The variational inequality formulation for unconfined seepage through three-dimensional dense fracture networks

The space block search technology is used to determine a connected three-dimensional fracture network in polygonal shapes, i.e., seepage paths. After triangulation on these polygons, a finite element mesh for 3D fracture network seepage is obtained. Through introduction of the generalized Darcy’s law, conservative equations for both fracture surface and fracture interactions are established. Combined with the boundary condition of Signorini’s type, a partial differential equation (PDE) formulation is presented for the whole domain concerned. To solve this problem efficiently, an equivalent variational inequality (VI) formulation is given. With the penalized Heaviside function, a finite element procedure for unconfined seepage problem in 3D fracture network is developed. Through an example in a homogeneous rectangular dam, validity of the algorithm is verified. The analysis of an unconfined seepage problem in a complex fracture network shows that the proposed algorithm is very applicable to complex three-dimensional problems, and is effective in describing some interesting phenomenon usually encountered in practice, such as “preferential flow”.

[1]  Pierre M. Adler,et al.  Fractures and Fracture Networks , 1999 .

[2]  Chin-Fu Tsang,et al.  Flow and Contaminant Transport in Fractured Rock , 1993 .

[3]  B. Berkowitz.  Characterizing flow and transport in fractured geological media: A review , 2002 .

[4]  Chuangbing Zhou,et al.  Seepage flow with free surface in fracture networks , 2013 .

[5]  Emmanuel Ledoux,et al.  Modeling fracture flow with a stochastic discrete fracture network: Calibration and validation: 2. The transport model , 1990 .

[6]  S. P. Neuman,et al.  SATURATED-UNSATURATED SEEPAGE BY FINITE ELEMENTS , 1973 .

[7]  Chuangbing Zhou,et al.  A numerical solution to seepage problems with complex drainage systems , 2008 .

[8]  J. Thovert,et al.  Permeability of isotropic and anisotropic fracture networks, from the percolation threshold to very large densities. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  A. Rouleau,et al.  Stochastic discrete fracture simulation of groundwater flow into an underground excavation in granite , 1987 .

[10]  Chuangbing Zhou,et al.  A new variational inequality formulation for unconfined seepage flow through fracture networks , 2012 .

[11]  Xu Weisheng,et al.  Coupling analysis of unsteady seepage and stress fields in discrete fractures network of rock mass in dam foundation , 2011 .

[12]  G. Marsily,et al.  Modeling fracture flow with a stochastic discrete fracture network: calibration and validation: 1. The flow model , 1990 .

[13]  Hong Zheng,et al.  A new formulation of Signorini's type for seepage problems with free surfaces , 2005 .

[14]  Pierre M. Adler,et al.  PERMEABILITY OF THREE-DIMENSIONAL FRACTURE NETWORKS , 1998 .

[15]  Wu Aiqing.  THREE-DIMENSIONAL ARBITRARY FRACTURE NETWORK SEEPAGE MODEL AND ITS SOLUTION , 2010 .

[16]  Masanobu Oda,et al.  An Equivalent Continuum Model for Coupled Stress and Fluid Flow Analysis in Jointed Rock Masses , 1986 .

[17]  M. Oda,et al.  Permeability tensor for discontinuous rock masses , 1985 .

[18]  Chin-Fu Tsang,et al.  A variable aperture fracture network model for flow and transport in fractured rocks , 1992 .

[19]  I. Neretnieks,et al.  Tracer movement in a single fissure in granitic rock: Some experimental results and their interpretation , 1982 .

[20]  Björn Dverstorp,et al.  Conditional simulations of fluid flow in three-dimensional networks of discrete fractures , 1987 .

[21]  J. Thovert,et al.  Permeability and percolation of anisotropic three-dimensional fracture networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Ivars Neretnieks,et al.  2 – Solute Transport in Fractured Rock — Applications to Radionuclide Waste Repositories , 1993 .