Modeling of elastic waves in a blocky medium based on equations of the Cosserat continuum

• We model the propagation of waves in a blocky medium with compliant interlayers.
• The model of orthotropic Cosserat continuum is also used to simulate this process.
• Parallel computational algorithms are developed for supercomputers of cluster type.
• The problems of instant rotation of central and boundary blocks are solved.
• Comparison of numerical results shows a good correspondence between two models.

Based on the equations of the dynamics of piecewise-homogeneous elastic material, parallel computational algorithms are developed to simulate the process of stress and strain wave propagation in a medium consisting of a large number of blocks interacting through compliant interlayers. Computations of waves caused by localized impulse perturbations show that such a medium can be considered as isotropic only in the case of sufficiently thin interlayers. In the case of relatively thick interlayers, the anisotropy effects are observed which consist in the appearance of elongated wave fronts along the coordinate directions and characteristic oscillations of velocities and stresses because of the rotational motion of blocks. For the description of waves in a blocky medium with thin interlayers, the equations of the isotropic Cosserat continuum are applicable. As the thickness of interlayers increases, the orthotropic Cosserat continuum theory which takes into account the symmetry of elastic properties relative to the coordinate planes can be applied. By comparing the elastic wave velocities in the framework of piecewise-homogeneous model and continuum model, a simple method is obtained to estimate the mechanical parameters of the orthotropic Cosserat continuum modeling a blocky medium. In two-dimensional formulation of the orthotropic model the computational algorithm and the program system are worked out for the analysis of propagation of elastic waves. The comparison showed good qualitative agreement between the results of computations of waves caused by localized impulses, in the framework of the model of a blocky medium with compliant interlayers and the model of orthotropic Cosserat continuum.