Distributed Damage, Faulting, and Friction

Pure and Applied Geophysics, 2011

Journal of Geophysical Research, 2000

We investigate the impact of variations in the friction and geometry on models of fault dynamics. We focus primarily on a three-dimensional continuum model with scalar displacements. Slip occurs on an embedded two-dimensional planar interface. Friction is characterized by a two-parameter rate and state law, incorporating a characteristic length for weakening, a characteristic time for healing, and a velocity-weakening steady state. As the friction parameters are varied, there is a crossover from narrow, self-healing slip pulses to crack-like solutions that heal in response to edge effects. For repeated ruptures the crack-like regime exhibits periodic or aperiodic systemwide events. The self-healing regime exhibits dynamical complexity and a broad distribution of rupture areas. The behavior can also change from periodicity or quasi-periodicity to dynamical complexity as the total fault size or the length-to-width ratio is increased. Our results for the continuum model agree qualitatively with analogous results obtained for a one-dimensional Burridõe-Knopoff model in which radiation effects are approximated by viscous dissipation. context of a three-dimensional continuum model and a one-dimensional Burridge-Knopoff model. In our studies, dynamical complexity refers to observations of a

Mechanics, Structure and …, 2010

We present results on evolving geometrical and material properties of large strike-slip fault zones and associated deformation fields, using 3-D numerical simulations in a rheologically-layered model with a seismogenic upper crust governed by a continuum brittle damage framework over a viscoelastic substrate. The damage healing parameters we employ are constrained using results of test models and geophysical observations of healing along active faults. The model simulations exhibit several results that are likely to have general applicability. The fault zones form initially as complex segmented structures and evolve overall with continuing deformation toward contiguous, simpler structures. Along relatively-straight mature segments, the models produce flower structures with depth consisting of a broad damage zone in the top few kilometers of the crust and highly localized damage at depth. The flower structures form during an early evolutionary stage of the fault system (before a total offset of about 0.05 to 0.1 km has accumulated), and persist as continued deformation localizes further along narrow slip zones. The tectonic strain at seismogenic depths is concentrated along the highly damaged cores of the main fault zones, although at shallow depths a small portion of the strain is accommodated over a broader region. This broader domain corresponds to shallow damage (or compliant) zones which have been identified in several seismic and geodetic studies of active faults. The models produce releasing stepovers between fault zone segments that are locations of ongoing interseismic deformation. Material within the fault stepovers remains damaged during the entire earthquake cycle (with significantly reduced rigidity and shearwave velocity) to depths of 10 to 15 km. These persistent damage zones should be detectable by geophysical imaging studies and could have important implications for earthquake dynamics and seismic hazard.

2010

In seismically active regions, faults nucleate, propagate, and form networks that evolve over time. Progressive strain localization and periodic fault pattern re-configuration induce the accumulation and healing of fault zone damage. The damage zones are characterized by distributed fractures, veins, and secondary faults, and may act as barriers for propagating earthquake ruptures, or as nucleation sites for earthquakes. They interact with seismic waves, promoting strong surface motions during earthquakes, and can focus fluid flow and enhance mineralization. In spite of their great scientific, social, and economic significance, interactions between these evolving damage zones and crustal deformation remain unresolved. Indeed, geodynamic models generally treat active faults as surfaces embedded in a medium with nonevolving material properties.

Pure and Applied Geophysics PAGEOPH, 1986

1998

We propose a fourth-order staggered-grid finite-difference method to study dynamic faulting in three dimensions. The method uses an implementation of the boundary conditions on the fault that allows the use of general friction models including slip weakening and rate dependence. Because the staggered-grid method defines stresses and particle velocities at different grid points, we preserve symmetry by implementing a two-grid-row "thick" fault zone. Slip is computed between points located at the borders of the fault zone, while the two components of shear traction on the fault are forced to be symmetric inside the fault zone. We study the properties of the numerical method comparing our simulations with well-known properties of seismic ruptures in 3D. Among the properties that are well modeled by our method are full elastic-wave interactions, frictional instability, rupture initiation from a finite initial patch, spontaneous rupture growth at subsonic and supersonic speeds, as well as healing by either stopping phases or rate-dependent friction. We use this method for simulating spontaneous rupture propagation along an arbitrarily loaded planar fault starting from a localized asperity on circular and rectangular faults. The shape of the rupture front is close to elliptical and is systematically elongated in the inplane direction of traction drop. This elongation is due to the presence of a strong shear stress peak that moves ahead of the rupture in the in-plane direction. At high initial stresses the rupture front becomes unstable and jumps to super-shear speeds in the direction of in-plane shear. Another interesting effect is the development of relatively narrow rupture fronts due to the presence of rate-weakening friction. The solutions for the "thick fault" boundary conditions scale with the slip-weakening distance (Do) and are stable and reproducible for Do greater than about 4 in terms of 2T,//.t × Ax. Finally, a comparison of scalar and vector boundary conditions for the friction shows that slip is dominant along the direction of the prestress, with the largest deviations in slip-rate direction occurring near the rupture front and the edges of the fault.

2006

As preparation for a workshop on "The Dynamics of Fault Zones" (95 th Dahlem Workshop, Berlin, January 2005), specifically on the sub-topic "Rheology of Fault Rocks and Their Surroundings", we addressed critical research issues for understanding the seismic response of fault zones in terms of the constitutive response of fault materials. That requires new concepts and a host of new observations and experiments to document material response, to understand the shear localization process and the inception of earthquake instability, and especially to understand the mechanisms of fault weakening and dynamics of rupture tip propagation and arrest during rapid, possibly large, slip in natural events. We examine in turn the geological structure of fault zones and its relation to earthquake dynamics, the description of rate and state friction at slow rates appropriate to the interseismic period and earthquake nucleation, and the dynamics of fault weakening during rapid sl...

SIAM Journal on Applied Mathematics, 2013

An isothermal small-strain model based on the concept of generalized standard materials is devised, combining Maxwell-type rheology, damage, and perfect plasticity in the bulk. An interface analogue of the model is prescribed at the lithospheric faults, exploiting concepts of adhesive contacts with interfacial plasticity. The model covers simultaneously features such as rupturing of the fault zone accompanied with weakening/healing effects and also seismic waves emission and propagation connected with the sudden ruptures of the fault or a fluid-like aseismic response between the ruptures. A stable numerical strategy based on semi-implicit discretization in time is devised, and its convergence is shown. Numerical simulations documenting the capacity of the model to simulate earthquakes with repeating occurrence are performed, too.

arXiv (Cornell University), 2023

Understanding rock shear failure behavior is crucial to gain insights into slip-related geohazards such as rock avalanches, landslides, and earthquakes. However, descriptions of the progressive damage on the shear surface are still incomplete or ambiguous. In this study, we use the hybrid finite-discrete element method (FDEM) to simulate a shear experiment and obtain a detailed comprehension of shear induced progressive damage and the associated seismic activity. We built a laboratory fault model from high resolution surface scans and micro-CT imaging. Our results show that under quasi-static shear loading, the fault surface experiences local dynamic seismic activities. We found that the seismic activity is related to the stress concentration on interlocking asperities. This interlocking behavior (i) causes stress concentration at the region of contact that could reach the compressive strength, and (ii) produces tensile stress up to the tensile strength in the region adjacent to the contact area. Thus, different failure mechanisms and damage patterns including crushing and sub-vertical fracturing are observed on the rough surface. Asperity failure creates rapid local slips resulting in significant stress perturbations that alter the overall stress condition and may trigger the slip of adjacent critically stressed asperities. We found that the 2 spatial distribution of the damaged asperities and the seismic activity is highly heterogeneous; regions with intense asperity interactions formed gouge material, while others exhibit minimal to no damage. These results emphasize the important role of surface roughness in controlling the overall shear behavior and the local dynamic seismic activities on faults.

2000

Lapusta et al., 2000(2) have developed an efficient and rigorous numerical pro- cedure for elastodynamic analysis of earthquake sequences on slowly loaded faults. This is done for a general class of rate and state friction laws with positive direct velocity effect. We use the procedure to study the response of a 2-D strike-slip fault model with depth-variable properties. We find the fol- lowing (as partially reported by Lapusta et al., 2000(2)): Small events appear in increasing numbers for decreasing values of the characteristic slip distance of the friction law. The nucleation phase of small and large events is very similar. For a large event that is preceded by a small event (and hence hetero- geneous stress distribution), moment acceleration in the beginning of dynamic propagation exhibits "slow-downs" and subsequent "speed-ups", consistently with some observations. Insufficient time and space discretization qualita- tively changes the results. Incorporating ...