Supercomputer Modeling of Wave Propagation in Blocky Media Accounting Fractures of Interlayers

Sadovskii, V. M.; Sadovskaya, O. V.

doi:10.1007/978-3-030-38708-2_22

Cited by 5 publications

(5 citation statements)

References 17 publications

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“…In general, modeling of rocks is usually performed within different approaches, such as multi-modular [23][24][25], block [26][27][28][29], hierarchy-block [30][31][32][33], and continuous medium [34][35][36]. In poromechanics, the dispersion of the elastic moduli of sedimentary rocks is considered by poroelastic models which describe the rock as a solid elastic matrix with infilling viscous fluid.…”

Section: Model Formulationmentioning

confidence: 99%

Modelling of the Dynamic Young’s Modulus of a Sedimentary Rock Subjected to Nonstationary Loading

et al. 2020

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This paper presents a mathematical model that reflects the nature of the dynamic Young’s modulus of a dry sedimentary rock during nonstationary uniaxial loading. The model is based on an idealized model of a system suggested by Jaeger J.C. A rock sample is considered as a spring with stiffness, the bottom point of which is fixed, while the upper point carries a mass. A sample experiences dynamic load and the rock matrix response. Displacement of the mass from the equilibrium state sets the variation of the sample’s length. Displacement of all the sample’s points goes according to the same law regardless of the point location. The response of a rock to a disturbing nonstationary load is selected based on the combination of conditions of each experiment, such as the load frequency and amplitude and the mass, length, and diameter of a sample. The mathematical model is consistent with experimental data, according to which an increase in load frequency leads to an increase in the dynamic Young’s modulus for each value of the load. The accuracy of the models is evaluated. The relations underlying the model can be used as a basis to describe the Young’s modulus dispersion of sedimentary rocks under the influence of nonstationary loads.

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Section: Model Formulationmentioning

confidence: 99%

Modelling of the Dynamic Young’s Modulus of a Sedimentary Rock Subjected to Nonstationary Loading

et al. 2020

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“…In [9], the qualitative correspondence of the finite-difference solution of the Lamb problem for a block medium according to this model with the results of field experiments carried out in a limestone quarry is shown. An alternative approach is based on a mathematical model of a block medium with elastic blocks interacting through compliant interlayers [5,10,11]. To describe interlayers, various versions of the model were proposed in [10,11], in which interlayers between elastic blocks can be elastic, viscoelastic, plastic, and porous.…”

Section: Introductionmentioning

confidence: 99%

“…An alternative approach is based on a mathematical model of a block medium with elastic blocks interacting through compliant interlayers [5,10,11]. To describe interlayers, various versions of the model were proposed in [10,11], in which interlayers between elastic blocks can be elastic, viscoelastic, plastic, and porous. In this article, the 3D model proposed in [8] is modified.…”

Section: Introductionmentioning

confidence: 99%

Model of Block Media Taking Into Account Internal Friction

Aleksandrova

2022

Mech. Solids

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The block medium is modeled by a discrete-periodic spatial lattice of masses connected by elastic springs and viscous dampers. To describe the viscoelastic behavior of the interblock layers, a rheological model of internal friction with two Maxwell elements and one Voigt element with the quality factor of the material as the determining parameter is proposed. Numerical experiments show that, within the framework of this interlayer model, it is possible to select the viscosity and stiffness of the Maxwell and Voigt elements so that the quality factor of the material differs from the given constant value by no more than 5%. In the one-dimensional case, within the framework of the proposed model, the influence of the quality factor on the dispersion properties of a block medium is studied and it is shown that the greatest effect of the quality factor on the dispersion is observed in the low-frequency part of the spectrum. In the three-dimensional case, within the framework of the proposed model, some geomechanical problems are numerically studied for a block half-space under the action of a surface concentrated vertical load. Namely, the attenuation of the velocity amplitudes of surface blocks was studied depending on the Q-factor under step action and under the action of a Gaussian pulse. In addition, we study a layer on the surface of a halfspace under the action of a concentrated vertical impulse load in the case when both the layer and the halfspace are block media but have different properties.

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“…Our aim is to find such appropriate approximations while remaining within the framework of conservative Godunov's scheme which is widely used in numerical solution of twoand three-dimensional problems [1]. The scheme can be modified to simulate wave propagation in granular and porous materials with different resistances to compression and tension [2][3][4], wave propagation and fracturing in blocky media [5][6][7] and other nonlinear processes.…”

Section: Introductionmentioning

confidence: 99%

Finite Difference Schemes for Modelling the Propagation of Axisymmetric Elastic Longitudinal Waves

Sadovskii

Sadovskaya

Efimov

et al. 2020

Journal of Siberian Federal University. Mathematics &Amp; Physics

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An efficient finite difference shock-capturing scheme for the solution of direct seismic problems is constructed. Problem formulation is based on equations of the dynamics of elastic medium with axial symmetry. When implementating the scheme on multiprocessor computing systems, the two-cyclic splitting method with respect to spatial variables is used. One-dimensional systems of equations that arise in the context of splitting procedure are represented as subsystems for longitudinal, transverse and torsional waves. The case of longitudinal waves is considered in this paper. The results of simulations with the use of explicit grid-characteristic schemes and implicit schemes of the "predictor–corrector" type with controllable dissipation of energy are compared with exact solutions that describe propagation of monochromatic waves

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Supercomputer Modeling of Wave Propagation in Blocky Media Accounting Fractures of Interlayers

Cited by 5 publications

References 17 publications

Modelling of the Dynamic Young’s Modulus of a Sedimentary Rock Subjected to Nonstationary Loading

Modelling of the Dynamic Young’s Modulus of a Sedimentary Rock Subjected to Nonstationary Loading

Model of Block Media Taking Into Account Internal Friction

Finite Difference Schemes for Modelling the Propagation of Axisymmetric Elastic Longitudinal Waves

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