# Dynamic Performance of Soil-Tunnel System under Transverse Sinusoidal Excitations
## 2 Test Design
### Model Ground  
Apart from the depth of the ground, the other two fundamental quantities of the site to be decided are the density and shear modulus of soil used to constitute the model ground. Artificial soil made up of sawdust and dry sand was here used to accommodate model soil, with regards to the dynamic characteristics of 'original soil' of the site. The average particle size of dry sand is 0.3 mm [12]. More details concerning the model soil can be seen in [PERSON]'s paper [12]. The black line in Figure 2 gives the target dimensionless  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Number** & **Type of Soil** & **Thickness** & **Depth** & **Weight** & **Density** & **Shear Velocity** \\  & **(m)** & **(m)** & **(kN/m3)** & **(kg/m3)** & **(m/s)** \\ \hline
1 & Backfill & 1.8 & 1.8 & 17.0 & 1730 & 137 \\ \hline
2 & Yellow/gray-yellow silty clay & 7.2 & 9.0 & 18.1 & 1846.94 & 140 \\ \hline
3 & Gray muddy silty clay & 3.3 & 12.3 & 17.6 & 1795.92 & 133 \\ \hline
4 & Gray clay & 4.7 & 17.0 & 17.4 & 1775.51 & 161 \\ \hline
5 & Gray silty clay & 10.0 & 27.0 & 17.8 & 1816.33 & 179 \\ \hline
6 & Dark green silty clay & 2.8 & 29.8 & 19.6 & 2000.00 & 311 \\ \hline
7 & Yellow-gray sandy silt with clay & 9.4 & 39.2 & 19.0 & 1938.78 & 289 \\ \hline
8 & Gray silty fine sand & 2.8 & 42.0 & 18.9 & 1928.57 & 346 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The stratigraphic parameters of Shanghai site.  
Figure 1: Cross-section of the prototype assembled lining.  
parameters of shear modulus ratio (Figure 2a) and damping ratio (Figure 2b) of prototype soil, measured by dynamic tri-axial tests. The other lines give the testing results of the same parameters for artificial soils with various proportion of sand and sawdust. It can be seen that, when the mass ratio of sand to sawdust is 1:2.5, the artificial soil is of better correlation with the prototype soil, in regard to the aspects of the shear modulus ratio or damping ratio. The model ground is considered as a uniform ground with respect to the consistency with the fundamental frequency of layered soils.  
To produce shear free boundary, a laminar box was used to contain models in this test, as shown in Figure 3. The outer dimension of the shear-free box is 4.8 \(\times\) 4.1 \(\times\) 3.0 m (length \(\times\) width \(\times\) height), and the inner dimension is 4.5 \(\times\) 3.5 \(\times\) 3.0 m. With this volume of laminar box, the model ground produced with 1:2.5 artificial soil meets the requirements of the similarity ratio of maximum dynamic shear modulus and the bearing capacity of the shaking equipment.  
The artificial soil was placed in the laminar box, layer by layer, with compaction, to the height of 2.8 m. The thickness of each layer is 0.2 m. The filling mass of the artificial soil is the same in each layer, aimed at a constant density of the model ground. Finally, the filling density could be guaranteed [13]. The design value of fundamental frequency of the uniform model ground is 4.4 Hz in the light of  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Physical Quantities** & **Symbol** & **Dimensions** & **Expression** &
\begin{tabular}{c} **Similarity Ratio** \\ **(Model/Prototype)** \\ \end{tabular} \\ \hline Geometrical dimension & \(l\) & L & \(S_{l}\) & 1/15 \\ \hline Density & \(\rho\) & M & \(S_{\rho}\) & 1/2.7 \\ \hline Shear modulus & \(G\) & ML\({}^{-1}\)T\({}^{-2}\) & \(S_{G}\) & 1/39.2 \\ \hline Elastic modulus & \(E\) & ML\({}^{-1}\)T\({}^{-2}\) & \(S_{E}=S_{G}\) & 1/39.2 \\ \hline Acceleration & \(a\) & LT\({}^{-2}\) & \(S_{a}=S_{G}S_{l}^{-1}S_{\rho}^{-1}\) & 1/1 \\ \hline Time & \(t\) & T & \(S_{t}=S_{l}S_{\rho}^{1/2}S_{G}^{-1/2}\) & 1/3.92 \\ \hline Frequency & \(f\) & T\({}^{-1}\) & \(S_{f}=S_{l}^{-1}S_{\rho}^{-1/2}S_{G}^{1/2}\) & 3.92/1 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Similarity relations.  
Figure 2: Dynamic characteristic curves of soils. (a) Dynamic shear modulus ratio versus shear strain.(b) Damping ratio versus shear strain.