A stabilized computational nonlocal poromechanics model for dynamic analysis of saturated porous media

Menon, Shashank; Song, Xiaoyu

doi:10.1002/nme.6762

Cited by 23 publications

(65 citation statements)

References 70 publications

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“…Periporomechanics is a reformulation of classical poromechanics through the peridynamic state concept 29 for modeling continuous or discontinuous deformation and fluid flow in variably saturated porous media 19,21‐24 . In periporomechanics, it is hypothesized that a porous material body can be represented by a finite number of mixed material points that are endowed with two kinds of degree of freedom, that is, solid displacement and fluid pressure.…”

Section: Unsaturated Fracture Periporomechanics For Unguided Crackingmentioning

confidence: 99%

“…In line with the stabilized multiphase correspondence principle, 24 the effective force state and unsaturated fluid flow state can be written as follows. First, the effective force state with stabilization reads

\overset{true‾}{\underline{T}} = \underline{ω} (\overset{true‾}{P} K^{- 1} ξ + \frac{G C}{ω_{0}} {\underline{R}}^{s}), C = \frac{18 K}{π δ^{4}},

where

\underline{ω}

is the influence function (also called weighting function),

\overset{true‾}{P}

is the effective Piola–Kirchhoff stress tensor,

K

is the shape tensor, 29

{\underline{R}}^{s}

is the residual deformation state (see Equation 10),

G

is a positive constant on the order of 1, and

K

is the elastic bulk modulus of the skeleton, and

ω_{0}

is defined as

ω_{0} = \int_{ℋ} \underline{ω} d V^{'} .

The shape tensor

K

is defined as

K = \int_{ℋ} \underline{ω} ξ \otimes ξ d V^{'} .

The residual deformation state

…”

Section: Unsaturated Fracture Periporomechanics For Unguided Crackingmentioning

confidence: 99%

“…With the advance of supercomputers, computational methods play an increasingly significant role in modeling the mechanical and physical behavior including cracking of unsaturated soils (e.g., Reference 9). In this study, different from the celebrated computational methods such as the extended finite element method (e.g., References 17 and 18) and as a new contribution, we develop a fully coupled nonlocal mathematical paradigm for modeling fracturing and fluid flow in unsaturated porous media using periporomechanics (e.g., References 19‐24 and see Section 2.1 for a brief review) that is a nonlocal reformulation of classical poromechanics 25‐27 through peridynamics 28,29 for modeling variably saturated porous media. We refer to the celebrated literature (see References 13 and 14, among many others) on other robust computational techniques for modeling cracking in fracturing porous media under variably saturated conditions.…”

Section: Introductionmentioning

confidence: 99%

“…In Reference 24, the authors formulated a stabilized coupled periporomechanics model for dynamic analysis of saturated porous media with no cracks. In the present article, as a new contribution the formulation in Reference 24 is extended to model unguided fracturing and fluid flow in unsaturated porous media. In this fracturing unsaturated periporomechanics model, the same governing equation for the solid phase applies on and off cracks.…”

Section: Introductionmentioning

confidence: 99%

“…Unsaturated fluid flow in the fracture space is coupled to the fluid flow in the bulk through a leak‐off term. Different from the fully coupled numerical implementation in Reference 24, the formulated unsaturated fracturing periporomechanics is numerically implemented through the celebrated fractional step algorithm (also called staggered algorithm in the literature, see Reference 13, 25, 26, 44, 55, and 57‐59, and others) for computational efficiency and accuracy. The two‐stage operator split converts the coupled fracturing periporomechanics problem into an undrained deformation and fracture problem and an unsaturated fluid flow problem in the deformed configuration.…”

Section: Introductionmentioning

confidence: 99%

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Computational multiphase periporomechanics for unguided cracking in unsaturated porous media

Menon

Song

2022

Numerical Meth Engineering

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In this article, we formulate and implement a computational multiphase periporomechanics paradigm for unguided fracturing in unsaturated porous media assuming passive pore air pressure. The same governing equation for the solid phase applies on and off cracks. Crack formation in this framework is autonomous, requiring no prior estimates of crack topology. As a new contribution, an energy-based criterion for arbitrary crack formation is formulated using the peridynamic effective force state for unsaturated porous media. Unsaturated fluid flow in the fracture space is modeled in a simplified way in line with the nonlocal formulation of unsaturated fluid flow in the bulk. The formulated unsaturated fracturing periporomechanics is numerically implemented through an implicit fractional step algorithm in time and a two-phase mixed meshless method in space. The two-stage operator split converts the coupled periporomechanics problem into an undrained deformation and fracture problem and an unsaturated fluid flow in the deformed skeleton configuration. Numerical simulations of in-plane open and shear cracking are conducted to validate the accuracy and robustness of the fracturing unsaturated periporomechanics model.Then numerical examples of wing cracking and nonplanar cracking in unsaturated soil specimens are presented to demonstrate the efficacy of the proposed multiphase periporomechanics paradigm for unguided cracking in unsaturated porous media.

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Section: Unsaturated Fracture Periporomechanics For Unguided Crackingmentioning

confidence: 99%

\overset{true‾}{\underline{T}} = \underline{ω} (\overset{true‾}{P} K^{- 1} ξ + \frac{G C}{ω_{0}} {\underline{R}}^{s}), C = \frac{18 K}{π δ^{4}},

where

\underline{ω}

is the influence function (also called weighting function),

\overset{true‾}{P}

is the effective Piola–Kirchhoff stress tensor,

K

is the shape tensor, 29

{\underline{R}}^{s}

is the residual deformation state (see Equation 10),

G

is a positive constant on the order of 1, and

K

is the elastic bulk modulus of the skeleton, and

ω_{0}

is defined as

ω_{0} = \int_{ℋ} \underline{ω} d V^{'} .

The shape tensor

K

is defined as

K = \int_{ℋ} \underline{ω} ξ \otimes ξ d V^{'} .

The residual deformation state

…”

Section: Unsaturated Fracture Periporomechanics For Unguided Crackingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Computational multiphase periporomechanics for unguided cracking in unsaturated porous media

Menon

Song

2022

Numerical Meth Engineering

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Poroelastic response of unsaturated soils to cyclic loads with arbitrary waveforms

Lo,

Borja,

Chao

et al. 2023

Num Anal Meth Geomechanics

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We develop an analytical solution to the problem of one‐dimensional consolidation of unsaturated soil subjected to cyclic loads with arbitrary waveforms. The solution predicts the excess pore water and pore air pressures and the accompanying vertical compression in a poroelastic, unsaturated soil material. Cyclic loading occurs in a variety of engineering applications and often generates higher excess pore fluid pressures and larger vertical compression than does a time‐invariant load. In the present study, the loading function is allowed to take on any arbitrary waveform represented by a Fourier trigonometric series. Analytical solution to the boundary‐value problem in one dimension is given in closed form describing the frequency‐independent and frequency‐dependent components of the poroelastic response. We verify the analytical solution through representative examples involving cyclic loads with square and triangular patterns. Apart from the shape of the forcing function, we also investigate the effects of initial water saturation, soil texture, and excitation frequency on the system response.

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Modeling dynamic crack branching in unsaturated porous media through multi‐phase micro‐periporomechanics

Pashazad,

Song

2024

Num Anal Meth Geomechanics

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Dynamic crack branching in unsaturated porous media holds significant relevance in various fields, including geotechnical engineering, geosciences, and petroleum engineering. This article presents a numerical investigation into dynamic crack branching in unsaturated porous media using a recently developed coupled micro‐periporomechanics (PPM) paradigm. This paradigm extends the PPM model by incorporating the micro‐rotation of the solid skeleton. Within this framework, each material point is equipped with three degrees of freedom: displacement, micro‐rotation, and fluid pressure. Consistent with the Cosserat continuum theory, a length scale associated with the micro‐rotation of material points is inherently integrated into the model. This study encompasses several key aspects: (1) Validation of the coupled micro‐PPM paradigm for effectively modeling crack branching in deformable porous media, (2) Examination of the transition from a single branch to multiple branches in porous media under drained conditions, (3) Simulation of single crack branching in unsaturated porous media under dynamic loading conditions, and (4) Investigation of multiple crack branching in unsaturated porous media under dynamic loading conditions. The numerical results obtained in this study are systematically analyzed to elucidate the factors that influence crack branching in porous media subjected to dynamic loading. Furthermore, the comprehensive numerical findings underscore the efficacy and robustness of the coupled micro‐PPM paradigm in accurately modeling dynamic crack branching in variably saturated porous media.

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A stabilized computational nonlocal poromechanics model for dynamic analysis of saturated porous media

Cited by 23 publications

References 70 publications

Computational multiphase periporomechanics for unguided cracking in unsaturated porous media

Computational multiphase periporomechanics for unguided cracking in unsaturated porous media

Poroelastic response of unsaturated soils to cyclic loads with arbitrary waveforms

Modeling dynamic crack branching in unsaturated porous media through multi‐phase micro‐periporomechanics

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