# Numerical Simulation-Based Study on the Arching Effect in Subsequent Backfill
## 1 Introduction  
Backfill mining [1, 2, 3] has obvious advantages over other methods. It can effectively improve the ground pressure conditions in the stope, increase the ore recovery rate, and reduce the ore dilution rate. Furthermore, this mining method realizes the resource utilization of tailings, thereby reducing the land area required for tailings storage and alleviating environmental pollution [4, 5, 6, 7]. In recent years, due to innovative measures such as process separation, backfilling optimization and centralized resource management, the subsequent backfilling mining method has outperformed the traditional backfilling method in terms of operational efficiency, economy, safety, and environmental protection performance. During the subsequent filling mining process, when the filling body material settles under its own weight, it will have complex interactions with the surrounding rock [8, 9, 10, 11]. This interaction will lead to a redistribution of stress, with a portion of the vertical stress transferring to the surrounding rock interfaces, thereby altering the stress distribution pattern of the filler. Therefore, accurately assessing these stress conditions is crucial forthe strength design of fillers, the determination of the retaining wall thickness, and the resolution of related engineering problems [12; 13; 14; 15]. The arch effect is very crucial in the stress distribution of the filling body, which was reflected in previous studies [2; 16; 17; 18]. The analytical solution method can quickly predict the stress distribution inside the backfill material by establishing an accurate mathematical model, and it provides a reliable theoretical basis for the design of strength parameters and stability assessment. The academic community has developed various arch effect stress models, but their applicability and accuracy vary greatly due to differences in basic assumptions, boundary conditions, and parameter selection. In the 21 st century, [PERSON]'s research team developed a more comprehensive mechanical model of filling by incorporating three-dimensional constraint effects and interfacial friction characteristics. These innovations, including the time-varying stress evolution equation and the interface slip correction factor, greatly enhanced the applicability of the theoretical model in engineering. However, due to the increasingly complex geometric shapes of ore bodies, theoretical models are difficult to accurately analyze the stress of on-site engineering, and numerical simulation technology is playing an increasingly crucial role. Among them, the finite element method is applicable to the continuum analysis of the stress-strain evolution of the filling body. This method not only compensates for the limitations of the analysis methods, but also can simulate more realistic and complex operational scenarios. The current strength design of the filling body is often overly conservative due to ignoring the arching effect. In recent years, many scholars have conducted in-depth studies on the arching effect: In the study by [PERSON] [19], theoretical analysis was carried out on the force characteristics of the filling body in the inclined mining area. By considering the difference in the inclination angle of the upper and lower plates and the friction effect at the interface between the surrounding rock and the filling body, an improved analytical model of vertical stress was established. The research results show that the deflection degree of the principal stress direction will significantly affect the stress distribution in the filling body, and this deflection effect presents nonlinear characteristics with the change of stope height. Among the geometric parameters of the stope, the increase of the upper plate inclination angle will weaken the principal stress deflection, thereby reducing the arching effect. The influence of the interfacial friction angle on the arching effect is much greater than that of the cohesion of the filling body.