# Numerical Simulation-Based Study on the Arching Effect in Subsequent Backfill
## 3 Numerical Simulation  
In actual mining stops, the particles at the interface between the backfill and the surrounding rock are not perfectly bonded. Slippage, rolling, or detachment of fragmented particles may occur at the boundary between the backfill material and the fractured edges of the surrounding rock, leading to a weakening of the shear interaction between the two materials. If the influence of the rock-fill interface is neglected in numerical simulations, the resulting stress distribution will be biased--underestimating the stress on the backfill while overestimating the stress on the surrounding rock. This can lead to an overestimation of the arching effect's influence on the stop stability. Therefore, before conducting backfill simulations, it is essential to analyze the impact of the rock-fill interface elements on stress distribution in numerical models [36]. The contact surface element in FLAC3D is an important tool for simulating discontinuous mechanical behavior in geotechnical engineering. It is specifically used to handle the interaction between rock masses and structures, or the mechanical responses of internal structural planes of rock masses such as joints and faults. This unit is capable of precisely simulating various complex behaviors of the contact surface, including nonlinear characteristics such as sliding, opening, and closing. The working principle of the contact surface unit is based on the Coulomb friction criterion, taking into account both the normal and tangential mechanical responses simultaneously. In the normal direction, it can simulate the pressure transmission under compression and the possible opening under tension. Users can set the tensile strength limit and the initial gap to simulate the actual situation. The tangential behavior follows the Coulomb friction model, controlling the shear resistance through cohesive force and friction angle. In numerical calculation, the software adopts the master-slave surface method for discretization processing, which can accurately calculate the relative displacement of the contact surface and the change of contact force. These units have extensive application scenarios in engineering practice. For example, when analyzing the interaction between piles and soil, the friction characteristics between the pile body and the surrounding soil can be accurately simulated. When studying tunnel engineering, it can reflect the contact state between the lining structure and the surrounding rock. In slope stability analysis, the sliding behavior of the internal structural planes of the rock mass can be simulated. In addition, when simulating support structures such as anchor rods and soil nails, the interaction between them and rock and soil masses can also be well demonstrated. The key parameters of the contact surface unit include normal stiffness: the stiffness of the contact surface against compression or separation in the normal direction. Shear stiffness: the stiffness of the contact surface against shear deformation in the tangential direction. Contact surface cohesion: the shear strength of the contact surface when it is not sliding. Contact surface friction angle: the internal friction angle when the contact surface \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Material** & **Density \(\rho\)** & **Elastic** & **Poisson’s** & **Internal** & **Cohesion** & **Tension** & **Shear** \\
**Type** & **(kg/m\({}^{3}\))** & **Modulus E** & **Ratio \(\mu\)** & **Ratio \(\mu\)** & **Angle \(\varphi\) (\({}^{\circ}\))** & **c (MPa)** & **(MPa)** & **Modulus** \\ \hline Copper- & & & & & & & \\ bearing Ore & 3970 & 34.35 & 0.253 & 45.07 & 3.69 & 3.06 & 13.71 \\ Body & & & & & & & \\ Cemented & & & & & & & \\ Backfill & 1830 & 0.573 & 0.20 & 35.7 & 0.546 & 0.4 & 0.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical parameters of materials used in numerical simulation tests. slides determines the shear strength after sliding.