A study on Zhukovsky’s analytic function

An in-depth analysis of Zhukovsky’s classic analytic function is presented. The Zhukovsky’s analytic function of the two complex variables needs to be defined in accordance with chosen direction of the ordinate. Assuming the ordinate y axis to be positive vertically downward, and accordingly applying a modified Zhukovsky’s analytic function, Vederinkov’s analysis of steady-state unconfined groundwater flow around a vertical sheet pile, embedded in a homogeneous isotropic porous medium of infinite depth, is revisited. The required depth of embedment of a vertical sheet pile, that keeps the body of an earth dam free from ingress of seepage water from the upstream side, is 21.05% of the sum of ponded depth of water and capillary suction head of the soil used in the earth dam. The abscissa at zero ordinate of the parabolic boundary of the saturated flow zone designated as b is presented for several capillary suction heads and depth of embedment of the sheet pile. A functional horizontal blanket drain needs to be located in the base of the earth dam within the pertinent abscissa b. The results presented are useful in design of an earth dam with an upstream vertical sheet pile and a rockfilled part. © 2020 Indian Society for Hydraulics.