## 2 Models: Design and Fabrication
### Model Fabrication  
The preparation of the model mainly included four steps: pouring of the light aggregate plaster lining, maintenance indoors, assembly of the lining, and pouring the foam concrete, and Figure 2 presents the construction process of the models. Foam concrete was molded in one pour for HRM model and four pours for JRM model. Because of the presence of construction joints at the poured layering and the drying shrinkage of foam concrete, artificial rock joints and discontinuous planes were created through a period of natural curing. A series of tests was conducted using a six-degrees-of-freedom shaking table system at Tongji University, which is 4.0 m long and 4.0 m wide with a load capacity of 25 tons. The outer contour of the whole model was 3.0 m long in the x-direction, 3.0 m wide in the \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Item**} & \multirow{2}{*}{**Density**} & \multirow{2}{*}{\begin{tabular}{c} **Black** \\ **(kg/m3)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Poisson’s** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Cohesion** \\ **Ratio** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Friction** \\ **(kPa)** \\ \end{tabular} } \\ \hline \multirow{3}{*}{Rock} & Prototype & 2550 & 11000 & 0.3 & 1100 & 27 \\  & Target & 765 & 110 & 0.3 & 11 & 27 \\  & Test & 730 & 110 & 0.3 & 15 & 33 \\ \hline \multirow{3}{*}{Lining} & Prototype & 2500 & 33500 & 0.2 & / & / \\  & Target & 750 & 335 & 0.2 & / & / \\ \cline{1-1}  & Test & 720 & 350 & 0.2 & / & / \\ \hline \end{tabular}
\end{table} 
Table 2: Properties of prototype and model materials. Figure 2: Model fabrication: (**a**) mold; (**b**) indoor maintenance; (**c**) assembly of the lining; (**d**) pouring the foam concrete. y-direction, and 2.0 m high in the z-direction. Figure 3 illustrates the complete test models, Figure 3a is an actual picture of HRM model, and Figure 3b is a sketch of the joints and discontinuous planes of JRM model. [PERSON] et al. [31; 32] combined the strain energy theories of continuum and fracture mechanics, the elastic stress-strain relationship of the jointed rock mass was proposed, and its elastic modulus was derived. The ratio of elastic modulus of jointed rock to that of an intact rock was defined, and when the joints were in compression (\(\sigma\leq 0\)), the formula was as follows:  
\[\frac{E_{m}}{E}=\frac{1}{1+\alpha\beta\sum_{p=1}^{m}\lambda\overline{a}h^{2} sin^{2}\delta\ cos^{2}\delta} \tag{2}\]  
where \(\alpha=\frac{8\left(1-v^{2}\right)}{\pi}\), \(\beta=\frac{2}{2-v}\), and \(v\) is [PERSON]'s ratio of the medium around the joints, and the Poisson's ratio of the model rock is 0.3; \(\delta\) is the inter-angle between the shear stress and the loading plane; \(m\) is the number of joint sets; \(\lambda\) and \(\overline{a}\) are the normal density and average radius of the joint sets, respectively; and \(h\) is the residual shear stress ratio, since the medium and roughness around the joints are the same, and it is assumed to be 0.9 for all cases. The joints on the model surface were categorized Into the left side (m\({}_{\rm l}\)), the front face (m\({}_{\rm f}\)), the right side (m\({}_{\rm r}\)), the back face (m\({}_{\rm b}\)), and the top face (m\({}_{\rm t}\)). Along the loading directions, the joints were divided into two sets: the side joint sets, consisting of left side m\({}_{\rm l}\) and right side m\({}_{\rm r}\) (in the x-direction); and the face joint sets, consisting of front face m\({}_{\rm f}\), back face m\({}_{\rm b}\), and top face m\({}_{\rm t}\) (in the y-direction). Under transverse (x-direction) loading, the angle between the side joint sets and the loading plane was 90\({}^{\circ}\), and the angle between  
Figure 3: The complete test models: (**a**) the homogeneous rock–station model; (**b**) the jointed rock–station model. the face joint sets and the loading plane was 15\({}^{\circ}\).