## 2 Test Design
### Design of the Model Segmental Lining
#### 2.2.3 Simulation of the Circumferential Joints  
In practical engineering, there are 28 evenly distributed mortises and tenons at the circumferential joints (between adjacent rings) to resist the staggering deformation and  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Symbol** & **Unit** & **Similarity Relations** \\ \hline Length & \(l\) & m & \(C_{l}=l_{p}/l_{m}=50\) \\ Elastic modulus & \(E\) & Pa & \(C_{E}=E_{p}/E_{m}=1\) \\ Displacement & \(\delta\) & m & \(C_{\delta}=\delta_{p}/\delta_{m}=50\) \\ Strain & \(\varepsilon\) & - & \(C_{c}=\varepsilon_{p}/\varepsilon_{m}=1\) \\ Stress & \(\sigma\) & Pa & \(C_{\sigma}=\sigma_{p}/\sigma_{m}=1\) \\ Concentrated load & \(F\) & N & \(C_{F}=F_{p}/F_{m}=50^{2}\) \\ Bending moment & \(M\) & N-m & \(C_{M}=M_{p}/M_{m}=50^{3}\) \\ Internal friction angle & \(\varphi\) & (\({}^{\circ}\)) & \(C_{\varphi}=\varphi_{p}/\varphi_{m}=1\) \\ Cohesion & \(c\) & Pa & \(C_{c}=c_{p}/c_{m}=1\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Similarity law of the centrifugal model tests.  
provide shear stiffness. Two inclined bolts are arranged at both sides of one couple of mortises and tenons along the circumferential direction to provide longitudinal connection and preload. Previous studies [24; 25] have demonstrated that the shear stiffness between adjacent rings is firstly provided by the friction of the segments, and when the mortise and tenon contact, the tenon-mortise structure will play a significant role.  
The area of a single tenon is \(A_{p}\) = (150 \(\times\) 120 + 3.14 \(\times\) 1502/4) mm\({}^{2}\) = 3.56 \(\times\) 104 mm\({}^{2}\). The elastic modulus, Poisson's ratio, and the shear modulus of C60 concrete are 36.5 GPa, 0.167, and 15.6 GPa, respectively. Thus, the shear stiffness of a single tenon can be calculated as \(G_{p}A_{p}\) = 15.6 GPa \(\times\) 3.56 \(\times\) 104 mm\({}^{2}\) = 5.55 \(\times\) 108 N. The average shear length of the long and short axes is 210 mm, so the shear stiffness coefficient of a single tenon is \(k_{sp}\) = \(GA^{\prime}/L^{\prime}\) = 5.55 \(\times\) 108 N/(210 mm) = 2.64 \(\times\) 109 N/m.  
In the tests, 28 straight bolts were chosen to simulate the shear stiffness of the practical tenons. The model bolt positions are determined according to the positions of the evenly distributed tenons and the segmentation of the lining ring. The lining ring was machined of counterbones and through holes on one side, and thread holes on the other side, to realize the ring-by-ring assembly of the model lining. According to the similarity principle, the stiffness of a single model bolt should be \(k_{sm}\) = \(k_{sp}/n\) = (2.64 \(\times\) 109/50) N/m = 5.28 \(\times\) 107 N/m. The size of the model bolts and bolt holes should not be too large to affect the mechanical characteristics of the lining ring, nor too small to make it hard to machine and assembly. Thus, Al alloy bolts (No. 6063) were used in the tests, whose elastic modulus and Poisson's ratio are 70 GPa and 0.33, respectively. The bolt diameter calculated is 2.55 mm, so Al alloy bolts with a diameter of 2.5 mm were employed as the circumferential joints. Specifically, the diameter of threaded holes, through holes, and counterbones are 2.5 mm, 2.8 mm, and 5 mm, respectively. When assembling the model lining, the pre-tightening force of a single bolt is about 440 N, so the compressive stress of the contact surface between adjacent rings is about 1.06 MPa. The overall photo and the local details of the joints are shown in Figure 3.