Modeling the elastic wave propagation in a block medium under the impulse loading

The wave propagation analysis revealed that the low-frequency pendulum wave propagating in a 2D block medium with periodic structure due to the action of local impulse has a two-wave structure. The shape of such wave depends on its propagation direction. Modeling the blast-induced seismic wave propagation in a two-layer block rock mass with the weak upper layer and stiff lower layer showed that the far distant point from the wave excitation source is first reached by the small amplitude pendulum wave running in the stiffer lower layer and then by the delayed maximum-amplitude wave propagating in the upper layer.     

Numerical simulation of shock wave processes in elastic media and structures. Part II: Application results

The authors present finite difference algorithms for solving nonstationary problems on dynamics of elastic media and structures, and perform numerical modeling of the following applied problems: stroke on an elastic half-plane by a rigid die; shock piling; generation of a pendulum wave in a blocky medium by a local impulse effect. One of the goals of the presented modeling is driving the problem solutions with minimized influence of spurious effects inherent to numerical approximation. Finally, the authors compare the results obtained in different models of elastic media.     

A Lattice Model for Viscoelastic Fracture

A plane, periodic, square-cell lattice is considered,consisting of point particles connected by mass-less viscoelastic bonds.Homogeneous and inhomogeneous problems for steady-state semi-infinitecrack propagation in an unbounded lattice and lattice strip are studied.Expressions for the local-to-global energy-release-rate ratios, stressesand strains of the breaking bonds as well as the crack openingdisplacement are derived. Comparative results are obtained forhomogeneous viscoelastic materials, elastic lattices and homogeneouselastic materials. The influences of viscosity, the discrete structure,cell size, strip width and crack speed on the wave/viscous resistancesto crack propagation are revealed. Some asymptotic results related to animportant asymptotic case of large viscosity (on a scale relative to thelattice cell) are shown. Along with dynamic crack propagation, a theoryfor a slow crack in a viscoelastic lattice is derived.     

Influence of the block-hierarchical structure of rocks on the peculiarities of seismic wave propagation

The analysis is performed for the parameters of long pendulum-type waves in a one-dimensional periodic system with an arbitrary hierarchical structure. A case study is carried out into the wave propagation peculiarities in an impact-excited system of equal rigid blocks with parting layers differing in rigidity. The pendulum wave velocity in the automodel block-hierarchical system is determined. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 6, pp. 20–27, November–December, 2007.