Fractional Order Analysis of Creep Characteristics of Sandstone with Multiscale Damage
Abstract
1. Introduction
2. Mathematical Modeling
2.1. Definition of Fractional Derivative
2.2. Multiscale Damage Mechanics
2.3. Fractional Multiscale Damage Creep Model
2.3.1. Multiscale Damage Viscoelastic Body
2.3.2. Multiscale Damage Viscoplastic Body
3. Results and Discussion
3.1. Model Validation
3.2. Parameter Sensitivity Analysis
4. Conclusions
- (1)
- By introducing fractional calculus and multiscale damage theory, the Nishihara model is improved by replacing the Newtonian dashpot with an Abel dashpot, thereby establishing a fractional-order multiscale damage creep model. Compared with the traditional integer-order multiscale damage model, the proposed model demonstrates better fitting performance, especially in capturing the accelerated creep stage. This advantage is mainly attributed to the higher fitting degrees of freedom of the fractional-order model and its realistic characterization of time dependence. The results confirmed the effectiveness and broad applicability of the proposed model in describing the multiscale damage creep behavior of rock masses, providing theoretical support for its practical engineering applications.
- (2)
- The creep data were fitted using the least squares method to determine the model parameters, which were then compared with the integer-order damage creep model. The results showed that the established fractional-order damage creep model can more accurately reflect the complete creep process. The fractional-order has more advantages than the integer-order in terms of fitting degrees of freedom, and the fractional-order damage viscoplastic elements can better describe the accelerated creep stage.
- (3)
- Through a sensitivity analysis of the model parameters, the specific effects of each parameter on the creep behavior of the rock mass during different stages of the creep process, including the decelerated, steady-state, and accelerated stages, were thoroughly examined. This analysis not only revealed the sensitivity of the model outputs to variations in each parameter but also helped to clarify the mechanisms by which these parameters regulate the creep response.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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DT | γ | α | Ee/GPa | Eve/GPa | ηve/GPa.h | ηvp/GPa.h | β | R2 |
---|---|---|---|---|---|---|---|---|
0.227 | 0.79 | 0.1002 | 7.33 | 46.73 | 62.41 | 875.87 | 0.6165 | 0.9976 |
1 | 0.0504 | 7.30 | 40.76 | 77.56 | 977.97 | 0.5922 | 0.9897 | |
0.383 | 0.82 | 0.0923 | 7.82 | 75.06 | 62.02 | 440.65 | 0.6222 | 0.9971 |
1 | 0.1002 | 7.75 | 73.19 | 81.34 | 416.05 | 0.4201 | 0.9863 | |
0.505 | 0.57 | 0.0101 | 8.23 | 177.32 | 541.75 | 8888.91 | 0.3686 | 0.9910 |
1 | 0.0082 | 8.25 | 244.13 | 570.72 | 6474.22 | 0.3002 | 0.9580 |
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Yang, S.; Zhou, W.; Xie, S.; Lei, B.; Song, H. Fractional Order Analysis of Creep Characteristics of Sandstone with Multiscale Damage. Mathematics 2025, 13, 2551. https://doi.org/10.3390/math13162551
Yang S, Zhou W, Xie S, Lei B, Song H. Fractional Order Analysis of Creep Characteristics of Sandstone with Multiscale Damage. Mathematics. 2025; 13(16):2551. https://doi.org/10.3390/math13162551
Chicago/Turabian StyleYang, Shuai, Wentao Zhou, Senlin Xie, Bo Lei, and Hongchen Song. 2025. "Fractional Order Analysis of Creep Characteristics of Sandstone with Multiscale Damage" Mathematics 13, no. 16: 2551. https://doi.org/10.3390/math13162551
APA StyleYang, S., Zhou, W., Xie, S., Lei, B., & Song, H. (2025). Fractional Order Analysis of Creep Characteristics of Sandstone with Multiscale Damage. Mathematics, 13(16), 2551. https://doi.org/10.3390/math13162551