## 4 Discrete Element Modelling  
Numerical modelling of the behaviour of the rock slope was carried out using discrete element method (DEM), for two purposes, the first one was to perform analysis to influence of joint spacing on rock slope failure induced by mining, and to determine a representative joint spacing for informing the model design of the reduced-scale rock slope models. The second purpose was to back-analyse the physical model tests to improve the understanding of the rock mass deformation and failure characteristics upon mining. In this paper, the DEM software, Three-dimensional Distinct Element Code (3 DEC) [33], was adopted in all numerical simulations. 3 DEC can simulate the mechanical behaviour of a discountinuum material, such as a jointed rock mass. The material is represented as a collection of three-dimensional blocks. The discontinuities which bound the blocks are treated as boundary conditions, large displacements are permitted along the boundary [34]. 3 DEC simulated mining by the \"null\" blocks. Using numerical modelling method to study the rock slope behaviour overcame the difficulties encountered in the physical tests, whereby once large deformation of rock mass occurs, any sensor installed within the slope mass would be displaced or even destroyed. Through numerical back-analysis, it is possible to determine the stress and strain induced in each individual block and hence to investigate the stress transfer mechanisms upon mining-induced unloading, providing new insights into the deformation and failure mechanisms of the rock slope. With regard to the first objective, analysis to the influence of joint spacing on rock slope failure induced by mining was conducted to determine a critical joint spacing (\(l_{\sigma}\)), which would \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Cohesion (MPa)** & **Friction Angle (\({}^{\circ}\))** & **Tensile Strength (MPa)** \\ \hline Joint strength of model slope & 0.164 & 20.45 & 0.00698 \\ \hline Joint strength of field rock & 33 & 21 & 1.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Mechanical properties of rock joint strength (model scale). Figure 6: Illustration of the mining process. be practical for modelling in the model container, while not compromising the deformation and failure characteristics of the mine in prototype scale. Eleven rock slope models that have the same geometry to the physical models were created in the software (Figure 7). The dimension of the numerical model is also with a length of 2.3 m, width of 1.5 m and height of 2.0 m, the numerical model is composed of 8747 elements and 10373 nodes. In all the analyses, the constitutive model used is Mohr-Coulomb failure criterion model. The rigid stress-strain constitutive criterion is applied to the materials. A range of joint spacing between 5 cm and 10 cm (0.5 cm interval) was examined to investigate its effects on discrete element modelling (DEM) analyses were conducted to determine a representative joint spacing used for physical model tests. In this analysis, different numerical slope models having different joint spacings were constructed in the DEM software, 3 DEC, for predicting the slope corresponding strata and surface movements when having different values of joint spacing. The input parameters of rock mass and rock joints are summarised in Tables 4 and 6, respectively. The horizontal direction (X) of the eastern and western boundaries, as well as the horizontal direction (Y) of the southern and northern boundaries of the model slopes were all fixed boundaries. On the other hand, the bottom boundary was also set fixed in the vertical direction (Z). No mechanical constraints were applied to the surface of the model (i.e., free to deform). In each analysis, the slope was subjected to the identical mining methods and procedures as in the physical model tests. Four blocks having the same size of the sandbag were set void sequentially (following Figure 6), to simulate the process of sand removal and hence unloading.