The 3D Nonstationary Creep Constitutive Model of Sandstone Based on Fractional Order

Zhang, Shuguang; Liu, Wenbo

doi:10.1155/2019/6031842

Cited by 4 publications

(3 citation statements)

References 18 publications

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“…e basic idea using the fractional calculus theory to establish the creep constitutive model of rocks is described as follows: (1) a nonlinear dashpot (Abel dashpot) is proposed based on the fractional calculus theory and (2) the creep constitutive model of rock can be obtained by replacing the conventional viscous element in existing models with an Abel dashpot or combining the Abel dashpot with other basic elements in different forms [127].…”

Section: Fractional Derivatives Creep Constitutivementioning

confidence: 99%

Creep Properties and Constitutive Model of Salt Rock

Zhang

Song

Wang

et al. 2021

Advances in Civil Engineering

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Due to the advantages of low porosity, low permeability, high ductility, and excellent capacities for creep and damage self-healing, salt rock is internationally considered as the ideal medium for underground storage of energy and disposal of radioactive waste. As one of the most important mechanical properties of salt rock, creep properties are closely related to the long-term operation stability and safety of salt rock underground storage cavern. A comprehensive review on the creep properties and constitutive model of salt rock is put forward in this paper. The opinions and suggestions on the research priority and direction of salt rock's mechanical properties in the future are put forward: (1) permeability variation of salt rock under the coupling effect of temperature and stress; (2) damage mechanism and evolution process under the effect of creep-fatigue interaction and low frequency cyclic loading; (3) microdeformation mechanisms of salt rock and the relationship between microstructure variations and macrocreep behavior during creep process; (4) the establishment of the creep damage constitutive model with simple form, less parameters, easy application, and considering the damage self-healing ability of salt rock simultaneously.

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Section: Fractional Derivatives Creep Constitutivementioning

confidence: 99%

Creep Properties and Constitutive Model of Salt Rock

Zhang

Song

Wang

et al. 2021

Advances in Civil Engineering

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“…Almeida et al systematically introduced the theory of fractional calculus and the calculus of variations, and they presented a new numerical tool for the solution of diferential equations involving Caputo derivatives of fractional variable order [30]. Variable-order fractional derivatives have powerful properties for building nonlinear constitutive models and are thus widely used in various felds of natural science and engineering applications [31][32][33][34], such as biome analysis [35], mathematical modelling [36], infectious disease transmission [37], medical image denoising [38], and tumor growth analysis [39]. Yet, no studies have established the pressure-sinkage model of deep-sea sediments based on the variable-order fractional diferential theory.…”

Section: Introductionmentioning

confidence: 99%

A Pressure‐Sinkage Model for Deep‐Sea Sediments Based on Variable‐Order Fractional Derivatives

Wei

Cao

Xia

2023

Mathematical Problems in Engineering

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In order to better describe the pressure-sinkage process of deep-sea surface sediments, this article proposes a new four-element model. First, the pressure-sinkage process was divided into four components according to the change in the deep-sea sediment sinkage rate, and the time-dependent mechanical property of deep-sea sediments was described. Then, a new four-element pressure-sinkage model was established by introducing variable-order fractional derivatives into the modelling idea of classic element combination to describe the full pressure-sinkage regions of deep-sea sediments. Furthermore, by comparing with the experimental results from other literature, the proposed model was verified to predict the pressure-sinkage process of deep-sea sediments under static and dynamic loads. Finally, through a sensitivity analysis of model parameters, the effects of ground pressure and time on the law and mechanism of deep-sea sediment pressure sinkage were revealed. Results indicate that the deep-sea sediment pressure-sinkage process has obvious nonlinear characteristics and that the sinkage depth increases directly with ground-specific pressure and time. Through comparative analysis of both experimental and predicted results, the proposed pressure-sinkage constitutive model can describe the stress-strain of the full stages. Thus, the variable order model represents an effective method to predict the pressure-sinkage process of deep-sea sediments.

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“…Zhu et al [27] proposed a new nonlinear creep constitutive model by introducing a damage variable into the viscoplastic element to accurately describe the whole creep process for frozen sand with different dry densities and grain size distributions under different shear stress levels and temperatures. Analogously, to capture the deformation behavior of various geotechnical materials under different mechanical states, authors [28][29][30][31][32][33] constructed a series of significant constitutive models suitable for describing the accumulative deformation of geotechnical materials under static loading. However, element models used to depict the deformation characteristics of geotechnical materials under dynamic loads are comparatively few, though there are some research results in the literature.…”

Section: Introductionmentioning

confidence: 99%

A Variable-Order Dynamic Constitutive Model for Clay Based on the Fractional Calculus

Zhang

Chen

et al. 2022

Applied Sciences

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To accurately describe the deformation characteristics of clay under long-term cyclic load, based on fractional calculus theory, elastoplastic theory and the basic element model, a variable-order fractional dynamic model designed to predict accumulative strain of clay was exhibited. Firstly, the cyclic load was separated into static and alternating load in accordance with cyclic load characteristics, and the strain of clay under static and alternating load was analyzed. Then, on the basis of the variable-order Abel dashpot model, rheological theory and elastoplastic theory, the expressions of the rheological constitutive model and strain response were both obtained. Finally, in combination with the undrained dynamic triaxial testing of Zhan Jiang clay and Tian Jin soft clay, a series of analyses was carried out on the effectiveness and parameter sensitivity of the model when subjected to long-term cyclic loading. By comparing the dynamic constitutive model with pre-existing models, the superiority of the dynamic constitutive model is revealed. The results show that the dynamic constitutive model can characterize properly the deformation characteristics of clay under the action of long-term cyclic loading, especially in its accelerating stage. The parameter sensitivity of the model exhibits a growing trend with the increment of loading duration.

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The 3D Nonstationary Creep Constitutive Model of Sandstone Based on Fractional Order

Cited by 4 publications

References 18 publications

Creep Properties and Constitutive Model of Salt Rock

Creep Properties and Constitutive Model of Salt Rock

A Pressure‐Sinkage Model for Deep‐Sea Sediments Based on Variable‐Order Fractional Derivatives

A Variable-Order Dynamic Constitutive Model for Clay Based on the Fractional Calculus

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