Analytical solution to axisymmetric consolidation in unsaturated soils with linearly depth-dependent initial conditions

Ho, Liem; Fatahi, Behzad; Khabbaz, Hadi

doi:10.1016/j.compgeo.2015.12.019

Cited by 67 publications

(64 citation statements)

References 35 publications

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“…In general, the SAS had been developed considering all kinds of boundaries and time‐dependent loadings for 1D dimensional consolidation problem in unsaturated soils . The literature about the 2D plane strain consolidation in unsaturated soils are applicable to the homogeneous and mixed drainage boundary condition subjected to four time‐dependent loadings, and there are only analytical solutions for the axisymmetric consolidation in unsaturated soils with the homogeneous boundary and considering the smear effect and time‐dependent loading . However, there are no SAS of the 2D plane strain consolidation considering the LSDB.…”

Section: Introductionmentioning

confidence: 99%

“…However, there are no SAS of the 2D plane strain consolidation considering the LSDB. In addition, the consolidation property is significantly impacted by the lateral boundary for the 2D plane strain condition …”

Section: Introductionmentioning

confidence: 99%

“…21,23,38 The literature about the 2D plane strain consolidation in unsaturated soils are applicable to the homogeneous and mixed drainage boundary condition subjected to four time-dependent loadings, 25,34 and there are only analytical solutions for the axisymmetric consolidation in unsaturated soils with the homogeneous boundary and considering the smear effect and time-dependent loading. 28,[35][36][37] However, there are no SAS of the 2D plane strain consolidation considering the LSDB. In addition, the consolidation property is significantly impacted by the lateral boundary for the 2D plane strain condition.…”

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confidence: 99%

“…In addition, the consolidation property is significantly impacted by the lateral boundary for the 2D plane strain condition. 35 Therefore, this paper attempts to give the general SAS to study the changes of excess pore-air and pore-water pressures and settlement using the 2D plane strain consolidation theory of the unsaturated soil deposit with the LSDB. To obtain final solutions, the mathematical methods of Fourier sine series and Laplace transform are applied to turn the PDEs to the ODEs, which can be easily solved by the method of substitution.…”

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Semi‐analytical solutions of two‐dimensional plane strain consolidation in unsaturated soils subjected to the lateral semipermeable drainage boundary

Xia

2019

Num Anal Meth Geomechanics

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Summary The study presents semi‐analytical solutions of two‐dimensional plane strain consolidation problem in unsaturated soils incorporating the lateral semipermeable drainage boundary by adopting Fourier sine series and Laplace transform. The two‐dimensional plane strain consolidation equations in the form of two‐order partial differential equations with three variables are firstly converted to two‐order partial differential equations with two variables, which are similar to those of one‐dimensional consolidation problem. The four‐order ordinary differential equations about excess pore‐air and excess pore‐water pressures are got by applying Laplace transform and the substitution method. Then, the solutions of excess pore pressures and settlement are achieved in the Laplace transform domain. Afterwards, on the basis of Crump's method, the inverse Laplace transform is conducted to obtain the analytical solutions in time domain. The comparison is conducted to verify the exactness of the obtained solutions, and the two‐dimensional plane strain consolidation property with the lateral semipermeable drainage boundary is illustrated and discussed. Parametric studies are demonstrated for the excess pore pressures and normalized settlement with the change of the boundary parameters, air‐water and lateral‐vertical permeability coefficients, and the distance and depth. It can be found that the lateral semipermeable drainage boundary impedes the consolidation rate obviously, and when different investigated parameters are adopted, the consolidation property is similar to each other under the later permeable and semipermeable drainage boundary conditions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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Semi‐analytical solutions of two‐dimensional plane strain consolidation in unsaturated soils subjected to the lateral semipermeable drainage boundary

Xia

2019

Num Anal Meth Geomechanics

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“…Along with the publishing of Fredlund's book "Unsaturated Soil Mechanics" [1] and a large number of studies, the concept that the suction is a key element to influence the strength, deformation and seepage process of unsaturated soil has been established [2]. Many experts and scholars studied the characteristics of unsaturated soil based on the concept of suction, a lot of achievements were made [3][4][5][6][7][8][9][10][11]. As far as the remolded loess in the filling area of new urban district construction in Yan'an is concerned, the experimental study on the basis of theory of unsaturated soil is not common in the literature.…”

Section: Introductionmentioning

confidence: 99%

Test Study on Consolidation Character of Unsaturated Loess

Sheng-xia¹,

Dong²,

Wen-li³

2017

dteees

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Abstract. To calculate accurately settlement of loess foundation in filled area as the main goal, disturbed loess of filled project in Yan'an new district engineering construction in China as the research object, Q 3 disturbed loess samples were made indoor for consolidation test by the reference of geotechnical engineering design parameters of filled project loess in actual practical project. Four groups of unsaturated consolidation tests were carried out with matric suction ranging from 100kPa to 500kPa. Compressive curve of the unsaturated and undisturbed loess sample were obtained. The influence of matric suction to consolidation characteristics of disturbed loess was analyzed. Results show: (1) For same initial state disturbed loess soil samples, when matric suction increases from 100kPa to 500kPa, the compressibility coefficient reduces from 0.151MPa -1 to 0.095MPa -1 . Compressibility coefficient reduces with increasing the matric suction; (2) Compression index of unsaturated and disturbed loess sample was influenced not only by vertical pressure but also by matric suction. Compressibility index reduces when the matric suction increase; (3) The total vertical strain of disturbed loess sample which control parameters referred to the actual geotechnical engineering design plan was small under the 2MPa vertical stress. The biggest vertical strain was 0.7%.

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Analytical solution to axisymmetric consolidation of unsaturated soil stratum under equal strain condition incorporating smear effects

Ho¹,

Fatahi

2018

Num Anal Meth Geomechanics

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This paper proposes closed-form analytical solutions to the axisymmetric consolidation of an unsaturated soil stratum using the equal strain hypothesis. Following the 1-dimensional (1D) consolidation theory for unsaturated soil mechanics, polar governing equations describing the air and water flows are first presented on the basis of Fick's law and Darcy's law, respectively. The current study takes into account the peripheral smear caused by an installation of vertical drain. Separation of variables and Laplace transformation are mainly adopted in the analytical derivation to obtain final solutions. Then, the hydraulic conductivity ratio, the radius of influence zone and smear parameters influencing time-dependent excess pore pressures, and the average degree of consolidation are graphically interpreted. In this study, a comparison made between the proposed equal strain results and the existing free strain results suggests that both hypotheses would deliver similar predictions. Moreover, it is found that the smear zone resulting from vertical drain installations would hinder the consolidation rate considerably.

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Analytical solution to axisymmetric consolidation in unsaturated soils with linearly depth-dependent initial conditions

Cited by 67 publications

References 35 publications

Semi‐analytical solutions of two‐dimensional plane strain consolidation in unsaturated soils subjected to the lateral semipermeable drainage boundary

Semi‐analytical solutions of two‐dimensional plane strain consolidation in unsaturated soils subjected to the lateral semipermeable drainage boundary

Test Study on Consolidation Character of Unsaturated Loess

Analytical solution to axisymmetric consolidation of unsaturated soil stratum under equal strain condition incorporating smear effects

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