One-dimensional consolidation of layered soils with exponentially time-growing drainage boundaries

Abstract

Fully drained and undrained boundary conditions are commonly applied to solve the consolidation problems. In most practical situations, however, impeded drainage boundaries are really a matter of great concern. As an attempt to idealize such boundary conditions, a time-decaying exponential function has recently been suggested to describe the changes of excess pore water pressure at the boundaries of consolidating soils subjected to instantaneous loading. It allows the excess pore water pressure to dissipate smoothly rather than abruptly from its initial value given by the instantaneous loading to the value of zero, leading to an exponentially time-growing drainage boundary. In this study, a numerical solution of one-dimensional consolidation of layered soils with such defined boundaries is derived by using the method of Laplace transform and its numerical inverse. The solution is explicitly expressed and conveniently coded into a computer program for ease and efficiency of practical use. Analytical solutions of one-dimensional consolidation of single-layered soil are also derived by using the method of analytical inverse Laplace transform and the method of separation of variables as well. By comparing these two analytical solutions and comparing with an available analytical solution for two-layered soil with pervious boundaries, the proposed numerical solution for layered soils is validated. Good agreement is obtained, and the accuracy of the numerical solution is verified. Moreover, the dissipation of excess pore water pressure and the increase of degree of consolidation with time for a four-layered soil are investigated to assess the effects of the adopted drainage boundary conditions on consolidation.