A closed-form solution for axisymmetric electro-osmotic consolidation considering smear effects

Liu, Y.; Zheng, Junjie; Zhao, Xudong; Cao, Weizhong; Huang, Zhanfang

doi:10.1007/s11440-021-01353-z

Cited by 17 publications

(11 citation statements)

References 51 publications

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“…The orthogonal relationship [40][41][42][43][44][45] is important for the generalized Fourier-Bessel expansion. This appendix explains the detailed mathematical procedures for the orthogonal relationship as presented in Equation (63).…”

Section: Appendix B: the Orthogonal Relationshipmentioning

confidence: 99%

“…When = 0, the general solution for θ i (r,t) takes the following form according to the method of separation of variables. [40][41][42][43][44][45]…”

Section: Analytical Solution Without Considering the Pile Thermal Res...mentioning

confidence: 99%

“…When

\frac{{\partial {Q}_1( {r,t} )}}{{\partial t}} = \frac{{\partial {Q}_2( {r,t} )}}{{\partial t}}\ = \frac{{\partial {Q}_3( {r,t} )}}{{\partial t}}\ = \ 0

, the general solution for θ i ( r,t ) takes the following form according to the method of separation of variables 40–45

\begin{equation}{\theta }_i(r,t) = \sum_{n = 1}^\infty {{R}_{ni}(r){T}_n(t)} \end{equation}

…”

Section: Analytical Solutionmentioning

confidence: 99%

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Analytical solution for heat exchange in energy pile ground considering smear effects

Zhao,

Ni,

Liu

et al. 2023

Num Anal Meth Geomechanics

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Due to the installation of energy piles, the surrounding soil will be inevitably disturbed, leading to a smaller void ratio and larger thermal conductivity. This study proposes a new closed‐form solution to calculate the heat exchange of energy pile foundations considering smear effects on the different soil thermal properties in the smear zone and undisturbed zone. The analytical model adopts the separation of variables to solve the governing equations. The eigenvalues are obtained according to a series of recurrence formulas and a transcendental equation. The solution is verified against existing analytical solutions in literature and numerical simulation, and an excellent agreement is obtained. The parametric study shows that a larger thermal conductivity of the soil in the smear zone results in a lower temperature at any given time. If the smear effects are not considered, the temperature will be overpredicted, especially for the pile and the soil in the smear zone. The proposed solution precisely predicts the soil temperature in the smear zone and undisturbed zone, which can contribute to the thermo‐mechanical behaviour of energy pile foundations in further work.

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Section: Appendix B: the Orthogonal Relationshipmentioning

confidence: 99%

“…When = 0, the general solution for θ i (r,t) takes the following form according to the method of separation of variables. [40][41][42][43][44][45]…”

Section: Analytical Solution Without Considering the Pile Thermal Res...mentioning

confidence: 99%

“…When

\frac{{\partial {Q}_1( {r,t} )}}{{\partial t}} = \frac{{\partial {Q}_2( {r,t} )}}{{\partial t}}\ = \frac{{\partial {Q}_3( {r,t} )}}{{\partial t}}\ = \ 0

, the general solution for θ i ( r,t ) takes the following form according to the method of separation of variables 40–45

\begin{equation}{\theta }_i(r,t) = \sum_{n = 1}^\infty {{R}_{ni}(r){T}_n(t)} \end{equation}

…”

Section: Analytical Solutionmentioning

confidence: 99%

See 1 more Smart Citation

Analytical solution for heat exchange in energy pile ground considering smear effects

Zhao,

Ni,

Liu

et al. 2023

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

show abstract

“…[21][22][23][24][25][26][27][28][29][30][31][32][33] Most recently, Zhao et al 34,35 investigated electro-osmotic consolidation of double-layered soils. Liu et al 36 further considered the soil heterogeneity along the radial direction (i.e., smear zone) when studying the axisymmetric electro-osmotic consolidation model. All of these studies have shown significant differences in the consolidation properties of double-layered soils and single-layered soil.…”

Section: Introductionmentioning

confidence: 99%

Semi‐analytical solution for double‐layered elliptical cylindrical foundation model improved by prefabricated vertical drains

Zhao,

Guo,

Cao

et al. 2024

Num Anal Meth Geomechanics

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This work proposes a semi‐analytical solution for a double‐layered elliptical cylindrical soft foundation improved by prefabricated vertical drains. The governing equations, continuity conditions are boundary conditions in the elliptical cylindrical system are introduced first. The Laplace transform is employed to convert the time variable t in partial differential equations into the Laplace complex argument s. Based on the boundary condition and continuity condition, the solution in the frequency domain is derived. By using Abate's fixed Euler Algorithm, the solutions in the time domain are obtained. A finite element analysis is performed to demonstrate the accuracy of the proposed solution. Then, parametric studies reveal that soil permeability and soil compressibility have great influences on the second layer of soil in the elliptical cylindrical system, but relatively small effects on the first layer. Neglecting differences in the hydraulic conductivity and the coefficient of volume compressibility of multi‐layered soil in the elliptical cylindrical system could not predict the excess pore pressure in the second layer correctly.

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“…With the rapid consolidation process, soft soils gain shear strength rapidly which allows for a faster pace of construction works. Tis signifcantly increases the long-term stability of the structures built on clayey ground as the potential consolidation settlements are accomplished mostly before or during the construction phase [14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Consolidation Attributes and Deformation Response of Soft Clay Reinforced with Vertical Scoria Drains under Road Embankment

Gebretsadik

Melese

Negesa

2023

Advances in Materials Science and Engineering

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Application of vertical drains in soft clay soils is a common practice widely known to facilitate the consolidation rate. To overcome the adverse impact of a long-lasting consolidation process, highly permeable materials such as sand and crushed aggregates are used as drains. However, limited information exists regarding the applicability of scoria gravel as a vertical drain that no concisely documented information is observed in the literature. This study hence aimed at investigating suitability of scoria as a vertical drain in perpetuating the consolidation process of soft clay under highway embankment. Finite element-based numerical simulation was used to model the drain. The model was carried out by using 3D version of Plaxis software. In order to incorporate the effect of gradual load increment on the consolidation rate, the staged construction approach was employed. Both the square and triangular installation patterns were considered in the model in order to explore the critical effects of the drain installation pattern on the rate of consolidation. The numerical analysis also included varying dimensions of the vertical drain so as to investigate the effects of the dimension parameters of the vertically installed scoria drains. The conducted numerical analysis revealed that the rate of consolidation was considerably accelerated with provision of a group of scoria drains. With increase in the diameter of the drain, the consolidation rate increases, whereas the consolidation rate is inversely related to increase in drain spacing. For the drain installed at a spacing of 2 m, a diameter of 0.4 m, and a length of 8 m any arbitrary settlement magnitude is achieved 25 days earlier than the case without drains. Besides, incorporation of scoria drains lessens the pore pressure developed. The comparative analysis conducted on the effect of drain arrangement revealed that no considerable difference was witnessed in the performance of the square and triangular installation patterns even though the consolidation rate remains slightly faster in the case of the triangular installation pattern.

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A closed-form solution for axisymmetric electro-osmotic consolidation considering smear effects

Cited by 17 publications

References 51 publications

Analytical solution for heat exchange in energy pile ground considering smear effects

Analytical solution for heat exchange in energy pile ground considering smear effects

Semi‐analytical solution for double‐layered elliptical cylindrical foundation model improved by prefabricated vertical drains

Consolidation Attributes and Deformation Response of Soft Clay Reinforced with Vertical Scoria Drains under Road Embankment

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