EFFECTIVE PRESSURE AND GENERALIZED EFFECTIVE BIOT STRESS OF POROUS CONTINUUM IN UNSATURATED GRANULAR MATERIALS
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摘要:多孔连续体理论框架下的非饱和多孔介质广义有效压力定义和Bishop参数的定量表达式长期以来存在争议, 这也影响了对与其直接相关联的非饱和多孔介质广义Biot有效应力的正确预测. 基于随时间演变的离散固体颗粒−双联液桥−液膜体系描述的Voronoi胞元模型, 利用由模型获得的非饱和颗粒材料表征元中水力-力学介观结构和响应信息, 文章定义了低饱和度多孔介质局部材料点的有效内状态变量: 非饱和多孔连续体的广义Biot有效应力和有效压力, 导出了其表达式. 所导出的有效压力公式表明, 非饱和多孔连续体的有效压力张量为各向异性, 它不仅对非饱和多孔连续体广义Biot有效应力张量的静水应力分量的影响呈各向异性, 同时也对其剪切应力分量有影响. 文章表明, 非饱和多孔连续体中提出的广义Biot理论和双变量理论的基本缺陷在于它们均假定反映非混和两相孔隙流体对固相骨架水力−力学效应的有效压力张量为各向同性. 此外, 为定义各向同性有效压力张量和作为加权系数而引入的Bishop参数并不包含对非饱和多孔连续体中局部材料点水力−力学响应具有十分重要效应的基质吸力. 所导出的非饱和多孔介质广义Biot有效应力和有效压力公式(包括反映有效压力各向同性效应的有效Bishop参数)可在以协同计算均匀化方法为代表的非饱和颗粒材料计算多尺度方法中上传到在宏观非饱和多孔连续体设置了表征元的局部材料点.Abstract:The definition of effective pressure with associated formula of the Bishop parameter for unsaturated porous medium proposed in the frame of the theory of macroscopic porous continuum has been controversial for a long time. This also affects the correct prediction of directly related generalized Biot effective stress. Based on the Voronoi cell model described with the discrete system composed of solid particles, binary bond liquid bridges and liquid films, the present paper presents the definitions of effective internal state variables at local material points in unsaturated porous continua with low saturation, i.e. effective pressure and generalized Biot effective stress. Using the proposed Voronoi cell model, their expressions are formulated with the information of hydro-mechanical meso-structure and moso-response evolved with incremental loading process exerted on the representative volume element (RVE) of unsaturated granular material. With the derived effective pressure formula, it is demonstrated that the effective pressure tensor of unsaturated porous continuum is anisotropic. It has not only an anisotropic effect on hydrostatic components, but also an effect on shear stress components, of generalized Biot effective stress tensor. It is demonstrated that the fundamental defect of both the generalized Biot theory and the so-called bivariate theory lies in that it is assumed that effective pore pressure tensor representing the hydro-mechanical effect of two immiscible pore fluids on the solid skeleton of unsaturated porous continua is isotropic. In addition, the Bishop parameter introduced as the weighted factor to define the isotropic effective pore pressure tensor is assumed not related to the matrix suction with very important effect on the hydro-mechanical response occurring at local material points over unsaturated porous continua. The derived formulae of both generalized Biot effective stress and effective pressure (including effective Bishop parameter reflecting the isotropic effect of effective pressure) can be upscaled to a local material point, where the RVE is assigned, in macroscopic unsaturated porous continua, for computational multi-scale methods represented by the concurrent computational homogenization method for unsaturated granular materials.
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图 1基于Voronoi胞元模型描述的非饱和颗粒材料的表征元
Figure 1.The RVE of unsaturated particle materials described with Voronoi cell models
图 2参考颗粒
$k$ 表面$\varGamma _{\text{s}}^k$ 上由一个以绿色标记的干表面段$\varGamma _{\text{s}}^{kq{\text{g}}}$ 隔开的以红色标记的两个相邻湿表面段$\varGamma _{\text{s}}^{kq{\text{l}}}$ 和$\varGamma _{\text{s}}^{k\left( {q + 1} \right){\text{l}}}$ Figure 2.Two neighboring wetted boundary segments
$\varGamma _{\text{s}}^{kq{\text{l}}}$ and$\varGamma _{\text{s}}^{k\left( {q + 1} \right){\text{l}}}$ marked with red color on the surface$\varGamma _{\text{s}}^k$ of the reference particlekisolated by a dry boundary segment$\varGamma _{\text{s}}^{kq{\text{g}}}$ marked with green color on$\varGamma _{\text{s}}^k$ 
图 3作用于第
$q$ 个双联液桥半月面与参考颗粒表面段$\varGamma _{\text{s}}^{kq{\text{l}}}$ 两个交汇处的孔隙液相与气相之间的表面张力向量Tkq1和Tkq2Figure 3.Interfacial tension force vectors
${{\boldsymbol{T}}^{kq1}}$ and${{\boldsymbol{T}}^{kq2}}$ between pore liquid and gaseous phases applied at the two intersections formed by the liquid meniscus of theqth binary bond liquid bridge with the particle surface segment$\varGamma _{\text{s}}^{kq{\text{l}}}$ -
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