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In order to obtain the seismic dynamic characteristics of a shallow-bias tunnel with a small space, a series of large-scale shaking table model tests were carried out. The key technology of the test is introduced in detail, for example, similar ratios of model, test equipment, testing model box, testing model, sensor arrangement, seismic waves, and testing system. The results show that the first predominant frequency is similar between measuring points. However, the second predominant frequency is highly different between measuring points. The first and second predominant frequencies gradually decrease with the increasing of input PGA. The rock stratum can shield seismic wave in the high frequency band. The research results provide reference for similar tunnels.

In recent years, with the development of Chinese Western Development and the construction of the Silk Roads, many tunnels will be constructed in the mountainous and earthquake-prone western area. The shallow-bias tunnel with a small space may be the best option due to the objective conditions of geological structure, environmental condition, and engineering cost. Moreover, the tunnel meets the requirements of special geological condition and line direction. Nowadays, the tunnel has been widely constructed in tunnel engineering practice.

Shaking table test is a kind of advanced and sophisticated method in the study of geotechnical earthquake. At present, some scholars have studied the dynamic response of tunnel by the shaking table model test [

The study on acceleration, strain, and internal force response of conventional tunnel has achieved rich results from above-mentioned literatures. However, there are few studies on the Fourier spectra response and variation laws of predominant frequencies for the tunnel. The variation rule of the frequency of the measuring point can be obtained by Fourier spectrum response. And the response characteristics of the measuring point further can be obtained. The study on Fourier spectra and predominant frequencies was never carried out in [

This paper mainly adopted the method of [

The similar constants.

Physical quantity | Similar relation | Similar constants |
---|---|---|

L(m) | | 10 |

^{−3}) | | 1 |

E(MPa) | | 10 |

| 1 | |

| 10 | |

| 1 | |

t(s) | | 3.16 |

a(m·s^{−2}) | | 1 |

u(mm) | | 10 |

v(mm·s^{−1}) | | 3.16 |

| 1 | |

| | 1 |

^{−3}) | | 1 |

C(kN·m^{−2}) | | 10 |

The shaking table model tests were carried out in the National Engineering Laboratory of the High-Speed Railway Construction Technology of Central South University. The main parameters of shaking table are given in Table

Main parameters of shaking table.

Parameters | Specification |
---|---|

Platform size | 4m×4m |

Degree of freedom of motion | 6Dofs in 3directions |

Center distance of table-board | 6-50m |

Load capacity | 30ton |

| |

Maximum displacement and acceleration | X:250mm, ±1.0g |

Y:250mm, ±1.0g | |

Z:250mm, ±1.6g | |

| |

Working frequency | 0.1-50Hz |

Maximum eccentricity moment | 20 ton·m |

Maximum overturning moment | 30ton·m |

Maximum seismic velocity | 1000mm/s |

Maximum vibration velocity of simple string | 750mm/s |

Considering the size of shaking table, the rigid model box is independently designed and made. The model box has been widely used to carry out many shaking table tests of underground structure [

Rigid model box.

Before pouring the physical model of the tunnel, the boundary of the model box should be treated to reduce the error caused by the model box effect. There are three boundary treatment methods of model in shaking table test, such as sliding boundary, friction boundary, and flexible boundary [

Treatment of model boundary [

The lining model is made of microconcrete. Galvanized iron wire is used to simulate steel fabric. The thickness of the lining is designed as 4cm. Each lining liner axial length is 0.5m. The abrasive tool is used to compose the prefabricated lining. According to multiple laboratory experiments, the better ratio of the lining model material is 1:6.9:1.3 (cement: sand: water). The steel mesh is used to simulate the mesh reinforcement in lining. After pouring the lining, it is maintained for 28 days in the natural state. The lining reaches a certain strength and the lining is placed in the model box. The lining mold is specially made to fabricate the linings (Figure

Mold and linings: (a) mold of lining; (b) prefabricated lining [

There is a natural slope in the overlying strata of the tunnel. The slope gradient is 1:1.04. The testing model internal dimensions are 3.5m (length), 1.5m (width), and 1.8m (height), respectively. The surrounding rock of the tunnel is composed of weakly weathered rock, weak rock, and hard rock. The buried depth of the tunnel is 0.9m. The clear width of each hole is 0.7m. The thickness of the middle partition wall is 0.4m. The mortar is used to simulate the surrounding rock of the tunnel. The different strength mortar is used to simulate the different surrounding rock layers. The parameters of surrounding rock and lining material are given in Table

Physical and mechanical parameters.

Materials | Material parameters | ||||
---|---|---|---|---|---|

| | ^{−3}) | | | |

Weakly weathered rock | 6000 | 0.25 | 23 | 39 | 700 |

Weak rock | 1300 | 0.3 | 20 | 27 | 200 |

Hard rock | 18900 | 0.3 | 25 | 50 | 1500 |

Lining | 34500 | 0.16 | 24 | - | - |

Surrounding rock and layout of transducers (unit: m).

The accelerometers are used in the experiment, which are used to measure the acceleration of tunnel lining. The type of accelerometer is 1221L-002. The measuring range is ±20m·s^{−2}. The sensitivity is 2000mv·g^{−1}. Five measuring points are designed at the arch foot, arch shoulder, and vault of the tunnel [

The buildings and structures are subjected to the action of the complicated seismic wave, when the earthquake occurs. In shaking table test, bidirectional seismic wave is used as loading wave in order to get better simulation results. The bidirectional seismic wave is the Kobe wave (kb-xz). The horizontal direction (x) and vertical direction (z) are perpendicular to the tunnel axis, and table-board, respectively. The acceleration time history curve and the Fourier spectrum of the seismic wave are shown in Figure

Loading scheme of shaking table test.

Cases | Seismic wave | Peak acceleration | |
---|---|---|---|

x-direction | z-direction | ||

1 | wn-xz | - | - |

2 | kb-xz | 0.1g | 0.067g |

3 | wn-xz | - | - |

4 | kb-xz | 0.2g | 0.133g |

5 | wn-xz | - | - |

6 | kb-xz | 0.4g | 0.267g |

7 | wn-xz | - | - |

8 | kb-xz | 0.6g | 0.400g |

9 | wn-xz | - | - |

Kobe wave: (a) time history curve; (b) Fourier spectrum.

Case 1 is used to study the Fourier spectra response of different measuring points. Fourier transform is used to obtain Fourier spectrum of each measuring point, and the Fourier spectrum of each measuring point is showed in Figure

Fourier spectra of different measuring points: (a) measuring point A1; (b) measuring point A2; (c) measuring point A3; (d) measuring point A4; (e) measuring point A5; (f) measuring point A6; (g) measuring point A7; (h) measuring point A8; (i) measuring point A9; (j) measuring point A10.

In Figure _{0} range, respectively. The component of first predominant frequency is basically similar between measuring points. However, the second predominant frequency is different, some of the measuring points are amplified, and some of the measuring points are deamplified. The reason is that the first predominant frequency mainly reflects on the dynamic characteristics of the prototype site, but the second predominant frequency mainly reflects on the dynamic characteristics of the lining structure whose dynamic response is different with different measuring point [

In order to obtain the effect caused by input PGA of seismic wave on the predominant frequency, cases 3, 5, 7, and 9 are used to study the dynamic response of measuring point 1. Fourier transform is also used to obtain Fourier spectrum of measuring point 1, and the Fourier spectra with different input PGA are showed in Figure

Predominant frequencies: (a) 0.1g; (b) 0.2g; (c) 0.4g; (d) 0.6g.

Predominant frequencies with input PGA.

In Figure

A physical test model of the tunnel was designed and manufactured to carry out a series of large-scale shaking table model test. Based on the results of shaking table tests, the following conclusions can be drawn.

The first predominant frequency is 9.72Hz, and the second predominant frequency is 25.97Hz. The characteristic periods 0.37s and 0.14s of the site are obtained from the similar constants. The sites (0.37s and 0.14s) correspond to the II range and I_{0} range, respectively.

The first predominant frequency is similar between measuring points. However, the second predominant frequency is different. The rock stratum and lining structure can shield the seismic wave in the high frequency band. The first and second predominant frequencies gradually decrease with the increasing of times loading and input PGA.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The research was supported from the National Natural Science Foundation (NNSF) of China (nos. 51204215, 51404309) and the Hunan Natural Science Foundation (no. 2018JJ3882). Finally, Feifei Wang wants to thank their supervisor, Professor Xueliang Jiang. Thank you for your meticulous teaching and careful cultivation in the past three years.