Mathematical Model for Unsteady Flow Filtration in Homogeneous Closing Dikes

Abstract

Adike is a barrier used to regulate or hold back water from a river, lake, or even the ocean. The performance of the dikes depends on various factors such as seepage area, height of seepage area, length of dike, filtration rate, etc. Our article considers filtration calculations of a homogeneous closing dike by determining the instantaneous filtration flow rate and seepage area and proposes a mathematical model to optimize the efficiency of dikes. It is known that the value of the height of seepage area (break in the depression curve) can be obtained from the equation of the Boussinesq initial and final boundary problem for a solitary flow wave. Further, it is proved experimentally by using closing dikes made of temporary hydraulic structures. The motion of the filtration stream is stabilized when the depression curve reaches the steady-state configuration, that is, when the flow wave travels a distance equal to the closing dike length. If the length of closing dike is large enough so that the outcrop point of the depression curve has sufficient time to reach the downstream, then there is no possibility for the formation of seepage area. If the length of closing dike is small, then the outcrop point does not have time to reach the downstream and so seepage area is formed. To avoid and solve this problem, the angular point of the depression curve and the finite period of seepage area formation are used. The stationary positions of the depression curve in a rectangular closing dike are obtained that results in an instantaneous monotonic (in the absence of infiltration and evaporation) curve, which is tangent to outcrop point in the downstream side and the initial water level inside the closing dike.