2017
Том 69
№ 7

All Issues

Hydrodynamic Calculation of Drained Aprons. II. Application of the Method of Successive Conformal Mappings

Fil'chakov F. P.

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Abstract

In tbe first communication [10] an exact hydrodynamie solution is giveri-for the general case of a flat split apron floodbed with T=∞ and then,the most interesting: special cases are discussed. In the present research the earlier developed method of successive con" formal mapping [5; 7] is employed to obtain a very simple approximate solution fôr a fiat drained apron, which is êxtënded in §§ 2 and 3 to the case of a apron of arbitrary practical profile with n drainage openings w ith a finite or infinite depth of water-permeable soil. The application of an extremely simple graphoanalytical method permits solving these problems, in most of the cases encountered in practice, by graphic means in the course of 20—30 minutes, using a compass, ruler and previously constructed nomograms [6; 11]. Conditions (35), (46), (52) are indicated which should be observed in order to avoid large errors on using the graphoanalytical method. The Accuracy of the approximate formulae are illustrated by six examples, in which a comparison is made either with exact bydrodynamical solutions or with résults of simulation on resistance paper [4; 12]. A means of extending the earlier obtained results for anisotropic soil [7; III] and two-layei soil [9] to the case of drained aprons is indicated.

Citation Example: Fil'chakov F. P. Hydrodynamic Calculation of Drained Aprons. II. Application of the Method of Successive Conformal Mappings // Ukr. Mat. Zh. - 1960. - 12, № 4. - pp. 439 - 462.

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