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Volume 2018, Article ID 9062569, 16 pages
Research Article

The Parabolic Variational Inequalities for Variably Saturated Water Flow in Heterogeneous Fracture Networks

1Hubei Key Laboratory for Efficient Utilization and Agglomeration of Metallurgical Mineral Resources, Wuhan University of Science and Technology, Wuhan 430081, China
2Rock Mechanics in Hydraulic Structural Engineering, Ministry of Education, Wuhan University, Wuhan 430072, China
3School of Civil Engineering, Wuhan University, Wuhan 430072, China
4School of Civil Engineering and Architecture, Nanchang University, Nanchang 330031, China
5Department of Mathematical and Statistical Sciences, University of Colorado Denver, Denver, CO 80204, USA

Correspondence should be addressed to Qinghui Jiang; nc.ude.uhw@2791hqj

Received 18 August 2017; Revised 14 November 2017; Accepted 13 December 2017; Published 11 January 2018

Academic Editor: Daniele Pedretti

Copyright © 2018 Zuyang Ye et al. 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.


Fractures are ubiquitous in geological formations and have a substantial influence on water seepage flow in unsaturated fractured rocks. While the matrix permeability is small enough to be ignored during the partially saturated flow process, water seepage in heterogeneous fracture systems may occur in a non-volume-average manner as distinguished from a macroscale continuum model. This paper presents a systematic numerical method which aims to provide a better understanding of the effect of fracture distribution on the water seepage behavior in such media. Based on the partial differential equation (PDE) formulations with a Signorini-type complementary condition on the variably saturated water flow in heterogeneous fracture networks, the equivalent parabolic variational inequality (PVI) formulations are proposed and the related numerical algorithm in the context of the finite element scheme is established. With the application to the continuum porous media, the results of the numerical simulation for one-dimensional infiltration fracture are compared to the analytical solutions and good agreements are obtained. From the application to intricate fracture systems, it is found that water seepage flow can move rapidly along preferential pathways in a nonuniform fashion and the variably saturated seepage behavior is intimately related to the geometrical characteristics orientation of fractures.