# Research on Predicting the Mechanical Characteristics of Deep-Sea Mining Transportation Pipelines
## 1 Introduction  
With the continual growth in global demand for mineral resources, deep-sea mining has become an important direction for resource development. The seabed is rich in mineral resources, including polymetallic nodules, cobalt-rich crusts, and hydrothermal sulfides [1; 2]. However, its development faces numerous technical challenges. Among these, the deep-sea mining transportation system plays a crucial role in deep-sea mining. This system, responsible for transporting seabed ore or slurry to the surface, is a central hub directly affecting mining efficiency and system safety [3]. The deep-sea mining transportation system connects the mining vehicle, intermediate storage, and the surface mothership through pipelines, with seabed collected slurry transported via flexible soft hoses and lifting hard pipes [4]. In the deep-sea environment, the transportation pipelines are subjected to various loads, including their own weight, buoyancy, forces from waves and currents, resistance and pressure from seawater. Studying the force situation of transportation pipelines and effectively predicting other mechanical parameters based on existing monitoring data to ensure the pipelines operate within a safe load range has significant implications for designing mining operation schemes, mining vehicle path ranges, and pipeline material performance. Due to the extreme complexity of the deep-sea environment, deep-sea mining experiments require significant financial and human resources and need to address many uncontrollable risks. Establishing mathematical models of ocean environments and system equipment through numerical simulation to study the stress conditions of transportation pipelines can yield vast amounts of simulation data for constructing predictive models ofpipeline mechanical characteristics. Currently, numerical simulation methods for calculating pipeline stress primarily include the concentrated mass method [5], finite difference method [6], and finite element method [7]. In the study of lifting hard pipe mechanics, American scholars such as [PERSON], [PERSON], and [PERSON] have employed the finite element method to analyze the kinematic and dynamic characteristics of a 5486 m long lifting hard pipe [8; 9; 10; 11; 12]. They used three-dimensional beam elements to build the model, which is capable of axial, bending, and torsional coupled deformation. The pipeline model includes 18 elements, 19 nodes, and 114 degrees of freedom. In subsequent studies by [PERSON] et al., the finite element method was further applied to research the static and dynamic behavior of deep-sea mining lift pipes and their attachments [13; 14; 15]. To reduce the vibration effects of marine hydrodynamics on lifting pipes, [PERSON], [PERSON], and others designed several elastic damping connection devices on the pipeline and modeled the pipeline system using the finite element method and mass-spring element method for static and dynamic analysis [16; 17; 18; 19; 20]. Moreover, [PERSON], [PERSON], [PERSON], and others used the Discrete Element Method (DEM) for the kinetic analysis of deep-sea mining lift pipes under 2D axial and bending coupling. This discrete element pipe description method is based on a system composed of rigid bodies connected by concentrated axial and bending stiffness. [PERSON] and others conducted four nonlinear dynamic analyses with a 2D DEM model of an 5486 m deep-sea mining pipeline [21; 22]. [PERSON] applied the Discrete Element Method to calculate a 1905 m long marine vertical pipeline, including axial and bending deformations, and compared the results with the finite element method and analytical method [23]. [PERSON] based on the concentrated mass method and incremental iterative method, conducted a three-dimensional dynamic analysis of the deep-sea subsea mining lift pipe system, completing axial forced vibration in a vertical state and three-dimensional nonlinear dynamic analysis within the time domain [24; 25].