Analytical solutions for 1D consolidation of unsaturated soils with mixed nonhomogeneous boundary conditions

LING Dao-sheng; ZHAO Tian-hao; NIU Jia-jun; ZHU Song; SHAN Zhen-dong

doi:10.16285/j.rsm.2020.1286

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Analytical solutions for 1D consolidation of unsaturated soils with mixed nonhomogeneous boundary conditions

更新时间：2026-06-25

- Analytical solutions for 1D consolidation of unsaturated soils with mixed nonhomogeneous boundary conditions
- Vol. 42, Issue 4, Pages: 883-891(2021)
- 作者机构：
  
  1. 浙江大学岩土工程研究所,浙江,杭州,310058
  2. 浙江大学软弱土与环境土工教育部重点实验室,浙江,杭州,310058
  3. 中国地震局工程力学研究所,黑龙江,哈尔滨,150080
- 作者简介：
- 基金信息：
- DOI：10.16285/j.rsm.2020.1286
  CLC： TU43
- Online First：21 April 2021，
  
  Published：2021
- 稿件说明：
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LING Dao-sheng, ZHAO Tian-hao, NIU Jia-jun, et al. Analytical solutions for 1D consolidation of unsaturated soils with mixed nonhomogeneous boundary conditions[J]. 2021, 42(4): 883-891.
DOI：

LING Dao-sheng, ZHAO Tian-hao, NIU Jia-jun, et al. Analytical solutions for 1D consolidation of unsaturated soils with mixed nonhomogeneous boundary conditions[J]. 2021, 42(4): 883-891. DOI： 10.16285/j.rsm.2020.1286.

摘要

非饱和土的固结研究对道路工程、软土地基处理工程等具有十分重要的意义。基于Fredlund和Hasan提出的非饱和土一维固结理论，给出了土体内孔隙水压力和孔隙气压力变化的控制方程，并给出了单层非饱和土的初始条件与一类随时间变化的混合非齐次边界条件，构成了非饱和土一维固结的定解问题。通过非齐次边界条件齐次化和特征函数展开法，得到了土体内孔隙水压力和孔隙气压力消散的精确时域解析解。最后，通过对比验证了解析方法的正确性，并分析了边界条件指数变化对非饱和土体内孔隙水压力和孔隙气压力的消散以及土体沉降的影响。结果表明，边界处孔压或孔压梯度随时间的指数变化对非饱和土固结过程有明显影响。

Abstract

The consolidation of unsaturated soil is of great significance to road engineering

soft foundation soil improvement

etc. Based on the one-dimensional consolidation theory of unsaturated soil proposed by Fredlund and Hasan

the governing equations for pore water pressure and pore air pressure in the soil are established. The initial conditions and a type of time-dependent mixed nonhomogeneous boundary conditions of single-layer unsaturated soil are presented which constitutes the solution of 1D consolidation of unsaturated soil. The homogenization of nonhomogeneous boundary conditions and the eigenfunction expansion method are adopted to derive exact analytical solutions in time domain for the dissipation of pore water pressure and pore air pressure in the soil. Finally

the method proposed in this paper is validated by experimental comparison

and several examples are used to analyze the effects of exponentially changing boundary conditions on the dissipation of pore water pressure

pore air pressure

and deformation of unsaturated soils. The results show that the speed of exponential change of pore pressure on the boundary or flux across the boundary has significant effect on the consolidation process of unsaturated soil.

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