Use of discriminated nondimensionalization in the search of universal solutions for 2-D rectangular and cylindrical consolidation problems

García‐Ros, Gonzalo; Alhama, Iván; Cánovas, Manuel

doi:10.1515/geo-2018-0016

Cited by 10 publications

(11 citation statements)

References 18 publications

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“…If the cell is not rectangular, e.g. in cylindrical coordinates (García-Ros et al, 2018b), the resistors of the model have different expressions and values on each spatial direction (in cylindrical coordinates, the resistors expression in the vertical direction would be the same inside the same cell, while this would not happen in the radial direction). Moreover, if Laplace equation Network method is used in a different coordinate system to obtain the expressions of the resistors, mathematical manipulation would be needed and more electrical devices would be involved.…”

Section: The Design Of the Network Modelmentioning

confidence: 99%

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

Martínez‐Moreno

García‐Ros

Alhama

2020

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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.

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Section: The Design Of the Network Modelmentioning

confidence: 99%

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

Martínez‐Moreno

García‐Ros

Alhama

2020

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“…Both the network simulation model and the nondimensionalization technique have demonstrated the effectiveness of their application in numerous engineering problems such as diffusion of chlorides, chemical reactors, soil consolidation, etc. [41][42][43][44]. Finally, there are several main contributions of this paper.…”

Section: Introductionmentioning

confidence: 97%

Mathematical Modeling and Analysis Using Nondimensionalization Technique of the Solidification of a Splat of Variable Section

Sánchez-Pérez,

Jorde-Cerezo,

Fernández-Roiz

et al. 2023

Mathematics

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In this work, the solidification and cooling process of an irregularly shaped splat is modeled using the network simulation method. The procedure for its implementation, which uses the finite difference method and optimized circuit analysis algorithms, allows the precise incorporation and assessment of the effect of certain conditions in the thermal process, offering its specificity and high performance in numerical simulation. It should be noted, on the one hand, that the geometry used for the simulation has been obtained from experimental splat data visualized using an electron microscope and, on the other hand, that the model implements both the phase change phenomenon and the variability of the material properties with temperature. Finally, the study of the physical behavior of the problem is carried out using the mathematical technique of nondimensionalization, allowing the interpretation of the results obtained by simulation, where the formation of horizontal bars and columns that maintain the structure of the splat while the solidification process is taking place stands out. It is worth highlighting the obtaining, among others, of two monomials. The first relates the phenomenon of radiation to conduction and is equivalent to the Nusselt number with convection, and the second relates the solidification time with the Stefan number.

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“…, 1989). Hence, several advanced methodologies have emerged to obtain solutions to this problem, such as the non-dimensionalization techniques (García-Ros et al ., 2018a, b; Alhama Manteca et al. , 2018) the numerical methods (García-Ros et al.…”

Section: Introductionmentioning

confidence: 99%

Physics-informed neural networks for consolidation of soils

Zhang

Lan²,

Li³

et al. 2022

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PurposePrediction of excess pore water pressure and estimation of soil parameters are the two key interests for consolidation problems, which can be mathematically quantified by a set of partial differential equations (PDEs). Generally, there are challenges in solving these two issues using traditional numerical algorithms, while the conventional data-driven methods require massive data sets for training and exhibit negative generalization potential. This paper aims to employ the physics-informed neural networks (PINNs) for solving both the forward and inverse problems.Design/methodology/approachA typical consolidation problem with continuous drainage boundary conditions is firstly considered. The PINNs, analytical, and finite difference method (FDM) solutions are compared for the forward problem, and the estimation of the interface parameters involved in the problem is discussed for the inverse problem. Furthermore, the authors also explore the effects of hyperparameters and noisy data on the performance of forward and inverse problems, respectively. Finally, the PINNs method is applied to the more complex consolidation problems.FindingsThe overall results indicate the excellent performance of the PINNs method in solving consolidation problems with various drainage conditions. The PINNs can provide new ideas with a broad application prospect to solve PDEs in the field of geotechnical engineering, and also exhibit a certain degree of noise resistance for estimating the soil parameters.Originality/valueThis study presents the potential application of PINNs for the consolidation of soils. Such a machine learning algorithm helps to obtain remarkably accurate solutions and reliable parameter estimations with fewer and average-quality data, which is beneficial in engineering practice.

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Use of discriminated nondimensionalization in the search of universal solutions for 2-D rectangular and cylindrical consolidation problems

Cited by 10 publications

References 18 publications

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

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

Mathematical Modeling and Analysis Using Nondimensionalization Technique of the Solidification of a Splat of Variable Section

Physics-informed neural networks for consolidation of soils

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