Fractional derivative modeling for axisymmetric consolidation of multilayered cross-anisotropic viscoelastic porous media

Ai, Zhi Yong; Zhao, Yong Zhi; Liu, Wen Jie

doi:10.1016/j.camwa.2019.08.033

Cited by 20 publications

(7 citation statements)

References 25 publications

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“…metode untuk menyelesaikan yang nonlinier model viskoelastik anisotropik adalah dengan menggambarkan perilaku mekanik komposit berserat. Adapun dengan menerapkan teori viskoelastisitas anisotropic adalah untuk memodelkan mekanisme membran biologis dan menyajikan solusi untuk kasus keadaan tegangan bidang Ai et al, (2020); Nguyen & Hwu, (2020). Peneliti juga telah menyelidiki perambatan gelombang pada pelat tipis viskoelastik isotropik transversal dalam penyelesaian eliptik masalah nilai batas, yang juga dirumuskan dalam bidang frekuensi-ruang dengan penggunaan elemen hingga prosedur Galerkin.…”

Section: Pendahuluanunclassified

Basis teoritis dari metode grid yang ditumpangkan

Lumbangaol

Purba

Marbun

et al. 2022

PSSA

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Masalah pemodelan sifat anisotropik yang benar dari bahan komposit sampai hari ini tidak sepenuhnya terungkap. Ini memaksa para insinyur dan ilmuwan untuk menyederhanakan deskripsi parameter fisik dan mekanik untuk menentukan perilaku mekanik padatan yang dapat dideformasi. Ini terutama berlaku untuk viskositas. Akibatnya dalam kompleks analisis perangkat lunak elemen hingga, sifat-sifat ini dimodelkan secara turun-temurun fungsi yang sebanding dengan tensor elastisitas awal, yang dalam beberapa kasus bukan asumsi yang benar. Adapun untuk menghilangkan kekurangan tersebut berdasarkan metode elemen hingga, maka metode grid yang ditumpangkan diusulkan, yang memungkinkan untuk memodelkan sifat fisik dan mekanik, khususnya viskoelastik, dengan mempertimbangkan tingkat anisotropi. Metode ini memungkinkan untuk memecahkan sejumlah masalah dalam teori viskoelastisitas anisotropik, menghasilkan diperoleh hasil yang benar. Makalah ini menyajikan pembenaran teoretis untuk metode ini, yang didasarkan pada: pertimbangan total energi fungsional dari benda cacat, untuk masalah statis dan dinamis linier teori elastisitas dan viskoelastisitas. Pendekatan terhadap masalah ini menetapkan aturan untuk memperoleh parameter tegangan-regangan keadaan benda yang dapat dideformasi sesuai dengan kekhasan metode kisi-kisi yang ditumpangkan dan skenario yang mungkin diidentifikasi aplikasinya.

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Section: Pendahuluanunclassified

Basis teoritis dari metode grid yang ditumpangkan

Lumbangaol

Purba

Marbun

et al. 2022

PSSA

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“…Compared with the classic integer‐order Merchant model, only a fractional order is added to the parameters of the fractional model. Moreover, the fractional model can more effectively simulate the rheological properties and better describe the results of creep tests 34 …”

Section: Fractional Derivative Merchant Rheological Modelmentioning

confidence: 99%

“…Moreover, the fractional model can more effectively simulate the rheological properties and better describe the results of creep tests. 34…”

Section: Fractional Derivative Merchant Modelmentioning

confidence: 99%

Semi‐analytical analysis of fractional derivative rheological consolidation considering the effect of self‐weight stress

Ding

et al. 2021

Num Anal Meth Geomechanics

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Studies have revealed that rheological characteristics and self‐weight stress are nonnegligible during a consolidation process, especially for land reclamation projects or dredged soils. However, they are rarely considered simultaneously in traditional consolidation theories. This paper presents a general solution to the consolidation system of rheological soils that incorporates a fractional derivative model and self‐weight stress. First, the theory of the fractional derivative is introduced to the Merchant model to describe the consolidation behaviours of rheological soils, and the self‐weight stress of soils is simultaneously considered. Based on this model, the governing equation of a rheological consolidation system that considers self‐weight stress is obtained. Second, the analytical solutions of the effective stress and settlement in the Laplace domain are obtained by applying the Laplace transform to the consolidation governing equation. Further, the actual solutions in the real domain are obtained by a numerical Laplace transform inversion method (Abate's fixed Talbot method). Finally, the reliability and correctness of the consolidation theories and the proposed solutions are verified by comparing the calculated results with the degenerate solutions and experimental results in the existing literature. Furthermore, parametric studies are conducted to investigate the influence of rheological parameters and self‐weight parameters on the consolidation settlement and consolidation rate.

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“…27,28 Scholars have conducted many beneficial studies on the static consolidation characteristics of clay-based on fractional order rheological models in recent years. [29][30][31] Under cyclic dynamic loading, the accumulation and dissipation of pore water pressure in saturated clay will occur cyclically, and the rheology of the soil skeleton and the permeation of pore water act simultaneously. Therefore, the dynamic consolidation of saturated clay will have more complex properties.…”

Section: Introductionmentioning

confidence: 99%

Rheological consolidation analysis of saturated clay ground under cyclic loading based on the fractional order Kelvin model

Wang,

Chen,

Liu

et al. 2024

Num Anal Meth Geomechanics

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Based on Biot porous medium theory, considering the coupled reaction of soil skeleton rheology and pore pressure dissipation, the present work investigates the dynamic consolidation characteristics of saturated clay ground under cyclic loading. First, the rheological behavior of the soil skeleton was described by the fractional order Kelvin model. The dynamic consolidation governing equations for the saturated clay were established theoretically in a three‐dimensional axisymmetric coordinate system. Second, the transform domain analytical solution of the dynamic consolidation of saturated clay was obtained using the Hankel–Laplace coupled transform method, and the solution in the time–space domain was further obtained through numerical inversion. Finally, the rheological consolidation behavior of saturated clay under cyclic loading and the influences of parameters were analyzed. The results show that the rheology of the soil skeleton had an inhibitory effect on pore water permeability; compared with elastic skeleton soil, the rheological clay had a slower settlement rate in the primary consolidation stage, a faster rate in the secondary consolidation stage, and greater long‐term settlement. In addition, under cyclic loading, the pore pressure response in saturated clay lags behind the effective stress, and a larger viscous order is associated with faster development of cumulative settlement.

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Fractional derivative modeling for axisymmetric consolidation of multilayered cross-anisotropic viscoelastic porous media

Cited by 20 publications

References 25 publications

Basis teoritis dari metode grid yang ditumpangkan

Basis teoritis dari metode grid yang ditumpangkan

Semi‐analytical analysis of fractional derivative rheological consolidation considering the effect of self‐weight stress

Rheological consolidation analysis of saturated clay ground under cyclic loading based on the fractional order Kelvin model

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