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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 6713452, 12 pages
Research Article

Development of Embedded Element Technique for Permeability Analysis of Cracked Porous Media

State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China

Correspondence should be addressed to Qianjun Xu

Received 27 June 2017; Accepted 14 September 2017; Published 17 October 2017

Academic Editor: Haifei Liu

Copyright © 2017 Peng Qian and Qianjun Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The widely used approach of mesoscale finite element modeling for permeability analysis is to simulate the matrix and cracks with continuum elements (CE), whereas this process brings technical difficulties in generating a satisfying mesh conformity at the interface. In this work, an alternative method based on embedded element (EE) technique is developed for the prediction of water pressure field and effective permeability in the numerical simulation. Based on the mathematical similarity between elasticity and seepage problems, water pressure can derive from the corresponding displacement through “elastic analogy.” To assess the capability of the EE technique, different cases are simulated and compared with the CE model. The results show that there is a satisfactory agreement in water pressures and velocities between the CE and EE modeling. In the CE model, different factors, such as permeability contrast between matrix and cracks and mesh size, are considered. It is obvious to find that results will become stable when reaches 104, and the mesh size has little impact. The effective permeability of 3D porous media with random cracks is evaluated and the results show that the differential method is accurate for 3D permeability analysis when the crack density is not large.