Multifractal analysis of thermal infrared of siltstone under uniaxial compression

Abstract

Engineering practices indicate that in geological engineering, rocks can be in a uniaxial loading state. Siltstone specimens were subjected to uniaxial compression with concurrent infrared thermal image monitoring. Multifractal theory was applied, utilizing the multifractal spectrum and its parameters as quantitative indices for characterizing the infrared field's evolution during failure. On this basis, the multifractal spectrum curvature coefficient was defined to describe the infrared field characteristics. Finally, the evolution relationship between the curvature coefficient and load was investigated, advancing from qualitative to quantitative assessment. The results show that: The multifractal spectrum of infrared thermal image of siltstone has left hook shape and bell shape. The evolution process of multifractal spectrum is closely related to the loading process of siltstone, the pre-peak stage is left hook-shaped, the post-peak stage evolves from left hook-shaped to bell-shaped, and when it fracture, it mutates into left hook-shaped. The evolution trends of multifractal parameters $\Delta \alpha$ and $\Delta f\left(\alpha \right)$ are similar, they change steadily in the pre-peak stage, increase continuously in the post-peak stage, and suddenly drop to the initial level when fracture occurs. The curvature coefficient of the multifractal spectrum exhibits a slow decrease before the peak, followed by a rapid decrease to a range of 2 to 4 after the peak, and a sudden increase to its initial level upon fracture, with an initial value of approximately 7.5. Through qualitative and quantitative analysis of the correlation between the curvature coefficient and load at the same moment, it was found that during the pre-peak stage, the correlation is predominantly negative, with the area of the negatively correlated envelope being 4.9 times larger than that of the positively correlated envelope. In the post-peak stage, the correlation is predominantly positive, with the area of the positively correlated envelope being 11.7 times larger than the negatively correlated area. This demonstrates that the curvature coefficient can effectively characterize the evolution of load during the loading process of siltstone. The research results provide a new method for the quantitative analysis of thermal infrared fields during the rock failure process, offering new insights for the early warning of engineering rock mass catastrophes.