Аналитическое решение задачи течения в пористой прямоугольной переборке
Автор: Ватин Н.И., Котов Е.В., Хоробров С.В.
Журнал: Строительство уникальных зданий и сооружений @unistroy
Статья в выпуске: 7 (105), 2022 года.
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Объектом исследования является нестационарное безнапорное фильтрационное течение в пористой изотропной среде, область движения которого сверху ограничена свободной поверхностью, на которой давление жидкости постоянно и равно внешнему атмосферному давлению. Такие течения характерны для фильтрации грунтовых вод через гидротехнические сооружения (плотины, водопонижения, дренажи, фундаменты, котлованы при их осушении). Целью исследования является решение задачи о нестационарном гравитационном течении жидкости в скалярной пористой среде с двумерным фильтрационным движением в вертикальной плоскости. Сформулирована предельная задача нестационарной теории фильтрации (Буссинеска) для скалярной пористой среды с использованием безразмерной факторизации, что позволяет решать группы задач для областей со схожими областями определения. Предельная задача Буссинеска сведена к типичной предельной задаче для обыкновенного дифференциального уравнения Крокко. Сформулирована и решена предельная задача Крокко. Получено аналитическое решение предельной задачи для прямоугольного моста. Решение определяет глубину фильтрационного потока за перемычкой. В работе доказано, что предельные задачи нестационарной фильтрации в вертикальной плоскости идентичны предельным задачам стационарной теории пограничного слоя в переменных Мизеса — продольная координата-функция тока.
Нестационарный фильтрационный поток, предельная задача Буссинеска, редукция, уравнение Крокко, прямоугольная плотина, кривая депрессии
Короткий адрес: https://sciup.org/143182683
IDR: 143182683 | УДК: 69 | DOI: 10.4123/CUBS.105.1
Analytical solution of the problem of flow in a porous rectangular bulkhead
The object of study is an unsteady pressureless filtration flow in a porous isotropic medium, in which the region of motion is limited from above by a free surface, on which the fluid pressure is constant and equal to the external atmospheric pressure. Such currents are characteristic of groundwater filtration through hydraulic structures (dams, water drawdowns, drainages, foundations, pits during their drainage). The study aims to solve the problem of the nonstationary gravitational flow of a fluid in a scalar porous medium with two-dimensional filtration motion in a vertical plane. The limiting problem of nonstationary filtration theory (Boussinesq) for a scalar porous medium is formulated using dimensionless factorization, which allows solving groups of problems for areas with similar domains of definition. The Boussinesq limit problem is reduced to a typical limit problem for Crocco's ordinary differential equation. Crocco's limiting problem is formulated and solved. An analytical solution to the limit problem for a rectangular bridge is obtained. The solution determines the depth of the filtration flow downstream of the cofferdam. The paper proves that the limiting problems of nonstationary filtration in the vertical plane are identical to the limiting problems of the stationary theory of the boundary layer in the von Mises variables - the longitudinal coordinate-current function.
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