Investigating the Deformation and Failure Mechanism of a Submarine Tunnel with Flexible Joints Subjected to Strike-Slip Faults

Knowledge from historical earthquake events indicates that a submarine tunnel crossing active strike-slip faults is prone to be damaged in an earthquake. Previous studies have demonstrated that the flexible joints are an effective measure for a submarine tunnel crossing a strike-slip fault. The background project of this paper is the second submarine tunnel of Jiaozhou bay. In this work, model tests and numerical simulations are conducted to investigate the deformation and failure mechanism of a submarine tunnel with flexible joints under a strike-slip fault dislocation. The influence of strike-slip faults on a tunnel with flexible joints has been investigated by examining the deformation of rock mass surface, analyzing lining stains, and crack propagation from model tests. Numerical simulations are conducted to study the effects of the design parameters of a tunnel with flexible joints on the mechanical response of the lining. The results showed that the ‘articulated design’ measure can improve the ability of the tunnel to resist the strike-slip faults. In terms of the mechanism of design parameters of a tunnel with flexible joints, this paper finds that increasing the lining thickness, decreasing the lining segment length, and decreasing the tunnel diameter to a reasonable extent could effectively improve the performance of this faulting resistance measure for a tunnel under the strike-slip fault zone dislocation. Compared with the horseshoe tunnel cross-section, the circular tunnel cross-section can improve the ability of the faulting resistance of a tunnel with flexible joints, while the optimal angle of the tunnel crossing the fault zone is 90º. It is concluded that the wider fault zone, smaller flexible joint width, and less stiffness of the flexible joint could make lining safer under a strike-slip fault dislocation. The above research results can serve as a necessary theoretical reference and technical support for the design of reinforcement measures for a submarine tunnel with flexible joints under strike-slip fault dislocation.

Constraint-Following Servo Control for the Trajectory Tracking of Manipulator with Flexible Joints and Mismatched Uncertainty

Trajectory tracking is a common application method for manipulators. However, the tracking performance is hard to improve if the manipulators contain flexible joints and mismatched uncertainty, especially when the trajectory is nonholonomic. On the basis of the Udwadia–Kalaba Fundamental Equation (UKFE), the prescribed position or velocity trajectories are creatively transformed into second-order standard differential form. The constraint force generated by the trajectories is obtained in closed form with the help of UKFE. Then, a high-order fractional type robust control with an embedded fictitious signal is proposed to achieve practical stability of the system, even if the mismatched uncertainty exists. Only the bound of uncertainty is indispensable, rather than the exact information. A leakage type of adaptive law is proposed to estimate such bound. By introducing a dead-zone, the control will be simplified when the specific parameter enters a certain area. Validity of the proposed controller is verified by numerical simulation with two-link flexible joint manipulator.

Three-Dimensional Nonlinear Seismic Response of Shield Tunnel Spatial End Structure

The stiffness mutation of shield tunnel-shaft junction makes the tunnel structure affected by the differential displacement and forms a complex spatial effect. Taking the subsea shield tunnel crossing under the Shantou Gulf, China, as a case study, a three-dimensional finite element global model and a refined local spatial end submodel are established. The nonlinear dynamic behaviors of the seabed soil and concrete, the simulation of the bolt joints between ring segments by using cohesive models and the SMA shape memory alloy flexible joints, and the input ground motions produced by scaling from the high-level earthquake records are considered in detail. The results show that the shield tunnel spatial end structure increases nonlinearly in response to the increase of seismic motion intensity. The opening width and the deformation between ring segments at the vault and the outside spandrel are larger, and serious seismic damage and stress concentration exist at the conjugate 45° directions of shaft. The seismic responses of the tunnel-shaft junction subjected to the seismic motions with rich low-frequency components are much stronger than those of seismic motions with rich high-frequency components. Adding SMA flexible joints, the structural deformation caused by seismic motion propagation can be induced to the preset flexible joint, and the structural damage and stress concentration can be effectively reduced. The seismic response characteristics of shield tunnel spatial end structure calculated by the global model are consistent with those calculated by the submodel, while the seismic response of the submodel is greater than that of the global model.