## 4 Conclusions  
This study employed an integrated approach combining physical experiments and numerical simulations to investigate the dissolution mechanisms of carbonate rocks with varying fracture apertures under phosphogypsum leachate exposure across different pH levels. Key findings are summarized as follows:  
1. It is known from physical experiments that phosphogypsum leachate-carbonate rock interactions exhibit rapid initial dissolution followed by progressive stabilization. In this study, lower leachate pH correlated with accelerated dissolution rates, a phenomenon directly evidenced by microscale morphological alterations on carbonate rock surfaces. EDS analysis confirmed that dissolution-induced secondary minerals accumulate extensively on rock specimen surfaces. Fracture aperture minimally affects static dissolution patterns but critically influences dynamic systems--smaller apertures exhibit limited enlargement and delayed pH stabilization with higher final pH. 2. Comparative analysis of different physical experiments shows that the hydrodynamic conditions dramatically intensify dissolution. Dynamic systems exhibit 10-15 times greater dissolution amount per unit area than static conditions. Notably, the evolution trends of key geochemical parameters (pH, Ca\({}^{2+}\), SO\({}_{4}\)\({}^{2-}\), F\({}^{-}\), and total P concentrations) displayed opposing patterns between dynamic and static systems. Static dissolution experiments revealed a linear positive correlation between chemical dissolution rates of carbonate rocks and solution conductivity. Concurrently, phosphogypsum leachate pH demonstrated an exponential negative correlation with rock dissolution amount per unit area, while exhibiting a power-law negative correlation with chemical dissolution rates. 3. Numerical simulation results demonstrated that preferential flow through fracture channels led to higher reactant concentrations near fractures due to incomplete reactions, whereas lower concentrations occurred in sub-fracture regions. As the fracture aperture increased, the concentration disparity between these regions became more pronounced, with higher concentration of reactants at the outlet. This study innovatively combines physical experimentation with numerical simulations to analyze and characterize the transport and transformation mechanisms of phosphogypsum leachate within rock fractures, employing more practical conditions for the reaction of phosphogypsum leachate with carbonate rock. This study provides novel insights into the geochemical interaction mechanisms of acidic fluids within geological matrices, providing a theoretical basis for the research of other acidic aqueous solutions. The findings offer critical guidelines for sustainable phosphogypsum management strategies and provide technical guidance for optimizing site selection and safety protocols in tailings disposal engineering, particularly in karst terrain with active dissolution processes. This study acknowledges limitations in physical experimentation and numerical modeling:  
1. The experimental analysis focused exclusively on limestone, excluding other carbonate variants (e.g., dolomite, magnesite). Future investigations should incorporate diverse carbonate lithologies with varying mineralogical compositions to comprehensively characterize dissolution mechanisms. 2. The numerical model simplified environmental variables, omitting temperature gradients, CO\({}_{2}\) partial pressure, and chemo-hydro-mechanical couplings. Enhanced simulations integrating these multi-physics interactions are required to improve predictive accuracy. **Author Contributions:** W.Y. : Software, Experiment, Formal Analysis, Writing-Original Draft. G.D.: Conceptualization Methodology, Validation. C.Z. : Formal Analysis, Writing--Review & Editing. M.J.: Software, Experiment. Z.C. : Conceptualization, Validation, Writing-Original Draft, Writing--Review & Editing, Visualization. All authors have read and agreed to the published version of the manuscript.