Coupling of non‐ordinary state‐based peridynamics and finite element method for fracture propagation in saturated porous media

Sun, Wei; Fish, Jacob

doi:10.1002/nag.3200

Cited by 53 publications

(22 citation statements)

References 46 publications

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“…After discretization, the PD force vector state in the coupling zone is given by

\underset{true_}{\overset{T}{true}} false[\overset{x}{true}, t false] ⟨ {\overset{x}{true}}^{'} - \overset{true^}{bold-italicx} ⟩ = ω false(| {\overset{true^}{bold-italicx}}^{'} goodbreak- \overset{x}{true} | false) \overset{true^}{bold-italicQ} \cdot σ false(\overset{true‾}{bold-italicϵ} + \overset{true^}{bold-italicϵ}, bold-italicζ false) + {\overset{true^}{bold-italicE} \overset{true^}{bold-italicU}}_{x_{i}},

where for the definition of

\overset{true^}{bold-italicQ}

\overset{true^}{bold-italicE}

, and

{\overset{U}{true}}_{x_{i}}

, we refer to Reference 44.…”

Section: Superposition Of the Pd Discretization Of The Fractured Solid Skeleton On The Fe Discretization Of The Biot's Model Of Porous Mementioning

confidence: 99%

“…The nonlinear system of equations are solved by a fully‐implicit algorithm as in Reference 44 with primary unknowns,

\overset{true‾}{bold-italicu}

\overset{true^}{bold-italicu}

\overset{true‾}{p}

, updated simultaneously.…”

Section: Superposition Of the Pd Discretization Of The Fractured Solid Skeleton On The Fe Discretization Of The Biot's Model Of Porous Mementioning

confidence: 99%

“…Herein, we study pressure‐driven fracture propagation problem. Similar problem has been studied by the authors using a PD‐FEM coupling approach where the full domain has been discretized by PD particles, 44 which renders the simulation time‐consuming.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Superposition‐based concurrent multiscale approaches for poromechanics

Sun

Fish

2021

Numerical Meth Engineering

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Superposition‐based concurrent multiscale approaches for poromechanical problems aimed at resolving localized fluid flow and deformation of a solid skeleton including its possible fracture are developed. The main departure of the proposed formulation is that the primary unknowns in the coupling zone, the solid displacement u and pore pressure p, are discretized by possibly different numerical models. Two discretization schemes are studied: (i) superposition of two or more finite element (FE) discretizations of the Biot's u‐p model of a porous medium, and (ii) superposition of the peridynamics (PD) discretization of the fractured solid phase on the FE discretization of the Biot's u‐p model of a porous medium. In the latter case, the total stress of the fluid–solid mixture in the coupling domain is derived from the effective stress obtained from the combined PD and finite element method solutions while the pore pressure is obtained from the FE solution. The accuracy of the superposition‐based concurrent multiscale method is studied on several benchmark problems including the classical Terzaghi's one‐dimensional consolidation problem, the two‐dimensional strip footing problem, and the pressure‐ and fluid‐driven fracture propagation problem in saturated porous media. The main hydraulic fracture characteristics, including complex crack paths and fluid flow patterns, have been found to be reasonably well reproduced by the proposed method.

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“…After discretization, the PD force vector state in the coupling zone is given by

\underset{true_}{\overset{T}{true}} false[\overset{x}{true}, t false] ⟨ {\overset{x}{true}}^{'} - \overset{true^}{bold-italicx} ⟩ = ω false(| {\overset{true^}{bold-italicx}}^{'} goodbreak- \overset{x}{true} | false) \overset{true^}{bold-italicQ} \cdot σ false(\overset{true‾}{bold-italicϵ} + \overset{true^}{bold-italicϵ}, bold-italicζ false) + {\overset{true^}{bold-italicE} \overset{true^}{bold-italicU}}_{x_{i}},

where for the definition of

\overset{true^}{bold-italicQ}

\overset{true^}{bold-italicE}

, and

{\overset{U}{true}}_{x_{i}}

, we refer to Reference 44.…”

Section: Superposition Of the Pd Discretization Of The Fractured Solid Skeleton On The Fe Discretization Of The Biot's Model Of Porous Mementioning

confidence: 99%

“…The nonlinear system of equations are solved by a fully‐implicit algorithm as in Reference 44 with primary unknowns,

\overset{true‾}{bold-italicu}

\overset{true^}{bold-italicu}

\overset{true‾}{p}

, updated simultaneously.…”

Section: Superposition Of the Pd Discretization Of The Fractured Solid Skeleton On The Fe Discretization Of The Biot's Model Of Porous Mementioning

confidence: 99%

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Superposition‐based concurrent multiscale approaches for poromechanics

Sun

Fish

2021

Numerical Meth Engineering

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“…Among them, Vazaios et al [23] used the self-developed program to realize the progressive failure of the URL test tunnel and compared it with calculated results of the continuous analysis method. In addition, some scholars have combined extended finite element and discrete element [24], peridynamics, and finite element [25][26][27] for similar research, and the essence is also the coupling of the finite element method and other failure analysis method.…”

Section: Introductionmentioning

confidence: 99%

Techniques for Progressive Failure Simulation of Hard Brittle Surrounding Rockmass: Taking the URL Test Tunnel as an Example

Zhong

Chen

Zhou

et al. 2021

Advances in Civil Engineering

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Accurate simulation of the failure process of hard brittle surrounding rockmass is very important for the analysis and control of the structural stability in deep underground engineering. In order to simulate the progressive failure process of the hard brittle surrounding rockmass, a continuous discontinuous deformation analysis method that couples the finite element and discrete element is adopted. Taking the URL test tunnel in Canada as an engineering case, the constitutive model of the contact considering the effects of cohesion weakening and friction strengthening is applied, and the 2D approximation to 3D excavation by applying elastic modulus reduction technology is adopted to simulate the range and depth of crack growth of the surrounding rockmass. Then, the comparison between simulated results and on-site monitoring results is performed, which shows good consistency. At the same time, the key factors in the numerical simulation of progressive failure in hard brittle rockmass are identified, including the number of elements, excavation effects, and constitutive models. The results show that the constitutive model determines the basic form of crack propagation, but in order to accurately simulate the progressive propagation of cracks, the number of elements must be sufficient enough and the effects of 3D excavation must be considered. The analysis accurately simulates the progressive failure characteristics of hard brittle surrounding rockmass under high stress, achieving the purpose of reasonably grasping the degree of damage to the surrounding rockmass, and provides technical reference and support on how to accurately simulate the failure of hard brittle surrounding rockmass using the finite discrete element method.

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“…Owing to these advantages, it has been successfully applied to crack propagation problems [21,22], composite material damage [23,24], fluid mechanics and acoustics [25], and heat conduction analysis [26,27] etc. There are several kinds of peridynamics, such as bond-based PD [19], state-based PD [28], and element-based PD [29] etc., and they can be easily coupled with other numerical methods to deal with the interaction between different materials, such as PD-FEM [30], PD-SPH [31], and PD-DEM [32].…”

Section: Introductionmentioning

confidence: 99%

Numerical Modeling on Crack Propagation Based on a Multi-Grid Bond-Based Dual-Horizon Peridynamics

Dai

Xie

et al. 2021

Mathematics

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Peridynamics (PD) is a novel nonlocal theory of continuum mechanics capable of describing crack formation and propagation without defining any fracture rules in advance. In this study, a multi-grid bond-based dual-horizon peridynamics (DH-PD) model is presented, which includes varying horizon sizes and can avoid spurious wave reflections. This model incorporates the volume correction, surface correction, and a technique of nonuniformity discretization to improve calculation accuracy and efficiency. Two benchmark problems are simulated to verify the reliability of the proposed model with the effect of the volume correction and surface correction on the computational accuracy confirmed. Two numerical examples, the fracture of an L-shaped concrete specimen and the mixed damage of a double-edged notched specimen, are simulated and analyzed. The simulation results are compared against experimental data, the numerical solution of a traditional PD model, and the output from a finite element model. The comparisons verify the calculation accuracy of the corrected DH-PD model and its advantages over some other models like the traditional PD model.

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Coupling of non‐ordinary state‐based peridynamics and finite element method for fracture propagation in saturated porous media

Cited by 53 publications

References 46 publications

Superposition‐based concurrent multiscale approaches for poromechanics

Superposition‐based concurrent multiscale approaches for poromechanics

Techniques for Progressive Failure Simulation of Hard Brittle Surrounding Rockmass: Taking the URL Test Tunnel as an Example

Numerical Modeling on Crack Propagation Based on a Multi-Grid Bond-Based Dual-Horizon Peridynamics

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