## 1 Introduction  
Penetrating and coring technology is an effective method for obtaining long columnar seabed sediment cores, which is widely used in marine mineral resource exploration, ocean and climate observation, marine geology research and other fields [1, 2]. The Pressure Core Barrel (PCB) used in the International Deepsea Drilling Program recovered a 6.8 m core [3]. Additionally, the International Ocean Drilling Program's PCS and EU-Fugro's FPC collected multi-meter sediment cores per sampling [4, 5, 6, 7, 8]. Currently, the main target of the penetrating and coring projects in marine mineral resource exploration is to gather quantitative samples at a certain depth below the seabed, while analysis focused on the penetration process should be strengthened. In future exploration, this traditional penetrating mission may be displaced by miniaturized and precision-optimized coring technology integrated with Remotely Operated Vehicles (ROVs) [9; 10], creating a demand for research on penetration performance of penetrators in clay within the deep-sea environment. Experimental approaches have been applied to investigate the penetration performance in previous studies. Particle Image Velocimetry (PIV) was used as a visualization tool to monitor the penetration mechanics of bucket foundations and quantify soil deformation characteristics [11; 12]. While all PIV implementations were conducted under two-dimensional plane-strain conditions, these fundamental limitations created a significant discrepancy between experimental findings and the three-dimensional real-world scenarios encountered in practical engineering applications. Meanwhile, [PERSON] et al. and [PERSON] et al. investigated the lateral bearing response of offshore wind turbine systems through centrifuge testing [13; 14]. Additionally, [PERSON] et al. and [PERSON] et al. conducted a series of centrifuge tests to investigate the bearing capacity of spudcan foundations for offshore jack-up drilling platforms [15; 16]. Centrifuge testing incurs prohibitively high costs and faces significant challenges in observing soil deformation within scaled models. Furthermore, the deep-sea environment cannot be fully simulated in laboratory settings, highlighting the limitations of the experimental approaches. In addition to experimental approaches, the Finite Element Method (FEM) has also been applied to analyzing the penetration process with large deformation clay. Traditional FEM faces severe mesh distortion during large deformation penetration analysis, causing computational errors and convergence issues. Advanced techniques like RITSS (Remeshing and interpolation technique with small strain model), ALE (Arbitrary Lagrangian-Eulerian), and CEL (Coupled Eulerian-Lagrangian) methods have been developed to address these limitations. When simulating interactions between mechanical structures and soil in marine engineering, such as pipeline launching, spudcan penetration, and anchors installation, the CEL method has been widely and efficiently used as RITSS involves intensive computations and ALE introduces artificial interface artifacts [17]. [PERSON] et al. proposed a Coupled Eulerian-Lagrangian (CEL) numerical simulation method to model spudcan penetration tests, successfully reproducing the penetration behavior observed experimentally [18]. [PERSON] et al. simulated the deep burial process of a T-shaped rod in soft clay using the CEL method, and the simulated penetration resistance agreed with the previous centrifugal test data [19]. [PERSON] et al. effectively conducted CEL modelling to evaluate installation-phase penetration resistance mechanics for bucket foundations in clay deposits [20]. The CEL method has been proved to be an effective approach for analyzing penetration performance of mechanical structures in soil, including aspects like penetration resistance and soil flow characteristics.