Characterization of Flow under Impervious Dams: Dimensionless Groups and Universal Solutions

Abstract

As far as we know, no dimensionless solutions for infiltrated flow under dams in anisotropic media exist since those that can be found in manuals refer to isotropic soils. The novelty of this work is the presentation of universal solutions in the form of abaci for water flow, average exit gradient, uplift force, and its application point for this type of soil. These solutions are obtained by the application of the discriminated nondimensionalization technique to the governing equations in order to find accurate dimensionless groups that control the results of the problem. In particular, the ratio of permeabilities corrected by a geometrical aspect relationship appears as a governing group, so anisotropy can be considered as input information. In this way, the sought solutions are a function of the emerging groups. Numerical solutions are used to successfully verify the results obtained, which in turn are compared to those of other authors for isotropic scenarios.

A Universal Graphical Solution to Calculating Seepage in Excavation of Anisotropic Soils and Non-Limited Scenarios

“…Dimensionless groups were assembled using discriminated non-dimensionalization, a technique that has been applied in anisotropic scenarios involving hydraulic conductivity (with k x and k y ) to solve problems of soil consolidation, seepage under dams and heat transport in aquifers [22][23][24]. This technique has allowed us to determine the parameters according to the two dimensions of the problem (x, y), that is, k x , L * and c (in the x direction) and k y , b , a and T * (in the y direction), so every monomial respects the basic rule of including only parameters defined in the selected direction.…”

An Application of Inverse Problem and Universal Solutions for Pumping Wells in Unconfined Aquifers

“…According to this method, both the governing equations and boundary conditions are transformed into dimensionless expressions to obtain the lowest number of independent dimensionless monomials that rule the problem [12]. Examples of problems that have been approached employing the discriminated nondimensionalization technique are flow under dams [13], solute and temperature flow [14] and soil consolidation [15]. In addition, this work is also an approach to an inverse engineering problem [16], as it aims to infer the value of some properties, in this case, the hydraulic horizontal and vertical conductivity values from measured variables that are unknown in directs problems (in these scenarios, pumping flow and seepage surface).…”