A cross-anisotropic formulation for elasto-plastic models

Mánica, Miguel A.; Gens, Antonio; Vaunat, Jean; Ruiz, Daniel F.

doi:10.1680/jgele.15.00182

Cited by 20 publications

(14 citation statements)

References 26 publications

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“…Yet, this isotropic strength criterion cannot characterize strength anisotropy in rocks. We follow the elastoplastic models of Mánica et al 71 and Forero et al 70 and formulate an anisotropic strength criterion with the help of the unitless scalar orientation parameters, 𝐶 N and 𝐶 S . As the strength of anisotropic rocks depends on how the loading is applied relative to the orientation of their anisotropy planes, this approach provides a simple way to relate the loading direction to the anisotropy direction.…”

Section: Model Descriptionmentioning

confidence: 99%

“…Another recent study by Ref. 70 used Bayesian inference to back out the twelve coefficients of the Lade-Kim isotropic model using a non-uniform scaling of the stress tensor 71 and two scaling factors, 𝐶 N and 𝐶 S , that link the orientation of the anisotropy planes with the loading direction. The maximum deviatoric stresses and stressstrain curves predicted and simulated by their model were shown to be in good agreement with experimental data, but the authors did not present and investigate the uncertainty of the predicted maximum deviatoric stresses.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian inference of rock strength anisotropy: Uncertainty analysis of the Hoek–Brown failure criterion

Gomes¹,

Forero²,

Vargas³

et al. 2021

International Journal of Rock Mechanics and Mining Sciences

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Strength properties of most sedimentary and metamorphic rocks are known to vary with direction. Knowledge of this so-called rock anisotropy is of utmost importance for reliability analysis and engineering design. The purpose of this paper is twofold. First, we propose a formulation of the Hoek-Brown (HB) failure criterion, which calculates strength anisotropy using a non-uniform scaling of the stress tensor. We use two scaling factors, 𝐶 N and 𝐶 S , to link the orientation of the anisotropy planes with the loading direction. As we assume isotropic parameters for intact rock, our HB model formulation is relatively easy to use and has the additional advantage that it does not demand any modifications to the HB failure criterion. Second, we embed our HB model formulation in a Bayesian framework and illustrate its power and usefulness using experimental data of anisotropic rock samples published in the literature. Results demonstrate that our HB model formulation predicts accurately measured peak strengths of rocks with different degrees of anisotropy, confining stresses and anisotropy orientations. The uncertainty in peak strength of anisotropic rocks can be quite large, reiterating the need for an explicit treatment of strength anisotropy uncertainty in rock mechanics studies. The Bayesian methodology is general-purpose, and, as such, can help better inform geotechnical engineers, contractors and other professionals about rock conditions and design reliability and assist decision makers in determining the overall risks of engineering structures.

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Section: Model Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bayesian inference of rock strength anisotropy: Uncertainty analysis of the Hoek–Brown failure criterion

Gomes¹,

Forero²,

Vargas³

et al. 2021

International Journal of Rock Mechanics and Mining Sciences

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“…where g is the plastic potential and  is a constant that controls the volumetric component The model has been extended to consider cross-anisotropy through a non-uniform scaling of the stress tensor, as described in [23]. As Figure 2 shows, the local coordinate system 1-2-3 corresponds to the principal axes of anisotropy with direction "2" oriented orthogonal to the isotropic plane.…”

Section: Instantaneous Mechanismmentioning

confidence: 99%

“…An appropriate selection of strength parameters and scaling factors allows a satisfactory matching of a specified strength variation with loading orientation. Details about the physical meaning of the anisotropy parameters, their effects and of the derivation of the corresponding elastoplastic constitutive matrix are given in [23]. .…”

Section: Instantaneous Mechanismmentioning

confidence: 99%

A time-dependent anisotropic model for argillaceous rocks. Application to an underground excavation in Callovo-Oxfordian claystone

Mánica

Gens

Vaunat

et al. 2017

Computers and Geotechnics

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The paper presents a constitutive model for argillaceous rocks, developed within the framework of elastoplasticity, that includes a number of features that are relevant for a satisfactory description of their hydromechanical behaviour: anisotropy of strength and stiffness, behaviour nonlinearity and occurrence of plastic strains prior to peak strength, significant softening after peak, time-dependent creep deformations and permeability increase due to damage. Both saturated and unsaturated conditions are envisaged. The constitutive model is then applied to the simulation of triaxial and creep tests on Callovo-Oxfordian (COx) claystone. Although the main objective has been the simulation of the COx claystone behaviour, the model can be readily used for other argillaceous materials. The constitutive model developed is then applied, via a suitable coupled hydromechanical formulation, to the analysis of the excavation of a drift in the Meuse/Haute-Marne 2 Underground Research Laboratory. The pattern of observed pore water pressures and displacements, as well as the shape and extent of the damaged zone, are generally satisfactorily reproduced. The relevance and importance of rock anisotropy and of the development of a damaged zone around the excavations are clearly demonstrated.

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“…To include strength anisotropy in slope stability computations two main steps are required: the first one is to stablish a failure criterion introducing a dependency with loading direction, able to account for the observed variation of strength. A number of anisotropic failure criteria for soils have been proposed; a review can be found in Mánica et al (2016). The second step is to introduce the anisotropic criterion into an appropriate methodology for assessing the stability of slopes, such as: limit equilibrium methods, limit analyses or numerical methods.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of the undrained stability of slopes in anisotropic fine-grained soils

Conesa

Mánica

Gens

et al. 2018

Geomechanics and Geoengineering

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The undrained stability of slopes in anisotropic fine-grained soils is studied in this paper using the finite element method (FEM). A constitutive model is presented, able to account for the observed variation of undrained strength with loading direction. The model is able to encompass the different strength distributions observed in normally, slightly overconsolidated and heavily overconsolidated soils. A series of stability analyses have been performed to explore the effect of the type of undrained strength anisotropy on the stability and failure mechanisms of slopes of different inclinations. In addition, a real case study of the failure of an underwater slope is analysed with the numerical approach presented. It suggests that, by considering undrained strength anisotropy, the failure can be satisfactorily explained.

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A cross-anisotropic formulation for elasto-plastic models

Cited by 20 publications

References 26 publications

Bayesian inference of rock strength anisotropy: Uncertainty analysis of the Hoek–Brown failure criterion

Bayesian inference of rock strength anisotropy: Uncertainty analysis of the Hoek–Brown failure criterion

A time-dependent anisotropic model for argillaceous rocks. Application to an underground excavation in Callovo-Oxfordian claystone

Numerical simulation of the undrained stability of slopes in anisotropic fine-grained soils

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