Experimental and Numerical Analysis of PIP Slip Joint Subjected to Bending

<jats:p>Detachable circular hollow sections (CHSs) offer an innovative solution to tackle the complexities of installation, maintenance, upgrades, and repairs in offshore monopile systems, particularly in challenging environments with limited access. As an alternative to traditional tubular joints, the PIP slip joint presents advantages in terms of ease of installation, time efficiency, and reduced susceptibility to failure. This study conducts an experimental investigation on PIP (Pile-in-Pile) slip joints under pure bending conditions, accompanied by comprehensive numerical analyses to examine the relationship between section slenderness, contact properties, and structural performance. The results highlight a strong correlation between force-displacement curves and include a comparison of compressive and tensile strain values for both experimental and numerical models. The experimental and numerical models showed strong agreement across all results, demonstrating the robustness of the findings. Additionally, numerical models were utilized to investigate various D/t ratios, revealing insights into the normalized moment, rotational capacity, and the impact of local buckling and contact mechanics. Furthermore, a comparison of these findings with established code guidelines, such as Eurocode and AISC-LRFD, has been conducted and reviewed in the context of this study. From analysis, it was found that the rise in the D/t ratio prompted a transformation in the buckling mode, which substantially altered the rotational ratio. This shift indicates the importance of understanding how these variables interact in engineering applications. These findings significantly enhance the understanding of PIP slip joints and emphasize their potential as a compelling alternative for offshore wind turbine support structures.</jats:p>

section_content: Offshore wind turbines are supported by various foundations, each with its own considerations in design and construction. The exploration of fixed offshore support structures, such as monopiles and jackets, alongside floating platforms like spar-buoy, semi-submersible, and tension leg platforms, is crucial for advancing the global shift towards renewable energy [1, 2]. Investing in these innovative technologies not only enhances energy efficiency but also fosters sustainable development, paving the way for a cleaner and greener future. Among them, steel monopiles have dominated the offshore wind turbine support structures market in the last two decades. Despite having thin walls, monopiles can take a considerably large amount of load. Moreover, their ability to reduce hydrodynamic and aerodynamic drag and uniformly distribute stress makes them structurally more effective than other support structure systems. Additionally, because of their easy fabrication and installation process, they are a cost-effective solution in the wind industry [3] [4] [5] [6] [7]. However, since monopiles are primarily used as support structures in offshore systems, installation, maintenance, and repair will be hindered due to the lack of easy access. In this case, detachable joints can facilitate easier access, thus enhancing the effectiveness of installation, maintenance, and repair. This type of properly designed detachable joint can also provide advantages for structural safety and integrity by allowing controlled dissipation of stress and loads. 

The most commonly used joint mechanism to attach two tubular sections is the use of preloaded high-strength bolts with ring flanges [8]. Nevertheless, the multitude of failure mechanisms has rendered it particularly susceptible to improvement. Moreover, when manufacturing the flange, it is crucial to incorporate a slope on the flange surface. It's important to note that this slope could potentially lead to adverse effects on the stress distribution of the bolts [9, 10]. Tran et al. (2023) also developed a finite element model and verified its accuracy through experimental test results to investigate the influences of geometrical imperfections on the structural response using the same loading conditions and material properties [11]. Shaheen et al. (2020) have provided a comprehensive analysis of the failure mechanisms associated with various grade bolts, outlining five distinct failure mechanisms [12]. In their 2023 study, Ji et al. (2023) delved into the critical impact of initial flatness divergence on the structural response of flange connections in offshore wind turbines. Their findings underscore the profound implications of this factor on fatigue damage, shedding light on the urgent need for further attention and proactive measures in this area [13]. Furthermore, it's crucial to consider potential challenges during the installation process, including misalignment and the risk of under-or over-tightening when setting up an L-type flange joint. Similarly, the time-consuming process of assembling and disassembling the L-type flange joint can have a significant impact on project timelines and costs. When considering the available alternative options, slip joints stand out as the simplest and most promising choice. The idea behind a slip joint is rather intuitive, resulting in a substantial reduction of installation and decommissioning time [14] [15] [16]. Additionally, frictional grip plays a crucial role in construction and has proven effective in various sectors [17]. Its application in offshore substructure joints could significantly enhance stability and safety. The efficient transfer of load between two circular hollow sections (CHSs) hinges upon the precise contact and frictional interplay between the two overlapping surfaces. This critical mechanism ensures the seamless and reliable distribution of forces, making it an indispensable factor in engineering and construction applications. In this case, installation efficiency, reduced maintenance, and facilitated decommissioning are also potential benefits. In light of this, Islam et al. (2024) undertook a study to pioneer a novel form of pipe-in-pipe (PIP) slip joint designed to withstand pure bending, as well as combined loadings, with a specific focus on addressing buckling [18, 19]. These studies focused on numerical analysis and were verified by comparing results with experimental analysis of tubular structures without any joints. To further strengthen this research, conducting an experimental analysis on PIP slip joints with overlapping lengths is essential, as it could provide a solid foundation for future studies. PIP (Pile-in-Pile) slip joints are unique structural joints that allow the contact surfaces of circular hollow sections (CHSs) to slip away from each other as shown in Figure 1. They involve connecting two overlapping hollow cylindrical sections, typically composed of piles with different diameters-one fitting inside the other-that can slide relative to each other. The length of the overlap is the critical parameter for resisting bending. In addition to the aforementioned benefits, this arrangement can mobilize the wind turbine structure in weather-sensitive situations and offers cost-effective maintenance and upgrade options. 

Numerous research and industrial institutes have diligently contributed their expertise to developing advanced methods for accurately predicting the lateral response of monopile foundations under diverse loading scenarios [20]. Therefore, the current experimental study is conducted to bolster the pure bending case and the findings of a previous study on the rotational capacity of PIP slip joints. 

The experimental analysis was conducted under simply supported beam conditions, applying displacement-controlled loadings. The strain and displacement at selected points were then analyzed and interpreted. Subsequently, the finite element model (FEM) was developed and compared with the experimental responses. Furthermore, the newly verified FEA model will be prepared through a rigorous process of comparison with the performed experiments, ensuring its accuracy and reliability. It is crucial to thoroughly check variations in strain at different points of the arrangement, as this will provide a comprehensive understanding of the behavior of the PIP slip joints under pure bending. Following the verified model, the study will be expanded to different D/t ratios, and the generalized section slenderness will be compared with the established design codes. During the investigation, it was observed that the bending capacity of the arrangement varied with changes in the D/t ratio, as the failure mechanism evolved as well. Additionally, frictional stress and pressure significantly influence the bending capacity of the slip joint arrangement. These findings greatly deepen the understanding of PIP slip joints, underscoring their promise as a viable and innovative alternative for supporting offshore wind turbines. The experimental analysis was conducted under simply supported beam conditions, applying displacement-controlled loadings. The strain and displacement at selected points were then analyzed and interpreted. Subsequently, the finite element model (FEM) was developed and compared with the experimental responses. Furthermore, the newly verified FEA model will be prepared through a rigorous process of comparison with the performed experiments, ensuring its accuracy and reliability. It is crucial to thoroughly check variations in strain at different points of the arrangement, as this will provide a comprehensive understanding of the behavior of the PIP slip joints under pure bending. Following the verified model, the study will be expanded to different D/t ratios, and the generalized section slenderness will be compared with the established design codes. During the investigation, it was observed that the bending capacity of the arrangement varied with changes in the D/t ratio, as the failure mechanism evolved as well. Additionally, frictional stress and pressure significantly influence the bending capacity of the slip joint arrangement. These findings greatly deepen the understanding of PIP slip joints, underscoring their promise as a viable and innovative alternative for supporting offshore wind turbines. 

For reader convenience, a Nomenclature and Abbreviation section is included in Tables 1 and 2 to clarify the terminology and symbols used throughout the manuscript. For reader convenience, a Nomenclature and Abbreviation section is included in Tables 1 and 2 to clarify the terminology and symbols used throughout the manuscript.
section_name: Introduction

section_name: Materials and Methods

section_content: The design incorporates inner and outer piles that are arranged to overlap. The overlap length, L o, measures 1400 mm, almost twice the inner pile's dimension. The total length (L) of the arrangement is 10,300 mm. Both CHS (circular hollow section) segments have a thickness (t) of 9. 5 mm. The loads are applied 3650 mm away from the support. The inner and outer piles have diameters of 715 mm and 734 mm, respectively. Therefore, the D/t ratio is 77. 26 and 74. 84, respectively. The specimen details are provided in Table 3. A two-dimensional representation of the arrangement is presented in Figure 2.
section_name: Geometry

section_content: Tangent
section_name: Et

section_content: The design incorporates inner and outer piles that are arranged to overlap. The overlap length, Lo, measures 1400 mm, almost twice the inner pile's dimension. The total length (L) of the arrangement is 10,300 mm. Both CHS (circular hollow section) segments have a thickness (t) of 9. 5 mm. The loads are applied 3650 mm away from the support. The inner and outer piles have diameters of 715 mm and 734 mm, respectively. Therefore, the D/t ratio is 77. 26 and 74. 84, respectively. The specimen details are provided in Table 3. A twodimensional representation of the arrangement is presented in Figure 2.
section_name: Geometry

section_content: This study conducted a meticulous four-point bending test to analyze the pure bending behavior of a PIP slip joint to create a pure bending region between the central loading points. To prevent early local buckling of the CHS structure, four substantial stiffeners, each with a 20 mm thickness, were expertly welded onto the specimens at both ends and
section_name: Experimental Setup

section_content: This study conducted a meticulous four-point bending test to analyze the pure bending behavior of a PIP slip joint to create a pure bending region between the central loading points. To prevent early local buckling of the CHS structure, four substantial stiffeners, each with a 20 mm thickness, were expertly welded onto the specimens at both ends and the loading points, as vividly illustrated in Figure 2. The boundary conditions of the total arrangement were considered as simply supported, ensuring the utmost accuracy and reliability of the results. The loading was displacement-based which was up to 150 mm. For data acquisition, 30 different strain gauges and three LVDTs were strategically employed, and the data logger ID was also provided in Figures 3 and 4. The total arrangement is divided into three distinct regions, each possessing unique properties to enhance clarity and precision. Region A represents the overlapping area, while Region B encompasses the loading part of the arrangement. Figure 4 illustrates the four-point bending test setup. Notable grid markings are present on the slip joint arrangement, which are utilized for accurately tracking the displacement. Utilizing a variety of colors, each section and component is clearly identifiable, enhancing both usability and efficiency. The specimen is secured in position with straps and a lifting mechanism. Central to the setup are vertical pneumatic pistons and loading beams, which are employed to apply displacement to the specimen and simulate bending. The ends of the specimen are supported by two saddles. 

arrangement were considered as simply supported, ensuring the utmost accuracy and reliability of the results. The loading was displacement-based which was up to 150 mm. For data acquisition, 30 different strain gauges and three LVDTs were strategically employed, and the data logger ID was also provided in Figures 3 and 4. The total arrangement is divided into three distinct regions, each possessing unique properties to enhance clarity and precision. Region A represents the overlapping area, while Region B encompasses the loading part of the arrangement. Figure 4 illustrates the four-point bending test setup. Notable grid markings are present on the slip joint arrangement, which are utilized for accurately tracking the displacement. Utilizing a variety of colors, each section and component is clearly identifiable, enhancing both usability and efficiency. The specimen is secured in position with straps and a lifting mechanism. Central to the setup are vertical pneumatic pistons and loading beams, which are employed to apply displacement to the specimen and simulate bending. The ends of the specimen are supported by two saddles.
section_name: Experimental Setup

section_content: To determine the steel material properties, three tensile coupons were cut from each pile and tested according to the Korean standard 'KS B 0802:2003' [21]. The details of the sample preparation are provided in Figure 4. From this coupon test, the yield strength (σs), ultimate tensile strength (σu), modulus of elasticity (Es), Poisson's ratio (υ), and the elongation (δ) were calculated. The tangent modulus (Et) was calculated from the acquired data and is used in FEA modeling for bilinear models. For the selection of strength parameters, the average and RMS values were calculated for different parameters. RMS is a robust statistical tool that provides a comprehensive measure of the size of data, their variability, and their effective value, making it suitable for a wide range of applications over the average value [22]. Therefore, the RMS value was utilized while modeling the PIP arrangement for verification. These strength parameters are presented in Table 4. the loading points, as vividly illustrated in Figure 2. The boundary conditions of the total arrangement were considered as simply supported, ensuring the utmost accuracy and reliability of the results. The loading was displacement-based which was up to 150 mm. For data acquisition, 30 different strain gauges and three LVDTs were strategically employed, and the data logger ID was also provided in Figures 3 and 4. The total arrangement is divided into three distinct regions, each possessing unique properties to enhance clarity and precision. Region A represents the overlapping area, while Region B encompasses the loading part of the arrangement. Figure 4 illustrates the four-point bending test setup. 

Notable grid markings are present on the slip joint arrangement, which are utilized for accurately tracking the displacement. Utilizing a variety of colors, each section and component is clearly identifiable, enhancing both usability and efficiency. The specimen is secured in position with straps and a lifting mechanism. Central to the setup are vertical pneumatic pistons and loading beams, which are employed to apply displacement to the specimen and simulate bending. The ends of the specimen are supported by two saddles.
section_name: Material Properties

section_content: To determine the steel material properties, three tensile coupons were cut from each pile and tested according to the Korean standard 'KS B 0802:2003' [21]. The details of the sample preparation are provided in Figure 4. From this coupon test, the yield strength (σs), ultimate tensile strength (σu), modulus of elasticity (Es), Poisson's ratio (υ), and the elongation (δ) were calculated. The tangent modulus (Et) was calculated from the acquired data and is used in FEA modeling for bilinear models. For the selection of strength parameters, the average and RMS values were calculated for different parameters. RMS is a robust statistical tool that provides a comprehensive measure of the size of data, their variability, and their effective value, making it suitable for a wide range of applications over the average value [22]. Therefore, the RMS value was utilized while modeling the PIP arrangement for verification. These strength parameters are presented in Table 4.
section_name: Material Properties

section_content: To determine the steel material properties, three tensile coupons were cut from each pile and tested according to the Korean standard 'KS B 0802:2003' [21]. The details of the sample preparation are provided in Figure 4. From this coupon test, the yield strength (σ s ), ultimate tensile strength (σ u ), modulus of elasticity (E s ), Poisson's ratio (υ), and the elongation (δ) were calculated. The tangent modulus (E t ) was calculated from the acquired data and is used in FEA modeling for bilinear models. For the selection of strength parameters, the average and RMS values were calculated for different parameters. RMS is a robust statistical tool that provides a comprehensive measure of the size of data, their variability, and their effective value, making it suitable for a wide range of applications over the average value [22]. Therefore, the RMS value was utilized while modeling the PIP arrangement for verification. These strength parameters are presented in Table 4.
section_name: Material Properties

section_content: Complementary to the experiment analysis and to understand the complex behavior, a numerical analysis was also conducted, which will also help us with parametric optimization. Moreover, a verified FEA model can provide a firm foundation for future studies. The geometry has been chosen with exactly the same dimensions as per Table 3. In case of material strength, Table 4 has been used. 

'ANSYS Workbench 2023/R2' was utilized to replicate the experimental model into a simulation model. The guidelines of the ANSYS workbench and previous studies have been followed to ensure an effective mesh distribution [23, 24]. To facilitate the adjustment of large deformations and local buckling in the material, a secondary meshing element, HEX20, was utilized. The specimen was meshed using side sizing, edge sizing, and face meshing to reduce the possibility of distortion in perturbation. The element and node numbers were 272,668 and 75,788, respectively. Mesh quality was checked using the Jacobian Ratio (JR), which yielded a JR of 0. 99078 and an average of 0. 99572, indicating a high level of uniformity in the meshing process. The mesh statistics are provided in Table 5. A mesh sensitivity analysis was also conducted, and the results are illustrated in Figure 5. This analysis indicated that with a 50 mm mesh size, the model is well converged. Therefore, to achieve an optimal balance between accuracy and computational efficiency, a mesh size of 50 mm was chosen. Some examples of the meshing are provided in Figure 6. Complementary to the experiment analysis and to understand the complex behavior, a numerical analysis was also conducted, which will also help us with parametric optimization. Moreover, a verified FEA model can provide a firm foundation for future studies. The geometry has been chosen with exactly the same dimensions as per Table 3. In case of material strength, Table 4 has been used. 

'ANSYS Workbench 2023/R2' was utilized to replicate the experimental model into a simulation model. The guidelines of the ANSYS workbench and previous studies have been followed to ensure an effective mesh distribution [23, 24]. To facilitate the adjustment of large deformations and local buckling in the material, a secondary meshing element, HEX20, was utilized. The specimen was meshed using side sizing, edge sizing, and face meshing to reduce the possibility of distortion in perturbation. The element and node numbers were 272,668 and 75,788, respectively. Mesh quality was checked using the Jacobian Ratio (JR), which yielded a JR of 0. 99078 and an average of 0. 99572, indicating a high level of uniformity in the meshing process. The mesh statistics are provided in Table 5. A mesh sensitivity analysis was also conducted, and the results are illustrated in Figure 5. This analysis indicated that with a 50 mm mesh size, the model is well converged. Therefore, to achieve an optimal balance between accuracy and computational efficiency, a mesh size of 50 mm was chosen. Some examples of the meshing are provided in Figure 6. Friction plays a crucial role in transferring loads between the inner and outer piles of a slip joint. The frictional force acting on the slip joint can also impact its fatigue life. Therefore, in this study, friction between the contact surfaces of the two pipes was considered by following a previous rigorous experimental study, and frictional faces with a coefficient of friction of 0. 4 were taken into account [25]. The algorithm used for contact detec- Friction plays a crucial role in transferring loads between the inner and outer piles of a slip joint. The frictional force acting on the slip joint can also impact its fatigue life. Therefore, in this study, friction between the contact surfaces of the two pipes was considered by following a previous rigorous experimental study, and frictional faces with a coefficient of friction of 0. 4 were taken into account [25]. The algorithm used for contact detection is the Augmented Lagrange method, specifically applied at the Gauss integration points. This approach allows for frictional contact in a multiple-to-multiple configuration. In this setup, the outer pile is designated as the contact body, while the inner pile surface acts as the target body. It's important to note that no stabilization damping factor has been incorporated in this configuration. Moreover, to replicate the experimental model, rigid MPC contact connection at the support was used, and the point of concentrated force, two plate stiffeners were placed as shown in Figure 7. These plate stiffeners were used to resist local buckling in the experimental analysis. Friction plays a crucial role in transferring loads between the inner and outer piles of a slip joint. The frictional force acting on the slip joint can also impact its fatigue life. Therefore, in this study, friction between the contact surfaces of the two pipes was considered by following a previous rigorous experimental study, and frictional faces with a coefficient of friction of 0. 4 were taken into account [25]. The algorithm used for contact detection is the Augmented Lagrange method, specifically applied at the Gauss integration points. This approach allows for frictional contact in a multiple-to-multiple configuration. In this setup, the outer pile is designated as the contact body, while the inner pile surface acts as the target body. It's important to note that no stabilization damping factor has been incorporated in this configuration. Moreover, to replicate the experimental model, rigid MPC contact connection at the support was used, and the point of concentrated force, two plate stiffeners were placed as shown in Figure 7. These plate stiffeners were used to resist local buckling in the experimental analysis.
section_name: Development of Finite Element Modeling

section_content: The study acknowledges several limitations, which, however, do not undermine the validity of its findings. 

Specifically, the numerical analysis did not incorporate initial geometric imperfections or the gap between the piles in the experimental specimens, which could affect the load-carrying capacity, especially for models with varying diameter-to-thickness (D/t) ratios. In the experimental study, some strain gauges became inactive after several load steps. Additionally, the study also did not address eccentric loading, biaxial bending, or variations in frictional coefficients. Variables such as the total length of the arrangement
section_name: Limitations

section_content: The study acknowledges several limitations, which, however, do not undermine the validity of its findings. 

Specifically, the numerical analysis did not incorporate initial geometric imperfections or the gap between the piles in the experimental specimens, which could affect the loadcarrying capacity, especially for models with varying diameter-to-thickness (D/t) ratios. In the experimental study, some strain gauges became inactive after several load steps. Additionally, the study also did not address eccentric loading, biaxial bending, or variations in frictional coefficients. Variables such as the total length of the arrangement were also not considered. In future studies, these limitations can be improved by conducting an in-depth study of each section.
section_name: Limitations

section_name: Results and Discussion

section_content: Initially, the force versus displacement data for experimental analysis were plotted for two different specimens. In Figure 8, this relationship is illustrated, showing two specimens with an equal capacity of 70 tons, each experiencing approximately 90 mm of displacement. 

However, in the inelastic zone, there is some variation between the specimens. It is possible that the variation is due to different initial geometric inaccuracies (IGIs) in each specimen. Some previous studies found that the response of tubular structures can vary by a maximum of 10% to 30% due to the IGI effect [26]. Hence, the variability in the experimental analysis is justified. The force-displacement relationship appeared almost linear up to a 60 mm displacement, and beyond 100 mm, it gradually declined up to 150 mm. Additionally, there was some initial slippage within the first 20 mm, likely due to the initial gap and minor inaccuracies. Both specimens have the same dimensions and loading conditions, resulting in identical capacities and trends. Two identical specimens were used to ensure the reliability of the test. However, as mentioned earlier, there were some negligible variations in initial stiffness due to geometric inaccuracies. The strain data were analyzed for both the tension and compression zones. As noted earlier, the total arrangement of PIP slip joints was divided into two different regions for ease of result presentation. In Figure 9, the strain vs. displacement for the compression zone of specimens 01 and 02 is provided, offering valuable insight. 

placement. 

However, in the inelastic zone, there is some variation between the specimens. It is possible that the variation is due to different initial geometric inaccuracies (IGIs) in each specimen. Some previous studies found that the response of tubular structures can vary by a maximum of 10% to 30% due to the IGI effect [26]. Hence, the variability in the experimental analysis is justified. The force-displacement relationship appeared almost linear up to a 60 mm displacement, and beyond 100 mm, it gradually declined up to 150 mm. Additionally, there was some initial slippage within the first 20 mm, likely due to the initial gap and minor inaccuracies. Both specimens have the same dimensions and loading conditions, resulting in identical capacities and trends. Two identical specimens were used to ensure the reliability of the test. However, as mentioned earlier, there were some negligible variations in initial stiffness due to geometric inaccuracies. The strain data were analyzed for both the tension and compression zones. As noted earlier, the total arrangement of PIP slip joints was divided into two different regions for ease of result presentation. In Figure 9, the strain vs. displacement for the compression zone of specimens 01 and 02 is provided, offering valuable insight. Both specimens display nearly identical values for compressive strain. Critical compression points are illustrated in Figure 9. Notably, the compressive strain of CH017 (outer pile edge) follows a different trend compared to the others. This discrepancy may be the cause of the buckling in the overlapped area of the inner pile, resulting in a tensile zone in that specific region. However, in the case of tensile strain, there can be discrepancies in the strain values for two specimens, as shown in Figure 10. Upon investigation, it was discovered that the strain gauges ceased to function accurately after approximately 60 mm, leading to inaccurate results. Before this displacement, the strain value and the trend were almost the same. Additionally, in CH033, the strain value is minimal compared to the other readings. Therefore, it can be inferred that the tension at the outer edge of the pile is negligible compared to other areas. The buckling observed in the experimental specimen is also shown in Figure 11. Both specimens display nearly identical values for compressive strain. Critical compression points are illustrated 9. Notably, the compressive strain of CH017 (outer pile edge) follows a different trend compared to the others. This discrepancy may be the cause of the buckling in the overlapped area of the inner pile, resulting in a tensile zone in that specific region. However, in the case of tensile strain, there can be discrepancies in the strain values for two specimens, as shown in Figure 10. Upon investigation, it was discovered that the strain gauges ceased to function accurately after approximately 60 mm, leading to inaccurate results. Before this displacement, the strain value and the trend were almost the same. Additionally, in CH033, the strain value is minimal compared to the other readings. Therefore, it can be inferred that the tension at the outer edge of the pile is negligible compared to other areas. The buckling observed in the experimental specimen is also shown in Figure 11. 

cause of the buckling in the overlapped area of the inner pile, resulting in a tensile zone in that specific region. However, in the case of tensile strain, there can be discrepancies in the strain values for two specimens, as shown in Figure 10. Upon investigation, it was discovered that the strain gauges ceased to function accurately after approximately 60 mm, leading to inaccurate results. Before this displacement, the strain value and the trend were almost the same. Additionally, in CH033, the strain value is minimal compared to the other readings. Therefore, it can be inferred that the tension at the outer edge of the pile is negligible compared to other areas. The buckling observed in the experimental specimen is also shown in Figure 11. Following this section, a finite element model (FEM) was developed and analyzed. Two buckling shapes are overlaid to compare the buckling behavior between the experimental and simulation models. The buckling shapes are nearly identical, with buckling occurring in the inner pile at the edge of the overlapping area.
section_name: Experimental Analysis Result

section_content: When the force-displacement curves for the numerical an model were juxtaposed, it was found that initially, the stiffness of the FEA and the experimental model was different, although the difference in maximum capacity was only 1. 82%, as shown in Figure 12. The IGI effect and the frictional coefficient might be the cause of this variation in stiffness. Importantly, the capacity and the trend of the forcedisplacement curves are identical, reinforcing the reliability of the findings. However, in the case of the FEM analysis in the inelastic zone after 120 mm, another wave was found in the force-displacement curve, representing the rippling in the outer pile. Due to this rippling, some energy is dissipated, and rotation is paused for 30 mm up to 150 mm, matching the previous trend. Following this section, a finite element model (FEM) was developed and analyzed. Two buckling shapes are overlaid to compare the buckling behavior between the experimental and simulation models. The buckling shapes are nearly identical, with buckling occurring in the inner pile at the edge of the overlapping area.
section_name: Results of Numerical Model

section_content: When the force-displacement curves for the numerical model and an experimental model were juxtaposed, it was found that initially, the stiffness of the FEA and the experimental model was different, although the difference in maximum capacity was only 1. 82%, as shown in Figure 12. The IGI effect and the frictional coefficient might be the cause of this variation in stiffness. Importantly, the capacity and the trend of the forcedisplacement curves are identical, reinforcing the reliability of the findings. However, in the case of the FEM analysis in the inelastic zone after 120 mm, another wave was found in the force-displacement curve, representing the rippling in the outer pile. Due to this rippling, some energy is dissipated, and rotation is paused for 30 mm up to 150 mm, matching the previous trend. 

The comparison of strain values between the experimental and numerical models for compressive and tensile zones is illustrated in Figures 13 and 14. Notably, the strain values for the compressive zone exhibit remarkable similarities between the experimental and numerical models, with a maximum difference of only 9. 89%. However, it is essential to highlight that the FEA model result does not indicate the same decline for CH017. On the other hand, the comparison of tensile strain is particularly intriguing. As the tensile strain for some cases malfunctioned after a 60mm displacement, the comparison is also confined to this range. However, in some cases, the strain gauges have functioned; therefore, for the simulation model, all the comparisons are mentioned up to 150 mm. Within this limit, the maximum discrepancy for region A is a significant 18. 18%, while for zone B, it stands at 13. 6%. These variations may be attributed to experimental uncertainties and simplifications in the numerical model. Nevertheless, despite these disparities, the variation margin falls within acceptable limits. The observed tensile strain has demonstrated remarkable significance. In every case, the tensile strain surpassed the yield strain value, highlighting a consistent pattern. Notably, the maximum strain approached 60 mm, closely resembling the behavior of compressive strain. Following this peak, the strain values showed a gradual decline. This crucial finding suggests that the maximum capacity of this arrangement is reached at 60 mm, corresponding to 40% of the overall displacement, emphasizing the effectiveness of the overlapped area as the stiffness also increases.
section_name: Results of Numerical Model

section_content: When the force-displacement curves for the numerical model and an experimental model were juxtaposed, it was found that initially, the stiffness of the FEA and the experimental model was different, although the difference in maximum capacity was only 1. 82%, as shown in Figure 12. The IGI effect and the frictional coefficient might be the cause of this variation in stiffness. Importantly, the capacity and the trend of the forcedisplacement curves are identical, reinforcing the reliability of the findings. However, in the case of the FEM analysis in the inelastic zone after 120 mm, another wave was found in the force-displacement curve, representing the rippling in the outer pile. Due to this rippling, some energy is dissipated, and rotation is paused for 30 mm up to 150 mm, matching the previous trend. The comparison of strain values between the experimental and numerical models for compressive and tensile zones is illustrated in Figures 13 and 14. Notably, the strain values for the compressive zone exhibit remarkable similarities between the experimental and numerical models, with a maximum difference of only 9. 89%. However, it is essential to highlight that the FEA model result does not indicate the same decline for CH017. On the other hand, the comparison of tensile strain is particularly intriguing. As the tensile strain for some cases malfunctioned after a 60mm displacement, the comparison is also confined to this range. However, in some cases, the strain gauges have functioned; therefore, for the simulation model, all the comparisons are mentioned up to 150 mm. Within this limit, the maximum discrepancy for region A is a significant 18. 18%, while for zone B, it stands at 13. 6%. These variations may be attributed to experimental uncertainties and simplifications in the numerical model. Nevertheless, despite these disparities, the variation margin falls within acceptable limits. The observed tensile strain has demonstrated remarkable significance. In every case, the tensile strain surpassed the yield strain value, highlighting a consistent pattern. Notably, the maximum strain approached 60 mm, closely resembling the behavior of compressive strain. Following this peak, the strain values showed a gradual decline. This crucial finding suggests that the maximum capacity of this arrangement is reached at 60 mm, corresponding to 40% of the overall displacement, emphasizing the effectiveness of the overlapped area as the stiffness also increases. Section slenderness is a vital parameter in the design and analysis of structural members, especially for thin-walled sections, which are used in monopile structures. This parameter significantly influences the member's behavior under different loading conditions and its susceptibility to buckling. Consequently, the PIP slip joint arrangement was analyzed using the same procedure for different D/t ratios to assess the behavior under varying section slenderness. Here, generalized section slenderness is expressed as λ = (D/t) × (σ s /250). The attained result of the normalized moment (M/M y ) vs. generalized section slenderness (λ), is also compared with the accepted code references like Eurocode and AISC-LRFD code, as shown in Figure 15 [27, 28]. Both of these codes specify requirements for offshore wind structures, including a range of section slenderness. In addition, two previous experimental analysis results were also compared to gain a deeper understanding [29, 30]. It's worth noting that the specified limits appear to be somewhat conservative, considering the current study's results. Furthermore, as the section slenderness (λ) increases, the normalized moment decreases, highlighting the different section classes and the impact of local buckling on moment resistance. In two cases of this study, failure occurred in the transition zone between elastic and plastic failure, which can be described by Engasser and Shanley's theory [31, 32]. In the remaining cases, failure was purely plastic. 

effectiveness of the overlapped area as the stiffness also increases. Section slenderness is a vital parameter in the design and analysis of structural members, especially for thin-walled sections, which are used in monopile structures. This parameter significantly influences the member's behavior under different loading conditions and its susceptibility to buckling. Consequently, the PIP slip joint arrangement was analyzed using the same procedure for different D/t ratios to assess the behavior under varying section slenderness. Here, generalized section slenderness is expressed as λ = (D/t) × (σs/250). The attained result of the normalized moment (M/My) vs. generalized section slenderness (λ), is also compared with the accepted code references like Eurocode and AISC-LRFD code, as shown in Figure 15 [27, 28]. Both of these codes specify requirements for offshore wind structures, including a range of section slenderness. In addition, two previous experimental analysis results were also compared to gain a deeper understanding [29, 30]. It's worth noting that the specified limits appear to be somewhat conservative, considering the current study's results. Furthermore, as the section slenderness (λ) increases, the normalized moment decreases, highlighting the different section classes and the impact of local buckling on moment resistance. In two cases of this study, failure occurred in the transition zone between elastic and plastic failure, which can be described by Engasser and Shanley's theory [31, 32]. In the remaining cases, failure was purely plastic.
section_name: Results of Numerical Model

section_content: The examination of frictional stress at different D/t ratios, as illustrated in Figure 16, has yielded valuable insights. Additionally, a radar diagram plotting pressure and sliding distance in the overlapped area has provided a deeper understanding of the influence of contact properties on bending resistance (Figure 17 ). It is evident that the maximum frictional stress decreases gradually with an increase in the D/t ratio, attributed to a more uniform distribution of friction across a larger surface area. Similarly, the gradual reduction in pressure and subsequent decrease in sliding with higher D/t ratios, as depicted in Figure 16, have significant implications for bending resistance. The frictional stress and pressure, although small in value, act across the entire surface area, making them important for the frictional slip joints. In practical applications, the friction and pressure in the overlapping area will be crucial factors in determining the bending capacity of the PIP slip joint arrangement for larger-diameter monopiles.
section_name: Contact Results

section_content: The examination of frictional stress at different D/t ratios, as illustrated in Figure 16, has yielded valuable insights. Additionally, a radar diagram plotting pressure and sliding distance in the overlapped area has provided a deeper understanding of the influence of contact properties on bending resistance (Figure 17 ). It is evident that the maximum frictional stress decreases gradually with an increase in the D/t ratio, attributed to a more uniform distribution of friction across a larger surface area. Similarly, the gradual reduction in pressure and subsequent decrease in sliding with higher D/t ratios, as depicted in Figure 16, have significant implications for bending resistance. The frictional stress and pressure, although small in value, act across the entire surface area, making them important for the frictional slip joints. In practical applications, the friction and pressure in the overlapping area will be crucial factors in determining the bending capacity of the PIP slip joint arrangement for larger-diameter monopiles. The relationship between the normalized moment and the rotational ratio provides valuable insight into the behavior of a section under bending and helps assess its structural performance. Engineers can confidently verify adequacy and ensure safety by comparing these calculations to design requirements. Consequently, the normalized moment versus rotational ratio is also presented in Figure 18. Notably, as the D/t ratio increases, the normalized moment and the corresponding rotational capacity gradually decrease, indicating a change in section type and the effect of local buckling. The increase in the D/t ratio led to a change in buckling mode, resulting in a significant shift in the rotational ratio. Moreover, the role of contact mechanics, as described in the previous section, is crucial to consider. The rotational capacity of D/t ratios 50 and 75 will be similar to that of D/t ratios 100 and 130, although, in the latter two cases, buckling will occur before the yield moment. Lastly, the rotational resistance of D/t ratio 160 is the least among all. The relationship between the normalized moment and the rotational ratio provides valuable insight into the behavior of a section under bending and helps assess its structural performance. Engineers can confidently verify adequacy and ensure safety by comparing these calculations to design requirements. Consequently, the normalized moment versus rotational ratio is also presented in Figure 18. Notably, as the D/t ratio increases, the normalized moment and the corresponding rotational capacity gradually decrease, indicating a change in section type and the effect of local buckling. The increase in the D/t ratio led to a change in buckling mode, resulting in a significant shift in the rotational ratio. Moreover, the role of contact mechanics, as described in the previous section, is crucial to consider. The rotational capacity of D/t ratios 50 and 75 will be similar to that of D/t ratios 100 and 130, although, in the latter two cases, buckling will occur before the yield moment. Lastly, the rotational resistance of D/t ratio 160 is the least among all. The relationship between the normalized moment and the rotational ratio provides valuable insight into the behavior of a section under bending and helps assess its structural performance. Engineers can confidently verify adequacy and ensure safety by comparing these calculations to design requirements. Consequently, the normalized moment versus rotational ratio is also presented in Figure 18. Notably, as the D/t ratio increases, the normalized moment and the corresponding rotational capacity gradually decrease, indicating a change in section type and the effect of local buckling. The increase in the D/t ratio led to a change in buckling mode, resulting in a significant shift in the rotational ratio. Moreover, the role of contact mechanics, as described in the previous section, is crucial to consider. The rotational capacity of D/t ratios 50 and 75 will be similar to that of D/t ratios 100 and
section_name: Contact Results

section_content: This study investigated the behavior of PIP slip joints under pure bending conditions. The primary focus was on understanding the relationship between section slenderness, contact properties, and the structural performance of the joints. 

The force-displacement relationship for two experimental specimens, each with a capacity of 70 tons, displayed a linear trend up to a displacement of 60 mm, followed by a gradual decline. After reviewing the strain data, it was clear that both specimens showed similar compressive strain values. However, there was a significant change in behavior at a specific point due to the perturbation of the CHS section in that area. The primary failure occurred due to buckling in the inner pile at the edge of the overlapping area, which was consistent in both the experimental and numerical models. 

The results of the experimental and numerical study demonstrated a strong correlation between the force-displacement curves, with a maximum capacity difference of only 1. 82%. The compressive strain values were consistent between the experimental and numerical models, while some discrepancies were noted in the tensile strain due to experimental limitations. As the D/t ratio increases, we observe a significant decrease in both the normalized moment and rotational capacity, signaling a shift in section type and highlighting the effects of local buckling. Importantly, increased D/t ratios contribute to a more uniform friction distribution and less sliding, leading to a transformation in bending and rotational resistance. Notably, when the D/t ratio is in the range of 75 to 130, the stability of the contact mechanics is superior compared to other ranges. For PIP slip joints, utilizing these specific D/t ratios alongside the optimal overlapping length promises substantial enhancements in bending resistance. Moreover, this study has benchmarked its findings against established code guidelines, suggesting that the current limits for section slenderness may be unnecessarily conservative. 

Additionally, the impact of the observed tensile strain cannot be overstated. Consistently, the tensile strain exceeded the yield strain value in all instances. Remarkably, the maximum strain approached 60 mm, displaying a behavior that mirrors compressive strain. Following this peak, a gradual decline in strain values was also noted. This crucial insight suggests that the maximum capacity of this configuration is reached at 40% of the overall displacement, underscoring the effectiveness of the overlapped area in enhancing stiffness.
section_name: Summary and Conclusions

section_content: This study investigated the behavior of PIP slip joints under pure bending conditions. The primary focus was on understanding the relationship between section slenderness, contact properties, and the structural performance of the joints. 

The force-displacement relationship for two experimental specimens, each with a capacity of 70 tons, displayed a linear trend up to a displacement of 60 mm, followed by a gradual decline. After reviewing the strain data, it was clear that both specimens showed similar compressive strain values. However, there was a significant change in behavior at a specific point due to the perturbation of the CHS section in that area. The primary failure occurred due to buckling in the inner pile at the edge of the overlapping area, which was consistent in both the experimental and numerical models. 

The results of the experimental and numerical study demonstrated a strong correlation between the force-displacement curves, with a maximum capacity difference of only 1. 82%. The compressive strain values were consistent between the experimental and numerical models, while some discrepancies were noted in the tensile strain due to experimental limitations. As the D/t ratio increases, we observe a significant decrease in both the normalized moment and rotational capacity, signaling a shift in section type and highlighting the effects of local buckling. Importantly, increased D/t ratios contribute to a more uniform friction distribution and less sliding, leading to a transformation in bending and rotational resistance. Notably, when the D/t ratio is in the range of 75 to 130, the stability of the contact mechanics is superior compared to other ranges. For PIP slip joints, utilizing these specific D/t ratios alongside the optimal overlapping length promises substantial enhancements in bending resistance. Moreover, this study has benchmarked its findings against established code guidelines, suggesting that the current limits for section slenderness may be unnecessarily conservative. 

Additionally, the impact of the observed tensile strain cannot be overstated. Consistently, the tensile strain exceeded the yield strain value in all instances. Remarkably, the maximum strain approached 60 mm, displaying a behavior that mirrors compressive strain. Following this peak, a gradual decline in strain values was also noted. This crucial insight suggests that the maximum capacity of this configuration is reached at 40% of the overall displacement, underscoring the effectiveness of the overlapped area in enhancing stiffness. 

In the context of further advancements in PIP slip joint technology, it is crucial to consider the impact of varied eccentric loads and section shapes. A comprehensive investigation into pressure-dependent friction is also significant. Additionally, upon validation of the slip joint model, incorporating dynamic loads can become a viable consideration.
section_name: Summary and Conclusions

section_content: Funding: This work was supported by the Human Resources Development of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korean government (Ministry of Trade, Industry and Energy) (No. 20214000000180 ), and the Regional Innovation Strategy (RIS) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (MOE) ( 2023RIS-008 ). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable.

section_name: Data Availability Statement:

section_content: The data presented in this study are available on request from the corresponding author.
section_name: Data Availability Statement:

section_name: Conflicts of Interest:

section_content: The authors declare no conflict of interest.
section_name: Conflicts of Interest: