To analyze the behavior of the vibrator–ground coupling vibration, a model containing equivalent dynamic stiffness and equivalent dynamic damping to describe the interaction between the vibrator and the ground is established based on half-space theory. According to load cell test, this model shows a good agreement with the experimental data. Dynamic responses of the structure are analyzed on displacement, velocity, acceleration, and ground force. Results show that the stroke and pump displacement are main constraints that limit the bandwidth of vibrator toward low frequency, and the stroke of conventional vibrator is not long enough to achieve lower frequency. Analysis of velocity response indicates that with the increase of frequency, a larger mass results in a lower velocity under external force. The influence of the ground acting on the baseplate is limited, and the acceleration of the baseplate is determined by its own mass beyond 80 Hz. Analysis of ground force shows that the response of the structure can be divided into three stages. The reaction mass, the baseplate, and the ground play different roles in dominating the ground force at different frequency bands.
This paper is focused on the influence of the rough contact interfaces on the dynamics of a coupled mechanical system. For this purpose, a two-degree-of-freedom model of a coupled seismic-vibrator-rough-ground system is proposed with which the nonlinear vibration properties are analyzed. In this model, the force-deflection characteristic of the contact interfaces is determined by finite element analysis. By analyzing the undamped free vibration, it was found that the variation of the second-order natural frequency with amplitude increases with rougher contact interfaces; however, the amplitude has little influence on the first-order natural frequency of the system. For the harmonic excited analysis, the jump frequencies and hysteretic region both decrease with rougher contact interfaces. Moreover, it is inferred from the bifurcation diagrams that, increasing the excitation force, the system can bring about chaotic motions on rough contact interfaces.
To study the dynamic response and spectrum characteristics of the three-dimensional crossing tunnel under the action of seismic load, we established a 1/50 downscale model based on a typical of the oblique overlapped tunnel and conducted a series of shaking table tests. Through examining the recorded dynamic responses (acceleration and dynamic strain measured at different locations in model tunnels), we found that the seismic response of the crown was the largest at the central section, and the invert of the tunnels was exactly opposite to the crown, which presented a “parabolic” distribution, and we inferred that the damage within the model may be mainly concentrated on the crown of the tunnels. Additionally, the dynamic strain showed obvious nonlinear and nonstationary characteristics under the action of different degrees of seismic intensities. Different from a single tunnel, the acceleration superposition effect appears in the cross section of two tunnels because of the spatial effect of overlapping tunnels, resulting in the obvious seismic response in the cross section. Meanwhile, we also found that the 1st dominant frequency (0.1–6.26 Hz) seismic wave played a leading role in the process of tunnel slope failure. Furthermore, the analysis of the acceleration response spectrum also showed that the surrounding rock mass has an amplification effect on low-frequency seismic waves. These results help us better understand the features of the dynamic responses and also provide evidence to reinforce the overlapped tunnels against earthquakes.
This paper presents the seismic dynamic response and spectrum characteristics of an orthogonal overlapped tunnel by shaking table tests. First, a prototype of the engineering and shaking table test device, which was used to design details of the experiment, was developed. Then, the sensors used in the test were selected, and the measurement points were arranged. Subsequently, the Wenchuan seismic wave with horizontal direction in different peak ground accelerations was inputted into the model, followed by a short analysis of the seismic response of the overlapped tunnel in the shaking table test as well as the distribution of the peak acceleration. Throughout the studies, the model exhibited obvious deformation stages during the seismic wave loading process, which can be divided into elastic, plastic, plastic enhancement, and failure stage. In particular, the time- and frequency-domain characteristics of the key parts of the tunnel were discussed in detail by using the continuous wavelet transform (CWT) based on the Morlet wavelet as the basis function. We found that the acceleration response was more intense within 25–60 s after the seismic wave was inputted. Furthermore, owing to “the superposition effect,” the seismic response at the crown of the under-crossing tunnel was stronger than that at the invert of the upper-span tunnel. The low and medium frequencies in the transformation of small scales (5–20) significantly affected the overlapped tunnel. These results elucidate the seismic dynamic response of the overlapped tunnel and provide guidance for the design of stabilizing structures for reinforcing tunnels against earthquakes.
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