Case-wise investigation of body-wave propagation in a cross-anisotropic soil with multiple inhomogeneity coefficients

Abstract

The article investigates the propagation behavior of SV-wave, SH-wave, and P-wave in a continuously inhomogeneous cross-anisotropic material. The material properties such as Young’s moduli, shear modulus, and density have been assumed to vary as a function of depth. These functions have been considered as the possible combinations of a polynomial function, exponential function, and trigonometric function. A suitable mathematical formulation of the physical problem has been developed (an eigenvalue problem) with displacement components as fundamental variables. With the help of separation of variables, appropriate substitution, and applicable mathematical treatment, displacement components have been deduced. Furthermore, employing intrinsic boundary conditions, the closed-form expressions for quasi-wave velocities have been derived. Numerical examples have been investigated, and the dependency of phase velocity on phase angle and inhomogeneity coefficients have been shown graphically. It has been observed that the increment and decrement in the degree of material anisotropy disturb the magnitude of phase velocity to a great extent.