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<p>In numerical calculation for the unsaturated consolidation, the explicit difference method has rarely been used to deal with the soil-cushion system; even the conditional stability of the explicit difference method has never been discussed. In order to improve the computational efficiency of the numerical simulation for the consolidation of the soil-cushion system, a matrix-formed implicit difference method is proposed to solve the consolidation problem of the system, which is described by two partial differential equations. The implicit difference scheme is strictly demonstrated to be unconditionally stable using the von Neumann criterion. Considering three typical examples, the comparisons among explicit difference solutions, implicit difference solutions, and analytical solutions validate that the proposed algorithms can efficiently reduce the computational cost. The proposed numerical solution is used to predict the consolidation behavior of unsaturated soil foundations with two horizontal drainage sand cushions. The results show that the cushions are embedded at the optimal designed depth and will elevate the consolidation rate of the soil-cushion system.</p>

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Implicit Difference Solution for One-Dimensional Consolidation of Unsaturated Soil: Numerical Verification and Application to Soil-Cushion System

  • 期刊论文

  • 发表日期：

    2025年3月14日

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  • Qian He,
  • Quan Yuan,
  • Lin Lang,
  • Jixing Cao

摘要

In numerical calculation for the unsaturated consolidation, the explicit difference method has rarely been used to deal with the soil-cushion system; even the conditional stability of the explicit difference method has never been discussed. In order to improve the computational efficiency of the numerical simulation for the consolidation of the soil-cushion system, a matrix-formed implicit difference method is proposed to solve the consolidation problem of the system, which is described by two partial differential equations. The implicit difference scheme is strictly demonstrated to be unconditionally stable using the von Neumann criterion. Considering three typical examples, the comparisons among explicit difference solutions, implicit difference solutions, and analytical solutions validate that the proposed algorithms can efficiently reduce the computational cost. The proposed numerical solution is used to predict the consolidation behavior of unsaturated soil foundations with two horizontal drainage sand cushions. The results show that the cushions are embedded at the optimal designed depth and will elevate the consolidation rate of the soil-cushion system.