开裂孔隙材料渗透率的细观力学模型研究

PERMEABILITY OF MICROCRACKED POROUS SOLIDS THROUGH A MICROMECHANICAL MODEL

采用细观力学方法对含随机裂纹网络的孔隙材料渗透性进行研究.开裂孔隙材料渗透性的影响因素包括裂纹网络的密度、连通度、裂纹的开度以及孔隙材料基体渗透性.对于不连通的裂纹网络,该文采用已有的相互作用直推法(interaction direct derivative, IDD)的理论框架,引入裂纹的密度ρ和裂纹开度比b,提出了裂纹夹杂-基体两相复合材料渗透率的IDD理论解.对于部分连通裂纹网络,考虑局部裂纹团内部各个裂纹对有效渗透率的相互放大作用,引入裂纹网络的连通度f,定义与连通度相关的水平裂纹密度ρ~h,按照增量法将表征连通特征的水平裂纹嵌入有效基体中,以此方式来考虑裂纹夹杂间的相互搭接,提出了考虑裂纹连通特征的扩展IDD理论解,分别考虑了基体材料渗透率K_m、裂纹密度ρ、裂纹开度比b以及与连通度f相关的ρ~h.最后通过对有限区域内含随机裂纹网络孔隙材料渗透过程的有限元模拟分别验证了不连通和部分连通裂纹网络扩展IDD模型的适用性:(1)当裂纹不连通时,由于基体对流体渗透的阻隔作用,裂纹的开度对有效渗透率影响不大;(2)当裂纹部分连通时,裂纹密度分别小于1.1 (无关联裂纹网络,分形维数为2.0)、1.2 (关联裂纹网络,分形维数为1.75)时,扩展IDD模型能够很好地估计开裂孔隙材料的有效渗透率,但是随着裂纹进一步扩展,最大裂纹团主导作用凸显,扩展IDD模型不再适用.

This paper investigates the permeability of solids containing a crack network with finite connectivity through micromechanical method.The main factors of permeability include crack density,connectivity,crack opening and permeability of porous matrix.Firstly,for solids with unconnected cracks,the interaction direct derivative(IDD)method is employed to obtain the crack-altered permeability considering crack densityρand crack opening b.Then,for networks containing randomly oriented cracks with intersection,the amplification of permeability by crack connectivity is quantified for local crack clusters.This amplification effect is modeled by arranging parallel cracks on transport direction.By introducing the definition of hypothetically parallel crack densityρ^h,the hypothetically parallel cracks are embedded in a host matrix whose permeability are those of the effective medium.In this way the IDD model is extended to evaluate the permeability of part-connected networks before total percolation occurs,considering the permeability of porous matrix Km,crack densityρ,opening aperture b and parallel crack densityρ^h.Finally,the representative volume element is built for cracked solids with cracks having random spatial locations and the permeability is solved by finite element method.Through this numerical tool,the validity and accuracy of IDD solutions for non-connected and part-connected crack networks are confirmed by several case analysis.The results show that:(1)For non-connected networks,crack opening is found to have little impact on the effective permeability due to the continuous matrix and its low permeability;(2)For part-connected networks,when crack densityρ<1:1(uncorrelated networks,the fractal dimension is 2.0),1.2(correlated networks,the fractal dimension is 1.75),the IDD extended model show a good agreement with numerical results and loses its accuracy due to the clustering effect at more higherρlevel.