Viscoelastic analysis of transversely isotropic multilayered porous rock foundation by fractional Poyting-Thomson model

Chen, Yuan Feng; Ai, Zhi Yong

doi:10.1016/j.enggeo.2019.105327

Cited by 19 publications

(4 citation statements)

References 34 publications

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“…To overcome these disadvantages a new group of fractional viscoelastic models (Heymans and Bauwens, 1994;Long et al, 2018;Mainardi, 2010;Schiessel et al, 1995;Xu and Jiang, 2017) based on the idea of non-integer order of derivative have been proposed and proven to be an effective tool for description of experimental viscoelastic data (creep, stress relaxation) of the most diverse systems ranging from shape memory polymers (Fang et al, 2015) over gels (Faber et al, 2017;Holder et al, 2018;Rosalina and Bhattacharya, 2002;Zhang et al, 2018) and food (Mahiuddin et al, 2020) to biological (Bonfanti et al, 2020a;Carmichael et al, 2015;Craiem et al, 2006;Li and Tian, 2021;Mahiuddin et al, 2020) and geological systems (Di Giuseppe et al, 2009;Chen and Ai, 2020;Wang, 2021). The key concept is an introduction of another element called a spring-pot which exhibits behavior between the spring and the dashpot and by design captures power-law materials (Bonfanti et al, 2020b).…”

Section: Introductionmentioning

confidence: 99%

Fractional viscoelastic models of porcine skin and its gelatin-based surrogates

Moučka

Sedlačík

Pátíková

2023

Mechanics of Materials

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Section: Introductionmentioning

confidence: 99%

Fractional viscoelastic models of porcine skin and its gelatin-based surrogates

Moučka

Sedlačík

Pátíková

2023

Mechanics of Materials

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“…The basic element of the fractional-order creep model can be divided into three types: conventional fractional-order element, fractional-order damage element with parameter degradation and fractional variable-order element (Tang et al., 2018; Zhou et al., 2012). At present, most fractional-order creep models mainly combine the three kinds of fractional-order element with traditional element models, which can be divided into three categories: the first category is to replace the Newtonian dashpot in the traditional element model with the fractional-order element to form a fractional-order element model (Bai et al., 2020; Chen and Ai, 2020; Wu et al., 2018; Zhou et al., 2011); the second type is to introduce the fractional-order elements and the fractional-order damage elements based on the traditional element model to form a fractional-order damage element model (Kang et al., 2015; Wang et al., 2020; Zhang et al., 2021; Zhou et al., 2012); and the third kind is to combine traditional elements with fractional variable-order elements to form a variable-order fractional model (Liu et al., 2021; Tang et al., 2018). However, the study of these fractional-order element creep models is based on the results and analysis of rock creep tests under uniaxial and conventional triaxial stress, and it is difficult to describe the creep characteristics of rock under true triaxial stresses.…”

Section: Introductionmentioning

confidence: 99%

A new fractional-order model for time-dependent damage of rock under true triaxial stresses

Zheng

Cai

Guo-sao

et al. 2022

International Journal of Damage Mechanics

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To reasonably describe the time-dependent characteristics of rock under true triaxial stresses and analyze the long-term stability of deep underground engineering, based on the understanding of time-dependent mechanical properties of rock under true triaxial stresses, a new fractional-order damage element and the method in which the crack initiation stress is taken as the starting point of creep and the crack damage stress as the starting point of creep accelerating stage were established. Then, combined with the Mogi-Coulomb strength criterion, a fractional-order creep damage model of rock under true triaxial stresses was proposed. The proposed model was further verified based on uniaxial, conventional triaxial and true triaxial creep test results. The theoretical curves of the model are highly consistent with the test curves, indicating that the proposed model has wide applicability and rationality. Meanwhile the sensitivity of true triaxial stress states and model parameters to the creep characteristics was further investigated. Finally, based on the proposed creep model, the time-dependent characteristics of rock under untested true triaxial stress levels were predicted. The research provides a theoretical basis for the prediction of time-dependent disasters and the long-term stability analysis of surrounding rock in deep engineering.

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“…14,15 Koeller 16 established a new spring-pot element with fractional theory and replaced Newton's dashpot in the classic Kelvin model and classic Maxwell model with the new element. Chen and Ai 17 proposed a fractional Poyting-Thomson model and compared the ability of the integer-order model and fractional derivative model to simulate the creep behaviours of geotechnical materials. The research shows that the fractional derivative model can better simulate soil behaviour than an integer-order model.…”

Section: Introductionmentioning

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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Viscoelastic analysis of transversely isotropic multilayered porous rock foundation by fractional Poyting-Thomson model

Cited by 19 publications

References 34 publications

Fractional viscoelastic models of porcine skin and its gelatin-based surrogates

Fractional viscoelastic models of porcine skin and its gelatin-based surrogates

A new fractional-order model for time-dependent damage of rock under true triaxial stresses

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

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