Visco‐poroelastic damage model for brittle‐ductile failure of porous rocks

Lyakhovsky, Vladimir; Zhu, Wenlu; Shalev, Eyal

doi:10.1002/2014jb011805

Cited by 49 publications

(39 citation statements)

References 82 publications

(151 reference statements)

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“…Previous numerical studies on brittle‐ductile transition have successfully developed macroscopic phenomenological models, in particular, cap plasticity models, to replicate the brittle‐ductile behavior at the continuum scale [ Sun et al , ; Lyakhovsky et al , ]. Nevertheless, since the brittle‐ductile transition is originated from a combination of microstructural deformation mechanisms of discrete natures (e.g., crushing and rolling of particles), discrete models, such as the lattice spring model [ Katsman et al , ] and the discrete element method [ Cundall and Strack , ], may shed light on connecting the macroscopic mechanical responses to the microstructural origins.…”

Section: Dem Model For Bonded Cohesive‐frictional Materialsmentioning

confidence: 99%

Micropolar effect on the cataclastic flow and brittle‐ductile transition in high‐porosity rocks

2016

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A micromechanical distinct element method (DEM) model is adopted to analyze the grain‐scale mechanism that leads to the brittle‐ductile transition in cohesive‐frictional materials. The cohesive‐frictional materials are idealized as particulate assemblies of circular disks. While the frictional sliding of disks is sensitive to the normal compressive stress exerted on contacts, normal force can be both caused by interpenetration and long‐range cohesive bonding between two particles. Our numerical simulations indicate that the proposed DEM model is able to replicate the gradual shift of porosity change from dilation to compaction and failure pattern from localized failures to cataclastic flow upon rising confining pressure in 2‐D biaxial tests. More importantly, the micropolar effect is examined by tracking couple stress and microcrack initiation to interpret the transition mechanism. Numerical results indicate that the first invariant of the couple stress remains small for specimen sheared under low confining pressure but increases rapidly when subjected to higher confining pressure. The micropolar responses inferred from DEM simulations reveal that microcracking may occur in a more diffuse and stable manner when the first invariant of the macroscopic couple stress are of higher magnitudes.

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Section: Dem Model For Bonded Cohesive‐frictional Materialsmentioning

confidence: 99%

Micropolar effect on the cataclastic flow and brittle‐ductile transition in high‐porosity rocks

2016

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“…The deviatoric elastic strain tensor e e i is expressed as e e i = e i − 1 3 e v i . In a similar way as discussed by Lyakhovsky et al (2015), we adopt the following description of the elastic moduli as a function of damage:…”

Section: Thermodynamics For Damage Rheologymentioning

confidence: 99%

“…wherep ′0 and̄0 e are the projections of the undamaged effective pressure and equivalent stress, respectively, on the yield function. Note that from equation (17), the yield function is formulated in the undamaged stress space, which is equivalent to the elastic strain formulation as adopted by Lyakhovsky et al (2015).…”

Section: Flow Laws and Damage Rheologymentioning

confidence: 99%

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

Jacquey

Cacace

2020

JGR Solid Earth

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The 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.

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“…After integration over [0, t], we use the Gronwall inequality and exploit the control of the initial condition |θ 0ε | ≤ 1/ε due to (26b). The last boundary term in (42) can be controlled as |θ ,ε | ≤ 1/ε, again due to (26b).…”

Section: Convergence Of Galerkin Approximationsmentioning

confidence: 99%

“…Such extension was suggested in [4] and later augmented by the nonlinear (also called non-Hookean) γ-term in [5] at small strains. The special form of this last term was suggested in [40] (alternatively considered as −γI 1 I 2 −I 2 1 /3 in [41]), validated, and used in series of works [23,25,34,35,38,42]. The reader is referred to [26] for a comprehensive discussion on such choices.…”

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confidence: 99%

Thermodynamics of Elastoplastic Porous Rocks at Large Strains Towards Earthquake Modeling

Roubíček¹,

Stefanelli²

2018

SIAM J. Appl. Math.

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A mathematical model for an elastoplastic porous continuum subject to large strains in combination with reversible damage (aging), evolving porosity, water and heat transfer is advanced. The inelastic response is modeled within the frame of plasticity for nonsimple materials. Water and heat diffuse through the continuum by a generalized Fick-Darcy law in the context of viscous Cahn-Hilliard dynamics and by Fourier law, respectively. This coupling of phenomena is paramount to the description of lithospheric faults, which experience ruptures (tectonic earthquakes) originating seismic waves and flash heating. In this regard, we combine in a thermodynamic consistent way the assumptions of having a small Green-Lagrange elastic strain and nearly isochoric plastification with the very large displacements generated by fault shearing. The model is amenable to a rigorous mathematical analysis. Existence of suitably defined weak solutions and a convergence result for Galerkin approximations is proved.

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Visco‐poroelastic damage model for brittle‐ductile failure of porous rocks

Cited by 49 publications

References 82 publications

Micropolar effect on the cataclastic flow and brittle‐ductile transition in high‐porosity rocks

Micropolar effect on the cataclastic flow and brittle‐ductile transition in high‐porosity rocks

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

Thermodynamics of Elastoplastic Porous Rocks at Large Strains Towards Earthquake Modeling

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