One-Dimensional Consolidation of Multilayered Soil with Continuous Drainage Boundaries and under Time-Dependent Loading

In the practice of reclamation engineering, surcharge loading is gradually applied to preconsolidate soft clayed soil. The in situ drainage boundaries are usually not perfect and can be in a state between fully impermeable and permeable with time. Traditional consolidation theories for homogenous soil with drainage boundaries under instantaneous loading thus cannot provide accurate prediction of the consolidation behavior. This paper extends the one-dimensional consolidation solution by considering the multilayered inhomogeneity of soil, general time-dependent loading and continuous drainage boundaries. Laplace transform and a novel transfer matrix formulation developed in this paper are used to solve the problem. Analytical solutions of excess pore water pressure and average degree of consolidation are derived and expressed in term of inverse Laplace transform. Numerical results in the physical domain are obtained with the aid of Crump's algorithm. The present solutions are verified by comparing with the results in the literatures for some special cases, including multilayered soil and two-layered soils with continuous drainage boundaries under instantaneous loading. For the limiting case of homogenous soil, the present solution can analytically reduce to closed-form Terzaghi's solution. Parametric studies are performed using the new solutions to investigate the consolidation behavior of a four-layered soil. It is shown that the drainage boundary condition, loading path, and loading rate can have a considerable effect on the excess pore water pressure and average degree of consolidation.