About Filtration in a Geophysical Bridge with a Seepage Site

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Аннотация

Based on the representation of a modular elliptic function in the form of a combination of simple algebraic formulas that conformally map the area of the velocity hodograph (curved triangle) onto a half-plane, a direct definition of filtration rates in a geophysical bridge is given. For the first time, a family of isotope lines of equal filtration rates was constructed for the inner area of the bridge in the absence of water in the downstream. For special cases, the values of the proposed formulas almost completely coincide with the hydromechanical solution of Masket M. (for 4 cases) and the numerical calculations of Khairullin Z.E. (for 2 cases). The well-known Nelson-Skornyakov F.B. formula for the output filtration rates through the lower face of the jumper, adopted by analogy with the flow outlet from the base of the flatbed into the horizontal drainage, gives an underestimation of the results by up to 45%, and therefore cannot be recommended for practical use.

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Авторлар туралы

K. Anakhaev

Institute of Applied Mathematics and Automation of the Kabardino-Balkar Scientific Center of the Russian Academy of Sciences

Хат алмасуға жауапты Автор.
Email: anaha13@mail.ru
Ресей, Nalchik

Әдебиет тізімі

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Әрекет
1. JATS XML
Жүктеу
2. Fig. 1. Filtration in a geophysical cofferdam with complex regions of: a) physical flow ; b) velocity hodograph ; c) intermediate half-plane

Жүктеу (25KB)
Метадеректер
3. Fig. 2. Comparison of the results of filtration velocities: symbol ○ denotes calculations 1 - according to the author; curves 2-5 - according to [10,11] for the top face and bottom face of the cofferdams, respectively (I-III,VI), as well as for the bottom face for case I (curves 2); curves 6, 7 - according to the numerical solution [21] for the bottom face of cofferdams VII, VIII; dashed curve 8 - according to [22] for the seepage section VIII; symbol × denotes calculations 9 - according to the formula (2. 19) for the dropout section VIII.

Жүктеу (27KB)
Метадеректер
4. Fig. 3. Filtration in the geophysical cofferdam in the absence of water in the downstream: , , , , , (case IX): 1 - family of isotopes on the internal area of the cofferdam; 2 - epuple of input filtration velocities on the upper face ; 3 - epuple of longitudinal filtration velocities along the bottom line ; 4 and 5 - epuple of full output filtration velocities and on the lower face .

Жүктеу (33KB)
Метадеректер

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