Analytical Solutions for Plane Strain Consolidation of Layered Unsaturated–Saturated Ground With Vertical Drains: Role of Lateral Semi‐Permeable Boundaries

IF 3.6 2区工程技术 Q2 ENGINEERING, GEOLOGICAL

International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2026-09-16 DOI:10.1002/nag.70446

Linzhong Li, Yu Han, Lianghua Jiang, Jing He, Zhen Yang

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引用次数: 0

Abstract

The coexistence of saturated and unsaturated soil layers is common for soil subgrade improvement by a combination of prefabricated vertical drains (PVDs) and surcharge preloading. In such scenarios, the smear effect of PVDs and the layered hydraulic properties significantly influence the time‐dependent settlement. Under plane strain conditions, this paper analytically investigates the consolidation behavior of a composite subgrade consisting of a two‐phase (air‐water) flow unsaturated layer and a single‐phase (water) flow saturated layer, with PVDs installed on both lateral sides. By integrating classic consolidation theories for saturated and unsaturated porous media, and featuring the smear effect induced by PVDs using lateral semi‐permeable boundary conditions, Laplace‐domain analytical formulas for excess pore‐air pressure, excess pore‐water pressure, and surface settlement are derived. The proposed solutions are validated against the special cases of a homogeneous single soil ground with lateral semi‐permeable boundaries. A convergence study indicates that truncating 40 terms in the infinite series achieves a good trade‐off between accuracy and efficiency. This paper, with the present solution, conducts parametric investigations to examine how the lateral boundary parameter, PVD spacing, and hydraulic anisotropy affect the consolidation behavior. The results show that when the unsaturated layer has lower hydraulic conductivity than the saturated layer, the lateral semi‐permeable boundary condition significantly influences the pore‐water‐dominated consolidation stage across all examined PVD spacings and anisotropy ratios. This finding indicates that mitigating the smear effect is consistently beneficial for accelerating the consolidation of unsaturated–saturated soil composite strata across all examined PVD spacings and permeability anisotropy ratios.

查看原文本刊更多论文

纵向排水层状非饱和-饱和地基平面应变固结解析解：侧向半渗透边界的作用

在预制垂直排水沟与堆载预压相结合的土基改良中，饱和与非饱和土层共存是常见的现象。在这种情况下，PVDs的涂抹效应和层状水力特性显著影响随时间变化的沉降。在平面应变条件下，分析研究了由两相（气-水）流非饱和层和单相（水）流饱和层组成的复合路基的固结行为，并在两侧安装了PVDs。通过整合饱和和非饱和多孔介质的经典固结理论，并考虑侧向半渗透边界条件下PVDs引起的涂污效应，导出了超孔隙-空气压力、超孔隙-水压力和表面沉降的拉普拉斯域解析公式。针对具有横向半渗透边界的均匀单一土壤的特殊情况，验证了所提出的解决方案。收敛性研究表明，在无穷级数中截断40项可以在精度和效率之间取得很好的平衡。本文利用本解进行了参数化研究，考察了侧向边界参数、PVD间距和水力各向异性对固结行为的影响。结果表明，当非饱和层的水力导率低于饱和层时，横向半渗透边界条件显著影响了所有PVD间距和各向异性比中孔隙水主导的固结阶段。这一发现表明，在所有测试的PVD间距和渗透率各向异性比中，减轻涂抹效应始终有利于加速非饱和-饱和土壤复合地层的固结。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal for Numerical and Analytical Methods in Geomechanics 工程技术-材料科学：综合

CiteScore

6.40

自引率

12.50%

发文量

160

审稿时长

9 months

期刊介绍： The journal welcomes manuscripts that substantially contribute to the understanding of the complex mechanical behaviour of geomaterials (soils, rocks, concrete, ice, snow, and powders), through innovative experimental techniques, and/or through the development of novel numerical or hybrid experimental/numerical modelling concepts in geomechanics. Topics of interest include instabilities and localization, interface and surface phenomena, fracture and failure, multi-physics and other time-dependent phenomena, micromechanics and multi-scale methods, and inverse analysis and stochastic methods. Papers related to energy and environmental issues are particularly welcome. The illustration of the proposed methods and techniques to engineering problems is encouraged. However, manuscripts dealing with applications of existing methods, or proposing incremental improvements to existing methods – in particular marginal extensions of existing analytical solutions or numerical methods – will not be considered for review.