Numerical Analysis of the Effect of an Inverted Cone Angle on the Penetration Behavior of the Jack-Up Leg Foundation for Offshore Wind Turbines in Uniform Clay

Article information

J. Ocean Eng. Technol. 2024;38(6):438-448
Publication date (electronic) : 2024 December 3
doi : https://doi.org/10.26748/KSOE.2024.089
1Graduate Student, Department of Civil and Environmental Engineering, Kongju National University, Cheonan, Korea
2Professor, Department of Civil and Environmental Engineering, Kongju National University, Cheonan, Korea
Corresponding author Yun Wook Choo: +82-41-521-9314, ywchoo@kongju.ac.kr
Received 2024 October 31; Revised 2024 November 14; Accepted 2024 November 17.

Abstract

The design of a jack-up leg foundation as a fixed substructure for offshore wind turbines requires a thorough investigation of the effects of the detailed spudcan geometry, leg type, and soil condition on the penetration resistance. Therefore, this study evaluated the effect of the bottom-shape inverted cone angle of the spudcan on penetration resistance in uniform clay using large-deformation finite element analyses. The soil was idealized as a homogeneous, elastic, perfectly plastic material obeying the Mohr–Coulomb yield criterion. A numerical analysis was performed using the Coupled Eulerian–Lagrangian technique. A complete parametric study was performed to quantify the influence of undrained shear strength, cone angle, and roughness. The results showed that the cone angle and roughness affected the penetration resistance, and a higher cone angle resulted in higher penetration resistance. Moreover, the leg type and soil backflow affected the ultimate bearing capacity factor. As a foundation for offshore wind turbines, this study proposed that a spudcan connected to a cylindrical pile leg with cone tip angles greater than 150° and 120° can be used in stiff and soft clays, respectively, as a substitute for a pile foundation.

1. Introduction

Offshore wind turbines (OWTs) have fewer restrictions on installation space and can be used to build larger-scale wind farms (Musial et al., 2006) than onshore wind turbines. They are commonly supported by either fixed- or floating-type substructures. A fixed-type substructure includes a gravity-based foundation, a monopile, a jacket structure, tripods, and tripiles. Fixed foundations are installed primarily at water depths of less than 50 m (Guo et al., 2022; Wu et al., 2019). Owing to the increasing demand for renewable energy, offshore wind power and related technological developments are of great interest. The Government of Korea established a plan for Renewable Energy 3020 in 2017 (Ministry of Trade, Industry and Energy 2017), emphasizing the demand for increased power generation through wind turbine generators capable of producing renewable energy. The increase in renewable energy production has led to the development and advancement of turbines, blades, and substructures. To address the development of the substructure, a new jack-up spudcan-type substructure that adopts the benefits of mobile jack-up units was proposed (Horwath et al., 2020; Lee and Choo, 2024). This type of substructure allows eco-friendly self-installation using a jacking system (without drilling and driving), thus reducing the levelized cost of energy because it does not require wind turbine installation vessels. It has a flexible jacking system for movement, extraction, and reinstallation under extreme conditions (Randolph et al., 2005; Tirant and Pérol, 1993; Zhang et al., 2011).

A modern jack-up unit consists of a buoyant triangular hull supported by a spudcan footing attached to a k-lattice leg structure. The spudcan is effectively circular or polygonal with a shallow, inverted conical underside profile (in the order of 15°–30° from the horizontal plane), sometimes incorporating a central spigot to facilitate the initial seabed location and providing additional horizontal ability (SNAME, 1994). A simplified conical shape can be used to predict spudcan penetration via numerical analyses and centrifuge tests (Hossain et al., 2014a, 2024b). The influence of the conical angle on the ultimate penetration resistance can also be analyzed using finite element analyses (FEAs), the limit equilibrium method, slip line equations, and the method of characteristics; however, these methods are limited to surface and pre-embedded foundations (Chakraborty and Kumar, 2015; Houlsby and Martin, 2003; Zhang and Liu, 2018). In addition, the design of conical surface foundations (cone angles: 80° and 90°) under the influence of horizontal tensile strains and increasing bearing capacity of the foundation during settlement were studied by Zhussupbekov et al. (2024) through laboratory experiments and numerical analyses. However, the effect of cylindrical column or lattice legs on penetration resistance was ignored in current design guidelines (ABS, 2017; ISO, 2023; SNAME, 1994), numerical analyses and model tests (Falcon et al., 2023; Hossain and Hu, 2004;

Hossain et al., 2003, 2004; Hossain and Randolph, 2009a), and mechanism-based design approaches (Hossain et al., 2006; Hossain and Randolph, 2009b). Therefore, the type of leg connected affects the penetration resistance of the spudcan (Keat, 2012; Li et al., 2012) owing to the amount of soil backflow on top of the spudcan. Moreover, cylindrical columns produce skin friction similar to that produced by pile foundations, as demonstrated by Park et al. (2024) and Zhanabayeva et al. (2022), which contributes to the total capacity of the foundation. Several studies have investigated the cone angle of jacked-in and preinstalled piles. Sheng et al. (2005) and Tan et al. (2023) modeled the installation of single axial and jacked-in piles in clay, respectively, whereas Tovar-Valencia et al. (2021) studied the effects of base geometry in sand. However, the cone angles used in these studies were limited to 60°.

Because the spudcan can be assumed to be circular in design, the bearing capacity coefficient for the circular footing was used in offshore design guidelines (i.e., ISO Guideline, SNAME) by Skempton (1951). However, this underestimates the prediction of the bearing resistance of the spudcan (Hossain et al., 2014b). In addition, current design approaches consider the soil failure mechanism (i.e., cavity formation and backflow of soil over a spudcan) when predicting spudcan penetration (Hossain et al., 2006; Hossain and Randolph, 2009b). Therefore, spudcans with cylindrical pile legs (no backflow) of equal diameter require a different design approach.

Previous studies on the influence of cone angles have primarily focused on surface and pre-embedded foundations using theoretical and numerical analyses by assuming a small strain, leaving the continuous penetration of foundations insufficiently addressed. Moreover, studies involving pile foundations, such as jacked-in and preinstalled piles, have predominantly utilized a cone angle of 60°. Therefore, it is essential to study the effects of different cone angles of spudcans integrated with cylindrical jack-up legs. Thus, for the design of the newly proposed jack-up leg substructure, it is crucial to investigate the effects of detailed spudcan geometry (i.e., inverted cone shape), leg type, and soil condition with a large deformation simulation to improve the comprehensive understanding of spudcan penetration resistance. This study aimed to investigate the effect of the spudcan cone angle attached to a cylindrical pile leg of equal diameter in uniform clay during penetration through a large-deformation numerical analysis and to evaluate the impact of cone roughness on the final penetration resistance of the spudcan. Based on the results, this study recommends the inverted spudcan cone angle for jack-up-type fixed substructures supporting OWTs for practical applications.

2. Methodology

2.1 Geometry and Parameters

Four cone angles were investigated in this study: 60°, 90°, 120°, and 150° (Fig. 1). The configuration of the spudcan was adopted from the ongoing development of OWT jack-up substructures and was attached to the bottom of a cylindrical pile–shaped leg (Lee and Choo, 2024). The diameter D of both the spudcan and the leg was 4 m. The length of the leg was 12 m.

Fig. 1.

Simplified spudcan with a shaft model having different cone angles β

The clay had a uniform undrained shear strength Su and an effective unit weight γ′. The soil parameters were selected from the reported case histories of clays and multilayered clays (Castleberry and Prebaharan, 1985; Chan et al., 2008; Handidjaja et al., 2004; Hossain et al., 2014b; InSafeJIP, 2010; Kostelnik et al., 2007; Lunne et al., 1981). Previous studies suggested a typical undrained shear strength for uniform clay sediments, ranging between 10 and 40 kPa for soft clays and 40–120 kPa for stiff and hard clays. For multilayered clays, the typical maximum undrained shear strength is Sut = 200 kPa, and the minimum bottom layer strength is Sut = 10 kPa with a strength gradient k that typically varies from 0 to 2 kPa/m. In this study, undrained shear strengths of 20 and 120 kPa were used in the subsequent analyses.

The soil was modeled as an elastic, perfectly plastic material obeying the Mohr–Coulomb criterion (Nguyen et al., 2023; Yasser et al., 2022). The elastic behavior of clay was defined by a Poisson’s ratio of 0.49 for undrained conditions, and Young’s modulus was set to 500 Su throughout the soil profile. The soil parameters used in this study are listed in Table 1. The influence of the spudcan angle β and undrained shear strength Su were investigated. Strain softening and hardening were not considered in this study.

Soil parameters used in the numerical analysis

2.2 Numerical Analysis

2.2.1 Models and simulation conditions

Numerical models for the soil and spudcan were constructed using the coupled Eulerian–Lagrangian (CEL) technique available in Abaqus Cae 2017 software. Abaqus cae is an FEA tool capable of analyzing complex (Pichler et al., 2012) and nonlinear materials. The CEL approach is advantageous for circumventing mesh distortion problems caused by large deformations (Chen et al., 2013; Hu et al., 2014; Qiu et al., 2011; Qiu and Grabe, 2011, 2012; Qiu and Henke, 2011; Systemes, 2012; Tho et al., 2013; Zheng et al., 2015). The CEL approach comprises Lagrangian and Eulerian elements. In the Lagrangian element, material deformation is represented by the movement of the mesh. Thus, the Lagrangian elements are always 100% full of a single material. By contrast, in Eulerian elements, the mesh is fixed and the material flows through the mesh. The Eulerian element can consist of a void or be partially or fully occupied by more than one element, with the volume fraction representing the portion of that element filled with a specified material. In this study, the spudcan and pile shaft were discretized with Lagrangian elements, and the soil was discretized with Eulerian elements.

Considering the symmetry of the problem, only one-fourth of the spudcan, pile shaft, and soil were modeled to reduce the computational cost. The soil was modeled in an Eulerian domain discretized with an 8-noded linear brick element with reduced integration (element type: EC3D8R). The soil domain used was sufficiently large to avoid boundary effects during analysis. The typical mesh and geometry of the numerical model are shown in Fig. 2. The mesh comprised a fine mesh zone with a width of 1.25D and a depth of 5–6D depending on the cone angle to accommodate spudcan penetration during the entire installation and a larger mesh size to reduce the simulation time without compromising the accuracy of the result. A void with a thickness of 1D was set above the seabed, allowing the soil to flow into the empty Eulerian elements during the penetration process. The spudcan and pile shaft were modeled as discrete rigid bodies because the deformation was expected to be significantly smaller owing to the stiff structural material. The penetration of the spudcan into the soil was simulated under controlled displacement with a constant penetration velocity. In subsequent analyses, the depth of penetration was limited to 3D. The penetration depth was defined as zero after the largest cross-sectional area of the cone completely penetrated the soil. A numerical analysis was performed under water-free conditions using effective stresses.

Fig. 2.

spudcan–soil modeling using the CEL technique

The contact interaction between the soil materials in the Eulerian domain and the spudcan and shaft meshed with Lagrangian elements is described using the “general contact” algorithm (Systemes, 2012). Frictionless and rough contacts have a roughness factor α of 0 and 1, respectively. A frictionless surface was used in all subsequent analyses. In addition, the contact between the surface of the leg and the soil was set to be frictionless to eliminate the involvement of shaft resistance (Park et al., 2024; Zhanabayeva et al., 2022) in the reaction force of the spudcan–leg structural model.

2.2.2 Domain size

Six domain sizes ― 5D × 10D, 5D × 12D, 5D × 15D, 6D × 12D, 7.5D × 12D, and 3D × 7D (width × depth) ― were examined when choosing the domain size used in the numerical simulations to reduce the boundary effect. Fig. 3 shows the load-penetration curves for different domain sizes. The load-penetration curve of domain size 3D × 7D slightly deviates from those of other domains. In this study, a domain width and depth of 7.5D and 12D, respectively, were selected for all subsequent analyses.

Fig. 3.

Load-penetration curve for different domain sizes

2.2.3 Penetration velocity

The spudcan penetration rate in the field is typically in the order of 2 m/h (5.6 × 10−4 m/s) and 0.36 m/h (1.0 × 10−4 m/s) for simulating a relatively faster penetration rate at the beginning of preloading (i.e., at shallow depths with a very low shear strength) and a slower rate at later stages (i.e., at deeper depths with a higher shear strength), respectively (Hossain et al., 2014b; Tho et al., 2010). In the numerical model, it is neither necessary nor practical to set the penetration rate of the spudcan to be equal to the actual penetration rate in the field. A slower penetration rate requires significant computation time, whereas a faster penetration rate may be associated with a dynamic effect. Therefore, it is appropriate to apply a computationally effective penetration rate. Tho et al. (2010) adopted a penetration rate of 0.1672 m/s to achieve a balance between matching a quasi-static state as closely as possible and simultaneously reducing the computational time. Choi (2020) used a criterion to determine the penetration rate of a spudcan, wherein the speed decreased from 0.005D/s to 0.01D/s. Additionally, the influence of penetration velocity on the numerical results is limited when using rate-independent constitutive models such as the Mohr–Coulomb model (Tho et al., 2010). In the numerical simulations, the clay was simulated using the Mohr–Coulomb model.

A parametric study was conducted on the effects of penetration rates. Four spudcan penetration rates of 0.02, 0.1, 0.2, and 1 m/s, corresponding to total penetration times of 650 s, 130 s, 65 s, and 13 s, respectively, were considered in the parametric studies with a cone tip angle β of 150° and Su= 20 kPa. Because the stable time increment of the analysis is independent of the spudcan penetration rate, the total computational time is approximately proportional to the inverse of the spudcan penetration rate (Tho et al., 2010). In other words, the computational time for the analysis with a penetration rate of 0.02 m/s is approximately 10 times that of the analysis with a penetration rate of 0.2 m/s. The load-penetration curves based on these penetration rates are illustrated in Fig. 4. The figure shows that the load-penetration curves corresponding to the penetration rates of 0.02 and 1.0 m/s are erratic and slightly deviate from those with penetration rates of 0.1 and 0.2 m/s. Conversely, the load-penetration curves corresponding to the penetration rates of 0.1 and 0.2 m/s are practically identical. To shorten the computational time without compromising the accuracy, a penetration rate of 0.2 m/s was adopted for all subsequent analyses. The penetration used in the study is similar to that used by Tho et al. (2010).

Fig. 4.

Load-penetration curves of different penetration rates: 0.02, 0.1, 0.2, and 1.0 m/s

2.2.4 Penetration velocity

Mesh convergence studies were conducted to ensure that the mesh was sufficiently fine to obtain accurate results. Choi (2020) determined the mesh size by considering the diameter D of the spudcan, obtaining a mesh size of 0.025–0.05D. In this study, the mesh size used by Choi (2020) was adopted with an additional mesh size of 0.075D. The following soil parameters were considered: Su = 20 kPa, γ′ = 7 kN/m3, k = 0, and ESu = 500. Furthermore, a spudcan pile with β = 150° was chosen. Three different mesh densities were considered (see Table 2). The mesh density progressively increased from mesh 1 to mesh 3, with mesh 1 being the coarsest and mesh 3 being the finest. The load-penetration curves obtained based on each of these meshes are shown in Fig. 5. The numerical results based on meshes 1–3 started to converge with the mesh density of mesh 3 and were closer to that of mesh 2 than to that of mesh 1. The numerical results for meshes 2 and 3 were practically the same. The volume of the smallest element for mesh 3, located at the periphery of the cone penetration, was 0.0034 m3. Thus, mesh 3 was sufficiently fine to provide accurate results.

Parameters for mesh convergence studies

Fig. 5.

Load-penetration curves for three different mesh densities

3. Validation

3.1 Comparison Between CEL Results and Traditional Bearing Capacity Solutions

The accuracy of the numerical models in this study was validated using a pile footing (β = 180°) against the bearing capacity factors ( Nc=quγdSu, qu = ultimate vertical bearing capacity) obtained from different plasticity solutions (i.e., limit equilibrium method, with exact or bound plasticity solutions) for circular footing in uniform clay using FEAs (Edwards et al., 2005; Salgado et al., 2004) and the method of characteristics (Houlsby and Martin, 2003; Martin and Randolph, 2001). Additionally, we employed the offshore design guidelines provided by the American Petroleum Institute (API) ― Nc = 6.05 ― for circular footing in addition to the correction factors accounting for the load inclination, footing shape, and embedment depth. The CEL technique was performed on piles that continuously penetrated the surface. In addition, pile simulation was performed using the small-strain finite element (SSFE) analysis with pre-embedded depth ratios d/D varying from 0 to 1.5. The spudcan pile was modeled as a rigid body with a smooth shaft and a rough pile tip. The contact interaction between the soil and the pile shaft was frictionless, whereas a penalty contact of 1 (for the CEL approach) and a tie constraint (for the SSFE approach) were adopted to simulate a rough tip surface. The undrained shear strength Su was 30 kPa, and the effective unit weight γ′ was 7 kN/m3. The results are presented in terms of the bearing capacity factor as a function of d/D.

The Nc values from the numerical analysis are plotted in Figs. 6 (a) and (b) along with the estimations of Nc using different approaches for flat circular footings. Figs. 6 (a) and (b) show a comparison between the FE results and the lower and upper limit values, respectively. The SSFE and CEL results of this study were found to be in good agreement with the upper limits reported by Salgado et al. (2004) and Edwards et al. (2005), as shown in Fig. 6(b). However, the FE results ranged between the upper and lower limits reported by Martin and Randolph (2001) and above the lower limit reported by Salgado et al. (2004). However, the widely used bearing capacity factors reported by Houlsby and Martin (2003) and the API design guidelines are over-conservative compared with the FE results obtained in this study.

Fig. 6.

Bearing resistance factor versus normalized depth of flat tip pile cases in this study compared with traditional solutions

4. Results and Discussion

4.1 Penetration Profile

Figs. 7 (a) and (b) show the penetration profiles at cone angles β of 60°, 90°, 120°, and 150° for each undrained shear strength in soft and stiff clays, respectively. The penetration profile between different cone angles for soft and stiff clays increased as the cone angle increased. A summary of the increased penetration resistance is presented in Table 3. For Su = 20 kPa, the penetration resistance increased (calculated as the average of penetration resistance values d/D ranging from 0–3) by approximately 6.77%, 5.38%, and 4.21% as the cone angle increased from 60° to 90°, 90° to 120°, and 120° to 150°, respectively. For Su = 120 kPa, the penetration increased at approximately 8.61%, 8.04%, and 6.00% as the cone angle increased from 60° to 90°, 90° to 120°, and 120° to 150°, respectively. In both cases, the difference in penetration resistance decreased as the cone angle increased. It was also observed that the difference in penetration resistance was larger for stiff clay than for soft clay. This difference is attributed to the contribution of the shear resistance of the clay, making the effect of the cone angle less pronounced in soft clay (low shear resistance) than in stiff clay (high shear resistance). Thus, undrained shear strength has a significant effect on the penetration profile of spudcan cone angles. Moreover, the cone angle significantly affected the penetration performance of the spudcan.

Fig. 7.

Penetration resistance profiles for (a) Su= 20 kPa and (b) Su= 120 kPa

Increase in penetration resistance at different cone angles

The differences in the penetration resistance of the flat pile (β = 180°) are presented in Table 4. The decreases in the penetration resistance of a flat pile at β = 150° and 120° were 2.68% and 6.61% in soft clay, respectively. At β = 90° and 60°, the differences in penetration resistance at β = 180° were 11.38% and 17.00%, respectively. By contrast, the decrease in penetration resistance at β = 150° for stiff clay was 3.76%, whereas, at β = 120°, 90°, and 60°, the differences were 9.21%, 15.97%, and 22.63%, respectively. Thus, a cone angle of 150° showed the least deviation from the flat pile, whereas a cone angle of 60° yielded the most significant difference in the penetration resistance of the flat pile. Therefore, as the cone angle decreases, the difference in penetration resistance decreases. In soft clay, cone angles greater than 120° can be used as the spudcan cone angle for OWT penetration, whereas, in stiff clay, cone angles greater than 150° can be used.

Decrease in the penetration resistance of the flat pile

4.2 Bearing Capacity Factor, Nc

Fig. 8 shows a comparison of Nc values at different cone angles using the CEL technique for soft and stiff clays, with the values obtained from the studies of Houlsby and Martin (2003) and Skempton (1951). The CEL results indicated that the bearing capacity factor increased as the cone angle increased. Moreover, the Nc values at a cone angle of 180° for stiff clay showed a trend similar to that at a cone angle of 150°for soft clay. However, the Nc values of soft clay were higher than those of stiff clay. This difference may be attributed to the low shear resistance of soft clay compared with that of stiff clay. However, Houlsby and Martin’s (2003) lower-bound collapse load for different cone angles deviated from the CEL results, thereby underestimating the penetration resistance of the spudcan. Notably, Houlsby and Martin (2003) used a method of characteristics that considered different parameters such as the dimensionless depth, cone angle, cone roughness factor, and rate of increase in strength with depth in weightless soil. Interestingly, the Nc values reported by Skempton (1951) were found to be in good agreement with those obtained at a cone angle of 60° in this study.

Fig. 8.

Bearing capacity factor Nc versus normalized depth d/D at different cone angles versus traditional solutions

A comparison of Nc values at a cone tip angle of 150° obtained using the CEL technique with those obtained using different design approaches (Hossain and Randolph, 2009b; ISO, 2023) and spudcan studies on uniform clay (Hossain, 2008; Hossain et al., 2004) is shown in Fig. 9. To determine the location of the ultimate Nc value, the simulation using a cone tip angle of 150° was extended to a depth of 7D. The results showed that the ultimate Nc value was 12 at d/D = 3.5. However, Hossain et al. (2004) and Hossain (2008) reported ultimate values of 10.50 and 9.20 at d/D = 1.5 and 1.25, respectively. However, the International Organization for Standardization (ISO) methods of Skempton (1951) and Houlsby and Martin (2003) are overly conservative in predicting spudcan penetration. Surprisingly, the Nc values of the CEL technique were in close agreement with those of Hossain and Randolph (2009b), with an ultimate Nc value of 11.3. However, the location of the ultimate Nc value, as reported by Hossain and Randolph (2009b), was at d/D = 2. This difference in the results is attributed to the type of leg used in the analysis (i.e., k-lattice, a cylindrical pile with a small/large diameter), limiting cavity space, amount of soil backflow, and different assumptions in the simulation (i.e., weightless soil or circular flat, strip, or pre-embedded footing). In contrast to the conventional spudcan penetration, where backflow occurs at a certain depth, in this study, the spudcan was connected to a cylindrical pile leg of equal diameter. Therefore, no backflow occurred through the penetration process, limiting the current design approaches for predicting spudcans with cylindrical piles of an equal diameter. Hence, the bearing capacity factor of the spudcan is greater in the absence of soil backflow than that when a backflow is anticipated owing to the overburden load contributed by the soil backflow.

Fig. 9.

Comparison between a spudcan with a cylindrical pile of equal diameter and spudcan design approaches

Fig. 10 shows the relationship between the cone tip angle and the bearing capacity factor at a normalized depth of 0 for a smooth surface obtained from the existing studies (Chakraborty and Kumar, 2015; Houlsby and Martin, 2003; Zhang and Liu, 2018), CEL technique, and SSFE simulation. To verify the Nc values obtained from the CEL technique, a simulation was performed using the SSFE technique with Su = 120 kPa (similar to that of the CEL technique) for different cone tip angles at the seabed surface, where the largest cross-sectional area of the cone was leveled with the seabed surface. The results showed that the CEL and SSFE results were in good agreement but slightly deviated from the upper and lower limit solutions reported by Chakraborty and Kumar (2015) and Houlsby and Martin (2003). The difference between SSFE and CEL results is attributed to the estimation of the location of the ultimate bearing capacity, wherein the Nc value was selected from the peak value of penetration resistance in the SSFEA. By contrast, in the CEL approach, the Nc value was selected from the location where the largest cross-sectional area of the cone angle completely penetrated the seabed. Therefore, the upper limit values were chosen based on the CEL and SSFE results. However, the Nc values were higher than the lower limits reported by Zhang and Liu (2018). Nevertheless, the results showed good agreement with the upper and lower limit solutions reported in existing studies, wherein the bearing capacity factor increased as the cone tip angle increased.

Fig. 10.

Ultimate bearing capacity with the smooth surface vs existing formulas

4.3 Effect of Cone Roughness

The cone angle β =150° for smooth and rough cones with a smooth shaft was compared. As shown in Fig. 11, the rough-surface cone had a slightly higher bearing capacity factor than the smooth-surface cone. Therefore, as the cone roughness increased, the bearing capacity factor increased. Therefore, the cone roughness has a limited effect on the bearing capacity.

Fig. 11.

Effect of cone roughness at β = 150°

4.4 Guidelines for Practitioners

In this study, large-deformation FEAs were conducted to analyze the penetration resistance of a spudcan footing with different cone angles attached to cylindrical pile legs of equal spudcan diameters in uniform clay. The CEL results for soft and stiff uniform clays provide valuable insights in terms of the use of the cone angle and the design of the leg. Some broad guidelines can be drawn for the practitioners, which are described as follows:

  • (1) In the design of spudcan foundations for offshore wind turbines installed in uniform clay, the penetration resistance and cone angle show a positive correlation. A higher cone angle provides a higher penetration resistance. Moreover, the effect of the cone angle in soft clay is less visible than that in stiff clay. Therefore, cone angles greater than 120° can be used as spudcan cone angles in the foundation for OWT penetration in soft clay. For stiff clay, a cone angle greater than 150° can be used. This is within the simplified cone tip angle of the spudcan used in the industry.

  • (2) The leg type significantly affects the penetration resistance of the spudcan. For cylindrical legs with equal spudcan diameters, no soil backflow occurs at the top of the spudcan. The amount of backflow on the spudcan affects the penetration resistance. Thus, the soil backflow decreases the penetration resistance of the spudcan owing to the overburden load contributed by the soil backflow. Spudcan foundations attached to cylindrical legs of equal diameters are beneficial for the foundations of offshore wind turbines to obtain increased bearing resistance and avoid soil backflow.

  • (3) A 20% reduction in the vertical penetration resistance is suggested, accounting for the strain-rate dependency of soils and their softening as the soil is sheared and remolded during spudcan penetration. This finding is consistent with that reported by Hossain and Randolph (2009b). Alternatively, the values of Houlsby and Martin (2003) for different cone angles can be adopted for designing the foundation for OWT penetration in uniform clay.

  • (4) The bearing capacity factor calculation by Skempton (1951) can be used as an alternative for calculating the bearing capacity factors at a cone angle of 60°. However, a reduction in the vertical penetration should be adopted to account for the strain dependency and softening of the soil. Alternatively, the values reported by Houlsby and Martin (2003) at a cone angle of 60° can be used.

5. Conclusions

This paper presents the results of numerical analyses using the CEL method to assess the effect of the spudcan cone angle on uniform clay during penetration. Cone angles of 60°, 90°, 120°, 150°, and 180° were used to determine the effect of the spudcan cone angle on penetration resistance. A spudcan was attached to a shaft of equal diameter to create a realistic offshore wind turbine foundation model.

The main variables used in this study were the effects of the cone angle, undrained shear strength, and roughness of the cone tip. Based on the numerical investigations, the cone angle was found to affect the penetration resistance of the spudcan. As the cone angle increased, the penetration resistance increased. Moreover, the increase in penetration resistance decreased as the cone angle increased. The increase in penetration resistance was more significant for stiff clays than for soft clays. Therefore, the undrained shear strength Su significantly affects the penetration resistance of the spudcan. Moreover, the cone roughness had a limited effect on the bearing capacity. The location of the ultimate bearing capacity factor for a spudcan with a cylindrical pile leg of equal diameter was deeper than that for a conventional spudcan. Therefore, the leg type and the amount of soil backflow affect the penetration performance of the spudcan.

As a footing for OWTs, this study proposed that spudcan cone tip angles greater than 150° and 120° can be used in stiff and soft clays, respectively. For minimum penetration resistance, a cone angle of 60° can be used in soft and stiff clays. Moreover, spudcan foundations attached to cylindrical legs with equal spudcan diameters are beneficial for the foundations of OWTs. Only uniform clays were considered in this study. Therefore, further studies are required on different soil types and layered soils considering strain softening and hardening, such as nonuniform clay, sand, sand-overlying-clay, clay-overlying-sand, and multilayered soil layers, to determine the influence of the cone angle on punching failure and squeezing in the soil.

Notes

No potential conflict of interest relevant to this article was reported.

This research was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korean government (MOTIE) (RS-2022-KP002820, Development of 10 MW or higher offshore wind power upper and lower package installation support structure systems for LCOE reduction).

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Article information Continued

Fig. 1.

Simplified spudcan with a shaft model having different cone angles β

Fig. 2.

spudcan–soil modeling using the CEL technique

Fig. 3.

Load-penetration curve for different domain sizes

Fig. 4.

Load-penetration curves of different penetration rates: 0.02, 0.1, 0.2, and 1.0 m/s

Fig. 5.

Load-penetration curves for three different mesh densities

Fig. 6.

Bearing resistance factor versus normalized depth of flat tip pile cases in this study compared with traditional solutions

Fig. 7.

Penetration resistance profiles for (a) Su= 20 kPa and (b) Su= 120 kPa

Fig. 8.

Bearing capacity factor Nc versus normalized depth d/D at different cone angles versus traditional solutions

Fig. 9.

Comparison between a spudcan with a cylindrical pile of equal diameter and spudcan design approaches

Fig. 10.

Ultimate bearing capacity with the smooth surface vs existing formulas

Fig. 11.

Effect of cone roughness at β = 150°

Table 1.

Soil parameters used in the numerical analysis

Soil type Effective unit weight, γ′ (kN/m3) Undrained shear strength, Su (kPa) Rigidity index, Ir = Es/Su Poisson ratio, ν
Uniform soft clay 7 20 500 0.49
Uniform stiff clay 7 120 500 0.49

Table 2.

Parameters for mesh convergence studies

Mesh Number of Eulerian Elements Mesh size
1 63,504 0.075D
2 149,040 0.05D
3 288,464 0.0375D

Table 3.

Increase in penetration resistance at different cone angles

Cone angle (°) Increase in penetration resistance (%) (reference = lower cone angle)

Soft clay Stiff clay
60 to 90 6.77 8.61
90 to 120 5.38 8.04
120 to 150 4.21 6.00
150 to 180 2.75 3.91

Table 4.

Decrease in the penetration resistance of the flat pile

Cone angle (°) Decrease in penetration resistance (%) (reference = 180°)

Soft clay Stiff clay
60 17.00 22.63
90 11.38 15.97
120 6.61 9.21
150 2.68 3.76