Axisymmetric elastic field in layered non-homogeneous and transversely isotropic geo-materials due to surface traction

Abstract

This paper examines the axisymmetric problem of layered and non-homogeneous geo-material halfspaces with transverse isotropy. The halfspace is subjected to normal traction over a circular area of the boundary surface. A n-layered halfspace system approximates the arbitrary variation of the elastic parameters of non-homogeneous geo-materials with depth. The two-dimensional Fourier integral transforms in the cylindrical coordinate system and the backward transfer matrix method are used for the mathematical formulation and derivation. The solutions of the displacement, stress and strain fields are explicitly expressed in the matrix form in terms of classical improper Hankel transform integrals. The kernel functions of the Hankel transform integrals are explicitly expressed in the forms of backward transfer matrix. The singular terms associated with the improper Hankel transform integrals are analytically isolated and expressed in the exact closed-form. Numerical results indicate that there is no problem in the evaluation of the solutions of non-homogeneous halfspaces with arbitrarily variable elastic parameters and the inhomogeneity and transverse isotropy of layered geo-materials have significant effect on the elastic fields.