不同裂纹分布的孔隙材料渗透系数  

PERMEABILITY OF POROUS MATERIAL WITH DIFFERENT CRACK DISTRIBUTIONS

作　　者：钱鹏[1] 徐千军[1] 

机构地区：[1]f清华大学水沙科学与水利水电工程国家重点实验室,北京100084

出　　处：《工程力学》2017年第12期39-47,共9页Engineering Mechanics

基　　金：国家重点研发计划课题项目(2017YFC0804602);国家自然科学基金重点项目(51339003);水沙科学与水利水电工程国家重点实验室自主科研课题项目(2016-KY-05)

摘　　要：含裂纹孔隙材料渗透性由裂纹的微观结构决定,其研究对工程实践意义重大。该文假设含裂纹孔隙材料是由孔隙基体和裂纹组成的二相复合材料,基于细观均匀化理论给出了四种不同裂纹分布的渗透张量稀疏解、相互作用直推(IDD)解和修正的IDD解。基于单元嵌入技术和弹性比拟的数值模拟方法,采用不连通的离散裂纹模型,研究了裂纹数目对有效渗透系数数值解收敛性的影响及不同裂纹分布的孔隙材料渗透性,并将得到的数值解和理论解对比分析,结果表明:随着裂纹数目的增加,有效渗透系数的变化范围逐渐减小,并最终趋于稳定,而且选择合适的裂纹数目,能同时保证计算的随机收敛性和合理的计算效率;对于所研究的四种分布的裂纹,相比稀疏解,IDD解更接近数值解,但随着裂纹密度的增加,裂纹间的相互作用增强,IDD解会逐渐偏离数值解;修正的IDD解充分考虑了裂纹间的相互作用和边界效应,能更好地估计含裂纹孔隙材料的渗透性。The effective permeability of cracked porous material depends on the microstructure of material and it is of great significance to practical engineering applications. Cracked porous material is considered to be a two-phase composite material with a porous matrix and cracks. Firstly, based on the homogenization theory, a dilute solution, an interaction direct derivative （IDD） solution and a modified IDD solution are derived to evaluate the permeability with four different crack distributions. Then a new method which combines embedded element technique with elastic analogy is developed to analyze the effective permeability and its convergence. Afterwards, the numerical result derived from the new method was compared with theoretical solutions. It can be concluded that the variation of the finite element results decreases by increasing the crack number. Moreover, an appropriate number of cracks can ensure both the convergence and computation efficiency. On the other hand, compared with the dilute solution, the IDD solution can provide a superior estimation for the numerical results with different distributions, but it underestimates the finite element results at higher crack density as the near-field interaction among cracks grows stronger. The modified IDD solution takes both the near-field interaction and edge effect into consideration, so it can estimate the permeability of cracked porous material more precisely.

关 键 词：含裂纹孔隙材料 有效渗透性 裂纹分布 细观均匀化 嵌入单元 弹性比拟 

分 类 号：TV331[水利工程—水工结构工程]