arXiv subjects

Dmitry I. Garagash

Publications and source records attributed to Dmitry I. Garagash.

8 recordsLinked to original sources

arXiv2026

Localization of fast and slow slip in fault gouge and fracture energy scaling

The localization of slow and fast slip in fault gouges may play a crucial role in understanding the mechanics of earthquakes and slow slip events. Here, we investigate the fracture energy accompanying this localization and the subsequent thermal weakening. We develop an analytical framework, complemented by numerical simulations, for a gouge governed by rate-and-state-dependent friction with flash-heating at high strain rate and thermal pressurization of pore fluids. The model captures the transition from initially distributed shearing to a co-seismic principal slip ``surface'' at slip $δ_{\mathrm{loc}} \approx γ_c h$, and yields a decomposition of the fracture energy, $G = G_\mathrm{loc}(h) + ΔG(δ)$. The minimum, localization-related component $G_\mathrm{loc}$ scales with gouge thickness $h$, which in turn scales linearly with fault size. Flash heating is activated only upon localization for fast earthquake slip, producing an abrupt strength drop, and contributing to the magnitude of $G_\mathrm{loc}$. The post-localization term $ΔG$ increases with co-seismic slip due to efficient thermal pressurization and is insensitive to $h$. Localization is predicted to occur for both rate-weakening and rate-strengthening gouges because transient state evolution drives apparent weakening after a slip-rate increase. These results unify field, laboratory, and seismological observations of shear band thickness, critical slip, and fracture-energy scaling, and they clarify why small events can be governed by scale-dependent $G_\mathrm{loc}$ whereas large ruptures become increasingly fault-invariant as $ΔG$ dominates. Our framework provides testable predictions for the relation of gouge thickness to lower bounds of co-seismic fracture energy, and the mechanics of slow-slip transients and fast earthquakes.

physics.geo-ph↗

arXiv2026

Linear and nonlinear stability of rate-and-state faults

Models of faults incorporating slip rate- and state-dependent friction have reproduced phenomena from spontaneous slow, aseismic slip to earthquake-generating dynamic rupture. Numerical explorations of model parameter space regularly show sudden transitions in behavior. However these boundaries are poorly constrained analytically, with commonly used scalings derived assuming unrepresentative conditions of uniform sliding on an infinite, homogeneous fault. In this work, we demonstrate that an analysis of linear stability can reflect model conditions. We examine two scenarios that move beyond the classical case: an asperity driven by the steady creep of its surroundings, and a finite fault experiencing a constant rate of shear loading. We identify the critical fault dimension $L_c$ at which point linear stability is lost. Beyond this linear regime, the non-linear nature of the friction law implies the loss of memory of loading conditions as instability progresses and the existence of universal solutions describing this process. We refine prior analyses of this non-linear instability and find the minimum fault size that can support self-sustaining, unstable acceleration towards dynamic rupture. We examine the role of the state evolution law and delineate conditions under which faults may be linearly stable but non-linearly unstable, requiring finitely large perturbations to trigger instability. On the basis of numerical solutions, approximate but accurate algebraic expressions for the transition boundaries are presented. These results provide means for careful model design and to delimit plausible regions of parameter space when considering physical observations of stable creep, aseismic (slow slip) or seismic transients.

physics.geo-ph↗

arXiv2025

Propagation of Elongated Fluid-Driven Fractures: Rock Toughness vs. Fluid Viscosity

This paper studies the effect of the rock fracture toughness on the propagation of elongated fluid-driven fractures. We use the `tough PKN' model of Sarvaramini and Garagash (2015), an extension of the classical PKN model(Perkins and Kern, 1961; Nordgren, 1972), which allows for a non-zero energy release rate into the advancing fracture front(s). We provide a self-consistent analysis of a `tough' elongated fracture driven by arbitrary fluid injection law under the assumption of negligible fluid leak-off. We use scaling considerations to identify the non-dimensional parameters governing the propagation regimes and their succession in time, provide a number of analytical solutions in the limiting regimes for an arbitrary power-law injection, and also posit a simplified, equation-of-motion, approach to solve a general elongated fracture propagation problem during the injection and shut-in periods. Finally, we use the developed solutions for a tough elongated fracture to surmise the relative importance of the viscous and toughness-related dissipation on the fracture dynamics and broach the implications of the possible toughness scale-dependence.

physics.geo-ph↗

arXiv2023

Fault-size dependent fracture energy explains multi-scale seismicity and cascading earthquakes

Earthquakes vary in size over many orders of magnitude, yet the scaling of the earthquake energy budget remains enigmatic. We propose that fundamentally different "small-slip" and "large-slip" fracture processes govern earthquakes. We combine seismological observations with a physics-based mechanical earthquake model under flash-heating friction. We find that dynamic weakening and restrengthening effects are non-negligible in the energy budget of small earthquakes and establish a simple linear scaling relationship between small-slip fracture energy and fault size. We use supercomputing to apply this scaling and unveil volumetric "Mode-4" earthquake cascades involving $>700$ multi-scale fractures within a fault damage zone, capable of dynamically triggering large earthquakes. Our findings provide an intuitive explanation of seismicity across all scales with important implications for comprehending earthquake nucleation and multi-fault rupture cascades.

physics.geo-ph↗

arXiv2022

Notes on Hydraulic Fracture Mechanics

These notes address the mechanics of propagating hydraulic fractures (HF). In the first part, we focus on how different physical mechanisms (dissipation in fluid and solid, fluid storage in fracture and its exchange with permeable rock, crack elasticity) manifest near the fracture tip and lead to a `zoo' of fracture propagation regimes, as correspond to the different coupling of predominant mechanisms depending on material parameters and fracture propagation speed. In the second part, we illustrate how different near-tip regimes dictate the propagation of finite fractures of simple geometries (e.g. 2D plane-strain, or 3D radial cracks) driven by fluid injection at the center of the crack. These notes are not a review of the research on the topic, which has seen tremendous renewed interest in the last 20 years or so, (for a review see, e.g., Detournay [2016]); but rather an attempt to introduce the mechanics and physics of HF in a simple and hopefully-logical way, from the fracture tip to finite fracture propagation.

physics.geo-ph↗

arXiv2022

Notes on Propagation of 3D Buoyant Fluid-Driven Cracks

Magma-driven fractures are the main mechanism for magma emplacement in the crust. A fundamental question is how the released fluid controls the propagation dynamics and fracture geometry (depth and breadth) in three dimensions. Analog experiments in gelatin have shown that fracture breadth remains nearly stationary when the process in the fracture head (where breadth is controlled) is dominated by solid toughness, whereas viscous fluid dissipation is dominant in the fracture tail. We model propagation of the resulting buoyant, finger-like fracture of stationary breadth with a slowly varying opening along the crack length. The elastic response to fluid loading in a horizontal cross-section is local and can be treated similarly to the classical Perkins-Kern-Nordgren (PKN) model of hydraulic fracturing. The propagation condition for a finger-like crack is based on balancing the global energy release rate due to a unit crack extension with the rock fracture toughness. It allows us to relate the net fluid pressure at the tip to the fracture breadth and rock toughness. Unlike laterally propagating PKN fracture, where breadth is known a priori, the final breadth of a finger-like vertically ascending fracture is a result of processes in the fracture head. Because the head is much more open than the tail, viscous pressure drop in the head can be neglected leading to a 3D analog of Weertman hydrostatic pulse. This requires relaxing the local elasticity assumption of the PKN model in the fracture head. As a result, we resolve the breadth, and then match the viscosity-dominated tail with the three dimensions, toughness-dominated head to obtain a complete closed-form solution. We then analyze the buoyancy-driven fracture propagation in conditions of either continuous injection or finite volume release for sets of parameters representative of low viscosity magma diking.

physics.geo-ph↗

arXiv2019

Stability of pulse-like earthquake ruptures

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 stress. These simulations indicate that steady-state pulses driven by thermal pressurisation are unstable. If the initial stress perturbation is negative, ruptures stop; conversely, if the perturbation is positive, ruptures grow and transition to either self-similar pulses (at low background stress) or expanding cracks (at elevated background stress). Based on a dynamic dislocation model, we develop an elastodynamic equation of motion for slip pulses, and demonstrate that steady-state slip pulses are unstable if their accrued slip $b$ is a decreasing function of the uniform background stress $τ_\mathrm{b}$. This condition is satisfied by slip pulses driven by thermal pressurisation. The equation of motion also predicts quantitatively the growth rate of perturbations, and provides a generic tool to analyse the propagation of slip pulses. The unstable character of steady-state slip pulses implies that this rupture mode is a key one determining the minimum stress conditions for sustainable ruptures along faults, i.e., their ``strength''. Furthermore, slip pulse instabilities can produce a remarkable complexity of rupture dynamics, even under uniform background stress conditions and material properties.

physics.geo-ph↗

arXiv2014

Confined flow of suspensions modeled by a frictional rheology

We investigate in detail the problem of confined pressure-driven laminar flow of neutrally buoyant non-Brownian suspensions using a frictional rheology based on the recent proposal of Boyer et al., 2011. The friction coefficient and solid volume fraction are taken as functions of the dimensionless viscous number I defined as the ratio between the fluid shear stress and the particle normal stress. We clarify the contributions of the contact and hydrodynamic interactions on the evolution of the friction coefficient between the dilute and dense regimes reducing the phenomenological constitutive description to three physical parameters. We also propose an extension of this constitutive law from the flowing regime to the fully jammed state. We obtain an analytical solution of the fully-developed flow in channel and pipe for the frictional suspension rheology. The result can be transposed to dry granular flow upon appropriate redefinition of the dimensionless number I. The predictions are in excellent agreement with available experimental results, when using the values of the constitutive parameters obtained independently from stress-controlled rheological measurements. In particular, the frictional rheology correctly predicts the transition from Poiseuille to plug flow and the associated particles migration with the increase of the entrance solid volume fraction. We numerically solve for the axial development of the flow from the inlet of the channel/pipe toward the fully-developed state. The available experimental data are in good agreement with our predictions. The solution of the axial development of the flow provides a quantitative estimation of the entrance length effect in pipe for suspensions. A analytical expression for development length is shown to encapsulate the numerical solution in the entire range of flow conditions from dilute to dense.

cond-mat.soft↗