# Numerical Simulation-Based Study on the Arching Effect in Subsequent Backfill
## 2 Research Methods
### Determination of Rock Mass Mechanical Parameters  
The engineering weakening treatment of rock mass strength parameters is a critical step in enhancing the reliability and computational accuracy of rock engineering analyses. In engineering practice, the use of modified strength indices as computational parameters has become a common approach [27; 28; 29; 30]. This parameter modification method not only represents an important research direction in rock mechanics but has also been widely applied in practical engineering. Particularly in cases where in situ testing is difficult to implement, the combination of laboratory rock testing and parameter modification has demonstrated significant engineering value. The [PERSON] method is a reduction method for rock mass strength parameters based on the statistical characteristics of joints and fissures, and it is particularly suitable for the weakening calculation of cohesion (c). This method was proposed by [PERSON] in the 1990s and is mainly used to solve the problem of determining the strength parameters of rock masses with well-developed joints (such as the surrounding rocks of mines and tunnels with dense fractures) [31]. This study adopts an innovative composite modification method, integrating empirical estimation [32] with the [PERSON] method, to perform weakening treatment on rock mechanical parameters. First, based on extensive expertise from domestic and international specialists, we systematically modified key parameters, including the internal friction angle, elastic modulus (E), and tensile strength. Second, considering the unique characteristics of joint and fracture development in the Dongguashan Copper Mine, we specifically applied the [PERSON]. [PERSON] method to modify the rock mass cohesion:  
(1) Modification Method for Internal Friction Angle  
The internal friction angle of rock mass exhibits a significant correlation with the intrinsic friction angle of intact rock [33], with typical engineering reduction factors ranging from 0.80 to 0.90. Considering the specific geological conditions of the mine--including the development of structural planes under high in situ stress at depth, the widespread distribution of alteration zones affecting frictional properties, and engineering-induced secondary fracture propagation--a comprehensive analysis integrating numerical simulation and expert judgment was conducted. The study systematically evaluated the reduction factor  
Figure 3: Numerical simulation schematic of subsequent backfilled stope. through numerical modeling and empirical expertise. Simulation results demonstrated that high in situ stress conditions and alteration zones substantially diminish the effective internal friction angle of the rock mass. Furthermore, engineering disturbances, leading to secondary fracturing, exacerbate the degradation of mechanical properties. The deformation characteristics of rock masses are primarily governed by two key parameters: the elastic modulus (E) and the Poisson's ratio [34]. In this investigation, the Poisson's ratio was maintained at its original laboratory-determined value to preserve the fundamental deformation behavior of the intact rock. However, the elastic modulus required significant modification to account for the field-scale geological conditions. This adjustment was systematically determined through a multi-factor analysis incorporating both empirical relationships and theoretical frameworks. The modification process considered two critical geological indicators: a structural plane connectivity exceeding 65% and a rock quality designation (RQD) of approximately 55%. These parameters reflect substantial structural discontinuity development and moderate rock mass integrity, respectively. Through rigorous numerical modeling that coupled the Hoek-Brown failure criterion with established empirical relationships, we derived an elastic modulus reduction factor of 0.33.