The Conductivity Matrix Reforming Method to Study Non-linear Seepage with Free Surface in Fracture Network of Rock Mass

The form of free surface for the seepage in fracture network of rock mass is different from the form in continuum. Defining the free surface is a non-linear problem on seepage area, and to solve this problem, the iterative methods must be used. There are a lot of seepage forms in fractures are non-linear fluid, to solve them also need use iterative methods. The nonlinear seepage with free surface is a dual nonlinear problem, which containing the non-linear problem on seepage area and the non-linear problem on seepage constitutive relation, and to solve this problem, the dual iterative methods must be used. The non-linear seepage in single fracture having been analyzed, based on this, the finite element equation for the water head of nodes has been derived by using the principle of water balance. Borrowing the idea from the fixed net method to define the free surface in continuum, the whole fracture network of the study rock mass has been analyzed, and then the free surface of the fracture network of rock mass can be defined by using the conductivity matrix reforming methods. The non-linear seepage in fracture network of rock mass with free surface has been analyzed, it can be found that: the flow pattern in the network is determined by the characteristics of network itself and the boundary condition; If existing non-linear seepage, that not means all the flow patterns in all the fractures of the network is non-linear seepage, while the linear seepage and the non-linear seepage co-exists; The seepage constitutive relation has very close relation to the free surface, as the hydraulic slope for most natural fractures is smaller than 1, the free surface for non-linear seepage of fracture network is higher than the linear seepage, while the total discharge is less. The dual non-linear seepage problem is much more complex than either single non-linear problem, and the conductivity matrix method to analyze non-linear seepage with free surface in network of rock mass is feasible, and the analysis for non-linear seepage in fractures is very essential, and the single non-linear seepage problem is the base of dual non-linear seepage problem even multiple non-linear seepage problem.