A numerical procedure for transient free surface seepage through fracture networks

- A parabolic variational inequality (PVI) formulation for transient seepage problem in fracture networks is established.
- A relative error formula for evaluating the flow losses at steady state caused by the penalty parameters is proposed.
- A finite element procedure to predict transient free surface response in fracture networks has been developed.

SummaryA parabolic variational inequality (PVI) formulation is presented for the transient free surface seepage problem defined for a whole fracture network. Because the seepage faces are specified as Signorini-type conditions, the PVI formulation can effectively eliminate the singularity of spillpoints that evolve with time. By introducing a continuous penalty function to replace the original Heaviside function, a finite element procedure based on the PVI formulation is developed to predict the transient free surface response in the fracture network. The effects of the penalty parameter on the solution precision are analyzed. A relative error formula for evaluating the flow losses at steady state caused by the penalty parameter is obtained. To validate the proposed method, three typical examples are solved. The solutions for the first example are compared with the experimental results. The results from the last two examples further demonstrate that the orientation, extent and density of fractures significantly affect the free surface seepage behavior in the fracture network.