The improved node vitual method for the seepage problem with free surface

Based on the solutions of the disadvantages in node virtual flow method, the improved node virtual flow method with continuous penalty function and modificatory coefficient of non saturation zone was presented for the seepage problem with free surface.The continuous penalized function,which has been used in the improved cut-off negative pressure method, was introduced to solve the inadequate consideration of the contribution to seepage matrix of the nodes in the non-saturation zone near the free surface.The modificatory coefficient presented was used to solve the over-dependence to the element form of the penalty function and the numerical stability of the old method. And to improve the solving precision of the free surface,a new convergence criteria was presented.At last,the improved method was applied to a numerical example and an engineering example. Application results showed that the disadvantages in the old method can be well solved by the improved method and the improved method can be used to slove strongly nonlinear seepage problems, provide theoretical support for the design of seepage control engineering.