Improvement of analysis of free surface seepage problem by using initial flow method

When the initial flow method is applied in solving problems of free surface seepage, we often find an oscillating solution determined due to the error caused by taking the Gaussian integration points as the assumed nodes based on calculation of nodal initial flow. In order to reduce the impact of this factor and to improve the efficiency of computation , an analysis is made with the free surface equation commonly used by 4-node plane elements and 8-node 6-plane three-dimensional elements , a technique of transformation of coordinates as well as isoparameters is proposed to improve the calculation of the nodal initial flow, and an introduction of partial integration is also suggested according to the state of free surface penetrating elements, making the integration upper limit and lower limit in consistence with the formatting of the Gaussian requirements. Accordingly, an exact nodal initial flow integration will be obtained by using the Gaussian method , and this accurate nodal initial flow will then benefit the itself improvement of the oscillating solution and increase the precision of the calculation . Through the analysis of a homogeneous rectangular case, it is shown that a fair state of stability and convergence has been achieved by using the proposed improved method.