Semi-Analytical Solutions for One-Dimensional Consolidation of Viscoelastic Unsaturated Soils Considering Variable Permeability Coefficient

This paper proposes a semi-analytical solution for one-dimensional consolidation of viscoelastic unsaturated soil considering a variable permeability coefficient under exponential loading. The governing equations of excess pore air pressure (EPAP) and excess pore water pressure (EPWP) were acquired by introducing the Merchant viscoelastic model. By employing Lee’s correspondence principle and the Laplace transform, the solutions for EPAP and EPWP were derived under the boundary conditions of the permeable top surface and impermeable bottom surface. Crump’s method was then used to execute the inverse Laplace transform, yielding a semi-analytical solution in the time domain. Through typical examples, the dissipation of EPAP and EPWP and the change of the average degree of consolidation over time under the influence of different elastic moduli, viscoelastic coefficients, and air-to-water permeability ratios were studied. The variation of the permeability coefficient and its influence on consolidation were also analyzed. The findings of this research show that the consolidation rate of viscoelastic unsaturated soil is slower than that of elastic unsaturated soil; however, an acceleration in the consolidation of the soil is observed when changes in the permeability coefficient are considered. These discoveries enhance our comprehension of the consolidation behaviors exhibited by viscoelastic unsaturated soil, thereby enriching the knowledge base on its consolidation traits.