Equivalent fracture network model for steady seepage problems with free surfaces

•An equivalent fracture network model is proposed for seepage flow in porous media.•The proposed model can be used for the fractured media as well as porous media.•The proposed model is feasible for the anisotropic media in engineering practice. Based on the back analysis of equivalent continuum theory in frcatued media by Snow (1969), an equivalent fracture network model is proposed to evaluate steady seepage problems with free surface in porous media. In contrast to the continuum-based approaches on seepage flow, the continuum is replaced by an artificial fracture network system formed by two sets of fractures. The relationships between the permeability coefficients of porous media and equivalent parameters of fracture dip, spacing and aperture are deduced. The corresponding governing equations and finite element procedure according to the variational inequality theory are developed. Through good agreements of free surface locations between the proposed method, numerical data and field measurement in four typical examples, the proposed equivalent fracture network model is validated in modelling free surface flow in porous media. The solutions on the isotropic and anisotropic rectangular dams show that the proposed model has weak sensitivity of the fracture dip and mesh size, and its equivalence to the continuum-based method is also proved. In addition, the proposed model can be successfully used for the fractured media as well as porous media, the fracture direction has a significant impact on the free surface flow behavior in the fractured media, in which the fracture directions are negative for the antidip slope and positive for the dip slope to drain ground water. Finally, the results from the zoned dam with clay core and sand shell and the left bank abutment demonstrate the feasibility of the proposed model in complex dam engineerings with isotropic and anisotropic heterogeneity media.