Derivation and validation of the motion equation for seepage in unsaturated soils

SHAO Long-tan; SUN Yan-pu; DONG Hao

doi:10.16285/j.rsm.2025.0453

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Derivation and validation of the motion equation for seepage in unsaturated soils

更新时间：2026-07-06

- Derivation and validation of the motion equation for seepage in unsaturated soils
- Vol. 47, Issue 2, Pages: 640-646(2026)
- 作者机构：
  
  1. 大连理工大学工程力学系,辽宁,大连,116024
  2. 大连理工大学工业装备结构分析优化与CAE软件全国重点实验室,辽宁,大连,116024
- 作者简介：
- 基金信息：
- DOI：10.16285/j.rsm.2025.0453
  CLC： TU43
- Online First：06 February 2026，
  
  Published：06 February 2026
- 稿件说明：
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SHAO Long-tan, SUN Yan-pu, DONG Hao. Derivation and validation of the motion equation for seepage in unsaturated soils[J]. 2026, 47(2): 640-646.
DOI：

SHAO Long-tan, SUN Yan-pu, DONG Hao. Derivation and validation of the motion equation for seepage in unsaturated soils[J]. 2026, 47(2): 640-646. DOI： 10.16285/j.rsm.2025.0453.

摘要

从非饱和土孔隙水的平衡微分方程出发，突破了传统以达西定律为预设条件的经验模型框架，由孔隙水的平衡微分方程推导出非饱和土渗流的运动方程。通过引入层流渗流时孔隙水的流动阻力与流速成正比的条件，建立了渗透系数的理论公式，揭示了渗流动力学中土-水作用机制的物理本质。为验证理论模型，采用改进的土-水特征曲线-渗透系数联合测定仪，采用多步渗流法对多种土类进行渗流试验，同步获取瞬态渗流速度及含水率参数。试验结果表明：理论公式计算的渗流速度与实测数据在有效饱和度变化范围内高度吻合，初步验证了所推导的非饱和土渗流的运动方程的适用性。

Abstract

Starting from the balance differential equation of pore water in unsaturated soils

this study transcends the traditional empirical model framework predicated on Darcy’s law. The equation of motion for unsaturated soil seepage was derived through rigorous mathematical derivation of the pore water balance differential equation. By introducing the condition that flow resistance is proportional to velocity during laminar seepage

a theoretical formula for permeability coefficient was established

revealing the physical essence of soil-water interaction mechanisms in seepage dynamics. To validate the theoretical model

an improved apparatus for simultaneous measurement of soil-water characteristic curve (SWCC) and permeability coefficient was employed. Multi-step seepage tests were conducted on various soil types

with transient seepage velocity and moisture content parameters obtained synchronously. Experimental results demonstrate that the calculated seepage velocities from the theoretical formula show excellent agreement with measured data across the effective saturation variation range

preliminarily verifying the applicability of the derived equation of motion for unsaturated soil seepage.

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