Analysis of Penetration Performance Between a Hollow Penetrator and Seabed Clay by Coupled Eulerian–Lagrangian Method

Abstract

Penetrating and coring technology is a critical approach for acquiring undisturbed long-columnar seabed sediment samples. The configuration and parameters of the penetrator structure directly affect penetration performance during the penetration process, which is critical for revealing penetration mechanics. A hollow penetrator structure was proposed, and its finite element model was built using the Coupled Eulerian–Lagrangian method with seabed clay to investigate the penetration performance. The penetration resistance exerted externally on the structure, the mean pressure distribution in the soil, and the soil flow after the penetration process were the main characteristics of the penetration performance. Sensitivity analysis on penetration velocity was carried out to balance the accuracy and the efficiency of the penetration simulation. Effects of penetrator structure parameters were assessed. Based on the simulations, the penetrator with a 15° penetrating head angle exhibited the minimum final penetration resistance, and the end face of the penetrating head had little effect on the soft clay penetration process. The diameter of the penetrator had a significant impact on the mean pressure distribution, and there was an almost linear relationship between its diameter and the penetration resistance. The results could provide critical evidence for optimizing the design of seabed sampling equipment.

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, X. Wang et al. and P. Ma et al. investigated the lateral bearing response of offshore wind turbine systems through centrifuge testing [13,14]. Additionally, Hossain et al. and Teh 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]. P. Hu et al. proposed a Coupled Eulerian–Lagrangian (CEL) numerical simulation method to model spudcan penetration tests, successfully reproducing the penetration behavior observed experimentally [18]. T. Wang 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]. W. Tu 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.

The purpose of this study is to investigate the penetration performance between a penetrator structure and seabed clay, including the penetration resistance exerted externally on the structure, the variation in soil mean pressure and the soil flow, in order to develop a low-disturbance penetrator structure suitable for the deep-sea environment. Firstly, a hollow penetrator structure was presented, and its finite element model was developed using the CEL method. Secondly, sensitivity analysis of penetration velocity was assessed to determine an appropriate velocity value, considering both the accuracy and the efficiency of the simulation. Finally, simulations of the penetration process were carried out under different penetrator structure parameters. The results of this study can improve the understanding of the penetration mechanics between a hollow penetrator structure and seabed clay, and provide critical evidence for optimizing the design for subsea excavation equipment.

2. Finite Element Model

2.1. 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. Parameters of the penetrator structure and penetration performance.

Parameter	Description	Value or Normalization
D	Diameter of the penetrator structure	D = 74 mm
L1	Height of the penetrating head	$L_1={\displaystyle \frac{D}{2\tan \alpha }}·0.25$
L2	Height of the penetrating tube	/
L	Height of the penetrator structure, which is equal to the sum of L1 and L2	L/D
b	Width of the end face on the penetrating head	b/D
α	Angle of the penetrating head	/
dp	Depth of the penetration process	dp/D
hs	Height of the soil heave	hs/D
ls	Distance from the penetrator structure to the margin of soil heave	ls/D
Fend	Resistance of the end face of the penetrator structure	/
Fside	Resistance of the side of the penetrator structure	/
Ftotal	Combination of Fend and Fside	/

. 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.

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.

2.2. FE Model Using the CEL Method

In geotechnical numerical analysis, soil is defined by an elastoplastic model. In ABAQUS, the elastic model and the plastic model are defined separately. This study adopts a combined Mohr–Coulomb model and linear elastic model. The linear elastic stress–strain relationship for soil is expressed as Equation (1).

$$\left\{\begin{array}{c}{\epsilon }_{11}\\ {\epsilon }_{12}\\ {\epsilon }_{13}\\ {\gamma }_{11}\\ {\gamma }_{12}\\ {\gamma }_{13}\end{array}\right\}=\left[\begin{array}{cccccc}\hfill 1/E& \hfill -\nu /E& \hfill -\nu /E& \hfill 0& \hfill 0& \hfill 0\\ \hfill -\nu /E& \hfill 1/E& \hfill -\nu /E& \hfill 0& \hfill 0& \hfill 0\\ \hfill -\nu /E& \hfill -\nu /E& \hfill 1/E& \hfill 0& \hfill 0& \hfill 0\\ \hfill 0& \hfill 0& \hfill 0& \hfill 1/G& \hfill 0& \hfill 0\\ \hfill 0& \hfill 0& \hfill 0& \hfill 0& \hfill 1/G& \hfill 0\\ \hfill 0& \hfill 0& \hfill 0& \hfill 0& \hfill 0& \hfill 1/G\end{array}\right]\left\{\begin{array}{c}{\sigma }_{11}\\ {\sigma }_{22}\\ {\sigma }_{33}\\ {\sigma }_{12}\\ {\sigma }_{13}\\ {\sigma }_{23}\end{array}\right\}$$

(1)

In Equation (1), E represents the elastic modulus of the soil. G represents the shear modulus of the soil. The relationship between G and E is G = E/[2/(1 + υ)], and υ represents the Poisson’s ratio of the soil.

In the Mohr–Coulomb model, the plastic failure of soil materials is governed by shear stress, as shown by the undrained shear strength, S_u, in Equation (2).

$$S_{\mathrm{u}}=c+\sigma \tan \phi$$

(2)

In Equation (2), c represents the cohesion of the soil, and φ represents the internal friction angle of the soil. Normal stress, σ, can be simplified to the self-weight stress of the soil at a certain depth, as σ = γd_p, where γ represents the unit weight of the soil and d_p represents the depth of the soil.

F_side and F_end are the integral results of the stresses exerted on the sidewall and the end face of the penetrator structure. In Abaqus, this process is accomplished through the Explicit Stress Integration Algorithm.

2.3. Soil Constitutive Model and Mean Pressure

The soil model was provided in Abaqus for the penetration process, incorporating the following characteristics:

(1)

The clay was modelled as an undrained elastic–perfectly plastic material during the penetration process, which was described by the Tresca yield criterion with an associated flow rule;

(2)

The strain rate of the soil was not considered in this study;

(3)

The penetration process was conducted using a displacement-controlled method.

Marine clay deposits are usually non-homogeneous and exhibited linear variation of S_u with depth [27]. The relationship between the undrained shear strength of the soil, S_u (kPa), and depth, z (m), is S_u = S_um + k z, where S_um (kPa) is the soil undrained shear strength at the ground surface and k (kPa/m) represents the rate of increase in shear resistance with depth. In general, the linear gradient k of S_u with depth ranges between 0 and 3 [28]. Chen reported that the undrained shear strength of seafloor sediments in the South China Sea ranges from 1 to 3 kPa [29]. S_um = 2.0 and k = 1 were considered in this analysis to ensure the value of S_u was the same as that of seafloor sediments in the South China Sea. The other parameters of the soil were also under consideration. The effective soil weight was adopted as γ = 8.7 kN/m³. The elastic modulus of the soil, E, was 500 times that of S_u, and Poisson’s ratio, υ, was taken as 0.499 [30]. The penetrator structure was penetrated using a displacement-controlled method with a soil–structure interface friction coefficient of 0.25. In the numerical simulation, it was modelled as a rigid body to simplify computational analysis.

Although the Explicit module of ABAQUS cannot explicitly account for pore water pressure, the soil mean pressure is presented as it effectively represents pore water pressure behavior [31]. Figure 4 illustrates the mean soil pressure before penetration. The results demonstrate that the mean pressure increases linearly with depth, attaining a maximum mean pressure (σ_m) of 315.3 Pa.

2.4. Validation of the Method

The Coupled Eulerian–Lagrangian (CEL) methodology was applied in this study to investigate the large deformation behavior of an undrained soil constitutive model. This CEL methodology was conducted through comparative evaluation of pipe penetration behavior with RITSS method predictions and centrifuge model test results [32,33]. With a pipe diameter (D_p) of 0.8 m, the soil’s undrained shear strength (S_u) followed the relationship S_u = 2.3 + 3.6z kPa, where z represented depth. The effective unit weight of the soil was 6.5 kN/m³, and the pipe–soil interface exhibited a friction coefficient of 0.3. The penetration velocity of the pipe was set at 1/20th of its diameter (40 mm/s). This CEL model was assessed in this study, as shown in Figure 5. The vertical resistance, V (N), was normalized by D_pS_u, and the pipe displacement, W (m), was normalized by D_p, while D_p was the diameter of the pipe and S_u was the undrained shear strength of the soil. The results simulated by the CEL method closely aligned with the predictions of the RITSS method and the centrifuge model test. Therefore, the CEL method can be effectively applied to simulate the penetration process of the penetrator under large soil deformation in this study.

3. Sensitivity Analysis of Penetration Velocity

Empirical evidence from Wang et al. [34] demonstrates that the performance of the CEL method is affected by the penetration velocity, as it can be very time-consuming to simulate the actual penetration process with the real penetration velocity. Thus, sensitivity analysis of the CEL method on penetration velocity needs to be conducted to identify the optimum penetration velocity. Four different penetration velocities, v = 7.4 mm/s, 5.55 mm/s, 3.7 mm/s, and 1.85 mm/s, were considered in this study. The penetration resistance of the penetrator structure is shown in Figure 6, where α = 15°, b/D = 0.027, and L₂ = 160 mm.

F_end exhibited identical behavior for d_p/D = 0.25; however, beyond a normalized depth of 0.25, F_end exhibited a positive correlation with velocity and demonstrated asymptotic convergence toward a stable value. The interaction between the end face of the penetrator and the soil could be regarded as a process of compression deformation. Since the soil was modelled as an elastic–perfectly plastic material, the soil was elastically deformed when d_p was low at the beginning of the penetration process, and F_end presented a linear relationship with d_p rather than penetration velocity. When d_p was larger than the elastic deformation displacement limit of the soil, the soil was compressed due to plastic deformation. As the kinetic energy of the penetrator structure increased with its velocity, the interaction between the penetrator and the soil became more intense, resulting in an increase in soil deformation and the resistance of the end face on the penetrator, F_end.

The trend in F_side was consistent before d_p/D = 1.0. When d_p/D > 1.0, F_side showed positive correlations with velocity. F_side is mainly the friction between the side face of the penetrator structure and the hole wall of the soil during the penetration process. As shown in the above analyses, the normal pressure between the side face of the penetrator structure and the hole wall of the soil increased as its normal pressure increased when the soil was plastically deformed beyond its elastic deformation displacement limit. Combined with the parameters of the penetrator structure, the coring tube was in contact with the hole wall to create friction when d_p/D = 1. When d_p/D > 1, F_side was positive with respect to penetrating velocity due to the increase in friction. However, the interaction between the side face of the penetrator structure and the hole wall of the soil was instability due to the flow of the soil during the penetration process. As a result, the increase in F_side presented a disturbing phenomenon. The value of F_total was not significantly different, as the maximum average deviation of penetration resistance did not exceed 10%, which showed that the resistance was slightly influenced by the velocity effect.

The mean pressures at maximum penetration depth at four different penetration velocities were analyzed, as shown in Figure 7. Based on the pressure variations in the soil induced by penetration, Zone II can be meticulously subdivided into Zone II-1, Zone II-2 and Zone II-3. Zone I presents the most pronounced soil compression with the highest pressure, with its minimum pressure being 13.2 times σ_m. Zone II-1 represents the second partitioned mean pressure area, exhibiting lower pressure compared with Zone I, with its minimum pressure being 10.3 times σ_m. Zone II-2 constitutes the third partitioned mean pressure area, characterized by reduced pressure compared with Zone II-1, with its minimum pressure being 2.65 times σ_m. Zone II-3, as the fourth partitioned mean pressure area, corresponds to the minimum pressure level, with its minimum pressure being 1.3 times σ_m. In this study, the area outside Zone II-3 is not studied, where the interaction between the penetrator and the soil is ignored. Amongst the four different penetration velocities, the maximum pressure was 15.9 times that of σ_m, the distribution pattern of mean pressure was generally consistent, and the size of Zone I also remained relatively consistent. When the velocity was 1.85 mm/s, the entire area of mean pressure was slightly larger.

To investigate the influence of velocity on soil behavior, the performance of the soil heave at four different depths was analyzed (with normalized penetration depths for d_p/D = 0.49, 0.96, 1.43, and 1.89), as shown in Figure 8. The height of the soil heave, h_p, exhibited a positive correlation with penetration depth. Furthermore, with increasing penetration velocity, the soil heave became more pronounced. The penetration velocity of 7.4 mm/s was four times that of 1.85 mm/s, and the h_p at different depths was approximately two times higher.

Due to the balance between CEL computational efficiency and the characteristic of the penetration performance, the proper penetration velocity was set to 7.4 mm/s in subsequent analyses. On the one hand, higher penetration velocity causes more pronounced soil heave, facilitating the observation of soil flow, while the resistance on the penetrator structure and the mean pressure of the soil are not sensitive to penetration velocity. On the other hand, the CEL computational efficiency at a penetration velocity of 1.85 mm/s is four times that of 7.4 mm/s.

4. Parametric Study of Penetrator Structure on the Penetration Performance

The parameters of the penetrator structure will affect the penetration performance during the penetration process. In this section, cross-simulation of penetrating head parameters was carried out first, including α (the angle of the penetrating head) and b (the width of the end face on the penetrating head), set as shown in

Table 2. Penetrating head parameters in cross-simulation.

Parameter	Value	Normalized Value
α	5°, 15°, 30°	/
b	2 mm, 4 mm, 6 mm, 10 mm	0.027, 0.054, 0.081, 0.135

. Then, the effect of the diameter on the penetration performance was presented through the normalized parameter, length/diameter ratio.

4.1. Effect of the Parameter of the Penetrating Head

The results of the penetration resistance with different parameters combinations are presented in Figure 9, Figure 10 and Figure 11. As d_p/D increased, F_end demonstrated a progressive increase and converged to a stable value, while F_side was positively correlated with d_p/D through the entire penetration process. This phenomenon could be attributed to the progressive increase in lateral contact area between the penetrator structure and the soil with advancing penetration depth, resulting in a positive correlation between F_side and penetration depth. In contrast, the basal contact area remained constant throughout the process, while the compressive pressure between the end face of the penetrator structure and the soil could be regarded as constant. Combining F_end and F_side, the F_total on the 15° penetrating head angle penetrator structure became the smallest among all the penetrator structures when d_p/D was approximately 1.0.

A boundary line was drawn to divide the penetration process into penetration area I and penetration area II, as shown in Figure 11. The value of the boundary line exhibited a continuous increase with the progressive augmentation of parameter b/D. At penetration area I, the penetration resistance with the 5° penetrating head angle was the smallest and the 30° penetrating head angle was the largest. At penetration area II, the penetration resistance with the 15° penetrating head was the smallest, and that with the 5° penetrating head was the largest. The simulation results of this study were similar to those of Shen Yi [35], which focused on the penetration mechanics between a penetrator and the lunar soil for extraterrestrial planetary explorations. It explored α = 15° as the optimal angle for the development of a low-disturbance penetrator structure in the deep-sea environment.

The mean pressure under different angles on the penetrating head is shown in Figure 12, when d_p/D = 1.89. Under the same value of b/D, the area of mean pressure for the 30° penetrating head angle penetrator structure was significantly larger than that of the 5° and 15° penetrating head angle penetrator structures, with the 5° penetrating head angle penetrator structure exhibiting the smallest extent. However, for Zone I, the area under the 15° penetrating head angle penetrator structure was the smallest (approximately half of that under the 30° penetrating head angle penetrator structure). This further indicated that the penetrator–soil interaction under the 15° penetrating head angle penetrator structure was more moderate.

As shown in Figure 9, the larger the value of b/D, the greater the F_end, and F_end tended to converge. However, the value of F_end showed no significant variation, which may be attributed to the low undrained shear strength of the soil, resulting in a decreased sensitivity to b/D. Among the four different values of b/D in the current study, the F_end under the 5° penetrating head angle penetrator structure was the largest. Furthermore, as b/D increased, the F_end values for the three different penetrating head angle penetrator structures became closer.

4.2. Effect of Width of the End Face on the Penetrating Head Under Higher S_u Condition

In order to increase the sensitivity of b/D, the S_um was stabilized at 20 kPa, which is 10 times the previous value, while the other parameters remained the same as in Section 3. The effects between 2.0 kPa and 20.0 kPa S_um on penetration resistance are shown in Figure 13. Under the two S_um conditions, the trend in penetration resistance remained consistent, showing a positive correlation with b/D, though numerical deviations became more significant at higher S_um values. The multiple of the increase in penetration resistance value was basically consistent with the multiple of the increase in S_um.

When d_p/D was 0.026, the penetration resistance showed a drop at different b/D conditions, which might be caused by the plastic compaction of the soil. Taking the penetrator structure, where α = 15° and b/D = 0.135, under 20.0 kPa S_um condition as an example, the mean pressure characteristics during the compaction process are shown in Figure 14. When d_p/D = 0.026, the penetration resistance reached its maximum, and the corresponding mean pressure peak was also at its highest. At d_p/D = 0.037, the penetration resistance decreased, accompanied by a reduction in the mean pressure peak. At d_p/D = 0.074, both the penetration resistance and mean pressure peak rebounded, and by d_p/D = 0.095, they returned to their maximum levels. It is clear that the mean pressure at the tip of the penetrator structure changed throughout the cycle due to plastic compaction of the soil.

4.3. Effect of the Length/Diameter Ratio of the Penetrator Structure

To study the effect of penetration performance on length-to-diameter ratio of the penetrator structure, four different length-to-diameter ratios, L/D = 3.45, 2.65, 1.85, and 1.05, were considered by adjusting D, D = 57 mm, 74 mm, 106 mm, and 187 mm, based on the diameter of drill pipes for the mineral resource exploration mission described above. The penetration resistance at four different L/D ratios is shown in Figure 15, when the other parameters remained the same as in Section 3.

It is evident that in different penetrator structures, the penetration resistance increased with the depth of penetration. The trend in F_total aligned with F_side, and F_end tended to converge. However, the smaller the L/D ratio, the greater the penetration resistance, and the more pronounced its growth. At d_p/D = 1.89, the F_total for the minimum L/D ratio was 4.8 times that of the maximum L/D ratio.

The penetration resistance is governed by the contact area between the penetrator and the soil. The following relationships can be formulated in this case, including the area of the end face on the penetrating head and the area of the side of the penetrating head, as shown in Equation (3).

$$\left\{\begin{array}{c}{S}_{end}=\pi b(D-b)\\ S_{side}=2\pi ·d_p\left(D-d_p\tan \alpha \right)\sqrt{4{\tan }^2\alpha +1}+\pi D\left(d_p-L_1\right)\end{array}\right.$$

(3)

However, the relationship between the penetration resistance and penetrator diameter from the FEM results was not the simple linear relationship shown in Equation (3). As shown in Figure 16, the growth rate of penetration resistance relative to diameter varied: when the diameter was smaller (or L/D was greater), the growth rate was lower; when the diameter was larger (or L/D was smaller), the growth rate was higher. While Equation (3) could explain the overall trend of increasing force, it could not account for all aspects of the penetrator–soil interaction mechanism, such as differences in the compression deformation process on the penetrator end face under different L/D ratios.

The mean pressure at maximum penetration depth for four different diameters is shown in Figure 17. As the L/D ratio decreased, the area of mean pressure gradually increased, while Zone I progressively diminished. When L/D = 1.05, Zone I nearly disappeared. Under a larger L/D ratio, the interaction between the penetrator structure and the soil tended to increase, while the unit action intensity increased, resulting in higher mean pressure. For a smaller L/D ratio, although Zone I (the primary interaction zone) was minimized, the penetrator structure influenced a significantly larger soil area. The resistance acting on the penetrator structure could be considered as an integration of the in situ mean pressure. Due to the substantial difference in integration domains (smaller L/D with higher pressure concentration vs. larger L/D with wider pressure distribution), it manifested as an inverse relationship between mean pressure and resistance—higher mean pressure with larger L/D corresponded to lower resistance, while smaller L/D with lower mean pressure produced higher resistance.

The performance of soil heave after the penetration process is shown in Figure 18. As D increased (L/D ratio decreased), the area of the interaction increased, h_s became relatively larger, and the soil heave became more pronounced. The height of the soil heave, h_s, and the distance from the penetrator structure to the margin of soil heave, l_s, were normalized by L since the value of D varied for different L/D ratios in this section. As a result, h_s/L was 0.0667, 0.0711, 0.072 and 0.073 when L/D was 3.45, 2.65, 1.85 and 1.05. In addition, the cross-sectional area of soil heave, S_soil, was 0.0128, 0.0135, 0.0147 and 0.0165 at different L/D ratios. These data also show that as the L/D ratio decreased, the flow of the soil increased.

5. Conclusions

This study focused on the penetration process of a hollow penetrator structure in seabed clay based on the CEL method. A finite element model was developed to simulate the interaction between the penetrator structure and the seabed clay, with a sensitivity analysis of penetration velocity. The effects of penetrator structure parameters were investigated. The main conclusions are drawn as follows:

• The CEL large deformation method effectively simulated the penetration processes, with the resistance of the side of the penetrator structure increasing synchronously with depth, while the resistance of the end face of the penetrator structure converged marginally.
• The kinetic energy of the penetrator structure critically influenced soil flow, while penetration resistance and mean pressure remained almost constant under different velocity conditions. Balancing computational efficiency with simulation accuracy for penetration performance, the penetration velocity was set at 7.4 mm/s.
• The penetrator structure with a 15° head angle achieved the minimal penetration resistance as depth increased progressively. This angle can be considered the optimal choice for developing a low-disturbance penetrator structure in the deep-sea environment.
• Plastic deformation of the in situ soil primarily occurred at the end face on the penetrating head. The width of the end face on the penetrating head (b/D) was the key parameter governing the area of the interaction region. When S_um was small, b/D had little effect on F_end; however, at 10 times S_um, F_end showed a positive correlation with b/D.
• The decrease in L/D ratios proportionally amplified both the penetration resistance and the soil heave characteristics. The selection of the penetrator structure diameter depends not only on the penetration performance described in this study but also on the requirements for soil sample collection in mineral resource exploration missions.

These results provide significant guidance for understanding the penetration mechanics between a hollow penetrator structure and seabed clay, as well as for optimizing the penetrator structure design. This study primarily discussed the penetration resistance exerted externally on the penetrator. However, some limitations remain: internal soil flow and the sample core will generate internal penetration resistance, affecting penetration performance; real-world conditions such as dynamic subsea condition, pore water pressure, or interactions with ROV-mounted systems will cause disturbance to the seabed clay, causing non-convergence of penetration resistance. These are aspects requiring investigation in future research.