## 2 Numerical Simulation with FLAC3D  
### Numerical Model  
Figure 2 shows the numerical model built with FLAC3D (v6.00) of the slope with a basket weave drift layout surrounded by a rock mass. Figure 1(a) illustrates half of the established model prior to excavation. The sizes of the numerical model are set as \(L_{\mathrm{r}}=B_{\mathrm{r}}=H_{\mathrm{r}}=128\) m to minimize boundary effects. The model comprises two regions: the ore rock in the scope and the surrounding rock mass. During subsequent mining and backfilling operations, ore rock in the stope is progressively replaced by the backfill. As shown in Figure 1(b), the stope consists of three layers, labeled L1, L2, and L3 from top to bottom. Among them, L1 and L3 contain five drifts oriented along the \(x\)-axis, while L2 contains seven drifts oriented along the \(y\)-axis. Drifts in adjacent layers are arranged perpendicularly to simulate the basket weave drift layout. All drifts have identical dimensions, with a span of \(W_{\mathrm{d}}\) and a height of \(H_{\mathrm{d}}\). Figure 2: _Cont._  
The numerical model employs cubic mesh elements. Based on comprehensive sensitivity analysis, the mesh size in the stope region is determined to be 0.25 m, while the maximum mesh size in the surrounding rock region is set to 8 m. An octree meshing technique is implemented to ensure a transition between the varying mesh sizes in these regions [18]. The numerical model assumes that both the surrounding rock and backfill are continuous, homogeneous, isotropic elastoplastic materials that obey the Mohr-Coulomb (MC) strength criterion. The MC model has been widely used for modeling backfill material due to its generality and simplicity and shows good agreement with experimental results [12; 19]. Therefore, the MC model is applied to the surrounding rock, while the Mohr-Coulomb tension (MohrT) model is used for the backfill. In FLAC3D, the standard MC model tends to produce excessive dilation in materials experiencing tensile failure due to irreversible tensile plastic strains. The MohrT model, an extension of the MC model, is designed to better simulate tensile failure by treating tensile plastic strains as reversible [18]. Given that tensile failure commonly occurs in the backfill roof, the MohrT model is employed to represent the backfill. Table 1 summarizes the physical and mechanical parameters of the rock mass and backfill used in the numerical model. The cohesion and tensile strength of the backfill are not predefined but are progressively adjusted through an iterative search process to evaluate the strength requirement. Generally, the tensile strength of the backfill is 1/10 of its uniaxial compressive strength (UCS) [20; 21]. According to the MC criterion, the tensile strength of the backfill is determined using the following equation [22; 23]:  
\[\sigma_{t}=\frac{c}{5}tan(45^{\circ}+\frac{\varphi}{2}) \tag{1}\]  
where \(\sigma_{t}\), \(c\), and \(\phi\) represent the tensile strength, cohesion, and friction angle of the backfill, respectively. Figure 2: A numerical model established in FLAC3D of the stope with a basket weave drift layout surrounded by the rock mass: (**a**) the model domain and meshing; (**b**) the basket weave drift layout. The depth \(D\) (m) is measured from the ground surface to the origin (point \(O\) in Figure 2b) of the built model. The modeled slope is located at a depth of around 600 m at the Maoping Lead-Zinc Mine. To set the gravity properly along the negative direction of the \(z\)-axis, a surcharge is applied to the top boundary of the model to simulate the overburden, as the model height is limited compared to the stop depth. For other boundary conditions, no displacement constraints are applied to the top boundary, while the \(x\)-, \(y\)-, and \(z\)-axes displacements are fixed at the bottom boundary of the model. Additionally, normal displacements are restricted while the \(z\)-axis displacements can occur freely at the four lateral boundaries.