3-D time-dependent analysis of multilayered cross-anisotropic saturated soils based on the fractional viscoelastic model

Ai, Zhi Yong; Gui, Jun Chao; Mu, Jin Jing

doi:10.1016/j.apm.2019.06.018

Cited by 22 publications

(14 citation statements)

References 37 publications

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“…For the Kelvin model, the stress remains the same when the strain is kept constant, which means that neither the Kelvin model nor the fractional Kelvin model is capable of reflecting the relaxation characteristics. The Merchant model can readily reflect both the creep behaviour and the stress relaxation behaviour and has been widely employed in geotechnical engineering 15 . In the derivation of the fractional derivative Merchant model, Newton's dashpot in the classic Merchant model is replaced by the above spring‐pot element.…”

Section: Fractional Derivative Merchant Rheological Modelmentioning

confidence: 99%

“…Fractional derivative theory is considered to be a powerful mathematical tool for solving the problems of physical mechanics 13 . Compared with the integer derivative model, the fractional model has the advantages of fewer parameters, a simpler expression and more accurate calculation results 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.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Fractional Derivative Merchant Rheological Modelmentioning

confidence: 99%

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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“…According to Equation (29), the CEL model goes through the origin and converges to τ p at infinity. Combining the similar items in the first derivative of Equation (29) gives…”

Section: Mathematical Cel Modelmentioning

confidence: 99%

“…In the past few years, mathematical models have been adopted to study the stress-strain response of soils [23][24][25][26][27][28][29][30][31]. In term of the stress-strain behaviors of cemented soil, a large number of researches have been reported [2,3,5,6,[13][14][15][16][17][18][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Mathematical Models for Stress–Strain Behavior of Nano Magnesia-Cement-Reinforced Seashore Soft Soil

Wang

Zhang

et al. 2020

Mathematics

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The stress–strain behavior of nano magnesia-cement-reinforced seashore soft soil (Nmcs) under different circumstances exhibits various characteristics, e.g., strain-hardening behavior, falling behavior, S-type falling behavior, and strong softening behavior. This study therefore proposes a REP (reinforced exponential and power function)-based mathematical model to simulate the various stress–strain behaviors of Nmcs under varying conditions. Firstly, the mathematical characteristics of different constitutive behaviors of Nmcs are explicitly discussed. Secondly, the conventional mathematical models and their applicability for modeling stress–strain behavior of cemented soil are examined. Based on the mathematical characteristics of different stress–strain curves and the features of different conventional models, a simple mathematical REP model for simulating the hardening behavior, modified falling behavior and strong softening behavior is proposed. Moreover, a CEL (coupled exponential and linear) model improved from the REP model is also put forth for simulating the S-type stress–strain behavior of Nmcs. Comparisons between conventional models and the proposed REP-based models are made which verify the feasibility of the proposed models. The proposed REP-based models may facilitate researchers in the assessment and estimation of stress–strain constitutive behaviors of Nmcs subjected to different scenarios.

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“…Most recently, [28][29][30][31] investigated fractional derivative models for various soils under different states. [32] employs a general and direct method to determine the time-dependent stress-strain behavior of soil using a Prony series method based on test of soil.…”

Section: Introductionmentioning

confidence: 99%

Identification of Viscoelastic Property of Pile-Soil Interactions with Fractional Derivative Model

Zatar

Xiao

Chen

et al. 2020

Journal of Low Frequency Noise, Vibration and Active Control

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The viscoelastic property of pile-soil interactions is modeled by fractional derivative method and is used to characterize the structural dynamics of pile and rheological behavior of a thawing frozen soil. A study of the thawing frozen soil impacts on pile structure’s dynamic characteristic is carried out. The frequency spectrum analysis and empirical modal decomposition are used to identify the pile structure dynamic properties. The rocking mode vibration in which pile behaviors like rigid body supported by viscoelastic soil is extracted to capture the viscoelastic property of pile-soil interactions. The rocking mode exhibiting time-varying frequency features is modeled with fractional derivative model and the fractional derivative order is identified. This study proposes a quick and reliable method to identify the viscoelastic property of pile-soil interactions.

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3-D time-dependent analysis of multilayered cross-anisotropic saturated soils based on the fractional viscoelastic model

Cited by 22 publications

References 37 publications

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

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

Mathematical Models for Stress–Strain Behavior of Nano Magnesia-Cement-Reinforced Seashore Soft Soil

Identification of Viscoelastic Property of Pile-Soil Interactions with Fractional Derivative Model

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