The transversely isotropic (TISO) constitutive and frost heave models for the freezing of fine-grained soils are more accurate than the isotropic model and simpler than the orthotropic models. First, in combination with the mesoscopic composition of freezing soils, a mechanical model for the interaction between the equivalent ice lens and the soil in frozen soils is established based on the series and parallel models in the theory of composite mechanics. Second, the TISO constitutive model together with the analytic expression of five elastic constants is provided for analysis of the freezing soils. Third, a preliminary elastoplastic model for TISO freezing soil is established based on the Hill plastic model. Fourth, the heat–moisture–deformation coupling TISO model and the hydrodynamic frost heave model are derived according to a thermodynamics equation, a soil water motion equation, and generalized Hooke’s law. Synchronization and uniformity of the TISO constitutive model and the TISO frost heave model are realized for analyzing the interaction between permafrost soils and buildings. Finally, an indoor standard frost heave test and the frost heave of a prototype canal are simulated based on the above models. The numerical results indicated that the models presented in this paper accurately described the frost heave and revealed the interaction between permafrost and buildings.

To explore the influence of shield construction on the stress of tunnels surrounding rock and linings in deep, high groundwater and low-permeability soft rock strata, a 3D coupled hydro-mechanical model of a low permeability mudstone tunnel was established with ABAQUS, based on the effective stress principle and the Mohr–Coulomb elastoplastic constitutive model, taking the Bailuyuan Tunnel of the Hanjiang to Weihe River Valley Water Diversion Project Phase II in China as an example. The tunnel shield construction was simulated, and the spatial-temporal variation in the pore water pressure and the internal forces of the lining were studied. The results show that the central pore water pressure of the low-permeability mudstone face presents a V-shaped variation with the tunnel excavation. When the face was approximately 15 m from the representative section, the pore pressure on the linings basically varied between 192.7 and 182.5 m. The bending moment and axial force of the lining increased by 7.4% and 12.8%, respectively, with shield tunnelling. When the tunnel diameter was constant, the axial force and bending moment of the lining decreased quadratically as the lining thickness increased. The influence of shield construction decreased as the lining thickness increased. The research results provide a reference for the safe and optimal construction of the Hanjiang to Weihe River Valley Water Diversion Project.

This note presents iterative formulas that can be used to calculate the normal depth for all types of horseshoe cross sections. Based on the principle of gradual optimization fitting, general estimation formulas were developed for direct computation of the normal depth for all types of the standard horseshoe cross sections. The estimation formulas have high accuracy for hydraulic designers to use in comparison with the accurate normal depths determined from iterative formulas, and the maximum relative error is less than 0.5%.

In this work, we applied the spectral element method (SEM) to analyze the dynamic characteristics of fluid conveying single-walled carbon nanotubes (SWCNTs). First, the dynamic equations for fluid conveying SWCNTs were deduced based on the nonlocal Timoshenko beam theory. Then, the spectral element formulation was established for a free/forced vibration analysis of fluid conveying SWCNTs by introducing discrete Fourier transform. Furthermore, the proposed method was validated using several comparison examples. Finally, the natural frequencies and dynamic responses of a simply-supported fluid conveying SWCNTs were calculated by the SEM, considering different internal fluid velocities and small-scale parameters (SSPs). The effects of fluid velocity and SSPs on the dynamic characteristics of SWCNTs conveying fluid were revealed by the numerical results. Compared with other methods, the SEM shows high accuracy and efficiency.

The Galerkin method is proposed to reveal the dynamic response of pipe conveying fluid (PCF), with lateral moving supports on both ends of the pipe. Firstly, the dynamic equation is derived by the Newtonian method after calculating the acceleration of the fluid element via the dynamics approach. Secondly, the discrete form of the dynamic equation is formulated by the Galerkin method. Thirdly, the numerical analysis of the system is carried out through the fourth‐order Runge–Kutta method, and the effectiveness of the proposed method is validated by comparison with the analytical results obtained by the mode superposition method. In the example analysis, the responses of the lateral deflection and bending moment are investigated for the pinned‐pinned, clamped‐pinned, and clamped‐clamped PCF. The effects of fluid velocity and the moving frequencies of supports are discussed. Especially, the deflection responses are analyzed under extreme condition; i.e., the moving frequency of a support is identical to the natural frequency of PCF.