Application of spectral Galerkin method for multilayer consolidation of soft soils stabilised by vertical drains or stone columns

The spectral Galerkin method is applied to three multilayer consolidation problems: vertical drains with vacuum, vertical drains with well-resistance, and stone columns. The spectral method provides a consistent approach to solving one-dimensional partial differential equations that arise in consolidation analyses. Material properties are allowed to vary with depth but not with time. Loads may vary with depth and time provided the load function is separable. Non-homogenous boundary conditions can be modelled and loading conditions can be built up through superposition. The starting point for each analysis is the governing equation(s) of existing single layer analytical solutions, before any simplifying assumptions have been made. The article is largely analytical in nature, pointing the way for researches to apply the spectral method to other problems. Practitioners will be interested in the python based geotecha (Walker, 2015) software package which implements the solutions. The computer programs are used to investigate differences between conventional Terzaghi-like consolidation and cases where permeability and compressibility vary with depth but the coefficient of consolidation is constant.