Purpose
This study aims to present a new numerical model for the simulation of water flow through porous media of anisotropic character, based on the network simulation method and with the use of the free code Ngspice.
Design/methodology/approach
For its design, it starts directly from the flow conservation equation, which presents several advantages in relation to the numerical simulation of the governing equation in terms of the potential head. The model provides very precise solutions of streamlines and potential patterns in all cases, with relatively small meshes and acceptable calculation times, both essential characteristics when developing a computational tool for engineering purposes. The model has been successfully verified with analytical results for non-penetrating dams in isotropic media.
Findings
Applications of the model are presented for the construction of the flow nets, calculation of uplift pressures, infiltrated flow and average exit gradient in anisotropic scenarios with penetrating dams with and without sheet piles, being all this output information part of the decision process in ground engineering problems involving these retaining structures.
Originality/value
This study presents, for the first time, a numerical network model for seepage problems that is not obtained from the Laplace's governing equation, but from the water flow conservation continuity equation.
Seepage maps formed by both stream and equipotential lines, emerging under dams with sheet piles on their ends, can be determined by simulating the Laplace conjugate equations using a numerical technique such as the network method. Based on these maps, engineers can immediately deduce the amount of water circulating under the structure and design the sheet piles depth to safe values that allow to limit risks such as siphoning or erosion of the base of the dam. For a fix depth of the upstream sheet pile, seepage maps are shown for different configurations of the downstream sheet pile, in a 2D scenario with finite depth and with large extensions both upstream and downstream of the dam.
The dimensional character of permeability in anisotropic porous media, that is, its dimension or dimensional equation, is an information that allows setting the dimensionless groups that govern the solution of the flow equation in terms of hydraulic potential patterns. However, employing the dimensional basis {L, M, T} (length, mass, time), the dimensionless groups containing the anisotropic permeability do not behave as independent monomials that rule the solutions. In this work, the contributions appearing in the literature on the dimensional character of permeability are discussed and a new approach based on discriminated and general dimensional analysis is presented. This approach leads to the emergence of a new and accurate dimensionless group, normalknormalxnormalknormalynormallnormaly∗2normallnormalx∗2$\frac{{{{\rm{k}}_{\rm{x}}}}}{{{{\rm{k}}_{\rm{y}}}}}\frac{{{\rm{l}}_{\rm{y}}^{{\rm{*}}2}}}{{{\rm{l}}_{\rm{x}}^{{\rm{*}}2}}}$, a ratio of permeabilities corrected by the squared value of an aspect factor, being normallnormalx*${\mathrm{l}}_{\mathrm{x}}^{\ast}$and normallnormaly∗${\rm{l}}_{\rm{y}}^{\rm{*}}$ two arbitrary lengths of the domain in the directions that are indicated in their subscripts. Specific values of this lengths, which we name ‘hidden characteristic lengths’, are also discussed in this article. To check the validity of this dimensionless group, numerical simulations of two illustrative 2‐D seepage scenarios have been solved.
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.
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