An analytical benchmark with combined pressure and shear loading for elastoplastic numerical models

Yarushina, Viktoriya; Dąbrowski, Marcin; Podladchikov, Y. Y.

doi:10.1029/2010gc003130

Cited by 21 publications

(31 citation statements)

References 21 publications

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“…Localizing plastic deformation is well known to be complicated to model numerically (e.g. Yarushina et al, 2010). Thus, I make a call to the community in order to improve this benchmark with high resolution models, similar perhaps to those that have been conducted for the problem of fault propagation in accretionary prisms (Buiter at al., 2008).…”

Section: Numerical Modeling Of Inflating Magma Chambers Numerical Metmentioning

confidence: 99%

“…A collective project such as that developed to compare the geometry of faults in thrust nappes (Buiter et al, 2008) would be recommended. This latter benchmark showed that whereas results are qualitatively similar, it remains difficult to match shear band geometries exactly, since the highly non-linear process of failure depends on specific formulations used in each numerical method (e.g .Kaus, 2010; Yarushina et al, 2010).…”

Section: A3) Benchmarks Without Gravity ∆P= 15 and 18 Mpamentioning

confidence: 99%

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Pressure conditions for shear and tensile failure around a circular magma chamber; insight from elasto-plastic modelling

Gerbault

2012

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International audienceOverpressure within a circular magmatic chamber embedded in an elastic half space is a widely used model in volcanology. However, this overpressure is generally assumed to be bounded by the bedrock tensile strength since gravity is neglected. Critical overpressure for wall failure is thus greater. It is shown analytically and numerically that wall failure occurs in shear rather than in tension, because the Mohr-Coulomb yield stress is less than the tensile yield stress. Numerical modelling of progressively increasing overpressure shows that bedrock failure develops in three stages: (1) tensile failure at the ground surface; (2) shear failure at the chamber wall; and (3) fault connection from the chamber wall to the ground surface. Predictions of surface deformation and stress with the theory of elasticity break down at stage 3. For wall tensile failure to occur at small overpressure, a state of lithostatic pore-fluid pressure is required in the bedrock which cancels the effect of gravity. Modelled eccentric shear band geometries are consistent with theoretical solutions from engineering plasticity and compare well with shear structures bordering exhumed intrusions. This study shows that the measured ground surface deformation may be misinterpreted when neither plasticity nor pore-fluid pressure is accounted for

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Section: Numerical Modeling Of Inflating Magma Chambers Numerical Metmentioning

confidence: 99%

Section: A3) Benchmarks Without Gravity ∆P= 15 and 18 Mpamentioning

confidence: 99%

Pressure conditions for shear and tensile failure around a circular magma chamber; insight from elasto-plastic modelling

Gerbault

2012

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“…This assumption requires that the inner cavity is fully enclosed by a continued plastic region. Limit conditions of this requirement will be approached while the vertices of the predicted elastic‐plastic boundary in the minor axis direction just reach the cavity wall . It gives

b_{ep} = α ((), 1 - (||, β)) \geq R .

Intermediate principal stress …”

Section: Discussion On Restrictions From the Assumptionsmentioning

confidence: 99%

“…As an extension of Galin's solution, this solution aims to provide an analytical method for the static stress analysis of the soil around a cavity under conditions of the following: ( a ) The inner cavity is fully enclosed by a connected plastic region, and the plastic stress field is statically determinate; ( b ) the plastic zone is developed under monotonic loading, and no elastic unloading occurs in any case; and ( c ) the out‐of‐plane stress component σ zz always remains as the intermediate principal stress regardless of other stresses …”

Section: Static Stress Analysismentioning

confidence: 99%

“…The location of the elastic‐plastic boundary is generally determined by analysing the continuity conditions of the elastic and plastic stresses across the interface. However, under non‐equal far‐field stresses, the elastic stress field cannot be obtained prior to knowing its inner boundary conditions, namely, the location of the elastic‐plastic boundary and stresses acting on it . Therefore, the elastic‐plastic boundary is described by a general form of the conformal mapping function first (ie, Equation ), and the elastic stresses are represented in terms of general forms of Kolosov‐Muskhelishvili complex potentials, Φ( ζ ) and Ψ( ζ ) .…”

Section: Static Stress Analysismentioning

confidence: 99%

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Two‐dimensional elastoplastic analysis of cylindrical cavity problems in Tresca materials

Zhuang

2019

Num Anal Meth Geomechanics

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Summary This paper presents analytical elastic‐plastic solutions for static stress loading analysis and quasi‐static expansion analysis of a cylindrical cavity in Tresca materials, considering biaxial far‐field stresses and shear stresses along the inner cavity wall. The two‐dimensional static stress solution is obtained by assuming that the plastic zone is statically determinate and using the complex variable theory in the elastic analysis. A rigorous conformal mapping function is constructed, which predicts that the elastic‐plastic boundary is in an elliptic shape under biaxial in situ stresses, and the range of the plastic zone extends with increasing internal shear stresses. The major axis of the elliptical elastic‐plastic boundary coincides with the direction of the maximum far‐field compression stress. Furthermore, considering the internal shear stresses, an analytical large‐strain displacement solution is derived for continuous cavity expansion analysis in a hydrostatic initial stress filed. Based on the derived analytical stress and displacement solutions, the influence of the internal shear stresses on the quasi‐static cavity expansion process is studied. It is shown that additional shear stresses could reduce the required normal expansion pressure to a certain degree, which partly explains the great reduction of the axial soil resistance due to rotations in rotating cone penetration tests. In addition, through additionally considering the potential influences of biaxial in situ stresses and shear stresses generated around the borehole during drillings, an improved cavity expansion approach for estimating the maximum allowable mud pressure of horizontal directional drillings (HDDs) in undrained clays is proposed and validated.

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(De)compaction of porous viscoelastoplastic media: Model formulation

2015

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A nonlinear viscoelastoplastic theory is developed for porous rate-dependent materials filled with a fluid in the presence of gravity. The theory is based on a rigorous thermodynamic formalism suitable for path-dependent and irreversible processes. Incremental evolution equations for porosity, Darcy's flux, and volumetric deformation of the matrix represent the simplest generalization of Biot's equations. Expressions for pore compressibility and effective bulk viscosity are given for idealized cylindrical and spherical pore geometries in an elastic-viscoplastic material with low pore concentration. We show that plastic yielding around pores leads to decompaction weakening and an exponential creep law. Viscous and plastic end-members of our model are consistent with experimentally verified models. In the poroelastic limit, our constitutive equations reproduce the exact Gassmann's relations, Biot's theory, and Terzaghi's effective stress law. The nature of the discrepancy between Biot's model and the True Porous Media theory is clarified. Our model provides a unified and consistent formulation for the elastic, viscous, and plastic cases that have previously been described by separate "end-member" models.

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An analytical benchmark with combined pressure and shear loading for elastoplastic numerical models

Cited by 21 publications

References 21 publications

Pressure conditions for shear and tensile failure around a circular magma chamber; insight from elasto-plastic modelling

Pressure conditions for shear and tensile failure around a circular magma chamber; insight from elasto-plastic modelling

Two‐dimensional elastoplastic analysis of cylindrical cavity problems in Tresca materials

(De)compaction of porous viscoelastoplastic media: Model formulation

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