An approach to model the mechanical behavior of transversely isotropic materials

Mahjoub, Mohamed; Rouabhi, Ahmed; Tijani, Michel; Granet, S.

doi:10.1002/nag.2469

Cited by 6 publications

(4 citation statements)

References 32 publications

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“…The smeared approach utilizes an implicit representation of layers to produce a fictitious continuous material within which the effect of layering is introduced at the level of constitutive laws. Deformation anisotropy is commonly captured using the theory of elasticity for transversely isotropic media , while strength anisotropy and progressive damage are captured by various anisotropic failure criteria along with specifying the directional dependence of material properties . Discrete approaches, instead, employ an explicit representation of layers in which mechanical anisotropy is introduced by a geometric description of layered structure with varying material parameters.…”

Section: Introductionmentioning

confidence: 99%

“…The smeared approach utilizes an implicit representation of layers to produce a fictitious continuous material within which the effect of layering is introduced at the level of constitutive laws. Deformation anisotropy is commonly captured using the theory of elasticity for transversely isotropic media [34], while strength anisotropy and progressive damage are captured by various anisotropic failure criteria [35,36,37,38,39] along with carbon,TOC, ranges from 1 to 2.5%) (Fig. 3a,b,c).…”

Section: Introductionmentioning

confidence: 99%

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A multiscale framework for the simulation of the anisotropic mechanical behavior of shale

Rezakhani

Jin

et al. 2017

Num Anal Meth Geomechanics

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Summary Shale, like many other sedimentary rocks, is typically heterogeneous and anisotropic and is characterized by partial alignment of anisotropic clay minerals and naturally formed bedding planes. In this study, a micromechanical framework based on the lattice discrete particle model is formulated to capture these features. Material anisotropy is introduced through an approximated geometric description of shale internal structure, which includes representation of material property variation with orientation and explicit modeling of parallel lamination. The model is calibrated by carrying out numerical simulations to match various experimental data, including the ones relevant to elastic properties, Brazilian tensile strength, and unconfined compressive strength. Furthermore, parametric study is performed to investigate the relationship between the mesoscale parameters and the macroscopic properties. It is shown that the dependence of the elastic stiffness, strength, and failure mode on loading orientation can be captured successfully. Finally, a homogenization approach based on the asymptotic expansion of field variables is applied to upscale the proposed micromechanical model, and the properties of the homogenized model are analyzed. Copyright © 2017 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

“…The smeared approach utilizes an implicit representation of layers to produce a fictitious continuous material within which the effect of layering is introduced at the level of constitutive laws. Deformation anisotropy is commonly captured using the theory of elasticity for transversely isotropic media [34], while strength anisotropy and progressive damage are captured by various anisotropic failure criteria [35,36,37,38,39] along with carbon,TOC, ranges from 1 to 2.5%) (Fig. 3a,b,c).…”

Section: Introductionmentioning

confidence: 99%

A multiscale framework for the simulation of the anisotropic mechanical behavior of shale

Rezakhani

Jin

et al. 2017

Num Anal Meth Geomechanics

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“…Hu JT et al [23] and Vu TM et al [24] proposed a calculation of p-wave travel time marching in a three-dimensional transversely isotropic medium wave step by step. Anisotropic damage models considering loading were induced [25], continuum damage ( [26]) was analyzed, and some suggestions were put forward.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Stress in a Transversely Isotropic Floor Rock Mass under Distributed Loading in an Arbitrary Direction

Zhao

Wang

et al. 2021

Applied Sciences

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Rock masses with a distinct structure may present a transversely isotropic character; thus, the stress state in a transversely isotropic elastic half-plane surface is an important way to assess the behavior of the interaction between the distributed loading and the surroundings. Most previous theoretical analyses have considered a loading direction that is either vertical or horizontal, and the stress distribution that results from the effect of different loading directions remains unclear. In this paper, based on the transversely isotropic elastic half-plane surface theory, a stress solution that is applicable to distributed loading in any direction is proposed to further examine the loading effect. The consistency between the analytical solution and numerical simulations showed the effectiveness of the proposal that was introduced. Then, it was utilized to analyze the stress distribution rule by changing the Poisson’s ratio and Young’s modulus of the model. The effects of the formation dip angle on the stress state are also examined. The stress distribution, depending on the physical property parameters and relative angle, is predicted using an analytical solution, and the mechanisms associated with the transversely isotropic elastic half-plane surface subjected to the loading in any direction are clarified. Additionally, extensive analyses regarding this case study, with respect to the mechanical behavior associated with changes in the stress boundary, is available. Hence, the proposed analytical solution can more realistically account for the loading problem in many engineering practices.

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“…Mahjoub et al used a fictitious isotropic material to represent the stress state in VTI rocks. They extended a Drucker‐Prager failure criterion for this fictitious isotropic formulation and studied the strength dependence with the orientation angle in brazilian tests.…”

Section: Introductionmentioning

confidence: 99%

Fracture behavior of transversely isotropic rocks with discrete weak interfaces

Celleri

Sánchez²,

Otegui

2018

Num Anal Meth Geomechanics

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Summary Anisotropic rocks have gained increasing attention due to the development of unconventional oil and gas reservoirs. This type of reservoir requires complex engineering procedures from drilling to completion, and the mechanical properties of the rocks play a significant role. One of the most important characteristics of unconventional formations is the presence of well‐defined layers, which greatly modify both elastic and fracture properties of the rocks. Rock elastic response is direction dependent, commonly described as vertically transversely isotropic (VTI), meaning that there is an isotropic plane of symmetry with respect to the vertical direction. Between layers, calcitic veins or ash beds alter the rock's properties substantially. These interfaces, which can have low or no cohesion at all, act as preferential planes for fracture nucleation and propagation, affecting the rocks strength. In this work, the fracture behavior of VTI rocks with weak interfaces is studied using numerical simulations of brazilian tests. A hybrid discontinuous Galerkin–cohesive zone model was used to simulate fracture initiation and propagation on discs in the presence of weak planes. With this approach, we determined the effective brazilian test strength of the rocks under different conditions, namely, relative angles between layers and the loading direction, densities, and cohesion of weak interfaces. Shear reactivation of the interfaces is analyzed using the Mohr‐Coulomb failure criterion and Mohr circles.

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An approach to model the mechanical behavior of transversely isotropic materials

Cited by 6 publications

References 32 publications

A multiscale framework for the simulation of the anisotropic mechanical behavior of shale

A multiscale framework for the simulation of the anisotropic mechanical behavior of shale

Analytical Solution of Stress in a Transversely Isotropic Floor Rock Mass under Distributed Loading in an Arbitrary Direction

Fracture behavior of transversely isotropic rocks with discrete weak interfaces

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