Creep constitutive model of logarithmic fractal structure derivative of deep hard brittle rock
ObjectiveIn the field of geotechnical engineering, it has always been a key issue to deeply explore the deformation law of surrounding rock under long-term load and accurately reveal its creep deformation mechanism.MethodsIn order to achieve this goal, in the rigorous derivation of the creep model,...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Editorial Department of Journal of Sichuan University (Engineering Science Edition)
2025-01-01
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| Series: | 工程科学与技术 |
| Subjects: | |
| Online Access: | http://jsuese.scu.edu.cn/thesisDetails#10.12454/j.jsuese.202400928 |
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| Summary: | ObjectiveIn the field of geotechnical engineering, it has always been a key issue to deeply explore the deformation law of surrounding rock under long-term load and accurately reveal its creep deformation mechanism.MethodsIn order to achieve this goal, in the rigorous derivation of the creep model, the mathematical tool of Hausdorff derivative is innovatively introduced. It can skillfully transform the traditional linear Newton's dashpot into a nonlinear dashpot. This transformation is of great significance, because in practical engineering, the deformation characteristics of surrounding rock often show significant nonlinear characteristics, and traditional linear dashpots are difficult to accurately describe. By introducing the Hausdorff derivative, the variable time fractal dimension dashpot considering the logarithmic fractal structure derivative is successfully constructed. The model is further optimized, and the nonlinear dashpot is deeply improved by using the logarithmic fractal structure derivative dashpot with variable time fractal dimension. This optimization method fully considers the dynamic influence of time factor on fractal dimension, so that the dashpot can be more suitable for the actual deformation behavior of surrounding rock under complex time history. On this basis, the improved nonlinear dashpot is connected in series with the improved Nishihara model. The Nishihara model has a certain foundation in describing the creep characteristics of rock, but it has limitations. And the improved nonlinear dashpot can make up for its shortcomings. Through the organic combination of the two, a new logarithmic fractal structure derivative rock creep constitutive model with variable time fractal dimension is obtained.Results and Discussions After a large number of experimental data verification, the model shows excellent performance. The model curve and the test curve show a high degree of agreement. Especially under the action of non-destructive load, the model curve of rock is almost perfectly coincident with the test curve. After calculation, the correlation coefficient is above 0.95, which indicates that the model can accurately simulate the creep behavior of rock under normal working conditions. Under the action of failure load, although the model curve of rock deviates obviously from the test curve in the stage of accelerated creep deformation, on the whole, the coincidence degree is still high, and the correlation coefficient is also maintained at a considerable level. This shows that the model can reflect the deformation trend of rock to a certain extent even under extreme conditions.In order to obtain the clear physical meaning of the introduced parameters, the sensitivity analysis of the parameters is carried out. Under the action of the same time, the greater the parameter αve, the greater the creep deformation value and the rate of decay creep deformation also increases, which may be that α<sub>ve</sub> is closely related to the microstructure and physical process inside the rock. From the microscopic point of view, the larger α<sub>ve</sub> means that some factors inside the rock make it more prone to deformation. Under the action of the same time, the larger the parameter α<sub>vp</sub>, the attenuation creep deformation almost coincides, but the accelerated creep stage appears in advance, reflecting that the rock damage accumulation rate is accelerated, and the nonlinear characteristics of the creep curve are more and more obvious. This phenomenon profoundly reflects the acceleration of rock damage accumulation rate. The advance of the accelerated creep stage means that the damage process inside the rock is carried out faster, and the damage mechanisms such as the expansion and confluence of microcracks and the crushing of mineral particles accelerate under the action of α<sub>vp</sub>.At the same time, it is worth mentioning that the model can describe the whole process of rock creep deformation in a complete and detailed manner, covering various stages such as initial creep, steady-state creep and accelerated creep. In contrast, the traditional Nishihara creep model cannot effectively describe the accelerated creep deformation characteristics, and the new model makes up for this defect well. Moreover, the model shows strong universality in the description of creep deformation law of different types of rocks. Whether it is hard red sandstone, its internal mineral particles are closely arranged, and the deformation is relatively slow and stable under load. Or relatively soft green mud shale, affected by interlayer sliding and mineral composition differences, creep deformation shows complex and changeable characteristics. The model can accurately capture its unique creep characteristics.ConclusionsThrough a large number of experimental fitting of different rock samples, it is found that the model parameters can be reasonably adjusted according to the mineral composition and mechanical properties of the rock. Therefore, it accurately reflect the creep deformation law of various rocks under different load conditions. This feature makes the model can be widely used in the prediction of most rock creep deformation laws. In deep buried tunnel projects, such as deep buried tunnel projects, in the face of complex geological conditions of different rock strata combinations, it can provide accurate surrounding rock deformation prediction data for the design of supporting structures. Based on the comprehensive performance, it can be fully determined that the construction process of the model is scientific and reasonable. It also provides a reliable and powerful tool for the prediction and analysis of surrounding rock deformation in geotechnical engineering. It is expected to be widely used in practical engineering to improve the safety and reliability of engineering design and construction. |
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| ISSN: | 2096-3246 |