Experimental Study of Negative Skin Friction of Pile Group Foundations for Offshore Wind Turbines on Artificial Islands

Abstract

Constructing offshore wind turbines on artificial islands is considered a viable option, but negative skin friction (NSF) is a significant adverse factor that cannot be ignored. The NSF adversely affects the bearing capacity of pile foundations. Currently, design methods for studying the impact of NSF group effects mainly rely on empirical approaches. Moreover, existing experimental studies do not simulate the NSF experienced by offshore wind turbine pile groups on artificial islands. In order to further explore the impact of pile group effects on NSF experienced by offshore wind turbine pile foundations on artificial islands, this study conducted indoor model tests on single piles and 3 × 3 rectangular pile groups in sandy soil under uniformly distributed loading on surrounding soil. The experiment measured the settlement of piles at various positions within single piles and rectangular pile groups, as well as the settlement of the soil surrounding the piles and the NSF. Through calculations, the experiment determined the neutral points and NSF group effect coefficients for each pile. The results indicate that densely spaced pile groups are advantageous in reducing settlement of the surrounding soil, thereby mitigating the adverse effects of NSF. Due to the influence of pile group effects, different positions within the group experience varying degrees of NSF. Consequently, in practical engineering applications, settlement of both the pile groups and the surrounding soil should be calculated separately. Furthermore, design considerations for the uplift forces and neutral points of piles at different positions within the pile group should adhere to distinct standards.

1. Introduction

Coastal regions host numerous economically developed areas with substantial electricity demands. However, these regions often face tight land constraints. Offshore wind power presents a solution by providing clean energy without occupying valuable land resources [1,2]. In recent years, offshore wind power has seen significant development, with larger turbines being installed closer to shore and a trend towards deeper offshore installations [3]. However, constructing offshore wind foundations in deep seas poses considerable challenges. Building offshore wind foundations on artificial islands offers a new approach to address these construction difficulties [4,5,6]. Artificial islands provide crucial infrastructure support for coastal development. Sand is currently one of the primary materials used in constructing artificial islands. However, the issue of negative skin friction (NSF) cannot be overlooked when constructing offshore wind foundations on artificial islands [7].

The NSF on pile foundations arises when the settlement deformation of the surrounding soil exceeds that of the pile shaft [8,9,10]. This phenomenon is primarily caused by several factors: significant surcharge near the pile foundation; consolidation settlement of the soil layer around the pile due to factors such as groundwater extraction or pre-consolidation; settlement due to dissipation of excess pore water pressure and subsequent re-consolidation; and ground subsidence from phenomena like collapsible loess or thawing permafrost [11,12,13]. However, pile foundations on artificially reclaimed islands will inevitably be affected by surcharge loading and consolidation [7]. In the construction process of offshore wind turbine foundations on artificial islands, surcharge loading is a primary cause of NSF. The placement of fill on the original soil induces settlement, while surcharge loading inevitably occurs during construction [7].

The NSF results in a reverse frictional resistance exerted on the pile foundation, where the weight of the surrounding soil is transferred as an external load acting on the pile shaft [14]. This not only fails to contribute to the pile’s bearing capacity, but also effectively reduces it. Therefore, in the design and construction of pile foundations, careful consideration and assessment of NSF are crucial for ensuring structural stability and load-bearing capacity [15,16,17].

Since the initial proposition of NSF on pile foundations, extensive scholarly research has been conducted using methods such as theoretical analysis, model tests, field study, and finite element analysis [18,19,20,21,22]. Among these methods, model testing stands out as a cost-effective means for investigating NSF relative to full-scale prototypes [23,24]. In recent years, a multitude of scholars have engaged in diverse model test studies. Leung et al. [25] employed centrifuge model tests to explore the impact of axial load on piles embedded in soft clay, where sand served as the load-bearing bed atop the piles. Mohsen et al. [26] investigated the effects of the length-to-diameter (L/D) ratio and saturation on NSF development in end-bearing piles using small-scale models. Additionally, Chai [27] conducted a series of tests, including both non-immersed and immersed scenarios, to investigate settlement, axial force, and lateral friction of piles in collapsible loess. In terms of material constitutive modeling for clays, the progress is substantial and the analyses provide more accurate estimations to engineers [28,29].

In recent years, research on the NSF of individual piles has deepened, with an increasing number of scholars turning their attention to the group effects of NSF. Kong [30] investigated the performance characteristics of dragload relative to pile–soil displacement, load sequencing, load rates, and the group effects of dragload concerning pile spacing using both model testing and numerical simulations. Su et al. [31] explored the influence of soil compressibility, pile installation methods, pile end conditions, and pile spacing on dragload development through a series of 1 g model tests. Zhang et al. [32] studied the impact of groundwater levels on the load-bearing characteristics of pile groups through a series of model tests. Bian et al. [33] conducted centrifuge tests to examine the effects of fluctuating groundwater levels on pile groups.

However, there remains inadequate research on the group effect mechanisms of NSF. Current design methods for non-structural fill (NSF) group impacts primarily rely on empirical approaches, and there are significant differences in the design methods adopted by different standards. These various design methods have varying degrees of deficiencies [34,35]. Therefore, when constructing offshore wind turbine foundations on artificial islands, it is crucial to consider the impact of surcharge-induced NSF on sandy soil, a common fill material for island construction [36]. Furthermore, there has been a lack of research on negative skin friction of pile groups under uniformly distributed loads, which can adequately simulate the impact of fill materials on existing soil on artificial islands. Therefore, conducting research on negative skin friction of pile groups under uniformly distributed loads is particularly crucial for the construction of pile foundations on artificial islands.

This study presents a series of model experiments designed to explore the influence of a uniformly distributed load on surrounding soil and pile spacing on NSF within 3 × 3 rectangular pile groups. The experiments specifically focused on analyzing the pile and surrounding soil settlement, forces acting on the pile shaft, and the position of the neutral point. These findings contribute to a deeper understanding of NSF impacts, potentially enhancing design methodologies for 3 × 3 rectangular pile groups for offshore wind turbines on artificial islands.

2. Model Test Overview

2.1. Test Description

In this experiment, model piles were arranged within a masonry test chamber with internal dimensions of 2000 mm × 2000 mm × 2000 mm (length × width × height). Given that the influence zone of the piles typically extends 3–8 times the pile diameter, the larger size range is advantageous for minimizing boundary effects. The walls of the test chamber were constructed with brick masonry and cement plaster, providing sufficient strength to effectively constrain lateral deformations.

In this study, 1 g indoor model tests were conducted, focusing primarily on the vertical load-bearing capacity of pile foundations, with particular emphasis on lateral resistance. To ensure that the test results reasonably reflect the vertical forces experienced by pile foundations in actual engineering scenarios, the following dimensionless framework is adopted [37]:

$$R_s={\displaystyle \frac{R_S}{L^{2}D{\gamma }^{\prime }}}$$

(1)

At a 100 cm spacing along the bottom edges of all four sides of the test chamber, there are two drainage switches each, with perforated pipes laid at the bottom of the test chamber. Geotextile fabric wraps around the drainage holes to prevent sand loss and blockage of the holes.

The model piles are fabricated from 7075 aluminum tubes, each with a length of 1000 mm and an outer diameter of 30 mm, and a wall thickness of 3 mm. The material properties of the aluminum tubes include an elastic modulus of 71.7 GPa and a Poisson ratio of 0.33.

During the application of strain gauges, it is crucial to clean the corresponding areas with 75% alcohol wipes to ensure accurate measurement of axial force distribution changes during the experimental process. Each pile is divided into sides A and B, with seven strain gauges uniformly distributed on each side of the model pile. The specific distribution can be found in Figure 1.

The model piles were connected to customized connection devices and mounted on steel pedestals measuring 250 mm × 250 mm. This setup allows for the assembly of both single-pile models and 3 × 3 rectangular pile group models. The steel pedestals ensure the relative positioning of the model piles and that they maintain verticality during backfilling. Additionally, the pedestals facilitate the use of lead weights for pile top loading calibration.

Model piles were installed within a uniform layer of quartz sand, 1000 mm thick, underlain by a 1000 mm layer of crushed stone. Two layers of geotextile cover were positioned between the sand and crushed stone, ensuring both adequate permeability and the prevention of upper sand from filling voids. The soil parameters of the tested sand were determined in accordance with the “Standard Test Methods for Geotechnical Testing”, as detailed in

Table 1. Geotechnical test parameters of the sandy soil used in the experiments.

Geotechnical Parameters	Experimental Value
Poisson’s ratio	0.26
$\mathrm{Bulk} \mathrm{density}, \gamma /(\mathrm{k}\mathrm{N}·{\mathrm{m}}^{-3})$	15.9
$\mathrm{Internal} \mathrm{friction} \mathrm{angle}, \phi /(°)$	35.2
$\mathrm{Water} \mathrm{content}, w_0/\left(\mathrm{\%}\right)$	16.87
$\mathrm{Maximum} \mathrm{dry} \mathrm{density}, {\rho }_{dmax}/(\mathrm{g}·{\mathrm{c}\mathrm{m}}^{-3})$	1.733
$\mathrm{Minimum} \mathrm{dry} \mathrm{density}, {\rho }_{dmin}/(\mathrm{g}·{\mathrm{c}\mathrm{m}}^{-3})$	1.429
Non-uniformity coefficient	5.29
Curvature coefficient	1.31

. To maintain consistency across test specimens, the sand was compacted manually in layers to achieve a relative density of 45% ± 3%. The sandy soil utilized in the experiments was quarried from a riverbed located in Jiangsu, China. It predominantly comprises quartz particles measuring less than 2 mm in diameter, with 13.1% of particles smaller than 0.075 mm and 66% larger than 0.25 mm. The particle size distribution curve of the soil is illustrated in Figure 2. Classified as medium fine sand, it possesses a fineness modulus of 2.4, a curvature coefficient of 1.31, and a coefficient of uniformity of 5.29, indicating relatively high uniformity.

2.2. Test Loading System

As shown in Figure 3, the top load of the test pile was applied using a 2 kg calibration weight for static loading, based on preliminary experiments to determine the pile’s bearing capacity, ultimately establishing a static load of 500 N at the pile top. A 30 mm thick steel plate was placed on the soil surface and uniformly distributed loading was provided using a jack and reaction frame structure, aiming to induce noticeable settlement conditions around the pile. The surface loading of the soil was incrementally applied in five stages up to 100 kPa.

An electric hydraulic pump was used for the loading device to ensure stable oil pressure under high loads. A reaction frame was designed at the top, and the soil loading was achieved through upper and lower loading plates. The jack employed a slow-load maintenance method, proceeding to the next stage only after measuring soil settlement rates (less than 0.01 mm/10 min) following each load increment.

Under uniformly distributed loading on surrounding soil, both the pile and the surrounding soil experience displacement. Obtaining displacement values for both is crucial for determining the position of the neutral point and studying the characteristics of NSF. This study employed homemade settlement markers buried at different depths, alongside vertically encased PVC hollow tubes coated with Vaseline to minimize the influence of sidewall soil. Settlement data variations were recorded using a dial gauge (precision 0.01 mm) mounted on a magnetic base, at depths corresponding to the burial depths of the pile and soil (0 mm, −300 mm, −600 mm, −900 mm).

2.3. Loading Procedure

To simulate uniformly distributed loading on surrounding soil, an electric hydraulic pump was used to pressurize a top jack. Each load increment was 20 kPa, and the loading duration for each increment was controlled to be 40 min. The load was maintained constant to prevent pressure drop in the hydraulic pump, with careful attention paid to promptly re-pressurizing as necessary. Steel plates were placed atop the soil to transmit the load, supporting columns and upper load plates were erected, and jacks were positioned against reaction frames.

This experiment investigated two types of pile arrangements: single piles and 3 × 3 rectangular pile groups. The three pile spacing configurations of 3D (three times the pile diameter), 4D, and 6D were considered for the 3 × 3 rectangular pile groups. The study involved applying incrementally staged uniformly distributed loading of 20 kPa, 40 kPa, 60 kPa, and 80 kPa on the surrounding soil, and 100 kPa with a static load of 500 N on the pile head, totaling 4 experimental conditions (the same loading method was used for all conditions), as detailed in

Table 2. Experimental conditions (“--” denotes “not applicable,” meaning that the parameter of pile spacing does not exist for a single pile.).

Number	Pile Type	Pile Spacing	Loading Method
1	single piles	--	Pile head static load (500 N) Uniformly distributed loading on soil (applied in 5 stages up to 100 kPa)
2	3 × 3 rectangular pile group	3D
3	3 × 3 rectangular pile group	4D
4	3 × 3 rectangular pile group	6D

. Analysis focused on understanding the axial forces in pile foundations, settlement characteristics of piles within sandy soil under varying pile spacings and load intensities, and the positioning of the neutral point. This research aimed to elucidate the mechanical behavior of piles at different positions, building upon the findings from single pile tests and exploring the synergistic effects within pile groups.

3. Analyses

3.1. Settlement of Piles

Figure 4 depicts the variation in settlement of single piles and 3 × 3 rectangular pile groups with different pile spacing as the loading level increases. It is evident that compared to single piles, rectangular pile groups exhibit smaller pile displacements at equivalent loading levels due to their restraining effect on soil settlement. However, increasing pile spacing among the pile group leads to escalated pile settlements, gradually approaching those of single piles.

For both single piles and rectangular pile groups across all spacings, pile settlement increases with the applied loading level. Notably, beyond a loading level of 60 kPa, the rate of settlement increase diminishes, which is particularly pronounced in configurations with 3D pile spacing of rectangular groups.

To further analyze the impact of pile group effects on pile settlement, the ratio of settlement between pile groups and single pile is defined as the pile settlement ratio. It is calculated using the following formula:

$$Pile Settlement Ratio={\displaystyle \frac{Settlement of Group Piles}{Settlement of Single Pile}}$$

(2)

Figure 5 illustrates the trend of pile settlement ratios with varying loading on surrounding soil. From the figure, it can be observed that the pile settlement ratio of 3 × 3 pile groups with different pile spacings is uniformly distributed within the range of 0.4 to 0.8. For piles with the same spacing, as the loading level increases, although there is a trend of an increased settlement ratio, the growth rate is relatively slow, indicating that the settlement ratio is less influenced by the loading level. Under the same loading conditions, as the pile spacing increases, the settlement ratio also increases, gradually approaching the value of single pile settlement.

This phenomenon also indicates that the surcharge generated on artificial landfills, as well as subsequent marine landfilling, although influencing the settlement values of pile groups, has a relatively minor impact on the pile settlement ratio. In practical engineering, when calculating the settlement of pile groups on artificially filled islands, it can be assumed that the pile settlement ratio remains unchanged with varying load levels. Settlement calculations for pile groups can be estimated based on the settlement of individual piles.

3.2. Settlement of Surrounding Soil

Figure 6a illustrates the relationship between settlement around a single pile and the varying loading levels. It can be observed that the settlement in deeper soil layers due to the load is much smaller compared to that in the surface layers. As the loading level increases, the settlement in the surface layers increases significantly, whereas the settlement in the deeper layers shows a smaller variation. This phenomenon occurs because superficial soil, being closer to the surface, possesses relatively stronger compressibility and deformability. In contrast, deeper soil, constrained by the superficial layers, experiences reduced compressibility and deformability, thus resulting in relatively smaller settlement.

Due to the minimal deformation of the pile itself, which can be considered as a rigid body, the settlement of the pile can be seen as the same at different depths. However, the settlement of the soil decreases with increasing depth. Therefore, there exists a certain depth where the settlements of both the pile and the soil are equal. Above this depth, the settlement of the soil exceeds that of the pile, resulting in NSF. NSF increases the axial force on the pile

Figure 6b–d show the layered settlement of the soil around 3 × 3 pile groups with different pile spacings during the loading process. It can be observed that the surface layer of the soil experiences the greatest settlement, with the settlement decreasing along the direction of the pile shaft. The pattern of change is consistent with the settlement pattern of a single pile, but the values are smaller than those of a single pile. As the pile spacing increases, the settlement around the piles significantly increases and gradually approaches the settlement of a single pile.

This phenomenon occurs because piles can restrict the settlement of surrounding soil. The further the soil is from the pile, the less it is restricted until it can be neglected beyond a certain range. In pile groups, the influence zones of individual piles overlap, resulting in cumulative restriction on the soil. As the spacing between piles increases, the cumulative effect on the soil diminishes. With closer pile spacing, settlement of soil around the piles is significantly restricted, which can to some extent reduce the adverse effects of NSF on the bearing capacity of pile groups on artificial islands.

3.3. Axial Force

The axial forces for pile groups were obtained through measurement and processing of strain gauge readings affixed at different locations along the pile shaft. Subsequently, shaft side friction was derived and compared with that of individual piles. The methodology involved affixing strain gauges at strategic points on the pile shaft to measure cross-sectional strains, allowing for the computation of axial forces based on principles of material mechanics.

$$Q_i=E_{p}A{\epsilon }_i, i=1,2,3,4,5$$

(3)

• E_p denotes the elastic modulus of the model pile;
• A represents the cross-sectional area of the model pile;
• ε_i denotes the strain measured by the instrument on the pile shaft.

From Figure 7, it is evident that the axial force relationship of a single pile increases with the applied loading level. At different loading levels, the maximum axial forces for the single pile are 791 N, 1453.2 N, 2143.7 N, 2662.6 N, and 3531.1 N. The maximum axial force occurs at a loading level of 100 kPa, exhibiting a distinct pattern of initial increase followed by subsequent decrease along the length of the pile shaft. Under the same loading level, as the embedment depth increases, the axial force initially rises, but the rate of increase gradually diminishes until it begins to decrease. This phenomenon occurs because the settlement induced in the shallow soil layers is greater compared to that in the pile, causing an increase in downward frictional forces on the pile and thereby increasing the axial force. However, as the depth increases, the difference between soil settlement and pile settlement decreases gradually. Eventually, when their displacements become equal, the pile settlement exceeds that of the soil. At this point, the pile begins to experience positive skin friction, leading to a reduction in axial force.

For the 3 × 3 rectangular pile group models, three representative positions—corner, side, and center piles—were selected for detailed study to facilitate analytical research. Based on Figure 8, it is evident that as the applied loading level increases, the axial force characteristics of rectangular pile groups at three different pile spacings closely resemble those of individual piles. Specifically, there is an initial increase followed by a subsequent decrease in axial force, depicting an approximate parabolic trend consistent with a single pile.

For the same location of piles at equal loading levels, the axial force increases with increasing pile spacing and gradually approaches the axial force of a single pile. This phenomenon occurs because the differential settlement between the surrounding soil and the pile diminishes as the pile spacing widens. As discussed earlier, when the pile spacing is smaller, the settlement of the surrounding soil is influenced by the group effect of the piles, resulting in less relative displacement and, consequently, a smaller maximum axial force.

From this phenomenon, a consistent conclusion can be drawn from the previous discussion, namely, that reducing the pile spacing is beneficial for mitigating the adverse effects of NSF. In engineering practice, in regions where NSF significantly affects performance, dense groups of piles can be employed to minimize these adverse effects.

At the same loading level and with the same pile spacing, the axial force varies among piles located at different positions within a 3 × 3 rectangular pile group. It is observed that corner piles experience greater axial forces than central piles, indicating that central piles are more affected by the group effect. This is due to central piles being surrounded by more adjacent piles, thereby experiencing a greater influence from adjacent piles, and consequently experiencing the maximum impact of the group effect while minimizing the adverse effects of NSF. In design practice, different calculation methods can be applied to address the influence of NSF on piles located at different positions within a group.

3.4. Lateral Frictional Resistance and Neutral Point of Pile Shaft

If the pile is divided into numerous small cross-sectional segments, the lateral frictional resistance at the i-th segment can be derived as follows:

$$f_{si}=(Q_i-Q_{i+1})/A_f$$

(4)

• $Q_i$ represents the axial force at the i-th cross-sectional segment of the pile;
• $A_f$ denotes the lateral surface area between the i-th and (i + 1)-th segments.

Taking a single pile as an example, through computational analysis, the distribution of lateral resistance along the pile can be obtained, as depicted in Figure 9. It is observed that with increasing levels of soil loading, the peak NSF also increases.

The neutral point marks the transition between positive and negative side frictional resistance. Therefore, the depth at which the curve in Figure 9 intersects with the line representing zero side friction can be identified as the coordinate of the neutral point under this operating condition.

After calculation, the ratios of the neutral points to the length of individual piles are 0.77 L, 0.83 L, 0.86 L, 0.89 L, and 0.93 L, respectively, for the various loading increments. These findings confirm that the depths of the neutral points obtained from this single pile test generally comply with the requirements specified in the “Technical Code for Building Pile Foundations” (JGJ94-2008) [38]. According to the code, for cohesive soil layers of medium to high density, the ratio of neutral point depth to pile length (L) should be between 0.7 L and 0.8 L; for gravel or cobble layers, the ratio should be 0.9 L.

Based on the provided calculations, the ratios of neutral point depths to pile length fall within the specified ranges for the respective bearing capacity layers, as outlined in the code, which further substantiates the validity of the model experiment conducted in this study.

Using this method, the neutral point positions can be determined for single piles, as well as for 3 × 3 pile groups with various pile spacings.

Figure 10 illustrates the trend of the ratio of neutral point depth to pile length for single piles and rectangular pile groups with different pile spacings as the loading level increases. It can be observed that the trend of neutral point positions for rectangular pile groups at all spacings is consistent with that of single piles—they all shift downwards as the loading level increases.

For piles located at different positions within rectangular pile groups with the same spacing, corner piles exhibit neutral point positions closest to those of single piles. As for pile groups with different spacings, the neutral point position approaches that of single piles more closely as the spacing increases. Notably, at a spacing of 6D, the neutral point position of corner piles in rectangular pile groups aligns closely with that of single piles.

To further analyze the influence of NSF due to pile group effects on the neutral point position, the ratio of neutral point positions between different types of pile configurations and various pile spacings relative to those observed in single pile tests was selected as the research object. Specifically, the ratio of neutral point positions between the pile group and a single pile is taken as the horizontal axis, while different soil loading levels are taken as the vertical axis, to measure the degree to which the neutral point position is affected by pile group effects.

From Figure 11, it can be seen that under the same loading level, the neutral point position ratio for corner piles is greater than that for side piles, which in turn is greater than that for center piles. This is because center piles are influenced by the superposition of adjacent multiple piles. Compared to center and side piles, corner piles are adjacent to the fewest number of piles and thus experience the least influence from pile group effects.

It can be observed that for all pile spacings in the 3 × 3 rectangular pile group configuration, the neutral point position ratio for corner piles exceeds 0.95. When the pile spacing is 6D, the neutral point position ratio essentially overlaps with the straight line where ratio = 1. Therefore, it can be considered that the neutral point position of corner piles in the 3 × 3 rectangular pile group configuration in sandy soil is minimally affected by pile group effects. In engineering design, the neutral point position of single piles can be approximately used as the calculation basis.

3.5. Dragload of Pile and Coefficient of Pile Group Effect on NSF

The axial force in piles indirectly reflects the distribution of NSF in pile foundations, while dragload represents the most direct consideration of NSF effects in pile design. According to references from “Technical Code for Building Pile Foundations” [38], this is articulated as follows:

$$N=\eta \times \mu \sum _{n-1}^n{f}_{i=1}^n{L}_i$$

(5)

• n denotes the sequential numbering of soil layers from the pile top to the neutral point;
• L_i represents the thickness of the (i)-th layer of soil section;
• η is the coefficient of pile group effect on NSF;
• μ denotes the perimeter of the pile section;
• $f_{i=1}^n$ stands for the side resistance of the (i)-th section.

Figure 12 presents the dragload of a 3 × 3 rectangular pile group at varying pile spacings under different loading conditions. It is evident that as the applied load increases, the dragload for all pile groups, regardless of spacing, follows a trend akin to that of a single isolated pile—rising proportionally with the load magnitude. However, as the loading levels escalate, the rate of dragload increment diminishes.

In configurations with different pile spacings, enlarging the spacing leads to a notable escalation in dragload, converging towards that observed for a single isolated pile. Among piles situated equidistantly within the group, corner piles manifest higher uplift forces compared to side piles, which in turn exhibit greater dragload than central piles under identical loading conditions. This behavior stems from side piles experiencing comparatively less influence from neighboring piles.

The pile group effect refers to the phenomenon where the combined bearing capacity of individual piles in a group differs from the actual total bearing capacity of the pile group, often characterized by a coefficient reduction relationship. In this context, the coefficient η for the pile group effect on NSF is used to quantify the extent of the pile group effect. It is defined as the ratio of the average dragload on the pile group foundation to the dragload on an individual pile. This coefficient serves to measure the interaction between piles within a group in the foundation system.

$$\eta ={\displaystyle \frac{{\int }_0^{l_n}{f}_s^{n}ds}{{\int }_0^{l_n}{f}_{s0}^{n}dz}}$$

(6)

• $l_n$ represents is the depth from the ground surface to the neutral point of the pile;
• $f_S$ represents the NSF of individual piles in a pile group foundation;
• $f_{S0}$ represents the NSF of a single pile;
• z represents the embedment depth of the pile.

Experimental results indicate that the dragload effect, primarily constituted by axial forces, is the main component generated by NSF. The mutual interaction among piles in a group foundation limits the development of NSF, resulting in a relative decrease in dragload. Consequently, the settlement values of pile group foundations are generally lower compared to single pile foundations, showcasing a distinct pile group effect of NSF. This effect contrasts with the influence of a pile group effect without NSF. Utilizing the results from single pile tests as a basis, the coefficients for dragload pile group effects under different pile spacings and loading levels for a rectangular 3 × 3 pile group can be derived using appropriate formulas

Figure 13 shows the pile group effect coefficients for 3 × 3 rectangular pile groups at different pile spacings and under varying loading levels. It can be observed that for the same loading level, smaller pile spacings result in smaller pile group effect coefficients. Additionally, within the same pile spacing, the central piles exhibit the smallest pile group effect coefficient, followed by the edge piles, and the corner piles show the largest coefficient. As the loading level increases, the pile group effect coefficients for all pile spacings generally increase.

Both the magnitude of the loading level and the size of the pile spacing significantly influence the pile group effect. Unlike a conventional pile group without surcharge, where settlement tends to exceed that of single piles (and are hence often greater than 1), pile group effect coefficients with NSF are generally less than 1. This demonstrates the pattern of NSF pile group effects, where the dragload in the pile group is smaller than that in single piles. This is due to the significant dragload generated under loading conditions, which predominates and is mitigated by the mutual interaction between adjacent piles.

From Figure 13, it can be observed that although the pile group effect coefficient of NSF gradually approaches 1 with increasing pile spacing, even at a spacing of 6D, the corner pile, which experiences the minimal influence, maintains a coefficient of the NSF pile group effect below 0.8 for most loading levels. This suggests that the impact of pile group effects on uplift forces remains significant until a pile spacing of 6D. Therefore, in engineering practice, utilizing dense pile groups is notably effective in combating NSF.

4. Discussion

This study conducted model experiments on 3 × 3 rectangular pile groups in sandy soil under balanced pile loading, aiming to investigate the influence of NSF of pile foundations for offshore wind turbines on artificial islands. The results indicate the following: (1) dense pile groups can restrict settlement of surrounding soil and mitigate the adverse effects of NSF; (2) pile group effects influence internal forces and neutral point positions of rectangular pile groups under uniformly distributed loading, with diminishing impact as pile spacing increases; and (3) piles at different positions within the group experience varying degrees of group effect, with the central pile experiencing the greatest influence. These findings are particularly significant when addressing challenges in constructing offshore wind turbine foundations on artificial islands. They contribute to mitigating the adverse effects of NSF on pile groups on artificial islands, thereby aiding in the design of offshore wind turbine foundations. In contrast to previous studies, our tests utilized uniform loading conditions more reflective of the issues faced by pile foundations on artificial islands, better simulating the NSF experienced during sediment deposition and reclamation processes [7].

The parabolic distribution of axial forces along the pile shaft observed in our experiments, with the neutral point shifting downwards as loading increases, aligns with findings in prior research on NSF [30,39,40]. For instance, Jiang’s theoretical [7] analysis of pile foundations for offshore wind turbines on artificial islands also supports the patterns observed in this study under surcharge load conditions. However, while Jiang et al. [7] focused on single piles, our study suggests that pile groups offer a more reliable solution for offshore wind turbine installations on artificial islands. Our findings demonstrate that pile groups are advantageous in mitigating the adverse effects of NSF, consistent with the conclusions drawn by Kong et al. [30]. Additionally, pile groups can provide greater load-bearing capacity.

Our experimental results highlight varying degrees of group effects on piles at different positions within a pile group. This observation, acknowledged by many scholars [30], underscores the need for targeted design approaches in current pile group designs. While this study provides valuable insights into the influence of pile group effects on negative skin friction (NSF) across varying pile spacings, the experimental conditions imposed limitations on analyzing additional scenarios. Moreover, the model tests themselves are inherently constrained; for instance, the impact of scale effects may prevent a complete reflection of the in situ NSF experienced by pile foundations. Therefore, based on the findings from the model tests, we plan to conduct further analysis using finite element simulations. Future studies will focus on systematically investigating the impact of pile group effects on piles at different positions within the group, aiming to refine calculations related to NSF in pile group design.

5. Conclusions

This study conducted a series of model experiments to investigate pile group effects of the negative skin friction of a single pile and 3 × 3 rectangular pile groups under balanced soil loading, aiming to investigate the influence of negative skin friction of pile group foundations for offshore wind turbines on artificial islands. It obtained the settlement of surrounding soil and internal forces of the piles under uniformly distributed loading conditions. Through data processing and analysis, this study determined the variation trend of the neutral point position and the coefficient of the pile group effect on NSF. Based on the measurements and processed results, the following conclusions were drawn:

(1) Due to the pile group effect, the settlement of the soil caused by uniformly distributed loads is significantly reduced, and the settlement of the pile shaft within the group is also smaller due to the mutual influence between piles. As the pile spacing increases, both the settlement of the pile shaft and the soil settlement increase. The pile spacing largely affects the settlement ratio of the pile groups, resulting in a certain reduction in the settlement value of the pile body. Therefore, in practical engineering, the settlement of the pile group needs to be calculated separately, with full consideration of the influence of the pile group effect.

(2) A 3 × 3 rectangular pile group exhibits differences in soil settlement, axial force, neutral point position, and NSF compared to single piles, due to the pile group effect between piles. Due to this effect, the axial force and side friction of the pile group change consistently with depth compared to single piles, but the values are generally smaller. The coefficient of NSF in the pile group is generally less than 1, indicating less downward force on the piles compared to single piles. As the pile spacing increases, the pile group effect diminishes.

(3) The pile group effect varies in its impact on different positions of the rectangular 3 × 3 pile group. The central pile is more significantly affected compared to edge and corner piles, which is evident in soil settlement, axial force, neutral point position, and NSF. Therefore, in engineering design, special attention should be given to the central pile.

(4) The pile group effect causes an upward shift in the neutral point position, which is more pronounced in central piles. However, as the range of NSF distribution increases, the neutral point gradually shifts downward. According to experimental results, in engineering design, the influence of the pile group effect on the neutral point of corner piles can be disregarded when the pile spacing exceeds 3 times the pile diameter (3D). For side piles, this can be disregarded when the spacing reaches 4 times the diameter (4D), and for central piles, when it reaches 6 times the diameter (6D).

Although this paper investigates the impact of NSF on 3 × 3 rectangular pile groups used as offshore wind turbine foundations on artificial islands, and proposes improvements to the design methods based on the analysis of experimental results, further research is needed on the horizontal load characteristics of such 3 × 3 rectangular pile groups on artificial islands. Subsequent studies should employ finite element simulations to analyze the structural response of pile foundations under wind loading, aiming to further refine the design methods.