# Dynamic Performance of Soil-Tunnel System under Transverse Sinusoidal Excitations
## 1 Introduction  
The seismic performance of tunnels in soft ground has attracted the attention of researchers worldwide. Whether in analysis [1] or with the shake table test [2], the transverse response under dynamic action is of fundamental importance for revealing the facts other than long tunnel [3]. A record of ground motion from real earthquake is a complicated composition of random frequencies. Input of sinusoidal excitation with specified frequency is an optimal way to capture the mechanism of soil-tunnel interaction. [PERSON] and [PERSON] [4] studied the dynamic responses of a tunnel under sinusoidal excitations of frequencies from 40 to 60 Hz, by means of a centrifuge test and numerical analysis. In this investigation, uniformed tunnels with a square section and circular section were modeled at a scale of 1:50 and were imbedded in sandy ground. Accelerations on and around the tunnel lining, as well as in the sand, and dynamic earth pressures on the tunnel lining were recorded and analyzed. [PERSON] and [PERSON] [5] conducted dynamic centrifuge tests to study the influence of input frequency on the seismic behavior of a square tunnel in soft ground. The geometric scaling factor was 1:100. The frequencies of sinusoidal excitation ranged from 50 to 200 Hz. Only acceleration response and strain response of tunnels were obtained. [PERSON] and [PERSON] [6] performed a series ofshaking table tests on a circular subway tunnel. The maximum frequency of the shaking table was limited to 20 Hz in the case of harmonic waves, considering the shaking table's capability. The tunnel was modeled by a uniformed tube in scale 1:32. The effect of the tunnel on the ground surface acceleration was studied, using the recorded acceleration data. The dynamic response of the tunnel was is presented here. The similarity ratios of tests mentioned above are too small; thus, the input frequency seriously deviates from the actual frequency of the prototype structures. Segmental assembled rings as linings are widely applied to the construction of tunnel in soft ground. To model the seismic performance of assembled linings of shield tunnels, [PERSON] and [PERSON] [7] conducted a shaking table test on a 1:100 scaled tunnel located at alluvium ground. Transverse joints (that is longitudinal joint in this paper) of the tunnel were modeled by a longitudinal groove on a uniform tube to produce equivalent stiffness. As the model tunnel is basically not a segmented one, the deformation response of longitudinal joints cannot be captured. [PERSON] et al. [8] used a similar method to produce a grooved model tunnel but focused on the discrepant responses of shaft-tunnel junction, that is, opening or closure of ring joint. A large-scale shaking table test with geometry similarity ratio 1:8 was conducted [9] to investigate the seismic response of a tunnel embedded in compacted clay. The tunnel lining was modeled with an uniformed ring, on the basis of equivalent stiffness principle. However, static analysis [10] and experiments [11] proved that the existence of longitudinal joints will have an important impact on the mechanical behavior of segmental tunnel. The transverse deformation in a cross-section of segmental tunnel should be properly captured with refined model lining for the purpose of dynamic testing. Focusing on the relationship between the frequency of input sinusoidal motions and the dynamic response of a system, this paper recounts a series of shaking table tests carried out on both a free-field model and soil-tunnel model. The geometrical scaling factor was set as 1:15 in the light of the diameter of prototype tunnel, 14.0 m. Seven sinusoidal excitations with frequencies from 2 to 17 Hz were designated to cover the fundamental frequency of the model ground. Accelerometers in the ground and on the model tunnel were instrumented to capture the dynamic characteristics of the models.