Phosphorus diffusion model in surrounding rock from phosphogypsum-based cemented paste backfill under multifactor coupling effect

Abstract Phosphogypsum (PG) is filled in the solidified filling body formed in the goaf of underground mines, and its leaching of toxic and harmful ions infiltrates and spreads to the groundwater in the surrounding rock, and there is a potential risk of environmental pollution. In order to grasp the diffusion law of pollutant ions in surrounding rock from phosphogypsum-based cemented paste backfill (PCPB), the diffusion coefficient equation of P ions in surrounding rock was established based on the electrolyte solution theory, taking phosphorus (P) ions leached from PCPB as the research object. Adopting Fick’s second law, the diffusion model of P ions in the surrounding rock from PCPB under multi-factor coupling was established by comprehensively considering the effects of multiple factors such as P ion binding capacity in the surrounding rock, time dependence of P ions diffusion coefficients, structural defects of the surrounding rock, stress level, temperature, and so on, and the effects of different factors on the diffusion of P ions in the surrounding rock were analysed. The results show that the larger the concentration of P ions in the surrounding rock, the larger the diffusion coefficient is. The larger the diffusion distance is, the smaller the concentration of P ions in the surrounding rock is. P ions binding capacity and time are negatively correlated with the diffusion coefficient, and the coefficient of deterioration effect of the surrounding rock, the coefficient of stress influence and temperature are positively correlated with the diffusion coefficient. Temperature is the most significant factor affecting the diffusion coefficient of P ions, and after a temperature of 40 °C, the diffusion coefficient of P ions increases rapidly.