A three-dimensional Generalized Finite Element Method for the simulation of wave propagation in fluid-filled fractures

Shauer, Nathan; Desmond, Kenneth W.; Gordon, Peter A.; Liu, Fushen; Duarte, C. Armando

doi:10.1016/j.cma.2021.114136

Cited by 6 publications

(23 citation statements)

References 61 publications

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“…A similar conclusion has also been reached by Shauer et al. (2021). Since we assume a quasi‐static solid response, it is reasonable that our results have a better agreement to those by GFEM without inertia.…”

Section: Verification and Examplessupporting

confidence: 88%

“…Tables 2 and 3 show the comparison of dimensionless resonant frequencies of selective eigenmodes from the GFEM program by Shauer et al (2021) with those by our method for a rectangular and elliptical crack, respectively, with an aspect ratio of 0.5, major axis length of 1, and C L of 100. The relative difference between our results and those from Shauer et al (2021) are near 2% or less, with or without solid inertia. This close agreement not only demonstrates the validity of our approach but also reassures that the quasi-static solid response is a very good approximation when computing the crack wave resonant frequencies, at least for a C L of 100.…”

Section: Comparison To Numerical Solutions By Existing Studiesmentioning

confidence: 99%

“…Therefore, the discrepancy between our results and those by Maeda and Kumagai (2017) is not primarily caused by the quasi-static approximation alone, especially at high values of C L . We suspect these discrepancies may come from differences in spatial and temporal sampling, or domain sizes and boundary conditions used in the FDM code (Chouet, 1986;Maeda & Kumagai, 2017) as Shauer et al (2021) solves the same continuous fully dynamic problem. On the other hand, the resonant frequencies by the finite-difference (FD) method were shown to match those by the boundary integral (BI) method (Yamamoto & Kawakatsu, 2008) in two dimensions.…”

Section: Comparison To Numerical Solutions By Existing Studiesmentioning

confidence: 99%

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Resonances of Fluid‐Filled Cracks With Complex Geometry and Application to Very Long Period (VLP) Seismic Signals at Mayotte Submarine Volcano

Liang,

Peng,

Ampuero

et al. 2024

JGR Solid Earth

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Fluid‐filled cracks sustain a slow guided wave (Krauklis wave or crack wave) whose resonant frequencies are widely used for interpreting long period (LP) and very long period (VLP) seismic signals at active volcanoes. Significant efforts have been made to model this process using analytical developments along an infinite crack or numerical methods on simple crack geometries. In this work, we develop an efficient hybrid numerical method for computing resonant frequencies of complex‐shaped fluid‐filled cracks and networks of cracks and apply it to explain the ratio of spectral peaks in the VLP signals from the Fani Maoré submarine volcano that formed in Mayotte in 2018. By coupling triangular boundary elements and the finite volume method, we successfully handle complex geometries and achieve computational efficiency by discretizing solely the crack surfaces. The resonant frequencies are directly determined through eigenvalue analysis. After proper verification, we systematically analyze the resonant frequencies of rectangular and elliptical cracks, quantifying the effect of aspect ratio and crack stiffness. We then discuss theoretically the contribution of fluid viscosity and seismic radiation to energy dissipation. Finally, we obtain a crack geometry that successfully explains the characteristic ratio between the first two modes of the VLP seismic signals from the Fani Maoré submarine volcano in Mayotte. Our work not only reveals rich eigenmodes in complex‐shaped cracks but also contributes to illuminating the subsurface plumbing system of active volcanoes. The developed model is readily applicable to crack wave resonances in other geological settings, such as glacier hydrology and hydrocarbon reservoirs.

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Section: Verification and Examplessupporting

confidence: 88%

Section: Comparison To Numerical Solutions By Existing Studiesmentioning

confidence: 99%

Section: Comparison To Numerical Solutions By Existing Studiesmentioning

confidence: 99%

See 1 more Smart Citation

Resonances of Fluid‐Filled Cracks With Complex Geometry and Application to Very Long Period (VLP) Seismic Signals at Mayotte Submarine Volcano

Liang,

Peng,

Ampuero

et al. 2024

JGR Solid Earth

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“…Several papers have been published recently on the topic of fractured and non-fractured porous media with single-and multi-phase fluid flow with potential application in geomechanics. [4][5][6][7][8][9] Several numerical models have been proposed over decades for simulation of porous media with multi-phase flow. Depending on the focus of the projects and objectives, the reported works have limitations and restrictions.…”

Section: Introductionmentioning

confidence: 99%

“…Simulation of groundwater contamination by industrial chemicals and hydrocarbons in applications like waste injection, modelling of steam and water injection in reservoir stimulation processes for enhanced recovery, and seismic and slope stability analysis in porous formations are only a few to be noted. Several papers have been published recently on the topic of fractured and non‐fractured porous media with single‐ and multi‐phase fluid flow with potential application in geomechanics 4–9 …”

Section: Introductionmentioning

confidence: 99%

An enriched mixed finite element model for the simulation of microseismic and acoustic emissions in fractured porous media with multi‐phase flow and thermal coupling

Komijani

Wriggers

Goudarzi

2023

Num Anal Meth Geomechanics

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A novel mixed enriched finite element model is developed for coupled non‐linear thermo‐hydro‐mechanical simulation of fractured porous media with three‐phase flow and thermal coupling. Simulation of induced acoustic emission (AE) and microseismic emission (ME) due to tensile fracturing and shear slip instability of pre‐existing fracture interfaces is carried out and the numerical results of the emitted signals are analysed. The mathematical model is based on the generalized Biot's theory for coupled interaction of solid and fluid phases. A computationally robust non‐linear solver is developed to handle the severe non‐linearities arising from fluid saturations, relative permeabilities of fluids, constitutive models of interfaces and convective thermal coupling. To model pre‐existing natural fractures and faults, discrete fracture propagation and nucleation of cracks (micro‐cracking) independently of the original mesh topology, a local Partition‐of‐Unity (PU) finite element method, namely, the Phantom Node Method (PNM) is implemented. The cohesive fracture modelling scheme is implemented to account for the non‐linear behaviour of fracturing and localization, and to rectify the non‐physical stress singularity condition at the fracture tip. Effects of different system parameters on fracturing, shear‐slip instability and the associated induced AEs and MEs are investigated through various numerical results.

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Thermodynamically consistent non-local damage formulation for fluid-driven fracture in poro-viscoelastic media

Chen

Mobasher

et al. 2022

Acta Geotech.

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A three-dimensional Generalized Finite Element Method for the simulation of wave propagation in fluid-filled fractures

Cited by 6 publications

References 61 publications

Resonances of Fluid‐Filled Cracks With Complex Geometry and Application to Very Long Period (VLP) Seismic Signals at Mayotte Submarine Volcano

Resonances of Fluid‐Filled Cracks With Complex Geometry and Application to Very Long Period (VLP) Seismic Signals at Mayotte Submarine Volcano

An enriched mixed finite element model for the simulation of microseismic and acoustic emissions in fractured porous media with multi‐phase flow and thermal coupling

Thermodynamically consistent non-local damage formulation for fluid-driven fracture in poro-viscoelastic media

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