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<p>Low-frequency cyclic loading commonly occurs in port logistics yards, bulk storage facilities, and similar loading–unloading facilities, where long-term consolidation of vertical-drain-improved soft ground is a key serviceability concern. To address this problem, this study develops a nonlinear consolidation framework that integrates stress-dependent soil compressibility and permeability, time- and depth-dependent well resistance, and vertical seepage within a unified formulation. A numerical solution procedure is established to evaluate the averaged excess pore-water pressure and consolidation response under externally applied trapezoidal cyclic loading. The method is verified through limiting-case comparisons and an independent published PVD unit-cell test under continuous cyclic loading. In the cyclic benchmark, the final cumulative settlement is predicted with a relative error of 3.04%, indicating satisfactory accuracy for the macroscopic cumulative response. The results show that the averaged excess pore-water pressure evolves through accumulation, oscillation, and stabilization before approaching a periodic state. Under the representative conditions examined, time- and depth-dependent well resistance is identified as the main retardation mechanism affecting long-term consolidation efficiency. Comparative analyses further show that the simplest uncoupled idealizations may underestimate the required consolidation time by about 95% relative to the fully coupled solution. Vertical seepage is particularly important for shallow foundations, for which the mid-stage degree of consolidation increases by about 10–15% and the residual pore-pressure retention between cycles is markedly reduced. For the representative cases studied, increasing the proportion of time spent in the high-level holding stage shows a clearer benefit to consolidation efficiency than merely increasing the peak load, whereas excessively high peak loading may become unfavorable when nonlinear drainage degradation is pronounced. These findings provide a practical basis for long-term performance assessment and loading-schedule optimization of drain-improved soft ground under operational low-frequency cyclic loading.</p>

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Nonlinear Consolidation of Vertical-Drain-Improved Soft Ground Under Trapezoidal Cyclic Loading with Time- and Depth-Dependent Well Resistance

  • 期刊论文

  • 发表日期：

    2026年4月1日

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  • Guanhao Wang,
  • Qiunan Chen

摘要

Low-frequency cyclic loading commonly occurs in port logistics yards, bulk storage facilities, and similar loading–unloading facilities, where long-term consolidation of vertical-drain-improved soft ground is a key serviceability concern. To address this problem, this study develops a nonlinear consolidation framework that integrates stress-dependent soil compressibility and permeability, time- and depth-dependent well resistance, and vertical seepage within a unified formulation. A numerical solution procedure is established to evaluate the averaged excess pore-water pressure and consolidation response under externally applied trapezoidal cyclic loading. The method is verified through limiting-case comparisons and an independent published PVD unit-cell test under continuous cyclic loading. In the cyclic benchmark, the final cumulative settlement is predicted with a relative error of 3.04%, indicating satisfactory accuracy for the macroscopic cumulative response. The results show that the averaged excess pore-water pressure evolves through accumulation, oscillation, and stabilization before approaching a periodic state. Under the representative conditions examined, time- and depth-dependent well resistance is identified as the main retardation mechanism affecting long-term consolidation efficiency. Comparative analyses further show that the simplest uncoupled idealizations may underestimate the required consolidation time by about 95% relative to the fully coupled solution. Vertical seepage is particularly important for shallow foundations, for which the mid-stage degree of consolidation increases by about 10–15% and the residual pore-pressure retention between cycles is markedly reduced. For the representative cases studied, increasing the proportion of time spent in the high-level holding stage shows a clearer benefit to consolidation efficiency than merely increasing the peak load, whereas excessively high peak loading may become unfavorable when nonlinear drainage degradation is pronounced. These findings provide a practical basis for long-term performance assessment and loading-schedule optimization of drain-improved soft ground under operational low-frequency cyclic loading.