Responses of chemically active and naturally fractured shale under time‐dependent mechanical loading and ionic solution exposure

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Many geomaterials, such as shale, and biomaterials, including human bone and cartilage, are anisotropic. Understanding the dynamic responses of such anisotropic porous media is essential in field operations and laboratory measurements. This paper presents analytical solutions to the transversely isotropic poroelastodynamics Mandel's problem, using the Fourier transform method and Cardano formula to solve coupled six‐order partial differential equations. Potential applications of the solutions include explaining coupled fluid‐solid dynamics, validating numerical algorithms, and interpreting dynamic responses of anisotropic porous media. As an example, we apply the solutions to simulate a fluid‐saturated transversely isotropic Trafalgar shale specimen subjected to harmonic excitation. The simulation shows that pore pressure builds up as frequency increases. The buildup occurs at a lower frequency for a lower horizontal permeability. The amount of pore pressure buildup due to the Mandel‐Cryer effect is sensitive to material anisotropy. The porous material's effective stiffness reaches its periodic minimum and maximum at the resonant and anti‐resonant frequencies controlled by mechanical anisotropy and pore fluid.

“…Together, this non‐monotonic pore pressure behavior was named the Mandel‐Cryer effect. Later, a similar phenomenon is also observed in porous cylinder geometry 4–6 …”

Section: Introductionsupporting

confidence: 67%

“…Multi‐porosity multi‐permeability generates multi pore pressure fields and multi Mandel‐Cryer effect 19 . Chemical attributes could produce osmotic pressure and chemically induced Mandel‐Cryer effect 5 . Viscoelasticity 20 and plasticity 28 would bring more complex mechanisms and phenomena.…”

Section: Discussionmentioning

confidence: 99%

Fundamental solutions to the transversely isotropic poroelastodynamics Mandel's problem

Liu

2021

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“…Anisotropy is a ubiquitous property of natural rocks. () Transverse isotropy is a particular type of anisotropy that arises from the existence of bedding planes. Transverse isotropy is defined by a plane of isotropy (ie, the bedding plane) and an axis of anisotropy (ie, the normal to the bedding plane).…”

Section: Introductionmentioning

confidence: 99%

On the strength of transversely isotropic rocks

Zhao

Semnani

Yin

et al. 2018

Summary Accurate prediction of strength in rocks with distinct bedding planes requires knowledge of the bedding plane orientation relative to the load direction. Thermal softening adds complexity to the problem since it is known to have significant influence on the strength and strain localization properties of rocks. In this paper, we use a recently proposed thermoplastic constitutive model appropriate for rocks exhibiting transverse isotropy in both the elastic and plastic responses to predict their strength and strain localization properties. Recognizing that laboratory‐derived strengths can be influenced by material and geometric inhomogeneities of the rock samples, we consider both stress‐point and boundary‐value problem simulations of rock strength behavior. Both plane strain and 3D loading conditions are considered. Results of the simulations of the strength of a natural Tournemire shale and a synthetic transversely isotropic rock suggest that the mechanical model can reproduce the general U‐shaped variation of rock strength with bedding plane orientation quite well. We show that this variation could depend on many factors, including the stress loading condition (plane strain versus 3D), degree of anisotropy, temperature, shear‐induced dilation versus shear‐induced compaction, specimen imperfections, and boundary restraints.

“…Cui and Abousleiman 47 presented the general analytical poroelastic solution for a fluid‐saturated cylindrical specimen subjected to an axial load and a confining pressure. The solution was further extended to consider dual‐porosity dual‐permeability, 42 chemical, 48 and chemo‐electrical activities 49 …”

Section: Introductionmentioning

confidence: 99%

Generalized solution to the anisotropic Mandel's problem

Liu

Abousleiman

2020

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Summary Existing solutions to Mandel's problem focus on isotropic, transversely isotropic, and orthotropic materials, the last two of which have one of the material symmetry axes coincide with the vertical loading direction. The classical plane strain condition holds for all these cases. In this work, analytical solution to Mandel's problem with the most general matrix anisotropy is presented. This newly derived analytical solution for fully anisotropic materials has all the three nonzero shear strains. Warping occurs in the cross sections, and a generalized plane strain condition is fulfilled. This solution can be applied to transversely isotropic and orthotropic materials whose material symmetry axes are not aligned with the vertical loading direction. It is the first analytical poroelastic solution considering mechanical general anisotropy of elasticity. The solution captures the effects of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction on the responses of pore pressure, stress, strain, and displacement. It can be used to match, calibrate, and simulate experimental results to estimate anisotropic poromechanical parameters. This generalized solution is capable of reproducing the existing solutions as special cases. As an application, the solution is used to study the responses of transversely isotropic and orthotropic materials whose symmetry axes are not aligned with the vertical loading direction. Examples on anisotropic shale rocks show that the effects of material anisotropy are significant. Mandel‐Cryer's effects are highly impacted by the degree of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction.