# Experimental Assessment of the Effect of Vertical Earthquake Motion on Underground Metro Station
## 2 Shaking Table Tests
### Model
\(S\) with the subscripts refers to the similitude ratio of the quantities corresponding to those subscripts, i.e., \(S_{G_{d}}\), \(S_{\rho}\), \(S_{a}\), and \(S_{l}\) represent the similitude ratios for soil dynamic shear modulus, soil density, soil acceleration, and soil geometry size, respectively. The similitude ratios corresponding to other quantities can also be obtained in a similar way. The similitude ratio of the length is set to 1/30 for both the model soil and model station. Table 2 shows the main parameters adopted in defining the similitude relations in this study. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Types**} & \multirow{2}{*}{**Properties**} & \multirow{2}{*}{**Similarity Relations**} & \multicolumn{2}{c}{**Similitude Ratios**} \\ \cline{3-5}  & & & **Model Structure** & **Model Soil** \\ \hline Geometry & Length \(l\) & S\({}_{l}\) & 1/30 & 1/30 \\  & Linear & S\({}_{r}=\) S\({}_{l}\) & 1/30 & 1/30 \\  & displacement \(r\) & S\({}_{l}\) & 0.42 & 0.033 \\ Material & Elastic modulus \(E\) & S\({}_{l}\) & 12.6 & 0.52 \\  & Equivalent density & S\({}_{\rho}=\) S\({}_{l}\)S\({}_{l}\)S\({}_{a}^{-1}\) & 12.6 & 0.52 \\  & \(\rho\) & Shear modulus \(G\) & S\({}_{G}\) & — & 0.033 \\ Dynamic & Mass \(m\) & S\({}_{m}=\) S\({}_{\rho}\)S\({}_{l}^{3}\) & \(4.4\times 10^{-4}\) & \(1.2\times 10^{-6}\) \\  & Acceleration \(a\) & S\({}_{a}\) & 1 & 1 \\  & Duration \(t\) & S\({}_{t}=\) S\({}_{t}^{-1}\)S\({}_{l}\)S\({}_{l}^{\frac{1}{3}}\) & 0.1826 & 0.1826 \\  & Frequency \(\omega\) & S\({}_{\omega}=\) 1/S\({}_{t}\) & 5.48 & 5.48 \\  & Dynamic stress \(\sigma\) & S\({}_{\sigma}=\) S\({}_{l}\)S\({}_{a}\)S\({}_{\rho}\) & 0.42 & 0.033 \\  & Dynamic strain \(\varepsilon\) & S\({}_{\varepsilon}\) & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Similitude relations. To satisfy the aforementioned similitude relations, an artificial model soil made of sand mixed with sawdust was selected, which had been studied and used by other researchers [29]. By targeting the curves of both the shear modulus and damping ratio decaying with the shear strain for the artificial model soil and prototype soil [30], the optimum mass ratio of sawdust to sand was determined to be 1:2.5 through a series of cyclic triaxial tests performed in the laboratory. The comparison of the curves between artificial model soil and prototype soil can be found in [24]. The prototype of the atrium-style metro station had the dimension of \(21.3\times 17.7\) m (width \(\times\) height) and had two stories, including the station hall floor and platform floor. No columns on the station hall floor and thin-walled columns with spacing 7.6 m on the platform floor were adopted. Both the ceiling and middle slabs were mostly replaced with the flat-beams, directly resulting in about 50% opening area of the floorage for both slabs. The prototype station was a cast-in-place reinforced concrete structure and the strength grades of concrete and steel rebar were C35 and HRB400, respectively. G galvanized steel wire and micro-concrete were adopted in the model station to represent two practical materials mentioned above. To satisfy the similitude relations, an optimum mass ratio of micro-concrete was determined to be as cement:sand:lime powder:water = 1:5:0.64:1.18 through a series of material tests, and the compressive yield strength and elastic modulus were measured to be 10.68 MPa and \(1.32\times 10^{4}\) MPa, respectively. Figure 2 shows the details of the model station, including three observation planes. The observation plane-1 was located within the central symmetrical plane of the whole container-soil-structure system, while observation plane-2 and plane-3 were both 50 mm away from it. Figure 2: Dimensions of the model station: (**a**) perspective view; (**b**) cross-section; (**c**) locations of three observation planes (unit: mm).