Analytical solution for nonlinear consolidation of combined electroosmosis-vacuum-surcharge preloading

Wang, Liujiang; Huang, Penghua; Liu, Sihong; Alonso, Eduardo E.

doi:10.1016/j.compgeo.2020.103484

Cited by 27 publications

(12 citation statements)

References 40 publications

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“…Several assumptions related to the mathematical model presented in this research are: The unsaturated soil layer is homogeneous, in which the compression of water or soil particles during consolidation is negligible. The strain occurring in the soil during consolidation is small. Ohm's law and Darcy's law are applicable to the water flow 13,32,33 ; Fick's law is effective for the air flow, 34 and both flows are independent and continuous. The voltage distribution,

\Phi ( r )

, is assumed to follow the law of charge conservation in the radial direction, which is independent of time 4,35 The coefficient of volume change, electro‐osmotic permeability k e , 18, 36 and permeability coefficient k a* ( k w* ) are constants 24,26,29 …”

Section: Mathematical Modelmentioning

confidence: 99%

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The role of free‐strain assumption in axisymmetric electro‐osmosis‐enhanced preloading consolidation of unsaturated soil

Jiang

Qin

2023

Num Anal Meth Geomechanics

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The axisymmetric, equal‐strain consolidation theory of soil is widely employed in engineering due to the user‐friendliness of its solution. However, the radially averaged excess pore pressure (EPP) is unable to reveal the coupling effect of the radial electric field when the soil is consolidated by electro‐osmotic and surcharge preloading. In this paper, the axisymmetric consolidation analytical models with free strain and equal strain assumptions are developed to investigate the importance of the free strain assumption in the consolidation of unsaturated soil by electro‐osmosis‐aided preloading. The finite Hankel transform, decoupling technique, and Laplace transform are then utilised to derive the semi‐analytical solutions. Finally, the comparison of EPP, surface settlement, and average degree of consolidation under the two assumptions reveals that the free‐strain solution accurately shows the distribution of EPP at any point in the soils and the development of surface settlement at different radii, thus helping to analyse the electro‐osmotic consolidation characteristics. Moreover, it was discovered that electro‐osmosis combined with preloading allows for a more uniform consolidation of unsaturated soil. The difference in the average degree of consolidation under both assumptions is insignificant, while the installation distance of the cathode and anode vertical wells has a significant effect.

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\Phi ( r )

Section: Mathematical Modelmentioning

confidence: 99%

“…The voltage distribution,

\Phi ( r )

, is assumed to follow the law of charge conservation in the radial direction, which is independent of time 4,35 …”

Section: Mathematical Modelmentioning

confidence: 99%

The role of free‐strain assumption in axisymmetric electro‐osmosis‐enhanced preloading consolidation of unsaturated soil

Jiang

Qin

2023

Num Anal Meth Geomechanics

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“…Tang et al [24] enriched and improved the shaft consolidation theory by considering the noninstantaneous loading and layered characteristics. In addition, many scholars have carried out numerical studies [25,26] on different process combinations such as vacuum preloading and electroosmosis [27,28], which were helpful for the better understanding of the mechanism of reinforcement. In the above-cited studies, different compression and permeability curves were used to describe the soil, and more accurate consolidation solutions were obtained, however, the basic framework was still the small deformation consolidation.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Vacuum Preloading for Chemically Conditioned Municipal Sludge

Li¹,

Zhan²,

Wang³

et al. 2023

Journal of Renewable Materials

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Municipal sludge is a sedimentation waste produced during the wastewater process in sewage treatment plants. Among recent studies, pilot and field tests showed that chemical conditioning combined with vacuum preloading can effectively treat municipal sludge. To further understand the drainage and consolidation characteristics of the conditioning sludge during vacuum preloading, a large deformation nonlinear numerical simulation model based on the equal strain condition was developed to simulate and analyze the pilot and field tests, whereas the simulation results were not satisfactory. The results of the numerical analysis of the pilot test showed that the predicted consolidation degree was greater than that measured by the field tests, which is attributed to the relatively low permeability layer formed during the preloading process of the prefabricated vertical drain. To better reflect the consolidation process of the conditioned sludge, a simplified analysis method considering the low permeability layer around the prefabricated vertical drain was proposed. The initial permeability coefficient of the low permeability layer is determined via numerical simulations using finite difference method. The predicted settlement curve was in good agreement with the measured results, which indicated that the numerical simulation based on the equal strain condition considering the relatively low permeability layer can better analyze the consolidation process of ferric chloride-conditioning sludge with vacuum preloading.

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“…On the basis of the above saturation changes, the large deformation theory is introduced to improve the influence of soil properties changes in the process of electroosmotic consolidation by Deng and Zhou [14] and Zhou et al [15][16][17]; the change of soil saturation also attracted the attention of Wang et al [18]. In the twodimensional model, the vacuum preloading method was introduced into the electroosmotic consolidation model, and the governing equation of this case was given and solved analytically by Wang et al [19]. Sheng et al [20] carried out experimental research on the two-dimensional potential distribution of electroosmotic under the action of plastic electrode plate, and the two-dimensional electroosmotic consolidation was calculated through the measured values.…”

Section: Introductionmentioning

confidence: 99%

Study on Electroosmosis Consolidation of Punctiform Electrode Unit

Yang

Xie

Dong

et al. 2021

Advances in Materials Science and Engineering

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In the electroosmosis method, when the distance between the opposite electrode and the same electrode is equal, the two-dimensional effect of electroosmotic consolidation is significant, and the use of one-dimensional model will overestimate the potential gradient, making the calculated pore pressure value too large. Aiming at this problem, according to the electrode arrangement rule and the minimum composition, a punctiform electrode unit model is proposed, and electroosmotic experiments are carried out on the symmetric and asymmetric unit models. The two-dimensional electroosmotic consolidation governing equation of the punctiform electrode unit is established. The electric potential field of the electrode unit and the finite element form of the electroosmotic consolidation equation are given by the Galerkin method. The PyEcFem finite-element numerical library is developed using Python programming to calculate. The research results show the following: (1) The two-dimensional effect of the potential field distribution of the punctiform electrode unit is significant. The reduction of spacing of the same nature electrode in the symmetrical unit can make the potential distribution close to a uniform electric field. The asymmetry prevents the electric potential field distribution from being reduced to a one-dimensional model. (2) The number of anodes will affect the electroosmosis effect of the soil. The more the anodes, the better the electroosmosis reinforcement effect of the soil, and the distribution of negative excess pore water pressure will be more uniform. (3) In the early stage of electroosmosis, the more the drainage boundaries, the faster the generation of negative pore pressure, but in the middle and late stages of electroosmosis, the potential value becomes the decisive factor, and the amplitude of negative pore water pressure in asymmetric units is higher than that in symmetric units. The potential distribution will not affect the degree of consolidation but will affect the extreme pore water pressure.

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Analytical solution for nonlinear consolidation of combined electroosmosis-vacuum-surcharge preloading

Cited by 27 publications

References 40 publications

The role of free‐strain assumption in axisymmetric electro‐osmosis‐enhanced preloading consolidation of unsaturated soil

The role of free‐strain assumption in axisymmetric electro‐osmosis‐enhanced preloading consolidation of unsaturated soil

Numerical Simulation of Vacuum Preloading for Chemically Conditioned Municipal Sludge

Study on Electroosmosis Consolidation of Punctiform Electrode Unit

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