Fractional derivative modelling for rheological consolidation of multilayered soil under time-dependent loadings and continuous permeable boundary conditions

This paper investigates the one-dimensional rheological consolidation problem of multilayered soils subjected to different time-dependent loadings and continuous permeable boundary conditions. First, by introducing fractional calculus, the conventional Merchant constitutive model is modified to the fractional derivative Merchant (FDM) model, and the newly established model is introduced to describe the rheological characteristics of soil. Subsequently, to simplify the solving process of the consolidation equation, the Laplace transform is utilized to convert the partial differential equations into ordinary differential equations, and the analytical solutions in the Laplace domain are obtained. Furthermore, the solutions in the time domain are obtained by using Abate's fixed Talbot method (AFT method), which is one of the numerical Laplace inversion methods, and the corresponding computer program for the AFT method is attached. A comparison between the degenerated results of this study and those in the literature suggests that the present solutions are more general and applicable. Finally, several instances are provided to study the impacts of model parameters on the consolidation phenomenon.