Modeling of Wave Propagation in Block Media

Aleksandrova, N. I.; Sher, Eran

doi:10.1007/s10913-005-0045-9

Cited by 41 publications

(16 citation statements)

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“…Among those dynamic phenomena we distinguish the propagation of the pendulum waves having a low velocity of spread and long length under a pulse action in rock masses with the block structure. Some peculiarities of the pendulum waves were studied on one-dimensional models of the block media in [3,4]. In these papers we calculated the wave motion in a chain of elastic rods, separated by compressible intermediate layers, and showed that a low-frequency disturbance caused by the pulse action is well described in the model of "rigid blocks and viscoelastic layers".…”

Section: Introductionmentioning

confidence: 99%

The discrete Lamb problem: Elastic lattice waves in a block medium

Aleksandrova

2014

Wave Motion

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Highlights• An asymptotic behavior of perturbations for the transient Lamb problem for a point step load in a discrete medium is obtained.• Numerical examples are given to demonstrate the accuracy of our analytical solutions.• AbstractWe study the propagation of transient waves under the action of a vertical step point load on the surface of a half-space filled by a block medium. The block medium is modeled by a square lattice of masses connected by springs in the directions of the axes x, y, and in the diagonal directions. The problem is solved by two methods. Analytically, we obtain asymptotic solutions in the vicinity of the Rayleigh wave at large time intervals. Numerically, we obtain a solution for any finite time interval. We compare these solutions with each other and with the solution to the Lamb problem for an elastic medium.

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Section: Introductionmentioning

confidence: 99%

The discrete Lamb problem: Elastic lattice waves in a block medium

Aleksandrova

2014

Wave Motion

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“…Similar problems were considered in [9,10]. In the present paper, we give more complete calculation results with the irreversible crumpling of the layers on the contact boundary taken into account.…”

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confidence: 90%

“…4) were also performed taking into account the presence of the zone of contact with irreversible crumpling of roughness [see (10)] for the following parameter values: E s = 2 · 10 3 MPa, R = 0.2h, 2h = 0.01 m, t 0 = 5 · 10 −5 sec, a = 1, and n = 20.…”

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confidence: 99%

Propagation of a low-frequency wave component in a model of a block medium

Saraikin

2009

J Appl Mech Tech Phy

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This paper studies the properties of a model of a block medium consisting of absolutely rigid blocks separated by deformable layers. The model is proposed to describe the low-frequency spectral region of a perturbation wave propagating in the medium of this structure. The model is based on the assumption that the low-frequency part of the wave train provides the least distorted information on the average characteristics of the structure of the medium on the wave pathway. Calculation of waves in a one-dimensional assembly of blocks (rods) and deformable layers show that the model ignoring the deformation of the blocks is applicable only in the case where the stiffness of the layer is low compared to the stiffness of the rod. A correction is applied to eliminate this restriction in the case of a long-wave approximation.The need to take into account the discrete structure of a real rock massif was noted in [1, 2]. The discrete structure of the material at various scale levels was taken into account in the solution of problems of dynamic crack propagation in [3,4]. A two-dimensional model for the dynamics of a discrete medium consisting of rigid rectangular blocks in contact through thin elastic layers was examined in [5]. It was assumed that layers between the blocks consisted of two parts, each of which was a surface layer of a block weakened by defects and hence loaded to a greater degree than the core of the block. Therefore, it was assumed in [5] that the kernel is absolutely rigid. Because inertia was ignored, the approximate consideration of the deformation of thin compound layers was actually reduced to their replacement by equivalent springs in both tension-compression and shear. Later, the possibility of crumpling of roughness uniformly distributed on the layer contact surface was taken into account with the use of Hertz theory [6][7][8].We study the specificity of wave propagation in a block medium using a one-dimensional model. An assembly consisting of n rectangular blocks (below, rods of length 2H) separated by thin layers of length 2h consisting of two identical parts is examined. The last rod of the assembly rests against an absolutely rigid wall. The entire assembly was initially statically compressed to eliminate tensile stresses and, hence, the possible loss of contacts during dynamic loading of the left end of the assembly. Therefore, all quantities to be calculated below should be understood as deviations from the given initial state; in other words, a tensile stress not exceeding the initial compression is admitted in the propagating waves.We will seek a numerical solution under the assumption that both the rods and layers are deformed elastically. A characteristic element of this chain is shown in Fig. 1a, where rectangles correspond to rods between which there is a spring layer. In this case, at the point of connection of the springs, the displacements of their ends are set equal to each other: v − = v + . The longitudinal displacement u k (t, x) in the kth rod is described by the wave equation

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“…The influence of the viscosity of the dampers on the attenuation of perturbations is studied. We compare our numerical results for the block medium with known analytical solutions for the elastic medium.In [4][5][6][7][8][9], we studied one-dimensional mathematical models of viscoelastic deformation of block media and have shown that the presentation of the blocks as massive rigid bodies allows us to distinguish from a complex dynamic state of the block medium that part of it, which is determined by the deformation of the interlayers between the blocks. The presentation of the blocks as massive rigid bodies made it possible to accurately describe the low-frequency pendulum waves arising under the impact load.…”

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Seismic waves in a three-dimensional block medium

Aleksandrova¹

2016

Proc. R. Soc. A.

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Abstract. We study numerically the propagation of seismic waves in a three-dimensional block medium. The medium is modeled by a spatial lattice of masses connected by elastic springs and viscous dampers. We study Lamb's problem under a surface point vertical load. The cases of both step and pulse load are considered. The displacements and velocities are calculated for surface masses. The influence of the viscosity of the dampers on the attenuation of perturbations is studied. We compare our numerical results for the block medium with known analytical solutions for the elastic medium.

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Modeling of Wave Propagation in Block Media

Cited by 41 publications

References 1 publication

The discrete Lamb problem: Elastic lattice waves in a block medium

The discrete Lamb problem: Elastic lattice waves in a block medium

Propagation of a low-frequency wave component in a model of a block medium

Seismic waves in a three-dimensional block medium

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