Optimal Load Attachment of a Deeply Embedded Ring Anchor in Clay

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The DERA boasts several key features, including its versatility in various soil types, compact size, compatibility with diverse mooring systems, multi-line potential, and robust performance even under unintentional loading conditions. While prior preliminary studies have provided valuable insights into how the DERA can enhance cost-effectiveness by offering a high load capacity, these studies have predominantly focused on optimizing anchor performance under translational horizontal and vertical loading. However, to design the DERA optimally, we must also consider its ability to handle inclined loading conditions in addition to lateral and axial loadings. Due to its shorter length compared to a conventional caisson, the DERA has less resistance to moments, making it more sensitive to horizontal load capacity and the optimal load attachment depth concerning load angle. For this reason, our study introduces an analytical approach to evaluate the effects of inclined loading on anchor performance, utilizing the previously validated upper bound plastic limit analysis (PLA) method. In investigating the optimal load attachment of the DERA, this paper conducts a parametric study to analyze how factors such as load attachment depth, anchor aspect ratio, and load inclination affect the DERA's load capacity. Our findings indicate that PLA can serve as a valuable analytical tool for assessing the ultimate load capacity of the DERA, particularly under inclined loading conditions. offshore wind ring anchor optimal load attachment clay Figures Figure 1 Figure 2 Figure 3 Figure 4 INTRODUCTION The offshore wind industry is rapidly transitioning from fixed to floating platforms due to factors like consistent wind resources, aesthetics, and site conditions (Cooperman et al. 2022 ; Barter et al. 2020 ; Musial et al. 2018). This shift to deeper waters requires cost-effective and durable anchors capable of withstanding extreme offshore conditions (Lee et al. 2020 ; Lee et al. 2021 ; Lee et al. 2022 ). These anchors are increasingly connected to taut or tension leg moorings, demanding substantial uplift resistance under extreme loading conditions (Lee et al. 2021 ). In response to industry challenges, the Deeply Embedded Ring Anchor (DERA) has been developed to secure floating offshore wind turbines (FOWTs) to the seabed. DERA offers advantages such as compact size, deep embedment capability, installability in various soil types, compatibility with diverse mooring systems, and exceptional uplift resistance (Lee and Aubeny 2020 ; Lee and Aubeny 2021 ; Lee et al. 2021 ; Lee and Aubeny 2023 ). Its smaller size results in cost savings and reduced logistical efforts, eliminating concerns about scouring issues near the seabed anchor point. This paper focuses on the comprehensive analysis and optimization of DERA's performance, particularly its ability to handle inclined loading conditions. While previous studies highlighted DERA's high load capacity under horizontal and vertical loading, its sensitivity to inclined loading conditions remains underexplored. Understanding these effects is crucial for optimal DERA design given its compact size and unique characteristics. Our study introduces an analytical approach using the upper bound plastic limit analysis (PLA) method to assess the impact of inclined loading on anchor performance. The core objective is a parametric study exploring key factors influencing DERA's load capacity, including load attachment location, depth, and anchor aspect ratio. Real-world scenarios and practical constraints are considered, reflecting current suction installation technology and seabed installation challenges. Findings contribute to a deeper understanding of DERA's behavior under inclined loading conditions, offering insights for advancing mooring systems in floating offshore wind turbines. Results represent a significant contribution to ongoing efforts in optimizing offshore wind infrastructure and promoting sustainable energy solutions. UPPER BOUND PLASTIC LIMIT ANALYSIS Key issues for the DERA The plastic limit analysis (PLA) methods serve as a means to assess the ultimate load capacity of both piles and caissons. The introduction of a plastic limit approach to evaluating the horizontal load capacity of piles can be traced back to the pioneering work of Murff and Hamilton in 1993. Their contributions involve the derivation of dissipation functions and the lateral bearing capacity factor Nps, grounded in von Mises and Tresca yield criteria, as well as an associated flow rule. Building on this foundation, Aubeny et al. ( 2001 ; 2003 ) proposed a simplified upper bound model for the suction caisson. In their work, they not only derived energy dissipation functions but also established relationships for the lateral-axial bearing capacity factor Nps-Nas along the side of the pile. Additionally, they explored interactions among the ultimate resistance to vertical, horizontal, and moment loading at the base of the pile. It is crucial to highlight that the studies mentioned earlier have been limited to structures characterized by a conventional cylindrical shape, extending from the surface to a specific depth. In contrast, the Deeply Embedded Ring Anchor (DERA) introduces distinctive features, including a relatively shorter length, deep embedment, and the absence of reverse end-bearing resistance, as illustrated in Fig. 3 . The DERA, due to its deep embedment depth coupled with a relatively shorter length, cannot rely on additional side resistance extending to the surface. Unlike the suction caisson, the DERA lacks reverse end-bearing resistance, a significant component of uplift resistance for the suction caisson. These unique attributes necessitate a primary modification to the existing upper bound PLA model developed by Aubeny et al. ( 2003 ). Modification Given the installation of the Deeply Embedded Ring Anchor (DERA) at significant depths, it induces moment resistance at the top of the anchor. Consequently, the formulation for lateral-moment resistance at the bottom of piles, as outlined by Aubeny in 2017, is adapted for application to the top of the DERA. The expression for mobilized moment resistance in the lateral-moment formula has been updated to encompass both top and base moment resistances. Previous findings illustrate the calculated base moment resistance, evaluated through numerical integration for centers of rotation ranging from each end (top and base) to large values approaching pure horizontal translation of the anchor (Aubeny 2017 ; Leet et al. 2020). Each calculated moment is normalized, as described in Equations (1) and (2). Subsequently, these normalized moments are aggregated to represent the total moment resistance at both the top and base of the ring anchor. We introduce an end axial-moment interaction denoted in Eq. ( 3 ). The resultant moment resistance, M = M b + M t , will be incorporated into Eq. ( 3 ). at tip, \({M}_{bo}= \left[2\left(\frac{{R}_{1}}{\pi R}\right)+\text{exp}\left(\frac{-{I}_{4}{R}_{1}}{R}\right)\right]\left(\frac{{\pi }^{2}{R}^{3}{S}_{ub}}{2}\right)\) (1) at top, \({M}_{t0}= \left[2\left(\frac{{R}_{3}}{\pi R}\right)+\text{exp}\left(\frac{-{I}_{4}{R}_{3}}{R}\right)\right]\left(\frac{{\pi }^{2}{R}^{3}{S}_{ut}}{2}\right)\) (2) where M t is the mobilized moment resistance at the top of the pile, R is the anchor radius, R 3 is the distance from the center of rotation to the anchor top (= L – R 1 ), R 4 is the radius of the spherical surface at the top, I 4 = 1.118, the coefficient of curve fitting, S u,t = undrained shear strength at the top, and M is the total moment resistance at top and base of the pile. For end axial-moment interaction, $${\text{f}}_{a} = {\left(\frac{\text{V}}{{\text{V}}_{\text{max}}}\right)}^{2}+ {\left(\frac{\text{M}}{{\text{M}}_{\text{max}}}\right)}^{2}-\text{1 }= \text{0}\text{ }$$ 3 $${V}_{0} ={V}_{b0} +{V}_{t0}={N}_{ab}\pi {R}^{2}{S}_{ub}+{N}_{c}\pi {R}^{2}{S}_{ut}$$ 4 where V 0 is total uplift capacity under pure vertical loading, V t0 is uplift capacity under vertical loading at the top of the anchor, and N ab is the reverse end bearing factor (9 to 12). The internal energy dissipation from the soil resistance in unit length on the side ( F as = N as S u D , F ls = N ps S u D ) and from the base and top ( V , M ) can be equated to the external work as follows: $$H \text{= }\frac{\int \left({\text{F}}_{\text{ls}}\left|\text{1 -}\frac{\text{z}}{{\text{L}}_{\text{0}}}\right|\text{+ }{\text{F}}_{\text{as}}\text{ξ}\right)\text{dz}\text{ +}\frac{\text{M}}{{\text{L}}_{\text{0}}}\text{+}\text{Vξ}}{\left(\text{ξ}\text{tan}\text{θ}\text{ + }\left|\text{1 - }\frac{{\text{L}}_{\text{i}}}{{\text{L}}_{\text{0}}}\right|\right)}$$ 5 V = Htanθ (6) where H , V are lateral and uplift load capacity of the anchor, z is the depth below mudline, ξ is the optimization parameter controlling the vertical velocity of the anchor, L i is the load attachment depth, and L 0 is the center of rotation. Validation The modified PLA model underwent validation by comparing its outcomes with both numerical studies and field data from previous research (Lee et al., 2020 ; Medeiros, 2002 ; Zhanabayeva et al, 2022 ; Vashishtha and Sawant 2021 ). Due to the absence of specific field test data, the study utilized test data derived from an embedded cylinder-shaped anchor, a torpedo anchor without flukes. The comparison between the modified PLA's results and both the finite element (FE) study and available field data revealed a robust agreement, with variances of within 2.5% in relation to the field data and within 1% in relation to the FE study (Lee et al. 2020 ). CONSIDERATIONS FOR THE PARAMETRIC STUDY Soil parameters The prospective locations for floating offshore wind installations are identified along the West Coast, as detailed in the previous study (Beiter et al. 2020 ). Ongoing comprehensive geotechnical investigations necessitate assumptions about specific soil profiles in this study. The earlier report foresaw clay as the predominant soil type in the Wind Energy Area (WEA) sites (Tajalli Bakhsh et al. 2021 ). Within the scope of this study, the soil profile is hypothesized to consist of normally consolidated clay, and its undrained shear strength is expressed as su = 5 + 2z kPa, where 'z' represents the depth in meters. Required anchor load capacity Optimization of the DERA dimensions is tailored to meet the demand for anchor load, specifically in addressing vertical load capacity. This emphasis is driven by various factors, including the significant water depths prevalent in the floating wind market, reaching up to 1,000 meters (NREL report). To address economic and ecological concerns, structures such as semi-submersible or tension leg (TL) platforms are being considered as the envisioned framework for the floating offshore wind industry. These platforms, connected to TL moorings or taut moorings, predominantly experience vertical loading. Therefore, the anchors for FOWTs must exhibit sufficient load capacity against uplift resistance, as highlighted by Lee et al. ( 2021 ). For the optimization of anchor design tailored to taut or TL moorings, it becomes imperative to estimate the extreme mooring vertical loads on a 15-MW FOWT under severe weather conditions. Pillai et al. ( 2022 ) have previously estimated the peak vertical load demand for 15-MW FOWTs in the Celtic Sea under design load case 6.1, which is considered representative of severe weather conditions (ABS 2020 ). The required anchor load capacity is calculated with a safety factor (F.S = 1.67 for DLC 6.1, ABS 2020 ) in mind. In this study, we assume a load capacity of 12.29 MN, calculated as 7.36 MN multiplied by the safety factor of 1.67. This study adopts optimized dimensions for the anchor, set at a 3.8-meter diameter and a 5.7-meter length, while adhering to a thickness ratio of D/t = 100. Given that the DERA typically exhibits higher horizontal capacity than vertical capacity, the optimized dimensions are also derived primarily from the vertical capacity. This alignment is further validated by comparing the horizontal capacity to previous research. For instance, the calculated horizontal capacity is approximately 30 MN, significantly surpassing the required anchor load demand in horizontal loading (Pillai et al. 2022 ; 23.28 MN = 13.98 multiplied by the safety factor of 1.67). PARAMETRIC STUDY Description To gain a deeper understanding of the impact of eccentricity in the DERA, a parametric study is conducted, exploring the effects of the following parameters: Load attachment depth from the top of the DERA Load attachment location Aspect ratio ( L / D ) representing the length of the DERA to the diameter of the DERA Utilizing the current suction installation technology, an anchor with a diameter of 3.8 meters and a length of 5.7 meters can be effectively installed in the seabed at a tip depth of 15D or greater. For the purposes of this paper, the assumption is made to consider a tip depth of 15D. The analyses encompass seven load inclinations (θ) with respect to the horizontal direction: 0° (lateral load), 15°, 30°, 45°, 60°, 75°, and 90° (axial load). Additionally, the entire range of load attachment depths (Li) will be explored to examine the impact of load attachment depth. Furthermore, the load attachment locations are contemplated at both the top and middle of the anchor, as well as the centerline and wall, given the relatively shorter length of the anchor. Effect of load attachment depth Figures 1 and 2 depict the load capacity trend and the influence of load attachment depth. In the case of lower loading angles (0° to 45°), the load capacity varies with the loading angle, and this variation is dependent on the load attachment depth. Notably, optimal anchor performance is anticipated when the load attachment depth is positioned at the midpoint of the anchor. This phenomenon is attributed to the availability of translational horizontal resistance when the load attachment is close to the middle of the anchor. This observed trend holds true for both load attachment locations: the centerline and the wall of the anchor. Lower inclinations exhibit a high sensitivity to load attachment depth. Conversely, for higher inclinations (above 45°), the load capacity remains consistent irrespective of the load attachment depth. This pattern aligns with findings from prior study (Aubeny et al. 2003 ). Effect of load attachment location Figure 3 illustrates the load capacity trend and the influence of load attachment location. The trend of load capacity for each load attachment location varies depending on the load attachment depth. For instance, with top attachment, the anchor performance trend remains consistent across different loading angles. However, in the case of middle attachment, particularly at lower angles (0° to 45°), the anchor load capacity exhibits a different trend, with optimal loading angles varying based on the load attachment location. Given that the DERA also integrates innerside load attachment using inner stiffeners, characterizing the load attachment location becomes crucial for a comprehensive understanding of anchor performance. Effect of aspect ratio To exclusively examine the impact of aspect ratio, this specific case adopts a uniform soil profile. This uniformity in soil conditions allows for a focused investigation into how the anchor's aspect ratios influence its performance. Figures 1 to 3 unveil a significant sensitivity of load capacity to load attachment depth, particularly at the top of the anchor under lower load inclinations. Additionally, a previous study (Lee and Aubeny 2020 ) emphasized that the horizontal load capacity's sensitivity to unintended moment loading can be more pronounced than in typical piles or caissons due to the anchor's relatively shorter length. Consequently, this study evaluates the aspect ratio's sensitivity depending on the load attachment location, whether on the wall or centerline. Figure 4 illustrates that the difference (|Maximum resultant force @ wall / Maximum resultant force @ centerline| − 1) diminishes with an increasing aspect ratio. In simpler terms, attaching the mooring line to the wall proves advantageous compared to attaching it to the centerline when the loading angle is below 45°. CONCLUDING REMARKS This study presents the potential advantages of the deeply embedded ring anchor concerning geotechnical efficiency and anchor logistics. Key findings are as follows: Load capacity is very sensitive to anchor line attachment location for load inclination angles less than 45°. At larger load inclination angles (> 45°), load capacity becomes less sensitive to anchor line attachment location. The sensitivity of the load attachment location decreases as the aspect ratio increases. DECLARATIONS ACKNOWLEDGMENTS The authors would also like to acknowledge the supports from the National Science Foundation, award numbers CMMI-1936901 and TI-2214009, and the Department of Energy, award number DE-SC0024062. CONFLICT OF INTEREST The authors declare no conflict of interest. REFERENCES ABS. (2020). "Guide for building and classing floating offshore wind turbine installations." The American Bureau of Shipping (ABS), Houston (TX), USA. Aubeny, C. (2017). Geomechanics of Marine Anchors, CRC Press, Taylor & Francis Group, Boca Raton, FL. Aubeny, C., Murf, J., and Moon, S. (2001). "Lateral undrained resistance of suction caisson anchors." International Journal of Offshore and Polar Engineering, 11(03). Aubeny, C. P., Han, S. W., and Murff, J. D. (2003). "Inclined load capacity of suction caissons." International Journal for Numerical and Analytical Methods in Geomechanics, 27(14), 1235-1254. Barter, G. E., Robertson, A., and Musial, W. (2020). "A systems engineering vision for floating offshore wind cost optimization." Renewable Energy Focus, 34, 1-16. Beiter, P., Musial, W., Duffy, P., Cooperman, A., Shields, M., Heimiller, D., & Optis, M. (2020). The cost of floating offshore wind energy in California between 2019 and 2032 (No. NREL/TP-5000-77384). National Renewable Energy Lab.(NREL), Golden, CO (United States). Cooperman, A., Duffy, P., Hall, M., Lozon, E., Shields, M., & Musial, W. (2022). Assessment of Offshore Wind Energy Leasing Areas for Humboldt and Morro Bay Wind Energy Areas, California (No. NREL/TP-5000-82341). National Renewable Energy Lab.(NREL), Golden, CO (United States). Lee, J., & Aubeny, C. P. (2023). Effect of Shared Anchor System for a Floating Offshore Wind Project on Reductions in CO2 Emissions. In Offshore Technology Conference (p. D011S009R005). OTC. Lee, J., and Aubeny, C. P. (2020). "Multiline Ring Anchor system for floating offshore wind turbines." Journal of Physics: Conference Series, 1452, 012036. Lee, J., Jung, J. S., Sim, Y. J., & Park, Y. B. (2020). Simplified Limit Solutions for the Inclined Load Capacity of a Dynamically Installed Pile in Soft Clay. LHI journal, 11(2), 87-94. Lee, J., Khan, M., Bello, L., and Aubeny, C. P. (2020). "Cost analysis of multiline ring anchor systems for offshore wind farm." Proc., Deep Foundation Institute 45th Conference, National Harbor, MD, USA, online, 484-493. Lee, J., and Aubeny, C. P. (2021). "Lateral undrained capacity of a multiline ring anchor in clay." International Journal of Geomechanics, DOI 10.1061/(ASCE)GM.1943-5622.0001995. Lee, J., Balakrishnan, K., Aubeny, C. P., Arwade, S., DeGroot, D., Martinez, A., and Beemer, R. (2021). "Uplift resistance of a multiline ring anchor system in soft clay to extreme conditions." Proc., Geo-Extreme Conference, Savannah, GA, USA. Lee, J., Hong, J., Aubeny, C. P., Arwade, S., DeGroot, D., Martinez, A., Beemer, R. Balakrishnan, K., and Nam, Y., (2021). "Installability of a multiline ring anchor system in a seabed under severe environmental conditions." Proc., Global OCEANS 2021, San Diego, CA, USA. Lee, J., Aubeny, C. P., Arwade, S., DeGroot, D., Martinez, A., and Beemer, R. (2022). "Effect of wing plates on vertical load capacity of a multiline ring anchor system in clay." Proc., Geo-Congress, Charlotte, NC, USA. Medeiros, C. J., Jr. (2002). "Low Cost Anchor System for Flexible Risers in Deep Waters." Offshore Technology Conference, Offshore Technology Conference, Houston, Texas, 5. Murff, J. D., and Hamilton, J. M. (1993). "P-Ultimate for Undrained Analysis of Laterally Loaded Piles." Journal of Geotechnical Engineering, 119(1), 91-107. Musial (2018) “Offshore wind energy facility characteristics”, BOEM’s offshore wind and maritime industry knowledge exchange workshop. Pillai, A. C., Gordelier, T. J., Thies, P. R., Cuthill, D., & Johanning, L. (2022). Anchor loads for shallow water mooring of a 15 MW floating wind turbine-Part II: Synthetic and novel mooring systems. Ocean Engineering, 266, 112619. Tajalli Bakhsh, T., Simpson, K., LaPierre, T., Monim, M., Dahl, J., Spaulding, M., Rowe, J., Miller, J. and O’Connell, D., (2021), February. Potential Geo-Hazards to Floating Offshore Wind Farms in the US Pacific. In International Conference on Offshore Mechanics and Arctic Engineering (Vol. 84768, p. V001T01A014). American Society of Mechanical Engineers. Vashishtha, H. R., & Sawant, V. A. (2021). An experimental investigation for pullout response of a single granular pile anchor in clayey soil. International Journal of Geo-Engineering, 12, 1-19. Zhanabayeva, A., Abdialim, S., Satyanaga, A., Kim, J., & Moon, S. W. (2022). Comparative analysis of international codes of practice for pile foundation design considering negative skin friction effect. International Journal of Geo-Engineering, 13(1), 11. Cite Share Download PDF Status: Published Journal Publication published 12 Dec, 2024 Read the published version in International Journal of Geo-Engineering → Version 1 posted Reviewers agreed at journal 27 Mar, 2024 Reviewers invited by journal 26 Mar, 2024 Editor assigned by journal 05 Feb, 2024 First submitted to journal 31 Jan, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3901534","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":284302683,"identity":"1f6aa6c5-4b78-499d-97f7-4d3862b4c10a","order_by":0,"name":"Junho Lee","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA00lEQVRIiWNgGAWjYJACAwaGAwz8IFZCASlaJBtAWgyIt+gAg8EBqG6CQN69+UAx7447csbnVyd+eGDAIM8vdgC/FsMzxxKMec88Mza78XazBNBhhjNnJxDQMiPHwJi37XDithtnN4C0JBjcJqRl/huIls0zzm7+QZQWeQkeiJYN/L3biLPFgCctwXBu22FjiRu82ywSDCQI+0W+/fAxg7dth+X4+89uvvmjwkaeX5qQLQcY2CCRIQFWKYFfOdiWBgbmB2AW/wHCqkfBKBgFo2BkAgD05EdW1603gQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0001-9644-3292","institution":"Texas A\u0026M University","correspondingAuthor":true,"prefix":"","firstName":"Junho","middleName":"","lastName":"Lee","suffix":""},{"id":284302684,"identity":"e6159de9-9cff-4bda-ab8b-f2dc99061c7b","order_by":1,"name":"Charles Aubeny","email":"","orcid":"","institution":"Texas A\u0026M University","correspondingAuthor":false,"prefix":"","firstName":"Charles","middleName":"","lastName":"Aubeny","suffix":""}],"badges":[],"createdAt":"2024-01-27 02:00:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3901534/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3901534/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s40703-024-00227-z","type":"published","date":"2024-12-12T15:57:55+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":53760016,"identity":"b331519e-340b-402c-a970-e8ac6aec6e2e","added_by":"auto","created_at":"2024-03-29 19:45:28","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":247313,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of load attachment depth on the centerline.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-3901534/v1/17ac3a130f50a7f14cde17ea.png"},{"id":53760215,"identity":"8ecd83d3-f28c-4dcb-ba63-c860117f2dcb","added_by":"auto","created_at":"2024-03-29 19:53:28","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":80755,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of load attachment depth on the wall.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-3901534/v1/5d385e1665405bc08b5c7544.png"},{"id":53760017,"identity":"bbb517a4-5381-49ab-b40b-45a93dee561d","added_by":"auto","created_at":"2024-03-29 19:45:28","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":59987,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of load attachment location.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-3901534/v1/52b63217287761dd1ae4a335.png"},{"id":53760015,"identity":"75b0ed5e-4f0d-4d2e-83dd-533d73b307e1","added_by":"auto","created_at":"2024-03-29 19:45:28","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":26832,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of the aspect ratio of the anchor.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-3901534/v1/601ef841524a4a49fe641313.png"},{"id":71552495,"identity":"866699f5-3659-4b69-bf7c-d5e34807c768","added_by":"auto","created_at":"2024-12-16 16:06:49","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":741741,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3901534/v1/e99e5125-45e8-4e67-b1fc-77cf93ca0b92.pdf"}],"financialInterests":"","formattedTitle":"Optimal Load Attachment of a Deeply Embedded Ring Anchor in Clay","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eThe offshore wind industry is rapidly transitioning from fixed to floating platforms due to factors like consistent wind resources, aesthetics, and site conditions (Cooperman et al. \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e; Barter et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Musial et al. 2018). This shift to deeper waters requires cost-effective and durable anchors capable of withstanding extreme offshore conditions (Lee et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Lee et al. \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e; Lee et al. \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e). These anchors are increasingly connected to taut or tension leg moorings, demanding substantial uplift resistance under extreme loading conditions (Lee et al. \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). In response to industry challenges, the Deeply Embedded Ring Anchor (DERA) has been developed to secure floating offshore wind turbines (FOWTs) to the seabed. DERA offers advantages such as compact size, deep embedment capability, installability in various soil types, compatibility with diverse mooring systems, and exceptional uplift resistance (Lee and Aubeny \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Lee and Aubeny \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e; Lee et al. \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e; Lee and Aubeny \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e). Its smaller size results in cost savings and reduced logistical efforts, eliminating concerns about scouring issues near the seabed anchor point. This paper focuses on the comprehensive analysis and optimization of DERA's performance, particularly its ability to handle inclined loading conditions. While previous studies highlighted DERA's high load capacity under horizontal and vertical loading, its sensitivity to inclined loading conditions remains underexplored. Understanding these effects is crucial for optimal DERA design given its compact size and unique characteristics. Our study introduces an analytical approach using the upper bound plastic limit analysis (PLA) method to assess the impact of inclined loading on anchor performance. The core objective is a parametric study exploring key factors influencing DERA's load capacity, including load attachment location, depth, and anchor aspect ratio. Real-world scenarios and practical constraints are considered, reflecting current suction installation technology and seabed installation challenges. Findings contribute to a deeper understanding of DERA's behavior under inclined loading conditions, offering insights for advancing mooring systems in floating offshore wind turbines. Results represent a significant contribution to ongoing efforts in optimizing offshore wind infrastructure and promoting sustainable energy solutions.\u003c/p\u003e"},{"header":"UPPER BOUND PLASTIC LIMIT ANALYSIS","content":"\u003cdiv id=\"Sec3\" class=\"Section3\"\u003e\n \u003ch2\u003eKey issues for the DERA\u003c/h2\u003e\n \u003cp\u003eThe plastic limit analysis (PLA) methods serve as a means to assess the ultimate load capacity of both piles and caissons. The introduction of a plastic limit approach to evaluating the horizontal load capacity of piles can be traced back to the pioneering work of Murff and Hamilton in 1993. Their contributions involve the derivation of dissipation functions and the lateral bearing capacity factor Nps, grounded in von Mises and Tresca yield criteria, as well as an associated flow rule. Building on this foundation, Aubeny et al. (\u003cspan class=\"CitationRef\"\u003e2001\u003c/span\u003e; \u003cspan class=\"CitationRef\"\u003e2003\u003c/span\u003e) proposed a simplified upper bound model for the suction caisson. In their work, they not only derived energy dissipation functions but also established relationships for the lateral-axial bearing capacity factor Nps-Nas along the side of the pile. Additionally, they explored interactions among the ultimate resistance to vertical, horizontal, and moment loading at the base of the pile. It is crucial to highlight that the studies mentioned earlier have been limited to structures characterized by a conventional cylindrical shape, extending from the surface to a specific depth. In contrast, the Deeply Embedded Ring Anchor (DERA) introduces distinctive features, including a relatively shorter length, deep embedment, and the absence of reverse end-bearing resistance, as illustrated in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e. The DERA, due to its deep embedment depth coupled with a relatively shorter length, cannot rely on additional side resistance extending to the surface. Unlike the suction caisson, the DERA lacks reverse end-bearing resistance, a significant component of uplift resistance for the suction caisson. These unique attributes necessitate a primary modification to the existing upper bound PLA model developed by Aubeny et al. (\u003cspan class=\"CitationRef\"\u003e2003\u003c/span\u003e).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003eModification\u003c/h2\u003e\n \u003cp\u003eGiven the installation of the Deeply Embedded Ring Anchor (DERA) at significant depths, it induces moment resistance at the top of the anchor. Consequently, the formulation for lateral-moment resistance at the bottom of piles, as outlined by Aubeny in 2017, is adapted for application to the top of the DERA. The expression for mobilized moment resistance in the lateral-moment formula has been updated to encompass both top and base moment resistances. Previous findings illustrate the calculated base moment resistance, evaluated through numerical integration for centers of rotation ranging from each end (top and base) to large values approaching pure horizontal translation of the anchor (Aubeny \u003cspan class=\"CitationRef\"\u003e2017\u003c/span\u003e; Leet et al. 2020). Each calculated moment is normalized, as described in Equations (1) and (2). Subsequently, these normalized moments are aggregated to represent the total moment resistance at both the top and base of the ring anchor. We introduce an end axial-moment interaction denoted in Eq.\u0026nbsp;(\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). The resultant moment resistance, \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e + \u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e, will be incorporated into Eq.\u0026nbsp;(\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eat tip,\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({M}_{bo}= \\left[2\\left(\\frac{{R}_{1}}{\\pi R}\\right)+\\text{exp}\\left(\\frac{-{I}_{4}{R}_{1}}{R}\\right)\\right]\\left(\\frac{{\\pi }^{2}{R}^{3}{S}_{ub}}{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e (1)\u003c/p\u003e\n \u003cp\u003eat top, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({M}_{t0}= \\left[2\\left(\\frac{{R}_{3}}{\\pi R}\\right)+\\text{exp}\\left(\\frac{-{I}_{4}{R}_{3}}{R}\\right)\\right]\\left(\\frac{{\\pi }^{2}{R}^{3}{S}_{ut}}{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e (2)\u003c/p\u003e\n \u003cp\u003ewhere \u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e is the mobilized moment resistance at the top of the pile, \u003cem\u003eR\u003c/em\u003e is the anchor radius, \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e is the distance from the center of rotation to the anchor top (=\u0026thinsp;\u003cem\u003eL\u003c/em\u003e \u0026ndash; \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e), \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003e4\u003c/em\u003e\u003c/sub\u003e is the radius of the spherical surface at the top, \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003e4\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.118, the coefficient of curve fitting, \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003eu,t\u003c/em\u003e\u003c/sub\u003e = undrained shear strength at the top, and \u003cem\u003eM\u003c/em\u003e is the total moment resistance at top and base of the pile.\u003c/p\u003e\n \u003cp\u003eFor end axial-moment interaction,\u003c/p\u003e\n \u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n \u003cdiv id=\"FileID_Equ1\" class=\"mathdisplay\"\u003e$${\\text{f}}_{a} = {\\left(\\frac{\\text{V}}{{\\text{V}}_{\\text{max}}}\\right)}^{2}+ {\\left(\\frac{\\text{M}}{{\\text{M}}_{\\text{max}}}\\right)}^{2}-\\text{1 }= \\text{0}\\text{ }$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\n \u003cdiv id=\"FileID_Equ2\" class=\"mathdisplay\"\u003e$${V}_{0} ={V}_{b0} +{V}_{t0}={N}_{ab}\\pi {R}^{2}{S}_{ub}+{N}_{c}\\pi {R}^{2}{S}_{ut}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003ewhere \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e is total uplift capacity under pure vertical loading, \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003et0\u003c/em\u003e\u003c/sub\u003e is uplift capacity under vertical loading at the top of the anchor, and \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eab\u003c/em\u003e\u003c/sub\u003e is the reverse end bearing factor (9 to 12).\u003c/p\u003e\n \u003cp\u003eThe internal energy dissipation from the soil resistance in unit length on the side (\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eas\u003c/em\u003e\u003c/sub\u003e=\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eas\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003eu\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eD\u003c/em\u003e, \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003els\u003c/em\u003e\u003c/sub\u003e=\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eps\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003eu\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eD\u003c/em\u003e) and from the base and top (\u003cem\u003eV\u003c/em\u003e, \u003cem\u003eM\u003c/em\u003e) can be equated to the external work as follows:\u003c/p\u003e\n \u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\n \u003cdiv id=\"FileID_Equ3\" class=\"mathdisplay\"\u003e$$H \\text{= }\\frac{\\int \\left({\\text{F}}_{\\text{ls}}\\left|\\text{1 -}\\frac{\\text{z}}{{\\text{L}}_{\\text{0}}}\\right|\\text{+ }{\\text{F}}_{\\text{as}}\\text{\u0026xi;}\\right)\\text{dz}\\text{ +}\\frac{\\text{M}}{{\\text{L}}_{\\text{0}}}\\text{+}\\text{V\u0026xi;}}{\\left(\\text{\u0026xi;}\\text{tan}\\text{\u0026theta;}\\text{ + }\\left|\\text{1 - }\\frac{{\\text{L}}_{\\text{i}}}{{\\text{L}}_{\\text{0}}}\\right|\\right)}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003cem\u003eV\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eHtan\u0026theta;\u003c/em\u003e (6)\u003c/p\u003e\n \u003cp\u003ewhere \u003cem\u003eH\u003c/em\u003e, \u003cem\u003eV\u003c/em\u003e are lateral and uplift load capacity of the anchor, \u003cem\u003ez\u003c/em\u003e is the depth below mudline, \u003cem\u003e\u0026xi;\u003c/em\u003e is the optimization parameter controlling the vertical velocity of the anchor, \u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e is the load attachment depth, and \u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e is the center of rotation.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003ch2\u003eValidation\u003c/h2\u003e\n \u003cp\u003eThe modified PLA model underwent validation by comparing its outcomes with both numerical studies and field data from previous research (Lee et al., \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Medeiros, \u003cspan class=\"CitationRef\"\u003e2002\u003c/span\u003e; Zhanabayeva et al, \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e; Vashishtha and Sawant \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). Due to the absence of specific field test data, the study utilized test data derived from an embedded cylinder-shaped anchor, a torpedo anchor without flukes. The comparison between the modified PLA\u0026apos;s results and both the finite element (FE) study and available field data revealed a robust agreement, with variances of within 2.5% in relation to the field data and within 1% in relation to the FE study (Lee et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e\n\u003c/div\u003e"},{"header":"CONSIDERATIONS FOR THE PARAMETRIC STUDY","content":"\u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\n\u003ch2\u003eSoil parameters\u003c/h2\u003e\n\u003cp\u003eThe prospective locations for floating offshore wind installations are identified along the West Coast, as detailed in the previous study (Beiter et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e). Ongoing comprehensive geotechnical investigations necessitate assumptions about specific soil profiles in this study. The earlier report foresaw clay as the predominant soil type in the Wind Energy Area (WEA) sites (Tajalli Bakhsh et al. \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). Within the scope of this study, the soil profile is hypothesized to consist of normally consolidated clay, and its undrained shear strength is expressed as su\u0026thinsp;=\u0026thinsp;5\u0026thinsp;+\u0026thinsp;2z kPa, where 'z' represents the depth in meters.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n\u003ch2\u003eRequired anchor load capacity\u003c/h2\u003e\n\u003cp\u003eOptimization of the DERA dimensions is tailored to meet the demand for anchor load, specifically in addressing vertical load capacity. This emphasis is driven by various factors, including the significant water depths prevalent in the floating wind market, reaching up to 1,000 meters (NREL report). To address economic and ecological concerns, structures such as semi-submersible or tension leg (TL) platforms are being considered as the envisioned framework for the floating offshore wind industry. These platforms, connected to TL moorings or taut moorings, predominantly experience vertical loading. Therefore, the anchors for FOWTs must exhibit sufficient load capacity against uplift resistance, as highlighted by Lee et al. (\u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). For the optimization of anchor design tailored to taut or TL moorings, it becomes imperative to estimate the extreme mooring vertical loads on a 15-MW FOWT under severe weather conditions. Pillai et al. (\u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e) have previously estimated the peak vertical load demand for 15-MW FOWTs in the Celtic Sea under design load case 6.1, which is considered representative of severe weather conditions (ABS \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e). The required anchor load capacity is calculated with a safety factor (F.S\u0026thinsp;=\u0026thinsp;1.67 for DLC 6.1, ABS \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e) in mind. In this study, we assume a load capacity of 12.29 MN, calculated as 7.36 MN multiplied by the safety factor of 1.67. This study adopts optimized dimensions for the anchor, set at a 3.8-meter diameter and a 5.7-meter length, while adhering to a thickness ratio of D/t\u0026thinsp;=\u0026thinsp;100. Given that the DERA typically exhibits higher horizontal capacity than vertical capacity, the optimized dimensions are also derived primarily from the vertical capacity. This alignment is further validated by comparing the horizontal capacity to previous research. For instance, the calculated horizontal capacity is approximately 30 MN, significantly surpassing the required anchor load demand in horizontal loading (Pillai et al. \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e; 23.28 MN\u0026thinsp;=\u0026thinsp;13.98 multiplied by the safety factor of 1.67).\u003c/p\u003e\n\u003c/div\u003e"},{"header":"PARAMETRIC STUDY","content":"\u003cdiv id=\"Sec10\" class=\"Section3\"\u003e\n \u003ch2\u003eDescription\u003c/h2\u003e\n \u003cp\u003eTo gain a deeper understanding of the impact of eccentricity in the DERA, a parametric study is conducted, exploring the effects of the following parameters:\u003c/p\u003e\n \u003cul\u003e\n \u003cli\u003e\n \u003cp\u003eLoad attachment depth from the top of the DERA\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eLoad attachment location\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eAspect ratio (\u003cem\u003eL\u003c/em\u003e/\u003cem\u003eD\u003c/em\u003e) representing the length of the DERA to the diameter of the DERA\u003c/p\u003e\n \u003c/li\u003e\n \u003c/ul\u003e\n \u003cp\u003eUtilizing the current suction installation technology, an anchor with a diameter of 3.8 meters and a length of 5.7 meters can be effectively installed in the seabed at a tip depth of 15D or greater. For the purposes of this paper, the assumption is made to consider a tip depth of 15D. The analyses encompass seven load inclinations (\u0026theta;) with respect to the horizontal direction: 0\u0026deg; (lateral load), 15\u0026deg;, 30\u0026deg;, 45\u0026deg;, 60\u0026deg;, 75\u0026deg;, and 90\u0026deg; (axial load). Additionally, the entire range of load attachment depths (Li) will be explored to examine the impact of load attachment depth. Furthermore, the load attachment locations are contemplated at both the top and middle of the anchor, as well as the centerline and wall, given the relatively shorter length of the anchor.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n \u003ch2\u003eEffect of load attachment depth\u003c/h2\u003e\n \u003cp\u003eFigures \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e depict the load capacity trend and the influence of load attachment depth. In the case of lower loading angles (0\u0026deg; to 45\u0026deg;), the load capacity varies with the loading angle, and this variation is dependent on the load attachment depth. Notably, optimal anchor performance is anticipated when the load attachment depth is positioned at the midpoint of the anchor. This phenomenon is attributed to the availability of translational horizontal resistance when the load attachment is close to the middle of the anchor. This observed trend holds true for both load attachment locations: the centerline and the wall of the anchor. Lower inclinations exhibit a high sensitivity to load attachment depth. Conversely, for higher inclinations (above 45\u0026deg;), the load capacity remains consistent irrespective of the load attachment depth. This pattern aligns with findings from prior study (Aubeny et al. \u003cspan class=\"CitationRef\"\u003e2003\u003c/span\u003e).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n \u003ch2\u003eEffect of load attachment location\u003c/h2\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates the load capacity trend and the influence of load attachment location. The trend of load capacity for each load attachment location varies depending on the load attachment depth. For instance, with top attachment, the anchor performance trend remains consistent across different loading angles. However, in the case of middle attachment, particularly at lower angles (0\u0026deg; to 45\u0026deg;), the anchor load capacity exhibits a different trend, with optimal loading angles varying based on the load attachment location. Given that the DERA also integrates innerside load attachment using inner stiffeners, characterizing the load attachment location becomes crucial for a comprehensive understanding of anchor performance.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n \u003ch2\u003eEffect of aspect ratio\u003c/h2\u003e\n \u003cp\u003eTo exclusively examine the impact of aspect ratio, this specific case adopts a uniform soil profile. This uniformity in soil conditions allows for a focused investigation into how the anchor\u0026apos;s aspect ratios influence its performance. Figures \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e to \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e unveil a significant sensitivity of load capacity to load attachment depth, particularly at the top of the anchor under lower load inclinations. Additionally, a previous study (Lee and Aubeny \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e) emphasized that the horizontal load capacity\u0026apos;s sensitivity to unintended moment loading can be more pronounced than in typical piles or caissons due to the anchor\u0026apos;s relatively shorter length. Consequently, this study evaluates the aspect ratio\u0026apos;s sensitivity depending on the load attachment location, whether on the wall or centerline. Figure \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates that the difference (|Maximum resultant force @ wall / Maximum resultant force @ centerline| \u0026minus;\u0026thinsp;1) diminishes with an increasing aspect ratio. In simpler terms, attaching the mooring line to the wall proves advantageous compared to attaching it to the centerline when the loading angle is below 45\u0026deg;.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"CONCLUDING REMARKS","content":"\u003cp\u003eThis study presents the potential advantages of the deeply embedded ring anchor concerning geotechnical efficiency and anchor logistics. Key findings are as follows:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eLoad capacity is very sensitive to anchor line attachment location for load inclination angles less than 45\u0026deg;.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eAt larger load inclination angles (\u0026gt;\u0026thinsp;45\u0026deg;), load capacity becomes less sensitive to anchor line attachment location.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eThe sensitivity of the load attachment location decreases as the aspect ratio increases.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e"},{"header":"DECLARATIONS","content":"\u003cp\u003e\u003cstrong\u003eACKNOWLEDGMENTS\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors would also like to acknowledge the supports from the National Science Foundation, award numbers CMMI-1936901 and TI-2214009, and the Department of Energy, award number DE-SC0024062.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCONFLICT OF INTEREST\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no conflict of interest.\u003c/p\u003e"},{"header":"REFERENCES","content":"\u003col\u003e\n\u003cli\u003eABS. (2020). \u0026quot;Guide for building and classing floating offshore wind turbine installations.\u0026quot; The American Bureau of Shipping (ABS), Houston (TX), USA.\u003c/li\u003e\n\u003cli\u003eAubeny, C. (2017). Geomechanics of Marine Anchors, CRC Press, Taylor \u0026amp; Francis Group, Boca Raton, FL.\u003c/li\u003e\n\u003cli\u003eAubeny, C., Murf, J., and Moon, S. (2001). \u0026quot;Lateral undrained resistance of suction caisson anchors.\u0026quot; International Journal of Offshore and Polar Engineering, 11(03).\u003c/li\u003e\n\u003cli\u003eAubeny, C. P., Han, S. W., and Murff, J. D. (2003). \u0026quot;Inclined load capacity of suction caissons.\u0026quot; International Journal for Numerical and Analytical Methods in Geomechanics, 27(14), 1235-1254.\u003c/li\u003e\n\u003cli\u003eBarter, G. E., Robertson, A., and Musial, W. (2020). \u0026quot;A systems engineering vision for floating offshore wind cost optimization.\u0026quot; Renewable Energy Focus, 34, 1-16.\u003c/li\u003e\n\u003cli\u003eBeiter, P., Musial, W., Duffy, P., Cooperman, A., Shields, M., Heimiller, D., \u0026amp; Optis, M. (2020). The cost of floating offshore wind energy in California between 2019 and 2032 (No. NREL/TP-5000-77384). National Renewable Energy Lab.(NREL), Golden, CO (United States).\u003c/li\u003e\n\u003cli\u003eCooperman, A., Duffy, P., Hall, M., Lozon, E., Shields, M., \u0026amp; Musial, W. (2022). Assessment of Offshore Wind Energy Leasing Areas for Humboldt and Morro Bay Wind Energy Areas, California (No. NREL/TP-5000-82341). National Renewable Energy Lab.(NREL), Golden, CO (United States).\u003c/li\u003e\n\u003cli\u003eLee, J., \u0026amp; Aubeny, C. P. (2023). Effect of Shared Anchor System for a Floating Offshore Wind Project on Reductions in CO2 Emissions. In Offshore Technology Conference (p. D011S009R005). 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Anchor loads for shallow water mooring of a 15 MW floating wind turbine-Part II: Synthetic and novel mooring systems. Ocean Engineering, 266, 112619.\u003c/li\u003e\n\u003cli\u003eTajalli Bakhsh, T., Simpson, K., LaPierre, T., Monim, M., Dahl, J., Spaulding, M., Rowe, J., Miller, J. and O\u0026rsquo;Connell, D., (2021), February. Potential Geo-Hazards to Floating Offshore Wind Farms in the US Pacific. In International Conference on Offshore Mechanics and Arctic Engineering (Vol. 84768, p. V001T01A014). American Society of Mechanical Engineers.\u003c/li\u003e\n\u003cli\u003eVashishtha, H. R., \u0026amp; Sawant, V. A. (2021). An experimental investigation for pullout response of a single granular pile anchor in clayey soil. International Journal of Geo-Engineering, 12, 1-19.\u003c/li\u003e\n\u003cli\u003eZhanabayeva, A., Abdialim, S., Satyanaga, A., Kim, J., \u0026amp; Moon, S. W. (2022). Comparative analysis of international codes of practice for pile foundation design considering negative skin friction effect. International Journal of Geo-Engineering, 13(1), 11.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"international-journal-of-geo-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"geoe","sideBox":"Learn more about [International Journal of Geo-Engineering](https://link.springer.com/journal/40703)","snPcode":"40703","submissionUrl":"https://submission.nature.com/new-submission/40703/3","title":"International Journal of Geo-Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"offshore wind, ring anchor, optimal load attachment, clay","lastPublishedDoi":"10.21203/rs.3.rs-3901534/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3901534/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA Deeply Embedded Ring Anchor (DERA) system has been developed as a cost-effective solution for mooring arrays of floating offshore wind turbines (FOWTs) to the seabed. The DERA boasts several key features, including its versatility in various soil types, compact size, compatibility with diverse mooring systems, multi-line potential, and robust performance even under unintentional loading conditions. While prior preliminary studies have provided valuable insights into how the DERA can enhance cost-effectiveness by offering a high load capacity, these studies have predominantly focused on optimizing anchor performance under translational horizontal and vertical loading. However, to design the DERA optimally, we must also consider its ability to handle inclined loading conditions in addition to lateral and axial loadings. Due to its shorter length compared to a conventional caisson, the DERA has less resistance to moments, making it more sensitive to horizontal load capacity and the optimal load attachment depth concerning load angle. For this reason, our study introduces an analytical approach to evaluate the effects of inclined loading on anchor performance, utilizing the previously validated upper bound plastic limit analysis (PLA) method. In investigating the optimal load attachment of the DERA, this paper conducts a parametric study to analyze how factors such as load attachment depth, anchor aspect ratio, and load inclination affect the DERA's load capacity. Our findings indicate that PLA can serve as a valuable analytical tool for assessing the ultimate load capacity of the DERA, particularly under inclined loading conditions.\u003c/p\u003e","manuscriptTitle":"Optimal Load Attachment of a Deeply Embedded Ring Anchor in Clay","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-29 19:45:24","doi":"10.21203/rs.3.rs-3901534/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2024-03-27T14:06:39+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-03-27T01:29:30+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-02-05T06:06:20+00:00","index":"","fulltext":""},{"type":"submitted","content":"International Journal of Geo-Engineering","date":"2024-01-31T22:50:16+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"international-journal-of-geo-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"geoe","sideBox":"Learn more about [International Journal of Geo-Engineering](https://link.springer.com/journal/40703)","snPcode":"40703","submissionUrl":"https://submission.nature.com/new-submission/40703/3","title":"International Journal of Geo-Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"751f89db-26c3-4114-8b2b-ec14b88a1a75","owner":[],"postedDate":"March 29th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-12-16T16:03:06+00:00","versionOfRecord":{"articleIdentity":"rs-3901534","link":"https://doi.org/10.1186/s40703-024-00227-z","journal":{"identity":"international-journal-of-geo-engineering","isVorOnly":false,"title":"International Journal of Geo-Engineering"},"publishedOn":"2024-12-12 15:57:55","publishedOnDateReadable":"December 12th, 2024"},"versionCreatedAt":"2024-03-29 19:45:24","video":"","vorDoi":"10.1186/s40703-024-00227-z","vorDoiUrl":"https://doi.org/10.1186/s40703-024-00227-z","workflowStages":[]},"version":"v1","identity":"rs-3901534","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3901534","identity":"rs-3901534","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}