Gradual Splitting Method For Solving Seepage Free Surface

The solution of seepage free surface is one of the most difficult problems in seepage analysis.Free surface is a unknwon boundary in seepage field,in which the free surface should meet that head equals to elevation(the first kind of boundary condition)and that flow exchange is none(the second kind of boundary condition)at the same time.During the past research,the finite element method of solving seepage free surface was applied to increase calculation accuracy,such as virtual element method and initial flow method,in which the seepage free surface is usually to further approach the first kind of boundary condition or the second kind of boundary condition by increasing the number of iterations.The gradual splitting method solving seepage free surface was put forward based on minimum of energy loss rate in real seepage field,whose physical meaning is clear and calculation accuracy is high.The main contents are as follows:1.The seepage free surface is optimized with the six-node triangular element.Comparing the triangular element and isoparametric quadrilateral element,used commonly in the calculation of plane seepage,the advantages of the six-node triangular element are obtained:(1)It can adapt to the complex shape of the seepage boundary;(2)It’s non-linear head interpolation function was expressed by the completely quadratic polynomial.Mesh grid with the six-node triangular element,and use the optimized virtual element method to solve seepage free surface of rectangular seepage model.The conclusion of comparation with test solution of electrical simulation is drawn that the seepage free surface has the high precision and is closer to its real state.2.Gradual splitting method solving seepage free surface was put forward based on minimum of energy loss rate in real seepage field.Divide the seepage flow,which have the known upper and lower boundary and the free exudation boundary,promote from the overflow boundary of seepage to the import boundary of seepage,and then solve the position of the free surface node based on the minimum of energy loss rate every time pushing a layer of units.At last a complete seepage free surface and seepage field are obtained.3.Program the calculation process of the gradual splitting method with the Fortran language.Based on the program,the seepage free surface of the rectangular dam having test solution of electric simulation,the rectangular dam having glycerol model test solution,and the trapezoidal dam having analytic solution were solved.The maximum of relative error compared the computation result obtained by the gradual splitting method,test solution of electric simulation,glycerol model test solution and analytic solution were 4.94%,1.37% and 2.57%.The analysis of the results shows that,the gradual splitting method has a high computational accuracy.