含裂隙饱和多孔介质流-固耦合的扩展有限元分析

发布时间：2018-05-08 17:05

本文选题：裂隙 + 饱和多孔介质　；参考：《岩土力学》2017年05期

【摘要】：基于应力平衡方程、渗流连续性方程以及改进的Biot有效应力原理,建立了含裂隙可变形饱和多孔介质流-固全耦合问题的控制方程。流体在介质和裂隙中的流动均满足达西定律,得到的非线性全耦合方程不仅反映多孔介质内部物理量的耦合效应,还考虑介质与裂隙之间的耦合作用。扩展有限元法在处理含裂隙问题时具有独特的优势,采用普通有限元和扩展有限元法构建了数值计算体系。在进行空间离散时,介质内部的位移和孔隙压力均采用普通的有限元进行离散;裂隙处的位移模式引入扩展有限元中的两类附加位移函数,以反映裂隙面的位移强不连续性和裂隙端部的应力奇异性;引入孔隙压力加强函数,以体现裂隙法向孔隙压力的弱不连续特征。使用向后差分格式进行时间离散。算例验证了该模型和算法的正确性和有效性,分析了裂隙的存在对流体流动的延迟作用、裂隙中张开位移及孔隙压力等物理量的分布情况,讨论了渗透率、外部流量的改变对计算结果的影响。
[Abstract]:Based on the stress balance equation, the seepage continuity equation and the improved Biot effective stress principle, the governing equations of fluid-solid coupling problem in deformable porous media with fractures are established. The flow of fluid in medium and fracture satisfies Darcy's law. The nonlinear fully coupled equation not only reflects the coupling effect of physical quantity in porous media, but also considers the coupling effect between medium and fracture. The extended finite element method (EFEM) has a unique advantage in dealing with the problem with cracks. The numerical calculation system is constructed by using the general finite element method and the extended finite element method. In the process of spatial discretization, the internal displacement and pore pressure of the medium are discretized by the ordinary finite element method, and the displacement mode in the fracture area is introduced into two kinds of additional displacement functions in the extended finite element method. In order to reflect the strong discontinuity of displacements and the stress singularity at the end of fractures, a strengthening function of pore pressure is introduced to reflect the weak discontinuity of normal pore pressure of fractures. The backward difference scheme is used for time discretization. An example is given to verify the correctness and validity of the model and algorithm. The delay effect of the existence of fracture on fluid flow, the distribution of physical quantities such as opening displacement and pore pressure in fracture are analyzed, and the permeability is discussed. The influence of the change of the external flow rate on the calculation results.
【作者单位】：河海大学力学与材料学院工程力学系;
【基金】：国家自然科学基金(No.11372099,No.11132003,No.11672101) 江苏省自然科学基金(No.BK20151493) 国家“十二五”科技支撑计划(No.2015BAB07B10)~~
【分类号】：TU452

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