The complex variable fast multipole boundary element method for the analysis of strongly inhomogeneous media

Rejwer-Kosińska, Ewa; Rybarska-Rusinek, Liliana; Linkov, A. M.

doi:10.1016/j.enganabound.2014.04.001

Cited by 19 publications

(12 citation statements)

References 45 publications

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“…We believe the difference lies probably in the crack orientations, that is the cracks in the model (Fig. 3) distributed in a preferential in-plane orientation rather than a random, uncorrelated pattern (Rejwer et al, 2014).…”

Section: Stress Interaction In Randomly Distributed Casesmentioning

confidence: 92%

Effect of stress interactions on anisotropic P‐SV‐wave dispersion and attenuation for closely spaced cracks in saturated porous media

Cao

Chen

et al. 2020

Geophysical Prospecting

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Generally, local stress induced by individual crack hardly disturbs their neighbours for small crack densities, which, however, could not be neglected as the crack density increases. The disturbance becomes rather complex in saturated porous rocks due to the wave‐induced diffusion of fluid pressures. The problem is addressed in this study by the comparison of two solutions: the analytical solution without stress interactions and the numerical method with stress interactions. The resultant difference of effective properties can be used to estimate the effect of stress interactions quantitatively. Numerical experiments demonstrate that the spatial distribution pattern of cracks strongly affects stress interactions. For regularly distributed cracks, the resulting stress interaction (shielding or amplification) shows strong anisotropy, depending on the arrangement and density of cracks. It has an important role in the estimation of effective anisotropic parameters as well as the incident‐angle‐dependency of P‐ and SV‐wave velocities. Contrarily, randomly distributed cracks with a relative small crack density generally lead to a strong cancellation of stress interactions across cracks, where both the numerical and analytical solutions show a good agreement for the estimation of effective parameters. However, for a higher crack density, the incomplete cancellation of stress interactions is expected, exhibiting an incidence‐angle dependency, slightly affecting effective parameters, and differentiating the numerical and analytical solutions.

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Section: Stress Interaction In Randomly Distributed Casesmentioning

confidence: 92%

Effect of stress interactions on anisotropic P‐SV‐wave dispersion and attenuation for closely spaced cracks in saturated porous media

Cao

Chen

et al. 2020

Geophysical Prospecting

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“…The division is continued until the number of sources in a cell exceeds a predefined number n l (n l ! 1), assigned from preliminary numerical tests (Rejwer et al, 2014). In this way, the region with sources is represented as a hierarchical tree, which consists of branches (cells with the number of sources greater than n l ) and leaves (cells with the number of sources not exceeding n l ) at successive levels of the division.…”

Section: Speeding Up Evaluation Of Pair-wise Influencesmentioning

confidence: 99%

“…Clearly it depends on the choice of the maximal number n l of sources in a leaf. A proper choice of n l is established from preliminary tests (Rejwer et al, 2014).…”

Section: Building the Hierarchical Treementioning

confidence: 99%

Speeded simulation of seismicity accompanying mining and hydrofracture

Rybarska-Rusinek

Rejwer-Kosińska

Linkov

2018

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Purpose At present numerical simulation of seismicity, used in mining and hydraulic fracturing practice, is quite time expensive what hampers its combined employing with observed seismicity in real time. The purpose of this paper is to suggest a mean for drastic speeding up numerical modeling seismic and aseismic events. Design/methodology/approach The authors propose the means to radically decrease the time expense for the bottleneck stage of simulation: calculations of stresses, induced by a large group of already activated flaws (sources of events), at locations of flaws of another large group, which may be activated by the stresses. This is achieved by building a hierarchical tree and properly accounting for the sizes of activated flaws, excluding check of their influence on flaws, which are beyond strictly defined near-regions of strong interaction. Findings Comparative simulations of seismicity by conventional and improved methods demonstrate high efficiency of the means developed. When applied to practical mining and hydrofracturing problems, it requires some two orders less time to obtain practically the same output results as those of conventional methods. Originality/value The proposed improvement provides a means for simulation of seismicity in real time of mining steps and hydrofracture propagation. It can be also used in other applications involving seismic and aseismic events and acoustic emission.

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“…Как правило, приближение невзаимодействия применимо в случае, если трещины достаточно удалены друг от друга. В случае близко расположенных трещин (большой плотности трещин) эффективные упругие свойства, как правило, определяются на основе численного решения соответствующих задач теории упругости [7][8][9][10][11][12]. В частности, в работах [12,13] показано, что упругие свойства материала, содержащего случайно расположенные и произвольно ориентированные трещины, остаются ортотропными при достаточно высоких плотностях трещин.…”

Section: Introductionunclassified

Calculation of the normal and shear compliances of a three-dimensional crack taking into account the contact between the crack surfaces

Lapin

Kuzkin

2019

Lett. Mater.

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The calculation of the effective mechanical properties of materials with cracks is a long-standing problem in micromechanics. Usually each crack is modeled by a mathematical cut with traction free surfaces. In this case, the normal and shear compliances of the crack are approximately equal. Then the effective elastic properties of the material with randomly located and arbitrary oriented cracks are orthotropic. If the partial contact between the crack surfaces is taken into account, then the normal and shear compliances are generally different, and the effective properties are no longer orthotropic. This paper proposes a three-dimensional model for estimation of the effect of contacts on the normal and shear compliances of the crack. An infinite flat crack is considered. The surfaces of the crack are connected by a doubly periodic system of identical contacts. Each contact has the shape of a rectangular parallelepiped. The centers of the contacts form a square lattice. The influence of contact sizes and distance between contacts on the ratio of the normal and shear compliances of the crack is investigated. The compliances are calculated numerically using the finite element method. Calculations are carried out for a periodic cell containing a single contact. It is shown that in all considered cases, the normal compliance of the crack is less than shear compliance. The difference between the compliances increases with increasing contact height. A comparison with similar results obtained in a two-dimensional formulation is carried out. It is shown that in the twodimensional case the ratio of compliances is larger than in the three-dimensional case.

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The complex variable fast multipole boundary element method for the analysis of strongly inhomogeneous media

Cited by 19 publications

References 45 publications

Effect of stress interactions on anisotropic P‐SV‐wave dispersion and attenuation for closely spaced cracks in saturated porous media

Effect of stress interactions on anisotropic P‐SV‐wave dispersion and attenuation for closely spaced cracks in saturated porous media

Speeded simulation of seismicity accompanying mining and hydrofracture

Calculation of the normal and shear compliances of a three-dimensional crack taking into account the contact between the crack surfaces

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