As the soil-resistance coefficient in a soft soil area is small, overlarge bending moment may cause exceeding transverse deformation for the shield tunnel and cause structural diseases and waterproof failure at the longitudinal segment joints. Hence, a new idea of cross-section design for a minimum bending moment shield tunnel was proposed. This article has first put forward the concept of a zero bending moment shield tunnel. Then, based on rational and feasible hypotheses, a structural mechanical model and an analytical expression of axis for the cross-section of the zero bending moment shield tunnel was obtained, and computational formulas of internal force and key geometry parameters were given. Based on the case of the metro shield tunnel constructed in the Shanghai soft soil area, the zero bending moment shield tunnel was designed, and its characteristics were analyzed. Considering only one cross-section of shield tunnel can be adopted in one metro line, the design method and procedure of the minimum bending moment shield tunnel were put forward. Finally, taking one of the Shanghai metro lines as an example, a cross-section of a minimum bending moment shield tunnel was designed, and its bending moment was compared with the bending moment of a circular section shield tunnel, which had the same horizontal diameter. The comparison revealed that the cross-section of the minimum bending moment can significantly reduce the bending moment of shield tunnel.

The third-generation gravity base foundation, which consists of a concrete-based structure with infill aggregates, is designed for water depths greater than 20 m. In this study, a simplified method in the time domain for predicting the nonlinear dynamic response of the offshore wind turbine supported on the third-generation gravity base foundation is proposed. The results obtained by the proposed method are compared with 3D finite element simulations, and the consistency of the results verifies the reliability of the simplified method. In addition, the dynamic response of the wind turbine supported on GBF under wind and wave loads is investigated. The results indicate that the lateral dynamic responses of the GBF are more affected by the thrust force than by the distributed force when the wind loads are only considered; the maximum dynamic displacement of the GBF caused by the drag force is almost the same as that of the GBF caused by the inertia force when the wave loads are only considered, and the dynamic response of the GBF under combined wind and wave loads show a similar trend to that of the GBF under the wind loads only, especially the existence of a large displacement on the horizontal direction at the beginning of the loading.

The tapered pile offers sustainable use of construction materials due to its higher axial and lateral capacity and better performance owing to its geometry. This paper develops a semi-analytical solution of the vertical dynamic impedance of the tapered pile based on the dynamic Winkler theory and transfer matrix method. The accuracy and reliability of the proposed approach are verified by comparing the impedance functions of cylindrical and tapered piles obtained from the analytical solution and finite element analysis. A parametric study is performed to investigate the influence of the taper angle on the vertical dynamic impedance and resonant frequency. The results reveal that the taper angle has a significant influence on the vertical dynamic impedance, while it does not affect the oscillation period of the dynamic impedance and the resonant frequency. Besides, the vibration performance of the tapered pile is better than that of a cylindrical pile with the same volume. For a fixed-volume tapered pile, varying the pile length while keeping the pile tip diameter constant yields a better dynamic impedance than varying the pile tip diameter while keeping the pile length constant. Finally, the vertical displacement amplitude of the tapered pile decreases as the taper angle increases, especially for high-frequency excitation.

Bridge foundations located in deep water are usually subjected to horizontal dynamic loads and moments which may be caused by the wind, waves, earthquake,

As a cross-sea or river deep-water foundation, it is clear that the caisson foundation will be subjected to significant lateral dynamic loads due to winds or waves and suffer from scouring under its long-term effect. In order to obtain the scour effect on the dynamic response of the foundation, an analytical model describing the scour-hole effect in terms of scour depth, scour width, and slope angle was constructed. Combined with the nonlinear Winkler theory, a method for the dynamic response of the caisson foundation considering the scour-hole dimensions was proposed. Comparisons against the results from the dynamic FEM demonstrate the reliability of this method. The effects of the scour width, slope angle, and scour depth on the dynamic response of the caisson were discussed. The results show that the scour depth affects the dynamic displacement and resonant frequency of the foundation most, whereas the scour width does less and the slope angle does the least; the dynamic response of caisson can be approximated as the case of the slope angle 5° and the scour width 5B when the slope angle is less than 5° and the scour width is greater than 5B, respectively; the effects of scour width and slope angle on the dynamic response of caisson have the similar change pattern in the displacement and resonant frequency when the scour depth is different. However, the effect of amplitude on dynamic response shows a nonlinear increase trend when the scour depth is relatively large.

Tapered piles are a new type of pile foundation known for their simple construction and high bearing capacity, commonly used in railway, highway, or building foundation treatment. This study proposes a unified dynamic Winkler model for vertical and lateral vibration response of tapered piles in the frequency domain using the impedance function transfer matrix method. The computational expressions are obtained for the different springs and damping of tapered piles with different dimensions using the elastodynamic theoretical of rigid embedded foundations, and the dynamic interaction mechanisms of vertical and lateral vibrations between tapered piles and soil are analyzed. The rationality of the simplified model is validated by comparison with existing literature and finite element simulation results. Finally, an example is provided to discuss the influences of the dimensional parameters of the pile and soil properties on vertical, lateral, and rocking dynamic impedance. The analytical findings demonstrate that the lateral and rocking dynamic impedances of tapered piles undergo a substantially greater enhancement relative to their vertical counterpart as the taper angle is progressively enlarged, assuming the pile volume remains constant. The dynamic impedance of tapered piles under vertical and lateral vibration in upper hard and lower weak soil layers, or upper weak and lower hard soil layers, are both greater than those in a homogeneous foundation. Specifically, the vertical dynamic stiffness of tapered piles in double-layered soils is approximately twice that of homogeneous soil. The rocking dynamic stiffness of the pile is significantly influenced by the soil properties around the pile foundation, whereas the soil properties have little impact on the rocking damping coefficient. Overall, the vertical dynamic characteristics are less influenced by the geometric features of the upper part of the tapered pile, while the lateral dynamic characteristics are significantly affected by these features. The lateral dynamic impedance of the tapered pile increases with the diameter of the upper part of the pile. Furthermore, the vertical, lateral, and rocking dynamic impedance of the pile can be effectively improved by enhancing the soil properties around its upper section. These results can provide theoretical references for the engineering practice.