Buried pipes are widely used for submarine water transportation, but the complex operating conditions in the seabed pose challenges for the modeling of buried pipes. In order to more accurately capture the dynamic behavior of the buried pipes in the seabed, in this study, considering the pipeline and soil as a systematic structure is proposed, improving the fluid-structure interaction four-equation model to make it applicable for the calculation of buried pipe system modes. After verifying the practicality of the model, considering the external seawater as uniform pressure, the coupling at the joints, and the Poisson coupling of submarine pipelines during transient processes are discussed, revealing that structural vibrations under both forms of coupling will cause greater hydraulic oscillations. The impact of soil elastic modulus on the system's response is further discussed, revealing that increasing the modulus from 0 to 1015 Pa raises the wave speed from 498 m/s to 1483 m/s, causing a 40% increase in the amplitude of pressure oscillations. Finally, the vibration modes of the combined structure of pipe wall and soil are discussed, revealing that the vibration modes are mainly dominated by water hammer pressure, with the superposition of pipeline stress waves and soil stress waves. In this study, the dynamic behavior of submarine pipelines is elucidated, providing a robust foundation for regulating and mitigating fatigue failures in such systems.

To investigate the three-dimensional dynamic response of a deeply buried storage and drainage tunnel in saturated soil subjected to water hammer, we propose a frequency-domain finite element method and boundary element method (FEM-BEM) coupling model for the fluid-lining-saturated soil system. The fluid is modeled as an inviscid and compressible fluid, the lining as an elastic medium conceptualized as a hollow cylinder of finite length, and the soil as a saturated poroelastic medium. Initially, the governing equations for the fluid and lining are solved using FEM in the frequency domain, while those for the soil are solved using BEM in the same domain. In the following, fluid, lining, and soil are coupled based on the conditions of deformation compatibility, force equilibrium, and impermeable boundary conditions at their interfaces. The presented model is verified through the comparison with the existing models. Finally, a case study of internal water pressure (water-hammer load) and the displacement and pore pressure of the saturated soil in a fluid-filled lined tunnel due to water hammer is presented. The results show that: (1) The dynamic response caused by the water hammer presents significant periodicity and attenuation. (2) The radial displacement of soil is significantly larger than that of axial displacement. (3) Modeling soil as a single-phase elastic medium inaccurately evaluates the dynamic response. (4) The water hammer makes an extensive impact on the ground surrounding the storage and drainage tunnel. (5) The peak values of internal fluid pressure, the soil displacement and pore pressure decrease with the decrease of soil permeability.

Finding the most suitable closing law is essential to decrease the shock wave pressure caused by transient flow and minimize the potential damage to equipment. The closure of a valve can occur instantly, rapidly, or gradually, and the appropriate law can be convex, linear, or concave, depending on various factors. These factors include the pipe's characteristics (type, diameter, roughness, and length), the conveyed fluid (nature and temperature), and operating conditions (pressure and flow rate). Other factors that receive less attention, such as the duration of slow closure and the impact of soil load on the pipe, are also considered in this study. The main focus of this article is to investigate how the optimal law evolves based on the time it takes for a valve to gradually close, specifically in the case of a valve located at the end of an underground gravity supply pipe. The findings reveal that when the slow closure time (t) exceeds 0.50 times the return period (t4), the exponent of the optimal law becomes a damped periodic function. Each closure time corresponds to a unique optimal law, and as the valve closure time increases, the range of optimal laws becomes narrower.

Dynamic stress responses of saturated soil around a fluid-filled lined tunnel caused by a water hammer are investigated by a frequency-domain FEM-BEM coupled model. The fluid is modeled as an inviscid and compressible fluid, the lining is modeled by elastic medium and conceptualized as a hollow cylinder of finite length, and the saturated poroelastic medium is adopted to model the soil. Initially, governing equations of fluid and those of lining are solved by FEM in the frequency domain, while those of soil are solved by BEM in the same domain. In the following, fluid, lining, and soil are coupled based on the conditions of deformation compatibility and force balance on their interfaces. Water pressure (inside the tunnel), the distribution of lining displacement and dynamic stress responses of saturated soil generated by the water hammer are presented. It is concluded that the dynamic stresses and the pore pressure change periodically in saturated soil under a water hammer. Modeling soil as an elastic medium inaccurately evaluates the distribution of lining displacement. The soil permeability has a significant influence on the normal stresses of soil and pore pressure but has a slight effect on the shear stresses of soil.