Characterizing three-dimensional creep of Beishan granite by the variable-coefficient Abel dashpot

Zhou, Hongwei; Su, Teng; Deng, Huilin; Wang, Rui; Zhao, Jiawei; Sun, Xiaoming; Liu, An

doi:10.1007/s11043-019-09428-x

Cited by 14 publications

(5 citation statements)

References 30 publications

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“…Recently, Okuka and Zorica 63 examined the thermodynamically consistent fractional models. Moreover, the previous studies indicate that the viscosity coefficient versus time obeys the attenuation law of the negative exponent 64 . Consequently, the damage variable is incorporated here into the fractional element to reflect the damaging effect on stress relaxation as follows, where ξ 0 denotes the initial viscosity coefficient during the relaxation process.…”

Section: Formulation Of Analytical Modelmentioning

confidence: 84%

A nonlinear fractional-order damage model of stress relaxation of net-like red soil

Wang

Liu

et al. 2021

Sci Rep

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It is essential to precisely describe the nonlinear characteristics of the stress relaxation behavior to ensure the long-term stability of geotechnical structures in the net-like red soil. A novel damage model of variable fractional-order was discussed here to accurately analyze the progress of stress relaxation for the net-like red soil. Moreover, unsaturated triaxial experiments on stress relaxation under a step-loading mode were performed to identify model parameters and investigate the nonlinear relaxation characteristics of the net-like red soil. The feasibility and validity of the proposed model were furthermore verified by comparisons with the experimental results and fitting curves obtained from the Nishihara model and the generalized Kelvin model. Results show that the analytical result by the proposed model is consistent with the measured data, and the proposed model can better depict the nonlinear characteristics of stress relaxation relative to other analytical models. It can better exhibit the relaxation evolution of soil compared with the conventional models.

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Section: Formulation Of Analytical Modelmentioning

confidence: 84%

A nonlinear fractional-order damage model of stress relaxation of net-like red soil

Wang

Liu

et al. 2021

Sci Rep

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“…Thus, it can be concluded that for accurate parameter determination and behavior characterization, the initial data should be taken into consideration, and the modified model should be used. If the model is of high complexity due to connecting many components using the Boltzmann superposition, such as the models in recent researches [7, 18, 20], the initial models can be used by fitting experimental curves discarding the initial ramp when the time ratio n is large.…”

Section: Discussionmentioning

confidence: 99%

“…Based on salt rock experimental observations, Zhou et al [14] proposed a new SB element considering an exponentially time-varying viscosity. Using the Boltzmann superposition, the exponential time-varying viscosity SB model (TVSM) has been applied to modeling various materials [15, 17–20]. The TVSM was able to describe the crack evolution during the creep of composites reported by Zhou et al [17].…”

Section: Introductionmentioning

confidence: 99%

Fractional derivative modeling of time-varying viscosity materials considering initial loading ramp in real experiments

Zhou

Zhao

et al. 2021

Mathematics and Mechanics of Solids

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The fractional derivative models with time-varying viscosity have been used in characterizing creep or relaxation properties of different viscoelastic material, and many combination models were presented using the Boltzmann superposition principle. However, those models defined as initial ones in this manuscript usually ignored the initial loading ramp, and the ideal-loading condition is commonly assumed as a step function in modeling. The real-loading conditions of tested samples are usually a ramp load followed by constant stress or strain. The difference in loading conditions between the theoretical modeling and experimental procedure strongly influences the models’ rheological property characterization and parameter determination. It is especially the case for the fractional derivative model due to its memory or history-dependent characters, even though the ramp time is short compared with the total experimental time. An application example of the Maxwell model with time-varying viscosity Scott–Blair model (TVSM) shows that the initial loading ramp has a strong influence. To solve this problem, the authors propose modified models of TVSM based on real-loading conditions. The relative errors between initial and modified models are presented. In addition, a history-dependent optimization algorithm for parameter determination is proposed. Three sets of polymer experimental data are employed to suggest that the fitting results of models disregarding initial ramp loads are unreliable. The modified model should be used for characterizing rheological behavior, as this leads to obtaining the best fitting results even for a short experimental time.

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“…All rocks display rheological features, which are emphasized to a larger degree in the case of soft rocks with high porosity rather than high strength rocks [1]. Various rock types have different creep predispositions [2].…”

Section: Introductionmentioning

confidence: 98%

Viscoelastic Strains of Palaeozoic Shales under the Burger’s Model Description

Wilczynski,

Cieslik,

Domonik

et al. 2023

Applied Sciences

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This article presents the results of creep studies of Palaeozoic shales from the Baltic Basin in which the exploitation of shale gas in Poland was planned. Knowledge of instantaneous and long-term properties investigated in triaxial stress conditions is important from the point of view of exploitation techniques related to hydraulic fracturing. Rheological phenomena also play an important role in the analysis of the initial stress in shales, the knowledge of which is indispensable in the hydraulic fracturing process. The tests were carried out on samples representing four siltstone–claystone lithostratigraphic units occurring in the Baltic Basin. The studies and analyses were aimed at determining the character of creep in shales, selection of the appropriate rheological model for the analyzed rocks, and determination of the threshold of the linear creep under triaxial compression conditions. An original approach together with analysis results are presented here, which enable the separation and monitoring of shear and volume creep effects, and on this basis, the determination of the significance of the contribution of volume creep in the entire creep process. A relatively simple methodology for determination of the parameters of the Burgers model using this division is presented. The original value of the article is also due to the test results themselves and the parameter values of the analyzed model for triaxial creep of shales, which are not numerous in the literature. The investigations were performed at various loading levels in relation to the triaxial strength of the shales. Depending on the load, at its low values up to 0.7 (σ1 − σ3)max, creep had a determined character and did not show features of progressive creep. The linear creep threshold was also analyzed in this range. The loading level of 0.7 (σ1 − σ3)max was the limit of linear creep. Exceeding this load resulted in the loss of the linear character of creep, which in consequence lead to the subsequent third creep phase ending with rock damage. Parameters of the Burger’s model for gas shales from the Baltic Basin (northern Poland) were identified. There are significant differences in the behavior of shales depending on the lithostratigraphic unit from which the samples were collected. The mineral composition of the shales also influenced their behavior.

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Characterizing three-dimensional creep of Beishan granite by the variable-coefficient Abel dashpot

Cited by 14 publications

References 30 publications

A nonlinear fractional-order damage model of stress relaxation of net-like red soil

A nonlinear fractional-order damage model of stress relaxation of net-like red soil

Fractional derivative modeling of time-varying viscosity materials considering initial loading ramp in real experiments

Viscoelastic Strains of Palaeozoic Shales under the Burger’s Model Description

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