The major goal of this paper is to address the derivation of the frequency equation of flexural vibrating cantilever beam considering the bending moment generated by an additional mass at the free end of beam, not just the shear force. It is a transcendental equation with two unambiguous physical meaning parameters. And the influence of the two parameters on the characteristics of frequency and shape mode was made. The results show that the inertial moment of the mass has the significant effect on the natural frequency and the shape mode. And it is more reasonable using this frequency equation to analyze vibration and measure modulus.

The evaluation of the trench stability under the action of ocean waves is an important issue in the construction of an immersed tunnel. In this study, a two-dimensional coupling model of a wave-seabed-immersed tunnel is proposed for the dynamic responses of a trench under wave action in the immersing process of tunnel elements. The porous seabed is characterized by Biot consolidation equations. The $k-\epsilon$ model and RANS equation are adopted to achieve the flow field simulation, and the level set method (LSM) is used to capture the free surface between the water and air. The proposed numerical model is verified using the experimental data and analytical results. Then, the transient liquefaction and shear failure in the vicinity of the trench are discussed at two different conditions, namely, after the foundation groove is excavated and after the tunnel element is placed. The pore pressure amplitude on the weather side slope is demonstrated to be significantly smaller than that on the lee side slope. Also, the distribution of the surrounding flow field and pressure field change dramatically after the tunnel element is settled, leading to the significant changes of seabed stability.

Dredging sea mud produced during the coastal infrastructure construction has been gradually becoming an environmental problem in China. Making ceramsite is an attractive way to convert the waste sea mud to resources used for many industrial sectors. However, the imapct of preheating and sintering conditions on the ceramsite properties and the biofilm formation capacity of the ceramsite are still poorly understood. This study aims to fill these knowledge gaps. Results suggested the optimal conditions for the preheating temperature was 350°C, the preheating time was 15 min, the sintering temperature was 1040°C, and the sintering time was 9 min. The dredging sea mud‐derived ceramsite showed better biofilm formation capacity with high COD and NH₄⁺‐N removal performance compared with the commercial ceramsites. The content of the chloride ion in the ceramist granules is close to zero, and the low cost of this material, implying this dredging sea mud‐derived ceramsite, could be an engineering favorable material for using it as a biocarrier in the real application.