A Unified Treatment to 1D Consolidation of Unsaturated Soils

Abstract

The initial conditions, boundary conditions, and external loading are the key factors influencing consolidation characteristics in the one-dimensional (1D) consolidation of unsaturated soils. In previous studies, it was necessary to establish different consolidation models for different conditions, which complicates the solution. To effectively unify these models, this paper establishes a generalized analytical model for 1D consolidation of unsaturated soils under a unified boundary condition. The model also considers the depth-dependent initial stress and time-dependent load. By employing the Laplace integral transform and Crump's numerical inverse transform, semi-analytical solutions for excess pore pressures (EPPs) and average degree of consolidation in the time domain are derived. The accuracy of the obtained solution is verified by comparison with existing solutions under fully permeable boundaries and numerical results under semi-permeable boundaries. Finally, the results under exponential loading show that, by appropriately setting boundary parameters, the unified boundary can be used to simulate arbitrary boundaries with different permeability characteristics, ranging from impermeable to permeable boundaries, thereby demonstrating the generality of the semi-analytical solution. Under different initial conditions, the time required for EPPs dissipation and for settlement stabilization remains the same, determined by the maximum initial EPP. Additionally, the boundary parameters exhibit distinct effects on the degree of consolidation, indicating that the geometric characteristics and permeability of the soil layer and horizontal drainage layer influence soil consolidation differently. Investigating these effects will provide important guidance for improving the consolidation period of unsaturated soils.