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<p>The consolidation behavior of unsaturated viscoporoelastic media under multi-dimensional, time-dependent loading remains a significant challenge in geotechnical engineering, with most existing solutions are limited to simplified one-dimensional or uncoupled theories. This study presents a fully coupled Biot-type consolidation model for layered unsaturated media subjected to an axisymmetric ramping load. The model is formulated based on Fredlund's two‑stress state variable theory and incorporates the Merchant viscoelastic model to accurately capture long-term secondary compression. The governing equations are solved using a robust semi-analytical approach combining the Laplace-Hankel transform and the precise integration method. Parametric analyses reveal that the elastic modulus <i>E</i><sub>0</sub> predominantly controls the instantaneous settlement, the final settlement, and the peak excess pore pressures, while the viscosity coefficient <i>η</i><sub>1</sub> and modulus <i>E</i><sub>1</sub> govern the rate of secondary consolidation. The proposed solution provides a more realistic and efficient tool for predicting the time-dependent settlement and pore pressure dissipation in complex unsaturated foundations.</p>

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Axisymmetric consolidation analysis of layered unsaturated viscoporoelastic media under a ramping load

  • 期刊论文

  • 发表日期：

    2026年5月10日

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  • Xianyu Zhu,
  • Qi Mu,
  • Liuyang Li,
  • Zi Ye

摘要

The consolidation behavior of unsaturated viscoporoelastic media under multi-dimensional, time-dependent loading remains a significant challenge in geotechnical engineering, with most existing solutions are limited to simplified one-dimensional or uncoupled theories. This study presents a fully coupled Biot-type consolidation model for layered unsaturated media subjected to an axisymmetric ramping load. The model is formulated based on Fredlund's two‑stress state variable theory and incorporates the Merchant viscoelastic model to accurately capture long-term secondary compression. The governing equations are solved using a robust semi-analytical approach combining the Laplace-Hankel transform and the precise integration method. Parametric analyses reveal that the elastic modulus E0 predominantly controls the instantaneous settlement, the final settlement, and the peak excess pore pressures, while the viscosity coefficient η1 and modulus E1 govern the rate of secondary consolidation. The proposed solution provides a more realistic and efficient tool for predicting the time-dependent settlement and pore pressure dissipation in complex unsaturated foundations.