饱和土一维有限应变固结控制方程辨析 English Version
Understanding the governing equations of one-dimensional finite strain consolidation of saturated soils
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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利于求解的固结问题，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透定律。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。将其退化到了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。
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关键词:
- 固相和液相的压缩性 /
- Eulerian和Lagrangian空间和时间转换 /
- 自然应变 /
- 考虑固相和液相惯性的达西定律
Abstract: 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 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 finite strain consolidation governing equations, and the applicability of these governing equations is clarified through the basic assumptions involved in the degenerating process.
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