饱和土一维有限应变固结控制方程辨析  

Understanding governing equations for one-dimensional finite strain consolidation of saturated soils

作　　者：王玮瑜 雷国辉[1,2] 赵鑫[1,2] 戴传杰 谷遇溪 WANG Weiyu;LEI Guohui;ZHAO Xin;DAI Chuanjie;GU Yuxi(Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering,Hohai University,Nanjing 210024,China;Jiangsu Research Center for Geotechnical Engineering Technology,Hohai University,Nanjing 210024,China)

机构地区：[1]河海大学岩土力学与堤坝工程教育部重点实验室,江苏南京210024 [2]河海大学江苏省岩土工程技术工程研究中心,江苏南京210024

出　　处：《岩土工程学报》2025年第4期829-839,共11页Chinese Journal of Geotechnical Engineering

基　　金：国家自然科学基金项目(52178326);江苏省研究生科研与实践创新计划项目(KYCX23_0697)。

摘　　要：饱和土的一维有限应变固结控制方程存在多种表达形式,有Eulerian描述和Lagrangian描述,各有不同的控制变量,包括孔隙率、孔隙比、应变、固结比和超静孔压。为明辨其适用条件,考虑固相的压缩性,建立了两种描述方法间基于孔隙率、孔隙比和位移的坐标转换关系,以及控制变量的时间导数间的转换关系,分析了两种描述方法便于求解的固结问题,并基于Eulerian描述,考虑固相和液相的压缩性和惯性,推导了一维有限应变固结控制方程组,包括连续性方程、动量平衡方程和达西渗流定律。忽略固相和液相的压缩性和惯性后,该方程组简化为一个具有单一控制变量的固结微分方程,通过坐标转换和时间导数转换,也得到了Lagrangian描述下的固结微分方程。将其退化为现有不同形式的有限应变固结控制方程,依据退化过程中涉及的基本假设,明确了这些控制方程的适用条件。Various forms of governing equations are available for one-dimensional finite strain consolidation of saturated soils.They are expressed using either Eulerian or Lagrangian description,each with different dependent variables,including porosity,void ratio,strain,consolidation ratio and excess pore pressure.To better understand the applicability of these equations,the coordinate transformation relationship between the two descriptions is established in terms of porosity,void ratio and displacement considering the compressibility of solid.The transformation relationship between the time derivatives of dependent variable in the two descriptions is also established.The applicability of the two descriptions to solving consolidation problems is analyzed.Considering the compressibility and inertia of solid and liquid,a governing equation system for one-dimensional finite strain consolidation in Eulerian description is derived,including continuity equation,momentum balance equation and Darcy's law.After neglecting the compressibility and inertia of solid and liquid,the system of equations is simplified into a differential equation with a single dependent variable.Through the coordinate transformation and time derivative transformation,the consolidation differential equation with Lagrangian description is also obtained.The differential equations are degenerated into various existing forms of the finite strain consolidation governing equations,and the applicability of these governing equations is clarified through the basic assumptions involved in the degenerating process.

关 键 词：固相和液相 压缩性 Eulerian和Lagrangian空间和时间转换 自然应变 固相和液相惯性 达西定律 

分 类 号：TU43[建筑科学—岩土工程]