Implicit Difference Solution for Position Optimization of a Sand Cushion in the Double-Layered Unsaturated Soil Ground

Sand cushion is widely used in engineering practice to accelerate the consolidation rate of soil ground. However, the consolidation behavior of unsaturated soil with a sand cushion (soil–sand system) remains unclear, and there is no systematic analysis of the optimal position of the sand cushion. Therefore, this study proposes an implicit difference solution with high accuracy and computational efficiency to predict the consolidation behavior of the soil–cushion system and optimize the position of the sand cushion. Two typical diffusion equations describe the transient flow paths of the air and water phases in each unsaturated soil layer. The consolidation equations (diffusion equations) are discretized using the cubic spline interpolation method to obtain a high-precision implicit difference scheme. A comparison with existing analytical solutions confirmed that the proposed numerical solution is reliable and effective. Based on the validated numerical solution, a series of examples was conducted to illustrate the influence of the air/water phase permeability ratio k1(l), interlayer permeability coefficient k2, clogging coefficient, and burial depth of sand cushion on the consolidation behavior of double-layered unsaturated soil.