Consolidation of multilayered soil with fractional derivative viscoelasticity due to surface loading and internal pumping

Abstract

Classical Terzaghi’s solution provides a useful tool to predict the one-dimensional consolidation of homogeneous elastic soil layer with fully drained/undrained boundary condition under instantaneous loading. Due to the sedimentation process and complex internal structure, natural soils usually exhibit multilayered inhomogeneity and viscoelastic behavior. In practical cases, the drainage capacity of the boundaries can change with time. Thus, these practical factors should be well in considered for accurate prediction of the consolidation. This paper extends the classical Terzaghi’s solution to multilayered viscoelastic soil with continuous drainage boundaries and subjected to time dependent loading. The fractional derivative Kelvin-Voigt model is used to describe the viscoelasticity of soil. Two loading cases namely surface loading and internal pumping are considered. The consolidation problem is solved by Laplace transform technique and a transfer matrix formulation. Analytical solutions for excess pore water pressure, effective stress and settlement are given. The present solution is general and can reduce to existing solutions available in the literatures. Numerical studies are conducted to investigate the effects of viscoelastic parameters, boundary drainage capacity and loading rate on the consolidation behavior. It is shown that the multilayered soil system with large viscosity coefficient and small fractional order can consolidate fast. For the consolidation due to internal pumping, the drainage parameters have no influence on the consolidation process.