Seepage flow with free surface in fracture networks

Authors

  • Qinghui Jiang,

    Corresponding author
    1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, China
    • School of Civil Engineering, Wuhan University, Wuhan, China
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  • Chi Yao,

    1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, China
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  • Zuyang Ye,

    1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, China
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  • Chuangbing Zhou

    1. School of Civil Engineering, Wuhan University, Wuhan, China
    2. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, China
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Corresponding author: Q. Jiang, School of Civil Engineering, Wuhan University, Wuhan University, Wuhan 430072, China. (jqh1972@yahoo.com.cn)

Abstract

[1] Crystalline rocks are often heterogeneous geological materials that contain numerous fractures of various attitudes and scales. Although considerable advances have been made in simulation of fluid flow through fractured media, our knowledge of seepage flow with free surfaces in fracture networks remains to be an outstanding issue. In this paper, the partial differential equations (PDEs) defined on the whole fracture network domain are formulated for free-surface seepage flow problems by an extension of Darcy's law. A variational inequality (VI) formulation is then presented, and the proof of the equivalence between the PDE and VI formulations is given. Since the boundary conditions involving the flux components in the PDE formulation become the natural conditions in the VI formulation, the difficulty of choosing the trial functions for numerical solutions is significantly reduced and the locations of seepage points can be easily determined. On the basis of the discrete VI, the corresponding numerical procedure for unconfined seepage analysis of discrete fracture network has been developed. The results from three typical examples demonstrate the validity and capability of the procedure for unconfined seepage problems involving complicated fracture networks.

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