Derivation of Universal Curves for Nonlinear Soil Consolidation with Potential Constitutive Dependences

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

doi:10.1155/2018/5837592

Cited by 7 publications

(9 citation statements)

References 22 publications

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“…Based on the dimensional analysis, the influence of various factors on the gas holdup in the reactor is studied. According to Buckingham's theorem (πprinciple), a general functional form of the independent variables was obtained and is given in the following equations [35][36][37]:…”

Section: Dimensional Analysis Of Gas Holdupmentioning

confidence: 99%

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Dimensional Analysis of Gas Holdup of Venturi Carbonation Reactor for Red Mud Processing

Xiao

Liu

Zhao

et al. 2020

Mathematical Problems in Engineering

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Gas holdup is an important parameter in the carbonation reaction for processing red mud. In this paper, for estimating the gas holdup of Venturi carbonation reactor, water model experiments were performed. The effects of superficial gas velocities, superficial liquid velocities, and liquid-to-solid and height-to-diameter ratio on the gas holdup are investigated. Through dimensional analysis using Buckingham π principle, a derivation of the empirical correlation is also proposed. The results indicate that gas holdup increases with the increase in gas velocity, with the decrease in liquid velocity, with the increase in liquid-to-solid ratio, and with the increase in height-to-diameter ratio. The calculated results from the empirical correlation agree well with the experimental data, which is important for designing a highly efficient Venturi reactor with a high temperature, high pressure, and three phases of gas, liquid, and solid.

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Section: Dimensional Analysis Of Gas Holdupmentioning

confidence: 99%

“…en, according to the π-principle, the dimensionless forms of the remaining n − k independent variables were defined as follows [35][36][37]:…”

Section: Dimensional Analysis Of Gas Holdupmentioning

confidence: 99%

Dimensional Analysis of Gas Holdup of Venturi Carbonation Reactor for Red Mud Processing

Xiao

Liu

Zhao

et al. 2020

Mathematical Problems in Engineering

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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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“…Recently, the dimensionless groups that characterize the aforementioned models, as well as their extensions to more general and precise formulations obtained from the elimination of several restrictive hypotheses [11], have been derived from their governing equations and the application of the pi theorem [12], which has allowed the construction of universal curves of easy use for the determination of the characteristic consolidation time, the average degree of pressure dissipation and the average degree of settlement [13][14][15][16]. The results obtained by these authors reduce the numerous coefficients (dimensional or not) involved in the models to a small number of dimensionless groups based on which the solution for each unknown is presented by a single universal curve.…”

Section: Introductionmentioning

confidence: 99%

Method to Determine the Constitutive Permeability Parameters of Non-Linear Consolidation Models by Means of the Oedometer Test

García‐Ros

Alhama

2020

Mathematics

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This paper presents an easy-to-apply methodology that allows obtaining the permeability index and the initial hydraulic conductivity of clayey soils, basic constitutive parameters in non-linear models of consolidation, based on the laboratory oedometer test. For this, the data of the void ratio, compressibility index and characteristic consolidation time are taken from the test and, as an inverse problem, the constitutive permeability parameters sought are determined by applying the universal solutions of the characteristic time for a general non-linear consolidation model with constitutive relations void ratio-effective soil stress and hydraulic conductivity-void ratio of logarithmic type. The application protocol of the inverse problem is described in detail and illustrated by a series of applications carried out on real laboratory data belonging to two different soils. The influence that errors in laboratory parameter measurements can have on the final values of the permeability index and initial hydraulic conductivity is studied, showing the maximum deviations that may appear and, by last, the precision of the results obtained.

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Derivation of Universal Curves for Nonlinear Soil Consolidation with Potential Constitutive Dependences

Cited by 7 publications

References 22 publications

Dimensional Analysis of Gas Holdup of Venturi Carbonation Reactor for Red Mud Processing

Dimensional Analysis of Gas Holdup of Venturi Carbonation Reactor for Red Mud Processing

Physics-informed neural networks for consolidation of soils

Method to Determine the Constitutive Permeability Parameters of Non-Linear Consolidation Models by Means of the Oedometer Test

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