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.