## 2 Finite Element Model  
### Model Description  
The penetrating and coring mechanism consists of a penetrating tube, a penetrating head, a sealing system with a ball valve, and a coring tube, as shown in Figure 1. Since this study primarily focuses on the penetration resistance exerted externally on the mechanism, the sealing system and the coring tube are simplified in subsequent analyses. The penetrator-soil interaction is shown in Figure 2. The definitions of the parameters illustrated in Figure 2 are presented in Table 1. According to the International Deep Sea Drilling Project (DSDP) and the Ocean Drilling Program (ODP), the standard diameter of drill pipes is typically 127 mm, with core diameters ranging from 51 mm to 86 mm [3; 4; 5]. This study focuses on a penetration diameter of 74 mm as the research subject.  
Figure 1: The penetrating and coring mechanism. It consists of a penetrating tube, penetrating head and sealing system. The area enclosed by the red dashed line represents the sealing system by a ball valve, and a coring tube.  
Figure 2: Illustration of the penetrator–soil interaction. \(F_{\text{end}}\) represents the resistance of the end face of the penetrator structure, due to the shear stress of clay on the end face of the penetrator structure during the penetration process. \(F_{\text{side}}\) represents the resistance of the side of the penetrator structure, a resultant force of the contact stress and friction force between the sidewall of the penetrator structure and the clay. The red line is the boundary between Zone I and Zone II. The blue line is the boundary between Zone II and the non-affected area. Zone I is the direct interaction area between the penetrator and the soil. Zone II represents the indirect interaction area.  
For undrained clay, the mean pressure, defined as one-third of the sum of principal stresses, is a critical parameter due to its direct correlation with pore water pressure. Based on the distribution of mean pressure after the penetration process, the penetrator-soil interaction zones can be categorized into Zone I and Zone II, as shown in Figure 2. Zone I is the direct interaction area between the penetrator and the soil, where the soil is squeezed, resulting in a significant increase in mean pressure. Zone II represents the indirect interaction area, where the mean pressure exceeds its original plastic stress.  
The finite element model (FEM) simulating the penetration process was developed in Abaqus 2022 software using the Coupled Eulerian-Lagrangian (CEL) method, where a symmetric model configuration was adopted to enhance computational efficiency [21; 22]. The axisymmetric geometric model is detailed in Figure 3. To mitigate boundary effects [23; 24], the finite element mesh of the soil domain was assigned dimensions of \(6D\) in radius and \(10D\) in height. A void layer was placed on top of the seabed to enable the soil to flow into the Eulerian elements during the penetration process [25; 26]. The boundary conditions for the normal direction at the bottom and periphery of the soil domain were set to zero velocity, ensuring that the Eulerian material remained within the Eulerian domain.