Stiffness matrices for layered soils

TLDR

The Haskell‑Thompson transfer matrix method derives layer stiffness matrices that can be used like conventional structural stiffness matrices. Exact expressions for the matrices, approximations for thin layers, and simple illustrative examples are provided. These layer stiffness matrices are symmetric, require fewer operations, handle multiple loadings more easily, allow substructuring, and yield natural asymptotic expressions; the method complements but does not surpass the original Haskell‑Thompson scheme.

Abstract

Abstract The Haskell-Thompson transfer matrix method is used to derive layer stiffness matrices which may be interpreted and applied in the same way as stiffness matrices in conventional structural analysis. These layer stiffness matrices have several advantages over the more usual transfer matrices: (1) they are symmetric; (2) fewer operations are required for analysis; (3) there is an easier treatment of multiple loadings; (4) substructuring techniques are readily applicable; and (5) asymptotic expressions follow naturally from the expressions (very thick layers; high frequencies, etc.). While the technique presented is not more powerful than the original Haskell-Thompson scheme, it is nevertheless an elegant complement to it. The exact expressions are given for the matrices, as well as approximations for thin layers. Also, simple examples of application are presented to illustrate the use of the method.