Cross-Scale Study on Lime Modified Phosphogypsum Cemented Backfill by Fractal Theory

Abstract

Pore structure is a critical factor affecting the strength characteristics of mine backfill materials. In this paper, based on the mechanical tests on lime modified phosphogypsum cemented backfill (LMPGCB), the microstructure of the LMPGCB sample was characterized by nuclear magnetic resonance (NMR) and scanning electron microscopy (SEM) imaging. Based on the fractal theory (FT), the values expressing the fractal characteristics of the NMR T2 spectrum and SEM images were determined. The mathematical model between the NMR-FT fractal dimension and the SEM-FT box dimension was developed to infer the overall pore characteristics from various pore characteristics. The functional relationships between the strength and pore content and dimension were established, and the effects of pore structure on the strength were discussed. The results indicate that: (1) in NMR-FT fractal dimension, the fractal effect of various types of pores is better. The fractal dimension of the small pore is between 0.86–1.38, in which the overall trend first decreases and then increases. (2) In the SEM-FT box dimension, the fractal effect of the overall pore is better. The overall trend of box dimension decreased first and then increased at each kind of magnification. Furthermore, with the increase of magnification, the box dimension decreases. (3) There is a linear direct proportional relationship between the SEM-FT box dimension and the fractal dimensions of NMR-FT of small pores. The relationship between SEM-FT box dimension and NMR-FT fractal dimensions of various types of pores conforms to the plane relationship. There is a linearly increasing relationship between dimension and pore content and a decreasing relationship between dimension and strength.

Study of the Macro and Micro Characteristics of and Their Relationships in Cemented Backfill Based on SEM

“…NMR was mainly used to test the pore size distribution and content of the samples [ 9 ]. Figure 4 shows the NMR characteristics of the pores of the backfill material sample (taking Group B as an example), and Figure 5 shows the contents of the various pores in all groups of samples.…”

“…Figure 4 shows the NMR characteristics of the pores of the backfill material sample (taking Group B as an example), and Figure 5 shows the contents of the various pores in all groups of samples. According to existing research [ 9 ], T 2 is used to characterize the pore size (the larger the T 2 , the larger the pore size). From Figure 4 , it can be seen that pores can be divided into two types: namely, small pores and big pores.…”

“…Jianhua Hu et al used SEM to magnify the pore structures in backfill by 500 times for observation, and used binaryzation processing so as to qualitatively analyze the pore distribution in the backfill [ 7 ]. In order to further study SEM images, some scholars have proposed fractal theory—as such, box dimensions can be used for the quantitative analysis of SEM images [ 7 , 9 , 10 ]. Fengwen Zhao et al used box dimensions to process SEM images of backfill materials to analyze their pore characteristics [ 9 ].…”

“…In order to further study SEM images, some scholars have proposed fractal theory—as such, box dimensions can be used for the quantitative analysis of SEM images [ 7 , 9 , 10 ]. Fengwen Zhao et al used box dimensions to process SEM images of backfill materials to analyze their pore characteristics [ 9 ].…”

Study on the detection of apple soluble solids based on fractal theory and hyperspectral imaging technology

“…The fractal theory is a science that studies a kind of irregular, chaotic and complex system with local and global similarities (Zhao et al, 2022). Fractal dimension is a basic measure used to describe the irregularity and self-similarity of objects in fractal theory (Acquisgrana et al, 2022;Han et al, 2022).…”