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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。
The effect of crack network of porous materials on the macroscopic permeability is significant. It is of important engineering significance to correctly describe the influence of crack networks on the permeability of materials. In this paper, the cracked porous material is regarded as a composite material composed of porous matrix and two-phase inclusions. The IDD theoretical solution of the permeability tensor is given based on the interaction push-back method (IDD) in the mesomechanical model. In order to analyze the effect of crack mesophase parameters such as crack length, density, orientation, spacing and connectivity on the macroscopic permeability, a two-dimensional numerical model was established by using a repeating unit model with periodic structure. The finite element method Numerical solution and IDD theoretical solution were compared and verified. Theoretical studies show that the IDD theoretical model uses a single crack density index to characterize the crack network in porous media, and can uniformly describe multiple mesoscopic features such as crack length, orientation, average lateral spacing and longitudinal spacing when cracking density is not high Which has good applicability and precision to the overall permeability of material. Numerical analysis shows that IDD theoretical solution gradually deviates from numerical solution and underestimates the crack in the process of increasing the density of crack network, the mutual approaching of cracks and the final communication In this case, the permeability of material is logarithmically related to the crack density. Once the network crack is connected, the overall permeability changes abruptly. At this time, the determination of permeability requires special consideration of the strong near-field interaction between the interconnected cracks.