## 3 Physical Model Tests
### Modelling of Rock Joints  
In reality, a rock mass has a complex rock joint system. However, it is often impractical to consider and model all the joint systems in a reduced-scaled physical model. In this study, only the joints that have frequent occurrences and that would potentially affect the structure, strength and deformation of rock mass were considered when constructing a physical model. Before construction, the predominant joints in a prototype rock mass were classified into several sets based on the frequency of their occurrences. Each set of joint surfaces was simulated using parallel planes, whereas the block geometry for the model construction was determined according to the mutual intersection of the actual predominant joints. For the case of the Yanqianshan iron mine, the rock joints were simplified into three predominant sets, of which any two sets would be orthogonal to each other (Figure 5). Hence, three idealised sets of predominant joints were created in the model at 90\({}^{\circ}\)/10\({}^{\circ}\), 0\({}^{\circ}\)/90\({}^{\circ}\) and 270\({}^{\circ}\)/80\({}^{\circ}\) \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Density** & **Uniaxial Compressive** & **Deformation** & **Cohesion** & **Friction Angle** \\
**(g/cm\({}^{3}\))** & **Strength (MPa)** & **Modulus (MPa)** & **(MPa)** & **(\({}^{\circ}\))** \\ \hline
2.56 & 0.80 & 200.61 & 0.1735 & 38.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mechanical properties of the model rock mass. Figure 4: The side view and the completed model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Similarity Relationship** & **Similarity Ratio** \\ \hline Geometry (\(\mathrm{C_{L}}\)) & — & 200 \\ Bulk Density (\(\mathrm{C_{r}}\)) & — & 1 \\ Stress (\(\mathrm{C_{\epsilon}}\)) & — & 1 \\ Poisson’s Ratio (\(\mathrm{C_{\mu}}\)) & — & 1 \\ Friction Angle (\(\mathrm{C_{\varphi}}\)) & — & 1 \\ Strain (\(\mathrm{C_{\sigma}}\)) & \(\mathrm{C_{\sigma}=C_{r}\times C_{L}}\) & 200 \\ Elastic Modulus & \(\mathrm{C_{E}=C_{\epsilon}^{\alpha}}\) & 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Similarity relationships of the main controlling parameters of the physical model. Each block was cubic. The contact surface between blocks was the joint surface, while the side length of each cubic block was the joint spacing. According to the similarity relationships and geometric similarity ratio shown in Table 2, the joint spacing of the prototype was divided by the geometric ratio to get the appropriate joint spacing required in the test. For the case of the Yanqianshan iron mine, the average joint spacing in the prototype is about 30-40 cm. Using the scaling factor of 200, the model joint spacing would be only 1.5-2 mm. When using cubic blocks with a length of 1.5-2 mm to construct a model with a total length of 2 m, approximately 580 million cubic blocks are required. The very small joint spacing and the huge number of blocks required at the 200 th scale created practical difficulties for the construction. To maintain the practicality of model construction while not compromising the deformation and failure characteristics of the mine in the prototype scale, discrete element modelling (DEM) analyses were conducted to determine a representative joint spacing used for physical model testing. More details of the numerical modelling are given in the next section. On the other hand, joint strength needs to be properly scaled because it is an important parameter that directly controls the deformation characteristics and failure modes of a rock mass. In this study, the equivalent discontinuous modelling method of jointed rock mass proposed by [PERSON] and [PERSON] was adopted to determine the model joint strength [27], and the relationship between joint spacing and joint mechanical parameters was built by them. In this study, the interfaces between the blocks represented rock joints in prototype. Thus, the friction between the blocks was simulated to follow the prototype joint strength.