One dimensional consolidation of multi-layered unsaturated soil under partially permeable boundary conditions and time-dependent loading

Moradi, Mohammadhossein; Keshavarz, Amin; Fazeli, A.

doi:10.1016/j.compgeo.2018.11.020

Cited by 42 publications

(26 citation statements)

References 33 publications

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“…With the one-dimensional two-way vertical drainage of water from the fully saturated stabilized peat element in Figure 1, two boundary conditions as shown in Equations 13 and 14 must be satisfied. u(0, t) = 0 for t ≥ 0 (13) u(H, t) = 0 for t ≥ 0…”

Section: Methodsmentioning

confidence: 99%

“…Recent advancement of mathematical modelling in geomechanics has seen the development of numerous published research works of one-dimensional consolidation of soils by analytical and numerical methods [1][2][3][4][5][6][7][8][9][10][11][12][13]. Despite of that, not many analytical and numerical solutions that solved one-dimensional consolidation problem of stabilized peat were found in the literature of geomechanics.…”

Section: Introductionmentioning

confidence: 99%

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Analytical and Numerical Modelling of One-Dimensional Consolidation of Stabilized Peat

Wong

Somanathan

2019

Civ Eng J

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The objective of the paper is to compare and evaluate analytical and numerical solutions of one-dimensional consolidation of stabilized peat. The type of analytical method used to solve the problem is exact method by separation of variables and utilization of Fourier series. Plaxis 2D 8.2 Professional version software was used to find numerical solution to the problem by employing the finite element method. One-dimensional consolidation problem of stabilized peat was solved numerically and validated with the one solved analytically based on laboratory experimental results. From the results, it was discovered that the consolidation characteristics of stabilized peat evaluated numerically were found to have close approximation to those evaluated analytically. There is a novel value in developing an accurate numerical prediction for the vertical consolidation of stabilized peat considering the complexity of the soil treatment method. It must be noted that peat is highly problematic because it is produced from plant decomposition with extremely high organic matter. 399 for 7 days before testing. It is notable that oedometer consolidation apparatus is sufficient for testing the stabilized soil due to the fact that the soil was homogeneously mixed with the binding admixtures and silica sand. As such, it could be reliably used to simulate the one-dimensional deformation and drainage characteristics of the stabilized soil as the soil dissipation of excess pore water pressure became less significant over time due to the cementation process in the stabilized soil. Furthermore, the equipment set up for oedometer testing is simple and not time consuming as compared to that of a more advanced equipment such as Rowe consolidometer. The complexity of Rowe consolidometer setup is evident in the published work of Baral et al. [18] which is about the study of radial consolidation characteristics of soft clay based on large specimens. To develop a proper understanding and to ensure the reliability of the test results, it would be helpful to back analyze and validate the experimental results based on the analytical equation with the ones developed from numerical solution using Plaxis 2D 8.2 Professional version software. As such, the paper is concentrated at evaluating the results of one-dimensional consolidation tests from standard oedometer consolidation apparatus, which were determined based on the idealization of analytical model and later, validating the results using the finite element software.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical and Numerical Modelling of One-Dimensional Consolidation of Stabilized Peat

Wong

Somanathan

2019

Civ Eng J

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“…Thus, many studies chose some alternative numerical approaches to solve governing equations. [1][2][3][4][5][6] Most recently, researchers have made significant contributions to the analytical solutions for the 1-D consolidation of unsaturated soil. Qin et al 7,8 used the Laplace transform technique to solve the governing equations proposed by Fredlund.…”

Section: Introductionmentioning

confidence: 99%

“…For many years, it has been a great challenge to solve this set of nonlinear PDEs using analytical methods. Thus, many studies chose some alternative numerical approaches to solve governing equations 1–6 …”

Section: Introductionmentioning

confidence: 99%

An explicit one‐dimensional consolidation solution with semi‐permeable drainage boundary for unsaturated soil

Zhao

ZHANG

et al. 2020

Num Anal Meth Geomechanics

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Existing solutions for analyzing one-dimensional (1-D) consolidation of unsaturated soil are only derived to cater to two extreme drainage conditions (fully drained and undrained). This study presents a new explicit solution for 1-D consolidation of unsaturated soil with semi-permeable drainage boundary. Based on the assumptions of two independent stress variables and the governing equations proposed by Fredlund, the eigenfunction expansion method is adopted to develop an explicit analytical solution to calculate excess pore-water and pore-air pressures in an unsaturated soil when it is subjected to external loads. The developed general solutions are expressed in terms of depth, z, and time, t. For the semi-permeable drainage boundary, eigenvalues and eigenfunctions in the space domain are developed. The technique of Laplace transform is used to solve the coupled ordinary differential equations in the time domain. The newly derived explicit solution is verified with the existing semi-analytical method in the literature, and an excellent agreement is obtained. Compared with the semi-analytical solution, the newly derived analytical solution is more straightforward and explicit so that this solution is relatively easier to be implemented into a computer program to carry out a preliminary assessment of 1-D consolidation of unsaturated soil.

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“…Wang et al (2017), Liu et al (2018), Zou et al (2018), and Zhao et al (2020), respectively, obtained analytical solutions for the one-dimensional consolidation of clayey soils considering different load and boundary conditions. When considering time-dependent loading, Deng et al (2019) presented closedform solutions for one-dimensional consolidation in saturated soils, Moradi et al (2019) analyzed the one-dimensional consolidation of a multilayered unsaturated soil under partially permeable boundary conditions, and Zhou et al (2020) obtained an analytical solution for a classical one-dimensional thaw consolidation model. However, due to the small sample used in the test, the applicability of this theory in the calculation of deep soft clay could not be verified.…”

Section: Introductionmentioning

confidence: 99%

Finite Difference Method for the One-Dimensional Non-linear Consolidation of Soft Ground Under Uniform Load

et al. 2020

Front. Earth Sci.

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Initial stress and additional effective stress distributions in soil greatly influence the degree of ground consolidation when calculating one-dimensional soft clay ground consolidation in deep soil. The one-dimensional non-linear consolidation governing equations of soft ground under uniform load are derived and solved with the finite difference method. This method is based on the assumptions that the initial stress in soil varies with the ground depth and that the additional effective stress caused by external loads changes with both the ground depth and consolidation time and the hyperbolic model of the soil stress-strain relationship. Formulas for the degree of consolidation and the settlement of the ground are presented. A case study shows that the degree of consolidation in the ground calculated with the finite difference method agrees well with the traditional analytical solution, and the computational efficiency of the finite difference method can be effectively improved when the segmental calculation method is used throughout the consolidation process. The results of another example show that the settlement of the ground calculated with the finite difference method agrees with the in situ data. The suggested method can greatly simplify the consolidation calculation and has a high application value in engineering.

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One dimensional consolidation of multi-layered unsaturated soil under partially permeable boundary conditions and time-dependent loading

Cited by 42 publications

References 33 publications

Analytical and Numerical Modelling of One-Dimensional Consolidation of Stabilized Peat

Analytical and Numerical Modelling of One-Dimensional Consolidation of Stabilized Peat

An explicit one‐dimensional consolidation solution with semi‐permeable drainage boundary for unsaturated soil

Finite Difference Method for the One-Dimensional Non-linear Consolidation of Soft Ground Under Uniform Load

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