Numerical domain is discretized by triangle elements; and local coordinate system is set up for each one. X-axis of local coordinate system is along one edge of the element; and the origin point is at the endpoint of the edge. In local coordinate system

based on Green formula and Darcy law

analytical expression of pressure gradient and flow velocity of element

discharges of each edge and each node are given. The seepage “pipeline” network similar to solid spring system is formed; and the relationship between pressure difference and discharge of pipeline is built. Flow velocity and discharge of each element in element local coordinate system should be transformed to global coordinate system

and should be accumulated in each node. By introducing fluid bulk modulus and node saturation

pore pressure of each node could be calculated explicitly and the unsaturated problems could be simulated well. The method based on local coordinate system is clear in physical meaning and simple in solution process. According to constructing the relationship between pressure difference and discharge of pipeline in local coordinate system

the seepage stiffness matrix of FEM is simplified to two seepage stiffness values; so the memory is saved and the efficiency is improved. The results of 4 numerical cases almost coincide with analytical solutions so as to demonstrate the solution precision when simulating steady-state

non-steady-state

saturated

unsaturated seepage problems.