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

The seepage calculations of dams and levees with mound and layer drains on impervious strata are introduced. The slope angle of drain boundary is greater than 90 ° . The main contents and results are as follows:1) For the mound drain with the downstream water depth H₂ =0, according to the Kochina ’s theory q / k = μ h ₀ , the reciprocal of ratio μ between the flow quantity and the height h₀ of release point is calculated, and the relevant fitting formula for 1 / μ #/is presented. By means of the transformed hypergeometric function, a formula for the exit gradient and its distributions with slope angles of 90 ° , 135 ° , 180 ° is given.2) The conformal mapping method is employed to get the critical water depth H_C of the mound drain, and its derivation process is much simpler than that of the Novmurov’s method.3) For the mound drain with H₂≥ H_C, according to the Novmurov’s theory Δ L₂= D₁ H₂+ D₂ q/k , the proportional coefficients D₁ and D₂ of additional length of downstream seepage path are calculated, and two fitting formulae for D₁ and D₂ with enough precision are presented. The conformal mapping method is used to get the exact seepage solution in downstream district with mound drains, combined with the corresponding solution by Normurov in the upstream district of dams and levees, an example is calculated accurately to get the flow quantity ratio q / k, height of release point h_s, distribution of exit gradient I, coordinates of the whole phreatic line and its inflection points to check the corresponding program of finite element and other approximate methods.4) For the mound drain with 0< H₂< H_C, two approximate formulae for the height h_s of release point and the additional length Δ L₂ of downstream seepage path are presented. The calculated results agree with the results of the finite element methods.