# Dynamic Performance of Soil-Tunnel System under Transverse Sinusoidal Excitations
## 6 Summary  
Putting attention on the relationship between the frequency of input motions and mechanism of soil-tunnel interaction, this study conducted FF model tests and ST model tests under seven sinusoidal excitations. Focusing on the responses of the ground and the tunnel, the conclusions are presented as below:  
(1) Comparing the FF model test and the ST model test, the influence of the tunnel on the fundamental frequency of the ground can be neglected.  
(2) The low-order modal amplitude decreases gradually, and the dominant role of low-order vibration modes weakens gradually with the increase of frequency of input  
Figure 27: Maximum dynamic earth pressures under different cases.  
Figure 28: Maximum dynamic strain of segments under different cases.  
motions. The change of the combination of modal amplitudes will affect the dynamic responses of the soil-tunnel system.  
(3) From the respect of waveform, phase, and peak, the differences of acceleration responses between the upper soil layer and the lower soil layer are obviously increasing with the increase of the input frequency. Except for the surface soil layer, the soft ground has damping effect on higher frequency excitations. Amplification effects of ground-surface acceleration are obvious under a higher excitation frequency. The presence of the tunnel induces a relatively high effect on acceleration responses of the ground within excitation frequency, varying from 9 to 17 Hz.  
(4) The variation trend of acceleration at the top and bottom of the tunnel are basically similar with the acceleration distribution in model soil at the near depth. The peak values of tunnel cross-sectional deformation, extension/closure of longitudinal joints, and dynamic normal earth pressures all appear in the conjugate 45-degree direction of the tunnel's cross-section. The response waveforms become more complex with the increase of sinusoidal frequency, and the waveforms of responses are closest to the sine function with the input frequency of 2 Hz. High-order vibration modes may distinctly affect the deformation of the ground under a higher frequency excitation. The maximum tunnel responses first increase and then decrease with the increase of sinusoidal frequency, and the maximum responses of the tunnel are influenced by both the fundamental frequency of the model ground and lower frequency excitations.  
Compared with the prototype site, the simplified homogeneous ground has certain limitations, thus requiring further study.  
Conceptualization, Y.Y. ([PERSON]) and S.Z.; methodology, Y.Y. ([PERSON]), H.A.M. and S.Z.; validation, Y.Y. ([PERSON]), S.Z., and Y.Y. ([PERSON]); investigation, S.Z.; resources, Y.Y. ([PERSON]); writing--original draft preparation, S.Z.; writing--review and editing, Y.Y. ([PERSON]); supervision, Y.Y. ([PERSON]), H.A.M., and C.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Research and Development Plan of China (2017 YFC1500703, 2018 YFC1504305, and 2018 YFC0809602), the National Natural Science Foundation of China (52061135112, 51908425, 41922059, 51678438, and 51778487), the Shanghai Committee of Science and Technology (18 DZ1205103 and 18 DZ1205106), and the support from the Fundamental Research Funds for the Central Universities of China.  
Not applicable.  
The research was supported by the National Key Research and Development Plan of China (2017 YFC1500703, 2018 YFC1504305, and 2018 YFC0809602), the National Natural Science Foundation of China (52061135112, 51908425, 41922059, 51678438, and 51778487), the Shanghai Committee of Science and Technology (18 DZ1205103 and 18 DZ1205106), and the support from the Fundamental Research Funds for the Central Universities of China. The above supports are greatly acknowledged.  
The authors declare no conflict of interest.