Damage Rheology Research Articles

Plume‐Driven Subduction Termination in 3‐D Mantle Convection Models

AbstractThe effect of mantle plumes is secondary to that of subducting slabs for modern plate tectonics when considering plate driving forces. However, the impact of plumes on tectonics and planetary surface evolution may nonetheless have been significant. We use numerical mantle convection models in a 3‐D spherical chunk geometry with damage rheology to study some of the dynamics of plume‐slab interactions. Substantiating our earlier 2‐D results, we observe a range of interaction scenarios, and that the plume‐driven subduction terminations we had identified earlier persist in more realistic convective flow. We analyze the dynamics of plume affected subduction, including in terms of their geometry, frequency, and the overall effect of plumes on surface dynamics as a function of the fraction of internal to bottom heating. Some versions of such plume‐slab interplay may be relevant for geologic events, for example, for the inferred ∼183 Ma Karoo large igneous province formation and associated slab disruption. More recent examples may include the impingement of the Afar plume underneath Africa leading to disruption of the Hellenic slab, and the current complex structure imaged for the subduction of the Nazca plate under South America. Our results imply that plumes may play a significant role not just in kick‐starting plate tectonics, but also in major modifications of slab‐driven plate motions, including for the present‐day mantle.

Uplift and subsidence at the periphery of the Lebanese Restraining Bend, Northern Dead Sea Fault

Bends and stepovers in strike-slip fault systems along active plate boundaries are widespread and introduce stress heterogeneities, affecting the regional strain field. The strain field associated with these complex fault structures has been extensively studied. Asymmetric uplift of the Lebanon Mountains, located at the fringe of an active plate boundary, the Dead Sea Fault system (DSF), together with subsidence of the Lower Galilee in northern Israel provides an exceptional example of the complex deformational pattern associated with a restraining bend. The deformation field with respect to the restraining bend is expressed by the asymmetric uplift of the Lebanon Mountains, west of the DSF. This asymmetry along with the subsidence of the Lower Galilee, an extensional region in northern Israel, could not be explained only by the impact of the restraining bend, ignoring additional regional tectonic features. We present the results of 3-D numerical modeling of the distributed deformation, utilizing damage rheology for brittle rock deformation of the seismogenic crust overlaying viscoelastic mantle. We use available geological and regional seismicity data to implement the realistic lithosphere structure and to delineate the major faults in the model as localized weak zones. The modeling results highlight the impact of several factors on the spatial distribution of crustal deformation, demonstrated by running different model scenarios. These scenarios allow us to isolate the impact of each tectonic element and show the strain pattern resulting from their superposition, starting with a restraining bend acting in a homogeneous layered crust. Our modeling results suggest that the extension observed in the Lower Galilee region and the asymmetric uplifted pattern west of the Lebanese Restraining Bend is the outcome of three interacting factors, which are the sinistral strike-slip motion along the Lebanese Restraining Bend, the significant variations in the crustal structure (depth to Moho), and the slow extension of the Irbid-Azraq rift zone.

A creep model coupling moisture and mechanical damage for water-bearing concrete

The influence of moisture content and overstress on the creep of concrete was investigated from the perspective of damage rheology theory. The weakening effects of moisture and overstress were characterized by a time-independent and a time-dependent damage functions, respectively, and then combined and applied to a modified creep model that can represent the elasto-visco-plastic creep deformation of concrete. Hence, a damage creep model is proposed to describe the creep behavior of water-bearing concrete. Theoretical and statistical analyses, as well as a comparison with the ACI-209 model were performed to examine the validity and superiority of the proposed model. Further analyses showed that not only the deformation parameters, but also the long-term strength parameters degraded with time and increasing moisture. Experiments were then conducted on saturated cement mortar with different static moisture holding durations to investigate the time correlation of moisture-induced damage on the mechanical properties of the material. The experimental results proved that moisture-induced damage was independent of time.

A new anisotropic poroelasticity model to describe damage accumulation during cyclic triaxial loading of rock

SUMMARY Crustal rocks undergo repeated cycles of stress over time. In complex tectonic environments where stresses may evolve both spatially and temporally, such as volcanoes or active fault zones, these rocks may experience not only cyclic loading and unloading, but also rotation and/or reorientation of stresses. In such situations, any resulting crack distributions form sequentially and may therefore be highly anisotropic. Thus, the tectonic history of the crust as recorded in deformed rocks may include evidence for complex stress paths, encompassing different magnitudes and orientations. Despite this, the ways in which variations in principal stresses influence the evolution of anisotropic crack distributions remain poorly constrained. In this work, we build on the previous non-linear anisotropic damage rheology model by presenting a newly developed poroelastic rheological model which accounts for both coupled anisotropic damage and porosity evolution. The new model shares the main features of previously developed anisotropic damage and scalar poroelastic damage models, including the ability to simulate the entire yield curve through a single formulation. In the new model, the yield condition is defined in terms of invariants of the strain tensor, and so the new formulation operates with directional yield conditions (different values for each principal direction) depending on the damage tensor and triaxial loading conditions. This allows us to discern evolving yield conditions for each principal stress direction and fit the measured amounts of accumulated damage from previous loading cycles. Coupling between anisotropic damage and anisotropic compaction along with the damage-dependent yield condition produces a reasonable fit to the experimentally obtained stress–strain curves. Furthermore, the simulated time-dependent cumulative damage is well correlated with experimentally observed acoustic emissions during cyclic loading in different directions. As such, we are able to recreate many of the features of the experimentally observed directional 3-D Kaiser ‘damage memory’ effect.

Runaway Versus Stable Fracturing During Hydraulic Stimulation: Insights from the Damage Rheology Modeling

Injection-induced seismicity might have unexpectedly large earthquake magnitudes. The rate of occurrence of seismic events is controlled by natural factors such as stress field and rock properties, as well as by operational factors such as injection pressure. Two faulting modes induced by fluid injection are considered: stable pressure controlled, in which the rupture is constrained to the high pore pressure locations and seismicity propagates away from the injection well as a diffusional front; and runaway mode, in which the rupture propagates beyond the high pore pressure zone and produces high-magnitude earthquakes. In this study, we simulate the injection-induced seismicity using a poro-elastic damage rheology model and determine the setups that lead to stable and unstable conditions. The value of the damage–permeability coupling parameter, which controls the increase of permeability with damage, has a major effect on the stability of the stimulated process. The role of injection pressure is also shown here to control the rate and stability of seismicity growth. The model is unique in its ability to spontaneously branch fractures in conjugate directions. At low injection pressures and weak permeability–damage coupling, branching occurs, and segments gradually grow in the two conjugate directions. Under higher injection pressure and strong permeability–damage coupling, active branching causes unstable segments that rapidly grow and produce hazardous conditions. Activation of pre-existing faults is also shown to be unsafe when the fault is optimally oriented with respect to the stress field. If the pre-existing faults are in other orientations, they may decrease the seismic hazard and even stabilize the system.

Borehole breakout modeling in arkose and granite rocks

The existence of a deep borehole in the Earth’s crust disturbs the local stresses and creates a stress concentration that may result in breakout and damage to the borehole. Maintaining wellbore integrity mitigates environmental impacts such as groundwater contamination, gas leakage to the atmosphere, and fluid spills and seepage at the surface. In this paper, the stability of deep boreholes (5 km) is examined by laboratory experiments and numerical models in the context of nuclear waste disposal in Israel. Two rock types in southern Israel are considered: the crystalline basement (granite) and the Zenifim Formation (arkose). A series of room-temperature triaxial rock deformation experiments were conducted at different confining pressures. This mechanical characterization was then used to parameterize the elastic properties and damage behavior of the rocks. This facilitated modeling the stability of the deep boreholes by two different formulations of damage rheology: a dynamic-oriented formulation used to model deformation immediately after the creation of the open hole and a quasi-static formulation used to model longer stress corrosion regime. The calibrated modeling results indicate greater stability with Zenifim arkose than the crystalline granite for deep borehole conditions despite the granite having a greater triaxial compressive strength. Dissipation associated with dilation and porous compaction in the arkose during deformation plays a significant stabilizing role in the borehole compared to crystalline rocks. These results suggest that common strength-based borehole stability assessment may lead to inaccurate predictions. Three-dimensional modeling of bottom-hole stress conditions and the effects of transient borehole geometry show conventional two-dimensional analysis may not be conservative when predicting borehole damage.

Non-linear anisotropic damage rheology model: Theory and experimental verification

We extend the isotropic non-linear damage rheology model with a scalar damage parameter to a more complex formulation that accounts for anisotropic damage growth under true triaxial loading. The model takes account of both the anisotropy of elastic properties (associated with textural rock structure) and the stress- and damage-induced anisotropy (associated with loading). The scalar, isotropic model is modified by assuming orthotropic symmetry and introducing a second-order damage tensor, the principal values of which describe damage in three orthogonal directions associated with the orientations of the principal loading axes. Different damage components, accumulated under true triaxial loading conditions, allows us to reproduce both stress-strain curves and damage- and stress-induced seismic wave velocity anisotropy. The suggested model generalization includes a non-classical energy term similar to the isotropic non-linear scalar damage model, which allows accounting for the abrupt change in the effective elastic moduli upon stress reversal.For calibration and verification of the model parameters, we use experimental stress-strain curves from deformation of dry sandstone under both conventional and true triaxial stress conditions. Cubic samples were deformed in three orthogonal directions with independently controlled stress paths. To characterize crack damage, changes in ultrasonic P-wave velocities in the three principal directions were measured, together with the bulk acoustic emission output. The parameters of the developed model were constrained using the conventional triaxial test data, and provided good fits to the stress-strain curves and P-wave velocity variations in the three orthogonal directions. Numerical simulation of the true triaxial test data demonstrates that the anisotropic damage rheology model adequately describes both non-linear stress-strain behavior and P-wave velocity variations in the tested Darley Dale sandstone.

Relating strain localization and Kaiser effect to yield surface evolution in brittle rocks

SUMMARY The yield surfaces of rocks keep evolving beyond the initial yield stress owing to the damage accumulation and porosity change during brittle deformation. Using a poroelastic damage rheology model, we demonstrate that the measure of coupling between the yield surface change and accumulated damage is correlated with strain localization and the Kaiser effect. Constant or minor yield surface change is associated with strong strain localization, as seen in low-porosity crystalline rocks. In contrast, strong coupling between damage growth and the yield surface leads to distributed deformation, as seen in high-porosity rocks. Assuming that during brittle deformation damage occurs primarily in the form of microcracks, we propose that the measured acoustic emission (AE) in rock samples correlates with the damage accumulation. This allows quantifying the Kaiser effect under cyclic loading by matching between the onset of AE and the onset of damage growth. The ratio of the stress at the onset of AE to the peak stress of the previous loading cycle, or Felicity Ratio (FR), is calculated for different model parameters. The results of the simulation show that FR gradually decreases in the case of weak coupling between yield surface and damage growth. For a strong damage-related coupling promoting significant yield surface change, the FR remains close to one and decreases only towards the failure. The model predicts that a steep decrease in FR is associated with a transition between distributed and localized modes of failure. By linking the evolving yield surface to strain localization patterns and the Kaiser effect, the poroelastic damage rheology model provides a new quantitative tool to study failure modes of brittle rocks.

Multiphysics Modeling of a Brittle‐Ductile Lithosphere: 2. Semi‐brittle, Semi‐ductile Deformation and Damage Rheology

AbstractThe brittle‐ductile transition is a domain of finite extent characterized by high differential stress where both brittle and ductile deformation are likely to occur. Understanding its depth location, extent, and stability through time is of relevance for diverse applications including subduction dynamics, mantle‐surface interactions, and, more recently, proper targeting of high‐enthalpy unconventional geothermal resources, where local thermal conditions may activate ductile creep at shallower depths than expected. In this contribution, we describe a thermodynamically consistent physical framework and its numerical implementation, therefore extending the formulation of the companion paper Jacquey and Cacace (2020, https://doi.org/10.1029/2019JB018474) to model thermo‐hydro‐mechanical coupled processes responsible for the occurrence of transitional semi‐brittle, semi‐ductile behavior in porous rocks. We make use of a damage rheology to account for the macroscopic effects of microstructural processes leading to brittle‐like material weakening and of a rate‐dependent plastic model to account for ductile material behavior. Our formulation additionally considers the role of porosity and its evolution during loading in controlling the volumetric mechanical response of a stressed rock. By means of dedicated applications, we discuss how our damage poro‐visco‐elasto‐viscoplastic rheology can effectively reconcile the style of localized deformation under different confining pressure conditions as well as the bulk macroscopic material response as recorded by laboratory experiments under full triaxial conditions.

InSAR Measurements and Viscoelastic Modeling of Sinkhole Precursory Subsidence: Implications for Sinkhole Formation, Early Warning, and Sediment Properties

AbstractDuring the past three decades, thousands of sinkholes were formed along the Dead Sea (DS) shorelines in Israel and Jordan, due to dissolution of subsurface salt by undersaturated groundwater. The sinkholes are associated with gradual subsidence preceding their collapse by periods ranging from a few days to almost 5 years. To determine the factors controlling this precursory subsidence, we examine tens of subsidence‐sinkhole sequences along the DS shorelines in Israel. The duration and magnitude of the precursory subsidence are determined by Interferometric Synthetic Aperture Radar (InSAR) measurements and simulated by viscoelastic damage rheology models. Longer periods of precursory subsidence are found in the cemented alluvial fans and in simulations of higher‐viscosity sediments. While surface subsidence accelerates during the precursory period, the widths of the subsiding areas remain uniform, suggesting that during this period upward propagation of damage from the subsurface cavity is not accompanied by upward migration of the actual cavity. Our observations and simulations are used to constrain the viscosity of the sediments along the DS and to reduce sinkhole hazards by assessing the precursory times of future sinkholes in the different sedimentary environments.

Shear-induced porosity bands in a compacting porous medium with damage rheology

Shear-induced porosity bands have been observed experimentally and have been the subject of a number of theoretical and numerical analyses in which a number of rheological laws governing the partial melt system have been proposed. These bands have been suggested to be important in Earth’s interior in focussing melt to Earth’s mid-ocean ridges, in reducing the effective viscosity of the asthenosphere, and in affecting seismic and electrical properties. Recently, a linear analysis of the formation of melt bands has been presented in which the viscosity of the solid matrix depends on the grain size and a parameter characterizing the roughness of the grain-liquid interface For some parameter values, this “damage” rheology mimics the effect of very strongly strain-rate dependent viscosity which can produce low angle bands, similar to those seen in experiments. In the present paper, I show full nonlinear simulations of melt bands with damage rheology. In agreement with the linear analysis, low angle bands are possible when the grain size and grain roughness evolve rapidly compared with the deformation of the sample. The grain size field evolves to form bands where grain-size anticorrelates with porosity. The effective viscosity and electrical conductivity of bands are also investigated. For low angle bands, the effective viscosity relative to the mean viscosity decreases and the electrical conductivity anisotropy increases with strain, indicating significant strain and electrical conduction localization.

Dynamic Ruptures on a Frictional Interface with Off-Fault Brittle Damage: Feedback Mechanisms and Effects on Slip and Near-Fault Motion

The spontaneous generation of brittle rock damage near and behind the tip of a propagating rupture can produce dynamic feedback mechanisms that modify significantly the rupture properties, seismic radiation, and generated fault zone structure. In this work, we study such feedback mechanisms for single rupture events and their consequences for earthquake physics and various possible observations. This is done through numerical simulations of in-plane dynamic ruptures on a frictional fault with bulk behavior governed by a brittle damage rheology that incorporates reduction of elastic moduli in off-fault yielding regions. The model simulations produce several features that modify key properties of the ruptures, local wave propagation, and fault zone damage. These include (1) dynamic generation of near-fault regions with lower elastic properties, (2) dynamic changes of normal stress on the fault, (3) rupture transition from crack-like to a detached pulse, (4) emergence of a rupture mode consisting of a train of pulses, (5) quasi-periodic modulation of slip rate on the fault, and (6) asymmetric near-fault ground motion with higher amplitude and longer duration on the side with reduced elastic moduli. The results can have significant implications to multiple topics ranging from rupture directivity and local amplification of seismic motion to near-fault tremor-like signals.

A damage rheology model applied to analysis of splitting failure in underground caverns of Jinping I hydropower station

The dominant geological features of southwest China are high mountains with deep, steep slope valleys. Typically engineering projects constructed in these mountain areas have significant overburden depth with associated high in-situ stresses. Characteristic rheological phenomena in the surrounding rock mass produced by these conditions are observed during, and often after excavation of the underground caverns for a hydropower station. This paper describes one such project, the excavation of the Jinping I hydropower Station, located in Sichuan Province. Other than the rheological characteristics, spalling, splitting (observed in local sections), bending and heaving are prominent in the surrounding rock mass of these underground caverns during and after excavation. Coupled damage and rheology models were adopted in numerical analysis for stability evaluation. In addition, a splitting failure criterion and a prediction method for incremental deformation due to crack opening were incorporated in the analysis to estimate the splitting failure zones in the rock surrounding the underground caverns produced by excavation stress release. A block model test was carried out to formulate a method to estimate the incremental deformation due to the opening of cracks. Subsequently, the results were employed to modify the displacements obtained by the damage rheology model. Finally, the displacements, stresses and damage zones in the surrounding rock mass of the underground caverns for the project were predicted and analyzed. The computation results presented herein were found to compare favorably with measurements obtained from the field monitoring.

Fault Wear by Damage Evolution During Steady-State Slip

Slip along faults generates wear products such as gouge layers and cataclasite zones that range in thickness from sub-millimeter to tens of meters. The properties of these zones apparently control fault strength and slip stability. Here we present a new model of wear in a three-body configuration that utilizes the damage rheology approach and considers the process as a microfracturing or damage front propagating from the gouge zone into the solid rock. The derivations for steady-state conditions lead to a scaling relation for the damage front velocity considered as the wear-rate. The model predicts that the wear-rate is a function of the shear-stress and may vanish when the shear-stress drops below the microfracturing strength of the fault host rock. The simulated results successfully fit the measured friction and wear during shear experiments along faults made of carbonate and tonalite. The model is also valid for relatively large confining pressures, small damage-induced change of the bulk modulus and significant degradation of the shear modulus, which are assumed for seismogenic zones of earthquake faults. The presented formulation indicates that wear dynamics in brittle materials in general and in natural faults in particular can be understood by the concept of a “propagating damage front” and the evolution of a third-body layer.

Numerical modelling of post-seismic rupture propagation after the Sumatra 26.12.2004 earthquake constrained by GRACE gravity data

In the last decades, the development of the surface and satellite geodetic and geophysical observations brought a new insights into the seismic cycle, documenting new features of inter-, co-, and post-seismic processes. In particular since 2002 satellite mission GRACE provides monthly models of the global gravity field with unprecedented accuracy showing temporal variations of the Earth's gravity field, including those caused by mass redistribution associated with earthquake processes. When combined with GPS measurements, these new data have allowed to assess the relative importance of afterslip and viscoelastic relaxation after the Sumatra 26.12.2004 earthquake. Indeed the observed post-seismic crustal displacements were fitted well by a viscoelastic relaxation model assuming Burgers body rheology for the asthenosphere (60–220 km deep) with a transient viscosity as low as 4 × 10^17 Pas and constant ~ 10^19 Pas steady state viscosity in the 60–660-km depth range. However, even the low-viscosity asthenosphere provides the amplitude of strain which gravity effect does not exceed 50 per cent of the GRACE gravity variations, thus additional localized slip of about 1 m was suggested at downdip extension of the coseismic rupture. Post-seismic slip at coseismic rupture or its downdip extension has been suggested by several authors but the mechanism of the post-seismic fault propagation has never been investigated numerically. Depth and size of localized slip area as well as rate and time decay during the post-seismic stage were either assigned a priory or estimated by fitting real geodesy or gravity data. In this paper we investigate post-seismic rupture propagation by modelling two consequent stages. First, we run a long-term, geodynamic simulation to self-consistently produce the initial stress and temperature distribution. At the second stage, we simulate a seismic cycle using results of the first step as initial conditions. The second short-term simulation involves three substeps, including additional stress accumulation after part of the subduction channel was locked; spontaneous coseismic slip; formation and development of damage zones producing afterslip. During the last substep post-seismic stress leads to gradual ~1 m slip localized at three faults around ~100-km downdip extension of the coseismic rupture. We used the displacement field caused by the slip to calculate pressure and density variations and to simulate gravity field variations. Wavelength of calculated gravity anomaly fits well to that of the real data and its amplitude provides about 60 per cent of the observed GRACE anomaly. Importantly, the surface displacements caused by the estimated afterslip are much smaller than those registered by GPS networks. As a result cumulative effect of Burgers rheology viscoelastic relaxation (which explains measured GPS displacements and about a half of gravity variations) plus post-seismic slip predicted by damage rheology model (which causes much smaller surface displacements but provides another half of the GRACE gravity variations) fits well to both sets of the real data. Hence, the presented numerical modelling based on damage rheology supports the process of post-seismic downdip rupture propagation previously hypothesized from the GRACE gravity data.

Damage and plastic deformation of reservoir rocks: Part 1. Damage fracturing

In this series of studies, we develop a numerical tool for modeling finite deformation of reservoir rocks. We present an attempt to eliminate the main limitations of idealized methods, for example, elastic or kinematic, that cannot account for the complexity of rock deformation. Our approach is to use rock mechanics experimental data and finite element models (Abaqus). To generate realistic simulations, the present numerical rheology incorporates the dominant documented deformation modes of rocks: (1) rock mechanics experimental observations, including finite strength, inelastic strain hardening, strength dependence on confining pressure, strain-induced dilation, pervasive and localized damage, and local tensile or shear failure without macroscopic disintegration; and (2) field observations, including large deformation, distributed damage, complex fracture networks, and multiple zones of failure. Our analysis starts with an elastic–plastic damage rheology that includes pressure-dependent yield criteria, stiffness degradation, and fracturing via a continuum damage approach, using the Abaqus materials library. We then use experimental results for Berea Sandstone in two configurations, four-point beam and dog-bone triaxial, to refine and calibrate the rheology. We find that damage and fracturing patterns generated in the numerical models match the experimental features well, and based on these observations, we define damage fracturing, the fracturing process by damage propagation in a rock with elastic–plastic damage rheology. In part 2, we apply this rheology to investigate fracture propagation at the tip of a hydrofracture.

Damage and plastic deformation of reservoir rocks: Part 2. Propagation of a hydraulic fracture

The aim of part 2 is to understand the development of complex hydraulic fractures (HFs) that are commonly observed in the field and in experiments but are not explained by most models. Our approach uses finite element simulations and a numerical rheology developed in part 1 to model damage fracturing, the fracturing process by damage propagation in a rock with elastic–plastic damage rheology. Using this rheology and a dynamic solution technique, we investigate the effect of far-field stresses and pressure distribution in the fracture on the geometric complexity of the fractures. The model is for the vertical propagation of an HF segment into an overlying bed located far from borehole effects. The layer is 2.3 m (7.5 ft) tall, has elastic–plastic damage rheology, and contains a 0.3-m (1-ft)–tall initial vertical fracture. Vertical and horizontal tectonic loads of 50 MPa (7252 psi) and 10 to 45 MPa (1450–6527 psi) are established, and then an internal fracture pressure of 10 MPa/s (1450 psi/s) is applied until the layer fails. The simulated fracturing is sensitive to the stress state and generated patterns range from single straight fractures to treelike networks. Reducing differential stress increases the injection pressure required to fracture and promotes off-plane damage, which increases fracture complexity. Consecutive periods of nonuniform weakening followed by unstable rupture generate multiple branches and segments. We find that the processes that form HF complexity occur under a range of in-situ reservoir conditions and are likely to contribute to complex far-field fracture geometry and enhanced network connectivity.

Viscoelastic damage modeling of sinkhole formation

The sinkholes along the Dead Sea coast are observed in two main sedimentary environments: alluvial fan sinkholes, which usually form abruptly as deep (∼20 m) and narrow (∼3 m) sinkholes, and mud-flat sinkholes, which usually form as shallow (a few centimeters) and wide (>5 m) sinkholes and deepen later. The mechanical collapse of all sinkholes is triggered by cavities created by the dissolution of an underlying salt layer by relatively fresh groundwater. The processes attributed to the mechanical formation of the sinkholes are viscous flow and brittle fracture failure. We use a two-dimensional viscoelastic damage rheology numerical model to quantitatively explain the brittle and ductile aspects of collapsed sinkholes. Three cases of the rheology of the collapsed sediments are simulated, 1) damage controlled failure, 2) viscoelastic controlled failure, and 3) an intermediate damage-viscoelastic case. Results show that viscoelasticity cannot be the sole process acting on the deformed layer because all sinkholes are characterized by sharp boundaries. The damage accumulation progresses until arched cavities are created in the soil layer. Because of the geometric heterogeneity of the layer (represented by the heterogeneity of the mesh) smaller blocks continue to fall after the first breakup into the cavity, advancing the arched cavity upwards. This propagation finally stops when the cavity is shallow enough to hold the irregular arch. The combination of these two processes creates competition within the stress reduction mechanism that may lead to either magnified or reduced deformation. The deformation is magnified in high shear stress locations, where the dispersion of the viscous flow spreads damage failure, and it is reduced in low shear stress locations where viscous flow disperses shear stress before the onset of damage.

Shear Band Formation in Numerical Simulations Applying a Continuum Damage Rheology Model

In seismically active regions, faults nucleate, propagate, and form networks that evolve over time. To simulate crustal faulting processes, including the evolution of fault-zone properties, a rheological model must incorporate concepts such as damage rheology that describe the various stages of the seismic cycle (strain localization, subcritical crack growth and macroscopic failure) while accounting for material degradation and healing and off-fault deformation. Here we study the fundamental patterns of strain-localisation within the framework of a continuum damage rheology by performing a shear band analysis (linear instability analysis) and comparing predictions of shear band orientations with numerical results of the nonlinear problem. We find (analytically and numerically) that the angle between the shear band and the less compressive (transverse) direction is between 47° in compression tests with a strain ratio of 0.25 (highly confined compression test), and 60° for a strain ratio higher than 1.4 (axial compression and transverse extension). In addition we find that shear bands exhibit local dilation (I1 > 0) in a wide range of strain ratios excluding only simulations with highly confined compression (which yield compacting shear bands or non-localized deformation). Finally, we discuss the applicability of the damage model for simulating deformation in the seismogenic, brittle crust.

Deformation and seismicity associated with continental rift zones propagating toward continental margins

We study the propagation of a continental rift and its interaction with a continental margin utilizing a 3‐D lithospheric model with a seismogenic crust governed by a damage rheology. A long‐standing problem in rift‐mechanics, known as thetectonic force paradox, is that the magnitude of the tectonic forces required for rifting are not large enough in the absence of basaltic magmatism. Our modeling results demonstrate that under moderate rift‐driving tectonic forces the rift propagation is feasible even in the absence of magmatism. This is due to gradual weakening and “long‐term memory” of fractured rocks that lead to a significantly lower yielding stress than that of the surrounding intact rocks. We show that the style, rate and the associated seismicity pattern of the rift zone formation in the continental lithosphere depend not only on the applied tectonic forces, but also on the rate of healing. Accounting for the memory effect provides a feasible solution for thetectonic force paradox. Our modeling results also demonstrate how the lithosphere structure affects the geometry of the propagating rift system toward a continental margin. Thinning of the crystalline crust leads to a decrease in the propagation rate and possibly to rift termination across the margin. In such a case, a new fault system is created perpendicular to the direction of the rift propagation. These results reveal that the local lithosphere structure is one of the key factors controlling the geometry of the evolving rift system and seismicity pattern.