摘要
多孔材料的裂纹网络对宏观渗透性的影响显著,正确描述裂纹网络对材料渗透率的影响具有重要的工程意义。该文将开裂多孔材料视作由多孔基体和裂纹夹杂二相组成的复合材料,基于细观力学理论模型中的相互作用直推法(IDD)给出了渗透率张量的IDD理论解。为分析裂纹长度、密度、取向、间距和连通度等裂纹网络细观形貌参数对宏观渗透率的影响,该文使用具有周期结构的重复单元模型建立了二维数值分析模型,采用有限单元法进行数值求解并与IDD理论解进行了对比验证。理论研究表明,IDD理论模型采用单一的开裂密度指标来表征多孔介质的裂纹网络,在开裂密度不大时能够统一地描述裂纹长度、取向、平均横向间距和纵向间距等多个细观形貌指标对材料整体渗透性能的影响,具有良好的适用性和精度;数值分析表明,在裂纹网络的密度不断增大、裂纹相互趋近并最终连通的过程中,IDD理论解逐渐偏离数值解并低估裂纹间相互作用,此时材料渗透率与裂纹密度呈对数关系;网络裂纹一旦连通,整体渗透率则发生突变,此时渗透率的确定需要特别考虑连通裂纹之间的强烈近场相互作用。
Cracked porous material is considered as a two phase composite with a porous matrix and cracking inclusions.An interaction direct derivative（IDD） solution is derived to analyze the permeability of this composite through classic micromechanics theory.Based on the repeating unit cell concept,a simple model with periodic microstructures is suggested to represent cracking geometry in order to study the impact of geometrical characteristics including cracking length,density,orientation,average spacing and connectivity.The finite element analysis is further developed to calculate its overall permeability,which is compared with the IDD explicit results.IDD solution employs the single parameter,cracking density,to capture the impact of cracking on permeability with good applicability and accuracy as cracking degree is not too high.Numerical simulation also shows that： IDD solution tends to deviate from numerical results and underestimate the interaction of cracks as the cracking density is further increasing and cracks approach more closer between one another.During this approaching course,the relationship between cracking density and overall permeability can be described by logarithm law.Once cracks are connected together eventually,the overall permeability would be mutated,and the strong near-field interaction of connectivity should be taken into account to estimate the overall permeability.
出处
《工程力学》
EI
CSCD
北大核心
2013年第4期150-156,共7页
Engineering Mechanics
基金
国家重点基础研究发展规划项目(2009CB623106)
关键词
多孔介质
裂纹夹杂
渗透性
有效介质理论
相互作用直推解
porous medium
cracking inclusion
permeability
effective medium theory
Interaction Direct Derivative（IDD）
