mode, characterized by marginal frictional dissipation, and similar to carpet fold propagation, may result in inversion of the frictional force direction; at longer time intervals the system demonstrates stick-slip behavior…
The strength and stability of frictional interfaces, ranging from tribological systems to earthquake faults, are intimately related to the underlying spatially-extended dynamics. Here we provide a comprehensive theoretical account, both analytic and numeric, of spatiotemporal interfacial dynamics in a realistic rate-and-state friction model, featuring both velocity-weakening and strengthening behaviors. Slowly extending, loading-rate dependent, creep patches undergo a linear instability at a critical nucleation size, which is nearly independent of interfacial history, initial stress conditions…
Long-term slow-slip events (LSSEs) usually occur on the deep, shallow parts of subducting plates and have substantial relation with adjacent megathrust fault motion. Conventional techniques of quantifying slow earthquake frictional features show that these features may be indicative of predictive seismic motion; however, quantifying high-accuracy uncertainty of the frictional fields has not yet been achieved. We therefore propose a method of uncertainty quantification for spatially inhomogeneous frictional features from slip motion on an LSSE fault--megathrust fault complex in southwestern Jap…
The rupture of the interface joining two materials under frictional contact controls their macroscopic sliding. Interface rupture dynamics depend markedly on the mechanical properties of the bulk materials that bound the frictional interface. When the materials are similar, recent experimental and theoretical work has shown that shear cracks described by Linear Elastic Fracture Mechanics (LEFM) quantitatively describe the rupture of frictional interfaces. When the elastic properties of the two materials are dissimilar, many new effects take place that result from bimaterial coupling: the norma…
In Stathas and Stefanou (2022) we presented the frictional response of a bounded fault gouge under largecoseismic slip. We did so by taking into account the evolution of the Principal Slip Zone (PSZ) thickness using a Cosserat micromorphic continuum model for the description of the fault's mechanical response. The numerical results obtained differ significantly from those predicted by the established model of thermal pressurization during slip on a mathematical plane (see Mase and Smith (1987); Rice (2006a); Platt et al. (2014a) among others). These differences prompt us to reconsider the basi…
Supershear Rupture Indicator in Near-fault Particle Motion
The Chinese University of Hong Kong（香港中文大学）；École Normale Supérieure, CNRS-UMR 8538, PSL Research University（巴黎高等师范学院，CNRS-UMR 8538，PSL研究大学）；Shenzhen Research Institute, The Chinese University of Hong Kong（香港中文大学深圳研究院）；Institute of Environment, Energy and Sustainability, The Chinese University of Hong Kong（香港中文大学环境、能源与可持续发展研究所）；Institute of Space and Earth Information Science, The Chinese University of Hong Kong（香港中文大学空间与地球信息科学研究所）；Bureau de Recherches Géologiques et Minières (BRGM)（法国地质与矿业研究局）
A widespread framework for understanding frictional rupture, such as earthquakes along geological faults, invokes an analogy to ordinary cracks. A distinct feature of ordinary cracks is that their near edge fields are characterized by a square root singularity, which is intimately related to the existence of strict dissipation-related lengthscale separation and edge-localized energy balance. Yet, the interrelations between the singularity order, lengthscale separation and edge-localized energy balance in frictional rupture are not fully understood, even in physical situations in which the conv…
Fluid pressure and flow in the crust is a key parameter controlling earthquake physics. Since earthquake slip is linked to spatio-temporal localisation of deformation, it is expected that the localised fluid pressure around the fault plane could potentially impact the dynamic strength of the slipping fault zone. Coseismic fluid pressure drops have been inferred from field studies, notably in gold deposits which are thought to be formed by this process, but reliable quantitative predictions are still lacking. Here, experimental results are presented where local on- and off-fault fluid pressure …
Description of the transitional process from a static to a dynamic frictional regime is a fundamental problem of modern physics. Previously we developed a model based on the well-known Frenkel-Kontorova model to describe dry macroscopic friction. Here this model has been modified to include the effect of dissipation in derived relations between the kinematic and dynamic parameters of a transition process. The main (somewhat counterintuitive) result is a demonstration that the rupture (i.e. detachment front) velocity of the slip pulse which arises during the transition does not depend on fricti…
Although our existing one-dimensional (1D) model provides a successful quantitative description of rupture events, a 1D description is somewhat limited. We therefore derive a two-dimensional (2D) model which allows us to investigate characteristics of earthquakes (EQs) and slow slip events (SSEs) that are only apparent in a second dimension. We find that the leading edge of an EQ rupture in the direction of the global shear stress (x-direction) is wider in the plane of the crustal fault (y-direction) than the trailing edge. The direction of the slip velocity is primarily in the x-direction. EQ…
We have developed a model that describes the major characteristics of a rupture, ranging from regular earthquakes (EQs) to slow slip events (SSEs), including episodic tremor and slip (ETS). Previous model predictions, while accurate, are based on a highly idealized initial stress distribution and a simple velocity-dependent expression for friction. The full scope of the model has, therefore, not been fully demonstrated. Further developments, presented here, include more physically realistic treatments of both the initial conditions and friction. Model predictions are: (1) The type of a seismic…
We compute a series of finite-source parameter inversions of the fault rupture of the 2004 Parkfield earthquake based on 1 Hz GPS records only. We confirm that some of the co-seismic slip at shallow depth (<5 km) constrained by InSAR data processing results from early post-seismic deformation. We also show 1) that if located very close to the rupture, a GPS receiver can saturate while it remains possible to estimate the ground velocity (~1.2 m/s) near the fault, 2) that GPS waveforms inversions constrain that the slip distribution at depth even when GPS monuments are not located directly above…
Spatio-temporal correlations of earthquakes are studied numerically on the basis of the one-dimensional spring-block (Burridge-Knopoff) model. As large events approach, the frequency of smaller events gradually increases, while, just before the mainshock, it is dramatically suppressed in a close vicinity of the epicenter of the upcoming mainshock, a phenomenon closely resembling the ``Mogi doughnut''
The failure of the population of micro-junctions forming the frictional interface between two solids is central to fields ranging from biomechanics to seismology. This failure is mediated by the propagation along the interface of various types of rupture fronts, covering a wide range of velocities. Among them are so-called slow fronts, which are recently discovered fronts much slower than the materials' sound speeds. Despite intense modelling activity, the mechanisms underlying slow fronts remain elusive. Here, we introduce a multi-scale model capable of reproducing both the transition from fa…
We have developed different network approaches to complex patterns of frictional interfaces (contact areas developments). Here, we analyze the dynamics of static friction. We found, under the correlation measure, the fraction of triangles correlates with the detachment fronts. Also, for all types of the loops (such as triangles), there is a universal power law between nodes' degree and motifs where motifs frequency follow a power law. This shows high energy localization is characterized by fast variation of the loops fraction. Also, this proves that the congestion of loops occurs around hubs. …
Self-Arresting and Runaway Earthquakes:Nucleation, Propagation, Gutenberg-Richter law and Dragon-King Events
Institute of Risk Analysis, Prediction and Management (Risks-X), Academy for Advanced Interdisciplinary Sciences, Southern University of Science and Technology（南方科技大学前沿交叉科学研究院风险分析与预测管理研究所）；Department of Earth and Space Sciences, Southern University of Science and Technology（南方科技大学地球与空间科学系）；School of Earth and Space Science and Technology, Wuhan University（武汉大学地球与空间科学技术学院）
In this paper, we study the role of thermal pressurization in the frictional response of a fault under large coseismic slip. We investigate the role of the seismic slip velocity, mixture compressibility, characteristic grain size and viscosity parameter in the frictional response of the coupled thermo-hydro-mechanical problem, taking into account the fault's microstructure. Starting from the mass, energy and momentum balance for Cosserat continua we derive the equations of our model. We complete the mathematical description using perfect plasticity and Perzyna viscoplasticity in the material c…
Physics-informed deep learning links geodetic data and fault friction
Stanford University（斯坦福大学）；Disaster Prevention Research Institute, Kyoto University（京都大学防灾研究所）；Japan Agency for Marine-Earth Science and Technology（日本海洋地球科学技术机构）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Kagawa University（香川大学）；Graduate School of Science, Kyoto University（京都大学理学研究科）
The surface morphology of faults controls the spatial anisotropy of their frictional properties, and hence their mechanical stability. Such anisotropy is only rarely studied in seismology models of fault slip, although it might be paramount to understand the seismic rupture in particular areas, notably where slip occurs in a direction different from that of the main striations of the fault. To quantify how the anisotropy of fault surfaces affects the friction coefficient during sliding, we sheared synthetic fault planes made of plaster of Paris. These fault planes were produced by 3D-printing …
The onset of frictional sliding between contacting bodies under shear load is nucleated by the quasi-static growth of localized slip patches. After reaching a certain critical size, these patches become unstable and continue growing dynamically, eventually causing the sliding of the entire interface. Two different theories have been used to compute the nucleation length of such patches depending on the dominant process driving their growth. If it is only the yielding of contact asperities (large-scale yielding), a stress criterion is applied, based on linear stability analysis, whereas if frac…
Numerous laboratory experiments have demonstrated the dependence of the friction coefficient on the interfacial slip rate and the contact history, a behavior generically called rate and state friction. Although numerical models have been widely used for analyzing rate and state friction, in general they consider infinite elastic domains surrounding the sliding interface and rely on boundary integral formulations. Much less work has been dedicated to modeling finite size systems to account for interactions with boundaries. This paper investigates rate and state frictional interfaces in the cont…
Frictional interfaces are abundant in natural and manmade systems and their dynamics still pose challenges of fundamental and technological importance. A recent extensive compilation of multiple-source experimental data has revealed that velocity-strengthening friction, where the steady-state frictional resistance increases with sliding velocity over some range, is a generic feature of such interfaces. Moreover, velocity-strengthening friction has very recently been linked to slow laboratory earthquakes and stick-slip motion. Here we elucidate the importance of velocity-strengthening friction …
In subduction zones, seismic slip at shallow crustal depths can lead to the generation of tsunamis. Large slip displacements during tsunamogenic earthquakes are attributed to the low coseismic shear strength of the fluid-saturated and non-lithified clay-rich fault rocks. However, because of experimental challenges in confining these materials, the physical processes responsible of the coseismic reduction in fault shear strength are poorly understood. Using a novel experimental setup, we measured pore fluid pressure during simulated seismic slip in clay-rich materials sampled from the deep ocea…
The spontaneous nucleation of accelerating slip along slowly driven frictional interfaces is central to a broad range of geophysical, physical and engineering systems, with particularly far-reaching implications for earthquake physics. A common approach to this problem associates nucleation with an instability of an expanding creep patch upon surpassing a critical length $L_c$. The critical nucleation length $L_c$ is conventionally obtained from a spring-block linear stability analysis extended to interfaces separating elastically-deformable bodies using model-dependent fracture mechanics esti…
We monitor dynamic rupture propagation during laboratory stick-slip experiments performed on saw-cut Westerly granite under upper crustal conditions (10-90 MPa). Spectral analysis of high-frequency acoustic waveforms provided evidence that energy radiation is enhanced with stress conditions and rupture velocity. Using acoustic recordings bandpass filtered to 400-800 kHz (7-14 mm wavelength) and highpass filtered above 800 kHz, we back projected high-frequency energy generated during rupture propagation. Our results show that the high-frequency radiation originates behind the rupture front duri…
The shear strength and stick-slip behavior of a rough rock joint are analyzed using the complex network approach. We develop a network approach on correlation patterns of void spaces of an evolvable rough fracture (crack type II). Correlation among networks properties with the hydro -mechanical attributes (obtained from experimental tests) of fracture before and after slip is the direct result of the revealed non-contacts networks. Joint distribution of locally and globally filtered correlation gives a close relation to the contact zones attachment-detachment sequences through the evolution of…
