Propagation of torsional surface wave in sandy layer sandwiched between a non-homogeneous and a gravitating anisotropic porous semi-infinite media

Abstract

The present paper attempts to study the propagation of torsional surface waves in a pre-stressed dry sandy layer sandwiched by a pre-stressed non-homogeneous semi-infinite medium and an anisotropic porous half-space under gravity. The non-homogeneity in the non-homogeneous layer is caused by the quadratic variation in rigidity, density and initial stress. The inhomogeneity has been assumed as hyperbolic variation in the dry sandy layer. The dispersion equation of motion has been derived under suitable boundary conditions in a close form, which shows the variation of phase velocity of the corresponding wave number. The velocities of torsional waves are calculated numerically as a function of kH and presented in a number of graphs where k is the wave number and H is the thickness of the sandy layer. The effect of inhomogeneity in the elastic modulus of rigidity, pre-stress, density, gravity and porosity depicted by means of graph, using MATLAB software. The study reveals that the torsional waves propagate in the pre-stress dry sandy layer sandwiched between the considered media. This work may be useful to understand the nature of seismic wave propagation during earthquakes.