A different approach to the network method: continuity equation in flow through porous media under retaining structures

Martínez‐Moreno, Encarnación; García‐Ros, Gonzalo; Alhama, Iván

doi:10.1108/ec-10-2019-0493

Cited by 8 publications

(8 citation statements)

References 15 publications

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“…The values of π ds are 0 and 0.25 for the first and second scenario, respectively. The numerical solution is carried out by the network method [31][32][33] and the free software Ngspice. 34 For the first application (π k = 5, π a = 20, π b = 1 and π e = 0), three cases with different physical and geometrical parameters are chosen (Table 5).…”

Section: Verification Of the Discriminated Dimensional Groups Involvi...mentioning

confidence: 99%

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The dimensional character of permeability: Dimensionless groups that govern Darcy's flow in anisotropic porous media

Alhama

Martínez‐Moreno

García‐Ros

2022

Num Anal Meth Geomechanics

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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.

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Section: Verification Of the Discriminated Dimensional Groups Involvi...mentioning

confidence: 99%

“…The values of π ds are 0 and 0.25 for the first and second scenario, respectively. The numerical solution is carried out by the network method 31–33 and the free software Ngspice 34…”

Section: Verification Of the Discriminated Dimensional Groups Involvi...mentioning

confidence: 99%

The dimensional character of permeability: Dimensionless groups that govern Darcy's flow in anisotropic porous media

Alhama

Martínez‐Moreno

García‐Ros

2022

Num Anal Meth Geomechanics

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“…The network simulation method has been successfully employed in numerous fields of applied engineering, such as ceramic coatings [36], dispersion of atmospheric pollutants [37], reinforced concrete corrosion [38], soil consolidation [39,40], seepage [41], heat transport [42][43][44], and many physical problems in engineering [30]. This technique makes use of the powerful algorithms of the circuit resolution codes [32,33] that are able to successfully cope with coupled and strong non-linear mathematical models, including Gear s fixed time methods [45], trapezoidal integration [31], and iterative methods, such as Runge-Kutta.…”

Section: Introductionmentioning

confidence: 99%

A Network Model for Electroosmotic and Pressure-Driven Flow in Porous Microfluidic Channels

et al. 2022

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In this work, the network simulation method is presented as a tool for the numerical resolution of the electroosmotic and pressure-driven flow problem in microchannels with rectangular and cylindrical geometries. Based on the Brinkman equation for steady flow and constant porosity, the network model is designed using spatial discretization. An equivalent electrical circuit is obtained by establishing an analogy between the physical variable fluid velocity and electric potential. The network model is solved quickly and easily employing an electrical circuit resolution code, providing solutions for the velocity profile in the channel cross-section and the total circulating flow. After simulating two practical cases, the suitability of the grid is discussed, relating the relative errors made in the variables of interest with the number of cells used. Finally, two other applications, one for rectangular geometries and the other for cylindrical channels, show the effects the main parameters controlling the flow in these types of channels have on velocities and total flow: the zeta potential of the soil pores, applied potential and pressure gradients, and the boundary condition modified by the zeta potential in the walls of the channel.

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“…Finally, numerical methods on which software are based can quantify these phenomena in isotropic and anisotropic soils. Among all the possible options, the tool that has been employed in this paper is the network method, which has already been applied in the study of different physical problems, such as flow in porous media [6], soil consolidation [7], and solute and heat transport [8,9]. The method employs the electrical analogy of the problem variables, so the hydraulic potential, h, is equivalent to the voltage, V, and the groundwater flow, Q, to the electric current or intensity, I.…”

Section: Introductionmentioning

confidence: 99%

Study of the Influence of Sheet Pile Location under Dams on Groundwater Flow and Pore Pressure with Network Method

Martínez‐Moreno¹,

García‐Ros²,

Alhama³

2021

World Congress on Civil, Structural, and Environmental Engineering

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The construction of a gravity dam leads to some verifications that may affect its safety, such as groundwater flow or pore pressure distribution under the structure. These phenomena, which are related to piping and the position of the uplift force, can be controlled by placing a sheet pile under the dam. The variables are commonly studied as if the soil was isotropic, simplifying universal results (either graphics or formulations). However, this assumption does not reflect real scenarios in most of the cases, for example anisotropic hydraulic conductivities. In this work, the effects of the sheet pile position in four different cases is studied: dam without a sheet pile and dam with a sheet pile located at the heel, centre and toe of the structure. In all of them two different media are modelled, with isotropic and anisotropic hydraulic conductivities, so its influence can be appraised from the point of view of safety. The scenarios are simulated with a tool based on the network method that, employing the electrical analogy, obtains the problem variables, 'hydraulic potential' (h) and 'water flow' (Q), solving electric quantities, 'voltage' (V) and 'electric current' (I), respectively.

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A different approach to the network method: continuity equation in flow through porous media under retaining structures

Cited by 8 publications

References 15 publications

The dimensional character of permeability: Dimensionless groups that govern Darcy's flow in anisotropic porous media

The dimensional character of permeability: Dimensionless groups that govern Darcy's flow in anisotropic porous media

A Network Model for Electroosmotic and Pressure-Driven Flow in Porous Microfluidic Channels

Study of the Influence of Sheet Pile Location under Dams on Groundwater Flow and Pore Pressure with Network Method

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