Analytic solution of seepage calculation for dams and levees on impervious strata

An idea of dividing the dams and levees into three regions by seepage flow state and the rule of no flow state influence between the upstream and downstream region under fixed flow quantity are proposed. It will enable the seepage analysis and calculation of dams and levees to be simplified and convenient. New theoretical formulae for the following aspects are derived: the location of inflection point of upstream phreatic line, the analytical extension formula of downstream phreatic line and the undetermined constant before this formula, the additional length of downstream seepage path. According to the Normurov′s theory ΔL1= C1H1 -C2q/k and the Kochina′s theory q/k=μh0, the proportional coefficients C1 & C2 of the additional length of upstream seepage path as well as the ratio μ between the flow quantity and the height of release point are calculated. As a result, C1 is entirely equal to the corresponding data C0 of slope with confined flows. On the basis of these data, the formulae with enough precision by fitting method are given for the purpose of convenient application. For the dams and levees with tail water, two empirical formulae for the height of release point and the additional length of downstream seepage path are presented. The results conform to those by the finite element methods.