Optimisation of the padeye location for dynamically embedded plate anchors

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Abstract

Dynamically embedded plate anchors (DEPLAs) are a relatively new anchor type that combine the advantages of dynamically installed anchors and conventional plate anchors. Through three dimensional finite element modelling, this paper first derives the combined loading yield surface of the anchor holding capacity in clay and then uses this yield surface in plasticity analyses to study the anchor trajectory under chain loading. These analyses reveal that the anchor padeye in the current DEPLA design is not optimally located as the anchor will eventually pull out of the seabed when loaded beyond its design capacity. It also shows that there are alternative padeye locations that lead to an equilibrium condition, where the DEPLA attains an ultimate holding capacity. The plasticity analyses are supplemented by simplified closed-form equations that are used in a parametric study to calculate the ultimate DEPLA holding capacity for various padeye positions. The optimal padeye location from the analyses is at a location that has a padeye offset ratio (ratio of the normal to the parallel distance between the padeye and the centre of rotation of the plate) in the range 0.55–0.65, varying slightly with chain loading angle.

Introduction

Increasing the efficiency and reducing the cost of anchoring systems, used to keep floating facilities on station, is becoming a priority for offshore developments, particularly for floating renewable energy devices, where the costs associated with the foundation elements represents a significant portion of the overall costs (Gaudin et al., 2014, Gaudin et al., 2017, Bosch et al., 2019). Dynamically installed anchors are essentially free-fall piles (often with stabilising fins towards the top of the pile) that are installed by allowing them to free-fall through the water column such that they impact the seabed with enough energy to penetrate into the (typically soft) seafloor sediments. In this respect, installation is quick and economical as the only mechanical operation required is to crane the anchor from the vessel into the water. Reduced scale anchor tests conducted in a centrifuge and in the field indicate that anchor capacity is typically in the range 2.4–4.1 times the anchor dry weight, varying with reconsolidation time after installation (Richardson et al., 2009, O'Beirne et al., 2015). Equivalent ratios for plate anchors are typically much higher (e.g. Murff et al., 2005, O'Loughlin et al., 2017), as capacity is derived from bearing resistance, unlike dynamically installed anchors where capacity is derived mainly from the friction that develops at the anchor-soil interface and potentially from passive resistance should the load magnitude and inclination cause the anchor to rotate.

A recent anchor concept, the Dynamic Embedded PLate Anchor (DEPLA) as described in O'Loughlin et al. (2014), combines the advantages of dynamically installed anchors and plate anchors. As shown by Fig. 1(a), the DEPLA comprises a removable central shaft or ‘follower’ and a set of four flukes (or plates) arranged on a cylindrical sleeve and connected to the follower with a shear pin. The mooring line connects to the anchor attachment point, termed the ‘padeye’, on one of the anchor flukes, with a further installation line (also used to retrieve the follower) connected to the top of the follower. The DEPLA is installed in the same manner as other dynamically installed anchors, by allowing the anchor to free-fall from a designated height above the seafloor such that it will self-bury in the seabed. After installation, the follower is retrieved for reuse on the next installation, causing the shear pin to part (if this did not already break when the anchor impacted with the seabed) and leaving the anchor flukes vertically embedded in the seabed. These embedded anchor flukes act as a buried plate anchor, providing capacity through bearing resistance. When sufficient load develops in the mooring chain the flukes will rotate or ‘key’ to an eventual orientation that is near perpendicular to the load inclination, such that the full potential bearing resistance can be mobilised.

The capacity of buried plate anchors was initially estimated with 2D plane strain and axisymmetric solutions, such as Rowe, 1978, Rowe and Davis, 1982, Bransby and O’Neill, 1999, and Merifield et al. (2001), as examples, before three-dimensional finite element studies (e.g. Wang et al., 2010, Wang and O’Loughlin, 2014), including the limit analyses approaches led by Professor Scott Sloan (Merifield et al., 2003, Merifield et al., 2006, Sloan, 2013), investigated the effect of the shape of the plate. Tian et al., 2014, Tian et al., 2015a, Tian et al., 2015b) highlight the influence of the padeye position on the kinematic response of an anchor, and ultimately the maximum obtainable anchor capacity. These studies utilised the concept of a ‘padeye offset ratio’ η, which when optimised, enables the anchor to reach an ultimate equilibrium state, where the anchor only travels horizontally without further vertical or rotational displacements. As illustrated in Fig. 2, the ultimate state represents equilibrium of anchor loading and soil resistance, where the anchor only translates horizontally without rising or diving. The padeye offset ratio, η = ep/en is defined in Fig. 3, where the padeye eccentricity, en, is the perpendicular distance between the padeye and the bearing plate, while the padeye offset, ep, is the distance parallel to the bearing plate between the padeye and the anchor centroid.

In the current DEPLA design, the mooring chain is connected to a padeye that is located at the ‘waist’ of one of the four flukes (see Fig. 1), such that η = 0. According to Tian et al. (2015b), this implies that the anchor is not capable of reaching its ultimate state, but rather will lose embedment depth when the mooring line tension exceeds the anchor capacity.

In order to enable DEPLAs to reach an ultimate equilibrium state and in turn, to achieve the ultimate holding capacity, this paper optimises the DEPLA geometry by investigating the effect of the padeye position. This was achieved by first obtaining the combined loading yield surface for the DEPLA under combined loading (normal, sliding and moment), which was derived from 43 three-dimensional finite element modelling cases. The yield surface was then used in a suite of plasticity analyses to calculate the anchor trajectories under chain loading. Finally, simplified closed-form expressions are proposed that correlate the beneficial padeye offset ratio range to the ultimate holding capacity as well as the ultimate embedment depth that the DEPLA can potentially achieve.

Section snippets

Finite element model

Three dimensional, small strain finite element analyses were conducted to derive the combined loading yield surface. The finite element model mesh is as shown in Fig. 4, where only half the DEPLA model was modelled to take advantage of the geometrical symmetry. The anchor was modelled as rigid body, whereas the soil was modelled as elastic perfect-plastic Tresca material with an undrained shear strength, su, that increases with depth according to su = sum + kz, where the soil strength at

Plasticity model

The kinematic response of the DEPLA due to a mooring chain load applied at the padeye was modelled using the plasticity analysis approach (see Cassidy et al., 2012, Yang et al., 2012 for more details) based on the yield surface just defined. In the plasticity analyses, rigid perfect plasticity (i.e. no elastic behaviour or hardening) and normality (associated flow rule) were adopted. Fig. 7 illustrates the calculation model for the plasticity analyses, where the anchor behaviour was calculated

Simplified closed-form analytical solution

According to Murff et al., 2005, Tian et al., 2015b, anchor weight has a negligible effect on plate anchor capacity. A significantly simplified closed-form analytical solution can be obtained if the effective anchor weight (the dry weight minus the buoyancy in soil) is considered as W' = 0, as summarised in Tian et al. (2015b). The ultimate embedment depth zp,u (measured at the DEPLA plate centroid) for varying padeye offset ratios, η, can be evaluated using the following equation based on Tian

Concluding remarks

The DEPLA is a relatively new dynamically installed anchor type that combines the advantages of dynamically installed anchors and conventional plate anchors. In the current design the padeye is located at the ‘waist’ of one of the flukes, meaning that the padeye offset ratio, η = 0. Although this design does provide holding capacity associated with the initial installed depth, if the anchor is overloaded, it will eventually pull out of the seabed. In order to reach an ultimate embedment depth,

CRediT authorship contribution statement

Yinghui Tian: Conceptualization, Methodology, Software, Validation, Formal analysis, Data curation, Writing - original draft, Funding acquisition. Conleth O’Loughlin: Conceptualization, Methodology, Validation, Formal analysis, Data curation, Writing - review & editing, Funding acquisition. Mark J. Cassidy: Conceptualization, Methodology, Validation, Formal analysis, Data curation, Writing - review & editing, Funding acquisition.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was undertaken with support from Australian Research Council Discovery Projects (DP180103314), Future Fellowship (FT200100457) and the Australian Research Council Industry Transformational Research Hub for Floating Facilities (IH140100012). Its genesis was from within the Australian Research Council Centre of Excellence for Geotechnical Science and Engineering (CGSE). The authors acknowledge, with deep appreciation, the contribution of the late Professor Scott Sloan for his

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