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Study on nonlinear creep damage model based on fractional derivative
Guanghe Li1, Hongjun Jia2,3
1College of Mining, Liaoning Technical University, Fuxin, 123000, China. li_7118@126.com.
Scientific Reports
|February 19, 2025
Summary
This study introduces a fractional nonlinear creep damage model to simulate rock behavior under varying water content. The model accurately predicts rock creep characteristics, offering insights for slope stability analysis.
Area of Science:
- Geotechnical Engineering
- Materials Science
- Applied Mathematics
Background:
- Fractional calculus offers advanced methods for mechanical modeling, particularly for materials exhibiting intermediate properties between solids and fluids.
- Understanding rock creep behavior under varying conditions is crucial for geotechnical engineering and slope stability.
- Existing models may not fully capture the complex nonlinear creep and damage processes in rocks.
Purpose of the Study:
- To develop and validate a fractional nonlinear creep damage model for simulating rock creep.
- To investigate the influence of water content on rock creep characteristics using fractional calculus.
- To provide a theoretical basis for the stability analysis and disaster prevention of soft rock slopes.
Main Methods:
- Application of Riemann-Liouville's fractional calculus operator to model viscous and viscoplastic elements.
- Establishment of a series connection of fractional order viscous element, nonlinear viscous element, and viscoplastic body.
- Construction of the constitutive equation for the fractional nonlinear creep damage model.
- Parameter identification using the principle of least squares and validation against experimental data.
Main Results:
- The developed fractional nonlinear creep damage model demonstrated a high correlation ( > 0.98) with experimental data.
- The model effectively simulates the nonlinear gradient process of rock creep under different water content conditions.
- Analysis of model parameters revealed their impact on deformation, enhancing model verification and applicability.
Conclusions:
- The fractional nonlinear creep damage model provides an accurate and effective tool for simulating rock creep behavior.
- The research offers valuable theoretical insights for assessing the stability of soft rock slopes and preventing disasters.
- The model's adaptability to various stress environments enhances its practical utility in geotechnical engineering.
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